Group #36448097 — subgroups

Subgroups — #36448097

Order 22784.

362 conjugacy classes of subgroups; only the 147 normal subgroups are shown.

normal subgroups only

This group has 362 conjugacy classes of subgroups — too many to draw. Only its 147 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	#26020403	C₂	1	2	yes	maximal
2	#26019997	C₂	1	1	yes	maximal, characteristic
3	#26018087	C₂	1	1	yes	maximal, characteristic
4	#26018086	C₂	1	2	yes	maximal
5	C₈₉×#1277	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄⋊#10623494	C₂²	1	2	yes	—
7	C₂×#15667941	—	2	2	no	—
8	C₂×#15667941	—	2	2	no	—
9	C₂×C₄×#10623494	C₂²	1	1	yes	characteristic
10	C₄²×Dic₈₉	C₂²	1	1	yes	characteristic
11	#19151352	C₄	1	2	yes	—
12	#19151352	C₄	1	2	yes	—
13	C₂×C₄⋊C₈×C₈₉	C₂²	1	2	yes	—
14	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
15	C₂²×#10623494	—	2	2	no	—
16	C₂²×#10623494	C₂×C₄	1	1	yes	characteristic
17	C₂²×#10623494	C₂×C₄	1	1	yes	characteristic
18	C₂×C₄×Dic₈₉	C₂×C₄	1	2	yes	—
19	C₂×C₄×Dic₈₉	D₄	1	1	yes	characteristic
20	C₂×C₄×Dic₈₉	D₄	1	1	yes	characteristic
21	C₂×C₄×Dic₈₉	Q₈	1	2	yes	—
22	C₄⋊#10623494	—	2	2	no	—
23	C₄⋊#10623494	—	2	2	no	—
24	#15667941	—	4	4	no	—
25	#15667941	—	4	4	no	—
26	C₄×#10623494	—	2	2	no	—
27	C₂²×C₈×C₈₉	—	2	2	no	—
28	C₂²×C₈×C₈₉	C₂×C₄	1	2	yes	—
29	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
30	C₄⋊C₈×C₈₉	—	2	2	no	—
31	C₄⋊C₈×C₈₉	—	2	2	no	—
32	C₄×C₈×C₈₉	—	2	2	no	—
33	C₂²×Dic₈₉	C₄⋊C₄	1	2	yes	—
34	C₂²×Dic₈₉	C₄⋊C₄	1	2	yes	—
35	C₂×#10623494	—	2	1	no	—
36	C₂×#10623494	—	2	1	no	—
37	C₂×#10623494	—	2	2	no	—
38	C₂×#10623494	—	2	2	no	—
39	C₂×#10623494	—	4	2	no	—
40	C₂×#10623494	—	4	2	no	—
41	C₂×#10623494	—	4	2	no	—
42	C₄×Dic₈₉	—	2	2	no	—
43	C₄×Dic₈₉	—	2	2	no	—
44	C₄×Dic₈₉	—	4	2	no	—
45	C₄×Dic₈₉	D₈	1	2	yes	—
46	C₄×Dic₈₉	SD₁₆	1	4	yes	—
47	C₄×Dic₈₉	Q₁₆	1	2	yes	—
48	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
49	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
50	C₂²×C₄×C₈₉	C₂×Q₈	1	1	yes	characteristic
51	C₂×C₈×C₈₉	—	2	2	no	—
52	C₂×C₈×C₈₉	—	2	2	no	—
53	C₂×C₈×C₈₉	—	2	2	no	—
54	C₂×C₈×C₈₉	—	4	2	no	—
