Finite Group Databasebeta

← C₃×C₁₁×D₃₈₃ #38760176

Subgroups — C₃×C₁₁×D₃₈₃ #38760176

Order 25278.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₁×C₃₈₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₁×D₃₈₃	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₁₁×C₃₈₃	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	C₃×D₃₈₃	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₃×C₃₈₃	C₂×C₁₁	1	1	yes	characteristic, complemented, Hall
6	D₃₈₃	C₃×C₁₁	1	1	yes	characteristic, direct product factor, Hall
7	C₃₈₃	C₂×C₃×C₁₁	1	1	yes	characteristic, complemented, Sylow
8	C₂×C₃×C₁₁	—	383	1	no	maximal, Hall
9	C₃×C₁₁	D₃₈₃	1	1	yes	characteristic, direct product factor, Hall
10	C₂×C₁₁	—	383	1	no	Hall
11	C₁₁	C₃×D₃₈₃	1	1	yes	characteristic, direct product factor, Sylow
12	C₂×C₃	—	383	1	no	Hall
13	C₃	C₁₁×D₃₈₃	1	1	yes	characteristic, direct product factor, Sylow
14	C₂	—	383	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₁₁	D₃₈₃
commutator, cosocle, hypocenter	C₃₈₃	C₂×C₃×C₁₁
Frattini	C₁	G
Fitting, socle	C₃×C₁₁×C₃₈₃	C₂
LCS	G ▷ C₃₈₃
UCS	C₁ ◁ C₃×C₁₁

Complements

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

N	H ≅ G/N	type
1. C₃×C₁₁×C₃₈₃	C₂	semidirect
2. C₁₁×D₃₈₃	C₃	direct (N × H)
3. C₁₁×C₃₈₃	C₂×C₃	semidirect
4. C₃×D₃₈₃	C₁₁	direct (N × H)
5. C₃×C₃₈₃	C₂×C₁₁	semidirect
6. D₃₈₃	C₃×C₁₁	direct (N × H)
7. C₃₈₃	C₂×C₃×C₁₁	semidirect
9. C₃×C₁₁	D₃₈₃	direct (N × H)
11. C₁₁	C₃×D₃₈₃	direct (N × H)
13. C₃	C₁₁×D₃₈₃	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×C₃₈₃	2
C₁₁×D₃₈₃	3
C₃×D₃₈₃	11
C₂×C₃×C₁₁	383