Subgroups — C₇⋊D₇×D₄₃⋊C₃ #38760479

Order 25284.

200 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇⋊D₇×C₄₃⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
2	(C₄₃⋊C₃)⋊(C₇⋊D₇)	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇²×D₄₃⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
4	D₄₃×C₇⋊D₇	C₃	1	1	yes	maximal, characteristic, complemented, Hall
5	C₇²×C₄₃⋊C₃	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₇⋊D₃₀₁	C₂×C₃	1	1	yes	characteristic, complemented
7	C₄₃×C₇⋊D₇	C₂×C₃	1	1	yes	characteristic, complemented
8	C₇²×D₄₃	C₂×C₃	1	1	yes	characteristic, complemented
9	D₇×D₄₃⋊C₃	—	7	8	no	maximal
10	C₇²×C₄₃	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
11	(C₄₃⋊C₃)⋊D₇	—	7	8	no	—
12	D₇×C₄₃⋊C₃	—	7	8	no	—
13	C₇×D₄₃⋊C₃	D₇	1	8	yes	complemented
14	D₇×D₄₃	—	7	8	no	—
15	C₇×C₄₃⋊C₃	C₂×D₇	1	8	yes	complemented
16	D₃₀₁	—	7	8	no	—
17	C₇×D₄₃	C₃×D₇	1	8	yes	complemented
18	D₇×C₄₃	—	7	8	no	—
19	C₂×C₃×C₇⋊D₇	—	43	1	no	maximal, Hall
20	C₂×D₄₃⋊C₃	—	49	1	no	Hall
21	C₇×C₄₃	C₂×C₃×D₇	1	8	yes	complemented
22	C₂×C₃×C₇²	—	43	1	no	—
23	C₃×C₇⋊D₇	—	43	1	no	—
24	C₃×C₇⋊D₇	—	86	1	no	—
25	C₂×C₄₃⋊C₃	—	49	1	no	—
26	D₄₃⋊C₃	—	49	1	no	—
27	D₄₃⋊C₃	C₇⋊D₇	1	1	yes	characteristic, direct product factor
28	C₂×C₇⋊D₇	—	43	1	no	Hall
29	C₂×D₄₃	—	49	1	no	Hall
30	C₃×C₇²	—	86	1	no	Hall
31	C₄₃⋊C₃	C₂×C₇⋊D₇	1	1	yes	characteristic, complemented, Hall
32	C₂×C₇²	—	43	1	no	—
33	C₇⋊D₇	—	43	1	no	—
34	C₇⋊D₇	D₄₃⋊C₃	1	1	yes	characteristic, direct product factor
35	C₂×C₄₃	—	49	1	no	—
36	D₄₃	—	49	1	no	—
37	D₄₃	C₃×C₇⋊D₇	1	1	yes	characteristic, complemented
38	C₂×C₃×D₇	—	301	8	no	—
39	C₇²	C₂×D₄₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
40	C₄₃	C₂×C₃×C₇⋊D₇	1	1	yes	characteristic, complemented, Sylow
41	C₂×C₃×C₇	—	43	8	no	—
42	C₃×D₇	—	301	8	no	—
43	C₃×D₇	—	602	8	no	—
44	C₂×D₇	—	301	8	no	—
45	C₃×C₇	—	86	8	no	—
46	C₂×C₇	—	43	8	no	—
47	D₇	—	7	8	no	—
48	D₇	—	301	8	no	—
49	C₂²×C₃	—	2107	1	no	Hall
50	C₇	D₇×D₄₃⋊C₃	1	8	yes	complemented
51	C₂×C₃	—	43	1	no	—
52	C₂×C₃	—	2107	1	no	—
53	C₂×C₃	—	4214	1	no	—
54	C₂²	—	2107	1	no	Sylow
55	C₃	—	86	1	no	Sylow
56	C₂	—	43	1	no	—
57	C₂	—	49	1	no	—
58	C₂	—	2107	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₇²×C₄₃	C₂²×C₃
LCS	G ▷ C₇²×C₄₃
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₇⋊D₇×C₄₃⋊C₃	C₂	semidirect
2. (C₄₃⋊C₃)⋊(C₇⋊D₇)	C₂	semidirect
3. C₇²×D₄₃⋊C₃	C₂	semidirect
4. D₄₃×C₇⋊D₇	C₃	semidirect
5. C₇²×C₄₃⋊C₃	C₂²	semidirect
6. C₇⋊D₃₀₁	C₂×C₃	semidirect
7. C₄₃×C₇⋊D₇	C₂×C₃	semidirect
8. C₇²×D₄₃	C₂×C₃	semidirect
10. C₇²×C₄₃	C₂²×C₃	semidirect
13. C₇×D₄₃⋊C₃	D₇	semidirect
15. C₇×C₄₃⋊C₃	C₂×D₇	semidirect
17. C₇×D₄₃	C₃×D₇	semidirect
21. C₇×C₄₃	C₂×C₃×D₇	semidirect
27. D₄₃⋊C₃	C₇⋊D₇	direct (N × H)
31. C₄₃⋊C₃	C₂×C₇⋊D₇	semidirect
34. C₇⋊D₇	D₄₃⋊C₃	direct (N × H)
37. D₄₃	C₃×C₇⋊D₇	semidirect
39. C₇²	C₂×D₄₃⋊C₃	semidirect
40. C₄₃	C₂×C₃×C₇⋊D₇	semidirect
50. C₇	D₇×D₄₃⋊C₃	semidirect

Maximal subgroups

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

subgroup	index
C₇⋊D₇×C₄₃⋊C₃	2
(C₄₃⋊C₃)⋊(C₇⋊D₇)	2
C₇²×D₄₃⋊C₃	2
D₄₃×C₇⋊D₇	3
D₇×D₄₃⋊C₃	7
C₂×C₃×C₇⋊D₇	43

Subgroups — C7⋊D7×D43⋊C3 #38760479

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇⋊D₇×D₄₃⋊C₃ #38760479