# Changes

Jump to: navigation, search

## Subgroup structure of dihedral group:D8

, 16:17, 29 June 2011
Subgroup series-defining functions
| [[upper central series]] || ascending || trivial || [[center]]: [itex]\{ e, a^2 \}[/itex] -- [[center of dihedral group:D8]] || [[second center]]: whole group || whole group || whole group
|-
| [[lower central series]] || descending || -- || whole group || [[derived subgroup]]: [itex]\{ e, a^2 \}[/itex] -- [[center of dihedral group:D8]] || trivial || trivial || trivial
|-
| [[derived series]] || descending || whole group || [[derived subgroup]]: [itex]\{ e, a^2 \}[/itex] -- [[center of dihedral group:D8]] || trivial || trivial || trivial || trivial
|-
| [[Frattini series]] || descending || whole group || [[Frattini subgroup]]: [itex]\{ e, a^2 \}[/itex] -- [[center of dihedral group:D8]] || trivial || trivial || trivial || trivial
|-
| [[Fitting series]] || ascending || trivial || [[Fitting subgroup]]: whole group || whole group || whole group || whole group
| [[socle series]] || ascending || trivial || [[socle]]: [itex]\{ e, a^2 \}[/itex] -- [[center of dihedral group:D8]] || whole group || whole group || whole group
|}

==Lattice of subgroups==
Bureaucrats, emailconfirmed, Administrators
38,827
edits