Group #24996623 — subgroups

Subgroups — #24996623

Order 11008.

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

normal subgroups only

This group has 434 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	C₄×#13063317	C₂	1	1	yes	maximal, characteristic
2	#19134341	C₂	1	1	yes	maximal, characteristic
3	#19132434	C₂	1	4	yes	maximal
4	C₄₃×#1831	C₂	1	1	yes	maximal, characteristic
5	C₂×#13063317	C₄	1	1	yes	characteristic
6	C₂×C₄×C₄₃⋊C₈	C₂²	1	2	yes	—
7	#14582797	C₄	1	2	yes	—
8	#14582783	—	2	2	no	—
9	#14582765	C₄	1	1	yes	characteristic
10	C₄×Dic₄₃⋊C₄	—	2	2	no	—
11	C₄×C₄⋊Dic₄₃	C₂²	1	2	yes	—
12	#14582654	—	2	2	no	—
13	C₂×C₄⋊C₈×C₄₃	C₂²	1	2	yes	—
14	C₄³×C₄₃	C₂²	1	1	yes	characteristic
15	C₄₃×#336	—	2	2	no	—
16	C₂²×C₄₃⋊C₈	—	2	2	no	—
17	#13063317	—	2	4	no	—
18	C₂×C₄⋊Dic₄₃	C₂×C₄	1	2	yes	—
19	C₂×C₄⋊Dic₄₃	C₂×C₄	1	2	yes	—
20	C₂×Dic₄₃⋊C₄	—	2	2	no	—
21	C₂×Dic₄₃⋊C₄	—	2	2	no	—
22	C₂×C₄×Dic₄₃	—	2	2	no	—
23	C₄×C₄₃⋊C₈	—	2	2	no	—
24	C₄×C₄₃⋊C₈	Q₈	1	4	yes	—
25	C₄₃⋊#95	—	2	2	no	—
26	C₄₃⋊#95	—	2	2	no	—
27	C₄₃⋊#95	—	2	2	no	—
28	C₂²×C₈×C₄₃	—	2	2	no	—
29	C₂×C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
30	C₂×C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
31	C₂×C₄²×C₄₃	D₄	1	2	yes	—
32	C₂×C₄²×C₄₃	D₄	1	2	yes	—
33	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
34	C₄⋊C₈×C₄₃	—	2	4	no	—
35	C₂²×C₄×C₄₃	C₂²⋊C₄	1	2	yes	—
36	C₂²×C₄×C₄₃	C₂²⋊C₄	1	2	yes	—
37	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
38	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
39	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
40	C₂²×Dic₄₃	—	2	2	no	—
41	C₂²×Dic₄₃	—	2	2	no	—
42	C₂×C₈×C₄₃	—	4	2	no	—
43	C₂×C₈×C₄₃	—	4	4	no	—
44	C₄²×C₄₃	—	2	2	no	—
45	C₄²×C₄₃	—	2	2	no	—
46	C₄²×C₄₃	—	2	4	no	—
47	C₄²×C₄₃	—	4	2	no	—
48	C₄²×C₄₃	C₂×Q₈	1	2	yes	—
49	C₄²×C₄₃	#41	1	2	yes	—
50	C₄⋊Dic₄₃	—	2	2	no	—
51	C₄⋊Dic₄₃	—	2	4	no	—
52	C₄⋊Dic₄₃	M₁₆	1	4	yes	—
53	Dic₄₃⋊C₄	—	2	8	no	—
54	Dic₄₃⋊C₄	—	4	4	no	—
55	C₄×Dic₄₃	—	4	4	no	—
56	C₂×C₄₃⋊C₈	—	2	4	no	—
57	C₂×C₄₃⋊C₈	—	4	4	no	—
