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.
The Greek
The spartans were
oligarchy
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".
Oligarchy, monarchy, democracy
It was an oligarchy, and was highly religious(Aarshad-patriot)
most of the greek city-states practiced oligarchy, including sparta and athens.