Subgroups — #21445425

Order 7808.

212 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16840142	C₂	1	1	yes	maximal, characteristic, complemented
2	#16840139	C₂	1	1	yes	maximal, characteristic
3	#16840109	C₂	1	4	yes	maximal, complemented
4	C₈²×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×Dic₂₄₄	—	2	2	no	—
6	C₂×D₄₈₈	—	2	2	no	—
7	#14519777	C₂²	1	2	yes	—
8	#14519774	C₂²	1	2	yes	—
9	#14519699	—	2	8	no	—
10	C₄×C₈×C₆₁	C₂²	1	2	yes	—
11	C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
12	C₂×D₂₄₄	—	2	4	no	—
13	C₂×D₂₄₄	—	2	2	no	—
14	C₂×Dic₁₂₂	—	2	2	no	—
15	C₂×C₈×C₆₁	D₄	1	4	yes	—
16	C₂×C₈×C₆₁	D₄	1	2	yes	—
17	C₄²×C₆₁	C₂³	1	1	yes	characteristic
18	C₄⋊Dic₆₁	—	2	4	no	—
19	Dic₂₄₄	—	4	4	no	—
20	D₄₈₈	—	4	4	no	—
21	C₂²×D₆₁	—	4	2	no	—
22	C₂×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
23	C₂×C₄×C₆₁	C₂×D₄	1	2	yes	—
24	C₂×Dic₆₁	—	4	2	no	—
25	D₂₄₄	—	4	4	no	—
26	D₂₄₄	—	4	8	no	—
27	Dic₁₂₂	—	4	4	no	—
28	C₈×C₆₁	—	2	4	no	—
29	C₈×C₆₁	D₈	1	4	yes	—
30	C₂²×C₆₁	#127	1	1	yes	characteristic
31	C₂×D₆₁	—	8	2	no	—
32	C₂×D₆₁	—	8	4	no	—
33	C₄×C₆₁	C₂×D₈	1	2	yes	—
34	C₄×C₆₁	#135	1	4	yes	—
35	Dic₆₁	—	8	2	no	—
36	#1709	—	61	1	no	maximal, Sylow
37	C₂×C₆₁	#493	1	1	yes	characteristic
38	C₂×C₆₁	#495	1	2	yes	—
39	D₆₁	—	16	2	no	—
40	#494	—	61	1	no	—
41	#493	—	61	1	no	—
42	#486	—	61	4	no	—
43	C₈²	D₆₁	1	1	yes	characteristic, complemented
44	C₆₁	#1709	1	1	yes	characteristic, complemented, Sylow
45	C₂×Q₁₆	—	122	2	no	—
46	C₂×D₈	—	122	2	no	—
47	C₄⋊Q₈	—	61	2	no	—
48	#127	—	61	2	no	—
49	#102	—	122	8	no	—
50	C₄×C₈	C₂×D₆₁	1	2	yes	—
51	C₄×C₈	C₂×D₆₁	1	1	yes	characteristic
52	C₂×Q₈	—	122	2	no	—
53	C₂×D₄	—	122	4	no	—
54	C₂×D₄	—	122	2	no	—
55	Q₁₆	—	244	4	no	—
56	D₈	—	244	4	no	—
57	C₂×C₈	D₂₄₄	1	4	yes	—
58	C₂×C₈	D₂₄₄	1	2	yes	—
59	C₄⋊C₄	—	122	4	no	—
60	C₄²	C₂²×D₆₁	1	1	yes	characteristic
61	C₂³	—	244	2	no	—
62	Q₈	—	244	4	no	—
63	D₄	—	244	4	no	—
64	D₄	—	244	8	no	—
65	C₂×C₄	—	244	2	no	—
66	C₂×C₄	C₂×D₂₄₄	1	1	yes	characteristic
67	C₂×C₄	C₂×D₂₄₄	1	2	yes	—
68	C₈	—	2	4	no	—
69	C₈	D₄₈₈	1	4	yes	—
70	C₂²	—	488	2	no	—
71	C₂²	—	488	4	no	—
72	C₂²	#14519774	1	1	yes	characteristic
73	C₄	—	488	2	no	—
74	C₄	C₂×D₄₈₈	1	2	yes	—
75	C₄	#14519799	1	4	yes	—
76	C₂	—	976	2	no	—
77	C₂	#16840139	1	1	yes	characteristic
78	C₂	#16840146	1	2	yes	—

	subgroup	G/H
center	C₂²	#14519774
commutator	C₄²×C₆₁	C₂³
Frattini	C₄²	C₂²×D₆₁
Fitting	C₈²×C₆₁	C₂
socle	C₂²×C₆₁	#127
hypercenter	C₈²	D₆₁
hypocenter	C₆₁	#1709
LCS	G ▷ C₄²×C₆₁ ▷ C₂²×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₈²

Complements

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

N	H ≅ G/N	type
1. #16840142	C₂	semidirect
3. #16840109	C₂	semidirect
4. C₈²×C₆₁	C₂	semidirect
43. C₈²	D₆₁	semidirect
44. C₆₁	#1709	semidirect