Group #28306129 — subgroups

Subgroups — #28306129

Order 13568.

510 conjugacy classes of subgroups; only the 132 normal subgroups are shown.

normal subgroups only

This group has 510 conjugacy classes of subgroups — too many to draw. Only its 132 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	#20290896	C₂	1	2	yes	maximal
2	#20290842	C₂	1	2	yes	maximal
3	#20290650	C₂	1	1	yes	maximal, characteristic
4	#20289909	C₂	1	1	yes	maximal, characteristic
5	#500×D₅₃	C₂	1	1	yes	maximal, characteristic
6	C₂×#13133285	—	2	2	no	—
7	C₂×#13133280	—	2	4	no	—
8	C₄×D₅₃⋊C₈	C₂²	1	1	yes	characteristic
9	C₄×D₅₃⋊C₈	C₂²	1	1	yes	characteristic
10	#16811569	C₂²	1	2	yes	—
11	#16811496	—	2	4	no	—
12	#16811464	—	2	2	no	—
13	C₄⋊Q₈×D₅₃	C₂²	1	2	yes	—
14	#16811028	C₄	1	1	yes	characteristic, complemented
15	#16811027	—	2	2	no	—
16	#16811026	C₄	1	2	yes	complemented
17	#107×D₅₃	—	2	2	no	—
18	C₄×C₈×D₅₃	C₂²	1	1	yes	characteristic
19	C₅₃×#500	C₄	1	1	yes	characteristic, complemented
20	C₂×D₅₃⋊C₈	D₄	1	2	yes	—
21	C₂×D₅₃⋊C₈	D₄	1	2	yes	—
22	C₂×C₄⋊#6157	—	2	2	no	—
23	C₂×C₄⋊#6157	—	2	2	no	—
24	C₂×C₄⋊#6157	—	2	2	no	—
25	#13133285	—	4	4	no	—
26	#13133280	—	4	8	no	—
27	C₄×#88324	—	2	1	no	—
28	C₄×#88324	—	2	1	no	—
29	C₄×#88324	—	2	1	no	—
30	C₄×#88324	—	2	1	no	—
31	C₂×Q₈×D₅₃	—	2	2	no	—
32	C₂×C₈×D₅₃	D₄	1	2	yes	—
33	#13133217	C₂×C₄	1	2	yes	—
34	#13133216	—	2	2	no	—
35	#13133216	—	2	2	no	—
36	#13133215	—	2	2	no	—
37	C₄⋊C₄×D₅₃	—	2	2	no	—
38	C₄⋊C₄×D₅₃	—	2	2	no	—
39	C₄²×D₅₃	C₂³	1	1	yes	characteristic
40	#13133151	—	2	2	no	—
41	#13133150	—	2	4	no	—
42	C₄×#88322	C₂×C₄	1	1	yes	characteristic
43	C₈×Dic₅₃	D₄	1	2	yes	—
44	C₄⋊Q₈×C₅₃	C₂×C₄	1	2	yes	—
45	#107×C₅₃	—	2	2	no	—
46	C₄×C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
47	C₂²×#6157	—	4	2	no	—
48	C₂×Q₈×C₅₃	—	2	2	no	—
49	Q₈×D₅₃	—	4	4	no	—
50	Q₈×D₅₃	—	4	4	no	—
51	C₂×C₄×D₅₃	—	4	2	no	—
52	C₂×C₄×D₅₃	C₂×D₄	1	1	yes	characteristic
53	C₂×C₄×D₅₃	C₂×D₄	1	1	yes	characteristic
54	C₂×C₄×D₅₃	C₂×D₄	1	1	yes	characteristic
55	C₂×Dic₁₀₆	—	2	2	no	—
56	C₂×Dic₁₀₆	—	4	2	no	—
57	C₂×#88324	—	2	2	no	—
58	C₂×#88324	—	2	2	no	—
59	C₄⋊#6157	—	4	4	no	—
60	C₄⋊#6157	—	4	4	no	—
61	C₄⋊#6157	—	4	4	no	—
62	D₅₃⋊C₈	—	2	4	no	—
63	D₅₃⋊C₈	—	2	4	no	—
64	C₂×C₈×C₅₃	C₂²⋊C₄	1	2	yes	—
65	C₄⋊C₄×C₅₃	—	2	2	no	—
66	C₄⋊C₄×C₅₃	—	2	2	no	—
