Group #11795217 — subgroups

Subgroups — #11795217

Order 1152.

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

normal subgroups only

This group has 336 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×#63378	C₂	1	1	yes	maximal, characteristic
2	C₂×Dic₉⋊C₈	C₂	1	1	yes	maximal, characteristic
3	#10588664	C₂	1	2	yes	maximal
4	C₉×#340	C₂	1	1	yes	maximal, characteristic
5	#10588206	C₂	1	2	yes	maximal
6	#68839	—	3	1	no	maximal
7	C₂²×C₈×C₉	C₂²	1	1	yes	characteristic
8	C₂×C₉×C₄⋊C₄	C₂²	1	2	yes	—
9	C₂×C₄⋊Dic₉	—	2	2	no	—
10	C₂×C₄⋊Dic₉	C₂²	1	2	yes	—
11	C₂×C₄×Dic₉	C₂²	1	1	yes	characteristic
12	C₂²×C₉⋊C₈	C₂²	1	1	yes	characteristic
13	C₉⋊#95	—	2	2	no	—
14	#63378	—	2	2	no	—
15	Dic₉⋊C₈	—	2	2	no	—
16	C₂×#818	—	3	1	no	—
17	C₂×Dic₃⋊C₈	—	3	1	no	—
18	#4984	—	3	2	no	—
19	C₃×#340	D₃	1	1	yes	characteristic
20	#4529	—	3	2	no	—
21	C₂²×C₄×C₉	—	2	2	no	—
22	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
23	C₂²×Dic₉	—	2	2	no	—
24	C₂²×Dic₉	D₄	1	1	yes	characteristic
25	C₂²×Dic₉	D₄	1	1	yes	characteristic
26	C₂×C₈×C₉	—	2	2	no	—
27	C₂×C₈×C₉	D₄	1	2	yes	—
28	C₉×C₄⋊C₄	—	2	2	no	—
29	C₉×C₄⋊C₄	Q₈	1	4	yes	—
30	C₄⋊Dic₉	—	2	2	no	—
31	C₄⋊Dic₉	—	2	2	no	—
32	C₄⋊Dic₉	—	4	4	no	—
33	C₄×Dic₉	—	2	1	no	—
34	C₄×Dic₉	—	2	1	no	—
35	C₂×C₉⋊C₈	—	2	1	no	—
36	C₂×C₉⋊C₈	—	2	2	no	—
37	#2087	—	9	1	no	Sylow
38	C₂²×C₃×C₈	C₂×D₃	1	1	yes	characteristic
39	C₂×C₃×C₄⋊C₄	C₂×D₃	1	2	yes	—
40	C₂×C₄⋊Dic₃	—	3	2	no	—
41	C₂×C₄⋊Dic₃	—	6	2	no	—
42	C₂×C₄×Dic₃	—	3	1	no	—
43	C₂²×C₃⋊C₈	—	3	1	no	—
44	C₃⋊#95	—	6	2	no	—
45	#818	—	6	2	no	—
46	Dic₃⋊C₈	—	6	2	no	—
47	C₂³×C₉	C₂×D₄	1	1	yes	characteristic
48	C₂×C₄×C₉	—	2	4	no	—
49	C₂×C₄×C₉	—	4	2	no	—
50	C₂×C₄×C₉	—	4	2	no	—
51	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
52	C₂×C₄×C₉	C₂×Q₈	1	2	yes	—
53	C₂×C₄×C₉	#41	1	2	yes	—
54	C₂×C₄×C₉	#41	1	1	yes	characteristic
55	C₂×Dic₉	—	2	1	no	—
56	C₂×Dic₉	—	2	1	no	—
57	C₂×Dic₉	—	2	1	no	—
58	C₂×Dic₉	—	2	2	no	—
59	C₂×Dic₉	—	4	2	no	—
60	C₂×Dic₉	—	4	2	no	—
