Abstract: A subgroup H of a finite group G is said to be conditionally permutable in G if for every subgroup T of G there exists an element x ∈ G such that HTx=TxH. If H is conditionally permutable in every subgroup of G containing H ,then H is said to be completely conditionally permutable subgroup in G .In this paper,some new results are obtained according to the conditional permutability of some subgroups.

Key words: completely conditionally permutable subgroups, fitting subgroups, maximal subgroups, conditionally permutable subgroups