Group #11796001 — subgroups

Subgroups — #11796001

Order 1152.

342 conjugacy classes of subgroups; only the 126 normal subgroups are shown.

normal subgroups only

This group has 342 conjugacy classes of subgroups — too many to draw. Only its 126 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×#63464	C₂	1	1	yes	maximal, characteristic
2	C₂×C₉×M₃₂	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₉⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	(C₂×D₉)⋊C₁₆	C₂	1	4	yes	maximal, complemented
5	#71432	—	3	1	no	maximal
6	C₂×#3697	C₄	1	1	yes	characteristic
7	C₂²×C₈×C₉	C₂²	1	1	yes	characteristic
8	C₂×#3667	C₄	1	1	yes	characteristic
9	#63464	—	2	2	no	—
10	#63464	—	2	2	no	—
11	C₂×#3663	C₄	1	2	yes	—
12	C₂×C₈×D₉	C₂²	1	2	yes	—
13	C₉×M₃₂	—	2	2	no	—
14	C₂×C₉×C₁₆	C₂²	1	2	yes	—
15	C₂×C₉⋊C₁₆	—	2	2	no	—
16	C₂×C₉⋊C₁₆	C₂²	1	2	yes	—
17	C₂×#901	—	3	1	no	—
18	C₂×C₃×M₃₂	D₃	1	1	yes	characteristic
19	C₂²×C₃⋊C₁₆	—	3	1	no	—
20	(C₂×D₃)⋊C₁₆	—	3	4	no	—
21	C₂²×C₄×C₉	C₂×C₄	1	1	yes	characteristic
22	C₂×#611	C₈	1	2	yes	—
23	#3697	—	2	2	no	—
24	#3697	—	2	2	no	—
25	C₂×D₃₆	C₈	1	1	yes	characteristic
26	C₂×C₄×D₉	C₂×C₄	1	2	yes	—
27	C₂×Dic₁₈	C₈	1	1	yes	characteristic
28	C₂×C₈×C₉	C₂×C₄	1	1	yes	characteristic
29	C₂×C₈×C₉	D₄	1	2	yes	—
30	C₂×C₈×C₉	D₄	1	2	yes	—
31	C₂×C₈×C₉	C₂³	1	1	yes	characteristic
32	#3667	—	2	2	no	—
33	C₂×C₉⋊C₈	C₂×C₄	1	2	yes	—
34	#3663	—	2	4	no	—
35	C₈×D₉	—	2	2	no	—
36	C₈×D₉	—	2	2	no	—
37	C₉×C₁₆	—	2	2	no	—
38	C₉⋊C₁₆	—	2	2	no	—
39	#2113	—	9	1	no	Sylow
40	C₂×#235	—	3	1	no	—
41	C₂²×C₃×C₈	C₂×D₃	1	1	yes	characteristic
42	C₂×#208	—	3	1	no	—
43	#901	—	6	2	no	—
44	#901	—	6	2	no	—
45	C₂×ΓL(1,𝔽₂₅)	—	3	2	no	—
46	C₂×D₃×C₈	—	3	2	no	—
47	C₃×M₃₂	—	2	2	no	—
48	C₂×C₃×C₁₆	C₂×D₃	1	2	yes	—
49	C₂×C₃⋊C₁₆	—	3	2	no	—
50	C₂×C₃⋊C₁₆	—	6	2	no	—
51	C₂³×C₉	C₂×C₈	1	1	yes	characteristic
52	C₂²×D₉	C₂×C₈	1	2	yes	—
53	C₂×C₄×C₉	C₂²⋊C₄	1	2	yes	—
54	C₂×C₄×C₉	C₂×C₈	1	1	yes	characteristic
55	C₂×C₄×C₉	M₁₆	1	2	yes	—
56	C₂×C₄×C₉	C₂²×C₄	1	1	yes	characteristic
57	#611	—	2	4	no	—
58	C₂×Dic₉	C₂×C₈	1	2	yes	—
59	D₃₆	—	2	2	no	—
60	C₄×D₉	—	2	2	no	—
61	C₄×D₉	—	2	2	no	—
62	Dic₁₈	—	2	2	no	—
63	C₈×C₉	C₂²⋊C₄	1	2	yes	—
64	C₈×C₉	C₂×D₄	1	1	yes	characteristic
65	C₈×C₉	C₂×D₄	1	1	yes	characteristic
66	C₉⋊C₈	—	2	2	no	—
67	C₂×#131	—	9	1	no	—
68	C₂×M₃₂	D₉	1	1	yes	characteristic, complemented
69	C₂²×C₁₆	—	9	1	no	—
70	C₂²⋊C₁₆	—	9	4	no	—
71	C₂²×C₃×C₄	C₄×D₃	1	1	yes	characteristic
72	C₂×#67	—	3	2	no	—
73	#235	—	6	2	no	—
74	#235	—	6	2	no	—
75	C₂×D₁₂	—	3	1	no	—
76	C₂×C₄×D₃	—	3	2	no	—
77	C₂×Dic₆	—	3	1	no	—
78	C₂×C₃×C₈	C₄×D₃	1	1	yes	characteristic
79	C₂×C₃×C₈	D₁₂	1	2	yes	—
80	C₂×C₃×C₈	#67	1	2	yes	—
81	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
82	#208	—	6	2	no	—
83	C₂×C₃⋊C₈	—	3	2	no	—
84	ΓL(1,𝔽₂₅)	—	6	4	no	—
85	D₃×C₈	—	6	2	no	—
86	D₃×C₈	—	6	2	no	—
87	C₃×C₁₆	—	2	2	no	—
88	C₃⋊C₁₆	—	6	2	no	—
89	C₂²×C₉	—	2	2	no	—
90	C₂²×C₉	C₂²⋊C₈	1	2	yes	—
