Group #21447615 — subgroups

Subgroups — #21447615

Order 7808.

160 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 160 conjugacy classes of subgroups — too many to draw. Only its 81 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₈×Dic₆₁	C₂	1	1	yes	maximal, characteristic
2	#16839580	C₂	1	2	yes	maximal, complemented
3	C₂²⋊#11758185	C₂	1	1	yes	maximal, characteristic
4	C₁₆×Dic₆₁	C₂	1	2	yes	maximal, complemented
5	C₆₁×C₂²⋊C₁₆	C₂	1	1	yes	maximal, characteristic
6	C₂²×#92418	C₄	1	1	yes	characteristic
7	C₂×C₄×Dic₆₁	C₄	1	1	yes	characteristic
8	C₂×#11758185	C₂²	1	2	yes	—
9	C₈×Dic₆₁	C₄	1	1	yes	characteristic
10	C₈×Dic₆₁	C₄	1	1	yes	characteristic
11	C₈×Dic₆₁	C₂²	1	1	yes	characteristic
12	C₈×Dic₆₁	C₂²	1	1	yes	characteristic
13	C₂²×C₈×C₆₁	C₂²	1	1	yes	characteristic
14	C₂×C₁₆×C₆₁	C₂²	1	2	yes	—
15	C₂²×C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
16	C₂²×Dic₆₁	C₈	1	1	yes	characteristic
17	C₂²×Dic₆₁	C₈	1	1	yes	characteristic
18	C₂×C₈×C₆₁	—	2	2	no	—
19	C₂×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
20	C₂×C₈×C₆₁	C₂³	1	1	yes	characteristic
21	C₄×Dic₆₁	C₈	1	1	yes	characteristic
22	C₄×Dic₆₁	C₈	1	1	yes	characteristic
23	C₄×Dic₆₁	C₂×C₄	1	1	yes	characteristic
24	C₄×Dic₆₁	C₂×C₄	1	1	yes	characteristic
25	C₂×#92418	—	2	2	no	—
26	C₂×#92418	C₂×C₄	1	1	yes	characteristic
27	C₂×#92418	C₂×C₄	1	1	yes	characteristic
28	C₁₆×C₆₁	—	2	2	no	—
29	#11758185	—	2	2	no	—
30	C₂³×C₆₁	C₂×C₈	1	1	yes	characteristic
31	C₂×C₄×C₆₁	—	2	1	no	—
32	C₂×C₄×C₆₁	—	2	1	no	—
33	C₂×C₄×C₆₁	C₂×C₈	1	1	yes	characteristic
34	C₂×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
35	C₂×Dic₆₁	—	2	2	no	—
36	C₂×Dic₆₁	C₁₆	1	4	yes	complemented
37	C₂×Dic₆₁	C₂×C₈	1	1	yes	characteristic
38	C₂×Dic₆₁	C₂×C₈	1	1	yes	characteristic
39	C₂×Dic₆₁	C₂×C₈	1	1	yes	characteristic
40	C₂×Dic₆₁	C₂×C₈	1	1	yes	characteristic
41	C₈×C₆₁	—	2	1	no	—
42	C₈×C₆₁	#41	1	2	yes	—
43	#92418	—	2	1	no	—
44	#92418	M₁₆	1	2	yes	—
45	C₂²×C₆₁	—	2	1	no	—
46	C₂²×C₆₁	—	2	1	no	—
47	C₂²×C₆₁	C₂×C₁₆	1	2	yes	—