61	C₂×Dic₉	—	4	2	no	—
62	C₂×Dic₉	Q₁₆	1	2	yes	—
63	C₈×C₉	—	2	2	no	—
64	C₉⋊C₈	—	4	1	no	—
65	C₂×#107	—	9	1	no	—
66	C₂×C₄⋊C₈	—	9	1	no	—
67	#389	—	9	2	no	—
68	#340	—	9	2	no	—
69	#340	D₉	1	1	yes	characteristic
70	C₂²×C₃×C₄	—	2	2	no	—
71	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
72	C₂²×Dic₃	—	3	1	no	—
73	C₂²×Dic₃	—	3	1	no	—
74	C₂²×Dic₃	—	6	2	no	—
75	C₂×C₃×C₈	—	2	2	no	—
76	C₂×C₃×C₈	D₁₂	1	2	yes	—
77	C₃×C₄⋊C₄	—	2	2	no	—
78	C₃×C₄⋊C₄	Dic₆	1	4	yes	—
79	C₄⋊Dic₃	—	6	2	no	—
80	C₄⋊Dic₃	—	6	2	no	—
81	C₄⋊Dic₃	—	12	4	no	—
82	C₄×Dic₃	—	6	1	no	—
83	C₄×Dic₃	—	6	1	no	—
84	C₂×C₃⋊C₈	—	6	1	no	—
85	C₂×C₃⋊C₈	—	6	2	no	—
86	C₂²×C₉	#121	1	1	yes	characteristic
87	C₂²×C₉	C₂²⋊Q₈	1	2	yes	—
88	C₂²×C₉	C₂×Q₁₆	1	1	yes	characteristic
89	C₂²×C₉	#135	1	1	yes	characteristic
90	C₂²×C₉	AGL(1,ℤ/8)	1	2	yes	—
91	C₄×C₉	—	4	4	no	—
92	C₄×C₉	#123	1	1	yes	characteristic
93	C₄×C₉	#125	1	2	yes	—
94	C₄×C₉	C₄⋊Q₈	1	1	yes	characteristic
95	Dic₉	—	2	2	no	—
96	Dic₉	—	4	1	no	—
97	Dic₉	—	8	2	no	—
98	C₂²×C₈	—	9	1	no	—
99	C₂²×C₈	C₂×D₉	1	1	yes	characteristic
100	C₂×C₄⋊C₄	—	9	2	no	—
101	C₂×C₄⋊C₄	—	18	2	no	—
102	C₂×C₄⋊C₄	C₂×D₉	1	2	yes	—
103	C₂×C₄²	—	9	1	no	—
104	#107	—	18	2	no	—
105	C₄⋊C₈	—	18	2	no	—
106	#95	—	18	2	no	—
107	C₂³×C₃	D₃×D₄	1	1	yes	characteristic
108	C₂×C₃×C₄	—	2	4	no	—
109	C₂×C₃×C₄	—	4	2	no	—
110	C₂×C₃×C₄	—	4	2	no	—
111	C₂×C₃×C₄	C₂×Dic₆	1	2	yes	—
112	C₂×C₃×C₄	C₂×D₁₂	1	1	yes	characteristic
113	C₂×C₃×C₄	#237	1	2	yes	—
114	C₂×C₃×C₄	#239	1	1	yes	characteristic
115	C₂×Dic₃	—	3	2	no	—
116	C₂×Dic₃	—	6	1	no	—
117	C₂×Dic₃	—	6	1	no	—
118	C₂×Dic₃	—	6	1	no	—
119	C₂×Dic₃	—	6	2	no	—
120	C₂×Dic₃	—	12	2	no	—
121	C₂×Dic₃	—	12	2	no	—
122	C₂×Dic₃	—	12	2	no	—
123	C₃×C₈	—	2	2	no	—
124	C₃⋊C₈	—	12	1	no	—
125	C₂×C₉	#398	1	1	yes	characteristic
126	C₂×C₉	#467	1	1	yes	characteristic
127	C₂×C₉	#469	1	1	yes	characteristic
128	C₂×C₉	#477	1	2	yes	—
129	C₂×C₉	#478	1	2	yes	—
130	C₂²×C₄	—	2	2	no	—
131	C₂²×C₄	—	9	1	no	—
132	C₂²×C₄	—	9	1	no	—
