Group #11785453 — subgroups

Subgroups — #11785453

Order 1152.

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

normal subgroups only

This group has 408 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	C₂²×#3667	C₂	1	1	yes	maximal, characteristic
2	C₉×#407	C₂	1	1	yes	maximal, characteristic
3	#10588887	C₂	1	1	yes	maximal, characteristic
4	C₂×#63381	C₂	1	2	yes	maximal, complemented
5	#10588231	C₂	1	2	yes	maximal, complemented
6	#69983	—	3	1	no	maximal
7	C₂³×C₄×C₉	C₂²	1	1	yes	characteristic
8	C₂×C₉×M₁₆	C₂²	1	2	yes	—
9	C₂×#3667	—	2	4	no	—
10	C₂×#3667	C₄	1	4	yes	—
11	C₂×#3667	C₂²	1	2	yes	—
12	C₂²×C₉⋊C₈	C₂²	1	1	yes	characteristic
13	C₂²×C₉⋊C₈	C₂²	1	1	yes	characteristic
14	C₉×C₂²⋊C₈	—	2	2	no	—
15	#63389	—	2	2	no	—
16	#63381	—	2	4	no	—
17	C₂²×#208	—	3	1	no	—
18	C₃×#407	D₃	1	1	yes	characteristic
19	#5207	—	3	1	no	—
20	C₂×#822	—	3	2	no	—
21	#4558	—	3	2	no	—
22	C₂⁴×C₉	Q₈	1	1	yes	characteristic
23	C₂²×C₄×C₉	—	2	2	no	—
24	C₂²×C₄×C₉	—	2	2	no	—
25	C₂²×C₄×C₉	C₂×C₄	1	2	yes	—
26	C₂²×C₄×C₉	D₄	1	2	yes	—
27	C₂²×C₄×C₉	Q₈	1	1	yes	characteristic
28	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
29	C₉×M₁₆	—	2	2	no	—
30	C₉×M₁₆	—	2	2	no	—
31	C₂×C₈×C₉	—	2	2	no	—
32	#3667	—	2	8	no	—
33	#3667	—	2	2	no	—
34	#3667	—	2	2	no	—
35	C₂×C₉⋊C₈	—	2	2	no	—
36	C₂×C₉⋊C₈	—	2	2	no	—
37	C₂×C₉⋊C₈	C₂×C₄	1	2	yes	—
38	C₂×C₉⋊C₈	C₂×C₄	1	2	yes	—
39	C₂×C₉⋊C₈	D₄	1	4	yes	—
40	#1811	—	9	1	no	Sylow
41	C₂³×C₃×C₄	C₂×D₃	1	1	yes	characteristic
42	C₂×C₃×M₁₆	C₂×D₃	1	2	yes	—
43	C₂×#208	—	3	4	no	—
44	C₂×#208	—	3	2	no	—
45	C₂×#208	—	6	4	no	—
46	C₂²×C₃⋊C₈	—	3	1	no	—
47	C₂²×C₃⋊C₈	—	3	1	no	—
48	C₃×C₂²⋊C₈	—	2	2	no	—
49	#830	—	6	2	no	—
50	#822	—	6	4	no	—
51	C₂³×C₉	—	2	2	no	—
52	C₂³×C₉	—	4	2	no	—
53	C₂³×C₉	C₄⋊C₄	1	2	yes	—
54	C₂³×C₉	C₂×Q₈	1	1	yes	characteristic
55	C₂×C₄×C₉	—	2	2	no	—
56	C₂×C₄×C₉	—	2	2	no	—
57	C₂×C₄×C₉	—	2	2	no	—
58	C₂×C₄×C₉	—	2	4	no	—
59	C₂×C₄×C₉	C₄⋊C₄	1	2	yes	—