48	C₂²×C₆₁	C₂²×C₈	1	1	yes	characteristic
49	C₄×C₆₁	—	2	1	no	—
50	C₄×C₆₁	#117	1	1	yes	characteristic
51	C₄×C₆₁	C₂×M₁₆	1	1	yes	characteristic
52	Dic₆₁	—	2	1	no	—
53	Dic₆₁	C₂×C₁₆	1	2	yes	—
54	Dic₆₁	C₂×C₁₆	1	2	yes	—
55	Dic₆₁	M₃₂	1	2	yes	—
56	#2162	—	61	1	no	maximal, Sylow
57	C₂×C₆₁	—	2	2	no	—
58	C₂×C₆₁	#431	1	1	yes	characteristic
59	C₂×C₆₁	C₂²×C₁₆	1	1	yes	characteristic
60	C₂×C₆₁	C₂×M₃₂	1	1	yes	characteristic
61	C₂×C₄×C₈	—	61	1	no	—
62	C₄⋊C₁₆	—	61	2	no	—
63	C₂²⋊C₁₆	—	61	1	no	—
64	C₂²⋊C₁₆	D₆₁	1	1	yes	characteristic
65	C₄×C₁₆	—	61	2	no	—
66	C₆₁	#2162	1	1	yes	characteristic, complemented, Sylow
67	C₂²×C₈	—	61	1	no	—
68	C₂²×C₈	C₂×D₆₁	1	1	yes	characteristic
69	C₂×C₄²	—	61	1	no	—
70	C₂×C₁₆	—	61	2	no	—
71	C₂×C₁₆	C₂×D₆₁	1	2	yes	—
72	C₄×C₈	—	61	1	no	—
73	C₄×C₈	—	61	1	no	—
74	C₄×C₈	—	61	1	no	—
75	C₄×C₈	—	61	1	no	—
76	C₂²×C₄	—	61	1	no	—
77	C₂²×C₄	—	61	1	no	—
78	C₂²×C₄	C₄×D₆₁	1	1	yes	characteristic
79	C₂×C₈	—	2	2	no	—
80	C₂×C₈	—	61	1	no	—
81	C₂×C₈	—	61	1	no	—
82	C₂×C₈	—	122	2	no	—
83	C₂×C₈	C₄×D₆₁	1	1	yes	characteristic
84	C₂×C₈	C₂²×D₆₁	1	1	yes	characteristic
85	C₄²	—	61	1	no	—
86	C₄²	—	61	1	no	—
87	C₄²	—	61	1	no	—
88	C₄²	—	61	1	no	—
89	C₁₆	—	2	2	no	—
90	C₁₆	—	122	2	no	—
91	C₂³	C₈×D₆₁	1	1	yes	characteristic
92	C₂×C₄	—	2	1	no	—
93	C₂×C₄	—	2	1	no	—
94	C₂×C₄	—	61	4	no	—
95	C₂×C₄	—	61	1	no	—
96	C₂×C₄	—	61	1	no	—
97	C₂×C₄	—	61	1	no	—
98	C₂×C₄	—	61	1	no	—
99	C₂×C₄	—	122	2	no	—
100	C₂×C₄	C₈×D₆₁	1	1	yes	characteristic
101	C₂×C₄	C₂×C₄×D₆₁	1	1	yes	characteristic
102	C₈	—	2	1	no	—
103	C₈	—	61	2	no	—
104	C₈	—	122	1	no	—
105	C₈	#11758224	1	2	yes	—
106	C₂²	—	2	1	no	—
107	C₂²	—	2	1	no	—
108	C₂²	C₁₆×D₆₁	1	2	yes	—
109	C₂²	C₂×C₈×D₆₁	1	1	yes	characteristic
110	C₄	—	2	1	no	—
111	C₄	—	61	2	no	—
112	C₄	—	61	2	no	—
113	C₄	—	61	2	no	—
114	C₄	—	122	1	no	—
115	C₄	#14519733	1	1	yes	characteristic
116	C₄	M₁₆×D₆₁	1	1	yes	characteristic
117	C₂	—	2	2	no	—
118	C₂	#16839812	1	1	yes	characteristic
119	C₂	C₂×C₁₆×D₆₁	1	1	yes	characteristic
120	C₂	M₃₂×D₆₁	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₈×Dic₆₁

