Skinner formed it as a section of the FBI, from out of Mulder and Reyes X-files department, and brought in Glyn Aberford and another guy who everybody has forgotten the name of (xxxxxxxxxx). Liz Lucek was made Director of Ops very soon (around 2001). Then it grew bigger, more PCs, more mayhem.
Eventually in June 2007, Liz was replaced as Director of Ops and Graeme III came in. This coincided with Spec Ops officially moving out of Quantico and initially into El Toro, before again moving to Hole in the Ground, Washington. Liz stayed on in Quantico as the liaison between Spec Ops and main FBI, but it was an administrative rather than operational role. She also had another side job running an FBI information gathering operation using a strip club in Northern Virginia, just down the road from Quantico called Landmarks.
Autumn 2008 there was a reorganisation, and Spec Ops swallowed up a small department that used to be in the Department of Defense that investigated similar things, called the Fringe Division, that had been led by Broyles. Broyles ended up as a Special Agent, and was put on military reserve.
Then in Winter 2008/2009 there was the incursion in to El Toro, and in the subsequent investigations Graeme resigned, and the section was taken out of the FBI, Skinner retired, and it was all put under the Department of Defense, and Broyles was made Director of Operations, and put back on military active service. By Spring 2009 (a year ago) pretty much all connections with the FBI had been broken, and Spec Ops was entirely a military operation, under Broyles, and at the same time, Stargate Command was moved from out of Air Force control and also put in Spec Ops as the Space Division. Colonel Samantha Carter was its Operations Chief, and General Jack O’Neil was in command of the whole Spec Ops umbrella from the Pentagon.
July 2009 saw the beginning of the end for Sam Carter at Space Division, as the off books mission about Lintra the Elder went pear shaped. She resigned and went to work in Casablanca. Head of Space Division is currently an undefined role.
Yes, they have…. well, almost everyone.