Subgroups — C₃×C₁₁×D₁₃×C₃₇ #44540794

Order 31746.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₁×C₁₃×C₃₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₁×D₁₃×C₃₇	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₁₁×C₁₃×C₃₇	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	C₃×D₁₃×C₃₇	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₃×C₁₁×C₃₇	—	13	1	no	maximal, Hall
6	C₃×C₁₃×C₃₇	C₂×C₁₁	1	1	yes	characteristic, complemented, Hall
7	C₃×C₁₁×C₃₇	D₁₃	1	1	yes	characteristic, direct product factor, Hall
8	D₁₃×C₃₇	C₃×C₁₁	1	1	yes	characteristic, direct product factor, Hall
9	C₃×C₁₁×D₁₃	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂×C₁₁×C₃₇	—	13	1	no	Hall
11	C₁₃×C₃₇	C₂×C₃×C₁₁	1	1	yes	characteristic, complemented, Hall
12	C₃×C₁₁×C₁₃	C₂×C₃₇	1	1	yes	characteristic, complemented, Hall
13	C₁₁×C₃₇	C₃×D₁₃	1	1	yes	characteristic, direct product factor, Hall
14	C₁₁×D₁₃	C₃×C₃₇	1	1	yes	characteristic, direct product factor, Hall
15	C₂×C₃×C₃₇	—	13	1	no	Hall
16	C₁₁×C₁₃	C₂×C₃×C₃₇	1	1	yes	characteristic, complemented, Hall
17	C₃×C₃₇	C₁₁×D₁₃	1	1	yes	characteristic, direct product factor, Hall
18	C₃×D₁₃	C₁₁×C₃₇	1	1	yes	characteristic, direct product factor, Hall
19	C₂×C₃₇	—	13	1	no	Hall
20	C₂×C₃×C₁₁	—	13	1	no	Hall
21	C₃×C₁₃	C₂×C₁₁×C₃₇	1	1	yes	characteristic, complemented, Hall
22	C₃₇	C₃×C₁₁×D₁₃	1	1	yes	characteristic, direct product factor, Sylow
23	C₃×C₁₁	D₁₃×C₃₇	1	1	yes	characteristic, direct product factor, Hall
24	D₁₃	C₃×C₁₁×C₃₇	1	1	yes	characteristic, direct product factor, Hall
25	C₂×C₁₁	—	13	1	no	Hall
26	C₁₃	C₂×C₃×C₁₁×C₃₇	1	1	yes	characteristic, complemented, Sylow
27	C₁₁	C₃×D₁₃×C₃₇	1	1	yes	characteristic, direct product factor, Sylow
28	C₂×C₃	—	13	1	no	Hall
29	C₃	C₁₁×D₁₃×C₃₇	1	1	yes	characteristic, direct product factor, Sylow
30	C₂	—	13	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₁₁×C₃₇	D₁₃
commutator, cosocle, hypocenter	C₁₃	C₂×C₃×C₁₁×C₃₇
Frattini	C₁	G
Fitting, socle	C₃×C₁₁×C₁₃×C₃₇	C₂
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₃×C₁₁×C₃₇

Complements

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

N	H ≅ G/N	type
1. C₃×C₁₁×C₁₃×C₃₇	C₂	semidirect
2. C₁₁×D₁₃×C₃₇	C₃	direct (N × H)
3. C₁₁×C₁₃×C₃₇	C₂×C₃	semidirect
4. C₃×D₁₃×C₃₇	C₁₁	direct (N × H)
6. C₃×C₁₃×C₃₇	C₂×C₁₁	semidirect
7. C₃×C₁₁×C₃₇	D₁₃	direct (N × H)
8. D₁₃×C₃₇	C₃×C₁₁	direct (N × H)
9. C₃×C₁₁×D₁₃	C₃₇	direct (N × H)
11. C₁₃×C₃₇	C₂×C₃×C₁₁	semidirect
12. C₃×C₁₁×C₁₃	C₂×C₃₇	semidirect
13. C₁₁×C₃₇	C₃×D₁₃	direct (N × H)
14. C₁₁×D₁₃	C₃×C₃₇	direct (N × H)
16. C₁₁×C₁₃	C₂×C₃×C₃₇	semidirect
17. C₃×C₃₇	C₁₁×D₁₃	direct (N × H)
18. C₃×D₁₃	C₁₁×C₃₇	direct (N × H)
21. C₃×C₁₃	C₂×C₁₁×C₃₇	semidirect
22. C₃₇	C₃×C₁₁×D₁₃	direct (N × H)
23. C₃×C₁₁	D₁₃×C₃₇	direct (N × H)
24. D₁₃	C₃×C₁₁×C₃₇	direct (N × H)
26. C₁₃	C₂×C₃×C₁₁×C₃₇	semidirect
27. C₁₁	C₃×D₁₃×C₃₇	direct (N × H)
29. C₃	C₁₁×D₁₃×C₃₇	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×C₁₃×C₃₇	2
C₁₁×D₁₃×C₃₇	3
C₃×D₁₃×C₃₇	11
C₂×C₃×C₁₁×C₃₇	13
C₃×C₁₁×D₁₃	37

Subgroups — C3×C11×D13×C37 #44540794

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₁₁×D₁₃×C₃₇ #44540794