No the ideas are mutually exclusive.
Socialism is a philosophy that everything is public - no one person owns anything of importance because, in theory, everyone owns everything equally. Communism is a brand of socialism in which the state government owns everything on behalf of the people, which of course, gives those in the government all the power. Public, government entities are in control.
Fascism is a philosophy that the elite should control everything of importance. The more you own (not always in money or property but in fanaticism) the more right you are given to control. Dictatorship is a common example. Individuals or private industry are in control.