91	C₂²×C₉	C₂²×C₈	1	1	yes	characteristic
92	C₂×D₉	—	2	2	no	—
93	C₂×D₉	—	2	4	no	—
94	C₄×C₉	C₂²⋊C₈	1	2	yes	—
95	C₄×C₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
96	C₄×C₉	C₂×M₁₆	1	1	yes	characteristic
97	Dic₉	—	2	2	no	—
98	C₂×#41	—	9	1	no	—
99	#131	—	18	2	no	—
100	#131	—	18	2	no	—
101	C₂×M₁₆	—	9	1	no	—
102	C₂×M₁₆	—	9	2	no	—
103	C₂²×C₈	—	9	2	no	—
104	C₂²×C₈	C₂×D₉	1	1	yes	characteristic
105	M₃₂	—	2	2	no	—
106	C₂×C₁₆	—	9	2	no	—
107	C₂×C₁₆	—	18	2	no	—
108	C₂×C₁₆	C₂×D₉	1	2	yes	—
109	C₂³×C₃	D₃×C₈	1	1	yes	characteristic
110	C₂²×D₃	—	3	2	no	—
111	C₂×C₃×C₄	D₃×C₈	1	1	yes	characteristic
112	C₂×C₃×C₄	ΓL(1,𝔽₂₅)	1	2	yes	—
113	C₂×C₃×C₄	(C₂×D₃)⋊C₄	1	2	yes	—
114	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
115	#67	—	6	4	no	—
116	C₂×Dic₃	—	3	2	no	—
117	D₁₂	—	6	2	no	—
118	C₄×D₃	—	6	2	no	—
119	C₄×D₃	—	6	2	no	—
120	Dic₆	—	6	2	no	—
121	C₃×C₈	(C₂×D₃)⋊C₄	1	2	yes	—
122	C₃×C₈	C₂×D₁₂	1	1	yes	characteristic
123	C₃×C₈	C₂×#67	1	1	yes	characteristic
124	C₃⋊C₈	—	6	2	no	—
125	C₂×C₉	—	2	2	no	—
126	C₂×C₉	C₂×C₂²⋊C₈	1	1	yes	characteristic
127	C₂×C₉	#504	1	2	yes	—
128	D₉	—	4	2	no	—
129	#41	—	18	2	no	—
130	#41	—	18	2	no	—
131	C₂×Q₈	—	9	1	no	—
132	C₂×D₄	—	9	2	no	—
133	C₂×D₄	—	9	1	no	—
134	C₂²×C₄	—	9	2	no	—
135	C₂²×C₄	C₄×D₉	1	1	yes	characteristic
136	M₁₆	—	18	2	no	—
137	M₁₆	—	18	4	no	—
138	C₂×C₈	—	9	2	no	—
139	C₂×C₈	—	18	2	no	—
140	C₂×C₈	—	18	2	no	—
141	C₂×C₈	C₄×D₉	1	1	yes	characteristic
142	C₂×C₈	D₃₆	1	2	yes	—
143	C₂×C₈	#611	1	2	yes	—
144	C₂×C₈	C₂²×D₉	1	1	yes	characteristic
145	C₁₆	—	2	2	no	—
146	C₁₆	—	18	2	no	—
147	C₂²×C₃	—	2	2	no	—
148	C₂²×C₃	(C₂×D₃)⋊C₈	1	2	yes	—
149	C₂²×C₃	C₂×D₃×C₈	1	1	yes	characteristic
150	C₂×D₃	—	6	4	no	—
151	C₂×D₃	—	6	2	no	—
152	C₃×C₄	(C₂×D₃)⋊C₈	1	2	yes	—
153	C₃×C₄	C₂×ΓL(1,𝔽₂₅)	1	1	yes	characteristic
154	C₃×C₄	C₂×(C₂×D₃)⋊C₄	1	1	yes	characteristic
155	Dic₃	—	6	2	no	—
156	C₉	#2113	1	1	yes	characteristic, complemented, Sylow
157	C₂³	—	9	2	no	—
158	C₂³	C₈×D₉	1	1	yes	characteristic
159	Q₈	—	18	2	no	—
160	D₄	—	18	4	no	—
161	D₄	—	18	2	no	—
162	C₂×C₄	—	9	2	no	—
163	C₂×C₄	—	18	2	no	—
164	C₂×C₄	—	18	2	no	—
165	C₂×C₄	C₈×D₉	1	1	yes	characteristic
166	C₂×C₄	#3663	1	2	yes	—
167	C₂×C₄	(C₂×D₉)⋊C₄	1	2	yes	—
168	C₂×C₄	C₂×C₄×D₉	1	1	yes	characteristic
169	C₈	—	18	2	no	—
170	C₈	(C₂×D₉)⋊C₄	1	2	yes	—
171	C₈	C₂×D₃₆	1	1	yes	characteristic
172	C₈	C₂×#611	1	1	yes	characteristic
173	C₂×C₃	—	2	2	no	—
174	C₂×C₃	#4907	1	2	yes	—
175	C₂×C₃	C₂×(C₂×D₃)⋊C₈	1	1	yes	characteristic
176	D₃	—	12	2	no	—
177	C₂²	—	2	2	no	—
178	C₂²	—	18	2	no	—
179	C₂²	—	18	4	no	—
180	C₂²	(C₂×D₉)⋊C₈	1	2	yes	—
181	C₂²	C₂×C₈×D₉	1	1	yes	characteristic
182	C₄	—	18	2	no	—
183	C₄	(C₂×D₉)⋊C₈	1	2	yes	—
184	C₄	C₂×#3663	1	1	yes	characteristic
185	C₄	C₂×(C₂×D₉)⋊C₄	1	1	yes	characteristic
186	C₃	#71432	1	1	yes	characteristic
187	C₂	—	2	2	no	—
188	C₂	—	36	2	no	—
189	C₂	#10588587	1	2	yes	—
190	C₂	C₂×(C₂×D₉)⋊C₈	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#63464

