# Marginality does not satisfy intermediate subgroup condition

From Groupprops

This article gives the statement, and possibly proof, of a subgroup property (i.e., marginal subgroup)notsatisfying a subgroup metaproperty (i.e., intermediate subgroup condition).

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## Statement

It is possible to have a group and subgroups of such that and:

- is a marginal subgroup of .
- is
*not*a marginal subgroup of .

## Proof

`Further information: dihedral group:D8, subgroup structure of dihedral group:D8`

Consider the following:

- is dihedral group:D8.
- is the center of dihedral group:D8.
- is one of the Klein four-subgroups of dihedral group:D8.

Then, we have:

- is marginal in , because center is marginal (it is marginal with respect to the variety of abelian groups).
- is not marginal in , because it is not characteristic in .