Subgroups — C₂×C₇×D₇×C₄₃⋊C₃ #38760506

Order 25284.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇²×C₄₃⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×D₇×C₄₃⋊C₃	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₇×D₇×C₄₃	C₃	1	1	yes	maximal, characteristic, complemented, Hall
4	C₇²×C₄₃⋊C₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₇×D₇×C₄₃	C₂×C₃	1	2	yes	complemented
6	C₂×C₇²×C₄₃	C₂×C₃	1	1	yes	characteristic, complemented
7	C₂²×C₇×C₄₃⋊C₃	—	7	1	no	maximal
8	C₂×D₇×C₄₃⋊C₃	C₇	1	1	yes	maximal, characteristic, direct product factor
9	C₇²×C₄₃	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
10	C₂×C₇×C₄₃⋊C₃	—	2	3	no	—
11	C₂×C₇×C₄₃⋊C₃	—	7	2	no	—
12	C₂×C₇×C₄₃⋊C₃	D₇	1	1	yes	characteristic, direct product factor
13	C₂×C₇×C₄₃⋊C₃	C₂×C₇	1	1	yes	characteristic, complemented
14	D₇×C₄₃⋊C₃	C₂×C₇	1	2	yes	direct product factor
15	C₂²×C₇×C₄₃	—	7	1	no	—
16	C₂×D₇×C₄₃	C₃×C₇	1	1	yes	characteristic, complemented
17	C₇×C₄₃⋊C₃	—	2	3	no	—
18	C₇×C₄₃⋊C₃	C₂×D₇	1	1	yes	characteristic, direct product factor
19	C₇×C₄₃⋊C₃	C₂²×C₇	1	1	yes	characteristic, complemented
20	C₂×C₇×C₄₃	—	2	3	no	—
21	C₂×C₇×C₄₃	—	7	2	no	—
22	C₂×C₇×C₄₃	C₃×D₇	1	1	yes	characteristic, complemented
23	C₂×C₇×C₄₃	C₂×C₃×C₇	1	1	yes	characteristic, complemented
24	D₇×C₄₃	C₂×C₃×C₇	1	2	yes	complemented
25	C₂×C₃×C₇×D₇	—	43	1	no	maximal, Hall
26	C₂²×C₄₃⋊C₃	—	7	1	no	Hall
27	C₇×C₄₃	—	2	3	no	—
28	C₇×C₄₃	C₂×C₃×D₇	1	1	yes	characteristic, complemented
29	C₇×C₄₃	C₂²×C₃×C₇	1	1	yes	characteristic, complemented
30	C₂×C₃×C₇²	—	43	1	no	—
31	C₃×C₇×D₇	—	43	2	no	—
32	C₂×C₄₃⋊C₃	—	7	2	no	—
33	C₂×C₄₃⋊C₃	C₇×D₇	1	1	yes	characteristic, direct product factor
34	C₂×C₇×D₇	C₄₃⋊C₃	1	1	yes	characteristic, direct product factor, Hall
35	C₂²×C₄₃	—	7	1	no	Hall
36	C₃×C₇²	—	43	1	no	Hall
37	C₄₃⋊C₃	C₂×C₇×D₇	1	1	yes	characteristic, direct product factor, Hall
38	C₂×C₇²	C₂×C₄₃⋊C₃	1	1	yes	characteristic, complemented
39	C₇×D₇	C₂×C₄₃⋊C₃	1	2	yes	direct product factor
40	C₂×C₄₃	—	7	2	no	—
41	C₂×C₄₃	C₃×C₇×D₇	1	1	yes	characteristic, complemented
42	C₂²×C₃×C₇	—	301	1	no	—
43	C₂×C₃×D₇	—	43	1	no	—
44	C₇²	C₂²×C₄₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
45	C₄₃	C₂×C₃×C₇×D₇	1	1	yes	characteristic, complemented, Sylow
46	C₂×C₃×C₇	—	43	1	no	—
47	C₂×C₃×C₇	—	43	1	no	—
48	C₂×C₃×C₇	—	301	2	no	—
49	C₂×C₃×C₇	—	86	3	no	—
50	C₃×D₇	—	43	2	no	—
51	C₂²×C₇	—	7	1	no	—
52	C₂×D₇	C₇×C₄₃⋊C₃	1	1	yes	characteristic, direct product factor
53	C₃×C₇	—	43	1	no	—
54	C₃×C₇	—	43	1	no	—
55	C₃×C₇	—	86	3	no	—
56	C₂×C₇	—	2	3	no	—
57	C₂×C₇	—	7	2	no	—
58	C₂×C₇	D₇×C₄₃⋊C₃	1	1	yes	characteristic, direct product factor
59	C₂×C₇	C₂×C₇×C₄₃⋊C₃	1	1	yes	characteristic, complemented
60	D₇	C₂×C₇×C₄₃⋊C₃	1	2	yes	direct product factor
61	C₂²×C₃	—	301	1	no	Hall
62	C₇	—	2	3	no	—
63	C₇	C₂×D₇×C₄₃⋊C₃	1	1	yes	characteristic, direct product factor
64	C₇	C₂²×C₇×C₄₃⋊C₃	1	1	yes	characteristic, complemented
65	C₂×C₃	—	43	1	no	—
66	C₂×C₃	—	301	2	no	—
67	C₂²	—	7	1	no	Sylow
68	C₃	—	43	1	no	Sylow
69	C₂	—	7	2	no	—
70	C₂	C₇×D₇×C₄₃⋊C₃	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₇	D₇×C₄₃⋊C₃
commutator, cosocle, hypocenter	C₇×C₄₃	C₂²×C₃×C₇
Frattini	C₁	G
Fitting, socle	C₂×C₇²×C₄₃	C₂×C₃
LCS	G ▷ C₇×C₄₃
UCS	C₁ ◁ C₂×C₇

