Group #11782818 — subgroups

Subgroups — #11782818

Order 1152.

279 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 279 conjugacy classes of subgroups — too many to draw. Only its 86 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	#10588376	C₂	1	1	yes	maximal, characteristic
2	#10588376	C₂	1	1	yes	maximal, characteristic
3	#10588375	C₂	1	1	yes	maximal, characteristic
4	#10588362	C₂	1	1	yes	maximal, characteristic, complemented
5	#10588361	C₂	1	1	yes	maximal, characteristic, complemented
6	#10588361	C₂	1	1	yes	maximal, characteristic, complemented
7	C₉×#322	C₂	1	1	yes	maximal, characteristic, complemented
8	#68093	—	3	1	no	maximal
9	C₂×#3664	—	2	2	no	—
10	#63436	C₂²	1	1	yes	characteristic
11	#63431	C₂²	1	1	yes	characteristic
12	#63431	C₂²	1	1	yes	characteristic
13	#63431	C₂²	1	1	yes	characteristic
14	C₄×C₈×C₉	C₂²	1	1	yes	characteristic
15	C₄×C₈×C₉	C₂²	1	1	yes	characteristic
16	C₄×C₈×C₉	C₂²	1	1	yes	characteristic
17	#63380	—	2	2	no	—
18	#63380	—	2	2	no	—
19	#63378	—	2	2	no	—
20	#63376	—	2	2	no	—
21	#63376	—	2	2	no	—
22	#4694	—	3	1	no	—
23	#4694	—	3	1	no	—
24	#4693	—	3	1	no	—
25	#4682	—	3	1	no	—
26	#4681	—	3	1	no	—
27	#4681	—	3	1	no	—
28	C₃×#322	D₃	1	1	yes	characteristic
29	C₂×D₃₆	—	2	1	no	—
30	C₂×D₃₆	—	2	1	no	—
31	C₂×D₃₆	—	2	1	no	—
32	C₂×Dic₁₈	—	2	1	no	—
33	C₂×Dic₁₈	—	2	1	no	—
34	C₂×Dic₁₈	—	2	1	no	—
35	C₂×C₈×C₉	D₄	1	2	yes	—
36	C₂×C₈×C₉	D₄	1	2	yes	—
37	C₂×C₈×C₉	D₄	1	2	yes	—
38	C₄²×C₉	C₂³	1	1	yes	characteristic
39	C₄⋊Dic₉	—	2	1	no	—
40	C₄⋊Dic₉	—	2	1	no	—
41	C₄⋊Dic₉	—	2	1	no	—
42	C₄⋊Dic₉	—	2	1	no	—
43	C₄⋊Dic₉	—	2	1	no	—
44	C₄⋊Dic₉	—	2	1	no	—
45	#3664	—	4	4	no	—
46	#1719	—	9	1	no	Sylow
47	C₂×#204	—	6	2	no	—
48	#874	—	3	1	no	—
49	#869	—	3	1	no	—
50	#869	—	3	1	no	—
51	#869	—	3	1	no	—
52	C₃×C₄×C₈	C₂×D₃	1	1	yes	characteristic
53	C₃×C₄×C₈	C₂×D₃	1	1	yes	characteristic
54	C₃×C₄×C₈	C₂×D₃	1	1	yes	characteristic
55	#821	—	6	2	no	—
56	#821	—	6	2	no	—
57	#818	—	6	2	no	—
