A matriarchy or matriarchical society was a society in which females held a dominant role over males. The leader of a matriarchy may be identified as the matriarch. The opposing sociological structure was known as a patriarchical society.
The Paraagans had been ruled by a matriarchy until the 2140s, but the Paraagan males had made great progress in gaining equal rights by 2152. T'Pol still considered it better for her to contact the Paraagan authorities than Malcolm Reed. (ENT: "Shockwave")
As of 2154, Orion society, while appearing to be extremely patriarchal, was actually the opposite, with the females exerting total control over the males according to Harrad-Sar. (ENT: "Bound")
In 2267, Cygnet XIV was a planet "dominated by women." (TOS: "Tomorrow is Yesterday")
In 2364, Angel I was a strongly matriarchal society, where the females were larger and stronger than males, taking the roles of soldier and hunter; this arrangement was described as "unusual" by Jean-Luc Picard. According to Deanna Troi, Betazoid society showed similar characteristics. (TNG: "Angel One")
In 2370, the Skrreea were a matriarchal society, since males were considered too emotional to be good leaders. (DS9: "Sanctuary")
In 2373, Tova Veer and Forra Gegen speculated that Humans might have a matriarchal society, after observing the hierarchy of the USS Voyager crew under Captain Kathryn Janeway. (VOY: "Distant Origin")