58	C₂³×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
59	C₂×C₄×C₄₃	—	2	2	no	—
60	C₂×C₄×C₄₃	—	2	2	no	—
61	C₂×C₄×C₄₃	—	2	2	no	—
62	C₂×C₄×C₄₃	—	2	2	no	—
63	C₂×C₄×C₄₃	—	2	2	no	—
64	C₂×C₄×C₄₃	—	2	2	no	—
65	C₂×C₄×C₄₃	—	2	2	no	—
66	C₂×C₄×C₄₃	C₄×Q₈	1	2	yes	—
67	C₂×C₄×C₄₃	C₂²⋊Q₈	1	2	yes	—
68	C₂×C₄×C₄₃	#124	1	1	yes	characteristic
69	C₂×C₄×C₄₃	C₄⋊Q₈	1	1	yes	characteristic
70	C₂×C₄×C₄₃	C₂×M₁₆	1	2	yes	—
71	C₂×C₄×C₄₃	#131	1	2	yes	—
72	C₂×C₄×C₄₃	#135	1	4	yes	—
73	C₂×Dic₄₃	—	2	4	no	—
74	C₂×Dic₄₃	—	4	2	no	—
75	C₂×Dic₄₃	—	4	2	no	—
76	C₂×Dic₄₃	—	4	2	no	—
77	C₂×Dic₄₃	—	4	2	no	—
78	C₂×Dic₄₃	—	4	2	no	—
79	C₈×C₄₃	—	8	2	no	—
80	C₄₃⋊C₈	—	4	4	no	—
81	#9875	—	43	1	no	maximal, Sylow
82	C₂²×C₄₃	#391	1	1	yes	characteristic
83	C₂²×C₄₃	#407	1	1	yes	characteristic
84	C₂²×C₄₃	#408	1	1	yes	characteristic
85	C₂²×C₄₃	#416	1	2	yes	—
86	C₂²×C₄₃	#421	1	2	yes	—
87	C₄×C₄₃	—	2	2	no	—
88	C₄×C₄₃	—	4	2	no	—
89	C₄×C₄₃	—	4	2	no	—
90	C₄×C₄₃	#446	1	4	yes	—
91	C₄×C₄₃	#488	1	2	yes	—
92	C₄×C₄₃	#499	1	2	yes	—
93	Dic₄₃	—	4	4	no	—
94	Dic₄₃	—	8	2	no	—
95	C₄×#125	—	43	1	no	—
96	#1831	D₄₃	1	1	yes	characteristic
97	#1744	—	43	1	no	—
98	#1279	—	43	4	no	—
99	C₂×C₄₃	#1482	1	2	yes	—
100	C₂×C₄₃	#1488	1	2	yes	—
101	C₂×C₄₃	#1985	1	1	yes	characteristic
102	C₂×C₄₃	#1991	1	1	yes	characteristic
103	C₂×C₄₃	#1995	1	1	yes	characteristic
104	C₂×#125	—	43	1	no	—
105	C₂×C₄⋊C₈	C₂×D₄₃	1	2	yes	—
106	C₂×C₄×C₈	—	43	2	no	—
107	#389	—	43	2	no	—
108	#387	—	86	2	no	—
109	#382	—	43	1	no	—
110	C₄×C₄⋊C₄	—	43	2	no	—
111	C₄×C₄⋊C₄	—	86	2	no	—
112	C₄³	C₂×D₄₃	1	1	yes	characteristic
113	#336	—	2	2	no	—
114	#336	—	86	2	no	—
115	C₄₃	#9875	1	1	yes	characteristic, complemented, Sylow
116	C₂²×C₈	—	2	2	no	—
117	C₂²×C₈	—	86	2	no	—
118	#125	—	86	4	no	—
119	C₂×C₄⋊C₄	—	43	2	no	—
120	C₂×C₄⋊C₄	—	43	2	no	—
121	C₂×C₄⋊C₄	—	86	2	no	—
122	C₂×C₄⋊C₄	—	86	2	no	—
123	C₂×C₄²	—	86	2	no	—
124	C₂×C₄²	C₄×D₄₃	1	1	yes	characteristic
125	C₂×C₄²	C₄×D₄₃	1	1	yes	characteristic
126	C₂×C₄²	D₁₇₂	1	2	yes	—
127	C₂×C₄²	C₂²⋊D₄₃	1	2	yes	—
128	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
