I'm not so sure it has anything to do with subtype but perhaps. What do you mean about reading your subtype?
I have been thinking about this a lot lately actually; I'll write more later. Regardless of how you identify with written descriptions, being around groups of predominantly one quadra can be very telling in terms of how you relate to them.
My opposing quadra seems the most psychologically foreign to me. That does not mean they are bad people of course, but that their motivations and implied values are different than mine. For example, I cannot "relax" or enjoy myself as easily as betas do, when they are doing what they want to do. Then again, my idea of relaxing and enjoying myself is also different.
Just to be clear, it is not a matter of socializing or, as I have said before, playing games and competing or whatever. It's how it's done, and in some ways why it's done that prevents me from enjoying it. One element is the Fe-group thing. It is somewhat described on the wikisocion, but generally it is about how if a beta group invites you to do something, you're supposed to do it because it is a group acceptance thing. They then get disappointed if you don't do it, and suppose you don't like them - where as, the whole time, my intention is to simply do what I want to do, all the time (and that is the case independent of the group). That is a very rough-and-ready way of describing it, but it is small pieces of the puzzle like that which start fitting together over time and confirming your quadra relations.