Finite Group Databasebeta

← C₃×C₂₃×D₂₂₇ #44531213

Subgroups — C₃×C₂₃×D₂₂₇ #44531213

Order 31326.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₂₃×C₂₂₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₂₃×D₂₂₇	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₂₃×C₂₂₇	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	C₃×D₂₂₇	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₃×C₂₂₇	C₂×C₂₃	1	1	yes	characteristic, complemented, Hall
6	D₂₂₇	C₃×C₂₃	1	1	yes	characteristic, direct product factor, Hall
7	C₂₂₇	C₂×C₃×C₂₃	1	1	yes	characteristic, complemented, Sylow
8	C₂×C₃×C₂₃	—	227	1	no	maximal, Hall
9	C₃×C₂₃	D₂₂₇	1	1	yes	characteristic, direct product factor, Hall
10	C₂×C₂₃	—	227	1	no	Hall
11	C₂₃	C₃×D₂₂₇	1	1	yes	characteristic, direct product factor, Sylow
12	C₂×C₃	—	227	1	no	Hall
13	C₃	C₂₃×D₂₂₇	1	1	yes	characteristic, direct product factor, Sylow
14	C₂	—	227	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₂₃	D₂₂₇
commutator, cosocle, hypocenter	C₂₂₇	C₂×C₃×C₂₃
Frattini	C₁	G
Fitting, socle	C₃×C₂₃×C₂₂₇	C₂
LCS	G ▷ C₂₂₇
UCS	C₁ ◁ C₃×C₂₃

Complements

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

N	H ≅ G/N	type
1. C₃×C₂₃×C₂₂₇	C₂	semidirect
2. C₂₃×D₂₂₇	C₃	direct (N × H)
3. C₂₃×C₂₂₇	C₂×C₃	semidirect
4. C₃×D₂₂₇	C₂₃	direct (N × H)
5. C₃×C₂₂₇	C₂×C₂₃	semidirect
6. D₂₂₇	C₃×C₂₃	direct (N × H)
7. C₂₂₇	C₂×C₃×C₂₃	semidirect
9. C₃×C₂₃	D₂₂₇	direct (N × H)
11. C₂₃	C₃×D₂₂₇	direct (N × H)
13. C₃	C₂₃×D₂₂₇	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₂₃×C₂₂₇	2
C₂₃×D₂₂₇	3
C₃×D₂₂₇	23
C₂×C₃×C₂₃	227