C₂

yes

maximal, characteristic

C₂×C₉×M₃₂

C₂

yes

maximal, characteristic, complemented

C₂²×C₉⋊C₁₆

C₂

yes

maximal, characteristic, complemented

(C₂×D₉)⋊C₁₆

C₂

yes

maximal, complemented

#71432

—

maximal

C₂×#3697

C₄

yes

characteristic

C₂²×C₈×C₉

C₂²

yes

characteristic

C₂×#3667

C₄

yes

—

—

C₄

yes

—

C₂×C₈×D₉

C₂²

yes

—

C₉×M₃₂

—

C₂×C₉×C₁₆

C₂²

yes

—

C₂×C₉⋊C₁₆

—

C₂×C₉⋊C₁₆

C₂²

yes

—

C₂×#901

—

C₂×C₃×M₃₂

D₃

yes

characteristic

C₂²×C₃⋊C₁₆

—

(C₂×D₃)⋊C₁₆

—

C₂²×C₄×C₉

C₂×C₄

yes

characteristic

C₂×#611

C₈

yes

—

#3697

—

#3697

—

C₂×D₃₆

C₈

yes

characteristic

C₂×C₄×D₉

C₂×C₄

yes

—

C₂×Dic₁₈

C₈

yes

characteristic

C₂×C₈×C₉

C₂×C₄

yes

characteristic

C₂×C₈×C₉

D₄

yes

—

C₂×C₈×C₉

D₄

yes

—

C₂×C₈×C₉

C₂³

yes

characteristic

#3667

—

C₂×C₉⋊C₈

C₂×C₄

yes

—

#3663

—

C₈×D₉

—

C₈×D₉

—

C₉×C₁₆

—

C₉⋊C₁₆

—

#2113

—

Sylow

C₂×#235

—

C₂²×C₃×C₈

C₂×D₃

yes

—

—

—

C₂×ΓL(1,𝔽₂₅)

