In this work we discuss three conjectures, raised in [3] on maximal subgroups in division rings. Recently M. Mahdavi-Hezavehi gave a negative answer to Conjecture 3 (see below) by constructing a counterexample in the division ring of real quaternions. Here, we show that the other conjectures have a positive answer for division rings of quaternions of characteristics different from 2. The description of all solvable maximal subgroups of the division ring of real quaternions is also given.