Subgroups — #21443876

Order 7808.

86 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16840167	C₂	1	1	yes	maximal, characteristic
2	#16839515	C₂	1	1	yes	maximal, characteristic
3	C₆₁×C₄⋊C₁₆	C₂	1	1	yes	maximal, characteristic
4	#14519777	—	2	1	no	—
5	#14519711	—	2	1	no	—
6	#14519711	C₄	1	2	yes	—
7	C₄⋊#92418	—	2	1	no	—
8	C₂×C₁₆×C₆₁	—	2	1	no	—
9	C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
10	C₂×Dic₁₂₂	—	4	1	no	—
11	C₂×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
12	C₂×C₈×C₆₁	D₄	1	1	yes	characteristic
13	C₄²×C₆₁	D₄	1	1	yes	characteristic
14	C₄⋊Dic₆₁	—	2	2	no	—
15	C₄⋊Dic₆₁	—	4	1	no	—
16	C₂×#92418	—	4	1	no	—
17	C₁₆×C₆₁	—	4	1	no	—
18	C₂×C₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
19	C₂×C₄×C₆₁	D₈	1	1	yes	characteristic
20	C₂×C₄×C₆₁	SD₁₆	1	1	yes	characteristic
21	C₂×Dic₆₁	—	4	2	no	—
22	Dic₁₂₂	—	8	2	no	—
23	C₈×C₆₁	—	2	1	no	—
24	C₈×C₆₁	SD₁₆	1	1	yes	characteristic
25	C₈×C₆₁	Q₁₆	1	1	yes	characteristic
26	#92418	—	8	1	no	—
27	C₂²×C₆₁	#102	1	1	yes	characteristic
28	C₄×C₆₁	—	2	1	no	—
29	C₄×C₆₁	#101	1	1	yes	characteristic
30	C₄×C₆₁	#103	1	1	yes	characteristic
31	C₄×C₆₁	SD₃₂	1	1	yes	characteristic
32	C₄×C₆₁	Q₃₂	1	1	yes	characteristic
33	Dic₆₁	—	8	2	no	—
34	#1365	—	61	1	no	maximal, Sylow
35	C₂×C₆₁	#332	1	1	yes	characteristic
36	C₂×C₆₁	#358	1	1	yes	characteristic
37	C₂×C₆₁	#361	1	1	yes	characteristic
38	#500	—	61	1	no	—
39	C₄⋊C₁₆	D₆₁	1	1	yes	characteristic
40	#335	—	61	1	no	—
41	C₆₁	#1365	1	1	yes	characteristic, complemented, Sylow
42	C₄⋊Q₈	—	122	1	no	—
43	C₂×C₁₆	—	2	1	no	—
44	#107	—	61	2	no	—
45	#107	—	122	1	no	—
46	C₄⋊C₈	—	122	1	no	—
47	C₄×C₈	C₂×D₆₁	1	1	yes	characteristic
48	C₂×Q₈	—	244	1	no	—
49	C₂×C₈	—	244	1	no	—
50	C₂×C₈	C₄×D₆₁	1	1	yes	characteristic
51	C₂×C₈	C₂²⋊D₆₁	1	1	yes	characteristic
52	C₄⋊C₄	—	122	2	no	—
53	C₄⋊C₄	—	244	1	no	—
54	C₄²	D₂₄₄	1	1	yes	characteristic
55	C₁₆	—	4	1	no	—
56	Q₈	—	488	2	no	—
57	C₂×C₄	—	244	2	no	—
58	C₂×C₄	#11758190	1	1	yes	characteristic
59	C₂×C₄	D₄₈₈	1	1	yes	characteristic
60	C₂×C₄	#11758198	1	1	yes	characteristic
61	C₈	—	2	1	no	—
62	C₈	—	488	1	no	—
63	C₈	#11758200	1	1	yes	characteristic
64	C₈	#11758202	1	1	yes	characteristic
65	C₂²	#14519699	1	1	yes	characteristic
66	C₄	—	2	1	no	—
67	C₄	—	488	2	no	—
68	C₄	#14519695	1	1	yes	characteristic
69	C₄	#14519700	1	1	yes	characteristic
70	C₄	#14519722	1	1	yes	characteristic
71	C₄	Dic₄₈₈	1	1	yes	characteristic
72	C₂	#16839507	1	1	yes	characteristic
73	C₂	#16839567	1	1	yes	characteristic
74	C₂	#16839576	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#14519699
commutator	C₂×C₈×C₆₁	C₂×C₄
Frattini	C₄×C₈	C₂×D₆₁
Fitting	C₆₁×C₄⋊C₁₆	C₂
socle	C₂²×C₆₁	#102
hypercenter	C₄⋊C₁₆	D₆₁
hypocenter	C₆₁	#1365
LCS	G ▷ C₂×C₈×C₆₁ ▷ C₂×C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ C₄⋊C₁₆

Complements

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

N	H ≅ G/N	type
41. C₆₁	#1365	semidirect