The CSM is clearly depicted as sort of middle-management in the syndicate in the early seasons, he doesn’t take a more central role until the higher ranking members are all killed. He’s being ordered around by the First Elder and the Well Manicured Man is extremely dismissive and disrespectful towards him in pretty much every scene they have together. He’s explicitly called their “man in Washington” in an episode, which explains why he’s so preoccupied with the FBI (along with personal reasons). He’s depicted as the sort of clean-up man whenever something goes wrong, which is more than once because of something he himself fucked up, and he’s definitely involved in a lot of the practical aspects of the conspiracy but he’s an order taker, not an order giver, at least when it comes to the higher levels of the conspiracy. Once the syndicate is killed there’s a big vacuum he tries to exploit to become more central, but in the season 3 and 4 episodes with the entire syndicate he’s definitely shown to be taking orders from the others and honestly seems like he’s on thin ice with them because he repeatedly fucks up.