The HP Mini 110-3712la actually have support from the most recent versions of the FSF-endorsed GNU/Linux-distros. However, due to the lack of updated information about some components such the Realtek RTL8188CE WiFi card, I decided to update the info about the compatibility with fully free distros.

This test has been made with the following distros:

1.- Trisquel 9.0 "Etiona" (kernel version: 4.15).

2.- Pure OS 9.0 (kernel version: 4.19).

3.- Parabola GNU/Linux-libre (kernel version: 5.9.12).

The BIOS version that the named netbook have installed is the version F.25, developed by the company Insyde for HP and updated via BIOS updated supplied by the manufacturer for Windows. The netbook model is identified as HP Mini 110-3700. However, the specific model of this model is the HP Mini 110-3712la, which haves an ISO-based Latin American keyboard layout and lacks of embedded 3G modem.

Actually, this netbook has installed Parabola GNU/Linux-libre to get the best results of a distro that uses the linux-libre kernel, discarding some variables as handheld flags for the compilation of the kernel.

In the case of Parabola GNU/Linux-libre, some cases as the xf86-input-libinput and the kernel udpates may cause some erratic behaviours and may disable the Realtek WiFi card and the touchpad will malfunctions.

UPDATE: The version 5.10.6 of the linux-libre kernel solved the many issues related with the WiFi driver for the Realtek RTL8188CE.

This is the log shown with sudo lspci -vnnnk:

00:00.0 Host bridge [0600]: Intel Corporation Atom Processor D4xx/D5xx/N4xx/N5xx DMI Bridge [8086:a010]
	Subsystem: Hewlett-Packard Company Device [103c:1584]
	Flags: bus master, fast devsel, latency 0
	Capabilities: [e0] Vendor Specific Information: Len=08 <?>
	Kernel modules: intel_agp

00:02.0 VGA compatible controller [0300]: Intel Corporation Atom Processor D4xx/D5xx/N4xx/N5xx Integrated Graphics Controller [8086:a011] (prog-if 00 [VGA controller])
	Subsystem: Hewlett-Packard Company Device [103c:1584]
	Flags: bus master, fast devsel, latency 0, IRQ 16
	Memory at 96180000 (32-bit, non-prefetchable) [size=512K]
	I/O ports at 40c0 [size=8]
	Memory at 80000000 (32-bit, prefetchable) [size=256M]
	Memory at 96000000 (32-bit, non-prefetchable) [size=1M]
	Expansion ROM at 000c0000 [virtual] [disabled] [size=128K]
	Capabilities: [90] MSI: Enable- Count=1/1 Maskable- 64bit-
	Capabilities: [d0] Power Management version 2
	Kernel driver in use: i915
	Kernel modules: i915

00:02.1 Display controller [0380]: Intel Corporation Atom Processor D4xx/D5xx/N4xx/N5xx Integrated Graphics Controller [8086:a012]
	Subsystem: Hewlett-Packard Company Device [103c:1584]
	Flags: bus master, fast devsel, latency 0
	Memory at 96100000 (32-bit, non-prefetchable) [size=512K]
	Capabilities: [d0] Power Management version 2

00:1b.0 Audio device [0403]: Intel Corporation NM10/ICH7 Family High Definition Audio Controller [8086:27d8] (rev 02)
	Subsystem: Hewlett-Packard Company Device [103c:1584]
	Flags: bus master, fast devsel, latency 0, IRQ 29
	Memory at 96200000 (64-bit, non-prefetchable) [size=16K]
	Capabilities: [50] Power Management version 2
	Capabilities: [60] MSI: Enable+ Count=1/1 Maskable- 64bit+
	Capabilities: [70] Express Root Complex Integrated Endpoint, MSI 00
	Capabilities: [100] Virtual Channel
	Capabilities: [130] Root Complex Link
	Kernel driver in use: snd_hda_intel
	Kernel modules: snd_hda_intel

00:1c.0 PCI bridge [0604]: Intel Corporation NM10/ICH7 Family PCI Express Port 1 [8086:27d0] (rev 02) (prog-if 00 [Normal decode])
	Flags: bus master, fast devsel, latency 0, IRQ 24
	Bus: primary=00, secondary=01, subordinate=01, sec-latency=0
	I/O behind bridge: 00003000-00003fff [size=4K]
	Memory behind bridge: 95000000-95ffffff [size=16M]
	Prefetchable memory behind bridge: 0000000090000000-0000000090ffffff [size=16M]
	Capabilities: [40] Express Root Port (Slot+), MSI 00
	Capabilities: [80] MSI: Enable+ Count=1/1 Maskable- 64bit-
	Capabilities: [90] Subsystem: Hewlett-Packard Company Device [103c:1584]
	Capabilities: [a0] Power Management version 2
	Capabilities: [100] Virtual Channel
	Capabilities: [180] Root Complex Link
	Kernel driver in use: pcieport

