Subgroups — #21443851

Order 7808.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16840127	C₂	1	1	yes	maximal, characteristic
2	#16839540	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₁×#347	C₂	1	1	yes	maximal, characteristic, complemented
4	#14519774	C₄	1	1	yes	characteristic
5	#14519769	C₄	1	1	yes	characteristic
6	#14519717	—	2	1	no	—
7	#14519699	—	2	1	no	—
8	#14519699	—	2	1	no	—
9	M₃₂×C₆₁	—	2	1	no	—
10	#97×C₆₁	C₂²	1	1	yes	characteristic
11	C₂×D₂₄₄	—	2	1	no	—
12	C₂×D₂₄₄	—	4	1	no	—
13	C₂×C₈×C₆₁	D₄	1	1	yes	characteristic
14	C₂×C₈×C₆₁	D₄	1	1	yes	characteristic
15	C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
16	C₄⋊Dic₆₁	—	2	1	no	—
17	#11758196	—	4	1	no	—
18	C₁₆×C₆₁	—	2	2	no	—
19	#11758185	—	2	2	no	—
20	C₂²×D₆₁	—	4	1	no	—
21	C₂×C₄×C₆₁	—	2	1	no	—
22	C₂×C₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
23	C₂×Dic₆₁	—	4	1	no	—
24	D₂₄₄	—	4	1	no	—
25	D₂₄₄	—	4	1	no	—
26	D₂₄₄	—	8	2	no	—
27	C₈×C₆₁	—	2	1	no	—
28	C₈×C₆₁	—	2	1	no	—
29	C₂²×C₆₁	#100	1	1	yes	characteristic
30	C₂×D₆₁	—	8	2	no	—
31	C₂×D₆₁	—	8	1	no	—
32	C₄×C₆₁	—	4	1	no	—
33	C₄×C₆₁	#104	1	1	yes	characteristic
34	C₄×C₆₁	#104	1	1	yes	characteristic
35	Dic₆₁	—	8	1	no	—
36	#1355	—	61	1	no	maximal, Sylow
37	C₂×C₆₁	—	2	1	no	—
38	C₂×C₆₁	#329	1	1	yes	characteristic
39	D₆₁	—	16	1	no	—
40	#490	—	61	1	no	—
41	#347	—	61	1	no	—
42	#347	D₆₁	1	1	yes	characteristic, complemented
43	C₆₁	#1355	1	1	yes	characteristic, complemented, Sylow
44	#127	—	61	1	no	—
45	#125	—	61	1	no	—
46	M₃₂	—	2	1	no	—
47	M₃₂	—	122	1	no	—
48	#102	—	122	1	no	—
49	#102	—	122	1	no	—
50	#97	C₂×D₆₁	1	1	yes	characteristic
51	C₂×D₄	—	122	1	no	—
52	C₂×D₄	—	244	1	no	—
53	C₂×C₈	D₂₄₄	1	1	yes	characteristic
54	C₂×C₈	C₂²⋊D₆₁	1	1	yes	characteristic
55	C₄⋊C₄	—	122	1	no	—
56	C₄⋊C₄	—	244	1	no	—
57	C₄²	C₄×D₆₁	1	1	yes	characteristic
58	C₁₆	—	2	2	no	—
59	C₁₆	—	122	2	no	—
60	C₂³	—	244	1	no	—
61	D₄	—	488	2	no	—
62	D₄	—	244	1	no	—
63	D₄	—	244	1	no	—
64	C₂×C₄	—	2	1	no	—
65	C₂×C₄	—	244	1	no	—
66	C₂×C₄	#11758198	1	1	yes	characteristic
67	C₈	—	2	1	no	—
68	C₈	—	2	1	no	—
69	C₂²	—	488	2	no	—
70	C₂²	—	488	1	no	—
71	C₂²	#14519693	1	1	yes	characteristic
72	C₄	—	4	1	no	—
73	C₄	—	488	1	no	—
74	C₄	#14519703	1	1	yes	characteristic
75	C₄	#14519705	1	1	yes	characteristic
76	C₂	—	2	1	no	—
77	C₂	—	976	1	no	—
78	C₂	#16839501	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#16839501
commutator	C₄²×C₆₁	C₂×C₄
Frattini	#97	C₂×D₆₁
Fitting	C₆₁×#347	C₂
socle	C₂×C₆₁	#329
hypercenter	#347	D₆₁
hypocenter	C₆₁	#1355
LCS	G ▷ C₄²×C₆₁ ▷ C₂×C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ #97 ◁ #347

Complements

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

N	H ≅ G/N	type
2. #16839540	C₂	semidirect
3. C₆₁×#347	C₂	semidirect
42. #347	D₆₁	semidirect
43. C₆₁	#1355	semidirect