1. Associate: You are not really in the family but you do jobs for the family. You would be this if you have no Italian or European decent.
2. Soldier: You work with the mafia and do jobs for the mafia such as hits, drug trafficking, etc. You have European or Italian decent, you are also the lowest ranking member of the family.
3. Capo: You are basically a captain or lieutenant of the mob. You can control a group of soldiers and you report to a boss or an underboss for a set of instructions. You are in charge of handling most money.
4. Chief Advisor: You play most of the important roles in the family. You are a trusted friend of the the family boss. And can give advice to the boss or underboss.
5. Underboss: You are second in command and you are ready to fill in for the boss when ready. ( say if the boss was offline). You control most of the family and plans many missions to take on in the family.
6. Boss: Commands the whole family and can rank up anyone he wishes.
P.S above capo can rank up anyone in the group who is a rank below them.