129	C₄⋊C₈	—	2	4	no	—
130	C₄×C₈	—	43	4	no	—
131	C₄×C₈	—	86	2	no	—
132	#95	—	86	2	no	—
133	#95	—	86	2	no	—
134	#95	—	86	2	no	—
135	C₂²×C₄	—	86	2	no	—
136	C₂²×C₄	—	86	2	no	—
137	C₂²×C₄	(C₂×D₄₃)⋊C₄	1	2	yes	—
138	C₂²×C₄	(C₂×D₄₃)⋊C₄	1	2	yes	—
139	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
140	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
141	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
142	C₂×C₈	—	4	2	no	—
143	C₂×C₈	—	4	4	no	—
144	C₂×C₈	—	86	4	no	—
145	C₂×C₈	—	172	4	no	—
146	C₄⋊C₄	—	43	4	no	—
147	C₄⋊C₄	—	86	8	no	—
148	C₄⋊C₄	—	86	2	no	—
149	C₄⋊C₄	—	86	4	no	—
150	C₄⋊C₄	—	172	4	no	—
151	C₄²	—	2	2	no	—
152	C₄²	—	2	2	no	—
153	C₄²	—	2	4	no	—
154	C₄²	—	4	2	no	—
155	C₄²	—	172	4	no	—
156	C₄²	#10621900	1	2	yes	—
157	C₄²	Q₈×D₄₃	1	2	yes	—
158	C₂³	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
159	C₂×C₄	—	2	2	no	—
160	C₂×C₄	—	2	2	no	—
161	C₂×C₄	—	2	2	no	—
162	C₂×C₄	—	2	2	no	—
163	C₂×C₄	—	2	2	no	—
164	C₂×C₄	—	2	2	no	—
165	C₂×C₄	—	2	2	no	—
166	C₂×C₄	—	86	4	no	—
167	C₂×C₄	—	172	2	no	—
168	C₂×C₄	—	172	2	no	—
169	C₂×C₄	—	172	2	no	—
170	C₂×C₄	—	172	2	no	—
171	C₂×C₄	—	172	2	no	—
172	C₂×C₄	#13063290	1	2	yes	—
173	C₂×C₄	#13063305	1	2	yes	—
174	C₂×C₄	#13063312	1	1	yes	characteristic
175	C₂×C₄	#13063323	1	1	yes	characteristic
176	C₂×C₄	M₁₆×D₄₃	1	2	yes	—
177	C₂×C₄	#13063331	1	2	yes	—
178	C₂×C₄	#13063345	1	4	yes	—
179	C₈	—	8	2	no	—
180	C₈	—	172	4	no	—
181	C₂²	#14582804	1	1	yes	characteristic
182	C₂²	#14582862	1	1	yes	characteristic
183	C₂²	#14582865	1	1	yes	characteristic
184	C₂²	#14582893	1	2	yes	—
185	C₂²	#14582915	1	2	yes	—
186	C₄	—	2	2	no	—
187	C₄	—	4	2	no	—
188	C₄	—	4	2	no	—
189	C₄	—	344	2	no	—
190	C₄	—	172	4	no	—
191	C₄	#14583028	1	4	yes	—
192	C₄	#14583253	1	2	yes	—
193	C₄	#14583298	1	2	yes	—
194	C₂	#19133001	1	2	yes	—
195	C₂	#19133027	1	2	yes	—
196	C₂	#19135534	1	1	yes	characteristic
197	C₂	#19135559	1	1	yes	characteristic
198	C₂	#19135575	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₄×#13063317

