Subgroups — #21443855

Order 7808.

112 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16840139	C₂	1	1	yes	maximal, characteristic
2	#16839583	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₁×#364	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₄₈₈	—	2	1	no	—
5	C₂×D₄₈₈	—	2	1	no	—
6	#14519774	C₄	1	2	yes	—
7	#14519717	—	2	1	no	—
8	M₃₂×C₆₁	—	2	1	no	—
9	C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
10	C₂×D₂₄₄	—	2	2	no	—
11	C₂×D₂₄₄	—	4	2	no	—
12	C₂×C₈×C₆₁	D₄	1	1	yes	characteristic
13	C₂×C₈×C₆₁	D₄	1	1	yes	characteristic
14	C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
15	D₄₈₈	—	4	1	no	—
16	D₄₈₈	—	4	1	no	—
17	D₄₈₈	—	4	1	no	—
18	D₄₈₈	—	4	1	no	—
19	C₁₆×C₆₁	—	4	1	no	—
20	#11758185	—	4	1	no	—
21	C₂²×D₆₁	—	4	2	no	—
22	C₂×C₄×C₆₁	—	2	1	no	—
23	C₂×C₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
24	D₂₄₄	—	4	2	no	—
25	D₂₄₄	—	4	2	no	—
26	D₂₄₄	—	8	4	no	—
27	C₈×C₆₁	D₈	1	1	yes	characteristic
28	C₈×C₆₁	D₈	1	1	yes	characteristic
29	C₈×C₆₁	SD₁₆	1	1	yes	characteristic
30	C₈×C₆₁	SD₁₆	1	1	yes	characteristic
31	C₂²×C₆₁	#100	1	1	yes	characteristic
32	C₂×D₆₁	—	8	4	no	—
33	C₂×D₆₁	—	8	2	no	—
34	C₄×C₆₁	—	2	2	no	—
35	C₄×C₆₁	#102	1	1	yes	characteristic
36	C₄×C₆₁	#102	1	1	yes	characteristic
37	#1357	—	61	1	no	maximal, Sylow
38	C₂×C₆₁	—	2	1	no	—
39	C₂×C₆₁	#331	1	1	yes	characteristic
40	D₆₁	—	16	2	no	—
41	#493	—	61	1	no	—
42	#364	—	61	1	no	—
43	#364	D₆₁	1	1	yes	characteristic, complemented
44	C₆₁	#1357	1	1	yes	characteristic, complemented, Sylow
45	C₂×D₈	—	122	1	no	—
46	C₂×D₈	—	122	1	no	—
47	#127	—	61	2	no	—
48	M₃₂	—	2	1	no	—
49	M₃₂	—	122	1	no	—
50	C₄×C₈	C₂×D₆₁	1	1	yes	characteristic
51	C₂×D₄	—	122	2	no	—
52	C₂×D₄	—	244	2	no	—
53	D₈	—	244	1	no	—
54	D₈	—	244	1	no	—
55	D₈	—	244	1	no	—
56	D₈	—	244	1	no	—
57	C₂×C₈	D₂₄₄	1	1	yes	characteristic
58	C₂×C₈	C₂²⋊D₆₁	1	1	yes	characteristic
59	C₄²	C₄×D₆₁	1	1	yes	characteristic
60	C₁₆	—	4	1	no	—
61	C₁₆	—	244	1	no	—
62	C₂³	—	244	2	no	—
63	D₄	—	488	4	no	—
64	D₄	—	244	2	no	—
65	D₄	—	244	2	no	—
66	C₂×C₄	—	2	1	no	—
67	C₂×C₄	#11758198	1	1	yes	characteristic
68	C₈	#11758190	1	1	yes	characteristic
69	C₈	D₄₈₈	1	1	yes	characteristic
70	C₈	#11758199	1	1	yes	characteristic
71	C₈	#11758201	1	1	yes	characteristic
72	C₂²	—	488	4	no	—
73	C₂²	—	488	2	no	—
74	C₂²	#14519693	1	1	yes	characteristic
75	C₄	—	2	2	no	—
76	C₄	#14519697	1	1	yes	characteristic
77	C₄	#14519699	1	1	yes	characteristic
78	C₂	—	2	1	no	—
79	C₂	—	976	2	no	—
80	C₂	#16839505	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#16839505
commutator	C₄²×C₆₁	C₂×C₄
Frattini	C₄×C₈	C₂×D₆₁
Fitting	C₆₁×#364	C₂
socle	C₂×C₆₁	#331
hypercenter	#364	D₆₁
hypocenter	C₆₁	#1357
LCS	G ▷ C₄²×C₆₁ ▷ C₂×C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #364

Complements

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

N	H ≅ G/N	type
2. #16839583	C₂	semidirect
3. C₆₁×#364	C₂	semidirect
43. #364	D₆₁	semidirect
44. C₆₁	#1357	semidirect