What was the nature of family regulation in sparta? what were the reasons for it? in what ways was the spartan family system patriarchal

I think in Spartan households, Men held more power than the Women, and total obedience was required for the Women. Spartan really value Strength (all of their boys already taken for military training from a very young age). Since Women is naturally weaker, they believe that Men were the one that should lead the city.