C₂

yes

maximal, characteristic

#19134341

C₂

yes

maximal, characteristic

#19132434

C₂

yes

maximal

C₄₃×#1831

C₂

yes

maximal, characteristic

C₂×#13063317

C₄

yes

characteristic

C₂×C₄×C₄₃⋊C₈

C₂²

yes

—

#14582797

C₄

yes

—

#14582783

—

#14582765

C₄

yes

characteristic

C₄×Dic₄₃⋊C₄

—

C₄×C₄⋊Dic₄₃

C₂²

yes

—

#14582654

—

C₂×C₄⋊C₈×C₄₃

C₂²

yes

—

C₄³×C₄₃

C₂²

yes

characteristic

C₄₃×#336

—

C₂²×C₄₃⋊C₈

—

#13063317

—

C₂×C₄⋊Dic₄₃

C₂×C₄

yes

—

C₂×C₄⋊Dic₄₃

C₂×C₄

yes

—

C₂×Dic₄₃⋊C₄

—

C₂×Dic₄₃⋊C₄

—

C₂×C₄×Dic₄₃

—

C₄×C₄₃⋊C₈

—

C₄×C₄₃⋊C₈

Q₈

yes

—

C₄₃⋊#95

—

C₄₃⋊#95

—

C₄₃⋊#95

—

C₂²×C₈×C₄₃

—

C₂×C₄²×C₄₃

C₂×C₄

yes

characteristic

C₂×C₄²×C₄₃

C₂×C₄

yes

characteristic

C₂×C₄²×C₄₃

D₄

yes

—

C₂×C₄²×C₄₃

D₄

yes

—

C₂×C₄²×C₄₃

C₂³

yes

characteristic

C₄⋊C₈×C₄₃

—

C₂²×C₄×C₄₃

C₂²⋊C₄

yes

—

C₂²×C₄×C₄₃

C₂²⋊C₄

yes

—

C₂²×C₄×C₄₃

C₂²×C₄

yes

characteristic

C₂²×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂²×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂²×Dic₄₃