67	C₄²×C₅₃	C₂²×C₄	1	1	yes	characteristic
68	C₄⋊Dic₅₃	—	2	2	no	—
69	C₄⋊Dic₅₃	—	2	2	no	—
70	#11719919	—	4	2	no	—
71	#11719919	—	4	2	no	—
72	C₄×Dic₅₃	C₂×D₄	1	1	yes	characteristic
73	C₄×Dic₅₃	#41	1	1	yes	characteristic
74	C₄×Dic₅₃	#41	1	1	yes	characteristic
75	C₂×#88322	C₂²⋊C₄	1	2	yes	—
76	C₈×D₅₃	SD₁₆	1	4	yes	—
77	C₈×D₅₃	Q₁₆	1	4	yes	—
78	C₂²×D₅₃	#127	1	1	yes	characteristic
79	C₂×#6157	—	8	2	no	—
80	C₂×#6157	—	8	2	no	—
81	C₂×#6157	—	8	2	no	—
82	Q₈×C₅₃	—	4	4	no	—
83	C₂×C₄×C₅₃	—	4	2	no	—
84	C₂×C₄×C₅₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
85	C₂×C₄×C₅₃	C₄×D₄	1	1	yes	characteristic
86	C₂×C₄×C₅₃	C₄×D₄	1	1	yes	characteristic
87	C₂×Dic₅₃	—	4	2	no	—
88	C₂×Dic₅₃	#121	1	1	yes	characteristic
89	C₂×Dic₅₃	#121	1	1	yes	characteristic
90	C₂×Dic₅₃	#124	1	1	yes	characteristic
91	C₄×D₅₃	—	8	2	no	—
92	C₄×D₅₃	—	8	2	no	—
93	C₄×D₅₃	C₂×SD₁₆	1	2	yes	—
94	C₄×D₅₃	C₂×Q₁₆	1	2	yes	—
95	C₄×D₅₃	AGL(1,ℤ/8)	1	4	yes	—
96	C₄×D₅₃	#137	1	4	yes	—
97	Dic₁₀₆	—	4	4	no	—
98	Dic₁₀₆	—	8	4	no	—
99	#88324	—	4	2	no	—
100	#88324	—	4	2	no	—
101	C₈×C₅₃	#103	1	4	yes	complemented
102	#88322	#103	1	4	yes	complemented
103	#9836	—	53	1	no	maximal, Sylow
104	C₂²×C₅₃	#390	1	1	yes	characteristic
105	C₂×D₅₃	#492	1	1	yes	characteristic
106	C₂×D₅₃	#494	1	1	yes	characteristic
107	C₂×D₅₃	#496	1	2	yes	—
108	C₂×D₅₃	#497	1	2	yes	—
109	#6157	—	16	2	no	—
110	C₄×C₅₃	—	8	2	no	—
111	C₄×C₅₃	C₂×#103	1	2	yes	—
112	C₄×C₅₃	#441	1	2	yes	—
113	C₄×C₅₃	#442	1	2	yes	—
114	Dic₅₃	—	8	2	no	—
115	Dic₅₃	#469	1	2	yes	—
116	Dic₅₃	#470	1	2	yes	—
117	Dic₅₃	#487	1	2	yes	—
118	C₂×#500	—	53	1	no	—
119	#1990	—	53	2	no	—
120	#1956	—	53	2	no	—
121	#1844	—	53	1	no	—
122	C₂×#322	—	53	1	no	—
123	C₂×C₅₃	#1956	1	1	yes	characteristic
124	C₂×C₅₃	#1971	1	1	yes	characteristic
125	C₂×C₅₃	#1972	1	1	yes	characteristic
126	D₅₃	#1714	1	2	yes	—
127	D₅₃	#1723	1	2	yes	—
128	C₂×C₄⋊Q₈	—	53	2	no	—
129	#500	—	53	2	no	—
130	#500	—	53	1	no	—
131	#500	—	106	2	no	—
132	#500	#6157	1	1	yes	characteristic, complemented
133	C₂×#107	—	106	2	no	—
134	C₂×#106	—	106	2	no	—
135	C₂×#103	—	106	4	no	—
136	C₂×C₄×C₈	—	53	1	no	—
137	C₂×C₄×C₈	—	53	1	no	—
138	C₂×C₄×C₈	—	53	1	no	—
139	#384	—	53	2	no	—
140	#340	—	106	4	no	—
141	#322	—	106	2	no	—
142	C₅₃	#9836	1	1	yes	characteristic, complemented, Sylow
143	C₂²×Q₈	—	106	2	no	—
