Subgroups — D₃×C₇×D₇×C₆₁ #49089979

Order 35868.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₇×D₇×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
2	D₃×C₇²×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×D₂₁×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₇×D₇×C₆₁	—	3	1	no	maximal, Hall
5	C₃×C₇²×C₆₁	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₇×D₇×C₆₁	—	3	1	no	—
7	C₇×D₇×C₆₁	D₃	1	1	yes	characteristic, direct product factor
8	C₂×C₇²×C₆₁	—	3	1	no	—
9	C₂×D₃×C₇×C₆₁	—	7	1	no	maximal
10	D₃×D₇×C₆₁	C₇	1	1	yes	maximal, characteristic, direct product factor
11	C₇²×C₆₁	C₂×D₃	1	1	yes	characteristic, complemented, Hall
12	D₂₁×C₆₁	C₂×C₇	1	1	yes	characteristic, complemented
13	D₃×C₇×C₆₁	—	2	3	no	—
14	D₃×C₇×C₆₁	—	7	1	no	—
15	D₃×C₇×C₆₁	D₇	1	1	yes	characteristic, direct product factor
16	D₃×C₇×C₆₁	C₂×C₇	1	1	yes	characteristic, complemented
17	C₃×D₇×C₆₁	C₂×C₇	1	1	yes	characteristic, complemented
18	C₂×C₃×C₇×C₆₁	—	7	1	no	—
19	C₂²×C₇×C₆₁	—	21	1	no	—
20	C₂×D₇×C₆₁	—	3	1	no	—
21	C₃×C₇×C₆₁	—	2	3	no	—
22	C₃×C₇×C₆₁	C₂×D₇	1	1	yes	characteristic, complemented
23	C₃×C₇×C₆₁	C₂²×C₇	1	1	yes	characteristic, complemented
24	C₂×C₇×C₆₁	—	3	1	no	—
25	C₂×C₇×C₆₁	—	3	1	no	—
26	C₂×C₇×C₆₁	—	6	3	no	—
27	C₂×C₇×C₆₁	—	7	1	no	—
28	C₂×C₇×C₆₁	—	21	1	no	—
29	D₇×C₆₁	—	3	1	no	—
30	D₇×C₆₁	D₃×C₇	1	1	yes	characteristic, direct product factor
31	C₂×D₃×C₆₁	—	7	1	no	Hall
32	D₃×C₇×D₇	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Hall
33	C₇×C₆₁	—	2	3	no	—
34	C₇×C₆₁	D₃×D₇	1	1	yes	characteristic, direct product factor
35	C₇×C₆₁	C₂×D₃×C₇	1	1	yes	characteristic, complemented
36	C₂×C₃×C₆₁	—	7	1	no	—
37	D₃×C₆₁	—	7	1	no	—
38	D₃×C₆₁	C₇×D₇	1	1	yes	characteristic, direct product factor
39	C₇×D₂₁	C₂×C₆₁	1	1	yes	characteristic, complemented
40	D₃×C₇²	C₂×C₆₁	1	1	yes	characteristic, complemented
41	C₃×C₇×D₇	C₂×C₆₁	1	1	yes	characteristic, complemented
42	C₂²×C₆₁	—	21	1	no	Hall
43	C₂×C₇×D₇	—	3	1	no	Hall
44	C₃×C₆₁	C₂×C₇×D₇	1	1	yes	characteristic, complemented, Hall
45	C₃×C₇²	C₂²×C₆₁	1	1	yes	characteristic, complemented, Hall
46	C₂×C₆₁	—	3	1	no	—
47	C₂×C₆₁	—	7	1	no	—
48	C₂×C₆₁	—	21	1	no	—
49	C₂×C₇²	—	3	1	no	—
50	C₇×D₇	—	3	1	no	—
51	C₇×D₇	D₃×C₆₁	1	1	yes	characteristic, direct product factor
52	C₂×D₃×C₇	—	7	1	no	—
53	D₃×D₇	C₇×C₆₁	1	1	yes	characteristic, direct product factor
54	C₆₁	D₃×C₇×D₇	1	1	yes	characteristic, direct product factor, Sylow
55	C₇²	C₂×D₃×C₆₁	1	1	yes	characteristic, complemented, Sylow
56	C₂×C₃×C₇	—	7	1	no	—
57	D₂₁	C₂×C₇×C₆₁	1	1	yes	characteristic, complemented
58	C₃×D₇	C₂×C₇×C₆₁	1	1	yes	characteristic, complemented
59	D₃×C₇	—	2	3	no	—
60	D₃×C₇	—	7	1	no	—
61	D₃×C₇	D₇×C₆₁	1	1	yes	characteristic, direct product factor
62	D₃×C₇	C₂×C₇×C₆₁	1	1	yes	characteristic, complemented
63	C₂²×C₇	—	21	1	no	—
64	C₂×D₇	—	3	1	no	—
65	C₃×C₇	—	2	3	no	—
66	C₃×C₇	C₂×D₇×C₆₁	1	1	yes	characteristic, complemented
67	C₃×C₇	C₂²×C₇×C₆₁	1	1	yes	characteristic, complemented
68	C₂×C₇	—	3	1	no	—
69	C₂×C₇	—	3	1	no	—
70	C₂×C₇	—	6	3	no	—
71	C₂×C₇	—	7	1	no	—
72	C₂×C₇	—	21	1	no	—
73	D₇	—	3	1	no	—
74	D₇	D₃×C₇×C₆₁	1	1	yes	characteristic, direct product factor
75	C₂×D₃	—	7	1	no	Hall
76	C₇	—	2	3	no	—
77	C₇	D₃×D₇×C₆₁	1	1	yes	characteristic, direct product factor
78	C₇	C₂×D₃×C₇×C₆₁	1	1	yes	characteristic, complemented
79	C₂×C₃	—	7	1	no	—
80	D₃	—	7	1	no	—
81	D₃	C₇×D₇×C₆₁	1	1	yes	characteristic, direct product factor
82	C₂²	—	21	1	no	Sylow
83	C₃	C₂×C₇×D₇×C₆₁	1	1	yes	characteristic, complemented, Sylow
84	C₂	—	3	1	no	—
85	C₂	—	7	1	no	—
86	C₂	—	21	1	no	—

