Group #21462050 — subgroups

Subgroups — #21462050

Order 7808.

228 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 76 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×#14519852	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×D₆₁⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	#16840657	C₂	1	2	yes	maximal, complemented
4	C₂²⋊#11758187	C₂	1	2	yes	maximal, complemented
5	C₂×#14519785	C₂	1	1	yes	maximal, characteristic
6	#14519852	—	2	2	no	—
7	D₆₁⋊C₁₆	—	2	2	no	—
8	C₂×#11758187	C₂²	1	2	yes	—
9	C₂×#11758187	C₂²	1	2	yes	—
10	C₂×#11758222	C₄	1	1	yes	characteristic
11	#14519785	—	2	2	no	—
12	#14519785	—	2	2	no	—
13	C₂×#11758189	C₄	1	1	yes	characteristic
14	C₂×#11758189	C₄	1	1	yes	characteristic
15	C₂²×#92418	C₂²	1	1	yes	characteristic
16	C₂×C₈×D₆₁	C₂²	1	1	yes	characteristic
17	C₂×C₈×D₆₁	C₂²	1	1	yes	characteristic
18	C₂×M₁₆×C₆₁	C₄	1	1	yes	characteristic
19	C₂²×C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
20	C₂×C₂²⋊D₆₁	C₈	1	1	yes	characteristic
21	C₂×C₂²⋊D₆₁	C₈	1	1	yes	characteristic
22	#11758222	—	2	2	no	—
23	#11758222	—	2	2	no	—
24	C₂×D₂₄₄	C₈	1	1	yes	characteristic
25	C₂×C₄×D₆₁	C₂×C₄	1	1	yes	characteristic
26	C₂×C₄×D₆₁	C₂×C₄	1	1	yes	characteristic
27	C₂×Dic₁₂₂	C₈	1	1	yes	characteristic
28	M₁₆×C₆₁	—	2	2	no	—
29	C₂×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
30	C₂×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
31	C₂×#92418	—	2	1	no	—
32	C₂×#92418	—	2	1	no	—
33	C₂×#92418	C₂×C₄	1	1	yes	characteristic
34	C₂×#92418	C₂³	1	1	yes	characteristic
35	#11758189	—	2	2	no	—
36	#11758189	—	2	2	no	—
37	C₈×D₆₁	—	2	1	no	—
38	C₈×D₆₁	—	2	1	no	—
39	C₈×D₆₁	D₄	1	2	yes	—
40	C₈×D₆₁	D₄	1	2	yes	—
41	#11758187	—	2	2	no	—
42	#11758187	—	2	2	no	—
43	C₂³×C₆₁	C₂×C₈	1	1	yes	characteristic
44	C₂²×D₆₁	C₂×C₈	1	1	yes	characteristic
45	C₂²×D₆₁	C₂×C₈	1	1	yes	characteristic
46	C₂×C₄×C₆₁	—	2	1	no	—
47	C₂×C₄×C₆₁	—	2	1	no	—
48	C₂×C₄×C₆₁	C₂×C₈	1	1	yes	characteristic
49	C₂×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
50	C₂²⋊D₆₁	—	2	2	no	—
51	C₂²⋊D₆₁	—	2	2	no	—
52	C₂×Dic₆₁	C₂×C₈	1	1	yes	characteristic
53	C₂×Dic₆₁	C₂×C₈	1	1	yes	characteristic
54	D₂₄₄	—	2	2	no	—
55	C₄×D₆₁	—	2	1	no	—
56	C₄×D₆₁	—	2	1	no	—
57	C₄×D₆₁	C₂²⋊C₄	1	2	yes	—
58	C₄×D₆₁	M₁₆	1	2	yes	—
59	Dic₁₂₂	—	2	2	no	—
60	C₈×C₆₁	—	2	1	no	—
61	C₈×C₆₁	C₂²⋊C₄	1	2	yes	—
62	#92418	—	2	1	no	—
63	#92418	C₂×D₄	1	1	yes	characteristic
64	#92418	C₂×D₄	1	1	yes	characteristic
65	C₂²×C₆₁	—	2	1	no	—
66	C₂²×C₆₁	—	2	2	no	—
67	C₂²×C₆₁	C₂²×C₈	1	1	yes	characteristic
68	C₂×D₆₁	—	2	2	no	—
