Group #11874199 — subgroups

Subgroups — D₉×#494 #11874199

Order 1152.

828 conjugacy classes of subgroups; only the 198 normal subgroups are shown.

normal subgroups only

This group has 828 conjugacy classes of subgroups — too many to draw. Only its 198 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×Q₁₆×D₉	C₂	1	4	yes	maximal
2	D₉×C₄⋊Q₈	C₂	1	2	yes	maximal
3	C₉×#494	C₂	1	1	yes	maximal, characteristic, complemented
4	#10588863	C₂	1	4	yes	maximal, complemented
5	#10588765	C₂	1	2	yes	maximal, complemented
6	C₄×C₈×D₉	C₂	1	1	yes	maximal, characteristic
7	#10588365	C₂	1	1	yes	maximal, characteristic, complemented
8	D₃×#494	—	3	1	no	maximal
9	C₂×Q₈×D₉	C₂²	1	4	yes	—
10	C₂×C₉×Q₁₆	C₂²	1	4	yes	—
11	C₉×C₄⋊Q₈	C₂²	1	2	yes	—
12	#63506	C₂²	1	4	yes	—
13	C₂×#3674	C₂²	1	8	yes	—
14	Q₁₆×D₉	—	2	16	no	—
15	C₂×C₈×D₉	C₂²	1	2	yes	—
16	C₂×Dic₃₆	C₂²	1	4	yes	—
17	C₄⋊C₄×D₉	—	2	4	no	—
18	#63450	—	2	4	no	—
19	C₄²×D₉	C₂²	1	1	yes	characteristic
20	#63431	C₂²	1	2	yes	—
21	C₄×C₈×C₉	C₂²	1	1	yes	characteristic
22	C₈×Dic₉	C₂²	1	2	yes	—
23	C₄×C₉⋊C₈	C₂²	1	1	yes	characteristic
24	C₂×D₃×Q₁₆	—	3	4	no	—
25	D₃×C₄⋊Q₈	—	3	2	no	—
26	C₃×#494	D₃	1	1	yes	characteristic
27	#5183	—	3	4	no	—
28	#5092	—	3	2	no	—
29	#4699	—	3	1	no	—
30	C₄×D₃×C₈	—	3	1	no	—
31	C₂×Q₈×C₉	C₂³	1	4	yes	—
32	Q₈×D₉	—	2	16	no	—
33	C₂×C₄×D₉	—	2	4	no	—
34	C₂×C₄×D₉	D₄	1	2	yes	—
35	C₂×C₄×D₉	C₂³	1	1	yes	characteristic
36	C₂×Dic₁₈	—	2	4	no	—
37	C₂×Dic₁₈	C₂³	1	4	yes	—
38	C₉×Q₁₆	—	2	8	no	—
39	C₂×C₈×C₉	C₂³	1	2	yes	—
40	C₉×C₄⋊C₄	—	2	4	no	—
41	C₄²×C₉	C₂³	1	1	yes	characteristic
42	#3674	—	2	16	no	—
43	C₄⋊Dic₉	—	2	4	no	—
44	Dic₉⋊C₄	—	2	8	no	—
45	C₄×Dic₉	D₄	1	2	yes	—
46	C₄×Dic₉	C₂³	1	1	yes	characteristic
47	C₂×C₉⋊C₈	C₂³	1	2	yes	—
48	C₈×D₉	D₄	1	8	yes	—
49	Dic₃₆	—	2	8	no	—
50	C₂×#494	—	9	1	no	Sylow
51	C₂×D₃×Q₈	—	3	4	no	—
52	C₂×C₃×Q₁₆	C₂×D₃	1	4	yes	—
53	C₃×C₄⋊Q₈	C₂×D₃	1	2	yes	—
54	#944	—	3	4	no	—
55	C₂×#216	—	3	8	no	—
56	D₃×Q₁₆	—	6	16	no	—
57	C₂×Dic₁₂	—	3	4	no	—
58	C₂×D₃×C₈	—	3	2	no	—
