Subgroups — C₂×(C₄₃⋊C₃)⋊(C₇⋊D₇) #38760534

Order 25284.

200 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇²×C₄₃⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
2	(C₄₃⋊C₃)⋊(C₇⋊D₇)	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₇⋊D₃₀₁	C₃	1	1	yes	maximal, characteristic, complemented, Hall
4	C₇²×C₄₃⋊C₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₇⋊D₃₀₁	C₂×C₃	1	2	yes	complemented
6	C₂×C₇²×C₄₃	C₂×C₃	1	1	yes	characteristic, complemented
7	C₂×(C₄₃⋊C₃)⋊D₇	—	7	1	no	maximal
8	C₂×(C₄₃⋊C₃)⋊D₇	—	7	7	no	maximal
9	C₇²×C₄₃	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
10	C₂×C₇×C₄₃⋊C₃	D₇	1	1	yes	characteristic, complemented
11	C₂×C₇×C₄₃⋊C₃	D₇	1	7	yes	complemented
12	(C₄₃⋊C₃)⋊D₇	—	7	2	no	—
13	(C₄₃⋊C₃)⋊D₇	—	7	14	no	—
14	C₂×D₃₀₁	—	7	1	no	—
15	C₂×D₃₀₁	—	7	7	no	—
16	C₇×C₄₃⋊C₃	C₂×D₇	1	1	yes	characteristic, complemented
17	C₇×C₄₃⋊C₃	C₂×D₇	1	7	yes	complemented
18	C₂×C₇×C₄₃	C₃×D₇	1	1	yes	characteristic, complemented
19	C₂×C₇×C₄₃	C₃×D₇	1	7	yes	complemented
20	D₃₀₁	—	7	2	no	—
21	D₃₀₁	—	7	14	no	—
22	C₂×C₃×C₇⋊D₇	—	43	1	no	maximal, Hall
23	C₂×D₄₃⋊C₃	—	49	1	no	Hall
24	C₇×C₄₃	C₂×C₃×D₇	1	1	yes	characteristic, complemented
25	C₇×C₄₃	C₂×C₃×D₇	1	7	yes	complemented
26	C₂×C₃×C₇²	—	86	1	no	—
27	C₃×C₇⋊D₇	—	43	2	no	—
28	C₂×C₄₃⋊C₃	C₇⋊D₇	1	1	yes	characteristic, complemented
29	D₄₃⋊C₃	—	49	2	no	—
30	C₂×C₇⋊D₇	—	43	1	no	Hall
31	C₂×D₄₃	—	49	1	no	Hall
32	C₃×C₇²	—	86	1	no	Hall
33	C₄₃⋊C₃	C₂×C₇⋊D₇	1	1	yes	characteristic, complemented, Hall
34	C₂×C₇²	D₄₃⋊C₃	1	1	yes	characteristic, complemented
35	C₇⋊D₇	—	43	2	no	—
36	C₂×C₄₃	C₃×C₇⋊D₇	1	1	yes	characteristic, complemented
37	D₄₃	—	49	2	no	—
38	C₂×C₃×D₇	—	301	1	no	—
39	C₂×C₃×D₇	—	301	7	no	—
40	C₇²	C₂×D₄₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
41	C₄₃	C₂×C₃×C₇⋊D₇	1	1	yes	characteristic, complemented, Sylow
42	C₂×C₃×C₇	—	43	1	no	—
43	C₂×C₃×C₇	—	86	7	no	—
44	C₃×D₇	—	301	2	no	—
45	C₃×D₇	—	301	14	no	—
46	C₂×D₇	—	301	1	no	—
47	C₂×D₇	—	301	7	no	—
48	C₃×C₇	—	43	1	no	—
49	C₃×C₇	—	86	7	no	—
50	C₂×C₇	(C₄₃⋊C₃)⋊D₇	1	1	yes	characteristic, complemented
51	C₂×C₇	(C₄₃⋊C₃)⋊D₇	1	7	yes	complemented
52	D₇	—	301	2	no	—
53	D₇	—	301	14	no	—
54	C₂²×C₃	—	2107	1	no	Hall
55	C₇	C₂×(C₄₃⋊C₃)⋊D₇	1	1	yes	characteristic, complemented
56	C₇	C₂×(C₄₃⋊C₃)⋊D₇	1	7	yes	complemented
57	C₂×C₃	—	2107	2	no	—
58	C₂×C₃	—	86	1	no	—
59	C₂²	—	2107	1	no	Sylow
60	C₃	—	86	1	no	Sylow
61	C₂	—	2107	2	no	—
62	C₂	(C₄₃⋊C₃)⋊(C₇⋊D₇)	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	(C₄₃⋊C₃)⋊(C₇⋊D₇)
commutator, cosocle, hypocenter	C₇²×C₄₃	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₂×C₇²×C₄₃	C₂×C₃
LCS	G ▷ C₇²×C₄₃
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
1. C₂×C₇²×C₄₃⋊C₃	C₂	semidirect
2. (C₄₃⋊C₃)⋊(C₇⋊D₇)	C₂	direct (N × H)
3. C₂×C₇⋊D₃₀₁	C₃	semidirect
4. C₇²×C₄₃⋊C₃	C₂²	semidirect
5. C₇⋊D₃₀₁	C₂×C₃	semidirect
6. C₂×C₇²×C₄₃	C₂×C₃	semidirect
9. C₇²×C₄₃	C₂²×C₃	semidirect
10. C₂×C₇×C₄₃⋊C₃	D₇	semidirect
11. C₂×C₇×C₄₃⋊C₃	D₇	semidirect
16. C₇×C₄₃⋊C₃	C₂×D₇	semidirect
17. C₇×C₄₃⋊C₃	C₂×D₇	semidirect
18. C₂×C₇×C₄₃	C₃×D₇	semidirect
19. C₂×C₇×C₄₃	C₃×D₇	semidirect
24. C₇×C₄₃	C₂×C₃×D₇	semidirect
25. C₇×C₄₃	C₂×C₃×D₇	semidirect
28. C₂×C₄₃⋊C₃	C₇⋊D₇	semidirect
33. C₄₃⋊C₃	C₂×C₇⋊D₇	semidirect
34. C₂×C₇²	D₄₃⋊C₃	semidirect
36. C₂×C₄₃	C₃×C₇⋊D₇	semidirect
40. C₇²	C₂×D₄₃⋊C₃	semidirect
41. C₄₃	C₂×C₃×C₇⋊D₇	semidirect
50. C₂×C₇	(C₄₃⋊C₃)⋊D₇	semidirect
51. C₂×C₇	(C₄₃⋊C₃)⋊D₇	semidirect
55. C₇	C₂×(C₄₃⋊C₃)⋊D₇	semidirect
56. C₇	C₂×(C₄₃⋊C₃)⋊D₇	semidirect
62. C₂	(C₄₃⋊C₃)⋊(C₇⋊D₇)	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×C₇²×C₄₃⋊C₃	2
(C₄₃⋊C₃)⋊(C₇⋊D₇)	2
C₂×C₇⋊D₃₀₁	3
C₂×(C₄₃⋊C₃)⋊D₇	7
C₂×C₃×C₇⋊D₇	43

Subgroups — C2×(C43⋊C3)⋊(C7⋊D7) #38760534

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×(C₄₃⋊C₃)⋊(C₇⋊D₇) #38760534