Group #25105462 — subgroups

Subgroups — #25105462

Order 11008.

662 conjugacy classes of subgroups; only the 255 normal subgroups are shown.

normal subgroups only

This group has 662 conjugacy classes of subgroups — too many to draw. Only its 255 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	#19145119	C₂	1	1	yes	maximal, characteristic
2	#19143525	C₂	1	2	yes	maximal
3	#19135575	C₂	1	2	yes	maximal
4	#19135346	C₂	1	4	yes	maximal
5	#19134477	C₂	1	4	yes	maximal
6	#19134283	C₂	1	1	yes	maximal, characteristic
7	C₄₃×#1849	C₂	1	1	yes	maximal, characteristic
8	#14583456	C₂²	1	2	yes	—
9	#14583308	C₄	1	8	yes	complemented
10	#14583026	—	2	4	no	—
11	#14583023	—	2	4	no	—
12	#14582937	C₂²	1	4	yes	—
13	#14582927	C₂²	1	4	yes	—
14	#14582857	C₂²	1	4	yes	—
15	C₂×#13063235	C₂²	1	2	yes	—
16	C₂×C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
17	C₂×C₈×Dic₄₃	C₂²	1	2	yes	—
18	#14582745	C₂²	1	1	yes	characteristic
19	#14582660	C₂²	1	8	yes	—
20	C₂×#108×C₄₃	C₂²	1	4	yes	—
21	C₄₃×#423	C₂²	1	2	yes	—
22	C₂×#97×C₄₃	C₂²	1	1	yes	characteristic
23	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
24	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
25	#13063325	C₂×C₄	1	4	yes	—
26	#13063317	C₂×C₄	1	4	yes	—
27	#13063304	—	2	4	no	—
28	C₄×Dic₈₆	—	2	4	no	—
29	#13063284	C₂³	1	4	yes	—
30	C₂×C₄×Dic₄₃	C₂³	1	2	yes	—
31	#13063259	C₂×C₄	1	8	yes	—
32	#13063257	C₂×C₄	1	8	yes	—
33	Dic₄₃⋊C₈	—	2	8	no	—
34	#13063235	—	2	4	no	—
35	#13063235	—	2	4	no	—
36	C₄×C₄₃⋊C₈	D₄	1	2	yes	—
37	C₄×C₄₃⋊C₈	D₄	1	2	yes	—
38	C₈×Dic₄₃	—	2	4	no	—
39	C₈×Dic₄₃	Q₈	1	8	yes	complemented
40	C₄₃⋊#95	—	2	2	no	—
41	C₂×M₁₆×C₄₃	C₂³	1	4	yes	—
42	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
43	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
44	#108×C₄₃	—	2	8	no	—
45	C₄⋊C₈×C₄₃	—	2	4	no	—
46	#97×C₄₃	C₂×C₄	1	4	yes	—
47	C₂²×C₄×C₄₃	#41	1	2	yes	—
48	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
49	C₂²×Dic₄₃	—	2	2	no	—
50	C₂×Dic₈₆	—	2	4	no	—
51	M₁₆×C₄₃	—	2	8	no	—
52	C₂×C₈×C₄₃	—	2	4	no	—
