Subgroups — C₁₃×C₁₁⋊(D₃₇⋊C₃) #44540824

Order 31746.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×C₁₃×C₃₇⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₃×D₄₀₇	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₁₁×C₁₃×C₃₇	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	C₁₃×D₃₇⋊C₃	—	11	1	no	maximal, Hall
5	C₁₁⋊(D₃₇⋊C₃)	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₁₃×C₃₇⋊C₃	D₁₁	1	1	yes	characteristic, complemented, Hall
7	C₁₁×C₃₇⋊C₃	C₂×C₁₃	1	1	yes	characteristic, complemented, Hall
8	C₁₃×D₃₇	—	11	1	no	Hall
9	C₃×C₁₃×D₁₁	—	37	1	no	maximal, Hall
10	D₄₀₇	C₃×C₁₃	1	1	yes	characteristic, complemented, Hall
11	C₁₃×C₃₇	C₃×D₁₁	1	1	yes	characteristic, complemented, Hall
12	C₃×C₁₁×C₁₃	—	37	1	no	Hall
13	C₁₁×C₃₇	C₂×C₃×C₁₃	1	1	yes	characteristic, complemented, Hall
14	C₁₃×D₁₁	—	37	1	no	Hall
15	D₃₇⋊C₃	—	11	1	no	Hall
16	C₁₁×C₁₃	D₃₇⋊C₃	1	1	yes	characteristic, complemented, Hall
17	C₃₇⋊C₃	C₁₃×D₁₁	1	1	yes	characteristic, complemented, Hall
18	C₂×C₃×C₁₃	—	407	1	no	Hall
19	D₃₇	—	11	1	no	Hall
20	C₃×D₁₁	—	37	1	no	Hall
21	C₃×C₁₃	—	37	1	no	Hall
22	C₃₇	C₃×C₁₃×D₁₁	1	1	yes	characteristic, complemented, Sylow
23	C₃×C₁₁	—	37	1	no	Hall
24	C₂×C₁₃	—	407	1	no	Hall
25	D₁₁	—	37	1	no	Hall
26	C₁₃	C₁₁⋊(D₃₇⋊C₃)	1	1	yes	characteristic, direct product factor, Sylow
27	C₁₁	C₁₃×D₃₇⋊C₃	1	1	yes	characteristic, complemented, Sylow
28	C₂×C₃	—	407	1	no	Hall
29	C₃	—	37	1	no	Sylow
30	C₂	—	407	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₃	C₁₁⋊(D₃₇⋊C₃)
commutator, cosocle, hypocenter	C₁₁×C₃₇	C₂×C₃×C₁₃
Frattini	C₁	G
Fitting, socle	C₁₁×C₁₃×C₃₇	C₂×C₃
LCS	G ▷ C₁₁×C₃₇
UCS	C₁ ◁ C₁₃

Complements

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

N	H ≅ G/N	type
1. C₁₁×C₁₃×C₃₇⋊C₃	C₂	semidirect
2. C₁₃×D₄₀₇	C₃	semidirect
3. C₁₁×C₁₃×C₃₇	C₂×C₃	semidirect
5. C₁₁⋊(D₃₇⋊C₃)	C₁₃	direct (N × H)
6. C₁₃×C₃₇⋊C₃	D₁₁	semidirect
7. C₁₁×C₃₇⋊C₃	C₂×C₁₃	semidirect
10. D₄₀₇	C₃×C₁₃	semidirect
11. C₁₃×C₃₇	C₃×D₁₁	semidirect
13. C₁₁×C₃₇	C₂×C₃×C₁₃	semidirect
16. C₁₁×C₁₃	D₃₇⋊C₃	semidirect
17. C₃₇⋊C₃	C₁₃×D₁₁	semidirect
22. C₃₇	C₃×C₁₃×D₁₁	semidirect
26. C₁₃	C₁₁⋊(D₃₇⋊C₃)	direct (N × H)
27. C₁₁	C₁₃×D₃₇⋊C₃	semidirect

Maximal subgroups

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

subgroup	index
C₁₁×C₁₃×C₃₇⋊C₃	2
C₁₃×D₄₀₇	3
C₁₃×D₃₇⋊C₃	11
C₁₁⋊(D₃₇⋊C₃)	13
C₃×C₁₃×D₁₁	37

Subgroups — C13×C11⋊(D37⋊C3) #44540824

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×C₁₁⋊(D₃₇⋊C₃) #44540824