00:1c.2 PCI bridge [0604]: Intel Corporation NM10/ICH7 Family PCI Express Port 3 [8086:27d4] (rev 02) (prog-if 00 [Normal decode])
	Flags: bus master, fast devsel, latency 0, IRQ 25
	Bus: primary=00, secondary=02, subordinate=02, sec-latency=0
	I/O behind bridge: 00002000-00002fff [size=4K]
	Memory behind bridge: 94000000-94ffffff [size=16M]
	Prefetchable memory behind bridge: 0000000091000000-0000000091ffffff [size=16M]
	Capabilities: [40] Express Root Port (Slot+), MSI 00
	Capabilities: [80] MSI: Enable+ Count=1/1 Maskable- 64bit-
	Capabilities: [90] Subsystem: Hewlett-Packard Company Device [103c:1584]
	Capabilities: [a0] Power Management version 2
	Capabilities: [100] Virtual Channel
	Capabilities: [180] Root Complex Link
	Kernel driver in use: pcieport

00:1c.3 PCI bridge [0604]: Intel Corporation NM10/ICH7 Family PCI Express Port 4 [8086:27d6] (rev 02) (prog-if 00 [Normal decode])
	Flags: bus master, fast devsel, latency 0, IRQ 26
	Bus: primary=00, secondary=03, subordinate=03, sec-latency=0
	I/O behind bridge: 00001000-00001fff [size=4K]
	Memory behind bridge: 93000000-93ffffff [size=16M]
	Prefetchable memory behind bridge: 0000000092000000-0000000092ffffff [size=16M]
	Capabilities: [40] Express Root Port (Slot+), MSI 00
	Capabilities: [80] MSI: Enable+ Count=1/1 Maskable- 64bit-
	Capabilities: [90] Subsystem: Hewlett-Packard Company Device [103c:1584]
	Capabilities: [a0] Power Management version 2
	Capabilities: [100] Virtual Channel
	Capabilities: [180] Root Complex Link
	Kernel driver in use: pcieport

00:1d.0 USB controller [0c03]: Intel Corporation NM10/ICH7 Family USB UHCI Controller #1 [8086:27c8] (rev 02) (prog-if 00 [UHCI])
	Subsystem: Hewlett-Packard Company Device [103c:1584]
	Flags: bus master, medium devsel, latency 0, IRQ 16
	I/O ports at 4080 [size=32]
	Kernel driver in use: uhci_hcd
	Kernel modules: uhci_hcd

00:1d.1 USB controller [0c03]: Intel Corporation NM10/ICH7 Family USB UHCI Controller #2 [8086:27c9] (rev 02) (prog-if 00 [UHCI])
	Subsystem: Hewlett-Packard Company Device [103c:1584]
	Flags: bus master, medium devsel, latency 0, IRQ 17
	I/O ports at 4060 [size=32]
	Kernel driver in use: uhci_hcd
	Kernel modules: uhci_hcd

00:1d.2 USB controller [0c03]: Intel Corporation NM10/ICH7 Family USB UHCI Controller #3 [8086:27ca] (rev 02) (prog-if 00 [UHCI])
	Subsystem: Hewlett-Packard Company Device [103c:1584]
	Flags: bus master, medium devsel, latency 0, IRQ 18
	I/O ports at 4040 [size=32]
	Kernel driver in use: uhci_hcd
	Kernel modules: uhci_hcd

00:1d.3 USB controller [0c03]: Intel Corporation NM10/ICH7 Family USB UHCI Controller #4 [8086:27cb] (rev 02) (prog-if 00 [UHCI])
	Subsystem: Hewlett-Packard Company Device [103c:1584]
	Flags: bus master, medium devsel, latency 0, IRQ 19
	I/O ports at 4020 [size=32]
	Kernel driver in use: uhci_hcd
	Kernel modules: uhci_hcd

