Section 31 Headquarters was a space station used during the mid-23rd century by the covert Starfleet organization Section 31. Listed as an abandoned penal colony, the station was used by Section 31 as a forward operating base and housed the AI known as Control.
Located in empty space at the coordinates 7-4 Mark 5.6, officially the base was listed as a former penal colony which, as of the mid-23rd century, had been abandoned over a century ago. It was surrounded by a dense minefield of alien origin that contained blade mines and blackout mines in addition to conventional explosive mines. Incoming vessels were required to take a circuitous route to avoid them.
In 2257, Control betrayed Starfleet and massacred the crew of Section 31 Headquarters by shutting off life support, though it was able to hide this fact by creating holograms of Admiral Patar and other Section 31 leaders for communications.
Two weeks later, the USS Discovery uncovered the station's location and was directed there by Admiral Katrina Cornwell in an effort to reset Control. Discovery came under attack by the mines, which had been reprogrammed by Control, and barely managed to reach the station.
After a boarding party from Discovery arrived on the station and learned of the events that had transpired there, it was found that Lieutenant Commander Airiam had been corrupted and was attempting to give Control information about artificial intelligence gathered by the Sphere. To stop her, Commander Nhan was forced to eject Airiam into space. (DIS: "Project Daedalus")
According to Luther Sloan, by the 24th century, Section 31 did not have headquarters or buildings whatsoever, instead keeping knowledge on its operations in the minds of a very select group of people, including Sloan. (DS9: "Extreme Measures")