59	D₃×C₄⋊C₄	—	6	4	no	—
60	#888	—	6	4	no	—
61	C₄²×D₃	—	3	1	no	—
62	#869	—	3	2	no	—
63	C₃×C₄×C₈	C₂×D₃	1	1	yes	characteristic
64	C₈×Dic₃	—	3	2	no	—
65	C₄×C₃⋊C₈	—	3	1	no	—
66	C₂²×D₉	C₂×D₄	1	1	yes	characteristic
67	Q₈×C₉	—	2	8	no	—
68	C₂×C₄×C₉	—	2	4	no	—
69	C₂×C₄×C₉	C₂×D₄	1	2	yes	—
70	C₂×C₄×C₉	C₂⁴	1	1	yes	characteristic
71	C₂×Dic₉	—	2	4	no	—
72	C₂×Dic₉	C₂×D₄	1	1	yes	characteristic
73	C₂×Dic₉	C₂×D₄	1	2	yes	—
74	C₄×D₉	—	4	8	no	—
75	C₄×D₉	Q₁₆	1	8	yes	complemented
76	C₄×D₉	C₂×D₄	1	4	yes	—
77	Dic₁₈	—	2	8	no	—
78	Dic₁₈	—	4	8	no	—
79	C₈×C₉	C₂×D₄	1	4	yes	—
80	C₉⋊C₈	C₂×D₄	1	4	yes	—
81	C₂²×Q₁₆	—	9	4	no	—
82	C₂×C₄⋊Q₈	—	9	2	no	—
83	#494	—	9	4	no	—
84	#494	—	9	2	no	—
85	#494	—	9	1	no	—
86	#494	D₉	1	1	yes	characteristic, direct product factor
87	C₂×C₄×C₈	—	9	1	no	—
88	C₂×C₃×Q₈	C₂²×D₃	1	4	yes	—
89	D₃×Q₈	—	6	16	no	—
90	C₂×C₄×D₃	—	3	2	no	—
91	C₂×C₄×D₃	—	3	1	no	—
92	C₂×C₄×D₃	—	6	4	no	—
93	C₂×Dic₆	—	3	4	no	—
94	C₂×Dic₆	—	6	4	no	—
95	C₃×Q₁₆	—	2	8	no	—
96	C₂×C₃×C₈	C₂²×D₃	1	2	yes	—
97	C₃×C₄⋊C₄	—	2	4	no	—
98	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
99	#216	—	6	16	no	—
100	C₄⋊Dic₃	—	6	4	no	—
101	Dic₃⋊C₄	—	6	8	no	—
102	C₄×Dic₃	—	3	2	no	—
103	C₄×Dic₃	—	3	1	no	—
104	C₂×C₃⋊C₈	—	3	2	no	—
105	Dic₁₂	—	6	8	no	—
106	D₃×C₈	—	3	8	no	—
107	C₂²×C₉	C₂²×D₄	1	1	yes	characteristic
108	C₂×D₉	#127	1	2	yes	—
109	C₂×D₉	C₂×Q₁₆	1	4	yes	—
110	C₄×C₉	—	4	4	no	—
111	C₄×C₉	C₂×Q₁₆	1	4	yes	complemented
112	C₄×C₉	C₂²×D₄	1	2	yes	—
113	Dic₉	—	4	4	no	—
114	Dic₉	#127	1	2	yes	—
115	Dic₉	C₂×Q₁₆	1	4	yes	complemented
116	C₂²×Q₈	—	9	4	no	—
117	C₂×Q₁₆	—	9	8	no	—
118	C₂×Q₁₆	—	9	4	no	—
119	C₂×Q₁₆	—	18	16	no	—
120	C₂×Q₁₆	C₂×D₉	1	4	yes	—
121	C₂²×C₈	—	9	2	no	—
122	C₄⋊Q₈	—	9	4	no	—
123	C₄⋊Q₈	—	9	2	no	—
124	C₄⋊Q₈	—	18	4	no	—
125	C₄⋊Q₈	C₂×D₉	1	2	yes	—
126	C₂×C₄⋊C₄	—	18	4	no	—
127	C₂×C₄²	—	9	1	no	—
128	C₄×C₈	—	9	2	no	—
129	C₄×C₈	—	9	1	no	—
130	C₄×C₈	C₂×D₉	1	1	yes	characteristic
131	C₂²×D₃	—	3	1	no	—
132	C₃×Q₈	—	2	8	no	—
133	C₂×C₃×C₄	—	2	4	no	—
