Do you mean that it does not appear in the drop-down menu in the Output Module Settings in the Main Options > Format section? Do all the other options show up?
As Zina suggests, please tell us exactly where you're looking. A screenshot of where you're looking would be especially useful.
You don't want to render H264 movies from the render cue anyway. You want to open up the AME (Adobe Media Encoder) open your After Effects Project there, pick the composition, and use one of the H264 presets to render your project.
From your screenshot, I can see that you're missing all of the MPEG-based output options. This likely means that you haven't entered the serial number to activate the application, and you're still running it in trial mode.
Choose Help > Activate and enter your serial number.
If that's not it, then it may be that the codecs that are only unlocked for the full version didn't get installed correctly. In that case, you need to uninstall the suite, deactivate, reinstall, and reactivate.
I cannot stress enough that you should not be rendering to compressed versions from After Effects.
Render to a lossless codec, preferably 10bit from a 16bit project, then compress afterwards.
It will look better and file size will be smaller.
You can't 2 pass encode whilst rendering.
This 2 step way is usually actually quicker as the initial rendering is quicker.
And you can then make different versions to get the size/setting/format you want.
Be aware that the default "Lossless" setting is Animation (8 bit RGB) and for some reason has the audio turned off.