Subgroups — #21460768

Order 7808.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16840658	C₂	1	2	yes	maximal
2	#16839788	C₂	1	1	yes	maximal, characteristic
3	#14519851	—	2	2	no	—
4	C₂×#11758194	C₂²	1	1	yes	characteristic
5	#14519736	C₄	1	1	yes	characteristic
6	#14519706	—	2	2	no	—
7	C₂²×C₈×C₆₁	C₄	1	1	yes	characteristic
8	C₂²×C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
9	C₂×C₈×C₆₁	—	2	1	no	—
10	C₂×C₈×C₆₁	—	4	1	no	—
11	C₂²⋊Dic₆₁	C₈	1	2	yes	—
12	C₄⋊Dic₆₁	—	2	1	no	—
13	C₄×Dic₆₁	—	2	1	no	—
14	#11758194	—	4	1	no	—
15	C₂×#92418	D₄	1	2	yes	—
16	#11758187	—	4	2	no	—
17	C₂³×C₆₁	C₂×C₈	1	1	yes	characteristic
18	C₂×C₄×C₆₁	—	2	1	no	—
19	C₂×C₄×C₆₁	—	2	1	no	—
20	C₂×C₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
21	C₂×C₄×C₆₁	M₁₆	1	1	yes	characteristic
22	C₂×Dic₆₁	—	2	2	no	—
23	C₈×C₆₁	—	4	1	no	—
24	#92418	—	2	2	no	—
25	C₂²×C₆₁	—	2	1	no	—
26	C₂²×C₆₁	—	4	1	no	—
27	C₂²×C₆₁	C₂²⋊C₈	1	1	yes	characteristic
28	C₄×C₆₁	—	2	1	no	—
29	C₄×C₆₁	#99	1	1	yes	characteristic
30	C₄×C₆₁	#101	1	1	yes	characteristic
31	Dic₆₁	—	4	2	no	—
32	#1328	—	61	1	no	maximal, Sylow
33	C₂×C₆₁	—	2	1	no	—
34	C₂×C₆₁	—	4	1	no	—
35	C₂×C₆₁	#324	1	1	yes	characteristic
36	#424	—	61	1	no	—
37	#349	—	61	2	no	—
38	C₆₁	#1328	1	1	yes	characteristic, complemented, Sylow
39	C₂×M₁₆	—	61	1	no	—
40	C₂²×C₈	#6923	1	1	yes	characteristic
41	#117	—	61	1	no	—
42	M₃₂	—	122	2	no	—
43	C₄⋊C₈	—	122	2	no	—
44	C₂²×C₄	C₂×#6923	1	1	yes	characteristic
45	M₁₆	—	244	1	no	—
46	C₂×C₈	—	2	1	no	—
47	C₂×C₈	—	4	1	no	—
48	C₂×C₈	—	61	2	no	—
49	C₄⋊C₄	—	122	1	no	—
50	C₂²⋊C₄	—	61	2	no	—
51	C₄²	—	122	1	no	—
52	C₁₆	—	244	2	no	—
53	C₂³	D₆₁⋊C₈	1	1	yes	characteristic
54	C₂×C₄	—	2	1	no	—
55	C₂×C₄	—	2	1	no	—
56	C₂×C₄	—	122	2	no	—
57	C₂×C₄	#11758213	1	1	yes	characteristic
58	C₂×C₄	C₂²⋊#6923	1	1	yes	characteristic
59	C₈	—	4	1	no	—
60	C₈	—	122	2	no	—
61	C₂²	—	2	1	no	—
62	C₂²	—	4	1	no	—
63	C₂²	#14519834	1	1	yes	characteristic
64	C₄	—	2	1	no	—
65	C₄	—	244	2	no	—
66	C₄	#14519835	1	1	yes	characteristic
67	C₄	#14519838	1	1	yes	characteristic
68	C₂	—	2	1	no	—
69	C₂	—	4	1	no	—
70	C₂	#16840608	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#14519835
commutator	C₂³×C₆₁	C₂×C₈
Frattini	C₂²×C₄	C₂×#6923
Fitting	C₂²×C₈×C₆₁	C₄
socle	C₂×C₆₁	#324
hypercenter	C₂²×C₈	#6923
hypocenter	C₆₁	#1328
LCS	G ▷ C₂³×C₆₁ ▷ C₂²×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂²×C₈

Complements

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

N	H ≅ G/N	type
38. C₆₁	#1328	semidirect