133	C₂²×C₄	—	18	2	no	—
134	C₂²×C₄	C₂²×D₉	1	1	yes	characteristic
135	C₂×C₈	—	2	2	no	—
136	C₂×C₈	—	18	1	no	—
137	C₂×C₈	—	18	2	no	—
138	C₂×C₈	D₃₆	1	2	yes	—
139	C₄⋊C₄	—	2	2	no	—
140	C₄⋊C₄	—	18	2	no	—
141	C₄⋊C₄	—	18	2	no	—
142	C₄⋊C₄	—	36	4	no	—
143	C₄⋊C₄	Dic₁₈	1	4	yes	—
144	C₄²	—	18	1	no	—
145	C₄²	—	18	1	no	—
146	C₂²×C₃	#878	1	2	yes	—
147	C₂²×C₃	#895	1	1	yes	characteristic
148	C₂²×C₃	#912	1	1	yes	characteristic
149	C₂²×C₃	#914	1	2	yes	—
150	C₂²×C₃	D₃×Q₁₆	1	1	yes	characteristic
151	C₃×C₄	—	4	4	no	—
152	C₃×C₄	#869	1	1	yes	characteristic
153	C₃×C₄	#886	1	1	yes	characteristic
154	C₃×C₄	#890	1	2	yes	—
155	Dic₃	—	6	2	no	—
156	Dic₃	—	12	1	no	—
157	Dic₃	—	24	2	no	—
158	C₉	#2087	1	1	yes	characteristic, complemented, Sylow
159	C₂³	D₄×D₉	1	1	yes	characteristic
160	C₂×C₄	—	2	4	no	—
161	C₂×C₄	—	4	2	no	—
162	C₂×C₄	—	4	2	no	—
163	C₂×C₄	—	9	2	no	—
164	C₂×C₄	—	18	1	no	—
165	C₂×C₄	—	18	1	no	—
166	C₂×C₄	—	18	1	no	—
167	C₂×C₄	—	18	2	no	—
168	C₂×C₄	—	36	2	no	—
169	C₂×C₄	—	36	2	no	—
170	C₂×C₄	—	36	2	no	—
171	C₂×C₄	C₂×Dic₁₈	1	2	yes	—
172	C₂×C₄	C₂×D₃₆	1	1	yes	characteristic
173	C₂×C₄	#3699	1	2	yes	—
174	C₂×C₄	#3701	1	1	yes	characteristic
175	C₈	—	2	2	no	—
176	C₈	—	36	1	no	—
177	C₂×C₃	#4661	1	1	yes	characteristic
178	C₂×C₃	#4766	1	2	yes	—
179	C₂×C₃	#4793	1	2	yes	—
180	C₂×C₃	#4865	1	1	yes	characteristic
181	C₂×C₃	#4887	1	1	yes	characteristic
182	C₂²	#63440	1	2	yes	—
183	C₂²	#63457	1	1	yes	characteristic
184	C₂²	#63474	1	1	yes	characteristic
185	C₂²	#63476	1	2	yes	—
186	C₂²	Q₁₆×D₉	1	1	yes	characteristic
187	C₄	—	4	4	no	—
188	C₄	—	18	2	no	—
189	C₄	—	36	1	no	—
190	C₄	—	72	2	no	—
191	C₄	#63431	1	1	yes	characteristic
192	C₄	#63448	1	1	yes	characteristic
193	C₄	#63452	1	2	yes	—
194	C₃	#68839	1	1	yes	characteristic
195	C₂	#10588341	1	1	yes	characteristic
196	C₂	#10588446	1	2	yes	—
197	C₂	#10588473	1	2	yes	—
198	C₂	#10588545	1	1	yes	characteristic
199	C₂	#10588567	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#63378

