That isn't even a question, but whatever.
The city-states, or polies, were ruled by hereditary male monarchies. The exception was Athens, which had a complex democratic system. Later Greek empires, like the Macedonian, Antigonid, Epirote, and ultimately Byzatine empires were also run by kings.
There were three main forms of government in ancient Greece: Monarchy, Oligarchy and Democracy. I am unable to locate how the government of the Greek cities reflected the structure of the Greek families.
oligarchy
The Greek
The spartans were
Its oligarchy from the Greek ολιγαρχία (oligarchia).
Oligarchy.
oligarchy
Oligarchy
The root word of oligarchy is "oligo-", which comes from the Greek word "oligoi" meaning "few".
The Greek city-state of Sparta was governed by an oligarchy. Its political system was characterized by a dual kingship and a council of elders known as the Gerousia, alongside an assembly of citizens. This oligarchic structure concentrated power in the hands of a few elite individuals, particularly the military and aristocratic class, which controlled the state's decisions and policies.
Oligarchy, monarchy, democracy
The Greek city-state of Sparta was governed by an oligarchy. It had a dual monarchy, but real power was held by a council of elders known as the Gerousia and a group of five elected officials called ephors. This oligarchic structure allowed a small elite to dominate political decision-making and maintain control over the larger population, including the enslaved Helots.