Finite Group Databasebeta

← C₃×D₁₁×C₂₈₃ #32916396

Subgroups — C₃×D₁₁×C₂₈₃ #32916396

Order 18678.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₁×C₂₈₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₁₁×C₂₈₃	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₁₁×C₂₈₃	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	C₂×C₃×C₂₈₃	—	11	1	no	maximal, Hall
5	C₃×C₂₈₃	D₁₁	1	1	yes	characteristic, direct product factor, Hall
6	C₂×C₂₈₃	—	11	1	no	Hall
7	C₂₈₃	C₃×D₁₁	1	1	yes	characteristic, direct product factor, Sylow
8	C₃×D₁₁	C₂₈₃	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₃×C₁₁	C₂×C₂₈₃	1	1	yes	characteristic, complemented, Hall
10	D₁₁	C₃×C₂₈₃	1	1	yes	characteristic, direct product factor, Hall
11	C₁₁	C₂×C₃×C₂₈₃	1	1	yes	characteristic, complemented, Sylow
12	C₂×C₃	—	11	1	no	Hall
13	C₃	D₁₁×C₂₈₃	1	1	yes	characteristic, direct product factor, Sylow
14	C₂	—	11	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₂₈₃	D₁₁
commutator, cosocle, hypocenter	C₁₁	C₂×C₃×C₂₈₃
Frattini	C₁	G
Fitting, socle	C₃×C₁₁×C₂₈₃	C₂
LCS	G ▷ C₁₁
UCS	C₁ ◁ C₃×C₂₈₃

Complements

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

N	H ≅ G/N	type
1. C₃×C₁₁×C₂₈₃	C₂	semidirect
2. D₁₁×C₂₈₃	C₃	direct (N × H)
3. C₁₁×C₂₈₃	C₂×C₃	semidirect
5. C₃×C₂₈₃	D₁₁	direct (N × H)
7. C₂₈₃	C₃×D₁₁	direct (N × H)
8. C₃×D₁₁	C₂₈₃	direct (N × H)
9. C₃×C₁₁	C₂×C₂₈₃	semidirect
10. D₁₁	C₃×C₂₈₃	direct (N × H)
11. C₁₁	C₂×C₃×C₂₈₃	semidirect
13. C₃	D₁₁×C₂₈₃	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×C₁₁×C₂₈₃	2
D₁₁×C₂₈₃	3
C₂×C₃×C₂₈₃	11
C₃×D₁₁	283