Group #25001392 — subgroups

Subgroups — #25001392

Order 11008.

310 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 310 conjugacy classes of subgroups — too many to draw. Only its 93 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	#19135415	C₂	1	1	yes	maximal, characteristic
2	#19134770	C₂	1	1	yes	maximal, characteristic
3	#19133266	C₂	1	2	yes	maximal
4	#19132454	C₂	1	2	yes	maximal
5	C₄₃×#1281	C₂	1	1	yes	maximal, characteristic
6	C₂×#13063325	C₂²	1	1	yes	characteristic
7	C₂×#13063261	—	2	1	no	—
8	C₂×#13063261	—	2	1	no	—
9	#14582923	C₂²	1	2	yes	—
10	C₂×#13063250	—	2	1	no	—
11	C₂×#13063250	—	2	1	no	—
12	#14582765	C₂²	1	1	yes	characteristic
13	#14582644	—	2	4	no	—
14	C₄₃×#431	C₂²	1	2	yes	—
15	C₂×#97×C₄₃	C₂²	1	1	yes	characteristic
16	C₂²×Dic₈₆	—	2	1	no	—
17	C₂×#10621877	—	2	2	no	—
18	#13063325	—	2	2	no	—
19	#13063325	—	2	1	no	—
20	#13063325	D₄	1	2	yes	—
21	C₂×C₄⋊Dic₄₃	—	2	2	no	—
22	C₂×C₄⋊Dic₄₃	—	2	1	no	—
23	#13063261	—	4	2	no	—
24	#13063261	—	4	2	no	—
25	C₄⋊(C₄₃⋊C₈)	—	2	2	no	—
26	C₄⋊(C₄₃⋊C₈)	—	2	2	no	—
27	#13063250	—	4	2	no	—
28	#13063250	—	4	2	no	—
29	C₄₃⋊#95	—	2	2	no	—
30	C₂²×C₈×C₄₃	D₄	1	1	yes	characteristic
31	C₂²×C₈×C₄₃	D₄	1	1	yes	characteristic
32	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
33	C₄⋊C₈×C₄₃	—	2	2	no	—
34	C₂²⋊C₈×C₄₃	—	2	2	no	—
35	#97×C₄₃	—	2	2	no	—
36	C₄×C₈×C₄₃	—	2	2	no	—
37	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
38	C₂²×C₄×C₄₃	#41	1	2	yes	—
39	C₂²×Dic₄₃	—	4	1	no	—
40	C₂²×Dic₄₃	—	4	1	no	—
41	C₂×Dic₈₆	—	2	2	no	—
42	C₂×Dic₈₆	—	4	1	no	—
43	C₂×Dic₈₆	—	4	1	no	—
44	C₂×Dic₈₆	—	4	1	no	—
45	C₂×Dic₈₆	—	4	1	no	—
46	C₂×Dic₈₆	—	4	1	no	—
47	C₂×C₈×C₄₃	—	2	1	no	—
48	C₂×C₈×C₄₃	—	2	1	no	—
49	C₂×C₈×C₄₃	—	2	1	no	—
50	C₂×C₈×C₄₃	—	2	1	no	—
51	C₂×C₈×C₄₃	—	4	2	no	—
52	C₂×C₈×C₄₃	D₈	1	2	yes	—
53	C₂×C₈×C₄₃	SD₁₆	1	2	yes	—
54	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
55	C₄²×C₄₃	#41	1	2	yes	—
56	C₄²×C₄₃	#41	1	1	yes	characteristic
57	C₄⋊Dic₄₃	—	2	4	no	—
58	C₄⋊Dic₄₃	—	4	2	no	—
59	C₄⋊Dic₄₃	—	4	1	no	—
60	C₄⋊Dic₄₃	—	4	1	no	—
61	#10621877	—	4	2	no	—
62	#10621877	—	4	2	no	—