58	#816	—	6	2	no	—
59	#816	—	6	2	no	—
60	C₂²×D₉	—	4	1	no	—
61	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
62	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
63	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
64	C₂×Dic₉	—	4	1	no	—
65	C₂×Dic₉	—	4	1	no	—
66	C₂×Dic₉	—	4	1	no	—
67	D₃₆	—	4	2	no	—
68	D₃₆	—	4	2	no	—
69	D₃₆	—	4	2	no	—
70	Dic₁₈	—	4	2	no	—
71	Dic₁₈	—	4	2	no	—
72	Dic₁₈	—	4	2	no	—
73	C₈×C₉	—	2	2	no	—
74	C₈×C₉	—	2	2	no	—
75	C₈×C₉	—	2	2	no	—
76	#500	—	9	1	no	—
77	#492	—	9	1	no	—
78	#487	—	9	1	no	—
79	#487	—	9	1	no	—
80	#486	—	9	1	no	—
81	#486	—	9	1	no	—
82	#322	D₉	1	1	yes	characteristic, complemented
83	C₂×D₁₂	—	6	1	no	—
84	C₂×D₁₂	—	6	1	no	—
85	C₂×D₁₂	—	6	1	no	—
86	C₂×Dic₆	—	6	1	no	—
87	C₂×Dic₆	—	6	1	no	—
88	C₂×Dic₆	—	6	1	no	—
89	C₂×C₃×C₈	D₁₂	1	2	yes	—
90	C₂×C₃×C₈	D₁₂	1	2	yes	—
91	C₂×C₃×C₈	D₁₂	1	2	yes	—
92	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
93	C₄⋊Dic₃	—	6	1	no	—
94	C₄⋊Dic₃	—	6	1	no	—
95	C₄⋊Dic₃	—	6	1	no	—
96	C₄⋊Dic₃	—	6	1	no	—
97	C₄⋊Dic₃	—	6	1	no	—
98	C₄⋊Dic₃	—	6	1	no	—
99	#204	—	12	4	no	—
100	C₂²×C₉	#127	1	1	yes	characteristic
101	C₂×D₉	—	8	1	no	—
102	C₂×D₉	—	8	1	no	—
103	C₂×D₉	—	8	1	no	—
104	C₄×C₉	#135	1	2	yes	—
105	C₄×C₉	AGL(1,ℤ/8)	1	2	yes	—
106	C₄×C₉	#137	1	2	yes	—
107	Dic₉	—	8	1	no	—
108	Dic₉	—	8	1	no	—
109	Dic₉	—	8	1	no	—
110	C₂×SD₁₆	—	18	2	no	—
111	C₄⋊Q₈	—	9	1	no	—
112	C₄⋊Q₈	—	9	1	no	—
113	C₄⋊Q₈	—	9	1	no	—
114	#127	—	9	1	no	—
115	#107	—	18	2	no	—
116	#103	—	18	2	no	—
117	#103	—	18	2	no	—
118	#102	—	18	2	no	—
119	#102	—	18	2	no	—
120	C₄×C₈	C₂×D₉	1	1	yes	characteristic
121	C₄×C₈	C₂×D₉	1	1	yes	characteristic
122	C₄×C₈	C₂×D₉	1	1	yes	characteristic
123	C₂²×D₃	—	12	1	no	—
124	C₂×C₃×C₄	C₂×D₁₂	1	1	yes	characteristic
125	C₂×C₃×C₄	C₂×D₁₂	1	1	yes	characteristic
126	C₂×C₃×C₄	C₂×D₁₂	1	1	yes	characteristic
127	C₂×Dic₃	—	12	1	no	—
128	C₂×Dic₃	—	12	1	no	—
129	C₂×Dic₃	—	12	1	no	—
130	D₁₂	—	12	2	no	—
131	D₁₂	—	12	2	no	—
132	D₁₂	—	12	2	no	—