134	C₂×C₃×C₄	D₃×D₄	1	2	yes	—
135	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
136	C₂×Dic₃	—	3	2	no	—
137	C₂×Dic₃	—	3	1	no	—
138	C₂×Dic₃	—	6	4	no	—
139	C₄×D₃	—	3	8	no	—
140	C₄×D₃	—	3	4	no	—
141	C₄×D₃	—	12	8	no	—
142	Dic₆	—	6	8	no	—
143	Dic₆	—	12	8	no	—
144	C₃×C₈	D₃×D₄	1	4	yes	—
145	C₃⋊C₈	—	3	4	no	—
146	C₂×C₉	C₂×#127	1	1	yes	characteristic
147	C₂×C₉	C₂²×Q₁₆	1	2	yes	—
148	D₉	#494	1	4	yes	direct product factor
149	C₂×Q₈	—	9	4	no	—
150	C₂×Q₈	—	18	4	no	—
151	C₂×Q₈	—	18	16	no	—
152	C₂×Q₈	C₂²×D₉	1	4	yes	—
153	C₂²×C₄	—	9	2	no	—
154	C₂²×C₄	—	9	1	no	—
155	C₂²×C₄	—	18	4	no	—
156	Q₁₆	—	2	8	no	—
157	Q₁₆	—	18	16	no	—
158	Q₁₆	—	18	8	no	—
159	C₂×C₈	—	9	2	no	—
160	C₂×C₈	—	9	8	no	—
161	C₂×C₈	C₂²×D₉	1	2	yes	—
162	C₄⋊C₄	—	2	4	no	—
163	C₄⋊C₄	—	18	8	no	—
164	C₄⋊C₄	—	18	4	no	—
165	C₄²	—	9	2	no	—
166	C₄²	—	9	1	no	—
167	C₄²	C₂²×D₉	1	1	yes	characteristic
168	C₂²×C₃	C₂×D₃×D₄	1	1	yes	characteristic
169	C₂×D₃	—	3	2	no	—
170	C₂×D₃	—	3	4	no	—
171	C₃×C₄	—	4	4	no	—
172	C₃×C₄	D₃×Q₁₆	1	4	yes	—
173	C₃×C₄	C₂×D₃×D₄	1	2	yes	—
174	Dic₃	—	3	2	no	—
175	Dic₃	—	3	4	no	—
176	Dic₃	—	12	4	no	—
177	C₉	C₂×#494	1	1	yes	characteristic, complemented, Sylow
178	C₂³	—	9	1	no	—
179	Q₈	—	2	8	no	—
180	Q₈	—	18	8	no	—
181	Q₈	—	36	8	no	—
182	C₂×C₄	—	2	4	no	—
183	C₂×C₄	—	9	2	no	—
184	C₂×C₄	—	9	1	no	—
185	C₂×C₄	—	9	4	no	—
186	C₂×C₄	—	9	8	no	—
187	C₂×C₄	—	18	4	no	—
188	C₂×C₄	—	36	8	no	—
189	C₂×C₄	D₄×D₉	1	2	yes	—
190	C₂×C₄	C₂³×D₉	1	1	yes	characteristic
191	C₈	—	9	4	no	—
192	C₈	D₄×D₉	1	4	yes	—
193	C₂×C₃	D₃×#127	1	1	yes	characteristic
194	C₂×C₃	C₂×D₃×Q₁₆	1	2	yes	—
195	D₃	—	3	4	no	—
196	C₂²	—	9	2	no	—
197	C₂²	—	9	4	no	—
198	C₂²	C₂×D₄×D₉	1	1	yes	characteristic
199	C₄	—	4	4	no	—
200	C₄	—	9	2	no	—
201	C₄	—	9	4	no	—
202	C₄	—	36	4	no	—
203	C₄	Q₁₆×D₉	1	4	yes	complemented
204	C₄	C₂×D₄×D₉	1	2	yes	—
205	C₃	D₃×#494	1	1	yes	characteristic
206	C₂	—	9	4	no	—
207	C₂	D₉×#127	1	1	yes	characteristic
208	C₂	C₂×Q₁₆×D₉	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×Q₁₆×D₉

