Finite Group Databasebeta

← C₂×C₂₃×D₂₃ #14523749

Subgroups — C₂×C₂₃×D₂₃ #14523749

Order 2116.

42 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃²	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₃×D₂₃	C₂	1	2	yes	maximal, direct product factor
3	C₂₃²	C₂²	1	1	yes	characteristic, complemented, Sylow
4	C₂²×C₂₃	—	23	1	no	maximal
5	C₂×D₂₃	C₂₃	1	1	yes	maximal, characteristic, direct product factor
6	C₂×C₂₃	—	2	11	no	—
7	C₂×C₂₃	—	23	2	no	—
8	C₂×C₂₃	D₂₃	1	1	yes	characteristic, direct product factor
9	C₂×C₂₃	C₂×C₂₃	1	1	yes	characteristic, complemented
10	D₂₃	C₂×C₂₃	1	2	yes	direct product factor
11	C₂₃	—	2	11	no	—
12	C₂₃	C₂×D₂₃	1	1	yes	characteristic, direct product factor
13	C₂₃	C₂²×C₂₃	1	1	yes	characteristic, complemented
14	C₂²	—	23	1	no	Sylow
15	C₂	—	23	2	no	—
16	C₂	C₂₃×D₂₃	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₂₃	D₂₃
commutator, cosocle, hypocenter	C₂₃	C₂²×C₂₃
Frattini	C₁	G
Fitting, socle	C₂×C₂₃²	C₂
LCS	G ▷ C₂₃
UCS	C₁ ◁ C₂×C₂₃

Complements

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

N	H ≅ G/N	type
1. C₂×C₂₃²	C₂	semidirect
2. C₂₃×D₂₃	C₂	direct (N × H)
3. C₂₃²	C₂²	semidirect
5. C₂×D₂₃	C₂₃	direct (N × H)
8. C₂×C₂₃	D₂₃	direct (N × H)
9. C₂×C₂₃	C₂×C₂₃	semidirect
10. D₂₃	C₂×C₂₃	direct (N × H)
12. C₂₃	C₂×D₂₃	direct (N × H)
13. C₂₃	C₂²×C₂₃	semidirect
16. C₂	C₂₃×D₂₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₂₃²	2
C₂₃×D₂₃	2
C₂²×C₂₃	23
C₂×D₂₃	23