For a finite group , the set of all prime divisors of is denoted by . P. Shumyatskii introduced the following conjecture, which is included in the "Kourovka Notebook" as Question 17.125: a finite group always contains a pair of conjugate elements and such that . Denote by the class of all finite groups such that for every maximal subgroup in . Shumyatskii's conjecture is equivalent to the following conjecture: every group from is generated by two conjugate elements. Let be the class of all finite groups in which every maximal subgroup is a Hall subgroup. It is clear that . We prove that every group from is generated by two conjugate elements. Thus, Shumyatskii's conjecture is partially supported. In addition, we study some properties of a smallest order counterexample to Shumyatskii's conjecture.