You almost have it.
With the information from Device Manager you can determine the VENdor and DEVice information:
Network Controller (\Device\NTPNP_PCI0019)
PCI*VEN_8086*&DEV_0084&SUBSYS_13158086&REV_00
PCI\VEN_8086&DEV_0084&SUBSYS_13158086
PCI\VEN_8086&DEV_0084&CC_028000
PCI\VEN_8086&DEV_0084&CC_0280
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:
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:
http://www.intel.com/content/www/us/en/support/detect.html
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.
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: