Subgroups — ((C₆₁⋊C₃)⋊D₇)⋊D₇ #49089874

Order 35868.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇⋊D₇×C₆₁⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×(C₆₁⋊C₃)⋊D₇	C₂	1	2	yes	maximal, complemented
3	(C₇⋊D₇)⋊D₆₁	C₃	1	1	yes	maximal, characteristic, complemented, Hall
4	C₇²×C₆₁⋊C₃	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	D₇×D₆₁⋊C₃	—	7	2	no	maximal
8	C₇²×C₆₁	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
9	(C₆₁⋊C₃)⋊D₇	D₇	1	2	yes	complemented
10	D₇×C₆₁⋊C₃	—	7	2	no	—
11	D₇×C₆₁⋊C₃	—	14	3	no	—
12	C₇×D₆₁⋊C₃	—	7	2	no	—
13	D₇×D₆₁	—	7	2	no	—
14	C₇×C₆₁⋊C₃	—	2	3	no	—
15	C₇×C₆₁⋊C₃	C₂×D₇	1	2	yes	complemented
16	D₄₂₇	C₃×D₇	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	C₃×D₇²	—	61	1	no	maximal, Hall
22	C₇×C₆₁	—	2	3	no	—
23	C₇×C₆₁	C₂×C₃×D₇	1	2	yes	complemented
24	C₂×C₆₁⋊C₃	—	49	1	no	—
25	D₆₁⋊C₃	—	7	2	no	—
26	C₃×C₇⋊D₇	—	61	1	no	—
27	C₃×C₇×D₇	—	61	2	no	—
28	C₂×D₆₁	—	49	1	no	Hall
29	D₇²	—	61	1	no	Hall
30	C₆₁⋊C₃	D₇²	1	1	yes	characteristic, complemented, Hall
31	C₃×C₇²	—	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×C₃×D₇	—	427	2	no	—
37	C₆₁	C₃×D₇²	1	1	yes	characteristic, complemented, Sylow
38	C₇²	C₂×D₆₁⋊C₃	1	1	yes	characteristic, complemented, Sylow
39	C₂×C₃×C₇	—	427	2	no	—
40	C₃×D₇	—	61	2	no	—
41	C₃×D₇	—	854	3	no	—
42	C₃×D₇	—	427	2	no	—
43	C₂×D₇	—	427	2	no	—
44	C₃×C₇	—	61	2	no	—
45	C₃×C₇	—	122	3	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	D₇×D₆₁⋊C₃	1	2	yes	complemented
53	C₂×C₃	—	427	2	no	—
54	C₂×C₃	—	2989	1	no	—
55	C₂²	—	2989	1	no	Sylow
56	C₃	—	61	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. C₇⋊D₇×C₆₁⋊C₃	C₂	semidirect
2. C₇×(C₆₁⋊C₃)⋊D₇	C₂	semidirect
3. (C₇⋊D₇)⋊D₆₁	C₃	semidirect
4. C₇²×C₆₁⋊C₃	C₂²	semidirect
5. C₆₁×C₇⋊D₇	C₂×C₃	semidirect
6. C₇×D₄₂₇	C₂×C₃	semidirect
8. C₇²×C₆₁	C₂²×C₃	semidirect
9. (C₆₁⋊C₃)⋊D₇	D₇	semidirect
15. C₇×C₆₁⋊C₃	C₂×D₇	semidirect
16. D₄₂₇	C₃×D₇	semidirect
23. C₇×C₆₁	C₂×C₃×D₇	semidirect
30. C₆₁⋊C₃	D₇²	semidirect
34. C₇⋊D₇	D₆₁⋊C₃	semidirect
37. C₆₁	C₃×D₇²	semidirect
38. C₇²	C₂×D₆₁⋊C₃	semidirect
52. C₇	D₇×D₆₁⋊C₃	semidirect

Maximal subgroups

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

subgroup	index
C₇⋊D₇×C₆₁⋊C₃	2
C₇×(C₆₁⋊C₃)⋊D₇	2
(C₇⋊D₇)⋊D₆₁	3
D₇×D₆₁⋊C₃	7
C₃×D₇²	61

Subgroups — ((C61⋊C3)⋊D7)⋊D7 #49089874

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — ((C₆₁⋊C₃)⋊D₇)⋊D₇ #49089874