Subgroups — C₇×C₄₇×C₃⋊D₁₅ #44444124

Order 29610.

96 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	C₇×D₁₅×C₄₇	—	3	4	no	maximal
3	C₇×C₃⋊D₃×C₄₇	—	5	1	no	maximal, Hall
4	C₃×C₅×C₇×C₄₇	D₃	1	4	yes	complemented
5	C₄₇×C₃⋊D₁₅	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₇×D₅×C₄₇	—	9	1	no	Hall
7	C₃²×C₇×C₄₇	D₅	1	1	yes	characteristic, complemented, Hall
8	C₃²×C₅×C₄₇	C₂×C₇	1	1	yes	characteristic, complemented, Hall
9	D₃×C₇×C₄₇	—	15	4	no	—
10	C₅×C₇×C₄₇	C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
11	D₁₅×C₄₇	—	3	4	no	—
12	C₃×C₇×C₄₇	D₁₅	1	4	yes	complemented
13	C₃⋊D₃×C₄₇	—	5	1	no	Hall
14	C₃×C₅×C₄₇	D₃×C₇	1	4	yes	complemented
15	C₂×C₇×C₄₇	—	45	1	no	Hall
16	C₇×C₃⋊D₁₅	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Hall
17	D₅×C₄₇	—	9	1	no	Hall
18	C₃²×C₄₇	C₇×D₅	1	1	yes	characteristic, complemented, Hall
19	C₇×C₄₇	C₃⋊D₁₅	1	1	yes	characteristic, direct product factor, Hall
20	C₃²×C₅×C₇	C₂×C₄₇	1	1	yes	characteristic, complemented, Hall
21	D₃×C₄₇	—	15	4	no	—
22	C₅×C₄₇	C₇×C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
23	C₇×D₁₅	—	3	4	no	—
24	C₃×C₄₇	C₇×D₁₅	1	4	yes	complemented
25	C₇×C₃⋊D₃	—	5	1	no	Hall
26	C₃×C₅×C₇	D₃×C₄₇	1	4	yes	complemented
27	C₂×C₄₇	—	45	1	no	Hall
28	C₃⋊D₁₅	C₇×C₄₇	1	1	yes	characteristic, direct product factor, Hall
29	C₇×D₅	—	9	1	no	Hall
30	C₃²×C₇	D₅×C₄₇	1	1	yes	characteristic, complemented, Hall
31	C₄₇	C₇×C₃⋊D₁₅	1	1	yes	characteristic, direct product factor, Sylow
32	C₃²×C₅	C₂×C₇×C₄₇	1	1	yes	characteristic, complemented, Hall
33	D₃×C₇	—	15	4	no	—
34	C₅×C₇	C₃⋊D₃×C₄₇	1	1	yes	characteristic, complemented, Hall
35	D₁₅	—	3	4	no	—
36	C₃×C₇	D₁₅×C₄₇	1	4	yes	complemented
37	C₃⋊D₃	—	5	1	no	Hall
38	C₃×C₅	D₃×C₇×C₄₇	1	4	yes	complemented
39	C₂×C₇	—	45	1	no	Hall
40	D₅	—	9	1	no	Hall
41	C₃²	C₇×D₅×C₄₇	1	1	yes	characteristic, complemented, Sylow
42	C₇	C₄₇×C₃⋊D₁₅	1	1	yes	characteristic, direct product factor, Sylow
43	D₃	—	15	4	no	—
44	C₅	C₇×C₃⋊D₃×C₄₇	1	1	yes	characteristic, complemented, Sylow
45	C₃	C₇×D₁₅×C₄₇	1	4	yes	complemented
46	C₂	—	45	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₇×C₄₇	C₃⋊D₁₅
commutator, cosocle, hypocenter	C₃²×C₅	C₂×C₇×C₄₇
Frattini	C₁	G
Fitting, socle	C₃²×C₅×C₇×C₄₇	C₂
LCS	G ▷ C₃²×C₅
UCS	C₁ ◁ C₇×C₄₇

Complements

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

N	H ≅ G/N	type
1. C₃²×C₅×C₇×C₄₇	C₂	semidirect
4. C₃×C₅×C₇×C₄₇	D₃	semidirect
5. C₄₇×C₃⋊D₁₅	C₇	direct (N × H)
7. C₃²×C₇×C₄₇	D₅	semidirect
8. C₃²×C₅×C₄₇	C₂×C₇	semidirect
10. C₅×C₇×C₄₇	C₃⋊D₃	semidirect
12. C₃×C₇×C₄₇	D₁₅	semidirect
14. C₃×C₅×C₄₇	D₃×C₇	semidirect
16. C₇×C₃⋊D₁₅	C₄₇	direct (N × H)
18. C₃²×C₄₇	C₇×D₅	semidirect
19. C₇×C₄₇	C₃⋊D₁₅	direct (N × H)
20. C₃²×C₅×C₇	C₂×C₄₇	semidirect
22. C₅×C₄₇	C₇×C₃⋊D₃	semidirect
24. C₃×C₄₇	C₇×D₁₅	semidirect
26. C₃×C₅×C₇	D₃×C₄₇	semidirect
28. C₃⋊D₁₅	C₇×C₄₇	direct (N × H)
30. C₃²×C₇	D₅×C₄₇	semidirect
31. C₄₇	C₇×C₃⋊D₁₅	direct (N × H)
32. C₃²×C₅	C₂×C₇×C₄₇	semidirect
34. C₅×C₇	C₃⋊D₃×C₄₇	semidirect
36. C₃×C₇	D₁₅×C₄₇	semidirect
38. C₃×C₅	D₃×C₇×C₄₇	semidirect
41. C₃²	C₇×D₅×C₄₇	semidirect
42. C₇	C₄₇×C₃⋊D₁₅	direct (N × H)
44. C₅	C₇×C₃⋊D₃×C₄₇	semidirect
45. C₃	C₇×D₁₅×C₄₇	semidirect

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
C₇×D₁₅×C₄₇	3
C₇×C₃⋊D₃×C₄₇	5
C₄₇×C₃⋊D₁₅	7
C₇×C₃⋊D₁₅	47

Subgroups — C7×C47×C3⋊D15 #44444124

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×C₄₇×C₃⋊D₁₅ #44444124