Patriarchy

A patriarchy is a society in which males hold a dominant role over females.

The Talarians, for example, are a "rigidly patriarchal society", believing women should only be used for mating and for work. They viewed females as unintelligent and weak and in need of their protection. As such, a female could never outrank a male in Talarian society. Because of these beliefs, Jeremiah Rossa, a Human raised by Talarians did not respond positively to the women serving aboard the USS Enterprise (NCC-1701-D). Because Rossa needed to build a relationship with a male, as he would not listen to a female, Captain Jean-Luc Picard had to serve as a "father figure" to help Rossa reintegrate into Human society. 

There have been many other examples of patriarchal societies throughout history, including the Kazon and the Ferengi, although the latter made notable strides towards equality in the 2370s. Several Human cultures were also once patriarchal, and some aspects of Klingon society (such as the restriction of women being able to hold the position of chancellor) may be seen as patriarchal as well.