Subgroups — C₆₁×#64423⋊C₂ #49089876

Order 35868.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#64423	C₂	1	2	yes	maximal, complemented
2	C₆₁×#64424	C₂	1	1	yes	maximal, characteristic, complemented
3	D₇²×C₆₁	C₃	1	1	yes	maximal, characteristic, complemented, Hall
4	C₆₁×#3861	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	AGL(1,𝔽₇)×C₆₁	—	14	3	no	—
12	C₂×ΓL(1,𝔽₈)×C₆₁	—	7	2	no	—
13	C₂×D₇×C₆₁	—	7	2	no	—
14	ΓL(1,𝔽₈)×C₆₁	—	7	2	no	—
15	ΓL(1,𝔽₈)×C₆₁	—	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×C₃×C₆₁	—	49	1	no	Hall
21	#64423⋊C₂	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Hall
22	C₇×C₆₁	—	2	3	no	—
23	C₇×C₆₁	C₂×AGL(1,𝔽₇)	1	2	yes	complemented
24	C₂×C₃×C₆₁	—	49	2	no	—
25	C₂×C₃×C₆₁	—	49	1	no	—
26	#64424	C₂×C₆₁	1	1	yes	characteristic, complemented
27	#64423	C₂×C₆₁	1	2	yes	complemented
28	C₂²×C₆₁	—	49	1	no	Hall
29	D₇²	C₃×C₆₁	1	1	yes	characteristic, complemented, Hall
30	C₃×C₆₁	—	49	1	no	Hall
31	#3861	C₂²×C₆₁	1	1	yes	characteristic, complemented, Hall
32	C₂×C₆₁	—	7	2	no	—
33	C₂×C₆₁	—	49	1	no	—
34	C₇⋊D₇	C₂×C₃×C₆₁	1	1	yes	characteristic, complemented
35	C₇×D₇	C₂×C₃×C₆₁	1	2	yes	complemented
36	C₂×AGL(1,𝔽₇)	—	7	2	no	—
37	C₆₁	#64423⋊C₂	1	1	yes	characteristic, direct product factor, Sylow
38	C₇²	C₂²×C₃×C₆₁	1	1	yes	characteristic, complemented, Sylow
39	C₂×ΓL(1,𝔽₈)	—	7	2	no	—
40	AGL(1,𝔽₇)	—	7	2	no	—
41	AGL(1,𝔽₇)	—	7	2	no	—
42	AGL(1,𝔽₇)	—	14	3	no	—
43	C₂×D₇	—	7	2	no	—
44	ΓL(1,𝔽₈)	—	7	2	no	—
45	ΓL(1,𝔽₈)	—	14	3	no	—
46	C₂×C₇	—	7	2	no	—
47	D₇	—	7	2	no	—
48	D₇	—	14	3	no	—
49	D₇	AGL(1,𝔽₇)×C₆₁	1	2	yes	complemented
50	C₂²×C₃	—	49	1	no	Hall
51	C₇	—	2	3	no	—
52	C₇	C₂×AGL(1,𝔽₇)×C₆₁	1	2	yes	complemented
53	C₂×C₃	—	49	2	no	—
54	C₂×C₃	—	49	1	no	—
55	C₂²	—	49	1	no	Sylow
56	C₃	—	49	1	no	Sylow
57	C₂	—	7	2	no	—
58	C₂	—	49	1	no	—

	subgroup	G/H
center, hypercenter	C₆₁	#64423⋊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×#64423	C₂	semidirect
2. C₆₁×#64424	C₂	semidirect
3. D₇²×C₆₁	C₃	semidirect
4. C₆₁×#3861	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
21. #64423⋊C₂	C₆₁	direct (N × H)
23. C₇×C₆₁	C₂×AGL(1,𝔽₇)	semidirect
26. #64424	C₂×C₆₁	semidirect
27. #64423	C₂×C₆₁	semidirect
29. D₇²	C₃×C₆₁	semidirect
31. #3861	C₂²×C₆₁	semidirect
34. C₇⋊D₇	C₂×C₃×C₆₁	semidirect
35. C₇×D₇	C₂×C₃×C₆₁	semidirect
37. C₆₁	#64423⋊C₂	direct (N × H)
38. C₇²	C₂²×C₃×C₆₁	semidirect
49. D₇	AGL(1,𝔽₇)×C₆₁	semidirect
52. 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×#64423	2
C₆₁×#64424	2
D₇²×C₆₁	3
C₂×AGL(1,𝔽₇)×C₆₁	7
#64423⋊C₂	61

Subgroups — C61×#64423⋊C2 #49089876

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#64423⋊C₂ #49089876