Nope. Usually not formally anyways. Of course, like any other organization the formal titles don't necessarily indicate someone's power. Soldiers can vary widely in their income/power. Some soldiers are "specials" and have so much knowledge or experience in a particular criminal endeavor that they more or less report to the Family's administration.

In other cases a captain may rely on a handful of soldiers he trusts to transmit orders, enforce discipline, and collect funds. But it all comes down to money. Over time, all else equal more "respect" and "power" will accrue to those soldiers who are better earners.