Pci Ven_10ec&dev_8136&subsys

You almost have it.

With the information from Device Manager you can determine the VENdor and DEVice information:

Network Controller (DeviceNTPNP_PCI0019)
PCIVEN_8086&DEV_0084&SUBSYS_13158086&REV_00
PCIVEN_8086&DEV_0084&SUBSYS_13158086
PCIVEN_8086&DEV_0084&CC_028000
PCIVEN_8086&DEV_0084&CC_0280

PCI VEN_10EC&DEV_8136 drivers download for Windows XP,Vista,7 & 8.
This page contains the driver installation download for Realtek RTL8102E. PCI VEN_10EC&DEV_8136&SUBSYS. WIN7 = Windows 7,WIN10= Windows 10.
Download PCI VEN_10EC&DEV_8136&REV_07 driver in Windows 7 x64 version for free.

If you were to hop out to:

and from what you see in Device Manager enter your VENdor and DEVice information from the network Controller, then click Search:

PCI VEN_10EC&DEV_8136&REV_05 device driver for Windows 7, XP, 10, 8, and 8.1.

You can see that that device is most likely an Intel wireless device:

This jives with what HP says about your system:

So your wireless component is an Intel part and Intel has a drivers download page that has a driver update utility you can download (perhaps to your desktop) and let it analyze your system and see if it suggests a driver for you:

It is generally not a good idea to use Windows Update for any hardware device drivers (video, audio, network) because Microsoft does not know what the best drivers are for your system. Always get hardware device drivers from the manufacturers WWW site if possible (if you want your system to work properly).

If you ever see any hardware driver updates offered by Windows update I would decline them, then hide them so you don't accidentally install the wrong drivers.

Here you can see where I have chosen not to install and then hidden Windows Updates for an NVIDIA video card since I know they are probably not right and I know I should only get NVIDIA drivers right from the NVIDIA WWW site.

Pci Ven_10ec&dev_8136&subsys

Here you can see the updates that were offered but I did not install them and hid them do I don't see them again:

Pci Ven 10ec Dev 8136 Driver Download Windows 7