Subgroups — #21460974

Order 7808.

78 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16840695	C₂	1	1	yes	maximal, characteristic, complemented
2	#16840691	C₂	1	1	yes	maximal, characteristic, complemented
3	D₁₆×D₆₁	C₂	1	1	yes	maximal, characteristic
4	#14519848	—	2	1	no	—
5	#14519827	—	2	1	no	—
6	D₈×D₆₁	—	2	1	no	—
7	D₉₇₆	C₄	1	1	yes	characteristic
8	#14519718	—	2	1	no	—
9	C₁₆×D₆₁	C₂²	1	1	yes	characteristic
10	D₁₆×C₆₁	C₄	1	1	yes	characteristic
11	D₄×D₆₁	—	4	1	no	—
12	#11758213	—	4	1	no	—
13	D₈×C₆₁	—	2	1	no	—
14	#11758199	—	4	1	no	—
15	D₄₈₈	—	2	1	no	—
16	C₈×D₆₁	D₄	1	1	yes	characteristic
17	C₁₆×C₆₁	C₂×C₄	1	1	yes	characteristic
18	#11758185	D₄	1	1	yes	characteristic
19	C₂²×D₆₁	—	8	1	no	—
20	D₄×C₆₁	—	4	1	no	—
21	C₂²⋊D₆₁	—	8	1	no	—
22	D₂₄₄	—	4	1	no	—
23	C₄×D₆₁	D₈	1	1	yes	characteristic
24	#92420	—	8	1	no	—
25	C₈×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
26	#92418	SD₁₆	1	1	yes	characteristic
27	C₂²×C₆₁	—	8	1	no	—
28	C₂×D₆₁	—	8	1	no	—
29	C₂×D₆₁	—	16	2	no	—
30	C₂×D₆₁	SD₃₂	1	1	yes	characteristic
31	C₄×C₆₁	#102	1	1	yes	characteristic
32	Dic₆₁	D₁₆	1	1	yes	characteristic
33	#1419	—	61	1	no	maximal, Sylow
34	C₂×C₆₁	—	16	1	no	—
35	C₂×C₆₁	#357	1	1	yes	characteristic
36	D₆₁	—	2	1	no	—
37	D₆₁	—	16	1	no	—
38	C₂×D₁₆	—	61	1	no	—
39	M₆₄	—	61	1	no	—
40	#368	—	61	1	no	—
41	C₆₁	#1419	1	1	yes	characteristic, complemented, Sylow
42	C₂×D₈	—	122	1	no	—
43	D₁₆	—	61	1	no	—
44	D₁₆	—	122	1	no	—
45	D₁₆	#6923	1	1	yes	characteristic
46	C₂×C₁₆	—	61	1	no	—
47	#108	—	122	1	no	—
48	C₃₂	—	122	1	no	—
49	C₂×D₄	—	244	1	no	—
50	D₈	—	2	1	no	—
51	D₈	—	122	1	no	—
52	D₈	—	244	1	no	—
53	M₁₆	—	244	1	no	—
54	C₂×C₈	—	61	1	no	—
55	C₁₆	—	61	1	no	—
56	C₁₆	C₂×#6923	1	1	yes	characteristic
57	C₂³	—	488	1	no	—
58	D₄	—	4	1	no	—
59	D₄	—	488	1	no	—
60	D₄	—	244	1	no	—
61	C₂×C₄	—	61	1	no	—
62	C₈	—	61	1	no	—
63	C₈	—	488	1	no	—
64	C₈	C₂²⋊#6923	1	1	yes	characteristic
65	C₂²	—	8	1	no	—
66	C₂²	—	61	1	no	—
67	C₂²	—	976	2	no	—
68	C₂²	—	488	1	no	—
69	C₄	—	61	1	no	—
70	C₄	#14519839	1	1	yes	characteristic
71	C₂	—	16	1	no	—
72	C₂	—	122	1	no	—
73	C₂	—	976	1	no	—
74	C₂	#16840674	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#16840674
commutator	C₁₆×C₆₁	C₂×C₄
Frattini	C₁₆	C₂×#6923
Fitting	D₁₆×C₆₁	C₄
socle	C₂×C₆₁	#357
hypercenter	D₁₆	#6923
hypocenter	C₆₁	#1419
LCS	G ▷ C₁₆×C₆₁ ▷ C₈×C₆₁ ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ C₁₆ ◁ D₁₆

Complements

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

N	H ≅ G/N	type
1. #16840695	C₂	semidirect
2. #16840691	C₂	semidirect
41. C₆₁	#1419	semidirect