Subgroups — #49089882

Order 35868.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#31822452	C₂	1	2	yes	maximal, complemented
2	#31822442	C₂	1	1	yes	maximal, characteristic, complemented
3	D₇²×C₆₁	C₃	1	1	yes	maximal, characteristic, complemented, Hall
4	#22582225	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₆₁×C₇⋊D₇	C₂×C₃	1	1	yes	characteristic, complemented
6	C₇×D₇×C₆₁	C₂×C₃	1	2	yes	complemented
7	C₂×#14579424	—	7	2	no	maximal
8	C₇²×C₆₁	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
9	#14579424	—	7	2	no	—
10	#14579424	—	7	2	no	—
11	#14579424	—	14	3	no	—
12	C₂×#13046197	—	7	2	no	—
13	C₂×D₇×C₆₁	—	7	2	no	—
14	#13046197	—	7	2	no	—
15	#13046197	—	14	3	no	—
16	C₂×C₇×C₆₁	—	7	2	no	—
17	D₇×C₆₁	—	7	2	no	—
18	D₇×C₆₁	—	14	3	no	—
19	D₇×C₆₁	AGL(1,𝔽₇)	1	2	yes	complemented
20	C₂²×C₆₁⋊C₃	—	49	1	no	Hall
21	#64423⋊C₂	—	61	1	no	maximal, Hall
22	C₇×C₆₁	—	2	3	no	—
23	C₇×C₆₁	C₂×AGL(1,𝔽₇)	1	2	yes	complemented
24	C₂×C₆₁⋊C₃	—	49	2	no	—
25	C₂×C₆₁⋊C₃	—	49	1	no	—
26	#64424	—	61	1	no	—
27	#64423	—	61	2	no	—
28	C₂²×C₆₁	—	49	1	no	Hall
29	D₇²	C₆₁⋊C₃	1	1	yes	characteristic, complemented, Hall
30	C₆₁⋊C₃	—	49	1	no	Hall
31	#3861	—	61	1	no	Hall
32	C₂×C₆₁	—	7	2	no	—
33	C₂×C₆₁	—	49	1	no	—
34	C₇⋊D₇	C₂×C₆₁⋊C₃	1	1	yes	characteristic, complemented
35	C₇×D₇	C₂×C₆₁⋊C₃	1	2	yes	complemented
36	C₂×AGL(1,𝔽₇)	—	427	2	no	—
37	C₆₁	#64423⋊C₂	1	1	yes	characteristic, complemented, Sylow
38	C₇²	C₂²×C₆₁⋊C₃	1	1	yes	characteristic, complemented, Sylow
39	C₂×ΓL(1,𝔽₈)	—	427	2	no	—
40	AGL(1,𝔽₇)	—	854	3	no	—
41	AGL(1,𝔽₇)	—	427	2	no	—
42	AGL(1,𝔽₇)	—	427	2	no	—
43	C₂×D₇	—	7	2	no	—
44	ΓL(1,𝔽₈)	—	854	3	no	—
45	ΓL(1,𝔽₈)	—	427	2	no	—
46	C₂×C₇	—	7	2	no	—
47	D₇	—	7	2	no	—
48	D₇	—	14	3	no	—
49	D₇	#14579424	1	2	yes	complemented
50	C₂²×C₃	—	2989	1	no	Hall
51	C₇	—	2	3	no	—
52	C₇	C₂×#14579424	1	2	yes	complemented
53	C₂×C₃	—	2989	2	no	—
54	C₂×C₃	—	2989	1	no	—
55	C₂²	—	49	1	no	Sylow
56	C₃	—	2989	1	no	Sylow
57	C₂	—	7	2	no	—
58	C₂	—	49	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₇²×C₆₁	C₂²×C₃
LCS	G ▷ C₇²×C₆₁
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. #31822452	C₂	semidirect
2. #31822442	C₂	semidirect
3. D₇²×C₆₁	C₃	semidirect
4. #22582225	C₂²	semidirect
5. C₆₁×C₇⋊D₇	C₂×C₃	semidirect
6. C₇×D₇×C₆₁	C₂×C₃	semidirect
8. C₇²×C₆₁	C₂²×C₃	semidirect
19. D₇×C₆₁	AGL(1,𝔽₇)	semidirect
23. C₇×C₆₁	C₂×AGL(1,𝔽₇)	semidirect
29. D₇²	C₆₁⋊C₃	semidirect
34. C₇⋊D₇	C₂×C₆₁⋊C₃	semidirect
35. C₇×D₇	C₂×C₆₁⋊C₃	semidirect
37. C₆₁	#64423⋊C₂	semidirect
38. C₇²	C₂²×C₆₁⋊C₃	semidirect
49. D₇	#14579424	semidirect
52. C₇	C₂×#14579424	semidirect

Maximal subgroups

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

subgroup	index
#31822452	2
#31822442	2
D₇²×C₆₁	3
C₂×#14579424	7
#64423⋊C₂	61