Early on Eddie McGrath was partnered with Cockeyed Dunn, hence the Gang's early name "The Dunn-McGrath Gang." After Dunn got fried in the chair Connie Noonan stepped up as McGrath's #2 I believe. But by at least the early 1950s Mulligan had been elevated. At least for control of all gambling and other rackets in Queens County.

You have to remember also that the Irish Mob never had a "formal" hierarchical structure the same way the Italians did with their "Roman Legion" type "Family" structure; Capo, Underboss, Consigliere, Capo di regime, soldiers, associates, etc.

The Irish were a loose conglomeration of hoodlums with recognized a "boss," and his second-in-command which you could liken to an "underboss."After that all the other guys just kinda fell in line as members of the gang, with some of them "specializing" in robberies, strong-arm work, or labor union activities, gambling, etc.

And of course based on fear or money-making capabilities some were more "recognized" and had more influence than others.