69	C₂×D₆₁	—	2	1	no	—
70	C₂×D₆₁	—	2	2	no	—
71	C₂×D₆₁	C₂²⋊C₈	1	2	yes	—
72	C₄×C₆₁	—	2	1	no	—
73	C₄×C₆₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
74	C₄×C₆₁	C₂×M₁₆	1	1	yes	characteristic
75	Dic₆₁	—	2	1	no	—
76	Dic₆₁	C₂²⋊C₈	1	2	yes	—
77	#2113	—	61	1	no	maximal, Sylow
78	C₂×C₆₁	—	4	1	no	—
79	C₂×C₆₁	C₂×C₂²⋊C₈	1	1	yes	characteristic
80	C₂×C₆₁	#504	1	2	yes	—
81	D₆₁	—	2	2	no	—
82	D₆₁	—	4	1	no	—
83	C₂×#131	—	61	1	no	—
84	C₂×M₃₂	—	61	1	no	—
85	C₂²×C₁₆	—	61	1	no	—
86	C₂²⋊C₁₆	—	61	2	no	—
87	C₂²⋊C₁₆	—	61	2	no	—
88	C₆₁	#2113	1	1	yes	characteristic, complemented, Sylow
89	C₂×#41	—	61	1	no	—
90	#131	—	122	2	no	—
91	#131	—	122	2	no	—
92	C₂×M₁₆	—	61	1	no	—
93	C₂×M₁₆	—	61	1	no	—
94	C₂×M₁₆	#6923	1	1	yes	characteristic
95	C₂²×C₈	—	61	1	no	—
96	C₂²×C₈	—	61	1	no	—
97	C₂²×C₈	—	61	1	no	—
98	M₃₂	—	122	2	no	—
99	C₂×C₁₆	—	61	2	no	—
100	C₂×C₁₆	—	61	2	no	—
101	C₂×C₁₆	—	122	2	no	—
102	#41	—	122	2	no	—
103	#41	—	122	2	no	—
104	C₂×Q₈	—	61	1	no	—
105	C₂×D₄	—	61	1	no	—
106	C₂×D₄	—	61	1	no	—
107	C₂×D₄	—	61	1	no	—
108	C₂²×C₄	—	61	1	no	—
109	C₂²×C₄	—	61	1	no	—
110	C₂²×C₄	C₂×#6923	1	1	yes	characteristic
111	M₁₆	—	2	2	no	—
112	M₁₆	—	122	2	no	—
113	M₁₆	—	122	2	no	—
114	C₂×C₈	—	61	1	no	—
115	C₂×C₈	—	61	2	no	—
116	C₂×C₈	—	61	2	no	—
117	C₂×C₈	—	61	1	no	—
118	C₂×C₈	—	122	1	no	—
119	C₂×C₈	—	122	1	no	—
120	C₂×C₈	—	122	1	no	—
121	C₂×C₈	—	122	1	no	—
122	C₂×C₈	C₂×#6923	1	1	yes	characteristic
123	C₂×C₈	C₂×#6923	1	1	yes	characteristic
124	C₁₆	—	122	2	no	—
125	C₁₆	—	122	2	no	—
126	C₂³	—	61	1	no	—
127	C₂³	—	61	1	no	—
128	C₂³	D₆₁⋊C₈	1	1	yes	characteristic
129	Q₈	—	122	2	no	—
130	D₄	—	122	2	no	—
131	D₄	—	122	2	no	—
132	D₄	—	122	2	no	—
133	C₂×C₄	—	2	1	no	—
134	C₂×C₄	—	2	1	no	—
135	C₂×C₄	—	61	1	no	—
136	C₂×C₄	—	61	2	no	—
137	C₂×C₄	—	61	2	no	—
138	C₂×C₄	—	61	1	no	—
139	C₂×C₄	—	122	1	no	—
140	C₂×C₄	—	122	1	no	—
141	C₂×C₄	D₆₁⋊C₈	1	1	yes	characteristic
142	C₂×C₄	C₂²×#6923	1	1	yes	characteristic
143	C₈	—	2	1	no	—
144	C₈	—	61	1	no	—
145	C₈	—	61	1	no	—
146	C₈	—	122	1	no	—
147	C₈	C₂²⋊#6923	1	2	yes	—
148	C₂²	—	2	1	no	—
149	C₂²	—	2	2	no	—
150	C₂²	—	61	2	no	—
151	C₂²	—	122	2	no	—
152	C₂²	—	122	1	no	—
153	C₂²	—	122	2	no	—
154	C₂²	C₂×D₆₁⋊C₈	1	1	yes	characteristic
155	C₄	—	2	1	no	—
156	C₄	—	61	2	no	—
157	C₄	—	122	1	no	—
158	C₄	C₂×C₂²⋊#6923	1	1	yes	characteristic
159	C₄	D₆₁⋊M₁₆	1	1	yes	characteristic
160	C₂	—	4	1	no	—
161	C₂	—	122	2	no	—
162	C₂	—	244	1	no	—
163	C₂	D₆₁⋊(C₂²⋊C₈)	1	1	yes	characteristic
164	C₂	#16840821	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14519852