C₂

yes

maximal

D₉×C₄⋊Q₈

C₂

yes

maximal

C₉×#494

C₂

yes

maximal, characteristic, complemented

#10588863

C₂

yes

maximal, complemented

#10588765

C₂

yes

maximal, complemented

C₄×C₈×D₉

C₂

yes

maximal, characteristic

#10588365

C₂

yes

maximal, characteristic, complemented

D₃×#494

—

maximal

C₂×Q₈×D₉

C₂²

yes

—

C₂×C₉×Q₁₆

C₂²

yes

—

C₉×C₄⋊Q₈

C₂²

yes

—

#63506

C₂²

yes

—

C₂×#3674

C₂²

yes

—

Q₁₆×D₉

—

C₂×C₈×D₉

C₂²

yes

—

C₂×Dic₃₆

C₂²

yes

—

C₄⋊C₄×D₉

—

#63450

—

C₄²×D₉

C₂²

yes

characteristic

#63431

C₂²

yes

—

C₄×C₈×C₉

C₂²

yes

characteristic

C₈×Dic₉

C₂²

yes

—

C₄×C₉⋊C₈

C₂²

yes

characteristic

C₂×D₃×Q₁₆

—

D₃×C₄⋊Q₈

—

C₃×#494

D₃

yes

—

—

—

C₄×D₃×C₈

—

C₂×Q₈×C₉

C₂³

yes

—

Q₈×D₉

—

C₂×C₄×D₉

—

C₂×C₄×D₉

D₄

yes

—

C₂×C₄×D₉

C₂³

yes

characteristic

C₂×Dic₁₈

—

C₂×Dic₁₈

C₂³

yes

—

C₉×Q₁₆

—

C₂×C₈×C₉

C₂³

yes

—

C₉×C₄⋊C₄

—

C₄²×C₉

C₂³

yes

characteristic

#3674

—

C₄⋊Dic₉

—

Dic₉⋊C₄

—

C₄×Dic₉

D₄

yes

—

C₄×Dic₉

C₂³

yes

characteristic

C₂×C₉⋊C₈

C₂³

yes

—

C₈×D₉

D₄

yes

—

Dic₃₆

—

C₂×#494

—

Sylow

C₂×D₃×Q₈

—

C₂×C₃×Q₁₆

C₂×D₃

yes

—

C₃×C₄⋊Q₈

C₂×D₃

yes

—

#944

—

C₂×#216

—

D₃×Q₁₆

—

C₂×Dic₁₂

—

C₂×D₃×C₈

—

D₃×C₄⋊C₄

—

#888

—

C₄²×D₃

—

#869

—

C₃×C₄×C₈

C₂×D₃

yes

characteristic

C₈×Dic₃

—

C₄×C₃⋊C₈

—

C₂²×D₉

C₂×D₄

yes

characteristic

Q₈×C₉

—

C₂×C₄×C₉

—

C₂×C₄×C₉

C₂×D₄

yes

—

C₂×C₄×C₉

C₂⁴

yes

characteristic

C₂×Dic₉

—

C₂×Dic₉

C₂×D₄

yes

characteristic

C₂×Dic₉

C₂×D₄

yes

—

C₄×D₉

—

C₄×D₉

Q₁₆

yes

complemented

C₄×D₉

C₂×D₄

yes

—

Dic₁₈

—

Dic₁₈

—

C₈×C₉

C₂×D₄

yes

—

C₉⋊C₈

C₂×D₄

yes

—

C₂²×Q₁₆

—

C₂×C₄⋊Q₈

—

—

—

—

D₉

yes

characteristic, direct product factor

C₂×C₄×C₈

—

C₂×C₃×Q₈

C₂²×D₃

yes

—

D₃×Q₈

—

C₂×C₄×D₃

—

C₂×C₄×D₃

—

C₂×C₄×D₃

—

C₂×Dic₆

—

C₂×Dic₆

—

C₃×Q₁₆

—

C₂×C₃×C₈

C₂²×D₃

yes

—

C₃×C₄⋊C₄

—

C₃×C₄²

C₂²×D₃

yes

characteristic

#216

