Subgroups — #21448061

Order 7808.

152 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16840164	C₂	1	1	yes	maximal, characteristic, complemented
2	#16840139	C₂	1	1	yes	maximal, characteristic
3	#16839564	C₂	1	4	yes	maximal, complemented
4	C₆₁×#346	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×D₄₈₈	—	2	1	no	—
6	C₂×D₄₈₈	C₂²	1	2	yes	—
7	#14519774	—	2	1	no	—
8	#14519769	—	2	1	no	—
9	#14519711	C₂²	1	2	yes	—
10	#14519709	—	2	1	no	—
11	C₂×C₁₆×C₆₁	C₂²	1	2	yes	—
12	C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
13	C₂×D₂₄₄	—	2	2	no	—
14	C₂×D₂₄₄	—	4	2	no	—
15	C₂×C₈×C₆₁	D₄	1	1	yes	characteristic
16	C₂×C₈×C₆₁	C₂³	1	1	yes	characteristic
17	C₄²×C₆₁	D₄	1	1	yes	characteristic
18	C₄⋊Dic₆₁	—	2	2	no	—
19	#11758196	—	4	2	no	—
20	D₄₈₈	—	2	4	no	—
21	D₄₈₈	—	4	2	no	—
22	C₁₆×C₆₁	—	2	2	no	—
23	C₂²×D₆₁	—	4	2	no	—
24	C₂×C₄×C₆₁	D₈	1	2	yes	—
25	C₂×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
26	C₂×Dic₆₁	—	4	2	no	—
27	D₂₄₄	—	4	2	no	—
28	D₂₄₄	—	4	2	no	—
29	D₂₄₄	—	8	4	no	—
30	C₈×C₆₁	SD₁₆	1	2	yes	—
31	C₈×C₆₁	#41	1	2	yes	—
32	C₂²×C₆₁	C₂×D₈	1	1	yes	characteristic
33	C₂×D₆₁	—	8	2	no	—
34	C₂×D₆₁	—	8	4	no	—
35	C₄×C₆₁	—	2	2	no	—
36	C₄×C₆₁	#124	1	1	yes	characteristic
37	C₄×C₆₁	C₂×SD₁₆	1	1	yes	characteristic
38	Dic₆₁	—	8	2	no	—
39	#2244	—	61	1	no	maximal, Sylow
40	C₂×C₆₁	#486	1	1	yes	characteristic
41	C₂×C₆₁	#509	1	2	yes	—
42	D₆₁	—	16	2	no	—
43	#499	—	61	1	no	—
44	#493	—	61	1	no	—
45	#357	—	61	4	no	—
46	#346	D₆₁	1	1	yes	characteristic, complemented
47	C₆₁	#2244	1	1	yes	characteristic, complemented, Sylow
48	C₂×D₈	—	61	2	no	—
49	C₂×D₈	—	122	1	no	—
50	#127	—	122	1	no	—
51	#125	—	122	1	no	—
52	C₂×C₁₆	C₂×D₆₁	1	2	yes	—
53	#107	—	61	2	no	—
54	#106	—	122	1	no	—
55	C₄×C₈	C₂×D₆₁	1	1	yes	characteristic
56	C₂×D₄	—	122	2	no	—
57	C₂×D₄	—	244	2	no	—
58	D₈	—	122	4	no	—
59	D₈	—	244	2	no	—
60	C₂×C₈	D₂₄₄	1	1	yes	characteristic
61	C₂×C₈	C₂²×D₆₁	1	1	yes	characteristic
62	C₄⋊C₄	—	122	2	no	—
63	C₄⋊C₄	—	244	2	no	—
64	C₄²	D₂₄₄	1	1	yes	characteristic
65	C₁₆	—	2	2	no	—
66	C₂³	—	244	2	no	—
67	D₄	—	488	4	no	—
68	D₄	—	244	2	no	—
69	D₄	—	244	2	no	—
70	C₂×C₄	—	244	2	no	—
71	C₂×C₄	D₄₈₈	1	2	yes	—
72	C₂×C₄	C₂×D₂₄₄	1	1	yes	characteristic
73	C₈	#11758190	1	2	yes	—
74	C₈	#11758222	1	2	yes	—
75	C₂²	—	488	4	no	—
76	C₂²	—	488	2	no	—
77	C₂²	C₂×D₄₈₈	1	1	yes	characteristic
78	C₄	—	2	2	no	—
79	C₄	—	488	2	no	—
80	C₄	#14519765	1	1	yes	characteristic
81	C₄	C₂×#11758190	1	1	yes	characteristic
82	C₂	—	976	2	no	—
83	C₂	#16840109	1	1	yes	characteristic
84	C₂	#16840200	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×D₄₈₈
commutator	C₂×C₈×C₆₁	C₂³
Frattini	C₂×C₈	C₂²×D₆₁
Fitting	C₆₁×#346	C₂
socle	C₂²×C₆₁	C₂×D₈
hypercenter	#346	D₆₁
hypocenter	C₆₁	#2244
LCS	G ▷ C₂×C₈×C₆₁ ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #346

Complements

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

N	H ≅ G/N	type
1. #16840164	C₂	semidirect
3. #16839564	C₂	semidirect
4. C₆₁×#346	C₂	semidirect
46. #346	D₆₁	semidirect
47. C₆₁	#2244	semidirect