Although ignorant critics frequently claim that Director J. Edgar Hoover did not do enough to target the Mafia the fact is that there was little he could do given that most rackets with which it was involved such as gambling and loansharking were crimes only under state law beyond federal jurisdiction. This reality was reflected in a memo dated January 15, 1960 from the FBI's Special Agent in Charge of the Newark Office to Director Hoover calling for "Federal Legislation" targeting gambling:
Information has been developed from a source who is well-versed in organized crime concerning the numbers operation. According to this source, the Italian Lottery is the life blood of organized crime in this area. It is felt that a strong blow would be dealt organized crime through the passage of appropriate Federal Legislation which would bring these operations into violation of Federal laws.
And although many rackets were beyond the federal bailiwick that certainly did not hinder aggressive investigations by Hoover's FBI into the Mafia, and the 1960 memo by the Newark SAC concludes: "to accomplish the Bureau's aims and to effectively fulfill our obligation, the [investigation] should be viewed as a continuing and long-range one, close liaison should be maintained with other Law Enforcement agencies and information gathered regarding all types of criminal activity, irrespective of the Bureau's jurisdiction at the moment."
Further reading that may be of interest: