Subgroups — C₃×C₅×D₂₁×C₄₇ #44444114

Order 29610.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₅×C₇×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅×D₂₁×C₄₇	C₃	1	1	yes	maximal, characteristic, direct product factor
3	C₃×C₅×D₇×C₄₇	—	3	1	no	maximal
4	C₃×D₂₁×C₄₇	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₃×C₅×C₇×C₄₇	—	2	1	no	—
6	C₃×C₅×C₇×C₄₇	D₃	1	1	yes	characteristic, complemented
7	C₃×C₅×C₇×C₄₇	C₂×C₃	1	1	yes	characteristic, complemented
8	C₃×C₅×D₃×C₄₇	—	7	1	no	maximal, Hall
9	C₅×D₇×C₄₇	—	3	1	no	Hall
10	C₃²×C₇×C₄₇	C₂×C₅	1	1	yes	characteristic, complemented, Hall
11	C₃²×C₅×C₄₇	D₇	1	1	yes	characteristic, complemented, Hall
12	D₂₁×C₄₇	C₃×C₅	1	1	yes	characteristic, direct product factor
13	C₃×D₇×C₄₇	—	3	1	no	—
14	C₅×C₇×C₄₇	C₃×D₃	1	1	yes	characteristic, complemented, Hall
15	C₂×C₃×C₅×C₄₇	—	21	1	no	—
16	C₅×D₃×C₄₇	—	7	1	no	—
17	C₃×C₇×C₄₇	—	2	1	no	—
18	C₃×C₇×C₄₇	C₅×D₃	1	1	yes	characteristic, complemented
19	C₃×C₇×C₄₇	C₂×C₃×C₅	1	1	yes	characteristic, complemented
20	C₃×D₃×C₄₇	—	7	1	no	Hall
21	C₃×C₅×C₄₇	—	2	1	no	—
22	C₃×C₅×C₄₇	C₃×D₇	1	1	yes	characteristic, complemented
23	C₃×C₅×C₄₇	D₂₁	1	1	yes	characteristic, direct product factor
24	D₇×C₄₇	—	3	1	no	Hall
25	C₃×C₅×D₂₁	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Hall
26	C₂×C₅×C₄₇	—	21	1	no	Hall
27	C₃²×C₄₇	C₅×D₇	1	1	yes	characteristic, complemented, Hall
28	C₇×C₄₇	C₃×C₅×D₃	1	1	yes	characteristic, complemented, Hall
29	C₃²×C₅×C₇	C₂×C₄₇	1	1	yes	characteristic, complemented, Hall
30	C₂×C₃×C₄₇	—	21	1	no	—
31	D₃×C₄₇	—	7	1	no	—
32	C₅×C₄₇	C₃×D₂₁	1	1	yes	characteristic, direct product factor, Hall
33	C₅×D₂₁	C₃×C₄₇	1	1	yes	characteristic, direct product factor
34	C₃×C₅×D₇	—	3	1	no	—
35	C₃×C₄₇	—	2	1	no	—
36	C₃×C₄₇	C₃×C₅×D₇	1	1	yes	characteristic, complemented
37	C₃×C₄₇	C₅×D₂₁	1	1	yes	characteristic, direct product factor
38	C₃×D₂₁	C₅×C₄₇	1	1	yes	characteristic, direct product factor, Hall
39	C₃×C₅×C₇	—	2	1	no	—
40	C₃×C₅×C₇	D₃×C₄₇	1	1	yes	characteristic, complemented
41	C₃×C₅×C₇	C₂×C₃×C₄₇	1	1	yes	characteristic, complemented
42	C₂×C₄₇	—	21	1	no	Hall
43	C₃×C₅×D₃	—	7	1	no	Hall
44	C₅×D₇	—	3	1	no	Hall
45	C₃²×C₇	C₂×C₅×C₄₇	1	1	yes	characteristic, complemented, Hall
46	C₄₇	C₃×C₅×D₂₁	1	1	yes	characteristic, direct product factor, Sylow
47	C₃²×C₅	D₇×C₄₇	1	1	yes	characteristic, complemented, Hall
48	D₂₁	C₃×C₅×C₄₇	1	1	yes	characteristic, direct product factor
49	C₃×D₇	—	3	1	no	—
50	C₅×C₇	C₃×D₃×C₄₇	1	1	yes	characteristic, complemented, Hall
51	C₂×C₃×C₅	—	21	1	no	—
52	C₅×D₃	—	7	1	no	—
53	C₃×C₇	—	2	1	no	—
54	C₃×C₇	C₅×D₃×C₄₇	1	1	yes	characteristic, complemented
55	C₃×C₇	C₂×C₃×C₅×C₄₇	1	1	yes	characteristic, complemented
56	C₃×D₃	—	7	1	no	Hall
57	C₃×C₅	—	2	1	no	—
58	C₃×C₅	C₃×D₇×C₄₇	1	1	yes	characteristic, complemented
59	C₃×C₅	D₂₁×C₄₇	1	1	yes	characteristic, direct product factor
60	D₇	—	3	1	no	Hall
61	C₂×C₅	—	21	1	no	Hall
62	C₃²	C₅×D₇×C₄₇	1	1	yes	characteristic, complemented, Sylow
63	C₇	C₃×C₅×D₃×C₄₇	1	1	yes	characteristic, complemented, Sylow
64	C₂×C₃	—	21	1	no	—
65	D₃	—	7	1	no	—
66	C₅	C₃×D₂₁×C₄₇	1	1	yes	characteristic, direct product factor, Sylow
67	C₃	—	2	1	no	—
68	C₃	C₃×C₅×D₇×C₄₇	1	1	yes	characteristic, complemented
69	C₃	C₅×D₂₁×C₄₇	1	1	yes	characteristic, direct product factor
70	C₂	—	21	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₅×C₄₇	D₂₁
commutator, cosocle, hypocenter	C₃×C₇	C₂×C₃×C₅×C₄₇
Frattini	C₁	G
Fitting, socle	C₃²×C₅×C₇×C₄₇	C₂
LCS	G ▷ C₃×C₇
UCS	C₁ ◁ C₃×C₅×C₄₇

Complements

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

N	H ≅ G/N	type
1. C₃²×C₅×C₇×C₄₇	C₂	semidirect
2. C₅×D₂₁×C₄₇	C₃	direct (N × H)
4. C₃×D₂₁×C₄₇	C₅	direct (N × H)
6. C₃×C₅×C₇×C₄₇	D₃	semidirect
7. C₃×C₅×C₇×C₄₇	C₂×C₃	semidirect
10. C₃²×C₇×C₄₇	C₂×C₅	semidirect
11. C₃²×C₅×C₄₇	D₇	semidirect
12. D₂₁×C₄₇	C₃×C₅	direct (N × H)
14. C₅×C₇×C₄₇	C₃×D₃	semidirect
18. C₃×C₇×C₄₇	C₅×D₃	semidirect
19. C₃×C₇×C₄₇	C₂×C₃×C₅	semidirect
22. C₃×C₅×C₄₇	C₃×D₇	semidirect
23. C₃×C₅×C₄₇	D₂₁	direct (N × H)
25. C₃×C₅×D₂₁	C₄₇	direct (N × H)
27. C₃²×C₄₇	C₅×D₇	semidirect
28. C₇×C₄₇	C₃×C₅×D₃	semidirect
29. C₃²×C₅×C₇	C₂×C₄₇	semidirect
32. C₅×C₄₇	C₃×D₂₁	direct (N × H)
33. C₅×D₂₁	C₃×C₄₇	direct (N × H)
36. C₃×C₄₇	C₃×C₅×D₇	semidirect
37. C₃×C₄₇	C₅×D₂₁	direct (N × H)
38. C₃×D₂₁	C₅×C₄₇	direct (N × H)
40. C₃×C₅×C₇	D₃×C₄₇	semidirect
41. C₃×C₅×C₇	C₂×C₃×C₄₇	semidirect
45. C₃²×C₇	C₂×C₅×C₄₇	semidirect
46. C₄₇	C₃×C₅×D₂₁	direct (N × H)
47. C₃²×C₅	D₇×C₄₇	semidirect
48. D₂₁	C₃×C₅×C₄₇	direct (N × H)
50. C₅×C₇	C₃×D₃×C₄₇	semidirect
54. C₃×C₇	C₅×D₃×C₄₇	semidirect
55. C₃×C₇	C₂×C₃×C₅×C₄₇	semidirect
58. C₃×C₅	C₃×D₇×C₄₇	semidirect
59. C₃×C₅	D₂₁×C₄₇	direct (N × H)
62. C₃²	C₅×D₇×C₄₇	semidirect
63. C₇	C₃×C₅×D₃×C₄₇	semidirect
66. C₅	C₃×D₂₁×C₄₇	direct (N × H)
68. C₃	C₃×C₅×D₇×C₄₇	semidirect
69. C₃	C₅×D₂₁×C₄₇	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃²×C₅×C₇×C₄₇	2
C₅×D₂₁×C₄₇	3
C₃×C₅×D₇×C₄₇	3
C₃×D₂₁×C₄₇	5
C₃×C₅×D₃×C₄₇	7
C₃×C₅×D₂₁	47

Subgroups — C3×C5×D21×C47 #44444114

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×D₂₁×C₄₇ #44444114