C₂

yes

maximal, characteristic, complemented

C₂×D₆₁⋊C₁₆

C₂

yes

maximal, characteristic, complemented

#16840657

C₂

yes

maximal, complemented

C₂²⋊#11758187

C₂

yes

maximal, complemented

C₂×#14519785

C₂

yes

maximal, characteristic

#14519852

—

D₆₁⋊C₁₆

—

C₂×#11758187

C₂²

yes

—

C₂×#11758187

C₂²

yes

—

C₂×#11758222

C₄

yes

—

—

C₄

yes

characteristic

C₂×#11758189

C₄

yes

characteristic

C₂²×#92418

C₂²

yes

characteristic

C₂×C₈×D₆₁

C₂²

yes

characteristic

C₂×C₈×D₆₁

C₂²

yes

characteristic

C₂×M₁₆×C₆₁

C₄

yes

characteristic

C₂²×C₄×C₆₁

C₂×C₄

yes

characteristic

C₂×C₂²⋊D₆₁

C₈

yes

characteristic

C₂×C₂²⋊D₆₁

C₈

yes

characteristic

#11758222

—

#11758222

—

C₂×D₂₄₄

C₈

yes

characteristic

C₂×C₄×D₆₁

C₂×C₄

yes

characteristic

C₂×C₄×D₆₁

C₂×C₄

yes

characteristic

C₂×Dic₁₂₂

C₈

yes

characteristic

M₁₆×C₆₁

—

C₂×C₈×C₆₁

C₂×C₄

yes

characteristic

C₂×C₈×C₆₁

C₂×C₄

yes

—

—

C₂×C₄

yes

characteristic

C₂×#92418

C₂³

yes

characteristic

#11758189

—

#11758189

—

C₈×D₆₁

—

C₈×D₆₁

—

C₈×D₆₁

D₄

yes

—

C₈×D₆₁

D₄

yes

—

#11758187

—

#11758187

—

C₂³×C₆₁

C₂×C₈

yes

characteristic

C₂²×D₆₁

C₂×C₈

yes

characteristic

C₂²×D₆₁

C₂×C₈

yes

characteristic

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

C₂×C₈

yes

characteristic

C₂×C₄×C₆₁

C₂²×C₄

yes

characteristic

C₂²⋊D₆₁

—

C₂²⋊D₆₁

—

C₂×Dic₆₁

C₂×C₈

yes

characteristic

C₂×Dic₆₁

C₂×C₈

yes

characteristic

D₂₄₄

—

C₄×D₆₁

—

C₄×D₆₁

—

C₄×D₆₁

C₂²⋊C₄

yes

—

C₄×D₆₁

M₁₆

yes

—

Dic₁₂₂

—

C₈×C₆₁

—

C₈×C₆₁

C₂²⋊C₄

yes

—

#92418

—

#92418

C₂×D₄

yes

characteristic

#92418

C₂×D₄

yes

characteristic

C₂²×C₆₁

—

C₂²×C₆₁

—

C₂²×C₆₁

C₂²×C₈

yes

characteristic

C₂×D₆₁

—

C₂×D₆₁

—

C₂×D₆₁

—

C₂×D₆₁

C₂²⋊C₈

yes

—

C₄×C₆₁

—

C₄×C₆₁

C₂×C₂²⋊C₄

yes

characteristic

C₄×C₆₁

C₂×M₁₆

yes

characteristic

Dic₆₁

—

Dic₆₁

C₂²⋊C₈

yes

—

#2113

—

maximal, Sylow

C₂×C₆₁

—

C₂×C₆₁

C₂×C₂²⋊C₈

yes

characteristic

C₂×C₆₁

#504

yes

—

D₆₁

—

D₆₁

—

C₂×#131

—

C₂×M₃₂

—

C₂²×C₁₆

—

C₂²⋊C₁₆

—

C₂²⋊C₁₆

—

C₆₁

#2113

yes

characteristic, complemented, Sylow

C₂×#41

—

#131

—

122

—

#131

—

122

—

C₂×M₁₆

—

C₂×M₁₆

—

C₂×M₁₆

#6923

yes

characteristic

C₂²×C₈