133	Dic₆	—	12	2	no	—
134	Dic₆	—	12	2	no	—
135	Dic₆	—	12	2	no	—
136	C₃×C₈	—	2	2	no	—
137	C₃×C₈	—	2	2	no	—
138	C₃×C₈	—	2	2	no	—
139	C₂×C₉	#495	1	1	yes	characteristic
140	C₂×C₉	#496	1	1	yes	characteristic
141	C₂×C₉	#497	1	1	yes	characteristic
142	D₉	—	16	1	no	—
143	C₂×Q₈	—	18	1	no	—
144	C₂×Q₈	—	18	1	no	—
145	C₂×Q₈	—	18	1	no	—
146	C₂×D₄	—	18	1	no	—
147	C₂×D₄	—	18	1	no	—
148	C₂×D₄	—	18	1	no	—
149	SD₁₆	—	36	4	no	—
150	C₂×C₈	D₃₆	1	2	yes	—
151	C₂×C₈	D₃₆	1	2	yes	—
152	C₂×C₈	D₃₆	1	2	yes	—
153	C₄⋊C₄	—	18	1	no	—
154	C₄⋊C₄	—	18	1	no	—
155	C₄⋊C₄	—	18	1	no	—
156	C₄⋊C₄	—	18	1	no	—
157	C₄⋊C₄	—	18	1	no	—
158	C₄⋊C₄	—	18	1	no	—
159	C₄²	C₂²×D₉	1	1	yes	characteristic
160	C₂²×C₃	#874	1	1	yes	characteristic
161	C₂×D₃	—	24	1	no	—
162	C₂×D₃	—	24	1	no	—
163	C₂×D₃	—	24	1	no	—
164	C₃×C₄	#904	1	2	yes	—
165	C₃×C₄	#908	1	2	yes	—
166	C₃×C₄	#909	1	2	yes	—
167	Dic₃	—	24	1	no	—
168	Dic₃	—	24	1	no	—
169	Dic₃	—	24	1	no	—
170	C₉	#1719	1	1	yes	characteristic, complemented, Sylow
171	C₂³	—	36	1	no	—
172	Q₈	—	36	2	no	—
173	Q₈	—	36	2	no	—
174	Q₈	—	36	2	no	—
175	D₄	—	36	2	no	—
176	D₄	—	36	2	no	—
177	D₄	—	36	2	no	—
178	C₂×C₄	—	36	1	no	—
179	C₂×C₄	—	36	1	no	—
180	C₂×C₄	—	36	1	no	—
181	C₂×C₄	C₂×D₃₆	1	1	yes	characteristic
182	C₂×C₄	C₂×D₃₆	1	1	yes	characteristic
183	C₂×C₄	C₂×D₃₆	1	1	yes	characteristic
184	C₈	—	2	2	no	—
185	C₈	—	2	2	no	—
186	C₈	—	2	2	no	—
187	C₂×C₃	#4696	1	1	yes	characteristic
188	C₂×C₃	#4712	1	1	yes	characteristic
189	C₂×C₃	#4715	1	1	yes	characteristic
190	D₃	—	48	1	no	—
191	C₂²	—	72	1	no	—
192	C₂²	—	72	1	no	—
193	C₂²	—	72	1	no	—
194	C₂²	#63436	1	1	yes	characteristic
195	C₄	—	72	1	no	—
196	C₄	—	72	1	no	—
197	C₄	—	72	1	no	—
198	C₄	#63467	1	2	yes	—
199	C₄	#63470	1	2	yes	—
200	C₄	#63471	1	2	yes	—
201	C₃	#68093	1	1	yes	characteristic
202	C₂	—	144	1	no	—
203	C₂	#10588378	1	1	yes	characteristic
204	C₂	#10588393	1	1	yes	characteristic
205	C₂	#10588396	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#10588376

