Finite Group Databasebeta

← C₂₃×D₂₂₉⋊C₃ #44539160

Subgroups — C₂₃×D₂₂₉⋊C₃ #44539160

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	C₂₃×D₂₂₉	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₂₃×C₂₂₉	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	D₂₂₉⋊C₃	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂₂₉⋊C₃	C₂×C₂₃	1	1	yes	characteristic, complemented, Hall
6	D₂₂₉	C₃×C₂₃	1	1	yes	characteristic, complemented, Hall
7	C₂₂₉	C₂×C₃×C₂₃	1	1	yes	characteristic, complemented, Sylow
8	C₂×C₃×C₂₃	—	229	1	no	maximal, Hall
9	C₃×C₂₃	—	229	1	no	Hall
10	C₂×C₂₃	—	229	1	no	Hall
11	C₂₃	D₂₂₉⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
12	C₂×C₃	—	229	1	no	Hall
13	C₃	—	229	1	no	Sylow
14	C₂	—	229	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₂₃	D₂₂₉⋊C₃
commutator, cosocle, hypocenter	C₂₂₉	C₂×C₃×C₂₃
Frattini	C₁	G
Fitting, socle	C₂₃×C₂₂₉	C₂×C₃
LCS	G ▷ C₂₂₉
UCS	C₁ ◁ C₂₃

Complements

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

N	H ≅ G/N	type
1. C₂₃×C₂₂₉⋊C₃	C₂	semidirect
2. C₂₃×D₂₂₉	C₃	semidirect
3. C₂₃×C₂₂₉	C₂×C₃	semidirect
4. D₂₂₉⋊C₃	C₂₃	direct (N × H)
5. C₂₂₉⋊C₃	C₂×C₂₃	semidirect
6. D₂₂₉	C₃×C₂₃	semidirect
7. C₂₂₉	C₂×C₃×C₂₃	semidirect
11. C₂₃	D₂₂₉⋊C₃	direct (N × H)

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
C₂₃×D₂₂₉	3
D₂₂₉⋊C₃	23
C₂×C₃×C₂₃	229