53	C₂×C₈×C₄₃	C₂²×C₄	1	4	yes	—
54	C₂×C₈×C₄₃	C₂×Q₈	1	4	yes	—
55	C₂×C₈×C₄₃	#41	1	4	yes	—
56	C₄²×C₄₃	C₂²×C₄	1	2	yes	—
57	C₄²×C₄₃	C₂×D₄	1	2	yes	—
58	C₂²⋊Dic₄₃	—	2	4	no	—
59	C₄⋊Dic₄₃	—	2	4	no	—
60	C₄⋊Dic₄₃	C₂²×C₄	1	8	yes	—
61	Dic₄₃⋊C₄	—	2	8	no	—
62	C₄×Dic₄₃	—	2	4	no	—
63	C₄×Dic₄₃	—	2	2	no	—
64	C₄×Dic₄₃	C₂×Q₈	1	4	yes	—
65	C₂×C₄₃⋊C₈	—	2	2	no	—
66	C₂×C₄₃⋊C₈	C₂×D₄	1	2	yes	—
67	C₂×C₄₃⋊C₈	C₂×D₄	1	1	yes	characteristic
68	C₂×C₄₃⋊C₈	C₂×D₄	1	1	yes	characteristic
69	C₂×C₄₃⋊C₈	C₂×Q₈	1	4	yes	—
70	C₂³×C₄₃	C₂×#41	1	1	yes	characteristic
71	C₂×C₄×C₄₃	—	4	2	no	—
72	C₂×C₄×C₄₃	C₄×D₄	1	4	yes	—
73	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
74	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
75	C₂×C₄×C₄₃	C₂²×Q₈	1	2	yes	—
76	C₂×C₄×C₄₃	C₂×#41	1	2	yes	—
77	C₂×Dic₄₃	—	2	8	no	—
78	C₂×Dic₄₃	—	2	4	no	—
79	C₂×Dic₄₃	—	4	4	no	—
80	Dic₈₆	—	4	8	no	—
81	C₈×C₄₃	—	4	4	no	—
82	C₈×C₄₃	C₄×Q₈	1	8	yes	—
83	C₄₃⋊C₈	—	2	2	no	—
84	C₄₃⋊C₈	C₄⋊Q₈	1	2	yes	—
85	C₄₃⋊C₈	C₄⋊Q₈	1	2	yes	—
86	#21735	—	43	1	no	maximal, Sylow
87	C₂²×C₄₃	—	2	2	no	—
88	C₂²×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
89	C₂²×C₄₃	#533	1	2	yes	—
90	C₄×C₄₃	—	2	4	no	—
91	C₄×C₄₃	C₂×C₄×Q₈	1	2	yes	—
92	C₄×C₄₃	C₂×C₄⋊Q₈	1	1	yes	characteristic
93	C₄×C₄₃	#532	1	1	yes	characteristic
94	Dic₄₃	—	4	4	no	—
95	Dic₄₃	—	4	8	no	—
96	#3162	—	43	1	no	—
97	#2960	—	43	2	no	—
98	#1995	—	43	2	no	—
99	#1946	—	43	4	no	—
100	#1849	D₄₃	1	1	yes	characteristic
101	#1772	—	43	4	no	—
102	#1726	—	43	1	no	—
103	C₂×C₄₃	—	2	2	no	—
104	C₂×C₄₃	C₄×C₄⋊Q₈	1	1	yes	characteristic
105	C₂×C₄₃	#2955	1	2	yes	—
106	#533	—	43	2	no	—
107	#501	—	43	8	no	—
108	#446	—	86	4	no	—
109	C₈×Q₈	—	86	4	no	—
110	C₂×#108	C₂×D₄₃	1	4	yes	—
111	#427	—	43	4	no	—
112	#424	—	43	4	no	—
113	#423	C₂×D₄₃	1	2	yes	—
114	#405	—	43	4	no	—
115	C₂×#97	—	43	2	no	—
116	C₂×#97	C₂×D₄₃	1	1	yes	characteristic
117	C₂×C₄×C₈	—	43	2	no	—
118	C₂×C₄×C₈	—	43	1	no	—
119	#376	—	43	1	no	—
120	#339	—	43	8	no	—
121	C₄₃	#21735	1	1	yes	characteristic, complemented, Sylow
122	C₂×M₁₆	C₂²×D₄₃	1	4	yes	—
