Yes, that’s when they buried hi there . . .
More seriously, you aren’t going to find anything resembling a “chain of command” in the early church; it just didn’t work that way.
You
will find that some sees, notably Rome, Antioch, and Alexandria being more influential, and over time, Rome coming to be seen as a final arbiter in disputes as the centuries passed.
Also, St. Basil at one point, I believe it was during one of his periods as Patriarch of Constantinople, made a tour in which he deposed several bishops; I know of nothing comparable to Rome.
There is evidence of church council edicts being sent to Rome for approval afterwards, but East and West split in the descriptions about those and how they would be accepted/rejected.
The Byzantine emperor ratified Papal elections eventually. If memory serves, he once deposed a pope and installed his own candidate, but don’t hold me to that (and as late as the 20th century, the Austro-Hungarian emperor’s representative vetted the papal selection of the College of Cardinals–they elected another, who promptly rewrote the rules to eliminate the secular veto).
There were unsuccessful papal attempts by the late first millennium to assert authority outside of his own patriarchy.
Nothing like the authority of the current pope within the west ever existed before the schism, not even in the west. It is only recent that Rome has had a significant role in selection of bishops outside of Italy and the Americas.
AMDG
hawk