Question

Edit This answer is invalid to the question because the OP wanted embedded submanifolds. I'm leaving the answer up because it does handle a related question and contains a reference to a paper.

An arcwise connected subgroup of a Lie group is a Lie subgroup at least in the analytic case; cf. this. I recall that it's in the appendix to volume 1 of Kobayashi and Nomizu's Foundations of Differential Geometry.