Subgroups — C₂×C₇×D₈₆₁ #37563176

Order 24108.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×D₈₆₁	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃×C₇²×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₇×D₂₈₇	—	3	1	no	maximal, Hall
4	C₃×C₇²×C₄₁	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₇×D₂₈₇	—	3	2	no	—
6	C₂×C₇²×C₄₁	D₃	1	1	yes	characteristic, complemented
7	C₂×D₈₆₁	C₇	1	1	yes	maximal, characteristic, direct product factor
8	C₂×C₇×D₁₂₃	—	7	1	no	maximal
9	C₇²×C₄₁	C₂×D₃	1	1	yes	characteristic, complemented, Hall
10	C₂×C₃×C₇×C₄₁	—	2	3	no	—
11	C₂×C₃×C₇×C₄₁	D₇	1	1	yes	characteristic, complemented
12	C₂×C₃×C₇×C₄₁	C₂×C₇	1	1	yes	characteristic, complemented
13	D₈₆₁	C₂×C₇	1	2	yes	direct product factor
14	C₇×D₁₂₃	—	7	2	no	—
15	C₂×D₂₈₇	—	3	1	no	—
16	C₂×C₇×D₄₁	—	21	1	no	—
17	C₃×C₇×C₄₁	—	2	3	no	—
18	C₃×C₇×C₄₁	C₂×D₇	1	1	yes	characteristic, complemented
19	C₃×C₇×C₄₁	C₂²×C₇	1	1	yes	characteristic, complemented
20	C₂×C₇×D₂₁	—	41	1	no	maximal, Hall
21	C₂×C₇×C₄₁	—	2	3	no	—
22	C₂×C₇×C₄₁	D₃×C₇	1	1	yes	characteristic, complemented
23	C₂×C₇×C₄₁	D₂₁	1	1	yes	characteristic, complemented
24	D₂₈₇	—	3	2	no	—
25	C₇×D₄₁	—	21	2	no	—
26	C₂×D₁₂₃	—	7	1	no	Hall
27	C₂×C₃×C₇²	D₄₁	1	1	yes	characteristic, complemented
28	C₇×D₂₁	—	41	2	no	—
29	C₇×C₄₁	—	2	3	no	—
30	C₇×C₄₁	C₂×D₃×C₇	1	1	yes	characteristic, complemented
31	C₇×C₄₁	C₂×D₂₁	1	1	yes	characteristic, complemented
32	C₂×C₃×C₄₁	C₇×D₇	1	1	yes	characteristic, complemented
33	D₁₂₃	—	7	2	no	—
34	C₂×C₇×D₇	—	123	1	no	Hall
35	C₂×D₄₁	—	21	1	no	Hall
36	C₃×C₇²	C₂×D₄₁	1	1	yes	characteristic, complemented, Hall
37	C₃×C₄₁	C₂×C₇×D₇	1	1	yes	characteristic, complemented, Hall
38	C₂×C₇²	D₁₂₃	1	1	yes	characteristic, complemented
39	C₇×D₇	—	123	2	no	—
40	C₂×D₂₁	—	41	1	no	—
41	C₂×D₃×C₇	—	287	1	no	—
42	C₂×C₄₁	C₇×D₂₁	1	1	yes	characteristic, complemented
43	D₄₁	—	21	2	no	—
44	C₇²	C₂×D₁₂₃	1	1	yes	characteristic, complemented, Sylow
45	C₂×C₃×C₇	—	2	3	no	—
46	C₂×C₃×C₇	C₇×D₄₁	1	1	yes	characteristic, complemented
47	C₂×C₃×C₇	D₂₈₇	1	1	yes	characteristic, complemented
48	D₂₁	—	41	2	no	—
49	D₃×C₇	—	287	2	no	—
50	C₄₁	C₂×C₇×D₂₁	1	1	yes	characteristic, complemented, Sylow
51	C₂²×C₇	—	861	1	no	—
52	C₂×D₇	—	123	1	no	—
53	C₃×C₇	—	2	3	no	—
54	C₃×C₇	C₂×C₇×D₄₁	1	1	yes	characteristic, complemented
55	C₃×C₇	C₂×D₂₈₇	1	1	yes	characteristic, complemented
56	C₂×C₇	—	2	3	no	—
57	C₂×C₇	—	861	2	no	—
58	C₂×C₇	C₇×D₁₂₃	1	1	yes	characteristic, complemented
59	C₂×C₇	D₈₆₁	1	1	yes	characteristic, direct product factor
60	D₇	—	123	2	no	—
61	C₂×D₃	—	287	1	no	Hall
62	C₇	—	2	3	no	—
63	C₇	C₂×C₇×D₁₂₃	1	1	yes	characteristic, complemented
64	C₇	C₂×D₈₆₁	1	1	yes	characteristic, direct product factor
65	C₂×C₃	C₇×D₂₈₇	1	1	yes	characteristic, complemented
66	D₃	—	287	2	no	—
67	C₂²	—	861	1	no	Sylow
68	C₃	C₂×C₇×D₂₈₇	1	1	yes	characteristic, complemented, Sylow
69	C₂	—	861	2	no	—
70	C₂	C₇×D₈₆₁	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₇	D₈₆₁
commutator, cosocle, hypocenter	C₃×C₇×C₄₁	C₂²×C₇
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₇²×C₄₁	C₂
LCS	G ▷ C₃×C₇×C₄₁
UCS	C₁ ◁ C₂×C₇