—

100

C₄⋊Dic₃

—

101

Dic₃⋊C₄

—

102

C₄×Dic₃

—

103

C₄×Dic₃

—

104

C₂×C₃⋊C₈

—

105

Dic₁₂

—

106

D₃×C₈

—

107

C₂²×C₉

C₂²×D₄

yes

characteristic

108

C₂×D₉

#127

yes

—

109

C₂×D₉

C₂×Q₁₆

yes

—

110

C₄×C₉

—

111

C₄×C₉

C₂×Q₁₆

yes

complemented

112

C₄×C₉

C₂²×D₄

yes

—

113

Dic₉

—

114

Dic₉

#127

yes

—

115

Dic₉

C₂×Q₁₆

yes

complemented

116

C₂²×Q₈

—

117

C₂×Q₁₆

—

118

C₂×Q₁₆

—

119

C₂×Q₁₆

—

120

C₂×Q₁₆

C₂×D₉

yes

—

121

C₂²×C₈

—

122

C₄⋊Q₈

—

123

C₄⋊Q₈

—

124

C₄⋊Q₈

—

125

C₄⋊Q₈

C₂×D₉

yes

—

126

C₂×C₄⋊C₄

—

127

C₂×C₄²

—

128

C₄×C₈

—

129

C₄×C₈

—

130

C₄×C₈

C₂×D₉

yes

characteristic

131

C₂²×D₃

—

132

C₃×Q₈

—

133

C₂×C₃×C₄

—

134

C₂×C₃×C₄

D₃×D₄

yes

—

135

C₂×C₃×C₄

C₂³×D₃

yes

characteristic

136

C₂×Dic₃

—

137

C₂×Dic₃

—

138

C₂×Dic₃

—

139

C₄×D₃

—

140

C₄×D₃

—

141

C₄×D₃

—

142

Dic₆

—

143

Dic₆

—

144

C₃×C₈

D₃×D₄

yes

—

145

C₃⋊C₈

—

146

C₂×C₉

C₂×#127

yes

characteristic

147

C₂×C₉

C₂²×Q₁₆

yes

—

148

D₉

#494

yes

direct product factor

149

C₂×Q₈

—

150

C₂×Q₈

—

151

C₂×Q₈

—

152

C₂×Q₈

C₂²×D₉

yes

—

153

C₂²×C₄

—

154

C₂²×C₄

—

155

C₂²×C₄

—

156

Q₁₆

—

157

Q₁₆

—

158

Q₁₆

—

159

C₂×C₈

—

160

C₂×C₈

—

161

C₂×C₈

C₂²×D₉

yes

—

162

C₄⋊C₄

—

163

C₄⋊C₄

—

164

C₄⋊C₄

—

165

C₄²

—

166

C₄²

—

167

C₄²

C₂²×D₉

yes

characteristic

168

C₂²×C₃

C₂×D₃×D₄

yes

characteristic

169

C₂×D₃

—

170

C₂×D₃

—

171

C₃×C₄

—

172

C₃×C₄

D₃×Q₁₆

yes

—

173

C₃×C₄

C₂×D₃×D₄

yes

—

174

Dic₃

—

175

Dic₃

—

176

Dic₃

—

177

C₉

C₂×#494

yes

characteristic, complemented, Sylow

178

C₂³

—

179

Q₈

—

180

Q₈

—

181

Q₈

—

182

C₂×C₄

—

183

C₂×C₄

—

184

C₂×C₄

—

185

C₂×C₄

—

186

C₂×C₄

—

187

C₂×C₄

—

188

C₂×C₄

—

189

C₂×C₄

D₄×D₉

yes

—

190

C₂×C₄

C₂³×D₉

yes

characteristic

191

C₈

—

192

C₈

D₄×D₉

yes

—

193

C₂×C₃

D₃×#127

yes

characteristic

