Subgroups — C₂×D₇×(C₄₃⋊C₃)⋊C₇ #38760389

Order 25284.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×(C₄₃⋊C₃)⋊C₇	C₂	1	1	yes	maximal, characteristic, complemented
2	D₇×(C₄₃⋊C₃)⋊C₇	C₂	1	2	yes	maximal, direct product factor
3	C₂×D₇×C₄₃⋊C₇	C₃	1	1	yes	maximal, characteristic, complemented, Hall
4	C₇×(C₄₃⋊C₃)⋊C₇	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₇×C₄₃⋊C₇	C₂×C₃	1	1	yes	characteristic, complemented
6	D₇×C₄₃⋊C₇	C₂×C₃	1	2	yes	complemented
7	C₂×D₇×C₄₃⋊C₃	C₇	1	1	yes	maximal, characteristic, complemented
8	C₂²×(C₄₃⋊C₃)⋊C₇	—	7	1	no	maximal
9	C₇×C₄₃⋊C₇	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
10	C₂×C₇×C₄₃⋊C₃	C₂×C₇	1	1	yes	characteristic, complemented
11	D₇×C₄₃⋊C₃	C₂×C₇	1	2	yes	complemented
12	C₂×(C₄₃⋊C₃)⋊C₇	—	2	3	no	—
13	C₂×(C₄₃⋊C₃)⋊C₇	—	7	2	no	—
14	C₂×(C₄₃⋊C₃)⋊C₇	D₇	1	1	yes	characteristic, direct product factor
15	C₂×D₇×C₄₃	C₃×C₇	1	1	yes	characteristic, complemented
16	C₂²×C₄₃⋊C₇	—	7	1	no	—
17	C₇×C₄₃⋊C₃	C₂²×C₇	1	1	yes	characteristic, complemented
18	(C₄₃⋊C₃)⋊C₇	—	2	3	no	—
19	(C₄₃⋊C₃)⋊C₇	C₂×D₇	1	1	yes	characteristic, direct product factor
20	C₂×C₇×C₄₃	C₂×C₃×C₇	1	1	yes	characteristic, complemented
21	D₇×C₄₃	C₂×C₃×C₇	1	2	yes	complemented
22	C₂×C₄₃⋊C₇	—	2	3	no	—
23	C₂×C₄₃⋊C₇	—	7	2	no	—
24	C₂×C₄₃⋊C₇	C₃×D₇	1	1	yes	characteristic, complemented
25	C₂×C₃×C₇×D₇	—	43	1	no	maximal, Hall
26	C₂²×C₄₃⋊C₃	—	7	1	no	Hall
27	C₇×C₄₃	C₂²×C₃×C₇	1	1	yes	characteristic, complemented
28	C₄₃⋊C₇	—	2	3	no	—
29	C₄₃⋊C₇	C₂×C₃×D₇	1	1	yes	characteristic, complemented
30	C₂×C₃×C₇²	—	43	1	no	—
31	C₃×C₇×D₇	—	43	2	no	—
32	C₂×C₄₃⋊C₃	—	7	2	no	—
33	C₂×C₄₃⋊C₃	C₇×D₇	1	1	yes	characteristic, complemented
34	C₂×C₇×D₇	—	43	1	no	Hall
35	C₂²×C₄₃	—	7	1	no	Hall
36	C₃×C₇²	—	43	1	no	Hall
37	C₄₃⋊C₃	C₂×C₇×D₇	1	1	yes	characteristic, complemented, Hall
38	C₂×C₇²	—	43	1	no	—
39	C₇×D₇	—	43	2	no	—
40	C₂×C₄₃	—	7	2	no	—
41	C₂×C₄₃	C₃×C₇×D₇	1	1	yes	characteristic, complemented
42	C₂²×C₃×C₇	—	301	1	no	—
43	C₂×C₃×D₇	—	43	1	no	—
44	C₇²	—	43	1	no	Sylow
45	C₄₃	C₂×C₃×C₇×D₇	1	1	yes	characteristic, complemented, Sylow
46	C₂×C₃×C₇	—	43	1	no	—
47	C₂×C₃×C₇	—	43	1	no	—
