Subgroups — (C₇⋊C₉)⋊D₃₀₁ #49181580

Order 37926.

64 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⋊D₃₀₁	C₃	1	1	yes	maximal, characteristic
3	C₃×C₇²×C₄₃	C₂×C₃	1	1	yes	characteristic
4	C₉×D₃₀₁	—	7	1	no	maximal
5	(C₇⋊C₉)⋊D₄₃	—	7	1	no	maximal
6	C₇⋊D₃₀₁	C₉	1	1	yes	characteristic, complemented, Hall
7	C₄₃×C₇⋊C₉	D₇	1	1	yes	characteristic, complemented
8	C₇×C₉×C₄₃	—	7	1	no	—
9	C₇²×C₄₃	C₂×C₉	1	1	yes	characteristic, complemented, Hall
10	C₃×D₃₀₁	—	7	1	no	—
11	C₃×D₃₀₁	—	7	1	no	—
12	C₃×D₃₀₁	—	21	2	no	—
13	C₃×C₇×C₄₃	—	3	2	no	—
14	C₃×C₇×C₄₃	AGL(1,𝔽₇)	1	1	yes	characteristic
15	C₃×C₇×C₄₃	C₃×D₇	1	1	yes	characteristic
16	(C₇⋊C₉)⋊D₇	—	43	1	no	maximal, Hall
17	C₉×D₄₃	—	49	1	no	Hall
18	D₃₀₁	—	7	1	no	—
19	D₃₀₁	—	7	1	no	—
20	D₃₀₁	—	21	2	no	—
21	C₇×C₇⋊C₉	D₄₃	1	1	yes	characteristic, complemented, Hall
22	C₉×C₄₃	—	7	1	no	Hall
23	C₇×C₄₃	—	3	2	no	—
24	C₇×C₄₃	D₇⋊C₉	1	1	yes	characteristic, complemented
25	C₇×C₄₃	C₉×D₇	1	1	yes	characteristic, complemented
26	C₃×C₇⋊D₇	—	43	1	no	—
27	C₃×D₄₃	—	49	1	no	—
28	C₃×C₇²	C₃×D₄₃	1	1	yes	characteristic
29	C₃×C₄₃	ΓL(1,𝔽₈)⋊D₇	1	1	yes	characteristic
30	C₉×D₇	—	301	1	no	—
31	D₇⋊C₉	—	301	1	no	—
32	C₇⋊D₇	—	43	1	no	Hall
33	D₄₃	—	49	1	no	Hall
34	C₇×C₉	—	7	1	no	—
35	C₇⋊C₉	D₃₀₁	1	1	yes	characteristic, complemented
36	C₇²	C₉×D₄₃	1	1	yes	characteristic, complemented, Sylow
37	C₄₃	(C₇⋊C₉)⋊D₇	1	1	yes	characteristic, complemented, Sylow
38	C₃×D₇	—	301	1	no	—
39	C₃×D₇	—	301	1	no	—
40	C₃×D₇	—	903	2	no	—
41	C₃×C₇	—	3	2	no	—
42	C₃×C₇	ΓL(1,𝔽₈)⋊D₄₃	1	1	yes	characteristic
43	C₃×C₇	C₃×D₃₀₁	1	1	yes	characteristic
44	C₂×C₉	—	2107	1	no	Hall
45	D₇	—	301	1	no	—
46	D₇	—	301	1	no	—
47	D₇	—	903	2	no	—
48	C₉	—	7	1	no	Sylow
49	C₇	—	3	2	no	—
50	C₇	(C₇⋊C₉)⋊D₄₃	1	1	yes	characteristic, complemented
51	C₇	C₉×D₃₀₁	1	1	yes	characteristic, complemented
52	C₂×C₃	—	2107	1	no	—
53	C₃	ΓL(1,𝔽₈)⋊D₃₀₁	1	1	yes	characteristic
54	C₂	—	2107	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₃	ΓL(1,𝔽₈)⋊D₃₀₁
commutator, hypocenter	C₇²×C₄₃	C₂×C₉
Fitting, socle, cosocle	C₃×C₇²×C₄₃	C₂×C₃
prime radical	C₃×C₇⋊D₃₀₁	C₃
LCS	G ▷ C₇²×C₄₃
UCS	C₁ ◁ C₃

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⋊D₃₀₁	C₉	semidirect
7. C₄₃×C₇⋊C₉	D₇	semidirect
9. C₇²×C₄₃	C₂×C₉	semidirect
21. C₇×C₇⋊C₉	D₄₃	semidirect
24. C₇×C₄₃	D₇⋊C₉	semidirect
25. C₇×C₄₃	C₉×D₇	semidirect
35. C₇⋊C₉	D₃₀₁	semidirect
36. C₇²	C₉×D₄₃	semidirect
37. C₄₃	(C₇⋊C₉)⋊D₇	semidirect
50. C₇	(C₇⋊C₉)⋊D₄₃	semidirect
51. C₇	C₉×D₃₀₁	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⋊D₃₀₁	3
C₉×D₃₀₁	7
(C₇⋊C₉)⋊D₄₃	7
(C₇⋊C₉)⋊D₇	43

Subgroups — (C7⋊C9)⋊D301 #49181580

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — (C₇⋊C₉)⋊D₃₀₁ #49181580