The Justice Department
Under the authority of Deputy Atty. Gen. Rod Rosenstein, special counsel Robert S. Mueller III will have a greater degree of autonomy to conduct investigations and prosecutions than congressional committees, which often are partisan. But Mueller still answers to Rosenstein, who in turn answers to the president.
This means President Trump has the authority to fire the special counsel for any reason. However, such a move is highly unlikely because of the political ramifications for Trump, who faced intense criticism when he fired FBI Director James B. Comey.