Subgroups — C₇×D₇×D₆₁⋊C₃ #49089857

Order 35868.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×D₇×C₆₁⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×(C₆₁⋊C₃)⋊D₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇²×D₆₁⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇×D₇×D₆₁	C₃	1	1	yes	maximal, characteristic, complemented, Hall
5	C₇²×C₆₁⋊C₃	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₇×D₄₂₇	C₂×C₃	1	1	yes	characteristic, complemented
7	C₇×D₇×C₆₁	C₂×C₃	1	1	yes	characteristic, complemented
8	C₇²×D₆₁	C₂×C₃	1	1	yes	characteristic, complemented
9	C₂×C₇×D₆₁⋊C₃	—	7	1	no	maximal
10	D₇×D₆₁⋊C₃	C₇	1	1	yes	maximal, characteristic, direct product factor
11	C₇²×C₆₁	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
12	(C₆₁⋊C₃)⋊D₇	C₂×C₇	1	1	yes	characteristic, complemented
13	D₇×C₆₁⋊C₃	C₂×C₇	1	1	yes	characteristic, complemented
14	C₇×D₆₁⋊C₃	—	2	3	no	—
15	C₇×D₆₁⋊C₃	—	7	1	no	—
16	C₇×D₆₁⋊C₃	D₇	1	1	yes	characteristic, direct product factor
17	C₇×D₆₁⋊C₃	C₂×C₇	1	1	yes	characteristic, complemented
18	C₂×C₇×C₆₁⋊C₃	—	7	1	no	—
19	C₂×C₇×D₆₁	—	7	1	no	—
20	D₇×D₆₁	C₃×C₇	1	1	yes	characteristic, complemented
21	C₇×C₆₁⋊C₃	—	2	3	no	—
22	C₇×C₆₁⋊C₃	C₂×D₇	1	1	yes	characteristic, complemented
23	C₇×C₆₁⋊C₃	C₂²×C₇	1	1	yes	characteristic, complemented
24	C₂×C₇×C₆₁	—	7	1	no	—
25	D₄₂₇	C₂×C₃×C₇	1	1	yes	characteristic, complemented
26	C₇×D₆₁	—	2	3	no	—
27	C₇×D₆₁	—	7	1	no	—
28	C₇×D₆₁	C₃×D₇	1	1	yes	characteristic, complemented
29	C₇×D₆₁	C₂×C₃×C₇	1	1	yes	characteristic, complemented
30	D₇×C₆₁	C₂×C₃×C₇	1	1	yes	characteristic, complemented
31	C₂×D₆₁⋊C₃	—	7	1	no	Hall
32	C₂×C₃×C₇×D₇	—	61	1	no	maximal, Hall
33	C₇×C₆₁	—	2	3	no	—
34	C₇×C₆₁	C₂×C₃×D₇	1	1	yes	characteristic, complemented
35	C₇×C₆₁	C₂²×C₃×C₇	1	1	yes	characteristic, complemented
36	C₂×C₆₁⋊C₃	—	7	1	no	—
37	D₆₁⋊C₃	—	7	1	no	—
38	D₆₁⋊C₃	C₇×D₇	1	1	yes	characteristic, direct product factor
39	C₂×C₃×C₇²	—	61	1	no	—
40	C₃×C₇×D₇	—	61	1	no	—
41	C₃×C₇×D₇	—	61	1	no	—
42	C₂×D₆₁	—	7	1	no	Hall
43	C₂×C₇×D₇	—	61	1	no	Hall
44	C₆₁⋊C₃	C₂×C₇×D₇	1	1	yes	characteristic, complemented, Hall
45	C₃×C₇²	—	61	1	no	Hall
46	C₂×C₆₁	—	7	1	no	—
47	D₆₁	—	7	1	no	—
48	D₆₁	C₃×C₇×D₇	1	1	yes	characteristic, complemented
49	C₂×C₇²	—	61	1	no	—
50	C₇×D₇	—	61	1	no	—
51	C₇×D₇	D₆₁⋊C₃	1	1	yes	characteristic, direct product factor
52	C₂²×C₃×C₇	—	427	1	no	—
53	C₂×C₃×D₇	—	61	1	no	—
54	C₆₁	C₂×C₃×C₇×D₇	1	1	yes	characteristic, complemented, Sylow
55	C₇²	C₂×D₆₁⋊C₃	1	1	yes	characteristic, complemented, Sylow
56	C₂×C₃×C₇	—	61	1	no	—
57	C₂×C₃×C₇	—	61	1	no	—
58	C₂×C₃×C₇	—	122	3	no	—
59	C₂×C₃×C₇	—	427	1	no	—
60	C₂×C₃×C₇	—	427	1	no	—
61	C₃×D₇	—	61	1	no	—
62	C₃×D₇	—	61	1	no	—
63	C₂²×C₇	—	427	1	no	—
64	C₂×D₇	—	61	1	no	—
65	C₃×C₇	—	61	1	no	—
66	C₃×C₇	—	61	1	no	—
67	C₃×C₇	—	122	3	no	—
68	C₂×C₇	—	7	1	no	—
69	C₂×C₇	—	61	1	no	—
70	C₂×C₇	—	61	1	no	—
71	C₂×C₇	—	122	3	no	—
72	C₂×C₇	—	427	1	no	—
73	D₇	—	61	1	no	—
74	D₇	C₇×D₆₁⋊C₃	1	1	yes	characteristic, direct product factor
75	C₂²×C₃	—	427	1	no	Hall
76	C₇	—	2	3	no	—
77	C₇	D₇×D₆₁⋊C₃	1	1	yes	characteristic, direct product factor
78	C₇	C₂×C₇×D₆₁⋊C₃	1	1	yes	characteristic, complemented
79	C₂×C₃	—	61	1	no	—
80	C₂×C₃	—	427	1	no	—
81	C₂×C₃	—	427	1	no	—
82	C₂²	—	427	1	no	Sylow
83	C₃	—	61	1	no	Sylow
84	C₂	—	7	1	no	—
85	C₂	—	61	1	no	—
86	C₂	—	427	1	no	—

