Is family an organization of hierarchy?

The composition of a usual family is normally structures by the role of a determinated person. The family tree itself is a hierarchy, and in much of ancient cultures, as well as most of African and Islamic countries, there is a sustained hierarchy in the family. The structure may be whatever (even much of them puts men in the top), but, just from the simple relation of parents and children, this structure is present. Consequently, I think like in every thpe of hierarchy, there are some types of rights and duties targeted specifically to each component of this hierarchy. However, this may contradict the idea of the equality for evey component of society.