C₂

yes

maximal, characteristic

C₂×Dic₉⋊C₈

C₂

yes

maximal, characteristic

#10588664

C₂

yes

maximal

C₉×#340

C₂

yes

maximal, characteristic

#10588206

C₂

yes

maximal

#68839

—

maximal

C₂²×C₈×C₉

C₂²

yes

characteristic

C₂×C₉×C₄⋊C₄

C₂²

yes

—

C₂×C₄⋊Dic₉

—

C₂×C₄⋊Dic₉

C₂²

yes

—

C₂×C₄×Dic₉

C₂²

yes

characteristic

C₂²×C₉⋊C₈

C₂²

yes

characteristic

C₉⋊#95

—

#63378

—

Dic₉⋊C₈

—

C₂×#818

—

C₂×Dic₃⋊C₈

—

#4984

—

C₃×#340

D₃

yes

characteristic

#4529

—

C₂²×C₄×C₉

—

C₂²×C₄×C₉

C₂³

yes

characteristic

C₂²×Dic₉

—

C₂²×Dic₉

D₄

yes

characteristic

C₂²×Dic₉

D₄

yes

characteristic

C₂×C₈×C₉

—

C₂×C₈×C₉

D₄

yes

—

C₉×C₄⋊C₄

—

C₉×C₄⋊C₄

Q₈

yes

—

C₄⋊Dic₉

—

C₄⋊Dic₉

—

C₄⋊Dic₉

—

C₄×Dic₉

—

C₄×Dic₉

—

C₂×C₉⋊C₈

—

C₂×C₉⋊C₈

—

#2087

—

Sylow

C₂²×C₃×C₈

C₂×D₃

yes

characteristic

C₂×C₃×C₄⋊C₄

C₂×D₃

yes

—

C₂×C₄⋊Dic₃

—

C₂×C₄⋊Dic₃

—

C₂×C₄×Dic₃

—

C₂²×C₃⋊C₈

—

C₃⋊#95

—

#818

—

Dic₃⋊C₈

—

C₂³×C₉

C₂×D₄

yes

characteristic

C₂×C₄×C₉

—

C₂×C₄×C₉

—

C₂×C₄×C₉

—

C₂×C₄×C₉

C₂×D₄

yes

characteristic

C₂×C₄×C₉

C₂×Q₈

yes

—

C₂×C₄×C₉

#41

yes

—

C₂×C₄×C₉

#41

yes

characteristic

C₂×Dic₉

—

C₂×Dic₉

—

C₂×Dic₉

—

C₂×Dic₉

—

C₂×Dic₉

—

C₂×Dic₉

—

C₂×Dic₉

—

C₂×Dic₉

Q₁₆

yes

—

C₈×C₉

—

C₉⋊C₈

—

C₂×#107

—

C₂×C₄⋊C₈

—

#389

—

#340

—

#340

D₉

yes

characteristic

C₂²×C₃×C₄

—

C₂²×C₃×C₄

C₂²×D₃

yes

characteristic

C₂²×Dic₃

—

C₂²×Dic₃

—

C₂²×Dic₃

—

C₂×C₃×C₈

—

C₂×C₃×C₈

D₁₂

yes

—

C₃×C₄⋊C₄

—

C₃×C₄⋊C₄

Dic₆

yes

—

C₄⋊Dic₃

—

C₄⋊Dic₃

—

C₄⋊Dic₃

—

C₄×Dic₃

—

C₄×Dic₃

—

C₂×C₃⋊C₈

—

C₂×C₃⋊C₈

—

C₂²×C₉

#121

yes

characteristic

C₂²×C₉

C₂²⋊Q₈

yes

—

C₂²×C₉

C₂×Q₁₆

yes

C₂²×C₉

yes

C₂²×C₉

yes

—

C₄×C₉

—

C₄×C₉

#123

yes

characteristic

C₄×C₉

#125

yes

—

C₄×C₉

C₄⋊Q₈

yes

characteristic

Dic₉

—

Dic₉

—

Dic₉

—

C₂²×C₈

—

C₂²×C₈

C₂×D₉

yes

characteristic

100

C₂×C₄⋊C₄

—

101

C₂×C₄⋊C₄

—

102

C₂×C₄⋊C₄

C₂×D₉

yes

—

103

C₂×C₄²

—

104

#107

—

105

C₄⋊C₈

—

106

#95

—

107

C₂³×C₃

D₃×D₄

yes

characteristic

108

C₂×C₃×C₄

—

109

C₂×C₃×C₄

—

110

C₂×C₃×C₄

—

111

C₂×C₃×C₄

C₂×Dic₆

yes

—

112

C₂×C₃×C₄

C₂×D₁₂

yes

characteristic

113

C₂×C₃×C₄

#237

yes

—

114

C₂×C₃×C₄

#239

yes

characteristic

115

C₂×Dic₃

—

116

C₂×Dic₃

—

117

C₂×Dic₃

—

118

C₂×Dic₃

—

119

C₂×Dic₃

—

120

C₂×Dic₃

—

121

C₂×Dic₃

—

122

C₂×Dic₃

—

123

C₃×C₈

—

124

C₃⋊C₈

—

125

C₂×C₉

#398

yes

characteristic

126

C₂×C₉

#467

yes

characteristic

127

C₂×C₉

#469

yes

characteristic

128

C₂×C₉

#477

yes

—

129

C₂×C₉

#478

yes

—

130

C₂²×C₄

—

131

