Subgroups — #49089879

Order 35868.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#31822449	C₂	1	2	yes	maximal, complemented
2	#31822441	C₂	1	1	yes	maximal, characteristic, complemented
3	(C₇⋊D₇)⋊D₆₁	C₃	1	1	yes	maximal, characteristic, complemented, Hall
4	#22582226	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₆₁×C₇⋊D₇	C₂×C₃	1	1	yes	characteristic, complemented
6	C₇×D₄₂₇	C₂×C₃	1	2	yes	complemented
7	#14579421⋊C₂	—	7	2	no	maximal
8	C₇²×C₆₁	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
9	#14579429	—	7	2	no	—
10	#14579425	—	7	2	no	—
11	#14579425	—	14	3	no	—
12	#14579421	—	7	2	no	—
13	D₇×D₆₁	—	7	2	no	—
14	#13046196	—	7	2	no	—
15	#13046196	—	14	3	no	—
16	D₄₂₇	AGL(1,𝔽₇)	1	2	yes	complemented
17	C₇×D₆₁	—	7	2	no	—
18	D₇×C₆₁	—	7	2	no	—
19	D₇×C₆₁	—	14	3	no	—
20	C₂×D₆₁⋊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	1	no	—
25	D₆₁⋊C₃	—	49	2	no	—
26	#64424	—	61	1	no	—
27	#64423	—	61	2	no	—
28	C₂×D₆₁	—	49	1	no	Hall
29	D₇²	—	61	1	no	Hall
30	C₆₁⋊C₃	—	49	1	no	Hall
31	#3861	—	61	1	no	Hall
32	C₂×C₆₁	—	49	1	no	—
33	D₆₁	—	7	2	no	—
34	C₇⋊D₇	D₆₁⋊C₃	1	1	yes	characteristic, complemented
35	C₇×D₇	—	61	2	no	—
36	C₂×AGL(1,𝔽₇)	—	427	2	no	—
37	C₆₁	#64423⋊C₂	1	1	yes	characteristic, complemented, Sylow
38	C₇²	C₂×D₆₁⋊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	—	427	2	no	—
44	ΓL(1,𝔽₈)	—	854	3	no	—
45	ΓL(1,𝔽₈)	—	427	2	no	—
46	C₂×C₇	—	427	2	no	—
47	D₇	—	7	2	no	—
48	D₇	—	14	3	no	—
49	D₇	—	61	2	no	—
50	C₂²×C₃	—	2989	1	no	Hall
51	C₇	—	2	3	no	—
52	C₇	#14579421⋊C₂	1	2	yes	complemented
53	C₂×C₃	—	2989	1	no	—
54	C₂×C₃	—	2989	2	no	—
55	C₂²	—	2989	1	no	Sylow
56	C₃	—	2989	1	no	Sylow
57	C₂	—	49	1	no	—
58	C₂	—	427	2	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. #31822449	C₂	semidirect
2. #31822441	C₂	semidirect
3. (C₇⋊D₇)⋊D₆₁	C₃	semidirect
4. #22582226	C₂²	semidirect
5. C₆₁×C₇⋊D₇	C₂×C₃	semidirect
6. C₇×D₄₂₇	C₂×C₃	semidirect
8. C₇²×C₆₁	C₂²×C₃	semidirect
16. D₄₂₇	AGL(1,𝔽₇)	semidirect
23. C₇×C₆₁	C₂×AGL(1,𝔽₇)	semidirect
34. C₇⋊D₇	D₆₁⋊C₃	semidirect
37. C₆₁	#64423⋊C₂	semidirect
38. C₇²	C₂×D₆₁⋊C₃	semidirect
52. C₇	#14579421⋊C₂	semidirect

Maximal subgroups

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

subgroup	index
#31822449	2
#31822441	2
(C₇⋊D₇)⋊D₆₁	3
#14579421⋊C₂	7
#64423⋊C₂	61