Finite Group Databasebeta

← C₂₃⋊(D₂₂₉⋊C₃) #44539162

Subgroups — C₂₃⋊(D₂₂₉⋊C₃) #44539162

Order 31602.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×C₂₂₉⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₅₂₆₇	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₂₃×C₂₂₉	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	D₂₂₉⋊C₃	—	23	1	no	maximal, Hall
5	C₂₂₉⋊C₃	D₂₃	1	1	yes	characteristic, complemented, Hall
6	D₂₂₉	—	23	1	no	Hall
7	C₂₂₉	C₃×D₂₃	1	1	yes	characteristic, complemented, Sylow
8	C₃×D₂₃	—	229	1	no	maximal, Hall
9	C₃×C₂₃	—	229	1	no	Hall
10	D₂₃	—	229	1	no	Hall
11	C₂₃	D₂₂₉⋊C₃	1	1	yes	characteristic, complemented, Sylow
12	C₂×C₃	—	5267	1	no	Hall
13	C₃	—	229	1	no	Sylow
14	C₂	—	5267	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₂₃×C₂₂₉	C₂×C₃
LCS	G ▷ C₂₃×C₂₂₉
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₂₃×C₂₂₉⋊C₃	C₂	semidirect
2. D₅₂₆₇	C₃	semidirect
3. C₂₃×C₂₂₉	C₂×C₃	semidirect
5. C₂₂₉⋊C₃	D₂₃	semidirect
7. C₂₂₉	C₃×D₂₃	semidirect
11. C₂₃	D₂₂₉⋊C₃	semidirect

Maximal subgroups

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

subgroup	index
C₂₃×C₂₂₉⋊C₃	2
D₅₂₆₇	3
D₂₂₉⋊C₃	23
C₃×D₂₃	229