	subgroup	G/H
center, hypercenter	C₇	D₇×D₆₁⋊C₃
commutator, cosocle, hypocenter	C₇×C₆₁	C₂²×C₃×C₇
Frattini	C₁	G
Fitting, socle	C₇²×C₆₁	C₂²×C₃
LCS	G ▷ C₇×C₆₁
UCS	C₁ ◁ C₇

Complements

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

N	H ≅ G/N	type
1. C₇×D₇×C₆₁⋊C₃	C₂	semidirect
2. C₇×(C₆₁⋊C₃)⋊D₇	C₂	semidirect
3. C₇²×D₆₁⋊C₃	C₂	semidirect
4. C₇×D₇×D₆₁	C₃	semidirect
5. C₇²×C₆₁⋊C₃	C₂²	semidirect
6. C₇×D₄₂₇	C₂×C₃	semidirect
7. C₇×D₇×C₆₁	C₂×C₃	semidirect
8. C₇²×D₆₁	C₂×C₃	semidirect
10. D₇×D₆₁⋊C₃	C₇	direct (N × H)
11. C₇²×C₆₁	C₂²×C₃	semidirect
12. (C₆₁⋊C₃)⋊D₇	C₂×C₇	semidirect
13. D₇×C₆₁⋊C₃	C₂×C₇	semidirect
16. C₇×D₆₁⋊C₃	D₇	direct (N × H)
17. C₇×D₆₁⋊C₃	C₂×C₇	semidirect
20. D₇×D₆₁	C₃×C₇	semidirect
22. C₇×C₆₁⋊C₃	C₂×D₇	semidirect
23. C₇×C₆₁⋊C₃	C₂²×C₇	semidirect
25. D₄₂₇	C₂×C₃×C₇	semidirect
28. C₇×D₆₁	C₃×D₇	semidirect
29. C₇×D₆₁	C₂×C₃×C₇	semidirect
30. D₇×C₆₁	C₂×C₃×C₇	semidirect
34. C₇×C₆₁	C₂×C₃×D₇	semidirect
35. C₇×C₆₁	C₂²×C₃×C₇	semidirect
38. D₆₁⋊C₃	C₇×D₇	direct (N × H)
44. C₆₁⋊C₃	C₂×C₇×D₇	semidirect
48. D₆₁	C₃×C₇×D₇	semidirect
51. C₇×D₇	D₆₁⋊C₃	direct (N × H)
54. C₆₁	C₂×C₃×C₇×D₇	semidirect
55. C₇²	C₂×D₆₁⋊C₃	semidirect
74. D₇	C₇×D₆₁⋊C₃	direct (N × H)
77. C₇	D₇×D₆₁⋊C₃	direct (N × H)
78. C₇	C₂×C₇×D₆₁⋊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×C₆₁⋊C₃	2
C₇×(C₆₁⋊C₃)⋊D₇	2
C₇²×D₆₁⋊C₃	2
C₇×D₇×D₆₁	3
C₂×C₇×D₆₁⋊C₃	7
D₇×D₆₁⋊C₃	7
C₂×C₃×C₇×D₇	61

Subgroups — C7×D7×D61⋊C3 #49089857

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×D₇×D₆₁⋊C₃ #49089857