Subgroups — #21447635

Order 7808.

122 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16839583	C₂	1	2	yes	maximal, complemented
2	#16839544	C₂	1	2	yes	maximal
3	#16839540	C₂	1	2	yes	maximal, complemented
4	C₆₁×#405	C₂	1	1	yes	maximal, characteristic
5	#14519717	C₂²	1	4	yes	—
6	C₂×M₁₆×C₆₁	C₂²	1	1	yes	characteristic
7	C₂²×C₈×C₆₁	C₄	1	1	yes	characteristic
8	#117×C₆₁	C₄	1	1	yes	characteristic
9	#97×C₆₁	C₄	1	1	yes	characteristic
10	#97×C₆₁	C₂²	1	1	yes	characteristic
11	C₄×C₈×C₆₁	C₄	1	1	yes	characteristic
12	C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
13	C₂²×C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
14	M₁₆×C₆₁	—	2	2	no	—
15	C₂×C₈×C₆₁	—	2	2	no	—
16	C₂×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
17	C₂×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
18	C₂×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
19	C₂×C₈×C₆₁	C₂³	1	1	yes	characteristic
20	C₄⋊C₄×C₆₁	—	2	1	no	—
21	C₂²⋊C₄×C₆₁	—	2	1	no	—
22	C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
23	C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
24	#11758185	—	2	4	no	—
25	C₂³×C₆₁	M₁₆	1	1	yes	characteristic
26	C₂×C₄×C₆₁	—	2	1	no	—
27	C₂×C₄×C₆₁	—	2	1	no	—
28	C₂×C₄×C₆₁	—	2	1	no	—
29	C₂×C₄×C₆₁	—	2	1	no	—
30	C₂×C₄×C₆₁	M₁₆	1	1	yes	characteristic
31	C₂×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
32	C₈×C₆₁	—	2	1	no	—
33	C₈×C₆₁	—	2	1	no	—
34	C₈×C₆₁	M₁₆	1	2	yes	—
35	C₈×C₆₁	#41	1	2	yes	—
36	C₂²×C₆₁	—	2	1	no	—
37	C₂²×C₆₁	—	4	1	no	—
38	C₂²×C₆₁	C₂×M₁₆	1	1	yes	characteristic
39	C₄×C₆₁	—	2	1	no	—
40	C₄×C₆₁	—	4	1	no	—
41	C₄×C₆₁	—	4	1	no	—
42	C₄×C₆₁	#117	1	1	yes	characteristic
43	C₄×C₆₁	C₂×M₁₆	1	1	yes	characteristic
44	#2166	—	61	1	no	maximal, Sylow
45	C₂×C₆₁	—	2	1	no	—
46	C₂×C₆₁	—	4	1	no	—
47	C₂×C₆₁	#432	1	1	yes	characteristic
48	#405	D₆₁	1	1	yes	characteristic
49	#364	—	61	2	no	—
50	#349	—	61	2	no	—
51	#347	—	61	2	no	—
52	C₆₁	#2166	1	1	yes	characteristic, complemented, Sylow
53	C₂×M₁₆	C₂×D₆₁	1	1	yes	characteristic
54	C₂²×C₈	Dic₆₁	1	1	yes	characteristic
55	#117	Dic₆₁	1	1	yes	characteristic
56	M₃₂	—	61	4	no	—
57	#97	Dic₆₁	1	1	yes	characteristic
58	#97	C₂×D₆₁	1	1	yes	characteristic
59	C₄×C₈	Dic₆₁	1	1	yes	characteristic
60	C₄×C₈	C₂×D₆₁	1	1	yes	characteristic
61	C₂²×C₄	C₂×Dic₆₁	1	1	yes	characteristic
62	M₁₆	—	2	2	no	—
63	C₂×C₈	—	2	2	no	—
64	C₂×C₈	C₂×Dic₆₁	1	1	yes	characteristic
65	C₂×C₈	C₂×Dic₆₁	1	1	yes	characteristic
66	C₂×C₈	C₂×Dic₆₁	1	1	yes	characteristic
67	C₂×C₈	C₂²×D₆₁	1	1	yes	characteristic
68	C₄⋊C₄	—	2	1	no	—
69	C₂²⋊C₄	—	2	1	no	—
70	C₄²	C₂×Dic₆₁	1	1	yes	characteristic
71	C₄²	C₂×Dic₆₁	1	1	yes	characteristic
72	C₁₆	—	122	4	no	—
73	C₂³	#11758194	1	1	yes	characteristic
74	C₂×C₄	—	2	1	no	—
75	C₂×C₄	—	2	1	no	—
76	C₂×C₄	—	2	1	no	—
77	C₂×C₄	—	2	1	no	—
78	C₂×C₄	#11758194	1	1	yes	characteristic
79	C₂×C₄	C₂²×Dic₆₁	1	1	yes	characteristic
80	C₈	—	2	1	no	—
81	C₈	—	2	1	no	—
82	C₈	#11758194	1	2	yes	—
83	C₈	#11758222	1	2	yes	—
84	C₂²	—	2	1	no	—
85	C₂²	—	4	1	no	—
86	C₂²	C₂×#11758194	1	1	yes	characteristic
87	C₄	—	2	1	no	—
88	C₄	—	4	1	no	—
89	C₄	—	4	1	no	—
90	C₄	#14519736	1	1	yes	characteristic
91	C₄	C₂×#11758194	1	1	yes	characteristic
92	C₂	—	2	1	no	—
93	C₂	—	4	1	no	—
94	C₂	#16839819	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#14519736
commutator	C₂×C₄×C₆₁	C₂²×C₄
Frattini	C₂×C₈	C₂²×D₆₁
Fitting	C₆₁×#405	C₂
socle	C₂×C₆₁	#432
hypercenter	#405	D₆₁
hypocenter	C₆₁	#2166
LCS	G ▷ C₂×C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₄ ◁ #97 ◁ #405

Complements

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

N	H ≅ G/N	type
1. #16839583	C₂	semidirect
3. #16839540	C₂	semidirect
52. C₆₁	#2166	semidirect