123	C₂²×C₈	—	43	1	no	—
124	C₂²×C₈	—	43	1	no	—
125	C₂²×C₈	C₂²×D₄₃	1	2	yes	—
126	C₄⋊Q₈	—	43	4	no	—
127	#125	—	43	4	no	—
128	C₂²⋊Q₈	—	86	4	no	—
129	C₄×Q₈	—	86	4	no	—
130	#117	—	43	4	no	—
131	C₂×C₄²	—	43	2	no	—
132	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
133	#108	—	2	8	no	—
134	#107	—	43	8	no	—
135	#106	—	43	8	no	—
136	C₄⋊C₈	—	2	4	no	—
137	C₄⋊C₈	—	86	8	no	—
138	#97	—	86	4	no	—
139	#97	—	86	4	no	—
140	#97	C₄×D₄₃	1	4	yes	—
141	C₄×C₈	—	43	8	no	—
142	C₄×C₈	—	43	2	no	—
143	C₄×C₈	—	43	2	no	—
144	C₄×C₈	—	86	4	no	—
145	#95	—	86	2	no	—
146	C₂×Q₈	—	86	4	no	—
147	C₂²×C₄	—	86	2	no	—
148	C₂²×C₄	#10621902	1	2	yes	—
149	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
150	M₁₆	—	2	8	no	—
151	C₂×C₈	—	2	4	no	—
152	C₂×C₈	—	43	1	no	—
153	C₂×C₈	—	43	1	no	—
154	C₂×C₈	—	43	4	no	—
155	C₂×C₈	—	43	2	no	—
156	C₂×C₈	—	86	2	no	—
157	C₂×C₈	C₂×C₄×D₄₃	1	4	yes	—
158	C₂×C₈	#10621900	1	4	yes	—
159	C₂×C₈	Q₈×D₄₃	1	4	yes	—
160	C₄⋊C₄	—	43	8	no	—
161	C₄⋊C₄	—	86	8	no	—
162	C₄⋊C₄	—	86	4	no	—
163	C₂²⋊C₄	—	86	4	no	—
164	C₄²	—	43	4	no	—
165	C₄²	—	86	4	no	—
166	C₄²	—	86	2	no	—
167	C₄²	C₂×C₄×D₄₃	1	2	yes	—
168	C₄²	D₄×D₄₃	1	2	yes	—
169	C₂³	C₂×#10621902	1	1	yes	characteristic
170	Q₈	—	172	8	no	—
171	C₂×C₄	—	4	2	no	—
172	C₂×C₄	—	86	8	no	—
173	C₂×C₄	—	86	4	no	—
174	C₂×C₄	—	172	4	no	—
175	C₂×C₄	#13063287	1	4	yes	—
176	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
177	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
178	C₂×C₄	C₂×Q₈×D₄₃	1	2	yes	—
179	C₂×C₄	C₂×#10621900	1	2	yes	—
180	C₈	—	4	4	no	—
181	C₈	—	43	2	no	—
182	C₈	—	43	2	no	—
183	C₈	—	86	2	no	—
184	C₈	#13063290	1	8	yes	—
185	C₂²	—	2	2	no	—
186	C₂²	C₂×#13063287	1	1	yes	characteristic
187	C₂²	#14583454	1	2	yes	—
188	C₄	—	2	4	no	—
189	C₄	—	172	4	no	—
190	C₄	—	172	8	no	—
191	C₄	C₂×#13063290	1	2	yes	—
192	C₄	C₄⋊Q₈×D₄₃	1	1	yes	characteristic
193	C₄	#14583447	1	1	yes	characteristic
194	C₂	—	2	2	no	—
195	C₂	#19137162	1	1	yes	characteristic
196	C₂	#19143497	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#19145119

