Subgroups — #21460738

Order 7808.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16840651	C₂	1	1	yes	maximal, characteristic
2	#16840603	C₂	1	1	yes	maximal, characteristic
3	#16839537	C₂	1	1	yes	maximal, characteristic
4	C₂×#11758187	C₄	1	2	yes	—
5	C₄×#92420	C₄	1	1	yes	characteristic
6	C₄×#92420	C₄	1	1	yes	characteristic
7	C₂×#11758185	C₄	1	1	yes	characteristic
8	C₈×Dic₆₁	C₂²	1	1	yes	characteristic
9	C₂×C₁₆×C₆₁	C₄	1	1	yes	characteristic
10	C₂×#92420	—	2	1	no	—
11	C₂×#92420	—	2	1	no	—
12	C₂×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
13	C₄×Dic₆₁	C₂×C₄	1	1	yes	characteristic
14	C₂×#92418	C₂×C₄	1	1	yes	characteristic
15	#11758187	C₈	1	4	yes	complemented
16	C₁₆×C₆₁	—	2	1	no	—
17	#11758185	—	2	1	no	—
18	C₂×C₄×C₆₁	C₄²	1	1	yes	characteristic
19	C₂×Dic₆₁	M₁₆	1	1	yes	characteristic
20	C₂×Dic₆₁	M₁₆	1	1	yes	characteristic
21	#92420	—	4	1	no	—
22	#92420	—	4	1	no	—
23	C₈×C₆₁	M₁₆	1	1	yes	characteristic
24	C₈×C₆₁	M₁₆	1	1	yes	characteristic
25	#92418	C₂×C₈	1	2	yes	—
26	C₂²×C₆₁	#97	1	1	yes	characteristic
27	C₄×C₆₁	C₄×C₈	1	1	yes	characteristic
28	C₄×C₆₁	#97	1	1	yes	characteristic
29	Dic₆₁	—	2	1	no	—
30	Dic₆₁	—	2	1	no	—
31	#1313	—	61	1	no	maximal, Sylow
32	C₂×C₆₁	#322	1	1	yes	characteristic
33	C₂×C₆₁	#347	1	1	yes	characteristic
34	C₂×C₆₁	#347	1	1	yes	characteristic
35	#346	—	61	1	no	—
36	#346	—	61	1	no	—
37	#322	—	61	1	no	—
38	C₆₁	#1313	1	1	yes	characteristic, complemented, Sylow
39	C₂×C₁₆	—	61	2	no	—
40	C₂×C₁₆	—	61	1	no	—
41	C₂×C₁₆	#6923	1	1	yes	characteristic
42	C₄×C₈	—	61	1	no	—
43	C₄×C₈	—	61	1	no	—
44	C₄×C₈	—	61	1	no	—
45	C₂×C₈	—	61	1	no	—
46	C₂×C₈	—	122	1	no	—
47	C₂×C₈	—	122	1	no	—
48	C₂×C₈	C₂×#6923	1	1	yes	characteristic
49	C₄²	—	61	1	no	—
50	C₁₆	—	2	1	no	—
51	C₁₆	—	61	4	no	—
52	C₁₆	—	122	1	no	—
53	C₂×C₄	—	61	1	no	—
54	C₂×C₄	—	61	1	no	—
55	C₂×C₄	C₄×#6923	1	1	yes	characteristic
56	C₈	—	61	2	no	—
57	C₈	—	244	1	no	—
58	C₈	—	244	1	no	—
59	C₈	#11758213	1	1	yes	characteristic
60	C₈	#11758217	1	1	yes	characteristic
61	C₂²	#14519831	1	1	yes	characteristic
62	C₄	—	122	1	no	—
63	C₄	—	122	1	no	—
64	C₄	C₈×#6923	1	1	yes	characteristic
65	C₄	#14519832	1	1	yes	characteristic
66	C₂	#92420⋊C₈	1	1	yes	characteristic
67	C₂	#16840652	1	1	yes	characteristic
68	C₂	#16840653	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₄×#6923
commutator	C₄×C₆₁	C₄×C₈
Frattini	C₂×C₈	C₂×#6923
Fitting	C₂×C₁₆×C₆₁	C₄
socle	C₂²×C₆₁	#97
hypercenter	C₂×C₁₆	#6923
hypocenter	C₆₁	#1313
LCS	G ▷ C₄×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₁₆

Complements

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

N	H ≅ G/N	type
15. #11758187	C₈	semidirect
38. C₆₁	#1313	semidirect