63	C₂×C₄₃⋊C₈	—	4	2	no	—
64	C₂³×C₄₃	#124	1	1	yes	characteristic
65	C₂×C₄×C₄₃	—	4	2	no	—
66	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
67	C₂×C₄×C₄₃	#123	1	2	yes	—
68	C₂×C₄×C₄₃	#123	1	1	yes	characteristic
69	C₂×C₄×C₄₃	#126	1	2	yes	—
70	C₂×C₄×C₄₃	C₂×D₈	1	1	yes	characteristic
71	C₂×C₄×C₄₃	C₂×SD₁₆	1	1	yes	characteristic
72	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	1	yes	characteristic
73	C₂×C₄×C₄₃	#137	1	1	yes	characteristic
74	C₂×Dic₄₃	—	4	2	no	—
75	C₂×Dic₄₃	—	8	1	no	—
76	C₂×Dic₄₃	—	8	1	no	—
77	C₂×Dic₄₃	—	8	2	no	—
78	C₂×Dic₄₃	—	8	1	no	—
79	Dic₈₆	—	4	2	no	—
80	Dic₈₆	—	4	2	no	—
81	Dic₈₆	—	8	1	no	—
82	Dic₈₆	—	8	1	no	—
83	C₈×C₄₃	—	2	2	no	—
84	C₈×C₄₃	—	2	2	no	—
85	C₈×C₄₃	—	8	2	no	—
86	C₄₃⋊C₈	—	8	2	no	—
87	#10632	—	43	1	no	maximal, Sylow
88	C₂²×C₄₃	—	2	2	no	—
89	C₂²×C₄₃	#397	1	1	yes	characteristic
90	C₂²×C₄₃	#486	1	1	yes	characteristic
91	C₂²×C₄₃	#489	1	1	yes	characteristic
92	C₄×C₄₃	—	2	2	no	—
93	C₄×C₄₃	—	2	2	no	—
94	C₄×C₄₃	#459	1	1	yes	characteristic
95	C₄×C₄₃	#461	1	1	yes	characteristic
96	C₄×C₄₃	#480	1	1	yes	characteristic
97	C₄×C₄₃	#481	1	1	yes	characteristic
98	Dic₄₃	—	8	2	no	—
99	Dic₄₃	—	16	1	no	—
100	#1960	—	43	1	no	—
101	#1849	—	43	1	no	—
102	#1546	—	43	2	no	—
103	#1286	—	43	2	no	—
104	#1281	D₄₃	1	1	yes	characteristic
105	C₂×C₄₃	—	2	1	no	—
106	C₂×C₄₃	—	2	1	no	—
107	C₂×C₄₃	#2071	1	1	yes	characteristic
108	C₂×C₄₃	#2082	1	2	yes	—
109	C₂×C₄⋊Q₈	—	43	1	no	—
110	#431	C₂×D₄₃	1	2	yes	—
111	C₂×#108	—	86	1	no	—
112	C₂×#108	—	86	1	no	—
113	#423	—	43	2	no	—
114	C₂×#103	—	86	1	no	—
115	C₂×#103	—	86	1	no	—
116	C₂×#97	C₂×D₄₃	1	1	yes	characteristic
117	#382	—	43	1	no	—
118	#332	—	86	4	no	—
119	C₄₃	#10632	1	1	yes	characteristic, complemented, Sylow
120	C₂²×Q₈	—	86	1	no	—
121	C₂×M₁₆	—	86	2	no	—
122	C₂²×C₈	D₁₇₂	1	1	yes	characteristic
123	C₂²×C₈	D₁₇₂	1	1	yes	characteristic
124	C₄⋊Q₈	—	43	2	no	—
125	C₄⋊Q₈	—	86	2	no	—
126	C₄⋊Q₈	—	86	1	no	—
127	C₂×C₄⋊C₄	—	86	2	no	—
128	C₂×C₄⋊C₄	—	86	1	no	—
129	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
130	#108	—	172	2	no	—
131	#108	—	172	2	no	—
132	C₄⋊C₈	—	2	2	no	—
