Subgroups — #21460975

Order 7808.

70 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16840695	C₂	1	1	yes	maximal, characteristic
2	#16840691	C₂	1	1	yes	maximal, characteristic
3	Q₃₂×D₆₁	C₂	1	1	yes	maximal, characteristic
4	#14519848	—	2	1	no	—
5	#14519827	—	2	1	no	—
6	Q₁₆×D₆₁	—	2	1	no	—
7	Dic₄₈₈	C₄	1	1	yes	characteristic
8	#14519723	—	2	1	no	—
9	C₁₆×D₆₁	C₂²	1	1	yes	characteristic
10	Q₃₂×C₆₁	C₄	1	1	yes	characteristic
11	Q₈×D₆₁	—	4	1	no	—
12	#11758213	—	4	1	no	—
13	Q₁₆×C₆₁	—	2	1	no	—
14	#11758202	—	4	1	no	—
15	Dic₂₄₄	—	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	Q₈×C₆₁	—	4	1	no	—
20	C₄×D₆₁	—	8	1	no	—
21	C₄×D₆₁	D₈	1	1	yes	characteristic
22	Dic₁₂₂	—	4	1	no	—
23	Dic₁₂₂	—	8	1	no	—
24	#92420	—	8	1	no	—
25	C₈×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
26	#92418	SD₁₆	1	1	yes	characteristic
27	C₂×D₆₁	SD₃₂	1	1	yes	characteristic
28	C₄×C₆₁	—	8	1	no	—
29	C₄×C₆₁	#102	1	1	yes	characteristic
30	Dic₆₁	—	8	1	no	—
31	Dic₆₁	D₁₆	1	1	yes	characteristic
32	#1420	—	61	1	no	maximal, Sylow
33	C₂×C₆₁	#357	1	1	yes	characteristic
34	D₆₁	—	2	1	no	—
35	C₂×Q₃₂	—	61	1	no	—
36	M₆₄	—	61	1	no	—
37	#368	—	61	1	no	—
38	C₆₁	#1420	1	1	yes	characteristic, complemented, Sylow
39	C₂×Q₁₆	—	122	1	no	—
40	Q₃₂	—	61	1	no	—
41	Q₃₂	—	122	1	no	—
42	Q₃₂	#6923	1	1	yes	characteristic
43	C₂×C₁₆	—	61	1	no	—
44	#108	—	122	1	no	—
45	C₃₂	—	122	1	no	—
46	C₂×Q₈	—	244	1	no	—
47	Q₁₆	—	2	1	no	—
48	Q₁₆	—	122	1	no	—
49	Q₁₆	—	244	1	no	—
50	M₁₆	—	244	1	no	—
51	C₂×C₈	—	61	1	no	—
52	C₁₆	—	61	1	no	—
53	C₁₆	C₂×#6923	1	1	yes	characteristic
54	Q₈	—	4	1	no	—
55	Q₈	—	488	1	no	—
56	Q₈	—	244	1	no	—
57	C₂×C₄	—	61	1	no	—
58	C₂×C₄	—	488	1	no	—
59	C₈	—	61	1	no	—
60	C₈	—	488	1	no	—
61	C₈	C₂²⋊#6923	1	1	yes	characteristic
62	C₂²	—	61	1	no	—
63	C₄	—	8	1	no	—
64	C₄	—	61	1	no	—
65	C₄	—	488	1	no	—
66	C₄	#14519839	1	1	yes	characteristic
67	C₂	—	122	1	no	—
68	C₂	#16840674	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#16840674
commutator	C₁₆×C₆₁	C₂×C₄
Frattini	C₁₆	C₂×#6923
Fitting	Q₃₂×C₆₁	C₄
socle	C₂×C₆₁	#357
hypercenter	Q₃₂	#6923
hypocenter	C₆₁	#1420
LCS	G ▷ C₁₆×C₆₁ ▷ C₈×C₆₁ ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ C₁₆ ◁ Q₃₂

Complements

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

N	H ≅ G/N	type
38. C₆₁	#1420	semidirect