The bases of the society are the Family and the Vung. Usually a Hangkerimian will consider family any relative in the same household. Most of the Hangkerimians, male mainly, will move out for starting a new family at marriage.
Hangkerim is a matrilineal society and the bases of any family group are the grown up females. In villages and rural areas, as well as in cities in former times, related women lived in neighboring houses and the oldest or stronger in character women where the natural leader of the stock. In large cities in modern Hangkerim, related women don't longer live together but the image of the Matron is still around.
For a Hangkerimian both men and women are equal as person and citizen rights, but they are not equal in all aspects of society.
Women have always been considered the base of the family, at least in the Kogila, Hembica and Moscha nations, while men have been considered the supporting part of the tribe-society, the ones that would go fighting other tribes, hunting big game. In the pre-Hangkerim societies usually tribe chiefs (then nation kings), where men, and they would handle all the diplomacy or decide if the tribes would go to war... after consulting with shamans (then priests) and their women. The king ruled over the free men as warriors or traders, but the base of the society where a women's job and the king couldn't rule over that.
This were very tight with a matrilineal relationship. When the society became more complex than the tribal societies of all-free-men-are-farmers-craftsmen-warriors-and-the-stronger-is-the-chief, a noble class appeared, and the inheritance should remain in the family steam because the men usually moved around while the women remained in the same place. A married woman would stay in the same home, village of their mother while a man would usually travel between his mother home and his wife home. Kingship would then be usually passed to the nephews rather than the sons.
This is a rough description, things were always a little more complex and there was variations from nation to nation, tribe to tribe, village to village, but overall the matrilineal relationships prevailed. When the Hangkerim nation begun, this matrilineal relationship where the norm and is reflected in the laws and language.
The legal name of a person is a name given by the father (or the husband of the mother or the patriarchal figure in the household, probably an uncle), and the family name of the mother house. This reflect that the men are supposed to give and support life, but the women are supposed to care for the life an the traditions.
But if the family relationship of men were weak, a powerful man would probably preferred their own offspring than his sister's, the traditions would forbid him to give the family heritage to the children of a woman from other family, even if they where the children of this man. Usually the man would give its craft to his sons (and probably even to his daughters), or establish any other kind of relationships based on friendship, craft, knowledge, common interests, etc. This was the origin of the Vung... well, one of the causes.
This matrilineal society has brought also an asymmetrical concept of incest. As most societies, sexual relationships and marriage between direct descendants or ascendants is considered incest and forbidden, regardless of sex. In the father-daughter relationship, father will be either the biological father or any man who had married the mother of the girl before the girl becomes a grownup woman. Relationship between siblings, even half siblings (offspring of the same man, even non-biological children) are also forbidden.
Sexual relationship or marriage to any direct matrilineal descendant of ones mother is also forbidden, as it is to descendants of the maternal grandmother down to forth level of consanguinity (aunts, uncles and cousins).
There is a weak taboo on paternal uncles, aunts and cousins, meaning that there is not real forbidding but are anyhow avoided the relationships between a man and its paternal aunt or a women and its paternal uncle, or cousins from a brother and a sister. Cousins from two brothers are not considered taboo at all (or from half siblings).