Subgroups — D₇×C₄₃×C₇⋊C₉ #49181586

Order 37926.

52 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₄₃×C₇⋊C₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×C₇×D₇×C₄₃	C₃	1	1	yes	maximal, characteristic
3	C₃×C₇²×C₄₃	C₂×C₃	1	1	yes	characteristic
4	C₉×D₇×C₄₃	—	7	1	no	maximal
5	C₂×C₄₃×C₇⋊C₉	—	7	1	no	maximal
6	C₇×D₇×C₄₃	C₉	1	1	yes	characteristic, complemented, Hall
7	C₄₃×C₇⋊C₉	D₇	1	1	yes	characteristic, direct product factor
8	C₇×C₉×C₄₃	—	7	1	no	—
9	C₇²×C₄₃	C₂×C₉	1	1	yes	characteristic, complemented, Hall
10	C₂×C₃×C₇×C₄₃	—	7	1	no	—
11	C₃×D₇×C₄₃	ΓL(1,𝔽₈)	1	1	yes	characteristic
12	C₃×C₇×C₄₃	—	6	1	no	—
13	C₃×C₇×C₄₃	C₂×ΓL(1,𝔽₈)	1	1	yes	characteristic
14	C₃×C₇×C₄₃	C₃×D₇	1	1	yes	characteristic
15	D₇×C₇⋊C₉	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Hall
16	C₂×C₉×C₄₃	—	49	1	no	Hall
17	C₂×C₇×C₄₃	—	7	1	no	—
18	D₇×C₄₃	C₇⋊C₉	1	1	yes	characteristic, direct product factor
19	C₇×C₇⋊C₉	C₂×C₄₃	1	1	yes	characteristic, complemented, Hall
20	C₉×C₄₃	—	7	1	no	Hall
21	C₇×C₄₃	—	6	1	no	—
22	C₇×C₄₃	C₂×C₇⋊C₉	1	1	yes	characteristic, complemented
23	C₇×C₄₃	C₉×D₇	1	1	yes	characteristic, complemented
24	C₃×C₇×D₇	C₃×C₄₃	1	1	yes	characteristic
25	C₂×C₃×C₄₃	—	7	1	no	—
26	C₃×C₇²	C₂×C₃×C₄₃	1	1	yes	characteristic
27	C₃×C₄₃	D₇×ΓL(1,𝔽₈)	1	1	yes	characteristic
28	C₉×D₇	—	7	1	no	—
29	C₂×C₇⋊C₉	—	7	1	no	—
30	C₇×D₇	C₉×C₄₃	1	1	yes	characteristic, complemented, Hall
31	C₂×C₄₃	—	7	1	no	Hall
32	C₇×C₉	—	7	1	no	—
33	C₇⋊C₉	D₇×C₄₃	1	1	yes	characteristic, direct product factor
34	C₇²	C₂×C₉×C₄₃	1	1	yes	characteristic, complemented, Sylow
35	C₄₃	D₇×C₇⋊C₉	1	1	yes	characteristic, direct product factor, Sylow
36	C₂×C₃×C₇	—	7	1	no	—
37	C₃×D₇	ΓL(1,𝔽₈)×C₄₃	1	1	yes	characteristic
38	C₃×C₇	—	6	1	no	—
39	C₃×C₇	C₂×ΓL(1,𝔽₈)×C₄₃	1	1	yes	characteristic
40	C₃×C₇	C₃×D₇×C₄₃	1	1	yes	characteristic
41	C₂×C₉	—	49	1	no	Hall
42	C₂×C₇	—	7	1	no	—
43	D₇	C₄₃×C₇⋊C₉	1	1	yes	characteristic, direct product factor
44	C₉	—	7	1	no	Sylow
45	C₇	—	6	1	no	—
46	C₇	C₂×C₄₃×C₇⋊C₉	1	1	yes	characteristic, complemented
47	C₇	C₉×D₇×C₄₃	1	1	yes	characteristic, complemented
48	C₂×C₃	—	7	1	no	—
49	C₃	D₇×ΓL(1,𝔽₈)×C₄₃	1	1	yes	characteristic
50	C₂	—	7	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₄₃	D₇×ΓL(1,𝔽₈)
commutator, hypocenter	C₇²	C₂×C₉×C₄₃
Frattini	C₃	D₇×ΓL(1,𝔽₈)×C₄₃
Fitting, socle	C₃×C₇²×C₄₃	C₂×C₃
prime radical	C₃×C₇×D₇×C₄₃	C₃
cosocle	C₃×C₇²	C₂×C₃×C₄₃
LCS	G ▷ C₇²
UCS	C₁ ◁ C₃×C₄₃

Complements

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

N	H ≅ G/N	type
1. C₇×C₄₃×C₇⋊C₉	C₂	semidirect
6. C₇×D₇×C₄₃	C₉	semidirect
7. C₄₃×C₇⋊C₉	D₇	direct (N × H)
9. C₇²×C₄₃	C₂×C₉	semidirect
15. D₇×C₇⋊C₉	C₄₃	direct (N × H)
18. D₇×C₄₃	C₇⋊C₉	direct (N × H)
19. C₇×C₇⋊C₉	C₂×C₄₃	semidirect
22. C₇×C₄₃	C₂×C₇⋊C₉	semidirect
23. C₇×C₄₃	C₉×D₇	semidirect
30. C₇×D₇	C₉×C₄₃	semidirect
33. C₇⋊C₉	D₇×C₄₃	direct (N × H)
34. C₇²	C₂×C₉×C₄₃	semidirect
35. C₄₃	D₇×C₇⋊C₉	direct (N × H)
43. D₇	C₄₃×C₇⋊C₉	direct (N × H)
46. C₇	C₂×C₄₃×C₇⋊C₉	semidirect
47. C₇	C₉×D₇×C₄₃	semidirect

Maximal subgroups

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

subgroup	index
C₇×C₄₃×C₇⋊C₉	2
C₃×C₇×D₇×C₄₃	3
C₉×D₇×C₄₃	7
C₂×C₄₃×C₇⋊C₉	7
D₇×C₇⋊C₉	43

Subgroups — D7×C43×C7⋊C9 #49181586

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₇×C₄₃×C₇⋊C₉ #49181586