C₂

yes

maximal, characteristic

#16839580

C₂

yes

maximal, complemented

C₂²⋊#11758185

C₂

yes

maximal, characteristic

C₁₆×Dic₆₁

C₂

yes

maximal, complemented

C₆₁×C₂²⋊C₁₆

C₂

yes

maximal, characteristic

C₂²×#92418

C₄

yes

characteristic

C₂×C₄×Dic₆₁

C₄

yes

characteristic

C₂×#11758185

C₂²

yes

—

C₈×Dic₆₁

C₄

yes

characteristic

C₈×Dic₆₁

C₄

yes

characteristic

C₈×Dic₆₁

C₂²

yes

characteristic

C₈×Dic₆₁

C₂²

yes

characteristic

C₂²×C₈×C₆₁

C₂²

yes

characteristic

C₂×C₁₆×C₆₁

C₂²

yes

—

C₂²×C₄×C₆₁

C₂×C₄

yes

characteristic

C₂²×Dic₆₁

C₈

yes

characteristic

C₂²×Dic₆₁

C₈

yes

characteristic

C₂×C₈×C₆₁

—

C₂×C₈×C₆₁

C₂×C₄

yes

characteristic

C₂×C₈×C₆₁

C₂³

yes

characteristic

C₄×Dic₆₁

C₈

yes

characteristic

C₄×Dic₆₁

C₈

yes

characteristic

C₄×Dic₆₁

C₂×C₄

yes

characteristic

C₄×Dic₆₁

C₂×C₄

yes

characteristic

C₂×#92418

—

C₂×#92418

C₂×C₄

yes

characteristic

C₂×#92418

C₂×C₄

yes

characteristic

C₁₆×C₆₁

—

#11758185

—

C₂³×C₆₁

C₂×C₈

yes

characteristic

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

C₂×C₈

yes

characteristic

C₂×C₄×C₆₁

C₂²×C₄

yes

characteristic

C₂×Dic₆₁

—

C₂×Dic₆₁

C₁₆

yes

complemented

C₂×Dic₆₁

C₂×C₈

yes

characteristic

C₂×Dic₆₁

C₂×C₈

yes

characteristic

C₂×Dic₆₁

C₂×C₈

yes

characteristic

C₂×Dic₆₁

C₂×C₈

yes

characteristic

C₈×C₆₁

—

C₈×C₆₁

#41

yes

—

#92418

—

#92418

M₁₆

yes

—

C₂²×C₆₁

—

C₂²×C₆₁

—

C₂²×C₆₁

C₂×C₁₆

yes

—

C₂²×C₆₁

C₂²×C₈

yes

characteristic

C₄×C₆₁

—

C₄×C₆₁

#117

yes

characteristic

C₄×C₆₁

C₂×M₁₆

yes

characteristic

Dic₆₁

—

Dic₆₁

C₂×C₁₆

yes

—

Dic₆₁

C₂×C₁₆

yes

—

Dic₆₁

M₃₂

yes

—

#2162

—

maximal, Sylow

C₂×C₆₁

—

C₂×C₆₁

#431

yes

characteristic

C₂×C₆₁

C₂²×C₁₆

yes

characteristic

C₂×C₆₁

C₂×M₃₂

yes

characteristic

C₂×C₄×C₈

—

C₄⋊C₁₆

—

C₂²⋊C₁₆

—

C₂²⋊C₁₆

D₆₁

yes

characteristic

C₄×C₁₆

—

C₆₁

#2162

yes

characteristic, complemented, Sylow

C₂²×C₈

—

C₂²×C₈

C₂×D₆₁

yes

characteristic

C₂×C₄²

—

C₂×C₁₆

—

C₂×C₁₆

C₂×D₆₁

yes

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₄×D₆₁

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

122

—

C₂×C₈

C₄×D₆₁

yes

characteristic

C₂×C₈

C₂²×D₆₁

yes

characteristic

C₄²

—

C₄²

—

C₄²

—

C₄²

—

C₁₆

—

C₁₆

—

122

—

C₂³

C₈×D₆₁

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

122

—

100

C₂×C₄

C₈×D₆₁

yes

characteristic

101

C₂×C₄

C₂×C₄×D₆₁

yes

characteristic

102

C₈

—

103

C₈

—

104

C₈

—

122

—

105

C₈

#11758224

yes

—

106

C₂²

—

107

C₂²

—

108

C₂²

C₁₆×D₆₁

yes

—

109

C₂²

C₂×C₈×D₆₁

yes

characteristic

110

C₄

—

111

C₄

—

112

C₄

—

113

C₄

—

114

C₄

—

122

—

115

C₄

#14519733

yes

characteristic

116

C₄

M₁₆×D₆₁

yes

characteristic

117

C₂

—

118

C₂

#16839812

yes

characteristic

119

C₂

C₂×C₁₆×D₆₁

yes

characteristic

120

C₂

M₃₂×D₆₁

yes

characteristic

	subgroup	G/H
center, Frattini	C₂×C₈	C₂²×D₆₁
commutator	C₂×C₆₁	C₂²×C₁₆
Fitting	C₆₁×C₂²⋊C₁₆	C₂
socle	C₂²×C₆₁	C₂²×C₈
hypercenter	C₂²⋊C₁₆	D₆₁
hypocenter	C₆₁	#2162
LCS	G ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂×C₈ ◁ C₂²⋊C₁₆

subgroup

G/H

center, Frattini

C₂×C₈

C₂²×D₆₁

commutator

C₂×C₆₁

C₂²×C₁₆

Fitting

C₆₁×C₂²⋊C₁₆

C₂

socle

C₂²×C₆₁

C₂²×C₈

hypercenter

C₂²⋊C₁₆

D₆₁

C₆₁

G ▷ C₂×C₆₁ ▷ C₆₁

C₁ ◁ C₂×C₈ ◁ C₂²⋊C₁₆

N	H ≅ G/N	type
2. #16839580	C₂	semidirect
4. C₁₆×Dic₆₁	C₂	semidirect
36. C₂×Dic₆₁	C₁₆	semidirect
66. C₆₁	#2162	semidirect

H ≅ G/N

type

2. #16839580

C₂

semidirect

4. C₁₆×Dic₆₁

C₂

semidirect

36. C₂×Dic₆₁

C₁₆

semidirect

66. C₆₁

#2162

semidirect

Subgroups — #21447615

Conjugacy classes of subgroups

Complements