Complements

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

N	H ≅ G/N	type
1. C₇×D₈₆₁	C₂	direct (N × H)
2. C₂×C₃×C₇²×C₄₁	C₂	semidirect
4. C₃×C₇²×C₄₁	C₂²	semidirect
6. C₂×C₇²×C₄₁	D₃	semidirect
7. C₂×D₈₆₁	C₇	direct (N × H)
9. C₇²×C₄₁	C₂×D₃	semidirect
11. C₂×C₃×C₇×C₄₁	D₇	semidirect
12. C₂×C₃×C₇×C₄₁	C₂×C₇	semidirect
13. D₈₆₁	C₂×C₇	direct (N × H)
18. C₃×C₇×C₄₁	C₂×D₇	semidirect
19. C₃×C₇×C₄₁	C₂²×C₇	semidirect
22. C₂×C₇×C₄₁	D₃×C₇	semidirect
23. C₂×C₇×C₄₁	D₂₁	semidirect
27. C₂×C₃×C₇²	D₄₁	semidirect
30. C₇×C₄₁	C₂×D₃×C₇	semidirect
31. C₇×C₄₁	C₂×D₂₁	semidirect
32. C₂×C₃×C₄₁	C₇×D₇	semidirect
36. C₃×C₇²	C₂×D₄₁	semidirect
37. C₃×C₄₁	C₂×C₇×D₇	semidirect
38. C₂×C₇²	D₁₂₃	semidirect
42. C₂×C₄₁	C₇×D₂₁	semidirect
44. C₇²	C₂×D₁₂₃	semidirect
46. C₂×C₃×C₇	C₇×D₄₁	semidirect
47. C₂×C₃×C₇	D₂₈₇	semidirect
50. C₄₁	C₂×C₇×D₂₁	semidirect
54. C₃×C₇	C₂×C₇×D₄₁	semidirect
55. C₃×C₇	C₂×D₂₈₇	semidirect
58. C₂×C₇	C₇×D₁₂₃	semidirect
59. C₂×C₇	D₈₆₁	direct (N × H)
63. C₇	C₂×C₇×D₁₂₃	semidirect
64. C₇	C₂×D₈₆₁	direct (N × H)
65. C₂×C₃	C₇×D₂₈₇	semidirect
68. C₃	C₂×C₇×D₂₈₇	semidirect
70. C₂	C₇×D₈₆₁	direct (N × H)

Maximal subgroups

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

subgroup	index
C₇×D₈₆₁	2
C₂×C₃×C₇²×C₄₁	2
C₂×C₇×D₂₈₇	3
C₂×D₈₆₁	7
C₂×C₇×D₁₂₃	7
C₂×C₇×D₂₁	41

Subgroups — C2×C7×D861 #37563176

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×D₈₆₁ #37563176