C₂

yes

maximal, characteristic

#10588376

C₂

yes

maximal, characteristic

#10588375

C₂

yes

maximal, characteristic

#10588362

C₂

yes

maximal, characteristic, complemented

#10588361

C₂

yes

maximal, characteristic, complemented

#10588361

C₂

yes

maximal, characteristic, complemented

C₉×#322

C₂

yes

maximal, characteristic, complemented

—

—

C₂²

yes

characteristic

#63431

C₂²

yes

characteristic

#63431

C₂²

yes

characteristic

#63431

C₂²

yes

characteristic

C₄×C₈×C₉

C₂²

yes

characteristic

C₄×C₈×C₉

C₂²

yes

characteristic

C₄×C₈×C₉

C₂²

yes

—

—

—

—

—

—

—

—

—

—

—

D₃

yes

characteristic

C₂×D₃₆

—

C₂×D₃₆

—

C₂×D₃₆

—

C₂×Dic₁₈

—

C₂×Dic₁₈

—

C₂×Dic₁₈

—

C₂×C₈×C₉

D₄

yes

—

C₂×C₈×C₉

D₄

yes

—

C₂×C₈×C₉

D₄

yes

—

C₄²×C₉

C₂³

yes

characteristic

C₄⋊Dic₉

—

C₄⋊Dic₉

—

C₄⋊Dic₉

—

C₄⋊Dic₉

—

C₄⋊Dic₉

—

C₄⋊Dic₉

—

—

—

—

—

—

—

—

C₃×C₄×C₈

C₂×D₃

yes

characteristic

C₃×C₄×C₈

C₂×D₃

yes

characteristic

C₃×C₄×C₈

C₂×D₃

yes

—

—

—

—

—

C₂²×D₉

—

C₂×C₄×C₉

C₂×D₄

yes

characteristic

C₂×C₄×C₉

C₂×D₄

yes

characteristic

C₂×C₄×C₉

C₂×D₄

yes

characteristic

C₂×Dic₉

—

C₂×Dic₉

—

C₂×Dic₉

—

D₃₆

—

D₃₆

—

D₃₆

—

Dic₁₈

—

Dic₁₈

—

Dic₁₈

—

C₈×C₉

—

C₈×C₉

—

C₈×C₉

—

—

—

—

—

—

—

D₉

yes

characteristic, complemented

C₂×D₁₂

—

C₂×D₁₂

—

C₂×D₁₂

—

C₂×Dic₆

—

C₂×Dic₆

—

C₂×Dic₆

—

C₂×C₃×C₈

D₁₂

yes

—

C₂×C₃×C₈

D₁₂

yes

—

C₂×C₃×C₈

D₁₂

yes

—

C₃×C₄²

C₂²×D₃

yes

characteristic

C₄⋊Dic₃

—

C₄⋊Dic₃

—

C₄⋊Dic₃

—

C₄⋊Dic₃

—

C₄⋊Dic₃

—

C₄⋊Dic₃

—

#204

—

100

C₂²×C₉

#127

yes

characteristic

101

C₂×D₉

—

102

C₂×D₉

—

103

C₂×D₉

—

104

C₄×C₉

#135

yes

—

105

C₄×C₉

AGL(1,ℤ/8)

