well, as a loner myself, what i would say to you is this: leave it be.
im wondering: do you wonder if you and your daughter have a good relationship? is there something more than what you are asking here? i mean, take her out to dinner, just the two of you. try not to pressure her to have conversation, after a little while, its not like shes going to sit there in silence; she will talk eventually. somehow as the moment presents itself, you can let her know unconditionally that if shes ever feeling lonely or upset about something, she can always come to you - even if its just to ask to go out to dinner with you or something like that.
but anyway, theres a lot of reasons that i used to be like this. no one fully accepted who i was, or they didnt want to do the things that i did, or whatever. i wanted to be included in things, but not to the point where i gave up who i was. your daughter not fully being included isnt a bad thing really, it means shes not conforming to the standards that the social situations are presenting. but it can be lonely, and it can feel sometimes as if the friendships you have are superficial, only on the surface, and you dont really have someone to share your secrets with or your feelings with.
are there church groups she can be involved in? what about scouting? 4h? is she interested in a sport or talent? dance? something? see if theres not something she can get involved in that might introduce her to a new friend or something. other than that, i would literally leave her alone, dont worry about her other than to reassure her that she can always come to you, judgement free, and always hold up that end of the bargain. ;) you sound like a great mom, but i wouldnt worry too much about this particular issue. i know my mom had nothing to worry about. ;)