Subgroups — #21445490

Order 7808.

198 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16840167	C₂	1	2	yes	maximal, complemented
2	#16840142	C₂	1	1	yes	maximal, characteristic, complemented
3	#16840135	C₂	1	1	yes	maximal, characteristic
4	#16840109	C₂	1	2	yes	maximal
5	C₆₁×#322	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×Dic₂₄₄	—	2	2	no	—
7	C₂×#11758190	—	2	2	no	—
8	#14519777	C₂²	1	2	yes	—
9	#14519777	C₂²	1	1	yes	characteristic
10	#14519774	C₂²	1	1	yes	characteristic
11	#14519711	—	2	4	no	—
12	#14519699	—	2	4	no	—
13	C₄×C₈×C₆₁	C₂²	1	2	yes	—
14	C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
15	C₂×D₂₄₄	—	2	2	no	—
16	C₂×D₂₄₄	—	2	1	no	—
17	C₂×Dic₁₂₂	—	2	1	no	—
18	C₂×Dic₁₂₂	—	2	2	no	—
19	C₂×C₈×C₆₁	D₄	1	4	yes	—
20	C₂×C₈×C₆₁	D₄	1	2	yes	—
21	C₄²×C₆₁	C₂³	1	1	yes	characteristic
22	C₄⋊Dic₆₁	—	2	2	no	—
23	C₄⋊Dic₆₁	—	2	2	no	—
24	C₄⋊Dic₆₁	—	2	2	no	—
25	Dic₂₄₄	—	4	4	no	—
26	#11758190	—	4	4	no	—
27	C₂²×D₆₁	—	4	1	no	—
28	C₂×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
29	C₂×C₄×C₆₁	C₂×D₄	1	2	yes	—
30	C₂×Dic₆₁	—	4	2	no	—
31	C₂×Dic₆₁	—	4	1	no	—
32	D₂₄₄	—	4	2	no	—
33	D₂₄₄	—	4	4	no	—
34	Dic₁₂₂	—	4	2	no	—
35	Dic₁₂₂	—	4	4	no	—
36	C₈×C₆₁	—	2	4	no	—
37	C₈×C₆₁	D₈	1	4	yes	—
38	C₂²×C₆₁	#127	1	1	yes	characteristic
39	C₂×D₆₁	—	8	1	no	—
40	C₂×D₆₁	—	8	2	no	—
41	C₄×C₆₁	C₂×D₈	1	2	yes	—
42	C₄×C₆₁	#137	1	4	yes	—
43	Dic₆₁	—	8	1	no	—
44	Dic₆₁	—	8	2	no	—
45	#1722	—	61	1	no	maximal, Sylow
46	C₂×C₆₁	#493	1	1	yes	characteristic
47	C₂×C₆₁	#497	1	2	yes	—
48	D₆₁	—	16	1	no	—
49	#500	—	61	2	no	—
50	#494	—	61	1	no	—
51	#492	—	61	1	no	—
52	#486	—	61	2	no	—
53	#322	D₆₁	1	1	yes	characteristic, complemented
54	C₆₁	#1722	1	1	yes	characteristic, complemented, Sylow
55	C₂×Q₁₆	—	122	2	no	—
56	C₂×SD₁₆	—	122	2	no	—
57	C₄⋊Q₈	—	61	2	no	—
58	C₄⋊Q₈	—	61	1	no	—
59	#127	—	61	1	no	—
60	#107	—	122	4	no	—
61	#102	—	122	4	no	—
62	C₄×C₈	C₂×D₆₁	1	2	yes	—
63	C₄×C₈	C₂×D₆₁	1	1	yes	characteristic
64	C₂×Q₈	—	122	1	no	—
65	C₂×Q₈	—	122	2	no	—
66	C₂×D₄	—	122	2	no	—
67	C₂×D₄	—	122	1	no	—
68	Q₁₆	—	244	4	no	—
69	SD₁₆	—	244	4	no	—
70	C₂×C₈	D₂₄₄	1	4	yes	—
71	C₂×C₈	D₂₄₄	1	2	yes	—
72	C₄⋊C₄	—	122	2	no	—
73	C₄⋊C₄	—	122	2	no	—
74	C₄⋊C₄	—	122	2	no	—
75	C₄²	C₂²×D₆₁	1	1	yes	characteristic
76	C₂³	—	244	1	no	—
77	Q₈	—	244	2	no	—
78	Q₈	—	244	4	no	—
79	D₄	—	244	4	no	—
80	D₄	—	244	2	no	—
81	C₂×C₄	—	244	2	no	—
82	C₂×C₄	—	244	1	no	—
83	C₂×C₄	C₂×D₂₄₄	1	2	yes	—
84	C₂×C₄	C₂×D₂₄₄	1	1	yes	characteristic
85	C₈	—	2	4	no	—
86	C₈	D₄₈₈	1	4	yes	—
87	C₂²	—	488	1	no	—
88	C₂²	—	488	2	no	—
89	C₂²	#14519774	1	1	yes	characteristic
90	C₄	—	488	1	no	—
91	C₄	—	488	2	no	—
92	C₄	C₂×D₄₈₈	1	2	yes	—
93	C₄	#14519810	1	4	yes	—
94	C₂	—	976	1	no	—
95	C₂	#16840139	1	1	yes	characteristic
96	C₂	#16840156	1	2	yes	—

	subgroup	G/H
center	C₂²	#14519774
commutator	C₄²×C₆₁	C₂³
Frattini	C₄²	C₂²×D₆₁
Fitting	C₆₁×#322	C₂
socle	C₂²×C₆₁	#127
hypercenter	#322	D₆₁
hypocenter	C₆₁	#1722
LCS	G ▷ C₄²×C₆₁ ▷ C₂²×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #322

Complements

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

N	H ≅ G/N	type
1. #16840167	C₂	semidirect
2. #16840142	C₂	semidirect
5. C₆₁×#322	C₂	semidirect
53. #322	D₆₁	semidirect
54. C₆₁	#1722	semidirect