133	C₄⋊C₈	—	86	2	no	—
134	C₄⋊C₈	—	86	2	no	—
135	#103	—	172	2	no	—
136	#103	—	172	2	no	—
137	C₂²⋊C₈	—	2	2	no	—
138	#97	—	2	2	no	—
139	C₄×C₈	—	2	2	no	—
140	#95	—	86	2	no	—
141	C₂×Q₈	—	86	2	no	—
142	C₂×Q₈	—	172	1	no	—
143	C₂×Q₈	—	172	1	no	—
144	C₂×Q₈	—	172	1	no	—
145	C₂×Q₈	—	172	1	no	—
146	C₂×Q₈	—	172	1	no	—
147	C₂²×C₄	—	172	1	no	—
148	C₂²×C₄	—	172	1	no	—
149	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
150	C₂²×C₄	#10621898	1	2	yes	—
151	M₁₆	—	172	2	no	—
152	M₁₆	—	172	2	no	—
153	C₂×C₈	—	2	1	no	—
154	C₂×C₈	—	2	1	no	—
155	C₂×C₈	—	2	1	no	—
156	C₂×C₈	—	2	1	no	—
157	C₂×C₈	—	4	2	no	—
158	C₂×C₈	—	172	2	no	—
159	C₂×C₈	#10621873	1	2	yes	—
160	C₂×C₈	D₃₄₄	1	2	yes	—
161	C₄⋊C₄	—	86	4	no	—
162	C₄⋊C₄	—	172	1	no	—
163	C₄⋊C₄	—	172	1	no	—
164	C₄⋊C₄	—	172	2	no	—
165	C₄²	D₄×D₄₃	1	1	yes	characteristic
166	C₄²	#10621900	1	2	yes	—
167	C₄²	#10621902	1	1	yes	characteristic
168	C₂³	#13063313	1	1	yes	characteristic
169	Q₈	—	344	1	no	—
170	Q₈	—	344	1	no	—
171	Q₈	—	172	2	no	—
172	Q₈	—	172	2	no	—
173	C₂×C₄	—	4	2	no	—
174	C₂×C₄	—	344	1	no	—
175	C₂×C₄	—	344	1	no	—
176	C₂×C₄	—	344	2	no	—
177	C₂×C₄	—	344	1	no	—
178	C₂×C₄	—	172	2	no	—
179	C₂×C₄	#13063300	1	1	yes	characteristic
180	C₂×C₄	#13063307	1	2	yes	—
181	C₂×C₄	#13063309	1	1	yes	characteristic
182	C₂×C₄	#13063320	1	2	yes	—
183	C₂×C₄	C₂×D₃₄₄	1	1	yes	characteristic
184	C₂×C₄	C₂×#10621873	1	1	yes	characteristic
185	C₂×C₄	#13063353	1	1	yes	characteristic
186	C₂×C₄	#13063358	1	1	yes	characteristic
187	C₈	—	2	2	no	—
188	C₈	—	2	2	no	—
189	C₈	—	8	2	no	—
190	C₈	—	344	2	no	—
191	C₂²	—	2	2	no	—
192	C₂²	#14582826	1	1	yes	characteristic
193	C₂²	#14583246	1	1	yes	characteristic
194	C₂²	#14583259	1	1	yes	characteristic
195	C₄	—	2	2	no	—
196	C₄	—	2	2	no	—
197	C₄	—	344	2	no	—
198	C₄	—	688	1	no	—
199	C₄	#14583095	1	1	yes	characteristic
200	C₄	#14583105	1	1	yes	characteristic
201	C₄	#14583213	1	1	yes	characteristic
202	C₄	#14583218	1	1	yes	characteristic
203	C₂	—	2	1	no	—
204	C₂	—	2	1	no	—
205	C₂	#19136000	1	1	yes	characteristic
206	C₂	#19136061	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#19135415