Complements

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

N	H ≅ G/N	type
1. C₂×C₇²×C₄₃⋊C₃	C₂	semidirect
2. C₇×D₇×C₄₃⋊C₃	C₂	direct (N × H)
3. C₂×C₇×D₇×C₄₃	C₃	semidirect
4. C₇²×C₄₃⋊C₃	C₂²	semidirect
5. C₇×D₇×C₄₃	C₂×C₃	semidirect
6. C₂×C₇²×C₄₃	C₂×C₃	semidirect
8. C₂×D₇×C₄₃⋊C₃	C₇	direct (N × H)
9. C₇²×C₄₃	C₂²×C₃	semidirect
12. C₂×C₇×C₄₃⋊C₃	D₇	direct (N × H)
13. C₂×C₇×C₄₃⋊C₃	C₂×C₇	semidirect
14. D₇×C₄₃⋊C₃	C₂×C₇	direct (N × H)
16. C₂×D₇×C₄₃	C₃×C₇	semidirect
18. C₇×C₄₃⋊C₃	C₂×D₇	direct (N × H)
19. C₇×C₄₃⋊C₃	C₂²×C₇	semidirect
22. C₂×C₇×C₄₃	C₃×D₇	semidirect
23. C₂×C₇×C₄₃	C₂×C₃×C₇	semidirect
24. D₇×C₄₃	C₂×C₃×C₇	semidirect
28. C₇×C₄₃	C₂×C₃×D₇	semidirect
29. C₇×C₄₃	C₂²×C₃×C₇	semidirect
33. C₂×C₄₃⋊C₃	C₇×D₇	direct (N × H)
34. C₂×C₇×D₇	C₄₃⋊C₃	direct (N × H)
37. C₄₃⋊C₃	C₂×C₇×D₇	direct (N × H)
38. C₂×C₇²	C₂×C₄₃⋊C₃	semidirect
39. C₇×D₇	C₂×C₄₃⋊C₃	direct (N × H)
41. C₂×C₄₃	C₃×C₇×D₇	semidirect
44. C₇²	C₂²×C₄₃⋊C₃	semidirect
45. C₄₃	C₂×C₃×C₇×D₇	semidirect
52. C₂×D₇	C₇×C₄₃⋊C₃	direct (N × H)
58. C₂×C₇	D₇×C₄₃⋊C₃	direct (N × H)
59. C₂×C₇	C₂×C₇×C₄₃⋊C₃	semidirect
60. D₇	C₂×C₇×C₄₃⋊C₃	direct (N × H)
63. C₇	C₂×D₇×C₄₃⋊C₃	direct (N × H)
64. C₇	C₂²×C₇×C₄₃⋊C₃	semidirect
70. C₂	C₇×D₇×C₄₃⋊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
C₂×C₇²×C₄₃⋊C₃	2
C₇×D₇×C₄₃⋊C₃	2
C₂×C₇×D₇×C₄₃	3
C₂²×C₇×C₄₃⋊C₃	7
C₂×D₇×C₄₃⋊C₃	7
C₂×C₃×C₇×D₇	43

Subgroups — C2×C7×D7×C43⋊C3 #38760506

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×D₇×C₄₃⋊C₃ #38760506