—

C₂²×Dic₄₃

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

—

C₄²×C₄₃

—

C₄²×C₄₃

—

C₄²×C₄₃

—

C₄²×C₄₃

—

C₄²×C₄₃

C₂×Q₈

yes

—

C₄²×C₄₃

#41

yes

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

M₁₆

yes

—

Dic₄₃⋊C₄

—

Dic₄₃⋊C₄

—

C₄×Dic₄₃

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂³×C₄₃

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₄×Q₈

yes

—

C₂×C₄×C₄₃

C₂²⋊Q₈

yes

—

C₂×C₄×C₄₃

#124

yes

characteristic

C₂×C₄×C₄₃

C₄⋊Q₈

yes

characteristic

C₂×C₄×C₄₃

C₂×M₁₆

yes

—

C₂×C₄×C₄₃

#131

yes

—

C₂×C₄×C₄₃

#135

yes

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₈×C₄₃

—

C₄₃⋊C₈

—

—

C₂²×C₄₃

yes

C₂²×C₄₃

yes

C₂²×C₄₃

yes

C₂²×C₄₃

yes

—

C₂²×C₄₃

#421

yes

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

#446

yes

—

C₄×C₄₃

#488

yes

—

C₄×C₄₃

#499

yes

—

Dic₄₃

—

Dic₄₃

—

C₄×#125

—

#1831

D₄₃

yes

characteristic

#1744

—

#1279

—

C₂×C₄₃

#1482

yes

—

100

C₂×C₄₃

#1488

yes

—

101

C₂×C₄₃

#1985

yes

characteristic

102

C₂×C₄₃

#1991

yes

characteristic

103

C₂×C₄₃

#1995

yes

characteristic

104

C₂×#125

—

105

C₂×C₄⋊C₈

C₂×D₄₃

yes

—

106

C₂×C₄×C₈

—

107

#389

—

108

#387

—

109

#382

—

110

C₄×C₄⋊C₄

—

111

C₄×C₄⋊C₄

—

112

C₄³

C₂×D₄₃

yes

characteristic

113

#336

—

114

#336

—

115

C₄₃

#9875

yes

characteristic, complemented, Sylow

116

C₂²×C₈

—

117

C₂²×C₈

—

118

#125

—

119

C₂×C₄⋊C₄

—

120

C₂×C₄⋊C₄

—

121

C₂×C₄⋊C₄

—

122

C₂×C₄⋊C₄

—

123

C₂×C₄²

—

124

C₂×C₄²

C₄×D₄₃

yes

characteristic

125

C₂×C₄²

C₄×D₄₃

yes

characteristic

126

C₂×C₄²

D₁₇₂

yes

—

127

C₂×C₄²

C₂²⋊D₄₃

yes

—

128

C₂×C₄²

C₂²×D₄₃

yes

characteristic

129

C₄⋊C₈

—

130

C₄×C₈

—

131

C₄×C₈

—

132

#95

—

133

#95

—

134

#95

—

135

C₂²×C₄

—

136

C₂²×C₄

—

137

C₂²×C₄

(C₂×D₄₃)⋊C₄

yes

—

138

C₂²×C₄

(C₂×D₄₃)⋊C₄

yes

—

139

C₂²×C₄

C₂×C₄×D₄₃

yes

characteristic

140

C₂²×C₄

C₂×D₁₇₂

yes

characteristic

141

C₂²×C₄

C₂×C₂²⋊D₄₃

yes

characteristic

142

C₂×C₈

—

143

C₂×C₈

—

144

C₂×C₈

—

145

C₂×C₈

—

172

—

146

C₄⋊C₄

—

147

C₄⋊C₄

—

148

C₄⋊C₄

—

149

C₄⋊C₄

—

150

C₄⋊C₄

—

172

—

151

C₄²

—

152

C₄²

—

153

C₄²

—

154

C₄²

—

155

C₄²

—

172

—

156

C₄²

#10621900

yes

—

157

C₄²

Q₈×D₄₃

yes

—

158

C₂³

C₂×(C₂×D₄₃)⋊C₄

yes

characteristic

159

C₂×C₄

—

160

C₂×C₄

—

161

C₂×C₄

—

162

C₂×C₄

—

163

C₂×C₄

—

164

C₂×C₄

—

165

C₂×C₄

—

166

C₂×C₄

—

167

C₂×C₄

—

172

—

168

C₂×C₄

—

172

—

169

C₂×C₄

—

172

—

170

C₂×C₄

—

172

—

171

C₂×C₄

—

172

—

172

C₂×C₄

#13063290

yes

—

173

C₂×C₄

#13063305

yes

—

174

C₂×C₄

#13063312

yes

characteristic

175

C₂×C₄

#13063323

yes

characteristic

176

C₂×C₄

M₁₆×D₄₃

yes

—

177

C₂×C₄

#13063331

yes

—

178

C₂×C₄

#13063345

yes

—

179

C₈

—

180

C₈

—

172

—

181

C₂²

#14582804

yes

characteristic

182

C₂²

#14582862

yes

characteristic

183

C₂²

#14582865

yes

characteristic

184

C₂²

#14582893

yes

—

185

C₂²

#14582915

yes

—

186

C₄

—

187

C₄

—

188

C₄

—

189

C₄

—

344

—

190

C₄

—

172

—

191

C₄

#14583028

yes

—

192

C₄

#14583253

yes

—

193

C₄

#14583298

yes

—

194

C₂

#19133001

yes

—

195

C₂

#19133027

yes

—

196

C₂

#19135534

yes

characteristic

197

C₂

#19135559

yes

characteristic

198

C₂

#19135575

yes

characteristic

	subgroup	G/H
center	C₂²×C₄	C₂×C₂²⋊D₄₃
commutator	C₂²×C₄×C₄₃	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₄₃
Fitting	C₄₃×#1831	C₂
socle, prime radical	C₂³×C₄₃	C₂×C₂²⋊C₄
cosocle	C₂×C₄²×C₄₃	C₂³
hypercenter	#1831	D₄₃
hypocenter	C₄₃	#9875
LCS	G ▷ C₂²×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₄³ ◁ #1831

subgroup

G/H

center

C₂²×C₄

C₂×C₂²⋊D₄₃

commutator

C₂²×C₄×C₄₃

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₄₃

Fitting

C₄₃×#1831

C₂

socle, prime radical

C₂³×C₄₃

C₂×C₂²⋊C₄

cosocle

C₂×C₄²×C₄₃

C₂³

D₄₃

C₄₃

G ▷ C₂²×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂²×C₄ ◁ C₄³ ◁ #1831

N	H ≅ G/N	type
115. C₄₃	#9875	semidirect

H ≅ G/N

type

115. C₄₃

#9875

semidirect

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

subgroup	index
C₄×#13063317	2
#19134341	2
#19132434	2
C₄₃×#1831	2
#9875	43

subgroup

index

C₄₃×#1831

Subgroups — #24996623

Conjugacy classes of subgroups

Complements

Maximal subgroups