The Taylor St. men were either with Fiore Bucciere (West Side), Sam Battaglia (West Suburbs) or were directly with Giancana/Ricca.

All the other crews were partnered in one way or another with Taylor St. There was no official Underboss of the Outfit during this reign.

The 3 Top Men were: Ricca, Accardo, Giancana.

If anything, You could say Battaglia & Bucciere were Giancana's underbosses. When Giancana wasn't available, and Ricca or Accardo were unavailable, other Crew Bosses would take some direction from Battaglia or Bucciere, in particular, Battaglia.

If it was more of a political concern, direction was given by Murray Humphreys, Boss of the Non-Italian faction and a very smart well respected Man.