Subgroups — #21443769

Order 7808.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16839785	C₂	1	1	yes	maximal, characteristic
2	#16839544	C₂	1	1	yes	maximal, characteristic
3	C₆₁×#349	C₂	1	1	yes	maximal, characteristic
4	C₂×#11758194	C₄	1	1	yes	characteristic
5	C₂×C₄×Dic₆₁	C₄	1	1	yes	characteristic
6	#14519717	—	2	1	no	—
7	#14519706	—	2	1	no	—
8	#14519706	—	2	1	no	—
9	C₂×M₁₆×C₆₁	C₂²	1	1	yes	characteristic
10	M₃₂×C₆₁	—	2	1	no	—
11	C₂²×C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
12	C₂²×Dic₆₁	—	2	1	no	—
13	M₁₆×C₆₁	—	4	1	no	—
14	C₂×C₈×C₆₁	D₄	1	1	yes	characteristic
15	C₂×C₈×C₆₁	D₄	1	1	yes	characteristic
16	C₄×Dic₆₁	—	2	1	no	—
17	C₄×Dic₆₁	C₈	1	1	yes	characteristic
18	C₄×Dic₆₁	C₈	1	1	yes	characteristic
19	#11758194	—	4	1	no	—
20	C₂×#92418	—	2	1	no	—
21	C₁₆×C₆₁	—	4	1	no	—
22	#11758185	—	4	1	no	—
23	C₂³×C₆₁	M₁₆	1	1	yes	characteristic
24	C₂×C₄×C₆₁	—	2	1	no	—
25	C₂×C₄×C₆₁	—	2	1	no	—
26	C₂×C₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
27	C₂×C₄×C₆₁	C₂×C₈	1	1	yes	characteristic
28	C₂×Dic₆₁	—	2	1	no	—
29	C₂×Dic₆₁	—	2	1	no	—
30	C₂×Dic₆₁	—	4	2	no	—
31	C₈×C₆₁	—	2	1	no	—
32	C₈×C₆₁	—	2	1	no	—
33	#92418	—	4	1	no	—
34	C₂²×C₆₁	—	2	1	no	—
35	C₂²×C₆₁	—	4	1	no	—
36	C₂²×C₆₁	C₂²⋊C₈	1	1	yes	characteristic
37	C₄×C₆₁	—	2	1	no	—
38	C₄×C₆₁	#99	1	1	yes	characteristic
39	C₄×C₆₁	#101	1	1	yes	characteristic
40	Dic₆₁	—	2	2	no	—
41	Dic₆₁	—	4	1	no	—
42	#1327	—	61	1	no	maximal, Sylow
43	C₂×C₆₁	—	2	1	no	—
44	C₂×C₆₁	—	4	1	no	—
45	C₂×C₆₁	#324	1	1	yes	characteristic
46	#423	—	61	1	no	—
47	#349	—	61	1	no	—
48	#349	D₆₁	1	1	yes	characteristic
49	C₆₁	#1327	1	1	yes	characteristic, complemented, Sylow
50	C₂×M₁₆	—	61	1	no	—
51	C₂×M₁₆	C₂×D₆₁	1	1	yes	characteristic
52	C₂×C₄²	—	61	1	no	—
53	M₃₂	—	2	1	no	—
54	M₃₂	—	122	1	no	—
55	C₄⋊C₈	—	122	1	no	—
56	C₄⋊C₈	—	122	1	no	—
57	C₂²×C₄	—	122	1	no	—
58	C₂²×C₄	C₄×D₆₁	1	1	yes	characteristic
59	M₁₆	—	4	1	no	—
60	M₁₆	—	244	1	no	—
61	C₂×C₈	—	122	1	no	—
62	C₂×C₈	D₂₄₄	1	1	yes	characteristic
63	C₂×C₈	C₂²⋊D₆₁	1	1	yes	characteristic
64	C₄²	—	61	1	no	—
65	C₄²	—	61	1	no	—
66	C₄²	—	122	1	no	—
67	C₁₆	—	4	1	no	—
68	C₁₆	—	244	1	no	—
69	C₂³	#11758189	1	1	yes	characteristic
70	C₂×C₄	—	2	1	no	—
71	C₂×C₄	—	2	1	no	—
72	C₂×C₄	—	122	1	no	—
73	C₂×C₄	—	122	1	no	—
74	C₂×C₄	—	244	2	no	—
75	C₂×C₄	C₈×D₆₁	1	1	yes	characteristic
76	C₂×C₄	#11758198	1	1	yes	characteristic
77	C₈	—	2	1	no	—
78	C₈	—	2	1	no	—
79	C₈	—	244	1	no	—
80	C₂²	—	2	1	no	—
81	C₂²	—	4	1	no	—
82	C₂²	#14519689	1	1	yes	characteristic
83	C₄	—	2	1	no	—
84	C₄	—	122	2	no	—
85	C₄	—	244	1	no	—
86	C₄	#14519691	1	1	yes	characteristic
87	C₄	#14519695	1	1	yes	characteristic
88	C₂	—	2	1	no	—
89	C₂	—	4	1	no	—
90	C₂	#16839487	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#14519691
commutator	C₂×C₄×C₆₁	C₂×C₈
Frattini	C₂×M₁₆	C₂×D₆₁
Fitting	C₆₁×#349	C₂
socle	C₂×C₆₁	#324
hypercenter	#349	D₆₁
hypocenter	C₆₁	#1327
LCS	G ▷ C₂×C₄×C₆₁ ▷ C₂²×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×M₁₆ ◁ #349

Complements

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

N	H ≅ G/N	type
49. C₆₁	#1327	semidirect