Subgroups — C₇×D₇×D₄₃⋊C₃ #38760448

Order 25284.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×D₇×C₄₃⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×(C₄₃⋊C₃)⋊D₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇²×D₄₃⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇×D₇×D₄₃	C₃	1	1	yes	maximal, characteristic, complemented, Hall
5	C₇²×C₄₃⋊C₃	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₇×D₃₀₁	C₂×C₃	1	1	yes	characteristic, complemented
7	C₇×D₇×C₄₃	C₂×C₃	1	1	yes	characteristic, complemented
8	C₇²×D₄₃	C₂×C₃	1	1	yes	characteristic, complemented
9	C₂×C₇×D₄₃⋊C₃	—	7	1	no	maximal
10	D₇×D₄₃⋊C₃	C₇	1	1	yes	maximal, characteristic, direct product factor
11	C₇²×C₄₃	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
12	C₂×C₇×C₄₃⋊C₃	—	7	1	no	—
13	(C₄₃⋊C₃)⋊D₇	C₂×C₇	1	1	yes	characteristic, complemented
14	D₇×C₄₃⋊C₃	C₂×C₇	1	1	yes	characteristic, complemented
15	C₇×D₄₃⋊C₃	—	2	3	no	—
16	C₇×D₄₃⋊C₃	—	7	1	no	—
17	C₇×D₄₃⋊C₃	D₇	1	1	yes	characteristic, direct product factor
18	C₇×D₄₃⋊C₃	C₂×C₇	1	1	yes	characteristic, complemented
19	C₂×C₇×D₄₃	—	7	1	no	—
20	D₇×D₄₃	C₃×C₇	1	1	yes	characteristic, complemented
21	C₇×C₄₃⋊C₃	—	2	3	no	—
22	C₇×C₄₃⋊C₃	C₂×D₇	1	1	yes	characteristic, complemented
23	C₇×C₄₃⋊C₃	C₂²×C₇	1	1	yes	characteristic, complemented
24	C₂×C₇×C₄₃	—	7	1	no	—
25	D₃₀₁	C₂×C₃×C₇	1	1	yes	characteristic, complemented
26	C₇×D₄₃	—	2	3	no	—
27	C₇×D₄₃	—	7	1	no	—
28	C₇×D₄₃	C₃×D₇	1	1	yes	characteristic, complemented
29	C₇×D₄₃	C₂×C₃×C₇	1	1	yes	characteristic, complemented
30	D₇×C₄₃	C₂×C₃×C₇	1	1	yes	characteristic, complemented
31	C₂×C₃×C₇×D₇	—	43	1	no	maximal, Hall
32	C₂×D₄₃⋊C₃	—	7	1	no	Hall
33	C₇×C₄₃	—	2	3	no	—
34	C₇×C₄₃	C₂×C₃×D₇	1	1	yes	characteristic, complemented
35	C₇×C₄₃	C₂²×C₃×C₇	1	1	yes	characteristic, complemented
36	C₂×C₃×C₇²	—	43	1	no	—
37	C₃×C₇×D₇	—	43	1	no	—
38	C₃×C₇×D₇	—	86	1	no	—
39	C₂×C₄₃⋊C₃	—	7	1	no	—
40	D₄₃⋊C₃	—	7	1	no	—
41	D₄₃⋊C₃	C₇×D₇	1	1	yes	characteristic, direct product factor
42	C₂×C₇×D₇	—	43	1	no	Hall
43	C₂×D₄₃	—	7	1	no	Hall
44	C₃×C₇²	—	86	1	no	Hall
45	C₄₃⋊C₃	C₂×C₇×D₇	1	1	yes	characteristic, complemented, Hall
46	C₂×C₇²	—	43	1	no	—
47	C₇×D₇	—	43	1	no	—
48	C₇×D₇	D₄₃⋊C₃	1	1	yes	characteristic, direct product factor
49	C₂×C₄₃	—	7	1	no	—
50	D₄₃	—	7	1	no	—
51	D₄₃	C₃×C₇×D₇	1	1	yes	characteristic, complemented
52	C₂²×C₃×C₇	—	301	1	no	—
53	C₂×C₃×D₇	—	43	1	no	—
54	C₇²	C₂×D₄₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
55	C₄₃	C₂×C₃×C₇×D₇	1	1	yes	characteristic, complemented, Sylow
56	C₂×C₃×C₇	—	43	1	no	—
57	C₂×C₃×C₇	—	43	1	no	—
58	C₂×C₃×C₇	—	301	1	no	—
59	C₂×C₃×C₇	—	86	3	no	—
60	C₂×C₃×C₇	—	602	1	no	—
61	C₃×D₇	—	43	1	no	—
62	C₃×D₇	—	86	1	no	—
63	C₂²×C₇	—	301	1	no	—
64	C₂×D₇	—	43	1	no	—
65	C₃×C₇	—	86	1	no	—
66	C₃×C₇	—	86	1	no	—
67	C₃×C₇	—	172	3	no	—
68	C₂×C₇	—	7	1	no	—
69	C₂×C₇	—	43	1	no	—
70	C₂×C₇	—	43	1	no	—
71	C₂×C₇	—	301	1	no	—
72	C₂×C₇	—	86	3	no	—
73	D₇	—	43	1	no	—
74	D₇	C₇×D₄₃⋊C₃	1	1	yes	characteristic, direct product factor
75	C₂²×C₃	—	301	1	no	Hall
76	C₇	—	2	3	no	—
77	C₇	D₇×D₄₃⋊C₃	1	1	yes	characteristic, direct product factor
78	C₇	C₂×C₇×D₄₃⋊C₃	1	1	yes	characteristic, complemented
79	C₂×C₃	—	43	1	no	—
80	C₂×C₃	—	301	1	no	—
81	C₂×C₃	—	602	1	no	—
82	C₂²	—	301	1	no	Sylow
83	C₃	—	86	1	no	Sylow
84	C₂	—	7	1	no	—
85	C₂	—	43	1	no	—
86	C₂	—	301	1	no	—