55	C₂×C₈×C₈₉	—	4	2	no	—
56	C₂×C₈×C₈₉	—	4	2	no	—
57	C₄²×C₈₉	#41	1	2	yes	—
58	C₄²×C₈₉	#41	1	2	yes	—
59	C₂³×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
60	C₂×C₄×C₈₉	—	2	2	no	—
61	C₂×C₄×C₈₉	#117	1	1	yes	characteristic
62	C₂×C₄×C₈₉	#117	1	1	yes	characteristic
63	C₂×C₄×C₈₉	#124	1	2	yes	—
64	C₂×C₄×C₈₉	#125	1	2	yes	—
65	C₂×C₄×C₈₉	#131	1	2	yes	—
66	C₂×C₄×C₈₉	#131	1	2	yes	—
67	C₂×C₄×C₈₉	C₂×D₈	1	1	yes	characteristic
68	C₂×C₄×C₈₉	C₂×SD₁₆	1	2	yes	—
69	C₂×C₄×C₈₉	C₂×Q₁₆	1	1	yes	characteristic
70	C₂×Dic₈₉	—	2	2	no	—
71	C₂×Dic₈₉	—	2	2	no	—
72	C₂×Dic₈₉	—	2	2	no	—
73	C₂×Dic₈₉	—	2	2	no	—
74	C₂×Dic₈₉	#106	1	4	yes	—
75	C₂×Dic₈₉	#107	1	4	yes	—
76	C₈×C₈₉	—	4	2	no	—
77	C₈×C₈₉	—	8	2	no	—
78	#10623494	—	4	1	no	—
79	#10623494	—	4	1	no	—
80	#10623494	—	8	2	no	—
81	C₂²×C₈₉	#382	1	1	yes	characteristic
82	C₂²×C₈₉	#424	1	2	yes	—
83	C₂²×C₈₉	C₂×#106	1	1	yes	characteristic
84	C₂²×C₈₉	C₂×#107	1	1	yes	characteristic
85	C₂²×C₈₉	#430	1	2	yes	—
86	C₄×C₈₉	—	2	2	no	—
87	C₄×C₈₉	#433	1	2	yes	—
88	C₄×C₈₉	#433	1	1	yes	characteristic
89	C₄×C₈₉	#433	1	1	yes	characteristic
90	C₄×C₈₉	#486	1	2	yes	—
91	C₄×C₈₉	#487	1	2	yes	—
92	Dic₈₉	—	2	4	no	—
93	Dic₈₉	—	2	4	no	—
94	#8787	—	89	1	no	maximal, Sylow
95	C₂×C₈₉	#1570	1	2	yes	—
96	C₂×C₈₉	#1571	1	2	yes	—
97	C₂×C₈₉	#1832	1	1	yes	characteristic
98	C₂×C₈₉	#1834	1	1	yes	characteristic
99	C₂×C₈₉	#1838	1	1	yes	characteristic
100	#1842	—	89	2	no	—
101	#1744	—	89	1	no	—
102	#1277	—	89	2	no	—
103	#1277	—	89	1	no	—
104	#1277	D₈₉	1	1	yes	characteristic
105	C₈₉	#8787	1	1	yes	characteristic, complemented, Sylow
106	C₂×C₄⋊C₈	—	89	2	no	—
107	C₂×C₄⋊C₈	—	178	2	no	—
108	C₂×C₄⋊C₈	—	178	2	no	—
109	C₂×C₄⋊C₈	C₂×D₈₉	1	2	yes	—
110	C₂×C₄×C₈	—	89	1	no	—
111	C₂×C₄×C₈	C₂×D₈₉	1	1	yes	characteristic
112	C₄³	—	89	1	no	—
113	#336	—	89	2	no	—
114	#336	—	89	2	no	—
115	C₂²×C₈	—	2	2	no	—
116	C₂²×C₈	—	89	1	no	—
117	C₂²×C₈	—	89	1	no	—
118	C₂²×C₈	—	178	2	no	—
119	C₂²×C₈	C₄×D₈₉	1	2	yes	—
120	C₂×C₄²	—	89	1	no	—
121	C₂×C₄²	—	89	1	no	—
122	C₂×C₄²	—	89	2	no	—
123	C₂×C₄²	—	89	2	no	—
124	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
