Group #24987289 — subgroups

Subgroups — #24987289

Order 11008.

428 conjugacy classes of subgroups; only the 143 normal subgroups are shown.

normal subgroups only

This group has 428 conjugacy classes of subgroups — too many to draw. Only its 143 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	#19143237	C₂	1	1	yes	maximal, characteristic
2	#19132975	C₂	1	2	yes	maximal
3	C₂×C₈×C₄₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	#19132431	C₂	1	2	yes	maximal, complemented
5	C₄₃×#1452	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄×#10621898	C₂²	1	1	yes	characteristic
7	#14582958	—	2	2	no	—
8	#14582950	—	2	2	no	—
9	#14582925	C₄	1	2	yes	—
10	#14582865	C₄	1	2	yes	—
11	C₄×#10621877	C₂²	1	1	yes	characteristic
12	C₂×C₄×C₄₃⋊C₈	C₂²	1	2	yes	—
13	#14582629	C₄	1	4	yes	—
14	#14582626	C₄	1	4	yes	—
15	C₈×C₄₃⋊C₈	—	2	2	no	—
16	C₄₃×#431	C₂²	1	2	yes	—
17	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
18	C₄₃×#322	—	2	2	no	—
19	C₂×#10621898	C₂×C₄	1	1	yes	characteristic
20	C₂×#10621877	C₂×C₄	1	2	yes	—
21	C₂²×C₄₃⋊C₈	—	2	2	no	—
22	C₄×Dic₈₆	C₂×C₄	1	2	yes	—
23	C₄×D₁₇₂	C₂×C₄	1	2	yes	—
24	C₄×C₂²⋊D₄₃	—	2	2	no	—
25	#13063284	C₂×C₄	1	1	yes	characteristic
26	#13063282	—	2	1	no	—
27	C₄²×D₄₃	—	2	1	no	—
28	Dic₄₃⋊C₈	—	2	4	no	—
29	(C₂×D₄₃)⋊C₈	—	2	4	no	—
30	#13063236	—	2	1	no	—
31	C₄×C₄₃⋊C₈	—	2	2	no	—
32	C₄×C₄₃⋊C₈	—	2	1	no	—
33	C₄×C₄₃⋊C₈	C₂×C₄	1	4	yes	—
34	C₂²×C₈×C₄₃	C₂×C₄	1	2	yes	—
35	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
36	C₄⋊C₈×C₄₃	C₂×C₄	1	4	yes	—
37	C₂²⋊C₈×C₄₃	—	2	2	no	—
38	C₄×C₈×C₄₃	—	2	2	no	—
39	C₄×C₈×C₄₃	D₄	1	2	yes	—
40	C₄×C₈×C₄₃	D₄	1	2	yes	—
41	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
42	C₂²×C₄×C₄₃	#41	1	2	yes	—
43	C₂×C₂²⋊D₄₃	—	2	1	no	—
44	#10621898	—	2	4	no	—
45	C₂×D₁₇₂	C₄²	1	1	yes	characteristic
46	C₂×C₄×D₄₃	—	2	1	no	—
47	C₂×C₄×D₄₃	—	2	2	no	—
48	C₂×Dic₈₆	C₄²	1	1	yes	characteristic
49	C₂×C₈×C₄₃	—	2	4	no	—
50	C₂×C₈×C₄₃	—	2	4	no	—
51	C₂×C₈×C₄₃	C₂²⋊C₄	1	4	yes	—
52	C₄²×C₄₃	C₂²×C₄	1	2	yes	—