C₂

yes

maximal, characteristic

#19134770

C₂

yes

maximal, characteristic

#19133266

C₂

yes

maximal

#19132454

C₂

yes

maximal

C₄₃×#1281

C₂

yes

maximal, characteristic

C₂×#13063325

C₂²

yes

—

—

C₂²

yes

—

C₂×#13063250

—

C₂×#13063250

—

#14582765

C₂²

yes

characteristic

#14582644

—

C₄₃×#431

C₂²

yes

—

C₂×#97×C₄₃

C₂²

yes

characteristic

C₂²×Dic₈₆

—

—

—

—

D₄

yes

—

C₂×C₄⋊Dic₄₃

—

C₂×C₄⋊Dic₄₃

—

#13063261

—

#13063261

—

C₄⋊(C₄₃⋊C₈)

—

C₄⋊(C₄₃⋊C₈)

—

#13063250

—

#13063250

—

C₄₃⋊#95

—

C₂²×C₈×C₄₃

D₄

yes

characteristic

C₂²×C₈×C₄₃

D₄

yes

characteristic

C₂×C₄²×C₄₃

C₂³

yes

characteristic

C₄⋊C₈×C₄₃

—

C₂²⋊C₈×C₄₃

—

#97×C₄₃

—

C₄×C₈×C₄₃

—

C₂²×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂²×C₄×C₄₃

#41

yes

—

C₂²×Dic₄₃

—

C₂²×Dic₄₃

—

C₂×Dic₈₆

—

C₂×Dic₈₆

—

C₂×Dic₈₆

—

C₂×Dic₈₆

—

C₂×Dic₈₆

—

C₂×Dic₈₆

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

D₈

yes

—

C₂×C₈×C₄₃

SD₁₆

yes

—

C₄²×C₄₃

C₂×D₄

yes

characteristic

C₄²×C₄₃

#41

yes

—

C₄²×C₄₃

#41

yes

characteristic

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

#10621877

—

#10621877

—

C₂×C₄₃⋊C₈

—

C₂³×C₄₃

#124

yes

characteristic

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

#121

yes

characteristic

C₂×C₄×C₄₃

#123

yes

—

C₂×C₄×C₄₃

#123

yes

characteristic

C₂×C₄×C₄₃

#126

yes

—

C₂×C₄×C₄₃

C₂×D₈

yes

characteristic

C₂×C₄×C₄₃

C₂×SD₁₆

yes

C₂×C₄×C₄₃

yes

C₂×C₄×C₄₃

yes

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

Dic₈₆

—

Dic₈₆

—

Dic₈₆

—

Dic₈₆

—

C₈×C₄₃

—

C₈×C₄₃

—

C₈×C₄₃

—

C₄₃⋊C₈

—

#10632

—

maximal, Sylow

C₂²×C₄₃

—

C₂²×C₄₃

yes

C₂²×C₄₃

yes

C₂²×C₄₃

yes

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

yes

C₄×C₄₃

yes

C₄×C₄₃

yes

C₄×C₄₃

yes

Dic₄₃

—

Dic₄₃

—

100

#1960

—

101

#1849

—

102

#1546

—

103

#1286

—

104

#1281

D₄₃

yes

characteristic

105

C₂×C₄₃

—

106

C₂×C₄₃

—

107

C₂×C₄₃

#2071

yes

characteristic

108

C₂×C₄₃

#2082

yes

—

109

C₂×C₄⋊Q₈

—

110

#431

C₂×D₄₃

yes

—

111

C₂×#108

—

112

C₂×#108

—

113

#423

—

114

C₂×#103

—

115

C₂×#103

—

116

C₂×#97

C₂×D₄₃

yes

characteristic

117

#382

—

118

#332

—

119

C₄₃

#10632

yes

characteristic, complemented, Sylow

120

C₂²×Q₈

—

121

C₂×M₁₆

—

122

C₂²×C₈

D₁₇₂

yes

characteristic

123

C₂²×C₈

D₁₇₂

yes

characteristic

124

C₄⋊Q₈

—

125

C₄⋊Q₈

—

126

C₄⋊Q₈

—

127

C₂×C₄⋊C₄

—

128

C₂×C₄⋊C₄

—

129

C₂×C₄²

C₂²×D₄₃

yes

characteristic

130

#108

—

172

—

131

#108

—

172

—

132

C₄⋊C₈

—

133

C₄⋊C₈

—

134

C₄⋊C₈

—

135

#103

—

172

—

136

#103

—

172

—

