Subgroups — D₆₁⋊#64425 #49089901

Order 35868.

100 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₆₁⋊#3862	C₂	1	1	yes	maximal, characteristic, complemented
2	#31822446	C₂	1	1	yes	maximal, characteristic, complemented
3	#31822445	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇⋊D₇×D₆₁	C₃	1	1	yes	maximal, characteristic, complemented, Hall
5	C₆₁⋊#3862	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₇⋊D₄₂₇	C₂×C₃	1	1	yes	characteristic, complemented
7	C₆₁×C₇⋊D₇	C₂×C₃	1	1	yes	characteristic, complemented
8	C₇²×D₆₁	C₂×C₃	1	1	yes	characteristic, complemented
9	#14579420⋊C₂	—	7	1	no	maximal
10	#14579421⋊C₂	—	7	1	no	maximal
11	C₇²×C₆₁	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
12	#14579429	—	7	1	no	—
13	#14579428	—	7	1	no	—
14	#14579425	—	7	1	no	—
15	#14579424	—	7	1	no	—
16	#14579421	—	7	1	no	—
17	#14579420	—	7	1	no	—
18	D₇×D₆₁	—	7	1	no	—
19	D₇×D₆₁	—	7	1	no	—
20	D₇×D₆₁	—	21	2	no	—
21	#13046197	—	7	1	no	—
22	#13046196	—	7	1	no	—
23	D₄₂₇	—	7	1	no	—
24	D₄₂₇	—	7	1	no	—
25	D₄₂₇	—	21	2	no	—
26	C₇×D₆₁	—	3	2	no	—
27	C₇×D₆₁	AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
28	C₇×D₆₁	AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
29	D₇×C₆₁	—	7	1	no	—
30	D₇×C₆₁	—	7	1	no	—
31	D₇×C₆₁	—	21	2	no	—
32	C₂×D₆₁⋊C₃	—	49	1	no	Hall
33	C₂×#64425	—	61	1	no	maximal, Hall
34	C₇×C₆₁	—	3	2	no	—
35	C₇×C₆₁	C₂×AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
36	C₇×C₆₁	C₂×AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
37	C₂×C₆₁⋊C₃	—	49	1	no	—
38	D₆₁⋊C₃	—	49	1	no	—
39	D₆₁⋊C₃	—	49	1	no	—
40	C₂×#3862	—	61	1	no	—
41	#64425	—	61	1	no	—
42	#64425	—	61	1	no	—
43	C₂×D₆₁	—	49	1	no	Hall
44	C₂×C₇⋊D₇	—	61	1	no	Hall
45	C₆₁⋊C₃	—	49	1	no	Hall
46	#3862	—	61	1	no	Hall
47	C₂×C₆₁	—	49	1	no	—
48	D₆₁	—	49	1	no	—
49	D₆₁	#64425	1	1	yes	characteristic, complemented
50	C₂×C₇²	—	61	1	no	—
51	C₇⋊D₇	—	61	1	no	—
52	C₇⋊D₇	D₆₁⋊C₃	1	1	yes	characteristic, complemented
53	C₂×AGL(1,𝔽₇)	—	427	1	no	—
54	C₂×AGL(1,𝔽₇)	—	427	1	no	—
55	C₆₁	C₂×#64425	1	1	yes	characteristic, complemented, Sylow
56	C₇²	C₂×D₆₁⋊C₃	1	1	yes	characteristic, complemented, Sylow
57	C₂×ΓL(1,𝔽₈)	—	427	1	no	—
58	C₂×ΓL(1,𝔽₈)	—	427	1	no	—
59	AGL(1,𝔽₇)	—	427	1	no	—
60	AGL(1,𝔽₇)	—	427	1	no	—
61	AGL(1,𝔽₇)	—	427	1	no	—
62	AGL(1,𝔽₇)	—	427	1	no	—
63	C₂×D₇	—	1281	2	no	—
64	C₂×D₇	—	427	1	no	—
65	C₂×D₇	—	427	1	no	—
66	ΓL(1,𝔽₈)	—	427	1	no	—
67	ΓL(1,𝔽₈)	—	427	1	no	—
68	C₂×C₇	—	61	1	no	—
69	C₂×C₇	—	61	1	no	—
70	C₂×C₇	—	183	2	no	—
71	D₇	—	1281	2	no	—
72	D₇	—	7	1	no	—
73	D₇	—	7	1	no	—
74	D₇	—	21	2	no	—
75	D₇	—	427	1	no	—
76	D₇	—	427	1	no	—
77	C₂²×C₃	—	2989	1	no	Hall
78	C₇	—	3	2	no	—
79	C₇	#14579421⋊C₂	1	1	yes	characteristic, complemented
80	C₇	#14579420⋊C₂	1	1	yes	characteristic, complemented
81	C₂×C₃	—	2989	1	no	—
82	C₂×C₃	—	2989	1	no	—
83	C₂×C₃	—	2989	1	no	—
84	C₂²	—	2989	1	no	Sylow
85	C₃	—	2989	1	no	Sylow
86	C₂	—	49	1	no	—
87	C₂	—	61	1	no	—
88	C₂	—	2989	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. D₆₁⋊#3862	C₂	semidirect
2. #31822446	C₂	semidirect
3. #31822445	C₂	semidirect
4. C₇⋊D₇×D₆₁	C₃	semidirect
5. C₆₁⋊#3862	C₂²	semidirect
6. C₇⋊D₄₂₇	C₂×C₃	semidirect
7. C₆₁×C₇⋊D₇	C₂×C₃	semidirect
8. C₇²×D₆₁	C₂×C₃	semidirect
11. C₇²×C₆₁	C₂²×C₃	semidirect
27. C₇×D₆₁	AGL(1,𝔽₇)	semidirect
28. C₇×D₆₁	AGL(1,𝔽₇)	semidirect
35. C₇×C₆₁	C₂×AGL(1,𝔽₇)	semidirect
36. C₇×C₆₁	C₂×AGL(1,𝔽₇)	semidirect
49. D₆₁	#64425	semidirect
52. C₇⋊D₇	D₆₁⋊C₃	semidirect
55. C₆₁	C₂×#64425	semidirect
56. C₇²	C₂×D₆₁⋊C₃	semidirect
79. C₇	#14579421⋊C₂	semidirect
80. C₇	#14579420⋊C₂	semidirect

Maximal subgroups

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

subgroup	index
D₆₁⋊#3862	2
#31822446	2
#31822445	2
C₇⋊D₇×D₆₁	3
#14579420⋊C₂	7
#14579421⋊C₂	7
C₂×#64425	61

Subgroups — D61⋊#64425 #49089901

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₆₁⋊#64425 #49089901