60	C₂×C₄×C₉	C₂²×C₄	1	1	yes	characteristic
61	C₂×C₄×C₉	C₂×D₄	1	2	yes	—
62	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
63	C₂×C₄×C₉	#41	1	2	yes	—
64	C₈×C₉	—	4	2	no	—
65	C₉⋊C₈	—	2	2	no	—
66	C₉⋊C₈	—	4	2	no	—
67	C₉⋊C₈	C₂²⋊C₄	1	4	yes	—
68	C₂²×M₁₆	—	9	1	no	—
69	C₂×#108	—	9	2	no	—
70	#407	—	9	1	no	—
71	#407	D₉	1	1	yes	characteristic
72	#341	—	9	2	no	—
73	C₂⁴×C₃	Dic₆	1	1	yes	characteristic
74	C₂²×C₃×C₄	—	2	2	no	—
75	C₂²×C₃×C₄	—	2	2	no	—
76	C₂²×C₃×C₄	Dic₆	1	1	yes	characteristic
77	C₂²×C₃×C₄	C₄×D₃	1	2	yes	—
78	C₂²×C₃×C₄	#67	1	2	yes	—
79	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
80	C₃×M₁₆	—	2	2	no	—
81	C₃×M₁₆	—	2	2	no	—
82	C₂×C₃×C₈	—	2	2	no	—
83	#208	—	6	8	no	—
84	#208	—	6	2	no	—
85	#208	—	6	2	no	—
86	C₂×C₃⋊C₈	—	3	2	no	—
87	C₂×C₃⋊C₈	—	3	4	no	—
88	C₂×C₃⋊C₈	—	3	2	no	—
89	C₂×C₃⋊C₈	—	6	2	no	—
90	C₂×C₃⋊C₈	—	6	2	no	—
91	C₂²×C₉	—	2	2	no	—
92	C₂²×C₉	—	2	2	no	—
93	C₂²×C₉	—	2	4	no	—
94	C₂²×C₉	—	4	4	no	—
95	C₂²×C₉	C₂×C₄⋊C₄	1	1	yes	characteristic
96	C₂²×C₉	C₂²⋊Q₈	1	2	yes	—
97	C₄×C₉	—	2	2	no	—
98	C₄×C₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
99	C₄×C₉	#117	1	1	yes	characteristic
100	C₄×C₉	#121	1	2	yes	—
101	C₂³×C₄	C₂×D₉	1	1	yes	characteristic
102	C₂×M₁₆	—	9	4	no	—
103	C₂×M₁₆	—	9	2	no	—
104	C₂×M₁₆	—	18	4	no	—
105	C₂×M₁₆	C₂×D₉	1	2	yes	—
106	C₂²×C₈	—	9	1	no	—
107	C₂²×C₈	—	9	1	no	—
108	#108	—	18	4	no	—
109	C₂²⋊C₈	—	2	2	no	—
110	C₂²⋊C₈	—	18	2	no	—
111	C₂³×C₃	—	2	2	no	—
112	C₂³×C₃	—	4	2	no	—
113	C₂³×C₃	Dic₃⋊C₄	1	2	yes	—
114	C₂³×C₃	C₂×Dic₆	1	1	yes	characteristic
115	C₂×C₃×C₄	—	2	2	no	—
116	C₂×C₃×C₄	—	2	2	no	—
117	C₂×C₃×C₄	—	2	2	no	—
118	C₂×C₃×C₄	—	2	4	no	—
119	C₂×C₃×C₄	Dic₃⋊C₄	1	2	yes	—
120	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
121	C₂×C₃×C₄	D₃×D₄	1	2	yes	—
122	C₂×C₃×C₄	#237	1	2	yes	—
123	C₂×C₃×C₄	C₂×#67	1	1	yes	characteristic
124	C₃×C₈	—	4	2	no	—
125	C₃⋊C₈	—	3	4	no	—
126	C₃⋊C₈	—	6	2	no	—
127	C₃⋊C₈	—	12	2	no	—