	subgroup	G/H
center, hypercenter	C₇×C₆₁	D₃×D₇
commutator, cosocle, hypocenter	C₃×C₇	C₂²×C₇×C₆₁
Frattini	C₁	G
Fitting, socle	C₃×C₇²×C₆₁	C₂²
LCS	G ▷ C₃×C₇
UCS	C₁ ◁ C₇×C₆₁

Complements

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

N	H ≅ G/N	type
1. C₃×C₇×D₇×C₆₁	C₂	semidirect
2. D₃×C₇²×C₆₁	C₂	semidirect
3. C₇×D₂₁×C₆₁	C₂	semidirect
5. C₃×C₇²×C₆₁	C₂²	semidirect
7. C₇×D₇×C₆₁	D₃	direct (N × H)
10. D₃×D₇×C₆₁	C₇	direct (N × H)
11. C₇²×C₆₁	C₂×D₃	semidirect
12. D₂₁×C₆₁	C₂×C₇	semidirect
15. D₃×C₇×C₆₁	D₇	direct (N × H)
16. D₃×C₇×C₆₁	C₂×C₇	semidirect
17. C₃×D₇×C₆₁	C₂×C₇	semidirect
22. C₃×C₇×C₆₁	C₂×D₇	semidirect
23. C₃×C₇×C₆₁	C₂²×C₇	semidirect
30. D₇×C₆₁	D₃×C₇	direct (N × H)
32. D₃×C₇×D₇	C₆₁	direct (N × H)
34. C₇×C₆₁	D₃×D₇	direct (N × H)
35. C₇×C₆₁	C₂×D₃×C₇	semidirect
38. D₃×C₆₁	C₇×D₇	direct (N × H)
39. C₇×D₂₁	C₂×C₆₁	semidirect
40. D₃×C₇²	C₂×C₆₁	semidirect
41. C₃×C₇×D₇	C₂×C₆₁	semidirect
44. C₃×C₆₁	C₂×C₇×D₇	semidirect
45. C₃×C₇²	C₂²×C₆₁	semidirect
51. C₇×D₇	D₃×C₆₁	direct (N × H)
53. D₃×D₇	C₇×C₆₁	direct (N × H)
54. C₆₁	D₃×C₇×D₇	direct (N × H)
55. C₇²	C₂×D₃×C₆₁	semidirect
57. D₂₁	C₂×C₇×C₆₁	semidirect
58. C₃×D₇	C₂×C₇×C₆₁	semidirect
61. D₃×C₇	D₇×C₆₁	direct (N × H)
62. D₃×C₇	C₂×C₇×C₆₁	semidirect
66. C₃×C₇	C₂×D₇×C₆₁	semidirect
67. C₃×C₇	C₂²×C₇×C₆₁	semidirect
74. D₇	D₃×C₇×C₆₁	direct (N × H)
77. C₇	D₃×D₇×C₆₁	direct (N × H)
78. C₇	C₂×D₃×C₇×C₆₁	semidirect
81. D₃	C₇×D₇×C₆₁	direct (N × H)
83. C₃	C₂×C₇×D₇×C₆₁	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₇×D₇×C₆₁	2
D₃×C₇²×C₆₁	2
C₇×D₂₁×C₆₁	2
C₂×C₇×D₇×C₆₁	3
C₂×D₃×C₇×C₆₁	7
D₃×D₇×C₆₁	7
D₃×C₇×D₇	61

Subgroups — D3×C7×D7×C61 #49089979

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×C₇×D₇×C₆₁ #49089979