Subgroups — #21460887

Order 7808.

132 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16840772	C₂	1	2	yes	maximal
2	C₂×#14519716	C₂	1	1	yes	maximal, characteristic
3	#14519856	—	2	2	no	—
4	#14519846	—	2	2	no	—
5	#14519845	C₄	1	4	yes	complemented
6	C₂×C₈×D₆₁	C₂²	1	1	yes	characteristic
7	#14519716	—	2	2	no	—
8	C₂×#11758185	C₄	1	1	yes	characteristic, complemented
9	C₂×C₁₆×C₆₁	C₄	1	1	yes	characteristic, complemented
10	C₂×C₄×D₆₁	D₄	1	1	yes	characteristic
11	C₂²⋊#6923	—	4	2	no	—
12	C₄⋊#6923	—	2	4	no	—
13	C₄×#6923	—	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	D₈	1	1	yes	characteristic
21	C₂×#6923	—	4	4	no	—
22	C₂×C₄×C₆₁	C₄⋊C₄	1	1	yes	characteristic
23	C₂×Dic₆₁	Q₁₆	1	1	yes	characteristic
24	C₄×D₆₁	C₂²⋊C₄	1	2	yes	—
25	C₄×D₆₁	SD₁₆	1	2	yes	—
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	#102	1	2	yes	—
32	#6923	—	8	4	no	—
33	C₄×C₆₁	#95	1	1	yes	characteristic
34	C₄×C₆₁	#106	1	1	yes	characteristic
35	Dic₆₁	#103	1	2	yes	—
36	#1384	—	61	1	no	maximal, Sylow
37	C₂×C₆₁	—	2	1	no	—
38	C₂×C₆₁	#340	1	1	yes	characteristic
39	D₆₁	—	2	2	no	—
40	C₂×M₃₂	—	61	1	no	—
41	#427	—	61	2	no	—
42	C₆₁	#1384	1	1	yes	characteristic, complemented, Sylow
43	C₂²×C₈	—	61	1	no	—
44	#117	—	122	2	no	—
45	M₃₂	—	122	2	no	—
46	C₂×C₁₆	—	61	1	no	—
47	C₂×C₁₆	#6923	1	1	yes	characteristic, complemented
48	#107	—	122	2	no	—
49	#106	—	61	4	no	—
50	C₂²×C₄	—	61	1	no	—
51	C₂×C₈	—	61	1	no	—
52	C₂×C₈	—	61	2	no	—
53	C₂×C₈	—	61	2	no	—
54	C₂×C₈	C₂×#6923	1	1	yes	characteristic
55	C₄⋊C₄	—	122	4	no	—
56	C₂²⋊C₄	—	244	2	no	—
57	C₄²	—	244	2	no	—
58	C₁₆	—	2	1	no	—
59	C₁₆	—	122	1	no	—
60	C₂³	—	61	1	no	—
61	C₂×C₄	—	61	1	no	—
62	C₂×C₄	—	61	2	no	—
63	C₂×C₄	—	61	2	no	—
64	C₂×C₄	—	244	4	no	—
65	C₂×C₄	C₄⋊#6923	1	1	yes	characteristic
66	C₈	—	61	2	no	—
67	C₈	C₄×#6923	1	1	yes	characteristic
68	C₈	C₂²⋊#6923	1	1	yes	characteristic
69	C₂²	—	61	2	no	—
70	C₂²	—	244	1	no	—
71	C₂²	#14519846	1	1	yes	characteristic
72	C₄	—	61	2	no	—
73	C₄	—	488	4	no	—
74	C₄	(C₂×#6923)⋊C₄	1	1	yes	characteristic
75	C₄	#14519845	1	1	yes	characteristic
76	C₂	—	2	1	no	—
77	C₂	—	122	2	no	—
78	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	#1384
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
5. #14519845	C₄	semidirect
8. C₂×#11758185	C₄	semidirect
9. C₂×C₁₆×C₆₁	C₄	semidirect
42. C₆₁	#1384	semidirect
47. C₂×C₁₆	#6923	semidirect