53	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
54	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
55	C₂²⋊Dic₄₃	—	2	1	no	—
56	(C₂×D₄₃)⋊C₄	—	2	2	no	—
57	C₄⋊Dic₄₃	C₄²	1	2	yes	—
58	Dic₄₃⋊C₄	—	2	2	no	—
59	C₄×Dic₄₃	—	2	1	no	—
60	C₄×Dic₄₃	—	2	2	no	—
61	#10621877	—	2	4	no	—
62	C₂×C₄₃⋊C₈	—	2	8	no	—
63	C₂×C₄₃⋊C₈	—	2	4	no	—
64	C₂×C₄₃⋊C₈	—	2	2	no	—
65	C₂³×C₄₃	#117	1	1	yes	characteristic
66	C₂²×D₄₃	—	2	1	no	—
67	C₂×C₄×C₄₃	—	2	4	no	—
68	C₂×C₄×C₄₃	C₂×C₄²	1	1	yes	characteristic
69	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
70	C₂×C₄×C₄₃	C₄×D₄	1	2	yes	—
71	C₂×C₄×C₄₃	C₄×D₄	1	2	yes	—
72	C₂×C₄×C₄₃	#131	1	4	yes	—
73	C₂²⋊D₄₃	—	4	2	no	—
74	C₂×Dic₄₃	—	2	1	no	—
75	C₂×Dic₄₃	—	2	2	no	—
76	D₁₇₂	—	2	2	no	—
77	C₄×D₄₃	—	4	2	no	—
78	C₄×D₄₃	—	4	4	no	—
79	Dic₈₆	—	2	2	no	—
80	C₈×C₄₃	—	2	4	no	—
81	C₈×C₄₃	—	4	4	no	—
82	C₄₃⋊C₈	—	2	8	no	—
83	C₄₃⋊C₈	—	4	2	no	—
84	#8187	—	43	1	no	maximal, Sylow
85	C₂²×C₄₃	—	2	2	no	—
86	C₂²×C₄₃	C₄×C₂²⋊C₄	1	1	yes	characteristic
87	C₂²×C₄₃	#433	1	2	yes	—
88	C₂×D₄₃	—	4	1	no	—
89	C₂×D₄₃	—	4	2	no	—
90	C₄×C₄₃	—	2	2	no	—
91	C₄×C₄₃	#405	1	2	yes	—
92	C₄×C₄₃	#408	1	2	yes	—
93	C₄×C₄₃	#443	1	4	yes	—
94	Dic₄₃	—	4	1	no	—
95	Dic₄₃	—	4	2	no	—
96	#2922	—	43	1	no	—
97	#1476	—	43	2	no	—
98	#1452	D₄₃	1	1	yes	characteristic, complemented
99	C₂×C₈²	—	43	1	no	—
100	#1278	—	43	2	no	—
101	C₂×C₄₃	—	2	2	no	—
102	C₂×C₄₃	#1750	1	1	yes	characteristic
103	C₂×C₄₃	#1764	1	2	yes	—
104	D₄₃	—	8	1	no	—
105	C₄×#41	—	43	1	no	—
106	#433	—	86	2	no	—
107	#431	—	86	2	no	—
108	#431	C₂×D₄₃	1	2	yes	—
109	#424	—	43	2	no	—
110	#408	—	43	2	no	—
111	C₄×M₁₆	—	43	1	no	—
112	C₂×C₄×C₈	—	43	2	no	—
113	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
114	Q₈⋊C₈	—	43	4	no	—
115	D₄⋊C₈	—	43	4	no	—
116	#322	—	2	2	no	—
117	C₈²	—	86	2	no	—
118	C₄₃	#8187	1	1	yes	characteristic, complemented, Sylow
119	C₂×#41	—	43	1	no	—
120	C₂×M₁₆	—	43	2	no	—
121	C₂²×C₈	—	86	2	no	—
122	C₂²×C₈	C₄×D₄₃	1	2	yes	—
123	C₄×Q₈	—	43	2	no	—
124	C₄×D₄	—	43	2	no	—
125	C₄×D₄	—	86	2	no	—
126	#117	—	43	1	no	—