128	C₂×C₉	—	2	2	no	—
129	C₂×C₉	—	4	2	no	—
130	C₂×C₉	#380	1	1	yes	characteristic
131	C₂×C₉	#430	1	2	yes	—
132	C₂⁴	Dic₁₈	1	1	yes	characteristic
133	C₂²×C₄	—	2	2	no	—
134	C₂²×C₄	—	2	2	no	—
135	C₂²×C₄	Dic₁₈	1	1	yes	characteristic
136	C₂²×C₄	C₄×D₉	1	2	yes	—
137	C₂²×C₄	#611	1	2	yes	—
138	C₂²×C₄	C₂²×D₉	1	1	yes	characteristic
139	M₁₆	—	2	2	no	—
140	M₁₆	—	2	2	no	—
141	M₁₆	—	18	8	no	—
142	M₁₆	—	18	2	no	—
143	M₁₆	—	18	2	no	—
144	C₂×C₈	—	2	2	no	—
145	C₂×C₈	—	9	2	no	—
146	C₂×C₈	—	9	4	no	—
147	C₂×C₈	—	9	2	no	—
148	C₂×C₈	—	18	2	no	—
149	C₂×C₈	—	18	2	no	—
150	C₂²×C₃	—	2	2	no	—
151	C₂²×C₃	—	2	4	no	—
152	C₂²×C₃	—	2	2	no	—
153	C₂²×C₃	—	4	4	no	—
154	C₂²×C₃	#878	1	2	yes	—
155	C₂²×C₃	C₂×Dic₃⋊C₄	1	1	yes	characteristic
156	C₃×C₄	—	2	2	no	—
157	C₃×C₄	#877	1	1	yes	characteristic
158	C₃×C₄	D₃×C₂²⋊C₄	1	1	yes	characteristic
159	C₃×C₄	#939	1	2	yes	—
160	C₉	#1811	1	1	yes	characteristic, complemented, Sylow
161	C₂³	—	2	2	no	—
162	C₂³	—	4	2	no	—
163	C₂³	Dic₉⋊C₄	1	2	yes	—
164	C₂³	C₂×Dic₁₈	1	1	yes	characteristic
165	C₂×C₄	—	2	2	no	—
166	C₂×C₄	—	2	4	no	—
167	C₂×C₄	—	2	2	no	—
168	C₂×C₄	—	2	2	no	—
169	C₂×C₄	Dic₉⋊C₄	1	2	yes	—
170	C₂×C₄	C₂×C₄×D₉	1	1	yes	characteristic
171	C₂×C₄	D₄×D₉	1	2	yes	—
172	C₂×C₄	#3699	1	2	yes	—
173	C₂×C₄	C₂×#611	1	1	yes	characteristic
174	C₈	—	4	2	no	—
175	C₈	—	9	4	no	—
176	C₈	—	18	2	no	—
177	C₈	—	36	2	no	—
178	C₂×C₃	—	2	2	no	—
179	C₂×C₃	—	4	2	no	—
180	C₂×C₃	#4942	1	1	yes	characteristic
181	C₂×C₃	#5124	1	2	yes	—
182	C₂²	—	2	2	no	—
183	C₂²	—	2	4	no	—
184	C₂²	—	2	2	no	—
185	C₂²	—	4	4	no	—
186	C₂²	#63440	1	2	yes	—
187	C₂²	C₂×Dic₉⋊C₄	1	1	yes	characteristic
188	C₄	—	2	2	no	—
189	C₄	#63439	1	1	yes	characteristic
190	C₄	C₂²⋊C₄×D₉	1	1	yes	characteristic
191	C₄	#63501	1	2	yes	—
192	C₃	#69983	1	1	yes	characteristic
193	C₂	—	2	2	no	—
194	C₂	—	4	2	no	—
195	C₂	#10588622	1	1	yes	characteristic
196	C₂	#10588799	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×#3667

