Subgroups — C₃×D₅₅×C₃₇⋊C₃ #49143751

Order 36630.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×C₁₁×C₃₇⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₅₅×C₃₇⋊C₃	C₃	1	3	yes	maximal, direct product factor
3	C₃×C₃₇×D₅₅	C₃	1	1	yes	maximal, characteristic, complemented
4	C₃×D₁₁×C₃₇⋊C₃	—	5	1	no	maximal, Hall
5	C₅×C₁₁×C₃₇⋊C₃	C₂×C₃	1	3	yes	complemented
6	C₃×C₅×C₁₁×C₃₇	C₂×C₃	1	1	yes	characteristic, complemented
7	C₃₇×D₅₅	C₃²	1	1	yes	characteristic, complemented, Hall
8	C₃×C₁₁×C₃₇⋊C₃	D₅	1	1	yes	characteristic, complemented, Hall
9	C₃×D₅×C₃₇⋊C₃	—	11	1	no	maximal, Hall
10	D₁₁×C₃₇⋊C₃	—	5	3	no	—
11	C₃×D₁₁×C₃₇	—	5	1	no	—
12	C₅×C₁₁×C₃₇	C₂×C₃²	1	1	yes	characteristic, complemented, Hall
13	C₃×C₅×C₃₇⋊C₃	D₁₁	1	1	yes	characteristic, complemented, Hall
14	C₃×C₁₁×C₃₇	C₃×D₅	1	1	yes	characteristic, complemented
15	C₁₁×C₃₇⋊C₃	C₃×D₅	1	3	yes	complemented
16	C₃×D₅×C₃₇	—	11	1	no	—
17	D₅×C₃₇⋊C₃	—	11	3	no	—
18	C₃²×D₅₅	—	37	1	no	maximal, Hall
19	D₁₁×C₃₇	—	5	1	no	Hall
20	C₂×C₃×C₃₇⋊C₃	—	55	1	no	Hall
21	C₃×C₅×C₃₇	C₃×D₁₁	1	1	yes	characteristic, complemented
22	C₅×C₃₇⋊C₃	C₃×D₁₁	1	3	yes	complemented
23	C₃²×C₅×C₁₁	—	37	1	no	Hall
24	C₁₁×C₃₇	C₃²×D₅	1	1	yes	characteristic, complemented, Hall
25	D₅×C₃₇	—	11	1	no	Hall
26	C₃×C₃₇⋊C₃	D₅₅	1	1	yes	characteristic, direct product factor, Hall
27	C₃×D₅₅	—	37	3	no	—
28	C₃×D₅₅	C₃₇⋊C₃	1	1	yes	characteristic, direct product factor
29	C₂×C₃×C₃₇	—	55	1	no	—
30	C₂×C₃₇⋊C₃	—	55	3	no	—
31	C₃²×D₁₁	—	185	1	no	Hall
32	C₅×C₃₇	C₃²×D₁₁	1	1	yes	characteristic, complemented, Hall
33	C₃×C₅×C₁₁	—	37	3	no	—
34	C₃×C₅×C₁₁	C₂×C₃₇⋊C₃	1	1	yes	characteristic, complemented
35	C₃×C₃₇	C₃×D₅₅	1	1	yes	characteristic, complemented
36	C₃₇⋊C₃	C₃×D₅₅	1	3	yes	direct product factor
37	D₅₅	C₃×C₃₇⋊C₃	1	1	yes	characteristic, direct product factor, Hall
38	C₃²×C₁₁	—	37	1	no	Hall
39	C₃²×D₅	—	407	1	no	Hall
40	C₂×C₃₇	—	55	1	no	Hall
41	C₃×D₁₁	—	5	1	no	—
42	C₃×D₁₁	—	185	3	no	—
43	C₅×C₁₁	C₂×C₃×C₃₇⋊C₃	1	1	yes	characteristic, complemented, Hall
44	C₃²×C₅	—	37	1	no	Hall