194

C₂×C₃

C₂×D₃×Q₁₆

yes

—

195

D₃

—

196

C₂²

—

197

C₂²

—

198

C₂²

C₂×D₄×D₉

yes

characteristic

199

C₄

—

200

C₄

—

201

C₄

—

202

C₄

—

203

C₄

Q₁₆×D₉

yes

complemented

204

C₄

C₂×D₄×D₉

yes

—

205

C₃

D₃×#494

yes

characteristic

206

C₂

—

207

C₂

D₉×#127

yes

characteristic

208

C₂

C₂×Q₁₆×D₉

yes

—

	subgroup	G/H
center	C₂²	C₂×D₄×D₉
commutator, cosocle	C₂×C₄×C₉	C₂⁴
Frattini	C₂×C₃×C₄	C₂³×D₃
Fitting	C₉×#494	C₂
socle	C₂²×C₃	C₂×D₃×D₄
prime radical	C₂²×D₉	C₂×D₄
hypercenter	#494	D₉
hypocenter	C₉	C₂×#494
LCS	G ▷ C₂×C₄×C₉ ▷ C₂×C₉ ▷ C₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #494

subgroup

G/H

center

C₂²

C₂×D₄×D₉

commutator, cosocle

C₂×C₄×C₉

C₂⁴

Frattini

C₂×C₃×C₄

C₂³×D₃

Fitting

C₉×#494

C₂

socle

C₂²×C₃

C₂×D₃×D₄

prime radical

C₂²×D₉

C₂×D₄

D₉

C₉

G ▷ C₂×C₄×C₉ ▷ C₂×C₉ ▷ C₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #494

N	H ≅ G/N	type
3. C₉×#494	C₂	semidirect
4. #10588863	C₂	semidirect
5. #10588765	C₂	semidirect
7. #10588365	C₂	semidirect
75. C₄×D₉	Q₁₆	semidirect
86. #494	D₉	direct (N × H)
111. C₄×C₉	C₂×Q₁₆	semidirect
115. Dic₉	C₂×Q₁₆	semidirect
148. D₉	#494	direct (N × H)
177. C₉	C₂×#494	semidirect
203. C₄	Q₁₆×D₉	semidirect

H ≅ G/N

type

3. C₉×#494

C₂

semidirect

4. #10588863

C₂

semidirect

5. #10588765

C₂

semidirect

7. #10588365

C₂

semidirect

75. C₄×D₉

Q₁₆

semidirect

86. #494

D₉

direct (N × H)

111. C₄×C₉

C₂×Q₁₆

semidirect

115. Dic₉

C₂×Q₁₆

semidirect

148. D₉

#494

direct (N × H)

177. C₉

C₂×#494

semidirect

203. C₄

Q₁₆×D₉

semidirect

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

subgroup	index
C₂×Q₁₆×D₉	2
D₉×C₄⋊Q₈	2
C₉×#494	2
#10588863	2
#10588765	2
C₄×C₈×D₉	2
#10588365	2
D₃×#494	3

subgroup

index

C₂×Q₁₆×D₉

D₉×C₄⋊Q₈

C₄×C₈×D₉

Subgroups — D₉×#494 #11874199

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D9×#494 #11874199

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₉×#494 #11874199