C₂²×C₄

—

132

C₂²×C₄

—

133

C₂²×C₄

—

134

C₂²×C₄

C₂²×D₉

yes

characteristic

135

C₂×C₈

—

136

C₂×C₈

—

137

C₂×C₈

—

138

C₂×C₈

D₃₆

yes

—

139

C₄⋊C₄

—

140

C₄⋊C₄

—

141

C₄⋊C₄

—

142

C₄⋊C₄

—

143

C₄⋊C₄

Dic₁₈

yes

—

144

C₄²

—

145

C₄²

—

146

C₂²×C₃

#878

yes

—

147

C₂²×C₃

#895

yes

characteristic

148

C₂²×C₃

#912

yes

characteristic

149

C₂²×C₃

#914

yes

—

150

C₂²×C₃

D₃×Q₁₆

yes

characteristic

151

C₃×C₄

—

152

C₃×C₄

#869

yes

characteristic

153

C₃×C₄

#886

yes

characteristic

154

C₃×C₄

#890

yes

—

155

Dic₃

—

156

Dic₃

—

157

Dic₃

—

158

C₉

#2087

yes

characteristic, complemented, Sylow

159

C₂³

D₄×D₉

yes

characteristic

160

C₂×C₄

—

161

C₂×C₄

—

162

C₂×C₄

—

163

C₂×C₄

—

164

C₂×C₄

—

165

C₂×C₄

—

166

C₂×C₄

—

167

C₂×C₄

—

168

C₂×C₄

—

169

C₂×C₄

—

170

C₂×C₄

—

171

C₂×C₄

C₂×Dic₁₈

yes

—

172

C₂×C₄

C₂×D₃₆

yes

characteristic

173

C₂×C₄

#3699

yes

—

174

C₂×C₄

#3701

yes

characteristic

175

C₈

—

176

C₈

—

177

C₂×C₃

#4661

yes

characteristic

178

C₂×C₃

#4766

yes

—

179

C₂×C₃

#4793

yes

—

180

C₂×C₃

#4865

yes

characteristic

181

C₂×C₃

#4887

yes

characteristic

182

C₂²

#63440

yes

—

183

C₂²

#63457

yes

characteristic

184

C₂²

#63474

yes

characteristic

185

C₂²

#63476

yes

—

186

C₂²

Q₁₆×D₉

yes

characteristic

187

C₄

—

188

C₄

—

189

C₄

—

190

C₄

—

191

C₄

#63431

yes

characteristic

192

C₄

#63448

yes

characteristic

193

C₄

#63452

yes

—

194

C₃

#68839

yes

characteristic

195

C₂

#10588341

yes

characteristic

196

C₂

#10588446

yes

—

197

C₂

#10588473

yes

—

198

C₂

#10588545

yes

characteristic

199

C₂

#10588567

yes

characteristic

	subgroup	G/H
center	C₂³	D₄×D₉
commutator, cosocle	C₂²×C₄×C₉	C₂³
Frattini	C₂²×C₃×C₄	C₂²×D₃
Fitting	C₉×#340	C₂
socle, prime radical	C₂³×C₃	D₃×D₄
hypercenter	#340	D₉
hypocenter	C₉	#2087
LCS	G ▷ C₂²×C₄×C₉ ▷ C₂×C₉ ▷ C₉
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ #340

subgroup

G/H

center

C₂³

D₄×D₉

commutator, cosocle

C₂²×C₄×C₉

C₂³

Frattini

C₂²×C₃×C₄

C₂²×D₃

Fitting

C₉×#340

C₂

socle, prime radical

C₂³×C₃

D₃×D₄

D₉

C₉

G ▷ C₂²×C₄×C₉ ▷ C₂×C₉ ▷ C₉

UCS

C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ #340

N	H ≅ G/N	type
158. C₉	#2087	semidirect

H ≅ G/N

type

158. C₉

#2087

semidirect

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

subgroup	index
C₂×#63378	2
C₂×Dic₉⋊C₈	2
#10588664	2
C₉×#340	2
#10588206	2
#68839	3

subgroup

index

C₂×Dic₉⋊C₈

Subgroups — #11795217

Conjugacy classes of subgroups

Complements

Maximal subgroups