Subgroups — C₁₃×C₃₇×D₃₃ #44540804

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	C₁₃×D₁₁×C₃₇	—	3	1	no	maximal, Hall
3	C₁₁×C₁₃×C₃₇	D₃	1	1	yes	characteristic, complemented, Hall
4	D₃×C₁₃×C₃₇	—	11	1	no	maximal, Hall
5	C₃₇×D₃₃	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₃×C₁₃×C₃₇	D₁₁	1	1	yes	characteristic, complemented, Hall
7	C₃×C₁₁×C₃₇	C₂×C₁₃	1	1	yes	characteristic, complemented, Hall
8	C₂×C₁₃×C₃₇	—	33	1	no	Hall
9	C₁₃×D₃₃	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Hall
10	D₁₁×C₃₇	—	3	1	no	Hall
11	C₁₃×C₃₇	D₃₃	1	1	yes	characteristic, direct product factor, Hall
12	C₃×C₁₁×C₁₃	C₂×C₃₇	1	1	yes	characteristic, complemented, Hall
13	C₁₁×C₃₇	D₃×C₁₃	1	1	yes	characteristic, complemented, Hall
14	C₁₃×D₁₁	—	3	1	no	Hall
15	D₃×C₃₇	—	11	1	no	Hall
16	C₁₁×C₁₃	D₃×C₃₇	1	1	yes	characteristic, complemented, Hall
17	C₃×C₃₇	C₁₃×D₁₁	1	1	yes	characteristic, complemented, Hall
18	D₃×C₁₃	—	11	1	no	Hall
19	C₂×C₃₇	—	33	1	no	Hall
20	D₃₃	C₁₃×C₃₇	1	1	yes	characteristic, direct product factor, Hall
21	C₃×C₁₃	D₁₁×C₃₇	1	1	yes	characteristic, complemented, Hall
22	C₃₇	C₁₃×D₃₃	1	1	yes	characteristic, direct product factor, Sylow
23	C₃×C₁₁	C₂×C₁₃×C₃₇	1	1	yes	characteristic, complemented, Hall
24	C₂×C₁₃	—	33	1	no	Hall
25	D₁₁	—	3	1	no	Hall
26	C₁₃	C₃₇×D₃₃	1	1	yes	characteristic, direct product factor, Sylow
27	C₁₁	D₃×C₁₃×C₃₇	1	1	yes	characteristic, complemented, Sylow
28	D₃	—	11	1	no	Hall
29	C₃	C₁₃×D₁₁×C₃₇	1	1	yes	characteristic, complemented, Sylow
30	C₂	—	33	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₃×C₃₇	D₃₃
commutator, cosocle, hypocenter	C₃×C₁₁	C₂×C₁₃×C₃₇
Frattini	C₁	G
Fitting, socle	C₃×C₁₁×C₁₃×C₃₇	C₂
LCS	G ▷ C₃×C₁₁
UCS	C₁ ◁ C₁₃×C₃₇

Complements

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

N	H ≅ G/N	type
1. C₃×C₁₁×C₁₃×C₃₇	C₂	semidirect
3. C₁₁×C₁₃×C₃₇	D₃	semidirect
5. C₃₇×D₃₃	C₁₃	direct (N × H)
6. C₃×C₁₃×C₃₇	D₁₁	semidirect
7. C₃×C₁₁×C₃₇	C₂×C₁₃	semidirect
9. C₁₃×D₃₃	C₃₇	direct (N × H)
11. C₁₃×C₃₇	D₃₃	direct (N × H)
12. C₃×C₁₁×C₁₃	C₂×C₃₇	semidirect
13. C₁₁×C₃₇	D₃×C₁₃	semidirect
16. C₁₁×C₁₃	D₃×C₃₇	semidirect
17. C₃×C₃₇	C₁₃×D₁₁	semidirect
20. D₃₃	C₁₃×C₃₇	direct (N × H)
21. C₃×C₁₃	D₁₁×C₃₇	semidirect
22. C₃₇	C₁₃×D₃₃	direct (N × H)
23. C₃×C₁₁	C₂×C₁₃×C₃₇	semidirect
26. C₁₃	C₃₇×D₃₃	direct (N × H)
27. C₁₁	D₃×C₁₃×C₃₇	semidirect
29. C₃	C₁₃×D₁₁×C₃₇	semidirect

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
C₁₃×D₁₁×C₃₇	3
D₃×C₁₃×C₃₇	11
C₃₇×D₃₃	13
C₁₃×D₃₃	37

Subgroups — C13×C37×D33 #44540804

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×C₃₇×D₃₃ #44540804