48	C₂×C₃×C₇	—	301	2	no	—
49	C₂×C₃×C₇	—	86	3	no	—
50	C₃×D₇	—	43	2	no	—
51	C₂²×C₇	—	301	1	no	—
52	C₂×D₇	(C₄₃⋊C₃)⋊C₇	1	1	yes	characteristic, direct product factor
53	C₃×C₇	—	43	1	no	—
54	C₃×C₇	—	43	1	no	—
55	C₃×C₇	—	86	3	no	—
56	C₂×C₇	—	43	1	no	—
57	C₂×C₇	—	301	2	no	—
58	C₂×C₇	—	86	3	no	—
59	C₂×C₇	C₂×(C₄₃⋊C₃)⋊C₇	1	1	yes	characteristic, complemented
60	D₇	C₂×(C₄₃⋊C₃)⋊C₇	1	2	yes	direct product factor
61	C₂²×C₃	—	301	1	no	Hall
62	C₇	—	43	1	no	—
63	C₇	—	86	3	no	—
64	C₇	C₂²×(C₄₃⋊C₃)⋊C₇	1	1	yes	characteristic, complemented
65	C₂×C₃	—	43	1	no	—
66	C₂×C₃	—	301	2	no	—
67	C₂²	—	7	1	no	Sylow
68	C₃	—	43	1	no	Sylow
69	C₂	—	7	2	no	—
70	C₂	D₇×(C₄₃⋊C₃)⋊C₇	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	D₇×(C₄₃⋊C₃)⋊C₇
commutator, cosocle, hypocenter	C₇×C₄₃	C₂²×C₃×C₇
Frattini	C₁	G
Fitting, socle	C₂×C₇×C₄₃	C₂×C₃×C₇
LCS	G ▷ C₇×C₄₃
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
1. C₂×C₇×(C₄₃⋊C₃)⋊C₇	C₂	semidirect
2. D₇×(C₄₃⋊C₃)⋊C₇	C₂	direct (N × H)
3. C₂×D₇×C₄₃⋊C₇	C₃	semidirect
4. C₇×(C₄₃⋊C₃)⋊C₇	C₂²	semidirect
5. C₂×C₇×C₄₃⋊C₇	C₂×C₃	semidirect
6. D₇×C₄₃⋊C₇	C₂×C₃	semidirect
7. C₂×D₇×C₄₃⋊C₃	C₇	semidirect
9. C₇×C₄₃⋊C₇	C₂²×C₃	semidirect
10. C₂×C₇×C₄₃⋊C₃	C₂×C₇	semidirect
11. D₇×C₄₃⋊C₃	C₂×C₇	semidirect
14. C₂×(C₄₃⋊C₃)⋊C₇	D₇	direct (N × H)
15. C₂×D₇×C₄₃	C₃×C₇	semidirect
17. C₇×C₄₃⋊C₃	C₂²×C₇	semidirect
19. (C₄₃⋊C₃)⋊C₇	C₂×D₇	direct (N × H)
20. C₂×C₇×C₄₃	C₂×C₃×C₇	semidirect
21. D₇×C₄₃	C₂×C₃×C₇	semidirect
24. C₂×C₄₃⋊C₇	C₃×D₇	semidirect
27. C₇×C₄₃	C₂²×C₃×C₇	semidirect
29. C₄₃⋊C₇	C₂×C₃×D₇	semidirect
33. C₂×C₄₃⋊C₃	C₇×D₇	semidirect
37. C₄₃⋊C₃	C₂×C₇×D₇	semidirect
41. C₂×C₄₃	C₃×C₇×D₇	semidirect
45. C₄₃	C₂×C₃×C₇×D₇	semidirect
52. C₂×D₇	(C₄₃⋊C₃)⋊C₇	direct (N × H)
59. C₂×C₇	C₂×(C₄₃⋊C₃)⋊C₇	semidirect
60. D₇	C₂×(C₄₃⋊C₃)⋊C₇	direct (N × H)
64. C₇	C₂²×(C₄₃⋊C₃)⋊C₇	semidirect
70. C₂	D₇×(C₄₃⋊C₃)⋊C₇	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₇×(C₄₃⋊C₃)⋊C₇	2
D₇×(C₄₃⋊C₃)⋊C₇	2
C₂×D₇×C₄₃⋊C₇	3
C₂×D₇×C₄₃⋊C₃	7
C₂²×(C₄₃⋊C₃)⋊C₇	7
C₂×C₃×C₇×D₇	43

Subgroups — C2×D7×(C43⋊C3)⋊C7 #38760389

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₇×(C₄₃⋊C₃)⋊C₇ #38760389