One of the most popular charges against Uthman is claim that he use to appoint his close relatives to the government positions.
In the time of Uthman’s ruling there were approximately 47 governors in the different places of Islamic caliphate. (see their names here)
And ONLY EIGHT from them were his close relatives.
1) Muawiya ibn Abu Sufyan.
2) Said ibn al-As.
3) al-Walid ibn Uqba.
4) Abdullah ibn Ammar ibn Kurayz.
5) Abdullah ibn Sad ibn Abu Sarkh
6) Abdullah ibn Samurah.
7) Ali ibn Ade
8.) Marwan ibn al-Hakam.
These governors didn’t rule in the same time. For example Uthman take al-Walid from his place and appointed Said ibn al-As instead of him. Close to his death time, Uthman discarded Said as well. When Uthman died only 3 governors from banu umeyah were ruling. Muawiya, Abdullah ibn Sad and Abdullah ibn Amir.
Also it’s necessary to note, that Muawiyah wasn’t appointed by Uthman, he was governor from the time of Umar.