45	C₃₇	C₃²×D₅₅	1	1	yes	characteristic, complemented, Sylow
46	C₃×C₁₁	—	37	3	no	—
47	C₃×C₁₁	D₅×C₃₇⋊C₃	1	1	yes	characteristic, complemented
48	C₃×D₅	—	11	1	no	—
49	C₃×D₅	—	407	3	no	—
50	D₁₁	—	5	1	no	Hall
51	C₂×C₃²	—	2035	1	no	Hall
52	C₃×C₅	—	37	3	no	—
53	C₃×C₅	D₁₁×C₃₇⋊C₃	1	1	yes	characteristic, complemented
54	C₁₁	C₃×D₅×C₃₇⋊C₃	1	1	yes	characteristic, complemented, Sylow
55	D₅	—	11	1	no	Hall
56	C₃²	—	37	1	no	Sylow
57	C₂×C₃	—	55	1	no	—
58	C₂×C₃	—	2035	3	no	—
59	C₅	C₃×D₁₁×C₃₇⋊C₃	1	1	yes	characteristic, complemented, Sylow
60	C₃	—	37	3	no	—
61	C₃	D₅₅×C₃₇⋊C₃	1	1	yes	characteristic, direct product factor
62	C₂	—	55	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃	D₅₅×C₃₇⋊C₃
commutator, cosocle, hypocenter	C₅×C₁₁×C₃₇	C₂×C₃²
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₁₁×C₃₇	C₂×C₃
LCS	G ▷ C₅×C₁₁×C₃₇
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×C₁₁×C₃₇⋊C₃	C₂	semidirect
2. D₅₅×C₃₇⋊C₃	C₃	direct (N × H)
3. C₃×C₃₇×D₅₅	C₃	semidirect
5. C₅×C₁₁×C₃₇⋊C₃	C₂×C₃	semidirect
6. C₃×C₅×C₁₁×C₃₇	C₂×C₃	semidirect
7. C₃₇×D₅₅	C₃²	semidirect
8. C₃×C₁₁×C₃₇⋊C₃	D₅	semidirect
12. C₅×C₁₁×C₃₇	C₂×C₃²	semidirect
13. C₃×C₅×C₃₇⋊C₃	D₁₁	semidirect
14. C₃×C₁₁×C₃₇	C₃×D₅	semidirect
15. C₁₁×C₃₇⋊C₃	C₃×D₅	semidirect
21. C₃×C₅×C₃₇	C₃×D₁₁	semidirect
22. C₅×C₃₇⋊C₃	C₃×D₁₁	semidirect
24. C₁₁×C₃₇	C₃²×D₅	semidirect
26. C₃×C₃₇⋊C₃	D₅₅	direct (N × H)
28. C₃×D₅₅	C₃₇⋊C₃	direct (N × H)
32. C₅×C₃₇	C₃²×D₁₁	semidirect
34. C₃×C₅×C₁₁	C₂×C₃₇⋊C₃	semidirect
35. C₃×C₃₇	C₃×D₅₅	semidirect
36. C₃₇⋊C₃	C₃×D₅₅	direct (N × H)
37. D₅₅	C₃×C₃₇⋊C₃	direct (N × H)
43. C₅×C₁₁	C₂×C₃×C₃₇⋊C₃	semidirect
45. C₃₇	C₃²×D₅₅	semidirect
47. C₃×C₁₁	D₅×C₃₇⋊C₃	semidirect
53. C₃×C₅	D₁₁×C₃₇⋊C₃	semidirect
54. C₁₁	C₃×D₅×C₃₇⋊C₃	semidirect
59. C₅	C₃×D₁₁×C₃₇⋊C₃	semidirect
61. C₃	D₅₅×C₃₇⋊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
C₃×C₅×C₁₁×C₃₇⋊C₃	2
D₅₅×C₃₇⋊C₃	3
C₃×C₃₇×D₅₅	3
C₃×D₁₁×C₃₇⋊C₃	5
C₃×D₅×C₃₇⋊C₃	11
C₃²×D₅₅	37

Subgroups — C3×D55×C37⋊C3 #49143751

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₅₅×C₃₇⋊C₃ #49143751