Subgroups — #20264939

Order 6464.

114 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#11717579	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄⋊Dic₁₀₁	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄⋊C₄×C₁₀₁	C₂	1	1	yes	maximal, characteristic
4	C₂²×Dic₁₀₁	—	2	1	no	—
5	C₂×#11717579	—	2	1	no	—
6	C₂×#11717579	—	2	1	no	—
7	C₂×#11717579	C₄	1	2	yes	complemented
8	C₄⋊Dic₁₀₁	—	2	1	no	—
9	C₄⋊Dic₁₀₁	C₄	1	2	yes	complemented
10	C₂²×C₄×C₁₀₁	—	2	1	no	—
11	C₂²×C₄×C₁₀₁	C₂²	1	1	yes	characteristic
12	C₄⋊C₄×C₁₀₁	—	2	1	no	—
13	C₄⋊C₄×C₁₀₁	C₄	1	2	yes	complemented
14	C₂³×C₁₀₁	D₄	1	1	yes	characteristic
15	C₂×C₄×C₁₀₁	—	2	2	no	—
16	C₂×C₄×C₁₀₁	—	4	1	no	—
17	C₂×C₄×C₁₀₁	—	4	1	no	—
18	C₂×C₄×C₁₀₁	C₂×C₄	1	1	yes	characteristic
19	C₂×C₄×C₁₀₁	C₂×C₄	1	1	yes	characteristic
20	C₂×C₄×C₁₀₁	C₂×C₄	1	1	yes	characteristic
21	C₂×C₄×C₁₀₁	D₄	1	1	yes	characteristic
22	C₂×C₄×C₁₀₁	D₄	1	1	yes	characteristic
23	C₂×C₄×C₁₀₁	Q₈	1	1	yes	characteristic
24	C₂×Dic₁₀₁	—	2	2	no	—
25	C₂×Dic₁₀₁	—	4	1	no	—
26	C₂×Dic₁₀₁	—	4	1	no	—
27	#11717579	—	2	2	no	—
28	C₂²×C₁₀₁	C₂²⋊C₄	1	1	yes	characteristic
29	C₂²×C₁₀₁	C₂²⋊C₄	1	1	yes	characteristic
30	C₂²×C₁₀₁	C₄⋊C₄	1	1	yes	characteristic
31	C₂²×C₁₀₁	D₈	1	1	yes	characteristic
32	C₂²×C₁₀₁	SD₁₆	1	1	yes	characteristic
33	C₂²×C₁₀₁	SD₁₆	1	1	yes	characteristic
34	C₂²×C₁₀₁	Q₁₆	1	1	yes	characteristic
35	C₄×C₁₀₁	—	4	2	no	—
36	C₄×C₁₀₁	C₄²	1	1	yes	characteristic
37	C₄×C₁₀₁	C₂²⋊C₄	1	1	yes	characteristic
38	C₄×C₁₀₁	C₄⋊C₄	1	1	yes	characteristic
39	C₄×C₁₀₁	C₄⋊C₄	1	1	yes	characteristic
40	Dic₁₀₁	—	4	2	no	—
41	C₂×C₁₀₁	#95	1	1	yes	characteristic
42	C₂×C₁₀₁	#102	1	1	yes	characteristic
43	C₂×C₁₀₁	#102	1	1	yes	characteristic
44	C₂×C₁₀₁	#103	1	1	yes	characteristic
45	C₂×C₁₀₁	#103	1	1	yes	characteristic
46	C₂×C₁₀₁	#106	1	1	yes	characteristic
47	C₂×C₁₀₁	#107	1	1	yes	characteristic
48	C₁₀₁	#340	1	1	yes	characteristic, complemented, Sylow
49	#340	—	101	1	no	maximal, Sylow
50	C₂²×C₈	—	101	1	no	—
51	C₂×C₄⋊C₄	—	101	1	no	—
52	C₂×C₄⋊C₄	D₁₀₁	1	1	yes	characteristic
53	C₂²×C₄	—	2	1	no	—
54	C₂²×C₄	—	202	1	no	—
55	C₂²×C₄	C₂×D₁₀₁	1	1	yes	characteristic
56	C₂×C₈	—	101	2	no	—
57	C₂×C₈	—	202	1	no	—
58	C₂×C₈	—	202	1	no	—
59	C₄⋊C₄	—	2	1	no	—
60	C₄⋊C₄	—	101	2	no	—
61	C₄⋊C₄	—	202	1	no	—
62	C₄⋊C₄	Dic₁₀₁	1	2	yes	complemented
63	C₂³	C₂²⋊D₁₀₁	1	1	yes	characteristic
64	C₂×C₄	—	2	2	no	—
65	C₂×C₄	—	4	1	no	—
66	C₂×C₄	—	4	1	no	—
67	C₂×C₄	—	404	1	no	—
68	C₂×C₄	—	404	1	no	—
69	C₂×C₄	—	202	2	no	—
70	C₂×C₄	Dic₂₀₂	1	1	yes	characteristic
71	C₂×C₄	C₄×D₁₀₁	1	1	yes	characteristic
72	C₂×C₄	C₄×D₁₀₁	1	1	yes	characteristic
73	C₂×C₄	D₄₀₄	1	1	yes	characteristic
74	C₂×C₄	C₂×Dic₁₀₁	1	1	yes	characteristic
75	C₂×C₄	C₂²⋊D₁₀₁	1	1	yes	characteristic
76	C₈	—	202	2	no	—
77	C₂²	#13108051	1	1	yes	characteristic
78	C₂²	C₂²⋊Dic₁₀₁	1	1	yes	characteristic
79	C₂²	#13108053	1	1	yes	characteristic
80	C₂²	#13108059	1	1	yes	characteristic
81	C₂²	#13108061	1	1	yes	characteristic
82	C₂²	#13108062	1	1	yes	characteristic
83	C₂²	#13108064	1	1	yes	characteristic
84	C₄	—	4	2	no	—
85	C₄	—	404	2	no	—
86	C₄	C₄×Dic₁₀₁	1	1	yes	characteristic
87	C₄	#13108051	1	1	yes	characteristic
88	C₄	#13108053	1	1	yes	characteristic
89	C₄	C₄⋊Dic₁₀₁	1	1	yes	characteristic
90	C₂	#15692162	1	1	yes	characteristic
91	C₂	#15692175	1	1	yes	characteristic
92	C₂	#15692176	1	1	yes	characteristic
93	C₂	#15692178	1	1	yes	characteristic
94	C₂	#15692179	1	1	yes	characteristic
95	C₂	#15692186	1	1	yes	characteristic
96	C₂	#15692188	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂²⋊D₁₀₁
commutator	C₄×C₁₀₁	C₄²
Frattini	C₂²×C₄	C₂×D₁₀₁
Fitting	C₂×C₄⋊C₄×C₁₀₁	C₂
socle	C₂³×C₁₀₁	D₄
hypercenter	C₂×C₄⋊C₄	D₁₀₁
hypocenter	C₁₀₁	#340
LCS	G ▷ C₄×C₁₀₁ ▷ C₂×C₁₀₁ ▷ C₁₀₁
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
7. C₂×#11717579	C₄	semidirect
9. C₄⋊Dic₁₀₁	C₄	semidirect
13. C₄⋊C₄×C₁₀₁	C₄	semidirect
48. C₁₀₁	#340	semidirect
62. C₄⋊C₄	Dic₁₀₁	semidirect