Subgroups — #21445121

Order 7808.

182 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16840128	C₂	1	3	yes	maximal
2	#16839504	C₂	1	3	yes	maximal, complemented
3	C₆₁×#564	C₂	1	1	yes	maximal, characteristic, complemented
4	#14519774	C₂²	1	1	yes	characteristic
5	#14519697	—	2	6	no	—
6	#14519688	C₂²	1	3	yes	—
7	#125×C₆₁	—	2	6	no	—
8	#125×C₆₁	C₂²	1	3	yes	—
9	C₂×D₂₄₄	—	2	3	no	—
10	C₄⋊C₄×C₆₁	—	2	6	no	—
11	C₄⋊C₄×C₆₁	—	2	6	no	—
12	C₄⋊C₄×C₆₁	D₄	1	6	yes	—
13	C₄²×C₆₁	—	2	2	no	—
14	C₄²×C₆₁	C₂³	1	1	yes	characteristic
15	C₂×#92418	—	2	3	no	—
16	C₂²×D₆₁	—	4	1	no	—
17	C₂×C₄×C₆₁	—	2	6	no	—
18	C₂×C₄×C₆₁	C₂×D₄	1	3	yes	—
19	D₂₄₄	—	4	6	no	—
20	#92418	—	4	3	no	—
21	C₂²×C₆₁	#120	1	1	yes	characteristic
22	C₂×D₆₁	—	8	3	no	—
23	C₄×C₆₁	—	2	3	no	—
24	C₄×C₆₁	—	4	6	no	—
25	#1658	—	61	1	no	maximal, Sylow
26	C₂×C₆₁	#454	1	3	yes	—
27	D₆₁	—	16	1	no	—
28	#564	D₆₁	1	1	yes	characteristic, complemented
29	#490	—	61	3	no	—
30	#330	—	61	3	no	—
31	C₆₁	#1658	1	1	yes	characteristic, complemented, Sylow
32	#127	—	61	1	no	—
33	#125	—	2	6	no	—
34	#125	C₂×D₆₁	1	3	yes	—
35	#102	—	122	6	no	—
36	#97	—	61	3	no	—
37	C₂×D₄	—	122	3	no	—
38	C₂×C₈	—	122	3	no	—
39	C₄⋊C₄	—	2	6	no	—
40	C₄⋊C₄	—	2	6	no	—
41	C₄⋊C₄	C₂²⋊D₆₁	1	6	yes	—
42	C₄²	—	2	2	no	—
43	C₄²	C₂²×D₆₁	1	1	yes	characteristic
44	C₂³	—	244	1	no	—
45	D₄	—	244	6	no	—
46	C₂×C₄	—	2	6	no	—
47	C₂×C₄	C₂×C₂²⋊D₆₁	1	3	yes	—
48	C₈	—	244	3	no	—
49	C₂²	—	488	3	no	—
50	C₂²	#14519746	1	1	yes	characteristic
51	C₄	—	2	3	no	—
52	C₄	—	4	6	no	—
53	C₂	—	976	1	no	—
54	C₂	#16839935	1	3	yes	—

	subgroup	G/H
center	C₂²	#14519746
commutator	C₄²×C₆₁	C₂³
Frattini	C₄²	C₂²×D₆₁
Fitting	C₆₁×#564	C₂
socle	C₂²×C₆₁	#120
hypercenter	#564	D₆₁
hypocenter	C₆₁	#1658
LCS	G ▷ C₄²×C₆₁ ▷ C₂²×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #564

Complements

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

N	H ≅ G/N	type
2. #16839504	C₂	semidirect
3. C₆₁×#564	C₂	semidirect
28. #564	D₆₁	semidirect
31. C₆₁	#1658	semidirect