The genealogy of female bees is a little more complex than that of the drones, as the queen can mate with up to 25 different drones. 

Unlike drones, both workers and queens have 2 sets of chromosomes (32), 1 set from each parent. 

Female siblings are one of three different types.  Super sisters have the same drone father.  Full sisters have drone fathers who are brothers. Half sisters have unrelated fathers.  Because drones receive their entire genetic make-up from only their mother, all drones with the same mother are genetically identical. That roughly translates into super sisters  being what we know as identical twins and full sisters being fraternal twins.  

Drones develop from unfertilized eggs, and so only have 1 set of chromosomes (16), those of their mother. Technically drones do not have a father, only a grandfather. Neither do they have sons, only grandsons.
Bee Genealogy

Honey bee queens are polyandrous (mate with more than one male). Multiple sperm lines may confer more variation in traits to the queen's offspring; providing bees that perform better at some tasks than others within a single hive. This genetic diversity not only helps the productivity needed to maintain large complex colonies; but also benefits the health of the hive as a whole, as genetic diversity also boosts the colony's resistance against disease.

For more information on bee genealogy and genetics:  http://members.aol.com/queenb95/genetics.html#anchor173808