Subgroups — C₃×C₇×(C₃₇⋊C₃)⋊D₇ #45657518

Order 32634.

132 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₇²×C₃₇⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×C₇×D₂₅₉	C₃	1	1	yes	maximal, characteristic, complemented
3	C₇×(C₃₇⋊C₃)⋊D₇	C₃	1	3	yes	maximal, direct product factor
4	C₇²×C₃₇⋊C₃	C₂×C₃	1	3	yes	complemented
5	C₃×C₇²×C₃₇	C₂×C₃	1	1	yes	characteristic, complemented
6	C₃×(C₃₇⋊C₃)⋊D₇	C₇	1	1	yes	maximal, characteristic, direct product factor
7	C₃×C₇×D₃₇⋊C₃	—	7	1	no	maximal
8	C₇×D₂₅₉	C₃²	1	1	yes	characteristic, complemented, Hall
9	C₃×C₇×C₃₇⋊C₃	—	2	3	no	—
10	C₃×C₇×C₃₇⋊C₃	D₇	1	1	yes	characteristic, complemented
11	C₃×C₇×C₃₇⋊C₃	C₂×C₇	1	1	yes	characteristic, complemented
12	C₇²×C₃₇	C₂×C₃²	1	1	yes	characteristic, complemented, Hall
13	C₃×D₂₅₉	C₃×C₇	1	1	yes	characteristic, complemented
14	C₃×C₇×D₃₇	—	7	1	no	—
15	(C₃₇⋊C₃)⋊D₇	C₃×C₇	1	3	yes	direct product factor
16	C₇×D₃₇⋊C₃	—	7	3	no	—
17	C₃²×C₇×D₇	—	37	1	no	maximal, Hall
18	C₃×C₇×C₃₇	—	2	3	no	—
19	C₃×C₇×C₃₇	C₃×D₇	1	1	yes	characteristic, complemented
20	C₃×C₇×C₃₇	C₂×C₃×C₇	1	1	yes	characteristic, complemented
21	C₇×C₃₇⋊C₃	—	2	9	no	—
22	C₇×C₃₇⋊C₃	C₃×D₇	1	3	yes	complemented
23	C₇×C₃₇⋊C₃	C₂×C₃×C₇	1	3	yes	complemented
24	C₃×D₃₇⋊C₃	—	7	1	no	Hall
25	D₂₅₉	C₃²×C₇	1	1	yes	characteristic, complemented
26	C₇×D₃₇	—	7	1	no	—
27	C₃²×C₇²	—	37	1	no	Hall
28	C₃×C₃₇⋊C₃	C₇×D₇	1	1	yes	characteristic, complemented, Hall
29	C₃×C₇×D₇	—	37	3	no	—
30	C₃×C₇×D₇	—	37	1	no	—
31	C₇×C₃₇	—	2	3	no	—
32	C₇×C₃₇	C₃²×D₇	1	1	yes	characteristic, complemented
33	C₇×C₃₇	C₂×C₃²×C₇	1	1	yes	characteristic, complemented
34	C₃×D₃₇	—	7	1	no	—
35	D₃₇⋊C₃	—	7	3	no	—
36	C₃×C₇²	—	37	3	no	—
37	C₃×C₇²	D₃₇⋊C₃	1	1	yes	characteristic, complemented
38	C₂×C₃²×C₇	—	259	1	no	—
39	C₃²×D₇	—	37	1	no	—
40	C₃×C₃₇	C₃×C₇×D₇	1	1	yes	characteristic, complemented
41	C₃₇⋊C₃	C₃×C₇×D₇	1	3	yes	complemented
42	C₇×D₇	—	37	1	no	Hall
43	D₃₇	—	7	1	no	Hall
44	C₃²×C₇	—	37	1	no	—
45	C₃²×C₇	—	37	1	no	—
46	C₃²×C₇	—	74	3	no	—
47	C₇²	C₃×D₃₇⋊C₃	1	1	yes	characteristic, complemented, Sylow
48	C₂×C₃×C₇	—	259	3	no	—
49	C₂×C₃×C₇	—	259	1	no	—
50	C₃×D₇	—	37	3	no	—
51	C₃×D₇	—	37	1	no	—
52	C₃₇	C₃²×C₇×D₇	1	1	yes	characteristic, complemented, Sylow
53	C₃×C₇	—	2	3	no	—
54	C₃×C₇	—	37	3	no	—
55	C₃×C₇	—	37	3	no	—
56	C₃×C₇	—	74	9	no	—
57	C₃×C₇	C₇×D₃₇⋊C₃	1	1	yes	characteristic, complemented
58	C₃×C₇	(C₃₇⋊C₃)⋊D₇	1	1	yes	characteristic, direct product factor
59	C₂×C₃²	—	259	1	no	Hall
60	C₂×C₇	—	259	1	no	—
61	D₇	—	37	1	no	—
62	C₃²	—	37	1	no	Sylow
63	C₇	—	2	3	no	—
64	C₇	C₃×C₇×D₃₇⋊C₃	1	1	yes	characteristic, complemented
65	C₇	C₃×(C₃₇⋊C₃)⋊D₇	1	1	yes	characteristic, direct product factor
66	C₂×C₃	—	259	3	no	—
67	C₂×C₃	—	259	1	no	—
68	C₃	—	37	3	no	—
69	C₃	C₇×(C₃₇⋊C₃)⋊D₇	1	1	yes	characteristic, direct product factor
70	C₂	—	259	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₇	(C₃₇⋊C₃)⋊D₇
commutator, cosocle, hypocenter	C₇×C₃₇	C₂×C₃²×C₇
Frattini	C₁	G
Fitting, socle	C₃×C₇²×C₃₇	C₂×C₃
LCS	G ▷ C₇×C₃₇
UCS	C₁ ◁ C₃×C₇

