Subgroups — #21443777

Order 7808.

100 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊#11758185	C₂	1	1	yes	maximal, characteristic, complemented
2	#16839538	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₁×#436	C₂	1	1	yes	maximal, characteristic
4	C₂×#11758185	—	2	1	no	—
5	C₂×#11758185	—	2	1	no	—
6	C₂×M₁₆×C₆₁	—	2	1	no	—
7	C₄×D₄×C₆₁	C₄	1	1	yes	characteristic
8	C₄⋊C₈×C₆₁	C₄	1	1	yes	characteristic
9	C₂²⋊C₈×C₆₁	—	2	1	no	—
10	C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
11	C₂×D₄×C₆₁	C₈	1	1	yes	characteristic
12	C₂²×C₄×C₆₁	—	2	1	no	—
13	M₁₆×C₆₁	—	4	1	no	—
14	M₁₆×C₆₁	—	4	1	no	—
15	C₂×C₈×C₆₁	—	2	1	no	—
16	C₂×C₈×C₆₁	D₄	1	1	yes	characteristic
17	C₂×C₈×C₆₁	D₄	1	1	yes	characteristic
18	C₄⋊C₄×C₆₁	C₈	1	1	yes	characteristic
19	C₂²⋊C₄×C₆₁	—	2	1	no	—
20	C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
21	#11758185	—	2	2	no	—
22	#11758185	—	4	1	no	—
23	C₂³×C₆₁	—	2	1	no	—
24	D₄×C₆₁	—	4	1	no	—
25	C₂×C₄×C₆₁	—	2	1	no	—
26	C₂×C₄×C₆₁	—	4	1	no	—
27	C₂×C₄×C₆₁	—	4	1	no	—
28	C₂×C₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
29	C₂×C₄×C₆₁	C₂×C₈	1	1	yes	characteristic
30	C₂×C₄×C₆₁	M₁₆	1	1	yes	characteristic
31	C₈×C₆₁	—	2	1	no	—
32	C₈×C₆₁	—	4	1	no	—
33	C₈×C₆₁	D₈	1	1	yes	characteristic
34	C₈×C₆₁	SD₁₆	1	1	yes	characteristic
35	C₂²×C₆₁	—	4	1	no	—
36	C₂²×C₆₁	—	4	1	no	—
37	C₂²×C₆₁	—	4	1	no	—
38	C₂²×C₆₁	C₂²⋊C₈	1	1	yes	characteristic
39	C₄×C₆₁	—	2	1	no	—
40	C₄×C₆₁	—	2	1	no	—
41	C₄×C₆₁	—	4	1	no	—
42	C₄×C₆₁	#102	1	1	yes	characteristic
43	C₄×C₆₁	#104	1	1	yes	characteristic
44	#1330	—	61	1	no	maximal, Sylow
45	C₂×C₆₁	—	8	1	no	—
46	C₂×C₆₁	D₄⋊C₈	1	1	yes	characteristic
47	C₂×C₆₁	#349	1	1	yes	characteristic
48	C₂×C₆₁	#350	1	1	yes	characteristic
49	#436	D₆₁	1	1	yes	characteristic
50	C₄⋊C₁₆	—	61	1	no	—
51	#346	—	61	1	no	—
52	C₆₁	#1330	1	1	yes	characteristic, complemented, Sylow
53	C₂×M₁₆	—	2	1	no	—
54	C₄×D₄	Dic₆₁	1	1	yes	characteristic
55	C₂×C₁₆	—	122	1	no	—
56	C₂×C₁₆	—	122	1	no	—
57	C₄⋊C₈	Dic₆₁	1	1	yes	characteristic
58	C₂²⋊C₈	—	2	1	no	—
59	C₄×C₈	C₂×D₆₁	1	1	yes	characteristic
60	C₂×D₄	#92418	1	1	yes	characteristic
61	C₂²×C₄	—	2	1	no	—
62	M₁₆	—	4	1	no	—
63	M₁₆	—	4	1	no	—
64	C₂×C₈	—	2	1	no	—
65	C₂×C₈	C₂²⋊D₆₁	1	1	yes	characteristic
66	C₂×C₈	C₂²⋊D₆₁	1	1	yes	characteristic
67	C₄⋊C₄	#92418	1	1	yes	characteristic
68	C₂²⋊C₄	—	2	1	no	—
69	C₄²	C₂×Dic₆₁	1	1	yes	characteristic
70	C₁₆	—	122	2	no	—
71	C₁₆	—	244	1	no	—
72	C₂³	—	2	1	no	—
73	D₄	—	4	1	no	—
74	C₂×C₄	—	2	1	no	—
75	C₂×C₄	—	4	1	no	—
76	C₂×C₄	—	4	1	no	—
77	C₂×C₄	C₂×#92418	1	1	yes	characteristic
78	C₂×C₄	#11758194	1	1	yes	characteristic
79	C₂×C₄	C₂²⋊Dic₆₁	1	1	yes	characteristic
80	C₈	—	2	1	no	—
81	C₈	—	4	1	no	—
82	C₈	#11758199	1	1	yes	characteristic
83	C₈	#11758200	1	1	yes	characteristic
84	C₂²	—	4	1	no	—
85	C₂²	—	4	1	no	—
86	C₂²	—	4	1	no	—
87	C₂²	C₂²⋊#92418	1	1	yes	characteristic
88	C₄	—	2	1	no	—
89	C₄	—	2	1	no	—
90	C₄	—	4	1	no	—
91	C₄	#14519698	1	1	yes	characteristic
92	C₄	#14519704	1	1	yes	characteristic
93	C₂	—	8	1	no	—
94	C₂	D₄⋊#92418	1	1	yes	characteristic
95	C₂	#16839544	1	1	yes	characteristic
96	C₂	#16839546	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²⋊Dic₆₁
commutator	C₂×C₄×C₆₁	C₂×C₈
Frattini	C₄×C₈	C₂×D₆₁
Fitting	C₆₁×#436	C₂
socle	C₂²×C₆₁	C₂²⋊C₈
hypercenter	#436	D₆₁
hypocenter	C₆₁	#1330
LCS	G ▷ C₂×C₄×C₆₁ ▷ C₂²×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #436

Complements

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

N	H ≅ G/N	type
1. C₄⋊#11758185	C₂	semidirect
2. #16839538	C₂	semidirect
52. C₆₁	#1330	semidirect