Regular symmetric groups of boolean functions

We show that with the exception of four known cases: C3C3, C4C4, C5C5, and S22, all regular permutation groups can be represented as symmetric groups of boolean functions. This solves the problem posed by A. Kisielewicz in the paper [A. Kisielewicz, Symmetry groups of boolean functions and constructions of permutation groups, J. Algebra 199 (1998) 379–403]. A slight extension of our proof yields the same result for semiregular groups.