125	C₄⋊C₈	—	2	2	no	—
126	C₄⋊C₈	—	2	2	no	—
127	C₄⋊C₈	—	356	4	no	—
128	C₄⋊C₈	—	356	4	no	—
129	C₄⋊C₈	—	178	2	no	—
130	C₄⋊C₈	—	178	2	no	—
131	C₄×C₈	—	2	2	no	—
132	C₄×C₈	—	178	2	no	—
133	C₂²×C₄	—	89	2	no	—
134	C₂²×C₄	—	89	2	no	—
135	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
136	C₂²×C₄	D₄×D₈₉	1	1	yes	characteristic
137	C₂²×C₄	Q₈×D₈₉	1	1	yes	characteristic
138	C₂×C₈	—	2	2	no	—
139	C₂×C₈	—	2	2	no	—
140	C₂×C₈	—	2	2	no	—
141	C₂×C₈	—	4	2	no	—
142	C₂×C₈	—	4	2	no	—
143	C₂×C₈	—	4	2	no	—
144	C₂×C₈	—	356	2	no	—
145	C₂×C₈	—	356	2	no	—
146	C₂×C₈	—	356	2	no	—
147	C₂×C₈	—	178	1	no	—
148	C₂×C₈	—	178	1	no	—
149	C₂×C₈	—	178	2	no	—
150	C₂×C₈	—	178	2	no	—
151	C₄²	—	89	2	no	—
152	C₄²	—	89	4	no	—
153	C₄²	—	89	2	no	—
154	C₄²	—	356	2	no	—
155	C₄²	—	178	2	no	—
156	C₄²	—	178	2	no	—
157	C₄²	#13083573	1	2	yes	—
158	C₄²	#13083574	1	2	yes	—
159	C₂³	C₄⋊C₄×D₈₉	1	1	yes	characteristic
160	C₂×C₄	—	2	2	no	—
161	C₂×C₄	—	89	4	no	—
162	C₂×C₄	—	89	4	no	—
163	C₂×C₄	—	178	2	no	—
164	C₂×C₄	—	178	2	no	—
165	C₂×C₄	—	178	2	no	—
166	C₂×C₄	—	178	2	no	—
167	C₂×C₄	#15667968	1	1	yes	characteristic
168	C₂×C₄	#15667969	1	1	yes	characteristic
169	C₂×C₄	#15667998	1	2	yes	—
170	C₂×C₄	#15668002	1	2	yes	—
171	C₂×C₄	#15668018	1	2	yes	—
172	C₂×C₄	#15668020	1	2	yes	—
173	C₂×C₄	D₈×D₈₉	1	1	yes	characteristic
174	C₂×C₄	SD₁₆×D₈₉	1	2	yes	—
175	C₂×C₄	Q₁₆×D₈₉	1	1	yes	characteristic
176	C₈	—	4	2	no	—
177	C₈	—	8	2	no	—
178	C₈	—	356	1	no	—
179	C₈	—	356	1	no	—
180	C₈	—	712	2	no	—
181	C₂²	#19151462	1	1	yes	characteristic
182	C₂²	#19151623	1	2	yes	—
183	C₂²	#106×D₈₉	1	1	yes	characteristic
184	C₂²	#107×D₈₉	1	1	yes	characteristic
185	C₂²	#19151645	1	2	yes	—
186	C₄	—	2	2	no	—
187	C₄	—	178	4	no	—
188	C₄	—	178	4	no	—
189	C₄	#19151656	1	2	yes	—
190	C₄	#19151657	1	1	yes	characteristic
191	C₄	#19151660	1	1	yes	characteristic
192	C₄	#19151943	1	2	yes	—
193	C₄	#19151947	1	2	yes	—
194	C₂	#26019021	1	2	yes	—
195	C₂	#26019025	1	2	yes	—
196	C₂	#26020370	1	1	yes	characteristic
197	C₂	#26020378	1	1	yes	characteristic
198	C₂	#26020391	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#26020403

