Subgroups — D₇×(C₄₃⋊C₃)⋊D₇ #38760455

Order 25284.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	(C₄₃⋊C₃)⋊(C₇⋊D₇)	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×D₇×C₄₃⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×(C₄₃⋊C₃)⋊D₇	C₂	1	1	yes	maximal, characteristic, complemented
4	D₇×D₃₀₁	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×D₃₀₁	C₂×C₃	1	1	yes	characteristic, complemented
8	C₇×D₇×C₄₃	C₂×C₃	1	1	yes	characteristic, complemented
9	C₂×(C₄₃⋊C₃)⋊D₇	—	7	1	no	maximal
10	D₇×D₄₃⋊C₃	—	7	1	no	maximal
11	C₇²×C₄₃	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
12	C₂×C₇×C₄₃⋊C₃	—	7	1	no	—
13	(C₄₃⋊C₃)⋊D₇	—	7	1	no	—
14	(C₄₃⋊C₃)⋊D₇	—	7	1	no	—
15	(C₄₃⋊C₃)⋊D₇	—	14	3	no	—
16	(C₄₃⋊C₃)⋊D₇	D₇	1	1	yes	characteristic, direct product factor
17	D₇×C₄₃⋊C₃	D₇	1	1	yes	characteristic, complemented
18	C₇×D₄₃⋊C₃	—	7	1	no	—
19	C₂×D₃₀₁	—	7	1	no	—
20	D₇×D₄₃	—	7	1	no	—
21	C₇×C₄₃⋊C₃	—	2	3	no	—
22	C₇×C₄₃⋊C₃	C₂×D₇	1	1	yes	characteristic, complemented
23	C₇×C₄₃⋊C₃	C₂×D₇	1	1	yes	characteristic, complemented
24	C₂×C₇×C₄₃	—	7	1	no	—
25	D₃₀₁	—	7	1	no	—
26	D₃₀₁	—	7	1	no	—
27	D₃₀₁	—	14	3	no	—
28	D₃₀₁	C₃×D₇	1	1	yes	characteristic, complemented
29	C₇×D₄₃	—	7	1	no	—
30	D₇×C₄₃	C₃×D₇	1	1	yes	characteristic, complemented
31	C₃×D₇²	—	43	1	no	maximal, Hall
32	C₂×D₄₃⋊C₃	—	49	1	no	Hall
33	C₇×C₄₃	—	2	3	no	—
34	C₇×C₄₃	C₂×C₃×D₇	1	1	yes	characteristic, complemented
35	C₇×C₄₃	C₂×C₃×D₇	1	1	yes	characteristic, complemented
36	C₃×C₇⋊D₇	—	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	—	49	1	no	—
42	D₇²	—	43	1	no	Hall
43	C₂×D₄₃	—	49	1	no	Hall
44	C₃×C₇²	—	86	1	no	Hall
45	C₄₃⋊C₃	D₇²	1	1	yes	characteristic, complemented, Hall
46	C₇⋊D₇	—	43	1	no	—
47	C₇×D₇	—	43	1	no	—
48	C₇×D₇	D₄₃⋊C₃	1	1	yes	characteristic, complemented
49	C₂×C₄₃	—	7	1	no	—
50	D₄₃	—	7	1	no	—
51	D₄₃	—	49	1	no	—
52	C₂×C₃×D₇	—	301	1	no	—
53	C₂×C₃×D₇	—	301	1	no	—
54	C₇²	C₂×D₄₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
55	C₄₃	C₃×D₇²	1	1	yes	characteristic, complemented, Sylow
56	C₂×C₃×C₇	—	301	1	no	—
57	C₂×C₃×C₇	—	602	1	no	—
58	C₃×D₇	—	43	1	no	—
59	C₃×D₇	—	301	1	no	—
60	C₃×D₇	—	301	1	no	—
61	C₃×D₇	—	86	1	no	—
62	C₃×D₇	—	602	3	no	—
63	C₂×D₇	—	301	1	no	—
64	C₂×D₇	—	301	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	—	301	1	no	—
70	D₇	—	43	1	no	—
71	D₇	—	301	1	no	—
72	D₇	—	301	1	no	—
73	D₇	—	602	3	no	—
74	D₇	(C₄₃⋊C₃)⋊D₇	1	1	yes	characteristic, direct product factor
75	C₂²×C₃	—	2107	1	no	Hall
76	C₇	—	2	3	no	—
77	C₇	D₇×D₄₃⋊C₃	1	1	yes	characteristic, complemented
78	C₇	C₂×(C₄₃⋊C₃)⋊D₇	1	1	yes	characteristic, complemented
79	C₂×C₃	—	301	1	no	—
80	C₂×C₃	—	2107	1	no	—
81	C₂×C₃	—	602	1	no	—
82	C₂²	—	2107	1	no	Sylow
83	C₃	—	86	1	no	Sylow
84	C₂	—	7	1	no	—
85	C₂	—	301	1	no	—
86	C₂	—	2107	1	no	—

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

Complements

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

N	H ≅ G/N	type
1. (C₄₃⋊C₃)⋊(C₇⋊D₇)	C₂	semidirect
2. C₇×D₇×C₄₃⋊C₃	C₂	semidirect
3. C₇×(C₄₃⋊C₃)⋊D₇	C₂	semidirect
4. D₇×D₃₀₁	C₃	semidirect
5. C₇²×C₄₃⋊C₃	C₂²	semidirect
6. C₇⋊D₃₀₁	C₂×C₃	semidirect
7. C₇×D₃₀₁	C₂×C₃	semidirect
8. C₇×D₇×C₄₃	C₂×C₃	semidirect
11. C₇²×C₄₃	C₂²×C₃	semidirect
16. (C₄₃⋊C₃)⋊D₇	D₇	direct (N × H)
17. D₇×C₄₃⋊C₃	D₇	semidirect
22. C₇×C₄₃⋊C₃	C₂×D₇	semidirect
23. C₇×C₄₃⋊C₃	C₂×D₇	semidirect
28. D₃₀₁	C₃×D₇	semidirect
30. D₇×C₄₃	C₃×D₇	semidirect
34. C₇×C₄₃	C₂×C₃×D₇	semidirect
35. C₇×C₄₃	C₂×C₃×D₇	semidirect
45. C₄₃⋊C₃	D₇²	semidirect
48. C₇×D₇	D₄₃⋊C₃	semidirect
54. C₇²	C₂×D₄₃⋊C₃	semidirect
55. C₄₃	C₃×D₇²	semidirect
74. D₇	(C₄₃⋊C₃)⋊D₇	direct (N × H)
77. C₇	D₇×D₄₃⋊C₃	semidirect
78. C₇	C₂×(C₄₃⋊C₃)⋊D₇	semidirect

Maximal subgroups

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

subgroup	index
(C₄₃⋊C₃)⋊(C₇⋊D₇)	2
C₇×D₇×C₄₃⋊C₃	2
C₇×(C₄₃⋊C₃)⋊D₇	2
D₇×D₃₀₁	3
C₂×(C₄₃⋊C₃)⋊D₇	7
D₇×D₄₃⋊C₃	7
C₃×D₇²	43

Subgroups — D7×(C43⋊C3)⋊D7 #38760455

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₇×(C₄₃⋊C₃)⋊D₇ #38760455