Finite Group Databasebeta

← C₃×C₂₃×D₂₆₃ #49136830

Subgroups — C₃×C₂₃×D₂₆₃ #49136830

Order 36294.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₂₃×C₂₆₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₂₃×D₂₆₃	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₂₃×C₂₆₃	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	C₃×D₂₆₃	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₃×C₂₆₃	C₂×C₂₃	1	1	yes	characteristic, complemented, Hall
6	D₂₆₃	C₃×C₂₃	1	1	yes	characteristic, direct product factor, Hall
7	C₂₆₃	C₂×C₃×C₂₃	1	1	yes	characteristic, complemented, Sylow
8	C₂×C₃×C₂₃	—	263	1	no	maximal, Hall
9	C₃×C₂₃	D₂₆₃	1	1	yes	characteristic, direct product factor, Hall
10	C₂×C₂₃	—	263	1	no	Hall
11	C₂₃	C₃×D₂₆₃	1	1	yes	characteristic, direct product factor, Sylow
12	C₂×C₃	—	263	1	no	Hall
13	C₃	C₂₃×D₂₆₃	1	1	yes	characteristic, direct product factor, Sylow
14	C₂	—	263	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₂₃	D₂₆₃
commutator, cosocle, hypocenter	C₂₆₃	C₂×C₃×C₂₃
Frattini	C₁	G
Fitting, socle	C₃×C₂₃×C₂₆₃	C₂
LCS	G ▷ C₂₆₃
UCS	C₁ ◁ C₃×C₂₃

Complements

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

N	H ≅ G/N	type
1. C₃×C₂₃×C₂₆₃	C₂	semidirect
2. C₂₃×D₂₆₃	C₃	direct (N × H)
3. C₂₃×C₂₆₃	C₂×C₃	semidirect
4. C₃×D₂₆₃	C₂₃	direct (N × H)
5. C₃×C₂₆₃	C₂×C₂₃	semidirect
6. D₂₆₃	C₃×C₂₃	direct (N × H)
7. C₂₆₃	C₂×C₃×C₂₃	semidirect
9. C₃×C₂₃	D₂₆₃	direct (N × H)
11. C₂₃	C₃×D₂₆₃	direct (N × H)
13. C₃	C₂₃×D₂₆₃	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×C₂₆₃	2
C₂₃×D₂₆₃	3
C₃×D₂₆₃	23
C₂×C₃×C₂₃	263