C₂

yes

maximal

#26019997

C₂

yes

maximal, characteristic

#26018087

C₂

yes

maximal, characteristic

#26018086

C₂

yes

maximal

C₈₉×#1277

C₂

yes

maximal, characteristic

C₂×C₄⋊#10623494

C₂²

yes

—

C₂×#15667941

—

C₂×#15667941

—

C₂×C₄×#10623494

C₂²

yes

characteristic

C₄²×Dic₈₉

C₂²

yes

characteristic

#19151352

C₄

yes

—

#19151352

C₄

yes

—

C₂×C₄⋊C₈×C₈₉

C₂²

yes

—

C₂×C₄×C₈×C₈₉

C₂²

yes

characteristic

C₂²×#10623494

—

C₂²×#10623494

C₂×C₄

yes

characteristic

C₂²×#10623494

C₂×C₄

yes

characteristic

C₂×C₄×Dic₈₉

C₂×C₄

yes

—

C₂×C₄×Dic₈₉

D₄

yes

characteristic

C₂×C₄×Dic₈₉

D₄

yes

characteristic

C₂×C₄×Dic₈₉

Q₈

yes

—

—

—

—

—

—

C₂²×C₈×C₈₉

—

C₂²×C₈×C₈₉

C₂×C₄

yes

—

C₂×C₄²×C₈₉

C₂³

yes

characteristic

C₄⋊C₈×C₈₉

—

C₄⋊C₈×C₈₉

—

C₄×C₈×C₈₉

—

C₂²×Dic₈₉

C₄⋊C₄

yes

—

C₂²×Dic₈₉

C₄⋊C₄

yes

—

—

—

—

—

—

—

—

C₄×Dic₈₉

—

C₄×Dic₈₉

—

C₄×Dic₈₉

—

C₄×Dic₈₉

D₈

yes

—

C₄×Dic₈₉

SD₁₆

yes

—

C₄×Dic₈₉

Q₁₆

yes

—

C₂²×C₄×C₈₉

C₂²×C₄

yes

characteristic

C₂²×C₄×C₈₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₈₉

C₂×Q₈

yes

characteristic

C₂×C₈×C₈₉

—

C₂×C₈×C₈₉

—

C₂×C₈×C₈₉

—

C₂×C₈×C₈₉

—

C₂×C₈×C₈₉

—

C₂×C₈×C₈₉

—

C₄²×C₈₉

#41

yes

—

C₄²×C₈₉

#41

yes

—

C₂³×C₈₉

C₂×C₄⋊C₄

yes

characteristic

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

yes

C₂×C₄×C₈₉

yes

C₂×C₄×C₈₉

yes

—

C₂×C₄×C₈₉

#125

yes

—

C₂×C₄×C₈₉

#131

yes

—

C₂×C₄×C₈₉

#131

yes

—

C₂×C₄×C₈₉

C₂×D₈

yes

characteristic

C₂×C₄×C₈₉

C₂×SD₁₆

yes

—

C₂×C₄×C₈₉

C₂×Q₁₆

yes

characteristic

C₂×Dic₈₉

—

C₂×Dic₈₉

—

C₂×Dic₈₉

—

C₂×Dic₈₉

—

C₂×Dic₈₉

#106

yes

—

C₂×Dic₈₉

#107

yes

—

C₈×C₈₉

—

C₈×C₈₉

—

#10623494

—

#10623494

—

#10623494

—

C₂²×C₈₉

#382

yes

characteristic

C₂²×C₈₉

#424

yes

—

C₂²×C₈₉

yes

C₂²×C₈₉

yes

C₂²×C₈₉

yes

—

C₄×C₈₉

—

C₄×C₈₉

#433

yes

—

C₄×C₈₉

yes

C₄×C₈₉

yes

C₄×C₈₉

yes

—

C₄×C₈₉

#487

yes

—

Dic₈₉

—

Dic₈₉

—

#8787

—

maximal, Sylow

C₂×C₈₉

#1570

yes

—

C₂×C₈₉

#1571

yes

—

C₂×C₈₉

yes

C₂×C₈₉

yes

C₂×C₈₉

yes

100

—

101

#1744

—

102

#1277

—

103

#1277

—

104

#1277

D₈₉

yes

characteristic

105

C₈₉

#8787

yes

characteristic, complemented, Sylow

106

C₂×C₄⋊C₈

—

107

C₂×C₄⋊C₈

—

178

—

108

C₂×C₄⋊C₈

—

178

—

109

C₂×C₄⋊C₈

C₂×D₈₉

yes

—

110

C₂×C₄×C₈

—

111

C₂×C₄×C₈

C₂×D₈₉

yes

characteristic

112

C₄³

—

113

#336

—

114

#336

—

115

C₂²×C₈

—

116

C₂²×C₈

—

117

C₂²×C₈

—

118

C₂²×C₈

—

178

—

119

C₂²×C₈

C₄×D₈₉

yes

—

120

C₂×C₄²

—

121

C₂×C₄²

—

122

C₂×C₄²

—

123

C₂×C₄²

—

124

C₂×C₄²

C₂²×D₈₉

yes

characteristic

125

C₄⋊C₈

—

126

C₄⋊C₈

—

127

C₄⋊C₈

—

356

—

128

C₄⋊C₈

—

356

—

129

C₄⋊C₈

—

178

—

130

C₄⋊C₈

—

178

