In the third aliyah Pharaoh gives Yosef stupendous honor and appoints him head of all of Egypt, with the only exception being Pharaoh's throne. Thus Yosef is now second in command only to Pharaoh. Yosef is 30 years old at this point, and he marries Potifar's daughter Osnat. (Our sages tell us that actually this was an adopted daughter by Potifar. Osnat was really Yosef's Niece - the daughter that Dinah had when she was raped by Shchem. This also explains why Potifar's wife made advances to Yosef as recorded earlier in the Torah. She acted so because she knew that she and Yosef would have common offspring, only she didn't know it would be from her [adopted] daughter and not her.
Yosef has two sons named Menashe and Ephraim.