Complements

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

N	H ≅ G/N	type
1. C₃×C₇²×C₃₇⋊C₃	C₂	semidirect
2. C₃×C₇×D₂₅₉	C₃	semidirect
3. C₇×(C₃₇⋊C₃)⋊D₇	C₃	direct (N × H)
4. C₇²×C₃₇⋊C₃	C₂×C₃	semidirect
5. C₃×C₇²×C₃₇	C₂×C₃	semidirect
6. C₃×(C₃₇⋊C₃)⋊D₇	C₇	direct (N × H)
8. C₇×D₂₅₉	C₃²	semidirect
10. C₃×C₇×C₃₇⋊C₃	D₇	semidirect
11. C₃×C₇×C₃₇⋊C₃	C₂×C₇	semidirect
12. C₇²×C₃₇	C₂×C₃²	semidirect
13. C₃×D₂₅₉	C₃×C₇	semidirect
15. (C₃₇⋊C₃)⋊D₇	C₃×C₇	direct (N × H)
19. C₃×C₇×C₃₇	C₃×D₇	semidirect
20. C₃×C₇×C₃₇	C₂×C₃×C₇	semidirect
22. C₇×C₃₇⋊C₃	C₃×D₇	semidirect
23. C₇×C₃₇⋊C₃	C₂×C₃×C₇	semidirect
25. D₂₅₉	C₃²×C₇	semidirect
28. C₃×C₃₇⋊C₃	C₇×D₇	semidirect
32. C₇×C₃₇	C₃²×D₇	semidirect
33. C₇×C₃₇	C₂×C₃²×C₇	semidirect
37. C₃×C₇²	D₃₇⋊C₃	semidirect
40. C₃×C₃₇	C₃×C₇×D₇	semidirect
41. C₃₇⋊C₃	C₃×C₇×D₇	semidirect
47. C₇²	C₃×D₃₇⋊C₃	semidirect
52. C₃₇	C₃²×C₇×D₇	semidirect
57. C₃×C₇	C₇×D₃₇⋊C₃	semidirect
58. C₃×C₇	(C₃₇⋊C₃)⋊D₇	direct (N × H)
64. C₇	C₃×C₇×D₃₇⋊C₃	semidirect
65. C₇	C₃×(C₃₇⋊C₃)⋊D₇	direct (N × H)
69. C₃	C₇×(C₃₇⋊C₃)⋊D₇	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×C₇²×C₃₇⋊C₃	2
C₃×C₇×D₂₅₉	3
C₇×(C₃₇⋊C₃)⋊D₇	3
C₃×(C₃₇⋊C₃)⋊D₇	7
C₃×C₇×D₃₇⋊C₃	7
C₃²×C₇×D₇	37

Subgroups — C3×C7×(C37⋊C3)⋊D7 #45657518

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₇×(C₃₇⋊C₃)⋊D₇ #45657518