—

131

C₄×C₈

—

132

C₄×C₈

—

178

—

133

C₂²×C₄

—

134

C₂²×C₄

—

135

C₂²×C₄

C₂×C₄×D₈₉

yes

characteristic

136

C₂²×C₄

D₄×D₈₉

yes

characteristic

137

C₂²×C₄

Q₈×D₈₉

yes

characteristic

138

C₂×C₈

—

139

C₂×C₈

—

140

C₂×C₈

—

141

C₂×C₈

—

142

C₂×C₈

—

143

C₂×C₈

—

144

C₂×C₈

—

356

—

145

C₂×C₈

—

356

—

146

C₂×C₈

—

356

—

147

C₂×C₈

—

178

—

148

C₂×C₈

—

178

—

149

C₂×C₈

—

178

—

150

C₂×C₈

—

178

—

151

C₄²

—

152

C₄²

—

153

C₄²

—

154

C₄²

—

356

—

155

C₄²

—

178

—

156

C₄²

—

178

—

157

C₄²

#13083573

yes

—

158

C₄²

#13083574

yes

—

159

C₂³

C₄⋊C₄×D₈₉

yes

characteristic

160

C₂×C₄

—

161

C₂×C₄

—

162

C₂×C₄

—

163

C₂×C₄

—

178

—

164

C₂×C₄

—

178

—

165

C₂×C₄

—

178

—

166

C₂×C₄

—

178

—

167

C₂×C₄

#15667968

yes

characteristic

168

C₂×C₄

#15667969

yes

characteristic

169

C₂×C₄

#15667998

yes

—

170

C₂×C₄

#15668002

yes

—

171

C₂×C₄

#15668018

yes

—

172

C₂×C₄

#15668020

yes

—

173

C₂×C₄

D₈×D₈₉

yes

characteristic

174

C₂×C₄

SD₁₆×D₈₉

yes

—

175

C₂×C₄

Q₁₆×D₈₉

yes

characteristic

176

C₈

—

177

C₈

—

178

C₈

—

356

—

179

C₈

—

356

—

180

C₈

—

712

—

181

C₂²

#19151462

yes

characteristic

182

C₂²

#19151623

yes

—

183

C₂²

#106×D₈₉

yes

characteristic

184

C₂²

#107×D₈₉

yes

characteristic

185

C₂²

#19151645

yes

—

186

C₄

—

187

C₄

—

178

—

188

C₄

—

178

—

189

C₄

#19151656

yes

—

190

C₄

#19151657

yes

characteristic

191

C₄

#19151660

yes

characteristic

192

C₄

#19151943

yes

—

193

C₄

#19151947

yes

—

194

C₂

#26019021

yes

—

195

C₂

#26019025

yes

—

196

C₂

#26020370

yes

characteristic

197

C₂

#26020378

yes

characteristic

198

C₂

#26020391

yes

characteristic

	subgroup	G/H
center	C₂²×C₄	D₄×D₈₉
commutator	C₂²×C₄×C₈₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₈₉
Fitting	C₈₉×#1277	C₂
socle, prime radical	C₂³×C₈₉	C₂×C₄⋊C₄
cosocle	C₂×C₄²×C₈₉	C₂³
hypercenter	#1277	D₈₉
hypocenter	C₈₉	#8787
LCS	G ▷ C₂²×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄² ◁ #1277

subgroup

G/H

center

C₂²×C₄

D₄×D₈₉

commutator

C₂²×C₄×C₈₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₈₉

Fitting

C₈₉×#1277

C₂

socle, prime radical

C₂³×C₈₉

C₂×C₄⋊C₄

cosocle

C₂×C₄²×C₈₉

C₂³

D₈₉

C₈₉

G ▷ C₂²×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉

UCS

C₁ ◁ C₂²×C₄ ◁ C₂×C₄² ◁ #1277

N	H ≅ G/N	type
105. C₈₉	#8787	semidirect

H ≅ G/N

type

105. C₈₉

#8787

semidirect

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

subgroup	index
#26020403	2
#26019997	2
#26018087	2
#26018086	2
C₈₉×#1277	2
#8787	89

subgroup

index

C₈₉×#1277

Subgroups — #36448097

Conjugacy classes of subgroups

Complements

Maximal subgroups