Subgroups — C₂×C₇×(C₄₃⋊C₃)⋊D₇ #38760505

Order 25284.

104 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	C₇×(C₄₃⋊C₃)⋊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	C₇	1	1	yes	maximal, characteristic, direct product factor
8	C₂×C₇×D₄₃⋊C₃	—	7	1	no	maximal
9	C₇²×C₄₃	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
10	C₂×C₇×C₄₃⋊C₃	—	2	3	no	—
11	C₂×C₇×C₄₃⋊C₃	D₇	1	1	yes	characteristic, complemented
12	C₂×C₇×C₄₃⋊C₃	C₂×C₇	1	1	yes	characteristic, complemented
13	(C₄₃⋊C₃)⋊D₇	C₂×C₇	1	2	yes	direct product factor
14	C₇×D₄₃⋊C₃	—	7	2	no	—
15	C₂×D₃₀₁	C₃×C₇	1	1	yes	characteristic, complemented
16	C₂×C₇×D₄₃	—	7	1	no	—
17	C₇×C₄₃⋊C₃	—	2	3	no	—
18	C₇×C₄₃⋊C₃	C₂×D₇	1	1	yes	characteristic, complemented
19	C₇×C₄₃⋊C₃	C₂²×C₇	1	1	yes	characteristic, complemented
20	C₂×C₇×C₄₃	—	2	3	no	—
21	C₂×C₇×C₄₃	C₃×D₇	1	1	yes	characteristic, complemented
22	C₂×C₇×C₄₃	C₂×C₃×C₇	1	1	yes	characteristic, complemented
23	D₃₀₁	C₂×C₃×C₇	1	2	yes	complemented
24	C₇×D₄₃	—	7	2	no	—
25	C₂×C₃×C₇×D₇	—	43	1	no	maximal, Hall
26	C₂×D₄₃⋊C₃	—	7	1	no	Hall
27	C₇×C₄₃	—	2	3	no	—
28	C₇×C₄₃	C₂×C₃×D₇	1	1	yes	characteristic, complemented
29	C₇×C₄₃	C₂²×C₃×C₇	1	1	yes	characteristic, complemented
30	C₂×C₃×C₇²	—	86	1	no	—
31	C₃×C₇×D₇	—	43	2	no	—
32	C₂×C₄₃⋊C₃	C₇×D₇	1	1	yes	characteristic, complemented
33	D₄₃⋊C₃	—	7	2	no	—
34	C₂×C₇×D₇	—	43	1	no	Hall
35	C₂×D₄₃	—	7	1	no	Hall
36	C₃×C₇²	—	86	1	no	Hall
37	C₄₃⋊C₃	C₂×C₇×D₇	1	1	yes	characteristic, complemented, Hall
38	C₂×C₇²	D₄₃⋊C₃	1	1	yes	characteristic, complemented
39	C₇×D₇	—	43	2	no	—
40	C₂×C₄₃	C₃×C₇×D₇	1	1	yes	characteristic, complemented
41	D₄₃	—	7	2	no	—
42	C₂²×C₃×C₇	—	301	1	no	—
43	C₂×C₃×D₇	—	43	1	no	—
44	C₇²	C₂×D₄₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
45	C₄₃	C₂×C₃×C₇×D₇	1	1	yes	characteristic, complemented, Sylow
46	C₂×C₃×C₇	—	301	2	no	—
47	C₂×C₃×C₇	—	86	3	no	—
48	C₂×C₃×C₇	—	86	1	no	—
49	C₂×C₃×C₇	—	86	1	no	—
50	C₃×D₇	—	43	2	no	—
51	C₂²×C₇	—	301	1	no	—
52	C₂×D₇	—	43	1	no	—
53	C₃×C₇	—	86	3	no	—
54	C₃×C₇	—	86	1	no	—
55	C₃×C₇	—	86	1	no	—
56	C₂×C₇	—	2	3	no	—
57	C₂×C₇	—	301	2	no	—
58	C₂×C₇	C₇×D₄₃⋊C₃	1	1	yes	characteristic, complemented
59	C₂×C₇	(C₄₃⋊C₃)⋊D₇	1	1	yes	characteristic, direct product factor
60	D₇	—	43	2	no	—
61	C₂²×C₃	—	301	1	no	Hall
62	C₇	—	2	3	no	—
63	C₇	C₂×C₇×D₄₃⋊C₃	1	1	yes	characteristic, complemented
64	C₇	C₂×(C₄₃⋊C₃)⋊D₇	1	1	yes	characteristic, direct product factor
65	C₂×C₃	—	301	2	no	—
66	C₂×C₃	—	86	1	no	—
67	C₂²	—	301	1	no	Sylow
68	C₃	—	86	1	no	Sylow
69	C₂	—	301	2	no	—
70	C₂	C₇×(C₄₃⋊C₃)⋊D₇	1	1	yes	characteristic, direct product factor

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

Complements

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

N	H ≅ G/N	type
1. C₂×C₇²×C₄₃⋊C₃	C₂	semidirect
2. C₇×(C₄₃⋊C₃)⋊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
7. C₂×(C₄₃⋊C₃)⋊D₇	C₇	direct (N × H)
9. C₇²×C₄₃	C₂²×C₃	semidirect
11. C₂×C₇×C₄₃⋊C₃	D₇	semidirect
12. C₂×C₇×C₄₃⋊C₃	C₂×C₇	semidirect
13. (C₄₃⋊C₃)⋊D₇	C₂×C₇	direct (N × H)
15. C₂×D₃₀₁	C₃×C₇	semidirect
18. C₇×C₄₃⋊C₃	C₂×D₇	semidirect
19. C₇×C₄₃⋊C₃	C₂²×C₇	semidirect
21. C₂×C₇×C₄₃	C₃×D₇	semidirect
22. C₂×C₇×C₄₃	C₂×C₃×C₇	semidirect
23. D₃₀₁	C₂×C₃×C₇	semidirect
28. C₇×C₄₃	C₂×C₃×D₇	semidirect
29. C₇×C₄₃	C₂²×C₃×C₇	semidirect
32. C₂×C₄₃⋊C₃	C₇×D₇	semidirect
37. C₄₃⋊C₃	C₂×C₇×D₇	semidirect
38. C₂×C₇²	D₄₃⋊C₃	semidirect
40. C₂×C₄₃	C₃×C₇×D₇	semidirect
44. C₇²	C₂×D₄₃⋊C₃	semidirect
45. C₄₃	C₂×C₃×C₇×D₇	semidirect
58. C₂×C₇	C₇×D₄₃⋊C₃	semidirect
59. C₂×C₇	(C₄₃⋊C₃)⋊D₇	direct (N × H)
63. C₇	C₂×C₇×D₄₃⋊C₃	semidirect
64. C₇	C₂×(C₄₃⋊C₃)⋊D₇	direct (N × H)
70. C₂	C₇×(C₄₃⋊C₃)⋊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
C₇×(C₄₃⋊C₃)⋊D₇	2
C₂×C₇×D₃₀₁	3
C₂×(C₄₃⋊C₃)⋊D₇	7
C₂×C₇×D₄₃⋊C₃	7
C₂×C₃×C₇×D₇	43

Subgroups — C2×C7×(C43⋊C3)⋊D7 #38760505

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×(C₄₃⋊C₃)⋊D₇ #38760505