	subgroup	G/H
center, hypercenter	C₇	D₇×D₄₃⋊C₃
commutator, cosocle, hypocenter	C₇×C₄₃	C₂²×C₃×C₇
Frattini	C₁	G
Fitting, socle	C₇²×C₄₃	C₂²×C₃
LCS	G ▷ C₇×C₄₃
UCS	C₁ ◁ C₇

Complements

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

N	H ≅ G/N	type
1. C₇×D₇×C₄₃⋊C₃	C₂	semidirect
2. C₇×(C₄₃⋊C₃)⋊D₇	C₂	semidirect
3. C₇²×D₄₃⋊C₃	C₂	semidirect
4. C₇×D₇×D₄₃	C₃	semidirect
5. C₇²×C₄₃⋊C₃	C₂²	semidirect
6. C₇×D₃₀₁	C₂×C₃	semidirect
7. C₇×D₇×C₄₃	C₂×C₃	semidirect
8. C₇²×D₄₃	C₂×C₃	semidirect
10. D₇×D₄₃⋊C₃	C₇	direct (N × H)
11. C₇²×C₄₃	C₂²×C₃	semidirect
13. (C₄₃⋊C₃)⋊D₇	C₂×C₇	semidirect
14. D₇×C₄₃⋊C₃	C₂×C₇	semidirect
17. C₇×D₄₃⋊C₃	D₇	direct (N × H)
18. C₇×D₄₃⋊C₃	C₂×C₇	semidirect
20. D₇×D₄₃	C₃×C₇	semidirect
22. C₇×C₄₃⋊C₃	C₂×D₇	semidirect
23. C₇×C₄₃⋊C₃	C₂²×C₇	semidirect
25. D₃₀₁	C₂×C₃×C₇	semidirect
28. C₇×D₄₃	C₃×D₇	semidirect
29. C₇×D₄₃	C₂×C₃×C₇	semidirect
30. D₇×C₄₃	C₂×C₃×C₇	semidirect
34. C₇×C₄₃	C₂×C₃×D₇	semidirect
35. C₇×C₄₃	C₂²×C₃×C₇	semidirect
41. D₄₃⋊C₃	C₇×D₇	direct (N × H)
45. C₄₃⋊C₃	C₂×C₇×D₇	semidirect
48. C₇×D₇	D₄₃⋊C₃	direct (N × H)
51. D₄₃	C₃×C₇×D₇	semidirect
54. C₇²	C₂×D₄₃⋊C₃	semidirect
55. C₄₃	C₂×C₃×C₇×D₇	semidirect
74. D₇	C₇×D₄₃⋊C₃	direct (N × H)
77. C₇	D₇×D₄₃⋊C₃	direct (N × H)
78. C₇	C₂×C₇×D₄₃⋊C₃	semidirect

Maximal subgroups

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

subgroup	index
C₇×D₇×C₄₃⋊C₃	2
C₇×(C₄₃⋊C₃)⋊D₇	2
C₇²×D₄₃⋊C₃	2
C₇×D₇×D₄₃	3
C₂×C₇×D₄₃⋊C₃	7
D₇×D₄₃⋊C₃	7
C₂×C₃×C₇×D₇	43

Subgroups — C7×D7×D43⋊C3 #38760448

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×D₇×D₄₃⋊C₃ #38760448