Subgroups — #49181587

Order 37926.

52 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#14582151	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	#19129334	—	7	1	no	maximal
5	(C₄₃⋊C₉)⋊D₇	—	7	1	no	maximal
6	C₇×D₃₀₁	C₉	1	1	yes	characteristic, complemented, Hall
7	#14582151	D₇	1	1	yes	characteristic, complemented
8	C₇×C₄₃⋊C₉	—	7	1	no	—
9	C₇²×C₄₃	C₂×C₉	1	1	yes	characteristic, complemented, Hall
10	C₃×D₃₀₁	ΓL(1,𝔽₈)	1	1	yes	characteristic
11	C₃×C₇×D₄₃	—	7	1	no	—
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	—	43	1	no	maximal, Hall
16	D₄₃⋊C₉	—	49	1	no	Hall
17	D₃₀₁	C₇⋊C₉	1	1	yes	characteristic, complemented
18	C₇×D₄₃	—	7	1	no	—
19	C₇×C₇⋊C₉	—	43	1	no	Hall
20	C₄₃⋊C₉	—	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	—	43	1	no	—
25	C₃×D₄₃	—	7	1	no	—
26	C₃×C₇²	D₄₃⋊C₃	1	1	yes	characteristic
27	C₃×C₄₃	D₇×ΓL(1,𝔽₈)	1	1	yes	characteristic
28	C₉×D₇	—	301	1	no	—
29	C₂×C₇⋊C₉	—	301	1	no	—
30	C₇×D₇	—	43	1	no	Hall
31	D₄₃	—	7	1	no	Hall
32	C₇×C₉	—	301	1	no	—
33	C₇⋊C₉	—	43	1	no	—
34	C₇²	D₄₃⋊C₉	1	1	yes	characteristic, complemented, Sylow
35	C₄₃	D₇×C₇⋊C₉	1	1	yes	characteristic, complemented, Sylow
36	C₂×C₃×C₇	—	301	1	no	—
37	C₃×D₇	—	43	1	no	—
38	C₃×C₇	—	6	1	no	—
39	C₃×C₇	(C₄₃⋊C₃)⋊D₇	1	1	yes	characteristic
40	C₃×C₇	#14268588	1	1	yes	characteristic
41	C₂×C₉	—	2107	1	no	Hall
42	C₂×C₇	—	301	1	no	—
43	D₇	—	43	1	no	—
44	C₉	—	301	1	no	Sylow
45	C₇	—	6	1	no	—
46	C₇	(C₄₃⋊C₉)⋊D₇	1	1	yes	characteristic, complemented
47	C₇	#19129334	1	1	yes	characteristic, complemented
48	C₂×C₃	—	301	1	no	—
49	C₃	#27162437	1	1	yes	characteristic
50	C₂	—	301	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₃	#27162437
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×#14582151	C₂	semidirect
6. C₇×D₃₀₁	C₉	semidirect
7. #14582151	D₇	semidirect
9. C₇²×C₄₃	C₂×C₉	semidirect
17. D₃₀₁	C₇⋊C₉	semidirect
22. C₇×C₄₃	C₂×C₇⋊C₉	semidirect
23. C₇×C₄₃	C₉×D₇	semidirect
34. C₇²	D₄₃⋊C₉	semidirect
35. C₄₃	D₇×C₇⋊C₉	semidirect
46. C₇	(C₄₃⋊C₉)⋊D₇	semidirect
47. C₇	#19129334	semidirect

Maximal subgroups

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

subgroup	index
C₇×#14582151	2
C₃×C₇×D₃₀₁	3
#19129334	7
(C₄₃⋊C₉)⋊D₇	7
D₇×C₇⋊C₉	43