There was a Mafia, of sorts, in Chicago during Capone's reign. It was called the Unione Siciliana, and it was something like a civic association with muscle. Capone always dealt with them respectfully, and always tried to have one of his Sicilians put in as chief of the Unione.
The guy closest to Capone in the Outfit was Jake Guzik, a Jew. Murray (the Camel) Humphries, a Welshman, was the Outfit's labor chief into the Sixties.