C₂

yes

maximal, characteristic

#19143525

C₂

yes

maximal

#19135575

C₂

yes

maximal

#19135346

C₂

yes

maximal

#19134477

C₂

yes

maximal

#19134283

C₂

yes

maximal, characteristic

C₄₃×#1849

C₂

yes

maximal, characteristic

#14583456

C₂²

yes

—

#14583308

C₄

yes

—

—

C₂²

yes

—

#14582927

C₂²

yes

—

#14582857

C₂²

yes

—

C₂×#13063235

C₂²

yes

—

C₂×C₄×C₄₃⋊C₈

C₂²

yes

characteristic

C₂×C₈×Dic₄₃

C₂²

yes

—

#14582745

C₂²

yes

characteristic

#14582660

C₂²

yes

—

C₂×#108×C₄₃

C₂²

yes

—

C₄₃×#423

C₂²

yes

—

C₂×#97×C₄₃

C₂²

yes

characteristic

C₂²×C₄₃⋊C₈

C₂³

yes

characteristic

C₂²×C₄₃⋊C₈

C₂³

yes

characteristic

#13063325

C₂×C₄

yes

—

#13063317

C₂×C₄

yes

—

#13063304

—

C₄×Dic₈₆

—

#13063284

C₂³

yes

—

C₂×C₄×Dic₄₃

C₂³

yes

—

#13063259

C₂×C₄

yes

—

#13063257

C₂×C₄

yes

—

Dic₄₃⋊C₈

—

#13063235

—

#13063235

—

C₄×C₄₃⋊C₈

D₄

yes

—

C₄×C₄₃⋊C₈

D₄

yes

—

C₈×Dic₄₃

—

C₈×Dic₄₃

Q₈

yes

complemented

C₄₃⋊#95

—

C₂×M₁₆×C₄₃

C₂³

yes

—

C₂²×C₈×C₄₃

C₂³

yes

—

C₂×C₄²×C₄₃

C₂³

yes

characteristic

#108×C₄₃

—

C₄⋊C₈×C₄₃

—

#97×C₄₃

C₂×C₄

yes

—

C₂²×C₄×C₄₃

#41

yes

—

C₂²×C₄×C₄₃

C₂⁴

yes

characteristic

C₂²×Dic₄₃

—

C₂×Dic₈₆

—

M₁₆×C₄₃

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

C₂²×C₄

yes

—

C₂×C₈×C₄₃

C₂×Q₈

yes

—

C₂×C₈×C₄₃

#41

yes

—

C₄²×C₄₃

C₂²×C₄

yes

—

C₄²×C₄₃

C₂×D₄

yes

—

C₂²⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

C₂²×C₄

yes

—

Dic₄₃⋊C₄

—

C₄×Dic₄₃

—

C₄×Dic₄₃

—

C₄×Dic₄₃

C₂×Q₈

yes

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

C₂×D₄

yes

—

C₂×C₄₃⋊C₈

C₂×D₄

yes

characteristic

C₂×C₄₃⋊C₈

C₂×D₄

yes

characteristic

C₂×C₄₃⋊C₈

C₂×Q₈

yes

—

C₂³×C₄₃

C₂×#41

yes

characteristic

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₄×D₄

yes

—

C₂×C₄×C₄₃

C₂³×C₄

yes

characteristic

C₂×C₄×C₄₃

C₂²×D₄

yes

characteristic

C₂×C₄×C₄₃

C₂²×Q₈

yes

—

C₂×C₄×C₄₃

C₂×#41

yes

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

Dic₈₆

—

C₈×C₄₃

—

C₈×C₄₃

C₄×Q₈

yes

—

C₄₃⋊C₈

—

C₄₃⋊C₈

C₄⋊Q₈

yes

—

C₄₃⋊C₈

C₄⋊Q₈

yes

—

#21735

—

maximal, Sylow

C₂²×C₄₃

—

C₂²×C₄₃

C₂×C₄×D₄

yes

characteristic

C₂²×C₄₃

#533

yes

—

C₄×C₄₃

—

C₄×C₄₃

C₂×C₄×Q₈

yes

—

C₄×C₄₃

C₂×C₄⋊Q₈

yes

characteristic

C₄×C₄₃

#532

yes

characteristic

Dic₄₃

—

Dic₄₃

—

—

—

—

—

100

#1849

D₄₃

yes

characteristic

101

#1772

—

102

#1726

—

103

C₂×C₄₃

—

104

C₂×C₄₃

C₄×C₄⋊Q₈

yes

characteristic

105

C₂×C₄₃

#2955

yes

—

106

#533

—

107

#501

—

108

#446

—

109

C₈×Q₈

—

110

C₂×#108

C₂×D₄₃

yes

—

111

#427

—

112

#424

—

113

#423

C₂×D₄₃

yes

—

114

#405

—

115

C₂×#97

—

116

C₂×#97

C₂×D₄₃

yes

characteristic

117

C₂×C₄×C₈

—

118

C₂×C₄×C₈

—

119

#376

