16 courses is 64 units only (on average)
You bring in 104 (rounded up)
that is only 168- not even enough to graduate.
If we add in 5 more preqs for Sociology (not sure if you even need that many) that would be 20 units.
So that is like 188. Lets say that you have not 16 courses but 20 for the major ( you dont, but lets really round all the way up there), so that is an extra 4 required courses, another 20 units, that puts you at 208 units--- still not at the unit max, and trust me , sociology doesnt require 20 courses.
You need at min 180 at most 216.
So yes you can switch majors and be well within the allowable.