Subgroups — C₆₁×#64422⋊C₂ #49089891

Order 35868.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#64422	C₂	1	2	yes	maximal, complemented
2	C₆₁×#64425	C₂	1	1	yes	maximal, characteristic, complemented
3	D₇²×C₆₁	C₃	1	1	yes	maximal, characteristic, complemented, Hall
4	C₆₁×#3862	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×AGL(1,𝔽₇)×C₆₁	—	7	2	no	maximal
8	C₇²×C₆₁	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
9	AGL(1,𝔽₇)×C₆₁	—	7	2	no	—
10	AGL(1,𝔽₇)×C₆₁	—	7	2	no	—
11	C₂×ΓL(1,𝔽₈)×C₆₁	—	7	2	no	—
12	C₂×D₇×C₆₁	—	7	2	no	—
13	ΓL(1,𝔽₈)×C₆₁	—	7	2	no	—
14	C₂×C₇×C₆₁	—	7	2	no	—
15	D₇×C₆₁	—	7	2	no	—
16	D₇×C₆₁	—	42	1	no	—
17	D₇×C₆₁	AGL(1,𝔽₇)	1	2	yes	complemented
18	C₂²×C₃×C₆₁	—	49	1	no	Hall
19	#64422⋊C₂	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Hall
20	C₇×C₆₁	—	6	1	no	—
21	C₇×C₆₁	C₂×AGL(1,𝔽₇)	1	2	yes	complemented
22	C₂×C₃×C₆₁	—	49	2	no	—
23	C₂×C₃×C₆₁	—	49	1	no	—
24	#64425	C₂×C₆₁	1	1	yes	characteristic, complemented
25	#64422	C₂×C₆₁	1	2	yes	complemented
26	C₂²×C₆₁	—	49	1	no	Hall
27	D₇²	C₃×C₆₁	1	1	yes	characteristic, complemented, Hall
28	C₃×C₆₁	—	49	1	no	Hall
29	#3862	C₂²×C₆₁	1	1	yes	characteristic, complemented, Hall
30	C₂×C₆₁	—	7	2	no	—
31	C₂×C₆₁	—	49	1	no	—
32	C₇⋊D₇	C₂×C₃×C₆₁	1	1	yes	characteristic, complemented
33	C₇×D₇	C₂×C₃×C₆₁	1	2	yes	complemented
34	C₂×AGL(1,𝔽₇)	—	7	2	no	—
35	C₆₁	#64422⋊C₂	1	1	yes	characteristic, direct product factor, Sylow
36	C₇²	C₂²×C₃×C₆₁	1	1	yes	characteristic, complemented, Sylow
37	C₂×ΓL(1,𝔽₈)	—	7	2	no	—
38	AGL(1,𝔽₇)	—	7	2	no	—
39	AGL(1,𝔽₇)	—	7	2	no	—
40	C₂×D₇	—	7	2	no	—
41	ΓL(1,𝔽₈)	—	7	2	no	—
42	C₂×C₇	—	7	2	no	—
43	D₇	—	7	2	no	—
44	D₇	—	42	1	no	—
45	D₇	AGL(1,𝔽₇)×C₆₁	1	2	yes	complemented
46	C₂²×C₃	—	49	1	no	Hall
47	C₇	—	6	1	no	—
48	C₇	C₂×AGL(1,𝔽₇)×C₆₁	1	2	yes	complemented
49	C₂×C₃	—	49	2	no	—
50	C₂×C₃	—	49	1	no	—
51	C₂²	—	49	1	no	Sylow
52	C₃	—	49	1	no	Sylow
53	C₂	—	7	2	no	—
54	C₂	—	49	1	no	—

	subgroup	G/H
center, hypercenter	C₆₁	#64422⋊C₂
commutator, cosocle, hypocenter	C₇²	C₂²×C₃×C₆₁
Frattini	C₁	G
Fitting, socle	C₇²×C₆₁	C₂²×C₃
LCS	G ▷ C₇²
UCS	C₁ ◁ C₆₁

Complements

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

N	H ≅ G/N	type
1. C₆₁×#64422	C₂	semidirect
2. C₆₁×#64425	C₂	semidirect
3. D₇²×C₆₁	C₃	semidirect
4. C₆₁×#3862	C₂²	semidirect
5. C₆₁×C₇⋊D₇	C₂×C₃	semidirect
6. C₇×D₇×C₆₁	C₂×C₃	semidirect
8. C₇²×C₆₁	C₂²×C₃	semidirect
17. D₇×C₆₁	AGL(1,𝔽₇)	semidirect
19. #64422⋊C₂	C₆₁	direct (N × H)
21. C₇×C₆₁	C₂×AGL(1,𝔽₇)	semidirect
24. #64425	C₂×C₆₁	semidirect
25. #64422	C₂×C₆₁	semidirect
27. D₇²	C₃×C₆₁	semidirect
29. #3862	C₂²×C₆₁	semidirect
32. C₇⋊D₇	C₂×C₃×C₆₁	semidirect
33. C₇×D₇	C₂×C₃×C₆₁	semidirect
35. C₆₁	#64422⋊C₂	direct (N × H)
36. C₇²	C₂²×C₃×C₆₁	semidirect
45. D₇	AGL(1,𝔽₇)×C₆₁	semidirect
48. C₇	C₂×AGL(1,𝔽₇)×C₆₁	semidirect

Maximal subgroups

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

subgroup	index
C₆₁×#64422	2
C₆₁×#64425	2
D₇²×C₆₁	3
C₂×AGL(1,𝔽₇)×C₆₁	7
#64422⋊C₂	61

Subgroups — C61×#64422⋊C2 #49089891

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#64422⋊C₂ #49089891