Subgroups — C₇×C₃⋊(Dic₄₃⋊C₇) #38760293

Order 25284.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₇×C₄₃⋊C₇	C₂	1	1	yes	maximal, characteristic
2	C₇×Dic₄₃⋊C₇	—	3	1	no	maximal, Hall
3	C₃×C₇×C₄₃⋊C₇	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₇×C₄₃⋊C₇	D₃	1	1	yes	characteristic
5	C₇×Dic₁₂₉	C₇	1	1	yes	maximal, characteristic, complemented
6	C₃⋊(Dic₄₃⋊C₇)	C₇	1	7	yes	maximal, direct product factor
7	C₇×C₄₃⋊C₇	Dic₃	1	1	yes	characteristic, complemented, Hall
8	C₂×C₃×C₇×C₄₃	C₂×C₇	1	1	yes	characteristic
9	C₂×C₃×C₄₃⋊C₇	C₂×C₇	1	7	yes	—
10	C₇×Dic₄₃	—	3	1	no	—
11	Dic₄₃⋊C₇	—	3	7	no	—
12	C₃×C₇×C₄₃	C₄×C₇	1	1	yes	characteristic, complemented
13	C₃×C₄₃⋊C₇	C₄×C₇	1	7	yes	complemented
14	C₂×C₇×C₄₃	D₃×C₇	1	1	yes	characteristic
15	C₂×C₄₃⋊C₇	D₃×C₇	1	7	yes	—
16	C₇²×Dic₃	—	43	1	no	maximal, Hall
17	Dic₁₂₉	C₇²	1	1	yes	characteristic, complemented, Hall
18	C₇×C₄₃	C₇×Dic₃	1	1	yes	characteristic, complemented
19	C₄₃⋊C₇	C₇×Dic₃	1	7	yes	complemented
20	C₂×C₃×C₇²	—	43	1	no	—
21	C₂×C₃×C₄₃	C₂×C₇²	1	1	yes	characteristic
22	C₄×C₇²	—	129	1	no	Hall
23	Dic₄₃	—	3	1	no	Hall
24	C₃×C₇²	—	43	1	no	Hall
25	C₃×C₄₃	C₄×C₇²	1	1	yes	characteristic, complemented, Hall
26	C₂×C₇²	—	43	1	no	—
27	C₂×C₄₃	D₃×C₇²	1	1	yes	characteristic
28	C₇×Dic₃	—	43	7	no	—
29	C₇×Dic₃	—	301	1	no	—
30	C₇²	—	43	1	no	Sylow
31	C₄₃	C₇²×Dic₃	1	1	yes	characteristic, complemented, Sylow
32	C₂×C₃×C₇	—	43	7	no	—
33	C₂×C₃×C₇	D₄₃⋊C₇	1	1	yes	characteristic
34	C₄×C₇	—	129	7	no	—
35	C₄×C₇	—	903	1	no	—
36	C₃×C₇	—	43	7	no	—
37	C₃×C₇	Dic₄₃⋊C₇	1	1	yes	characteristic, complemented
38	C₂×C₇	—	43	7	no	—
39	C₂×C₇	C₃⋊(D₄₃⋊C₇)	1	1	yes	characteristic
40	Dic₃	—	301	1	no	Hall
41	C₇	—	43	7	no	—
42	C₇	C₃⋊(Dic₄₃⋊C₇)	1	1	yes	characteristic, direct product factor
43	C₂×C₃	C₇×D₄₃⋊C₇	1	1	yes	characteristic
44	C₄	—	903	1	no	Sylow
45	C₃	C₇×Dic₄₃⋊C₇	1	1	yes	characteristic, complemented, Sylow
46	C₂	C₇×C₃⋊(D₄₃⋊C₇)	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₇	C₃⋊(D₄₃⋊C₇)
commutator, hypocenter	C₃×C₄₃	C₄×C₇²
Frattini	C₂	C₇×C₃⋊(D₄₃⋊C₇)
Fitting, socle	C₂×C₃×C₇×C₄₃	C₂×C₇
prime radical	C₂×C₃×C₇×C₄₃⋊C₇	C₂
cosocle	C₂×C₃×C₄₃	C₂×C₇²
LCS	G ▷ C₃×C₄₃
UCS	C₁ ◁ C₂×C₇

Complements

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

N	H ≅ G/N	type
3. C₃×C₇×C₄₃⋊C₇	C₄	semidirect
5. C₇×Dic₁₂₉	C₇	semidirect
6. C₃⋊(Dic₄₃⋊C₇)	C₇	direct (N × H)
7. C₇×C₄₃⋊C₇	Dic₃	semidirect
12. C₃×C₇×C₄₃	C₄×C₇	semidirect
13. C₃×C₄₃⋊C₇	C₄×C₇	semidirect
17. Dic₁₂₉	C₇²	semidirect
18. C₇×C₄₃	C₇×Dic₃	semidirect
19. C₄₃⋊C₇	C₇×Dic₃	semidirect
25. C₃×C₄₃	C₄×C₇²	semidirect
31. C₄₃	C₇²×Dic₃	semidirect
37. C₃×C₇	Dic₄₃⋊C₇	semidirect
42. C₇	C₃⋊(Dic₄₃⋊C₇)	direct (N × H)
45. C₃	C₇×Dic₄₃⋊C₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×C₇×C₄₃⋊C₇	2
C₇×Dic₄₃⋊C₇	3
C₇×Dic₁₂₉	7
C₃⋊(Dic₄₃⋊C₇)	7
C₇²×Dic₃	43

Subgroups — C7×C3⋊(Dic43⋊C7) #38760293

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×C₃⋊(Dic₄₃⋊C₇) #38760293