yes

—

106

C₄×C₉

#137

yes

—

107

Dic₉

—

108

Dic₉

—

109

Dic₉

—

110

C₂×SD₁₆

—

111

C₄⋊Q₈

—

112

C₄⋊Q₈

—

113

C₄⋊Q₈

—

114

#127

—

115

#107

—

116

#103

—

117

#103

—

118

#102

—

119

#102

—

120

C₄×C₈

C₂×D₉

yes

characteristic

121

C₄×C₈

C₂×D₉

yes

characteristic

122

C₄×C₈

C₂×D₉

yes

characteristic

123

C₂²×D₃

—

124

C₂×C₃×C₄

C₂×D₁₂

yes

characteristic

125

C₂×C₃×C₄

C₂×D₁₂

yes

characteristic

126

C₂×C₃×C₄

C₂×D₁₂

yes

characteristic

127

C₂×Dic₃

—

128

C₂×Dic₃

—

129

C₂×Dic₃

—

130

D₁₂

—

131

D₁₂

—

132

D₁₂

—

133

Dic₆

—

134

Dic₆

—

135

Dic₆

—

136

C₃×C₈

—

137

C₃×C₈

—

138

C₃×C₈

—

139

C₂×C₉

#495

yes

characteristic

140

C₂×C₉

#496

yes

characteristic

141

C₂×C₉

#497

yes

characteristic

142

D₉

—

143

C₂×Q₈

—

144

C₂×Q₈

—

145

C₂×Q₈

—

146

C₂×D₄

—

147

C₂×D₄

—

148

C₂×D₄

—

149

SD₁₆

—

150

C₂×C₈

D₃₆

yes

—

151

C₂×C₈

D₃₆

yes

—

152

C₂×C₈

D₃₆

yes

—

153

C₄⋊C₄

—

154

C₄⋊C₄

—

155

C₄⋊C₄

—

156

C₄⋊C₄

—

157

C₄⋊C₄

—

158

C₄⋊C₄

—

159

C₄²

C₂²×D₉

yes

characteristic

160

C₂²×C₃

#874

yes

characteristic

161

C₂×D₃

—

162

C₂×D₃

—

163

C₂×D₃

—

164

C₃×C₄

#904

yes

—

165

C₃×C₄

#908

yes

—

166

C₃×C₄

#909

yes

—

167

Dic₃

—

168

Dic₃

—

169

Dic₃

—

170

C₉

#1719

yes

characteristic, complemented, Sylow

171

C₂³

—

172

Q₈

—

173

Q₈

—

174

Q₈

—

175

D₄

—

176

D₄

—

177

D₄

—

178

C₂×C₄

—

179

C₂×C₄

—

180

C₂×C₄

—

181

C₂×C₄

C₂×D₃₆

yes

characteristic

182

C₂×C₄

C₂×D₃₆

yes

characteristic

183

C₂×C₄

C₂×D₃₆

yes

characteristic

184

C₈

—

185

C₈

—

186

C₈

—

187

C₂×C₃

#4696

yes

characteristic

188

C₂×C₃

#4712

yes

characteristic

189

C₂×C₃

#4715

yes

characteristic

190

D₃

—

191

C₂²

—

192

C₂²

—

193

C₂²

—

194

C₂²

#63436

yes

characteristic

195

C₄

—

196

C₄

—

197

C₄

—

198

C₄

#63467

yes

—

199

C₄

#63470

yes

—

200

C₄

#63471

yes

—

201

C₃

#68093

yes

characteristic

202

C₂

—

144

—

203

C₂

#10588378

yes

characteristic

204

C₂

#10588393

yes

characteristic

205

C₂

#10588396

yes

characteristic

	subgroup	G/H
center	C₂²	#63436
commutator, cosocle	C₄²×C₉	C₂³
Frattini	C₃×C₄²	C₂²×D₃
Fitting	C₉×#322	C₂
socle	C₂²×C₃	#874
prime radical	#63436	C₂²
hypercenter	#322	D₉
hypocenter	C₉	#1719
LCS	G ▷ C₄²×C₉ ▷ C₂²×C₉ ▷ C₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #322

subgroup

G/H

center

C₂²

#63436

commutator, cosocle

C₄²×C₉

C₂³

Frattini

C₃×C₄²

C₂²×D₃

C₂

C₂²×C₃

C₂²

D₉

C₉

G ▷ C₄²×C₉ ▷ C₂²×C₉ ▷ C₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #322

N	H ≅ G/N	type
4. #10588362	C₂	semidirect
5. #10588361	C₂	semidirect
6. #10588361	C₂	semidirect
7. C₉×#322	C₂	semidirect
82. #322	D₉	semidirect
170. C₉	#1719	semidirect

H ≅ G/N

type

4. #10588362

C₂

semidirect

5. #10588361

C₂

semidirect

6. #10588361

C₂

semidirect

7. C₉×#322

C₂

semidirect

82. #322

D₉

semidirect

170. C₉

#1719

semidirect

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

subgroup	index
#10588376	2
#10588375	2
#10588362	2
#10588361	2
C₉×#322	2
#68093	3

subgroup

index

Subgroups — #11782818

Conjugacy classes of subgroups

Complements

Maximal subgroups