Finite Group Databasebeta

← D₈×C₂₃ #67282

Subgroups — D₈×C₂₃ #67282

Order 368.

22 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₄×C₂₃	C₂	1	2	yes	maximal, complemented
2	C₈×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₂₃	—	2	2	no	—
4	C₄×C₂₃	C₂²	1	1	yes	characteristic
5	C₂×C₂₃	—	4	2	no	—
6	C₂×C₂₃	D₄	1	1	yes	characteristic
7	C₂₃	D₈	1	1	yes	characteristic, direct product factor, Sylow
8	D₈	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
9	D₄	C₂×C₂₃	1	2	yes	complemented
10	C₈	C₂×C₂₃	1	1	yes	characteristic, complemented
11	C₂²	—	2	2	no	—
12	C₄	C₂²×C₂₃	1	1	yes	characteristic
13	C₂	—	4	2	no	—
14	C₂	D₄×C₂₃	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₂₃	D₄
commutator, Frattini, cosocle	C₄	C₂²×C₂₃
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₂₃ ◁ C₄×C₂₃ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. D₄×C₂₃	C₂	semidirect
2. C₈×C₂₃	C₂	semidirect
7. C₂₃	D₈	direct (N × H)
8. D₈	C₂₃	direct (N × H)
9. D₄	C₂×C₂₃	semidirect
10. C₈	C₂×C₂₃	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
D₄×C₂₃	2
C₈×C₂₃	2
D₈	23