Subgroups — #21445571

Order 7808.

240 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14519688	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×#92418	C₂	1	1	yes	maximal, characteristic
3	#16839517	C₂	1	4	yes	maximal
4	C₆₁×#376	C₂	1	1	yes	maximal, characteristic
5	C₂²×#92418	C₂²	1	2	yes	—
6	C₂²×#92418	C₂²	1	2	yes	—
7	#14519688	C₄	1	4	yes	complemented
8	C₄×#92418	C₄	1	4	yes	complemented
9	C₂×C₄²×C₆₁	C₂²	1	2	yes	—
10	C₂×C₄²×C₆₁	C₂²	1	1	yes	characteristic
11	#95×C₆₁	C₄	1	4	yes	—
12	C₂²×C₄×C₆₁	C₂×C₄	1	4	yes	—
13	C₂²×C₄×C₆₁	C₂×C₄	1	2	yes	—
14	C₂²×C₄×C₆₁	C₂³	1	1	yes	characteristic
15	C₄²×C₆₁	—	2	4	no	—
16	C₄²×C₆₁	C₂×C₄	1	2	yes	—
17	C₄²×C₆₁	C₂×C₄	1	2	yes	—
18	C₂×#92418	—	2	4	no	—
19	C₂×#92418	—	2	4	no	—
20	C₂×#92418	C₂×C₄	1	4	yes	—
21	C₂×#92418	C₂×C₄	1	4	yes	—
22	C₂³×C₆₁	C₂²×C₄	1	1	yes	characteristic
23	C₂×C₄×C₆₁	—	2	4	no	—
24	C₂×C₄×C₆₁	—	2	4	no	—
25	C₂×C₄×C₆₁	—	2	8	no	—
26	C₂×C₄×C₆₁	C₄²	1	4	yes	—
27	C₂×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
28	C₂×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
29	C₂×C₄×C₆₁	#41	1	4	yes	—
30	#92418	—	2	4	no	—
31	#92418	—	2	4	no	—
32	C₂²×C₆₁	C₂×C₄²	1	1	yes	characteristic
33	C₂²×C₆₁	#117	1	2	yes	—
34	C₂²×C₆₁	#131	1	4	yes	—
35	C₄×C₆₁	—	2	4	no	—
36	C₄×C₆₁	—	4	4	no	—
37	C₄×C₆₁	#117	1	2	yes	—
38	C₄×C₆₁	#117	1	2	yes	—
39	#1746	—	61	1	no	maximal, Sylow
40	C₂×C₆₁	#376	1	1	yes	characteristic
41	C₂×C₆₁	#405	1	2	yes	—
42	C₂×C₆₁	#433	1	4	yes	—
43	C₂×#97	—	61	1	no	—
44	C₂×C₄×C₈	—	61	1	no	—
45	#376	D₆₁	1	1	yes	characteristic
46	#336	—	61	4	no	—
47	C₆₁	#1746	1	1	yes	characteristic, complemented, Sylow
48	C₂²×C₈	—	61	2	no	—
49	C₂²×C₈	—	61	2	no	—
50	C₂×C₄²	C₂×D₆₁	1	2	yes	—
51	C₂×C₄²	C₂×D₆₁	1	1	yes	characteristic
52	#97	—	61	4	no	—
53	C₄×C₈	—	61	4	no	—
54	#95	Dic₆₁	1	4	yes	—
55	C₂²×C₄	C₂×Dic₆₁	1	4	yes	—
56	C₂²×C₄	C₂×Dic₆₁	1	2	yes	—
57	C₂²×C₄	C₂²×D₆₁	1	1	yes	characteristic
58	C₂×C₈	—	61	4	no	—
59	C₂×C₈	—	61	4	no	—
60	C₂×C₈	—	122	4	no	—
61	C₂×C₈	—	122	4	no	—
62	C₄²	—	2	4	no	—
63	C₄²	C₄×D₆₁	1	2	yes	—
64	C₄²	C₄×D₆₁	1	2	yes	—
65	C₂³	C₂²×Dic₆₁	1	1	yes	characteristic
66	C₂×C₄	—	2	4	no	—
67	C₂×C₄	—	2	4	no	—
68	C₂×C₄	—	2	8	no	—
69	C₂×C₄	C₄×Dic₆₁	1	4	yes	—
70	C₂×C₄	C₂×C₄×D₆₁	1	1	yes	characteristic
71	C₂×C₄	C₂×C₄×D₆₁	1	1	yes	characteristic
72	C₂×C₄	#11758222	1	4	yes	—
73	C₈	—	122	4	no	—
74	C₈	—	122	4	no	—
75	C₂²	C₂×C₄×Dic₆₁	1	1	yes	characteristic
76	C₂²	#14519736	1	2	yes	—
77	C₂²	#14519784	1	4	yes	—
78	C₄	—	2	4	no	—
79	C₄	—	4	4	no	—
80	C₄	#14519734	1	2	yes	—
81	C₄	#14519734	1	2	yes	—
82	C₂	#16839608	1	1	yes	characteristic
83	C₂	#16839718	1	2	yes	—
84	C₂	#16839823	1	4	yes	—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂²×D₆₁
commutator	C₂²×C₆₁	C₂×C₄²
Fitting	C₆₁×#376	C₂
socle	C₂³×C₆₁	C₂²×C₄
hypercenter	#376	D₆₁
hypocenter	C₆₁	#1746
LCS	G ▷ C₂²×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂²×C₄ ◁ #376

Complements

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

N	H ≅ G/N	type
7. #14519688	C₄	semidirect
8. C₄×#92418	C₄	semidirect
47. C₆₁	#1746	semidirect