C₂

yes

maximal, characteristic

C₉×#407

C₂

yes

maximal, characteristic

#10588887

C₂

yes

maximal, characteristic

C₂×#63381

C₂

yes

maximal, complemented

#10588231

C₂

yes

maximal, complemented

#69983

—

maximal

C₂³×C₄×C₉

C₂²

yes

characteristic

C₂×C₉×M₁₆

C₂²

yes

—

C₂×#3667

—

C₂×#3667

C₄

yes

—

C₂×#3667

C₂²

yes

—

C₂²×C₉⋊C₈

C₂²

yes

characteristic

C₂²×C₉⋊C₈

C₂²

yes

characteristic

C₉×C₂²⋊C₈

—

#63389

—

#63381

—

C₂²×#208

—

C₃×#407

D₃

yes

—

—

—

C₂⁴×C₉

Q₈

yes

characteristic

C₂²×C₄×C₉

—

C₂²×C₄×C₉

—

C₂²×C₄×C₉

C₂×C₄

yes

—

C₂²×C₄×C₉

D₄

yes

—

C₂²×C₄×C₉

Q₈

yes

characteristic

C₂²×C₄×C₉

C₂³

yes

characteristic

C₉×M₁₆

—

C₉×M₁₆

—

C₂×C₈×C₉

—

#3667

—

#3667

—

#3667

—

C₂×C₉⋊C₈

—

C₂×C₉⋊C₈

—

C₂×C₉⋊C₈

C₂×C₄

yes

—

C₂×C₉⋊C₈

C₂×C₄

yes

—

C₂×C₉⋊C₈

D₄

yes

—

#1811

—

Sylow

C₂³×C₃×C₄

C₂×D₃

yes

characteristic

C₂×C₃×M₁₆

C₂×D₃

yes

—

C₂×#208

—

C₂×#208

—

C₂×#208

—

C₂²×C₃⋊C₈

—

C₂²×C₃⋊C₈

—

C₃×C₂²⋊C₈

—

#830

—

#822

—

C₂³×C₉

—

C₂³×C₉

—

C₂³×C₉

C₄⋊C₄

yes

—

C₂³×C₉

C₂×Q₈

yes

characteristic

C₂×C₄×C₉

—

C₂×C₄×C₉

—

C₂×C₄×C₉

—

C₂×C₄×C₉

—

C₂×C₄×C₉

C₄⋊C₄

yes

—

C₂×C₄×C₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₉

C₂×D₄

yes

—

C₂×C₄×C₉

C₂×D₄

yes

characteristic

C₂×C₄×C₉

#41

yes

—

C₈×C₉

—

C₉⋊C₈

—

C₉⋊C₈

—

C₉⋊C₈

C₂²⋊C₄

yes

—

C₂²×M₁₆

—

C₂×#108

—

#407

—

#407

D₉

yes

characteristic

#341

—

C₂⁴×C₃

Dic₆

yes

characteristic

C₂²×C₃×C₄

—

C₂²×C₃×C₄

—

C₂²×C₃×C₄

Dic₆

yes

characteristic

C₂²×C₃×C₄

C₄×D₃

yes

—

C₂²×C₃×C₄

#67

yes

—

C₂²×C₃×C₄

C₂²×D₃

yes

characteristic

C₃×M₁₆

—

C₃×M₁₆

—

C₂×C₃×C₈

—

#208

—

#208

—

#208

—

C₂×C₃⋊C₈

—

C₂×C₃⋊C₈

—

C₂×C₃⋊C₈

—

C₂×C₃⋊C₈

—

C₂×C₃⋊C₈

—

C₂²×C₉

—

C₂²×C₉

—

C₂²×C₉

—

C₂²×C₉

—

C₂²×C₉

C₂×C₄⋊C₄

yes

characteristic

C₂²×C₉

C₂²⋊Q₈

yes

—

C₄×C₉

—

C₄×C₉

C₂×C₂²⋊C₄

yes

characteristic

C₄×C₉

#117

yes

characteristic

100

C₄×C₉

#121

yes

—

101

C₂³×C₄

C₂×D₉

yes

characteristic

102

C₂×M₁₆

—

103

C₂×M₁₆

—

104

C₂×M₁₆

—

105

C₂×M₁₆

C₂×D₉

yes

—

106

C₂²×C₈

—

107

C₂²×C₈

—

108

#108

—

109

C₂²⋊C₈

—

110

C₂²⋊C₈

—

111

C₂³×C₃

—

112

C₂³×C₃

—

113

C₂³×C₃

Dic₃⋊C₄

yes

—

114

C₂³×C₃

C₂×Dic₆

yes

characteristic

115

C₂×C₃×C₄

—

116

C₂×C₃×C₄

—

117

C₂×C₃×C₄

—

118

C₂×C₃×C₄

—

119

C₂×C₃×C₄

Dic₃⋊C₄

yes

—

120

C₂×C₃×C₄

C₂×C₄×D₃

yes

characteristic

121

C₂×C₃×C₄

D₃×D₄

yes

—

122

C₂×C₃×C₄

#237

yes

—

123

C₂×C₃×C₄

C₂×#67

yes

characteristic

124

C₃×C₈

—

125

C₃⋊C₈

—

126

C₃⋊C₈

—

127

C₃⋊C₈

—

128

C₂×C₉

—

129

C₂×C₉

—

130