—

C₂×D₃×C₈

—

C₃×M₃₂

—

C₂×C₃×C₁₆

C₂×D₃

yes

—

C₂×C₃⋊C₁₆

—

C₂×C₃⋊C₁₆

—

C₂³×C₉

C₂×C₈

yes

characteristic

C₂²×D₉

C₂×C₈

yes

—

C₂×C₄×C₉

C₂²⋊C₄

yes

—

C₂×C₄×C₉

C₂×C₈

yes

characteristic

C₂×C₄×C₉

M₁₆

yes

—

C₂×C₄×C₉

C₂²×C₄

yes

characteristic

#611

—

C₂×Dic₉

C₂×C₈

yes

—

D₃₆

—

C₄×D₉

—

C₄×D₉

—

Dic₁₈

—

C₈×C₉

C₂²⋊C₄

yes

—

C₈×C₉

C₂×D₄

yes

characteristic

C₈×C₉

C₂×D₄

yes

characteristic

C₉⋊C₈

—

C₂×#131

—

C₂×M₃₂

D₉

yes

characteristic, complemented

C₂²×C₁₆

—

C₂²⋊C₁₆

—

C₂²×C₃×C₄

C₄×D₃

yes

characteristic

C₂×#67

—

#235

—

#235

—

C₂×D₁₂

—

C₂×C₄×D₃

—

C₂×Dic₆

—

C₂×C₃×C₈

C₄×D₃

yes

characteristic

C₂×C₃×C₈

D₁₂

yes

—

C₂×C₃×C₈

#67

yes

—

C₂×C₃×C₈

C₂²×D₃

yes

characteristic

#208

—

C₂×C₃⋊C₈

—

ΓL(1,𝔽₂₅)

—

D₃×C₈

—

D₃×C₈

—

C₃×C₁₆

—

C₃⋊C₁₆

—

C₂²×C₉

—

C₂²×C₉

C₂²⋊C₈

yes

—

C₂²×C₉

C₂²×C₈

yes

characteristic

C₂×D₉

—

C₂×D₉

—

C₄×C₉

C₂²⋊C₈

yes

—

C₄×C₉

C₂×C₂²⋊C₄

yes

characteristic

C₄×C₉

C₂×M₁₆

yes

characteristic

Dic₉

—

C₂×#41

—

#131

—

100

#131

—

101

C₂×M₁₆

—

102

C₂×M₁₆

—

103

C₂²×C₈

—

104

C₂²×C₈

C₂×D₉

yes

characteristic

105

M₃₂

—

106

C₂×C₁₆

—

107

C₂×C₁₆

—

108

C₂×C₁₆

C₂×D₉

yes

—

109

C₂³×C₃

D₃×C₈

yes

characteristic

110

C₂²×D₃

—

111

C₂×C₃×C₄

D₃×C₈

yes

characteristic

112

C₂×C₃×C₄

ΓL(1,𝔽₂₅)

yes

—

113

C₂×C₃×C₄

(C₂×D₃)⋊C₄

yes

—

114

C₂×C₃×C₄

C₂×C₄×D₃

yes

characteristic

115

#67

—

116

C₂×Dic₃

—

117

D₁₂

—

118

C₄×D₃

—

119

C₄×D₃

—

120

Dic₆

—

121

C₃×C₈

(C₂×D₃)⋊C₄

yes

—

122

C₃×C₈

C₂×D₁₂

yes

characteristic

123

C₃×C₈

C₂×#67

yes

characteristic

124

C₃⋊C₈

—

125

C₂×C₉

—

126

C₂×C₉

C₂×C₂²⋊C₈

yes

characteristic

127

C₂×C₉

#504

yes

—

128

D₉

—

129

#41

—

130

#41

—

131

C₂×Q₈

—

132

C₂×D₄

—

133

C₂×D₄

—

134

C₂²×C₄

—

135

C₂²×C₄

C₄×D₉

yes

characteristic

136

M₁₆

—

137

M₁₆

—

138

C₂×C₈

—

139

C₂×C₈

—

140

C₂×C₈

—

141

C₂×C₈

C₄×D₉

yes

characteristic

142

C₂×C₈

D₃₆

yes

—

143

C₂×C₈

#611

yes

—

144

C₂×C₈

C₂²×D₉

yes

characteristic

145

C₁₆

—

146

C₁₆

—

147

C₂²×C₃

—

148

C₂²×C₃

(C₂×D₃)⋊C₈

yes

—

149

C₂²×C₃

C₂×D₃×C₈

yes

characteristic

150

C₂×D₃

—

151

C₂×D₃

—

152

C₃×C₄

(C₂×D₃)⋊C₈

yes

—

153

C₃×C₄

C₂×ΓL(1,𝔽₂₅)

