Subgroups — #21447600

Order 7808.

152 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₆×D₆₁	C₂	1	1	yes	maximal, characteristic
2	#16839799	C₂	1	2	yes	maximal
3	#16839589	C₂	1	2	yes	maximal, complemented
4	#16839588	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₁×#366	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₈×D₆₁	C₂²	1	1	yes	characteristic
7	#14519735	—	2	2	no	—
8	C₂×#11758185	C₂²	1	1	yes	characteristic
9	C₁₆×D₆₁	C₄	1	4	yes	complemented
10	#14519711	C₂²	1	2	yes	—
11	#14519708	—	2	2	no	—
12	C₂×C₁₆×C₆₁	C₂²	1	1	yes	characteristic
13	#107×C₆₁	C₂²	1	2	yes	—
14	C₂×C₄×D₆₁	D₄	1	1	yes	characteristic
15	C₂×C₈×C₆₁	C₂³	1	1	yes	characteristic
16	C₄⋊C₄×C₆₁	—	2	2	no	—
17	#11758198	—	4	2	no	—
18	C₄⋊Dic₆₁	—	2	2	no	—
19	C₄×Dic₆₁	—	4	2	no	—
20	C₂×#92418	D₄	1	1	yes	characteristic
21	C₈×D₆₁	C₂×C₄	1	2	yes	—
22	C₈×D₆₁	Q₈	1	2	yes	—
23	C₁₆×C₆₁	C₂×C₄	1	2	yes	—
24	#11758185	C₂×C₄	1	2	yes	—
25	C₂²×D₆₁	D₈	1	1	yes	characteristic
26	C₂×C₄×C₆₁	—	4	2	no	—
27	C₂×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
28	C₂×Dic₆₁	—	4	2	no	—
29	C₂×Dic₆₁	D₈	1	1	yes	characteristic
30	C₄×D₆₁	C₄⋊C₄	1	2	yes	—
31	C₄×D₆₁	Q₁₆	1	2	yes	—
32	C₈×C₆₁	C₂²×C₄	1	1	yes	characteristic
33	C₈×C₆₁	C₂×Q₈	1	1	yes	characteristic
34	#92418	C₄⋊C₄	1	2	yes	—
35	C₂²×C₆₁	C₂×D₈	1	1	yes	characteristic
36	C₂×D₆₁	—	2	1	no	—
37	C₂×D₆₁	—	2	1	no	—
38	C₂×D₆₁	#107	1	2	yes	—
39	C₄×C₆₁	—	8	2	no	—
40	C₄×C₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
41	C₄×C₆₁	C₂×Q₁₆	1	1	yes	characteristic
42	Dic₆₁	—	8	2	no	—
43	Dic₆₁	#107	1	2	yes	—
44	#2158	—	61	1	no	maximal, Sylow
45	C₂×C₆₁	C₂×#107	1	1	yes	characteristic
46	C₂×C₆₁	#508	1	1	yes	characteristic
47	C₂×C₆₁	#508	1	1	yes	characteristic
48	D₆₁	—	2	2	no	—
49	C₂²×C₁₆	—	61	1	no	—
50	#427	—	61	2	no	—
51	#367	—	61	2	no	—
52	#366	—	61	1	no	—
53	#366	D₆₁	1	1	yes	characteristic, complemented
54	C₆₁	#2158	1	1	yes	characteristic, complemented, Sylow
55	C₂²×C₈	—	61	1	no	—
56	#117	—	122	2	no	—
57	C₂×C₁₆	—	61	1	no	—
58	C₂×C₁₆	—	61	4	no	—
59	C₂×C₁₆	C₂×D₆₁	1	1	yes	characteristic
60	#107	—	61	2	no	—
61	#107	C₂×D₆₁	1	2	yes	—
62	#106	—	122	2	no	—
63	C₂²×C₄	—	61	1	no	—
64	C₂×C₈	—	61	1	no	—
65	C₂×C₈	—	61	2	no	—
66	C₂×C₈	—	61	2	no	—
67	C₂×C₈	C₂²×D₆₁	1	1	yes	characteristic
68	C₄⋊C₄	—	2	2	no	—
69	C₄⋊C₄	—	122	2	no	—
70	C₂²⋊C₄	—	244	2	no	—
71	C₄²	—	244	2	no	—
72	C₁₆	—	61	2	no	—
73	C₁₆	C₄×D₆₁	1	2	yes	—
74	C₂³	—	61	1	no	—
75	C₂×C₄	—	4	2	no	—
76	C₂×C₄	—	61	1	no	—
77	C₂×C₄	—	61	2	no	—
78	C₂×C₄	—	61	2	no	—
79	C₂×C₄	—	244	2	no	—
80	C₂×C₄	D₄×D₆₁	1	1	yes	characteristic
81	C₈	—	61	2	no	—
82	C₈	C₂×C₄×D₆₁	1	1	yes	characteristic
83	C₈	Q₈×D₆₁	1	1	yes	characteristic
84	C₂²	—	61	2	no	—
85	C₂²	—	122	1	no	—
86	C₂²	—	122	1	no	—
87	C₂²	D₈×D₆₁	1	1	yes	characteristic
88	C₄	—	8	2	no	—
89	C₄	—	61	2	no	—
90	C₄	—	488	2	no	—
91	C₄	C₄⋊C₄×D₆₁	1	1	yes	characteristic
92	C₄	Q₁₆×D₆₁	1	1	yes	characteristic
93	C₂	—	122	2	no	—
94	C₂	#107×D₆₁	1	1	yes	characteristic
95	C₂	#16840191	1	1	yes	characteristic
96	C₂	#16840195	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₈×D₆₁
commutator	C₈×C₆₁	C₂²×C₄
Frattini	C₂×C₈	C₂²×D₆₁
Fitting	C₆₁×#366	C₂
socle	C₂²×C₆₁	C₂×D₈
hypercenter	#366	D₆₁
hypocenter	C₆₁	#2158
LCS	G ▷ C₈×C₆₁ ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ #366

Complements

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

N	H ≅ G/N	type
3. #16839589	C₂	semidirect
4. #16839588	C₂	semidirect
5. C₆₁×#366	C₂	semidirect
9. C₁₆×D₆₁	C₄	semidirect
53. #366	D₆₁	semidirect
54. C₆₁	#2158	semidirect