Subgroups — C₁₁×C₁₃×D₃₇⋊C₃ #44540808

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	C₁₁×C₁₃×D₃₇	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₁₁×C₁₃×C₃₇	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	C₁₃×D₃₇⋊C₃	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₁₁×D₃₇⋊C₃	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₁₃×C₃₇⋊C₃	C₂×C₁₁	1	1	yes	characteristic, complemented, Hall
7	C₁₁×C₃₇⋊C₃	C₂×C₁₃	1	1	yes	characteristic, complemented, Hall
8	C₁₃×D₃₇	C₃×C₁₁	1	1	yes	characteristic, complemented, Hall
9	C₂×C₃×C₁₁×C₁₃	—	37	1	no	maximal, Hall
10	C₁₁×D₃₇	C₃×C₁₃	1	1	yes	characteristic, complemented, Hall
11	C₁₃×C₃₇	C₂×C₃×C₁₁	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	C₂×C₁₁×C₁₃	—	37	1	no	Hall
15	D₃₇⋊C₃	C₁₁×C₁₃	1	1	yes	characteristic, direct product factor, Hall
16	C₁₁×C₁₃	D₃₇⋊C₃	1	1	yes	characteristic, direct product factor, Hall
17	C₃₇⋊C₃	C₂×C₁₁×C₁₃	1	1	yes	characteristic, complemented, Hall
18	C₂×C₃×C₁₃	—	37	1	no	Hall
19	D₃₇	C₃×C₁₁×C₁₃	1	1	yes	characteristic, complemented, Hall
20	C₂×C₃×C₁₁	—	37	1	no	Hall
21	C₃×C₁₃	—	37	1	no	Hall
22	C₃₇	C₂×C₃×C₁₁×C₁₃	1	1	yes	characteristic, complemented, Sylow
23	C₃×C₁₁	—	37	1	no	Hall
24	C₂×C₁₃	—	37	1	no	Hall
25	C₂×C₁₁	—	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, direct product factor, Sylow
28	C₂×C₃	—	37	1	no	Hall
29	C₃	—	37	1	no	Sylow
30	C₂	—	37	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₁×C₁₃	D₃₇⋊C₃
commutator, cosocle, hypocenter	C₃₇	C₂×C₃×C₁₁×C₁₃
Frattini	C₁	G
Fitting, socle	C₁₁×C₁₃×C₃₇	C₂×C₃
LCS	G ▷ C₃₇
UCS	C₁ ◁ C₁₁×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. C₁₁×C₁₃×D₃₇	C₃	semidirect
3. C₁₁×C₁₃×C₃₇	C₂×C₃	semidirect
4. C₁₃×D₃₇⋊C₃	C₁₁	direct (N × H)
5. C₁₁×D₃₇⋊C₃	C₁₃	direct (N × H)
6. C₁₃×C₃₇⋊C₃	C₂×C₁₁	semidirect
7. C₁₁×C₃₇⋊C₃	C₂×C₁₃	semidirect
8. C₁₃×D₃₇	C₃×C₁₁	semidirect
10. C₁₁×D₃₇	C₃×C₁₃	semidirect
11. C₁₃×C₃₇	C₂×C₃×C₁₁	semidirect
13. C₁₁×C₃₇	C₂×C₃×C₁₃	semidirect
15. D₃₇⋊C₃	C₁₁×C₁₃	direct (N × H)
16. C₁₁×C₁₃	D₃₇⋊C₃	direct (N × H)
17. C₃₇⋊C₃	C₂×C₁₁×C₁₃	semidirect
19. D₃₇	C₃×C₁₁×C₁₃	semidirect
22. C₃₇	C₂×C₃×C₁₁×C₁₃	semidirect
26. C₁₃	C₁₁×D₃₇⋊C₃	direct (N × H)
27. C₁₁	C₁₃×D₃₇⋊C₃	direct (N × H)

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
C₁₁×C₁₃×D₃₇	3
C₁₃×D₃₇⋊C₃	11
C₁₁×D₃₇⋊C₃	13
C₂×C₃×C₁₁×C₁₃	37

Subgroups — C11×C13×D37⋊C3 #44540808

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×C₁₃×D₃₇⋊C₃ #44540808