Subgroups — #49181567

Order 37926.

66 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#34038921	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	C₂×#14582150	—	7	1	no	maximal
5	#19129337	—	7	1	no	maximal
6	C₇×D₇×C₄₃	C₉	1	1	yes	characteristic, complemented, Hall
7	#14582150	—	7	1	no	—
8	#14582150	—	7	1	no	—
9	#14582150	—	14	3	no	—
10	C₇²×C₄₃	C₂×C₉	1	1	yes	characteristic, complemented, Hall
11	C₂×C₃×C₇×C₄₃	—	7	1	no	—
12	C₃×D₇×C₄₃	ΓL(1,𝔽₈)	1	1	yes	characteristic
13	C₃×C₇×C₄₃	—	2	3	no	—
14	C₃×C₇×C₄₃	AGL(1,𝔽₇)	1	1	yes	characteristic
15	C₃×C₇×C₄₃	C₂×ΓL(1,𝔽₈)	1	1	yes	characteristic
16	#11725076	—	43	1	no	maximal, Hall
17	C₂×C₄₃⋊C₉	—	49	1	no	Hall
18	C₂×C₇×C₄₃	—	7	1	no	—
19	D₇×C₄₃	C₇⋊C₉	1	1	yes	characteristic, complemented
20	#89204	—	43	1	no	Hall
21	C₄₃⋊C₉	—	49	1	no	Hall
22	C₇×C₄₃	—	2	3	no	—
23	C₇×C₄₃	D₇⋊C₉	1	1	yes	characteristic, complemented
24	C₇×C₄₃	C₂×C₇⋊C₉	1	1	yes	characteristic, complemented
25	C₃×C₇×D₇	C₄₃⋊C₃	1	1	yes	characteristic
26	C₂×C₃×C₄₃	—	7	1	no	—
27	C₃×C₇²	C₂×C₄₃⋊C₃	1	1	yes	characteristic
28	C₃×C₄₃	#64423	1	1	yes	characteristic
29	C₂×C₇⋊C₉	—	301	1	no	—
30	D₇⋊C₉	—	301	1	no	—
31	C₇×D₇	C₄₃⋊C₉	1	1	yes	characteristic, complemented, Hall
32	C₂×C₄₃	—	7	1	no	Hall
33	C₇⋊C₉	—	301	1	no	—
34	C₇⋊C₉	—	301	1	no	—
35	C₇⋊C₉	—	602	3	no	—
36	C₇²	C₂×C₄₃⋊C₉	1	1	yes	characteristic, complemented, Sylow
37	C₄₃	#11725076	1	1	yes	characteristic, complemented, Sylow
38	C₂×C₃×C₇	—	7	1	no	—
39	C₃×D₇	#11744748	1	1	yes	characteristic
40	C₃×C₇	—	2	3	no	—
41	C₃×C₇	#14268591	1	1	yes	characteristic
42	C₃×C₇	C₂×#11744748	1	1	yes	characteristic
43	C₂×C₉	—	2107	1	no	Hall
44	C₂×C₇	—	7	1	no	—
45	D₇	#14582150	1	1	yes	characteristic, complemented
46	C₉	—	2107	1	no	Sylow
47	C₇	—	2	3	no	—
48	C₇	#19129337	1	1	yes	characteristic, complemented
49	C₇	C₂×#14582150	1	1	yes	characteristic, complemented
50	C₂×C₃	—	7	1	no	—
51	C₃	#27162417	1	1	yes	characteristic
52	C₂	—	7	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₃	#27162417
commutator, hypocenter	C₇²×C₄₃	C₂×C₉
Fitting, socle, cosocle	C₃×C₇²×C₄₃	C₂×C₃
prime radical	C₃×C₇×D₇×C₄₃	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. #34038921	C₂	semidirect
6. C₇×D₇×C₄₃	C₉	semidirect
10. C₇²×C₄₃	C₂×C₉	semidirect
19. D₇×C₄₃	C₇⋊C₉	semidirect
23. C₇×C₄₃	D₇⋊C₉	semidirect
24. C₇×C₄₃	C₂×C₇⋊C₉	semidirect
31. C₇×D₇	C₄₃⋊C₉	semidirect
36. C₇²	C₂×C₄₃⋊C₉	semidirect
37. C₄₃	#11725076	semidirect
45. D₇	#14582150	semidirect
48. C₇	#19129337	semidirect
49. C₇	C₂×#14582150	semidirect

Maximal subgroups

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

subgroup	index
#34038921	2
C₃×C₇×D₇×C₄₃	3
C₂×#14582150	7
#19129337	7
#11725076	43