00:1d.7 USB controller [0c03]: Intel Corporation NM10/ICH7 Family USB2 EHCI Controller [8086:27cc] (rev 02) (prog-if 20 [EHCI])
	Subsystem: Hewlett-Packard Company Device [103c:1584]
	Flags: bus master, medium devsel, latency 0, IRQ 16
	Memory at 96204400 (32-bit, non-prefetchable) [size=1K]
	Capabilities: [50] Power Management version 2
	Capabilities: [58] Debug port: BAR=1 offset=00a0
	Kernel driver in use: ehci-pci
	Kernel modules: ehci_pci

00:1e.0 PCI bridge [0604]: Intel Corporation 82801 Mobile PCI Bridge [8086:2448] (rev e2) (prog-if 01 [Subtractive decode])
	Flags: bus master, fast devsel, latency 0
	Bus: primary=00, secondary=04, subordinate=04, sec-latency=32
	I/O behind bridge: [disabled]
	Memory behind bridge: [disabled]
	Prefetchable memory behind bridge: [disabled]
	Capabilities: [50] Subsystem: Hewlett-Packard Company Device [103c:1584]

00:1f.0 ISA bridge [0601]: Intel Corporation NM10 Family LPC Controller [8086:27bc] (rev 02)
	Subsystem: Hewlett-Packard Company Device [103c:1584]
	Flags: bus master, medium devsel, latency 0
	Capabilities: [e0] Vendor Specific Information: Len=0c <?>
	Kernel modules: lpc_ich

00:1f.2 SATA controller [0106]: Intel Corporation NM10/ICH7 Family SATA Controller [AHCI mode] [8086:27c1] (rev 02) (prog-if 01 [AHCI 1.0])
	Subsystem: Hewlett-Packard Company Device [103c:1584]
	Flags: bus master, 66MHz, medium devsel, latency 0, IRQ 27
	I/O ports at 40b8 [size=8]
	I/O ports at 40cc [size=4]
	I/O ports at 40b0 [size=8]
	I/O ports at 40c8 [size=4]
	I/O ports at 40a0 [size=16]
	Memory at 96204000 (32-bit, non-prefetchable) [size=1K]
	Capabilities: [80] MSI: Enable+ Count=1/1 Maskable- 64bit-
	Capabilities: [70] Power Management version 2
	Kernel driver in use: ahci

00:1f.3 SMBus [0c05]: Intel Corporation NM10/ICH7 Family SMBus Controller [8086:27da] (rev 02)
	Subsystem: Hewlett-Packard Company Device [103c:1584]
	Flags: medium devsel, IRQ 17
	I/O ports at 4000 [size=32]
	Kernel driver in use: i801_smbus
	Kernel modules: i2c_i801

01:00.0 Network controller [0280]: Realtek Semiconductor Co., Ltd. RTL8188CE 802.11b/g/n WiFi Adapter [10ec:8176] (rev 01)
	Subsystem: Hewlett-Packard Company Device [103c:1629]
	Flags: bus master, fast devsel, latency 0, IRQ 16
	I/O ports at 3000 [size=256]
	Memory at 95000000 (64-bit, non-prefetchable) [size=16K]
	Capabilities: [40] Power Management version 3
	Capabilities: [50] MSI: Enable- Count=1/1 Maskable- 64bit+
	Capabilities: [70] Express Endpoint, MSI 00
	Capabilities: [100] Advanced Error Reporting
	Capabilities: [140] Virtual Channel
	Capabilities: [160] Device Serial Number 01-91-81-fe-ff-4c-e0-00
	Kernel driver in use: rtl8192ce
	Kernel modules: rtl8192ce

03:00.0 Ethernet controller [0200]: Realtek Semiconductor Co., Ltd. RTL810xE PCI Express Fast Ethernet controller [10ec:8136] (rev 05)
	Subsystem: Hewlett-Packard Company Device [103c:1584]
	Flags: bus master, fast devsel, latency 0, IRQ 19
	I/O ports at 1000 [size=256]
	Memory at 92004000 (64-bit, prefetchable) [size=4K]
	Memory at 92000000 (64-bit, prefetchable) [size=16K]
	Capabilities: [40] Power Management version 3
	Capabilities: [50] MSI: Enable- Count=1/1 Maskable- 64bit+
	Capabilities: [70] Express Endpoint, MSI 01
	Capabilities: [b0] MSI-X: Enable+ Count=4 Masked-
	Capabilities: [d0] Vital Product Data
	Capabilities: [100] Advanced Error Reporting
	Capabilities: [140] Virtual Channel
	Capabilities: [160] Device Serial Number 90-03-00-00-36-4c-e0-00
	Kernel driver in use: r8169
	Kernel modules: r8169