Wait, so Cefalu was a Soldier in Conte's crew?

Were all the Gambino Sicilians in the same crew before Cefalu took over . . . As in Conte, Cefalu, Cali, John Gambino, Rosario Spatola?

I was under the impression that John Gambino/Rosario Spatola/Frank Cali were part of the Cherry Hill Boys that Don Carlo imported. Were Conte/Cefalu in the same crew or did they have a separate one with the sole connection being that they are all Zips.