Can I jailbreak iOS 7.1.2 untethered?

The answer is yes. iOS 7.1.2 contains no new patches for existing jailbreak exploits from Apple. This means that Pangu can be used to jailbreak iOS 7.1.2.

Both Mac OS X and Windows versions of the Pangu jailbreak tool version 1.1.0 have been released, with an improved interface and bug fixes.

See this link for Windows instructions on how to jailbreak iOS 7.1.2 with Pangu.