# Modular not implies permutable

From Groupprops

This article gives the statement and possibly, proof, of a non-implication relation between two subgroup properties. That is, it states that every subgroup satisfying the first subgroup property (i.e., modular subgroup) neednotsatisfy the second subgroup property (i.e., permutable subgroup)

View a complete list of subgroup property non-implications | View a complete list of subgroup property implications

Get more facts about modular subgroup|Get more facts about permutable subgroup

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## Statement

A modular subgroup of a group need not be permutable.

## Facts used

## Proof

By fact (1), it suffices to construct an example of a group with a maximal subgroup that is not permutable. Indeed, in the symmetric group:S3, the subgroup of order two generated by a transposition is maximal but not permutable.