127	#117	—	86	1	no	—
128	C₂×C₄²	—	86	1	no	—
129	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
130	C₄⋊C₈	—	86	4	no	—
131	C₄⋊C₈	C₄×D₄₃	1	4	yes	—
132	C₂²⋊C₈	—	2	2	no	—
133	C₂²⋊C₈	—	86	4	no	—
134	#97	—	86	1	no	—
135	C₄×C₈	—	2	2	no	—
136	C₄×C₈	—	43	4	no	—
137	C₄×C₈	—	86	2	no	—
138	C₄×C₈	—	86	1	no	—
139	C₄×C₈	D₁₇₂	1	2	yes	—
140	C₄×C₈	C₂²⋊D₄₃	1	2	yes	—
141	#41	—	86	4	no	—
142	C₂×Q₈	—	43	1	no	—
143	C₂×D₄	—	43	1	no	—
144	C₂×D₄	—	86	1	no	—
145	C₂²×C₄	—	86	1	no	—
146	C₂²×C₄	—	86	2	no	—
147	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
148	C₂²×C₄	#10621898	1	2	yes	—
149	M₁₆	—	86	4	no	—
150	C₂×C₈	—	2	4	no	—
151	C₂×C₈	—	2	4	no	—
152	C₂×C₈	—	86	8	no	—
153	C₂×C₈	—	86	4	no	—
154	C₂×C₈	—	86	2	no	—
155	C₂×C₈	(C₂×D₄₃)⋊C₄	1	4	yes	—
156	C₄⋊C₄	—	43	2	no	—
157	C₄⋊C₄	—	86	2	no	—
158	C₂²⋊C₄	—	86	1	no	—
159	C₂²⋊C₄	—	86	2	no	—
160	C₄²	—	86	1	no	—
161	C₄²	—	86	2	no	—
162	C₄²	C₂×C₄×D₄₃	1	2	yes	—
163	C₄²	C₂×D₁₇₂	1	1	yes	characteristic
164	C₄²	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
165	C₂³	—	86	1	no	—
166	C₂³	#13063282	1	1	yes	characteristic
167	Q₈	—	86	2	no	—
168	D₄	—	86	2	no	—
169	D₄	—	172	2	no	—
170	C₂×C₄	—	2	4	no	—
171	C₂×C₄	—	86	2	no	—
172	C₂×C₄	—	86	1	no	—
173	C₂×C₄	—	172	2	no	—
174	C₂×C₄	—	172	4	no	—
175	C₂×C₄	C₄²×D₄₃	1	1	yes	characteristic
176	C₂×C₄	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
177	C₂×C₄	C₄×C₂²⋊D₄₃	1	2	yes	—
178	C₂×C₄	C₄×D₁₇₂	1	2	yes	—
179	C₂×C₄	#13063333	1	4	yes	—
180	C₈	—	2	4	no	—
181	C₈	—	4	4	no	—
182	C₈	—	86	8	no	—
183	C₈	—	172	2	no	—
184	C₂²	—	2	2	no	—
185	C₂²	—	172	1	no	—
186	C₂²	—	172	2	no	—
187	C₂²	C₄×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
188	C₂²	#14582961	1	2	yes	—
189	C₄	—	2	2	no	—
190	C₄	—	172	1	no	—
191	C₄	—	172	2	no	—
192	C₄	#14582856	1	2	yes	—
193	C₄	#14582867	1	2	yes	—
194	C₄	#14583014	1	4	yes	—
195	C₂	—	2	2	no	—
196	C₂	—	344	1	no	—
197	C₂	#19134364	1	1	yes	characteristic
198	C₂	#19134434	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#19143237