C₂×C₉

#380

yes

characteristic

131

C₂×C₉

#430

yes

—

132

C₂⁴

Dic₁₈

yes

characteristic

133

C₂²×C₄

—

134

C₂²×C₄

—

135

C₂²×C₄

Dic₁₈

yes

characteristic

136

C₂²×C₄

C₄×D₉

yes

—

137

C₂²×C₄

#611

yes

—

138

C₂²×C₄

C₂²×D₉

yes

characteristic

139

M₁₆

—

140

M₁₆

—

141

M₁₆

—

142

M₁₆

—

143

M₁₆

—

144

C₂×C₈

—

145

C₂×C₈

—

146

C₂×C₈

—

147

C₂×C₈

—

148

C₂×C₈

—

149

C₂×C₈

—

150

C₂²×C₃

—

151

C₂²×C₃

—

152

C₂²×C₃

—

153

C₂²×C₃

—

154

C₂²×C₃

#878

yes

—

155

C₂²×C₃

C₂×Dic₃⋊C₄

yes

characteristic

156

C₃×C₄

—

157

C₃×C₄

#877

yes

characteristic

158

C₃×C₄

D₃×C₂²⋊C₄

yes

characteristic

159

C₃×C₄

#939

yes

—

160

C₉

#1811

yes

characteristic, complemented, Sylow

161

C₂³

—

162

C₂³

—

163

C₂³

Dic₉⋊C₄

yes

—

164

C₂³

C₂×Dic₁₈

yes

characteristic

165

C₂×C₄

—

166

C₂×C₄

—

167

C₂×C₄

—

168

C₂×C₄

—

169

C₂×C₄

Dic₉⋊C₄

yes

—

170

C₂×C₄

C₂×C₄×D₉

yes

characteristic

171

C₂×C₄

D₄×D₉

yes

—

172

C₂×C₄

#3699

yes

—

173

C₂×C₄

C₂×#611

yes

characteristic

174

C₈

—

175

C₈

—

176

C₈

—

177

C₈

—

178

C₂×C₃

—

179

C₂×C₃

—

180

C₂×C₃

#4942

yes

characteristic

181

C₂×C₃

#5124

yes

—

182

C₂²

—

183

C₂²

—

184

C₂²

—

185

C₂²

—

186

C₂²

#63440

yes

—

187

C₂²

C₂×Dic₉⋊C₄

yes

characteristic

188

C₄

—

189

C₄

#63439

yes

characteristic

190

C₄

C₂²⋊C₄×D₉

yes

characteristic

191

C₄

#63501

yes

—

192

C₃

#69983

yes

characteristic

193

C₂

—

194

C₂

—

195

C₂

#10588622

yes

characteristic

196

C₂

#10588799

yes

—

	subgroup	G/H
center	C₂×C₄	C₂×#611
commutator	C₂×C₄×C₉	C₂²×C₄
Frattini	C₂²×C₃×C₄	C₂²×D₃
Fitting	C₉×#407	C₂
socle	C₂²×C₃	C₂×Dic₃⋊C₄
prime radical	C₂⁴×C₃	Dic₆
cosocle	C₂²×C₄×C₉	C₂³
hypercenter	#407	D₉
hypocenter	C₉	#1811
LCS	G ▷ C₂×C₄×C₉ ▷ C₂×C₉ ▷ C₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ #407

subgroup

G/H

center

C₂×C₄

C₂×#611

commutator

C₂×C₄×C₉

C₂²×C₄

Frattini

C₂²×C₃×C₄

C₂²×D₃

Fitting

C₉×#407

C₂

socle

C₂²×C₃

C₂×Dic₃⋊C₄

prime radical

C₂⁴×C₃

Dic₆

cosocle

C₂²×C₄×C₉

C₂³

D₉

C₉

G ▷ C₂×C₄×C₉ ▷ C₂×C₉ ▷ C₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ #407

N	H ≅ G/N	type
4. C₂×#63381	C₂	semidirect
5. #10588231	C₂	semidirect
160. C₉	#1811	semidirect

H ≅ G/N

type

4. C₂×#63381

C₂

semidirect

5. #10588231

C₂

semidirect

160. C₉

#1811

semidirect

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

subgroup	index
C₂²×#3667	2
C₉×#407	2
#10588887	2
C₂×#63381	2
#10588231	2
#69983	3

subgroup

index

C₂²×#3667

Subgroups — #11785453

Conjugacy classes of subgroups

Complements

Maximal subgroups