Subgroups — D₇×D₄₂₉ #26046564

Order 12012.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₃₀₀₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×D₄₂₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₁₁×C₁₃×D₇	C₂	1	1	yes	maximal, characteristic, complemented
4	D₇×D₁₄₃	—	3	1	no	maximal, Hall
5	C₃×C₇×C₁₁×C₁₃	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₁₀₀₁	—	3	1	no	—
7	C₁₁×C₁₃×D₇	D₃	1	1	yes	characteristic, complemented
8	C₇×D₁₄₃	—	3	1	no	—
9	C₂×D₄₂₉	—	7	1	no	maximal, Hall
10	D₇×D₃₉	—	11	1	no	maximal, Hall
11	C₇×C₁₁×C₁₃	C₂×D₃	1	1	yes	characteristic, complemented, Hall
12	D₇×D₃₃	—	13	1	no	maximal, Hall
13	C₂×C₃×C₁₁×C₁₃	—	7	1	no	—
14	D₄₂₉	—	7	1	no	—
15	D₄₂₉	D₇	1	1	yes	characteristic, direct product factor
16	C₂×D₁₄₃	—	21	1	no	Hall
17	D₂₇₃	—	11	1	no	—
18	C₇×D₃₉	—	11	1	no	—
19	C₃×C₁₃×D₇	D₁₁	1	1	yes	characteristic, complemented
20	D₂₃₁	—	13	1	no	—
21	C₇×D₃₃	—	13	1	no	—
22	C₃×C₁₁×D₇	D₁₃	1	1	yes	characteristic, complemented
23	C₃×C₁₁×C₁₃	C₂×D₇	1	1	yes	characteristic, complemented, Hall
24	D₇×D₁₃	—	33	1	no	Hall
25	D₇×D₁₁	—	39	1	no	Hall
26	C₂×C₁₁×C₁₃	—	7	1	no	—
27	D₁₄₃	—	3	1	no	—
28	D₁₄₃	—	21	1	no	—
29	C₃×C₇×C₁₃	C₂×D₁₁	1	1	yes	characteristic, complemented, Hall
30	C₃×C₇×C₁₁	C₂×D₁₃	1	1	yes	characteristic, complemented, Hall
31	D₉₁	—	33	1	no	—
32	C₇×D₁₃	—	33	1	no	—
33	C₁₃×D₇	D₃₃	1	1	yes	characteristic, complemented
34	C₂×D₃₉	—	77	1	no	Hall
35	D₇₇	—	39	1	no	—
36	C₇×D₁₁	—	39	1	no	—
37	C₁₁×D₇	D₃₉	1	1	yes	characteristic, complemented
38	C₁₁×C₁₃	D₃×D₇	1	1	yes	characteristic, complemented, Hall
39	C₂×D₃₃	—	91	1	no	Hall
40	C₇×C₁₃	C₂×D₃₃	1	1	yes	characteristic, complemented, Hall
41	D₃×D₇	—	143	1	no	Hall
42	C₂×C₃×C₁₃	—	7	1	no	—
43	D₃₉	—	11	1	no	—
44	D₃₉	—	77	1	no	—
45	C₇×C₁₁	C₂×D₃₉	1	1	yes	characteristic, complemented, Hall
46	C₂×C₃×C₁₁	—	7	1	no	—
47	D₃₃	—	13	1	no	—
48	D₃₃	—	91	1	no	—
49	C₂×D₁₃	—	231	1	no	Hall
50	C₂×D₁₁	—	273	1	no	Hall
51	D₂₁	—	143	1	no	—
52	C₃×D₇	D₁₄₃	1	1	yes	characteristic, complemented
53	D₃×C₇	—	143	1	no	—
54	C₃×C₁₃	D₇×D₁₁	1	1	yes	characteristic, complemented, Hall
55	C₃×C₁₁	D₇×D₁₃	1	1	yes	characteristic, complemented, Hall
56	C₂×D₇	—	429	1	no	Hall
57	C₂×C₁₃	—	7	1	no	—
58	D₁₃	—	33	1	no	—
59	D₁₃	—	231	1	no	—
60	C₂×C₁₁	—	7	1	no	—
61	D₁₁	—	273	1	no	—
62	D₁₁	—	39	1	no	—
63	C₃×C₇	C₂×D₁₄₃	1	1	yes	characteristic, complemented, Hall
64	C₂×C₇	—	429	1	no	—
65	D₇	—	429	1	no	—
66	D₇	D₄₂₉	1	1	yes	characteristic, direct product factor
67	C₁₃	D₇×D₃₃	1	1	yes	characteristic, complemented, Sylow
68	C₂×D₃	—	1001	1	no	Hall
69	C₁₁	D₇×D₃₉	1	1	yes	characteristic, complemented, Sylow
70	C₇	C₂×D₄₂₉	1	1	yes	characteristic, complemented, Sylow
71	C₂×C₃	—	7	1	no	—
72	D₃	—	143	1	no	—
73	D₃	—	1001	1	no	—
74	C₂²	—	3003	1	no	Sylow
75	C₃	D₇×D₁₄₃	1	1	yes	characteristic, complemented, Sylow
76	C₂	—	7	1	no	—
77	C₂	—	429	1	no	—
78	C₂	—	3003	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₇×C₁₁×C₁₃	C₂²
LCS	G ▷ C₃×C₇×C₁₁×C₁₃
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. D₃₀₀₃	C₂	semidirect
2. C₇×D₄₂₉	C₂	semidirect
3. C₃×C₁₁×C₁₃×D₇	C₂	semidirect
5. C₃×C₇×C₁₁×C₁₃	C₂²	semidirect
7. C₁₁×C₁₃×D₇	D₃	semidirect
11. C₇×C₁₁×C₁₃	C₂×D₃	semidirect
15. D₄₂₉	D₇	direct (N × H)
19. C₃×C₁₃×D₇	D₁₁	semidirect
22. C₃×C₁₁×D₇	D₁₃	semidirect
23. C₃×C₁₁×C₁₃	C₂×D₇	semidirect
29. C₃×C₇×C₁₃	C₂×D₁₁	semidirect
30. C₃×C₇×C₁₁	C₂×D₁₃	semidirect
33. C₁₃×D₇	D₃₃	semidirect
37. C₁₁×D₇	D₃₉	semidirect
38. C₁₁×C₁₃	D₃×D₇	semidirect
40. C₇×C₁₃	C₂×D₃₃	semidirect
45. C₇×C₁₁	C₂×D₃₉	semidirect
52. C₃×D₇	D₁₄₃	semidirect
54. C₃×C₁₃	D₇×D₁₁	semidirect
55. C₃×C₁₁	D₇×D₁₃	semidirect
63. C₃×C₇	C₂×D₁₄₃	semidirect
66. D₇	D₄₂₉	direct (N × H)
67. C₁₃	D₇×D₃₃	semidirect
69. C₁₁	D₇×D₃₉	semidirect
70. C₇	C₂×D₄₂₉	semidirect
75. C₃	D₇×D₁₄₃	semidirect

Maximal subgroups

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

subgroup	index
D₃₀₀₃	2
C₇×D₄₂₉	2
C₃×C₁₁×C₁₃×D₇	2
D₇×D₁₄₃	3
C₂×D₄₂₉	7
D₇×D₃₉	11
D₇×D₃₃	13

Subgroups — D7×D429 #26046564

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₇×D₄₂₉ #26046564