yes

characteristic

154

C₃×C₄

C₂×(C₂×D₃)⋊C₄

yes

characteristic

155

Dic₃

—

156

C₉

#2113

yes

characteristic, complemented, Sylow

157

C₂³

—

158

C₂³

C₈×D₉

yes

characteristic

159

Q₈

—

160

D₄

—

161

D₄

—

162

C₂×C₄

—

163

C₂×C₄

—

164

C₂×C₄

—

165

C₂×C₄

C₈×D₉

yes

characteristic

166

C₂×C₄

#3663

yes

—

167

C₂×C₄

(C₂×D₉)⋊C₄

yes

—

168

C₂×C₄

C₂×C₄×D₉

yes

characteristic

169

C₈

—

170

C₈

(C₂×D₉)⋊C₄

yes

—

171

C₈

C₂×D₃₆

yes

characteristic

172

C₈

C₂×#611

yes

characteristic

173

C₂×C₃

—

174

C₂×C₃

#4907

yes

—

175

C₂×C₃

C₂×(C₂×D₃)⋊C₈

yes

characteristic

176

D₃

—

177

C₂²

—

178

C₂²

—

179

C₂²

—

180

C₂²

(C₂×D₉)⋊C₈

yes

—

181

C₂²

C₂×C₈×D₉

yes

characteristic

182

C₄

—

183

C₄

(C₂×D₉)⋊C₈

yes

—

184

C₄

C₂×#3663

yes

characteristic

185

C₄

C₂×(C₂×D₉)⋊C₄

yes

characteristic

186

C₃

#71432

yes

characteristic

187

C₂

—

188

C₂

—

189

C₂

#10588587

yes

—

190

C₂

C₂×(C₂×D₉)⋊C₈

yes

characteristic

	subgroup	G/H
center	C₂×C₈	C₂²×D₉
commutator	C₂²×C₉	C₂²×C₈
Frattini	C₂×C₃×C₈	C₂²×D₃
Fitting	C₂×C₉×M₃₂	C₂
socle	C₂²×C₃	C₂×D₃×C₈
prime radical	C₂×#3697	C₄
cosocle	C₂×C₈×C₉	C₂³
hypercenter	C₂×M₃₂	D₉
hypocenter	C₉	#2113
LCS	G ▷ C₂²×C₉ ▷ C₉
UCS	C₁ ◁ C₂×C₈ ◁ C₂×M₃₂

subgroup

G/H

center

C₂×C₈

C₂²×D₉

commutator

C₂²×C₉

C₂²×C₈

Frattini

C₂×C₃×C₈

C₂²×D₃

Fitting

C₂×C₉×M₃₂

C₂

socle

C₂²×C₃

C₂×D₃×C₈

prime radical

C₂×#3697

C₄

cosocle

C₂×C₈×C₉

C₂³

hypercenter

C₂×M₃₂

D₉

C₉

G ▷ C₂²×C₉ ▷ C₉

C₁ ◁ C₂×C₈ ◁ C₂×M₃₂

N	H ≅ G/N	type
2. C₂×C₉×M₃₂	C₂	semidirect
3. C₂²×C₉⋊C₁₆	C₂	semidirect
4. (C₂×D₉)⋊C₁₆	C₂	semidirect
68. C₂×M₃₂	D₉	semidirect
156. C₉	#2113	semidirect

H ≅ G/N

type

2. C₂×C₉×M₃₂

C₂

semidirect

3. C₂²×C₉⋊C₁₆

C₂

semidirect

4. (C₂×D₉)⋊C₁₆

C₂

semidirect

68. C₂×M₃₂

D₉

semidirect

156. C₉

#2113

semidirect

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×#63464	2
C₂×C₉×M₃₂	2
C₂²×C₉⋊C₁₆	2
(C₂×D₉)⋊C₁₆	2
#71432	3

subgroup

index

C₂×#63464

C₂×C₉×M₃₂

C₂²×C₉⋊C₁₆

(C₂×D₉)⋊C₁₆

#71432

Subgroups — #11796001

Conjugacy classes of subgroups

Complements

Maximal subgroups