137

C₂²⋊C₈

—

138

#97

—

139

C₄×C₈

—

140

#95

—

141

C₂×Q₈

—

142

C₂×Q₈

—

172

—

143

C₂×Q₈

—

172

—

144

C₂×Q₈

—

172

—

145

C₂×Q₈

—

172

—

146

C₂×Q₈

—

172

—

147

C₂²×C₄

—

172

—

148

C₂²×C₄

—

172

—

149

C₂²×C₄

C₂×D₁₇₂

yes

characteristic

150

C₂²×C₄

#10621898

yes

—

151

M₁₆

—

172

—

152

M₁₆

—

172

—

153

C₂×C₈

—

154

C₂×C₈

—

155

C₂×C₈

—

156

C₂×C₈

—

157

C₂×C₈

—

158

C₂×C₈

—

172

—

159

C₂×C₈

#10621873

yes

—

160

C₂×C₈

D₃₄₄

yes

—

161

C₄⋊C₄

—

162

C₄⋊C₄

—

172

—

163

C₄⋊C₄

—

172

—

164

C₄⋊C₄

—

172

—

165

C₄²

D₄×D₄₃

yes

characteristic

166

C₄²

#10621900

yes

—

167

C₄²

#10621902

yes

characteristic

168

C₂³

#13063313

yes

characteristic

169

Q₈

—

344

—

170

Q₈

—

344

—

171

Q₈

—

172

—

172

Q₈

—

172

—

173

C₂×C₄

—

174

C₂×C₄

—

344

—

175

C₂×C₄

—

344

—

176

C₂×C₄

—

344

—

177

C₂×C₄

—

344

—

178

C₂×C₄

—

172

—

179

C₂×C₄

#13063300

yes

characteristic

180

C₂×C₄

#13063307

yes

—

181

C₂×C₄

#13063309

yes

characteristic

182

C₂×C₄

#13063320

yes

—

183

C₂×C₄

C₂×D₃₄₄

yes

characteristic

184

C₂×C₄

C₂×#10621873

yes

characteristic

185

C₂×C₄

#13063353

yes

characteristic

186

C₂×C₄

#13063358

yes

characteristic

187

C₈

—

188

C₈

—

189

C₈

—

190

C₈

—

344

—

191

C₂²

—

192

C₂²

#14582826

yes

characteristic

193

C₂²

#14583246

yes

characteristic

194

C₂²

#14583259

yes

characteristic

195

C₄

—

196

C₄

—

197

C₄

—

344

—

198

C₄

—

688

—

199

C₄

#14583095

yes

characteristic

200

C₄

#14583105

yes

characteristic

201

C₄

#14583213

yes

characteristic

202

C₄

#14583218

yes

characteristic

203

C₂

—

204

C₂

—

205

C₂

#19136000

yes

characteristic

206

C₂

#19136061

yes

—

	subgroup	G/H
center	C₂²	#14582826
commutator, cosocle	C₂×C₄²×C₄₃	C₂³
Frattini	C₂×C₄²	C₂²×D₄₃
Fitting	C₄₃×#1281	C₂
socle	C₂²×C₄₃	#397
prime radical	C₂³×C₄₃	#124
hypercenter	#1281	D₄₃
hypocenter	C₄₃	#10632
LCS	G ▷ C₂×C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1281

subgroup

G/H

center

C₂²

#14582826

commutator, cosocle

C₂×C₄²×C₄₃

C₂³

Frattini

C₂×C₄²

C₂²×D₄₃

Fitting

C₄₃×#1281

C₂

C₂²×C₄₃

C₂³×C₄₃

D₄₃

C₄₃

G ▷ C₂×C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1281

N	H ≅ G/N	type
119. C₄₃	#10632	semidirect

H ≅ G/N

type

119. C₄₃

#10632

semidirect

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

subgroup	index
#19135415	2
#19134770	2
#19133266	2
#19132454	2
C₄₃×#1281	2
#10632	43

subgroup

index

C₄₃×#1281

Subgroups — #25001392

Conjugacy classes of subgroups

Complements

Maximal subgroups