—

120

#339

—

121

C₄₃

#21735

yes

characteristic, complemented, Sylow

122

C₂×M₁₆

C₂²×D₄₃

yes

—

123

C₂²×C₈

—

124

C₂²×C₈

—

125

C₂²×C₈

C₂²×D₄₃

yes

—

126

C₄⋊Q₈

—

127

#125

—

128

C₂²⋊Q₈

—

129

C₄×Q₈

—

130

#117

—

131

C₂×C₄²

—

132

C₂×C₄²

C₂²×D₄₃

yes

characteristic

133

#108

—

134

#107

—

135

#106

—

136

C₄⋊C₈

—

137

C₄⋊C₈

—

138

#97

—

139

#97

—

140

#97

C₄×D₄₃

yes

—

141

C₄×C₈

—

142

C₄×C₈

—

143

C₄×C₈

—

144

C₄×C₈

—

145

#95

—

146

C₂×Q₈

—

147

C₂²×C₄

—

148

C₂²×C₄

#10621902

yes

—

149

C₂²×C₄

C₂³×D₄₃

yes

characteristic

150

M₁₆

—

151

C₂×C₈

—

152

C₂×C₈

—

153

C₂×C₈

—

154

C₂×C₈

—

155

C₂×C₈

—

156

C₂×C₈

—

157

C₂×C₈

C₂×C₄×D₄₃

yes

—

158

C₂×C₈

#10621900

yes

—

159

C₂×C₈

Q₈×D₄₃

yes

—

160

C₄⋊C₄

—

161

C₄⋊C₄

—

162

C₄⋊C₄

—

163

C₂²⋊C₄

—

164

C₄²

—

165

C₄²

—

166

C₄²

—

167

C₄²

C₂×C₄×D₄₃

yes

—

168

C₄²

D₄×D₄₃

yes

—

169

C₂³

C₂×#10621902

yes

characteristic

170

Q₈

—

172

—

171

C₂×C₄

—

172

C₂×C₄

—

173

C₂×C₄

—

174

C₂×C₄

—

172

—

175

C₂×C₄

#13063287

yes

—

176

C₂×C₄

C₂²×C₄×D₄₃

yes

characteristic

177

C₂×C₄

C₂×D₄×D₄₃

yes

characteristic

178

C₂×C₄

C₂×Q₈×D₄₃

yes

—

179

C₂×C₄

C₂×#10621900

yes

—

180

C₈

—

181

C₈

—

182

C₈

—

183

C₈

—

184

C₈

#13063290

yes

—

185

C₂²

—

186

C₂²

C₂×#13063287

yes

characteristic

187

C₂²

#14583454

yes

—

188

C₄

—

189

C₄

—

172

—

190

C₄

—

172

—

191

C₄

C₂×#13063290

yes

—

192

C₄

C₄⋊Q₈×D₄₃

yes

characteristic

193

C₄

#14583447

yes

characteristic

194

C₂

—

195

C₂

#19137162

yes

characteristic

196

C₂

#19143497

yes

—

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₄₃
commutator	C₂×C₄×C₄₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₃
Fitting	C₄₃×#1849	C₂
socle	C₂²×C₄₃	C₂×C₄×D₄
prime radical	C₂³×C₄₃	C₂×#41
cosocle	C₂²×C₄×C₄₃	C₂⁴
hypercenter	#1849	D₄₃
hypocenter	C₄₃	#21735
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1849

subgroup

G/H

center

C₂×C₄

C₂×D₄×D₄₃

commutator

C₂×C₄×C₄₃

C₂³×C₄

Frattini

C₂²×C₄

C₂³×D₄₃

Fitting

C₄₃×#1849

C₂

socle

C₂²×C₄₃

C₂×C₄×D₄

prime radical

C₂³×C₄₃

C₂×#41

cosocle

C₂²×C₄×C₄₃

C₂⁴

D₄₃

C₄₃

G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1849

N	H ≅ G/N	type
9. #14583308	C₄	semidirect
39. C₈×Dic₄₃	Q₈	semidirect
121. C₄₃	#21735	semidirect

H ≅ G/N

type

9. #14583308

C₄

semidirect

39. C₈×Dic₄₃

Q₈

semidirect

121. C₄₃

#21735

semidirect

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

subgroup	index
#19145119	2
#19143525	2
#19135575	2
#19135346	2
#19134477	2
#19134283	2
C₄₃×#1849	2
#21735	43

subgroup

index

C₄₃×#1849

Subgroups — #25105462

Conjugacy classes of subgroups

Complements

Maximal subgroups