C₂

yes

maximal, characteristic

#19132975

C₂

yes

maximal

C₂×C₈×C₄₃⋊C₈

C₂

yes

maximal, characteristic, complemented

#19132431

C₂

yes

maximal, complemented

C₄₃×#1452

C₂

yes

maximal, characteristic, complemented

C₄×#10621898

C₂²

yes

—

—

C₄

yes

—

#14582865

C₄

yes

—

C₄×#10621877

C₂²

yes

characteristic

C₂×C₄×C₄₃⋊C₈

C₂²

yes

—

#14582629

C₄

yes

—

#14582626

C₄

yes

—

C₈×C₄₃⋊C₈

—

C₄₃×#431

C₂²

yes

—

C₂×C₄×C₈×C₄₃

C₂²

yes

characteristic

C₄₃×#322

—

C₂×#10621898

C₂×C₄

yes

characteristic

C₂×#10621877

C₂×C₄

yes

—

C₂²×C₄₃⋊C₈

—

C₄×Dic₈₆

C₂×C₄

yes

—

C₄×D₁₇₂

C₂×C₄

yes

—

C₄×C₂²⋊D₄₃

—

#13063284

C₂×C₄

yes

characteristic

#13063282

—

C₄²×D₄₃

—

Dic₄₃⋊C₈

—

(C₂×D₄₃)⋊C₈

—

#13063236

—

C₄×C₄₃⋊C₈

—

C₄×C₄₃⋊C₈

—

C₄×C₄₃⋊C₈

C₂×C₄

yes

—

C₂²×C₈×C₄₃

C₂×C₄

yes

—

C₂×C₄²×C₄₃

C₂³

yes

characteristic

C₄⋊C₈×C₄₃

C₂×C₄

yes

—

C₂²⋊C₈×C₄₃

—

C₄×C₈×C₄₃

—

C₄×C₈×C₄₃

D₄

yes

—

C₄×C₈×C₄₃

D₄

yes

—

C₂²×C₄×C₄₃

C₂²×C₄

yes

characteristic

C₂²×C₄×C₄₃

#41

yes

—

C₂×C₂²⋊D₄₃

—

#10621898

—

C₂×D₁₇₂

C₄²

yes

characteristic

C₂×C₄×D₄₃

—

C₂×C₄×D₄₃

—

C₂×Dic₈₆

C₄²

yes

characteristic

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

C₂²⋊C₄

yes

—

C₄²×C₄₃

C₂²×C₄

yes

—

C₄²×C₄₃

C₂×D₄

yes

characteristic

C₄²×C₄₃

C₂×D₄

yes

characteristic

C₂²⋊Dic₄₃

—

(C₂×D₄₃)⋊C₄

—

C₄⋊Dic₄₃

C₄²

yes

—

Dic₄₃⋊C₄

—

C₄×Dic₄₃

—

C₄×Dic₄₃

—

#10621877

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂³×C₄₃

#117

yes

characteristic

C₂²×D₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂×C₄²

yes

characteristic

C₂×C₄×C₄₃

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₄₃

C₄×D₄

yes

—

C₂×C₄×C₄₃

C₄×D₄

yes

—

C₂×C₄×C₄₃

#131

yes

—

C₂²⋊D₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

D₁₇₂

—

C₄×D₄₃

—

C₄×D₄₃

—

Dic₈₆

—

C₈×C₄₃

—

C₈×C₄₃

—

C₄₃⋊C₈

—

C₄₃⋊C₈

—

#8187

—

maximal, Sylow

C₂²×C₄₃

—

C₂²×C₄₃

C₄×C₂²⋊C₄

yes

characteristic

C₂²×C₄₃

#433

yes

—

C₂×D₄₃

—

C₂×D₄₃

—

C₄×C₄₃

—

C₄×C₄₃

#405

yes

—

C₄×C₄₃

#408

yes

—

C₄×C₄₃

#443

yes

—

Dic₄₃

—

Dic₄₃

—

#2922

—

#1476

—

#1452

D₄₃

yes

characteristic, complemented

C₂×C₈²

—

100

#1278

—

101

C₂×C₄₃

—

102

C₂×C₄₃

#1750

yes

characteristic

103

C₂×C₄₃

#1764

yes

—

104

D₄₃

—

105

C₄×#41

—

106

#433

—

107

#431

—

108

#431

C₂×D₄₃

yes

—

109

#424

—

110

#408

—

111

C₄×M₁₆

—

112

C₂×C₄×C₈

—

113

C₂×C₄×C₈

C₂×D₄₃

yes

characteristic

114

Q₈⋊C₈

—

115

D₄⋊C₈

—

116

#322

—

117

C₈²

—

118

C₄₃

#8187

yes

characteristic, complemented, Sylow

119

C₂×#41

—

120

C₂×M₁₆

—

121

C₂²×C₈

—

122

C₂²×C₈

C₄×D₄₃

yes

—

123

C₄×Q₈

—

124

C₄×D₄

—

125

C₄×D₄

—

126

#117

—

127

#117

