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Subgroup structure of dihedral group:D8

29 bytes removed, 16:17, 29 June 2011
Subgroup series-defining functions
| [[upper central series]] || ascending || trivial || [[center]]: <math>\{ e, a^2 \}</math> -- [[center of dihedral group:D8]] || [[second center]]: whole group || whole group || whole group
|-
| [[lower central series]] || descending || -- || whole group || [[derived subgroup]]: <math>\{ e, a^2 \}</math> -- [[center of dihedral group:D8]] || trivial || trivial || trivial
|-
| [[derived series]] || descending || whole group || [[derived subgroup]]: <math>\{ e, a^2 \}</math> -- [[center of dihedral group:D8]] || trivial || trivial || trivial || trivial
|-
| [[Frattini series]] || descending || whole group || [[Frattini subgroup]]: <math>\{ e, a^2 \}</math> -- [[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]]: <math>\{ e, a^2 \}</math> -- [[center of dihedral group:D8]] || whole group || whole group || whole group
|}
 
==Lattice of subgroups==
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