Subgroups — #21460889

Order 7808.

124 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₆₁⋊#108	C₂	1	2	yes	maximal
2	C₂×#14519716	C₂	1	1	yes	maximal, characteristic
3	D₆₁⋊M₁₆	—	2	2	no	—
4	#14519848	—	2	2	no	—
5	#14519847	C₄	1	4	yes	—
6	C₂×C₈×D₆₁	C₂²	1	1	yes	characteristic
7	#14519716	—	2	2	no	—
8	C₂×#11758185	C₄	1	1	yes	characteristic
9	C₂×C₁₆×C₆₁	C₄	1	1	yes	characteristic
10	C₂×C₄×D₆₁	D₄	1	1	yes	characteristic
11	#11758217	—	4	2	no	—
12	#11758213	—	2	4	no	—
13	D₆₁⋊C₈	—	4	2	no	—
14	C₂×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
15	C₂×#92418	Q₈	1	1	yes	characteristic
16	C₈×D₆₁	C₂×C₄	1	2	yes	—
17	C₈×D₆₁	D₄	1	2	yes	—
18	C₁₆×C₆₁	—	2	1	no	—
19	#11758185	—	2	1	no	—
20	C₂²×D₆₁	Q₁₆	1	1	yes	characteristic
21	C₂×C₄×C₆₁	C₄⋊C₄	1	1	yes	characteristic
22	C₂×Dic₆₁	D₈	1	1	yes	characteristic
23	C₄×D₆₁	C₂²⋊C₄	1	2	yes	—
24	C₄×D₆₁	SD₁₆	1	2	yes	—
25	#92420	—	4	4	no	—
26	C₈×C₆₁	C₄²	1	1	yes	characteristic
27	C₈×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
28	#92418	C₄⋊C₄	1	2	yes	—
29	C₂²×C₆₁	#107	1	1	yes	characteristic
30	C₂×D₆₁	—	4	1	no	—
31	C₂×D₆₁	#103	1	2	yes	—
32	C₄×C₆₁	#95	1	1	yes	characteristic
33	C₄×C₆₁	#106	1	1	yes	characteristic
34	Dic₆₁	#102	1	2	yes	—
35	#1385	—	61	1	no	maximal, Sylow
36	C₂×C₆₁	—	2	1	no	—
37	C₂×C₆₁	#340	1	1	yes	characteristic
38	D₆₁	—	2	2	no	—
39	C₂×M₃₂	—	61	1	no	—
40	C₂×#108	—	61	2	no	—
41	C₆₁	#1385	1	1	yes	characteristic, complemented, Sylow
42	C₂×M₁₆	—	122	2	no	—
43	C₂²×C₈	—	61	1	no	—
44	M₃₂	—	122	2	no	—
45	C₂×C₁₆	—	61	1	no	—
46	C₂×C₁₆	#6923	1	1	yes	characteristic
47	#108	—	61	4	no	—
48	#108	—	122	2	no	—
49	C₂²×C₄	—	61	1	no	—
50	M₁₆	—	122	4	no	—
51	M₁₆	—	244	2	no	—
52	C₂×C₈	—	61	1	no	—
53	C₂×C₈	—	61	2	no	—
54	C₂×C₈	—	61	2	no	—
55	C₂×C₈	—	244	2	no	—
56	C₂×C₈	C₂×#6923	1	1	yes	characteristic
57	C₁₆	—	2	1	no	—
58	C₁₆	—	122	1	no	—
59	C₂³	—	61	1	no	—
60	C₂×C₄	—	61	1	no	—
61	C₂×C₄	—	61	2	no	—
62	C₂×C₄	—	61	2	no	—
63	C₂×C₄	C₄⋊#6923	1	1	yes	characteristic
64	C₈	—	61	2	no	—
65	C₈	—	244	4	no	—
66	C₈	C₄×#6923	1	1	yes	characteristic
67	C₈	C₂²⋊#6923	1	1	yes	characteristic
68	C₂²	—	61	2	no	—
69	C₂²	—	244	1	no	—
70	C₂²	#14519846	1	1	yes	characteristic
71	C₄	—	61	2	no	—
72	C₄	(C₂×#6923)⋊C₄	1	1	yes	characteristic
73	C₄	#14519845	1	1	yes	characteristic
74	C₂	—	2	1	no	—
75	C₂	—	122	2	no	—
76	C₂	#16840636	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#14519845
commutator	C₈×C₆₁	C₄²
Frattini	C₂×C₈	C₂×#6923
Fitting	C₂×C₁₆×C₆₁	C₄
socle	C₂×C₆₁	#340
hypercenter	C₂×C₁₆	#6923
hypocenter	C₆₁	#1385
LCS	G ▷ C₈×C₆₁ ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆

Complements

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

N	H ≅ G/N	type
41. C₆₁	#1385	semidirect