—

128

C₂×C₄²

—

129

C₂×C₄²

C₂²×D₄₃

yes

characteristic

130

C₄⋊C₈

—

131

C₄⋊C₈

C₄×D₄₃

yes

—

132

C₂²⋊C₈

—

133

C₂²⋊C₈

—

134

#97

—

135

C₄×C₈

—

136

C₄×C₈

—

137

C₄×C₈

—

138

C₄×C₈

—

139

C₄×C₈

D₁₇₂

yes

—

140

C₄×C₈

C₂²⋊D₄₃

yes

—

141

#41

—

142

C₂×Q₈

—

143

C₂×D₄

—

144

C₂×D₄

—

145

C₂²×C₄

—

146

C₂²×C₄

—

147

C₂²×C₄

C₂×C₄×D₄₃

yes

characteristic

148

C₂²×C₄

#10621898

yes

—

149

M₁₆

—

150

C₂×C₈

—

151

C₂×C₈

—

152

C₂×C₈

—

153

C₂×C₈

—

154

C₂×C₈

—

155

C₂×C₈

(C₂×D₄₃)⋊C₄

yes

—

156

C₄⋊C₄

—

157

C₄⋊C₄

—

158

C₂²⋊C₄

—

159

C₂²⋊C₄

—

160

C₄²

—

161

C₄²

—

162

C₄²

C₂×C₄×D₄₃

yes

—

163

C₄²

C₂×D₁₇₂

yes

characteristic

164

C₄²

C₂×C₂²⋊D₄₃

yes

characteristic

165

C₂³

—

166

C₂³

#13063282

yes

characteristic

167

Q₈

—

168

D₄

—

169

D₄

—

172

—

170

C₂×C₄

—

171

C₂×C₄

—

172

C₂×C₄

—

173

C₂×C₄

—

172

—

174

C₂×C₄

—

172

—

175

C₂×C₄

C₄²×D₄₃

yes

characteristic

176

C₂×C₄

C₂×(C₂×D₄₃)⋊C₄

yes

characteristic

177

C₂×C₄

C₄×C₂²⋊D₄₃

yes

—

178

C₂×C₄

C₄×D₁₇₂

yes

—

179

C₂×C₄

#13063333

yes

—

180

C₈

—

181

C₈

—

182

C₈

—

183

C₈

—

172

—

184

C₂²

—

185

C₂²

—

172

—

186

C₂²

—

172

—

187

C₂²

C₄×(C₂×D₄₃)⋊C₄

yes

characteristic

188

C₂²

#14582961

yes

—

189

C₄

—

190

C₄

—

172

—

191

C₄

—

172

—

192

C₄

#14582856

yes

—

193

C₄

#14582867

yes

—

194

C₄

#14583014

yes

—

195

C₂

—

196

C₂

—

344

—

197

C₂

#19134364

yes

characteristic

198

C₂

#19134434

yes

—

	subgroup	G/H
center	C₄²	C₂×C₂²⋊D₄₃
commutator	C₂×C₄×C₄₃	C₂×C₄²
Frattini	C₂×C₄²	C₂²×D₄₃
Fitting	C₄₃×#1452	C₂
socle	C₂²×C₄₃	C₄×C₂²⋊C₄
prime radical	C₂×#10621898	C₂×C₄
cosocle	C₂×C₄²×C₄₃	C₂³
hypercenter	#1452	D₄₃
hypocenter	C₄₃	#8187
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₄² ◁ C₂×C₄×C₈ ◁ #1452

subgroup

G/H

center

C₄²

C₂×C₂²⋊D₄₃

commutator

C₂×C₄×C₄₃

C₂×C₄²

Frattini

C₂×C₄²

C₂²×D₄₃

Fitting

C₄₃×#1452

C₂

socle

C₂²×C₄₃

C₄×C₂²⋊C₄

prime radical

C₂×#10621898

C₂×C₄

cosocle

C₂×C₄²×C₄₃

C₂³

D₄₃

C₄₃

G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₄² ◁ C₂×C₄×C₈ ◁ #1452

N	H ≅ G/N	type
3. C₂×C₈×C₄₃⋊C₈	C₂	semidirect
4. #19132431	C₂	semidirect
5. C₄₃×#1452	C₂	semidirect
98. #1452	D₄₃	semidirect
118. C₄₃	#8187	semidirect

H ≅ G/N

type

3. C₂×C₈×C₄₃⋊C₈

C₂

semidirect

4. #19132431

C₂

semidirect

5. C₄₃×#1452

C₂

semidirect

98. #1452

D₄₃

semidirect

118. C₄₃

#8187

semidirect

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

subgroup	index
#19143237	2
#19132975	2
C₂×C₈×C₄₃⋊C₈	2
#19132431	2
C₄₃×#1452	2
#8187	43

subgroup

index

C₂×C₈×C₄₃⋊C₈

C₄₃×#1452

Subgroups — #24987289

Conjugacy classes of subgroups

Complements

Maximal subgroups