—

C₂²×C₈

—

C₂²×C₈

—

M₃₂

—

122

—

C₂×C₁₆

—

100

C₂×C₁₆

—

101

C₂×C₁₆

—

122

—

102

#41

—

122

—

103

#41

—

122

—

104

C₂×Q₈

—

105

C₂×D₄

—

106

C₂×D₄

—

107

C₂×D₄

—

108

C₂²×C₄

—

109

C₂²×C₄

—

110

C₂²×C₄

C₂×#6923

yes

characteristic

111

M₁₆

—

112

M₁₆

—

122

—

113

M₁₆

—

122

—

114

C₂×C₈

—

115

C₂×C₈

—

116

C₂×C₈

—

117

C₂×C₈

—

118

C₂×C₈

—

122

—

119

C₂×C₈

—

122

—

120

C₂×C₈

—

122

—

121

C₂×C₈

—

122

—

122

C₂×C₈

C₂×#6923

yes

characteristic

123

C₂×C₈

C₂×#6923

yes

characteristic

124

C₁₆

—

122

—

125

C₁₆

—

122

—

126

C₂³

—

127

C₂³

—

128

C₂³

D₆₁⋊C₈

yes

characteristic

129

Q₈

—

122

—

130

D₄

—

122

—

131

D₄

—

122

—

132

D₄

—

122

—

133

C₂×C₄

—

134

C₂×C₄

—

135

C₂×C₄

—

136

C₂×C₄

—

137

C₂×C₄

—

138

C₂×C₄

—

139

C₂×C₄

—

122

—

140

C₂×C₄

—

122

—

141

C₂×C₄

D₆₁⋊C₈

yes

characteristic

142

C₂×C₄

C₂²×#6923

yes

characteristic

143

C₈

—

144

C₈

—

145

C₈

—

146

C₈

—

122

—

147

C₈

C₂²⋊#6923

yes

—

148

C₂²

—

149

C₂²

—

150

C₂²

—

151

C₂²

—

122

—

152

C₂²

—

122

—

153

C₂²

—

122

—

154

C₂²

C₂×D₆₁⋊C₈

yes

characteristic

155

C₄

—

156

C₄

—

157

C₄

—

122

—

158

C₄

C₂×C₂²⋊#6923

yes

characteristic

159

C₄

D₆₁⋊M₁₆

yes

characteristic

160

C₂

—

161

C₂

—

122

—

162

C₂

—

244

—

163

C₂

D₆₁⋊(C₂²⋊C₈)

yes

characteristic

164

C₂

#16840821

yes

—

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×#6923
commutator, socle	C₂²×C₆₁	C₂²×C₈
Fitting	C₂×M₁₆×C₆₁	C₄
hypercenter	C₂×M₁₆	#6923
hypocenter	C₆₁	#2113
LCS	G ▷ C₂²×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂×M₁₆

subgroup

G/H

center, Frattini

C₂×C₄

C₂²×#6923

commutator, socle

C₂²×C₆₁

C₂²×C₈

Fitting

C₂×M₁₆×C₆₁

C₄

C₂×M₁₆

C₆₁

G ▷ C₂²×C₆₁ ▷ C₆₁

C₁ ◁ C₂×C₄ ◁ C₂×M₁₆

N	H ≅ G/N	type
1. C₂×#14519852	C₂	semidirect
2. C₂×D₆₁⋊C₁₆	C₂	semidirect
3. #16840657	C₂	semidirect
4. C₂²⋊#11758187	C₂	semidirect
88. C₆₁	#2113	semidirect

H ≅ G/N

type

1. C₂×#14519852

C₂

semidirect

2. C₂×D₆₁⋊C₁₆

C₂

semidirect

3. #16840657

C₂

semidirect

4. C₂²⋊#11758187

C₂

semidirect

88. C₆₁

#2113

semidirect

Subgroups — #21462050

Conjugacy classes of subgroups

Complements