144	C₂²×C₈	—	53	2	no	—
145	C₂²×C₈	—	53	2	no	—
146	C₂²×C₈	—	53	2	no	—
147	C₄⋊Q₈	—	53	2	no	—
148	C₄⋊Q₈	—	106	2	no	—
149	C₄⋊Q₈	—	106	2	no	—
150	C₄⋊Q₈	—	106	2	no	—
151	C₄⋊Q₈	C₂×#6157	1	2	yes	—
152	C₂×C₄⋊C₄	—	106	2	no	—
153	C₂×C₄⋊C₄	—	106	2	no	—
154	C₂×C₄⋊C₄	—	106	2	no	—
155	C₂×C₄⋊C₄	—	106	2	no	—
156	C₂×C₄⋊C₄	—	106	2	no	—
157	C₂×C₄²	—	53	1	no	—
158	#107	—	2	2	no	—
159	#107	—	106	4	no	—
160	#107	—	106	2	no	—
161	#106	—	212	4	no	—
162	#103	—	212	8	no	—
163	C₄×C₈	—	53	2	no	—
164	C₄×C₈	—	53	1	no	—
165	C₄×C₈	—	106	1	no	—
166	C₄×C₈	—	106	1	no	—
167	C₄×C₈	—	106	1	no	—
168	C₄×C₈	—	106	1	no	—
169	C₄×C₈	C₂×#6157	1	1	yes	characteristic
170	C₂×Q₈	—	2	2	no	—
171	C₂×Q₈	—	106	2	no	—
172	C₂×Q₈	—	212	2	no	—
173	C₂×Q₈	—	212	4	no	—
174	C₂×Q₈	—	212	4	no	—
175	C₂²×C₄	—	53	1	no	—
176	C₂²×C₄	—	53	1	no	—
177	C₂²×C₄	—	53	1	no	—
178	C₂²×C₄	—	212	2	no	—
179	C₂²×C₄	—	212	2	no	—
180	C₂×C₈	—	53	2	no	—
181	C₂×C₈	—	53	4	no	—
182	C₂×C₈	—	53	4	no	—
183	C₂×C₈	—	106	2	no	—
184	C₂×C₈	—	106	2	no	—
185	C₂×C₈	—	106	4	no	—
186	C₂×C₈	—	106	4	no	—
187	C₂×C₈	C₂²⋊#6157	1	2	yes	—
188	C₄⋊C₄	—	2	2	no	—
189	C₄⋊C₄	—	2	2	no	—
190	C₄⋊C₄	—	106	2	no	—
191	C₄⋊C₄	—	106	2	no	—
192	C₄⋊C₄	—	212	2	no	—
193	C₄⋊C₄	—	212	2	no	—
194	C₄⋊C₄	—	212	4	no	—
195	C₄⋊C₄	—	212	4	no	—
196	C₄⋊C₄	—	212	4	no	—
197	C₄²	—	53	1	no	—
198	C₄²	—	53	1	no	—
199	C₄²	—	53	1	no	—
200	C₄²	C₂²×#6157	1	1	yes	characteristic
201	C₂³	—	53	1	no	—
202	Q₈	—	4	4	no	—
203	Q₈	—	424	4	no	—
204	Q₈	—	212	4	no	—
205	C₂×C₄	—	4	2	no	—
206	C₂×C₄	—	53	1	no	—
207	C₂×C₄	—	53	1	no	—
208	C₂×C₄	—	53	1	no	—
209	C₂×C₄	—	53	2	no	—
210	C₂×C₄	—	53	2	no	—
211	C₂×C₄	—	53	4	no	—
212	C₂×C₄	—	53	4	no	—
213	C₂×C₄	—	424	2	no	—
214	C₂×C₄	—	424	2	no	—
215	C₂×C₄	—	424	2	no	—
216	C₂×C₄	—	424	2	no	—
217	C₂×C₄	—	424	2	no	—
218	C₂×C₄	—	212	2	no	—
219	C₂×C₄	C₂×C₂²⋊#6157	1	1	yes	characteristic
220	C₂×C₄	D₄×#6157	1	1	yes	characteristic
221	C₂×C₄	D₄×#6157	1	1	yes	characteristic
222	C₈	—	53	4	no	—
223	C₈	—	212	2	no	—
224	C₈	—	212	2	no	—
225	C₈	#13133280	1	4	yes	complemented
226	C₂²	—	53	1	no	—
227	C₂²	—	53	1	no	—
228	C₂²	—	53	2	no	—
229	C₂²	—	53	2	no	—
230	C₂²	#16811575	1	1	yes	characteristic
231	C₄	—	8	2	no	—
232	C₄	—	53	2	no	—
233	C₄	—	53	2	no	—
234	C₄	—	53	2	no	—
235	C₄	—	848	2	no	—
236	C₄	—	424	2	no	—
237	C₄	C₂×#13133280	1	2	yes	—
238	C₄	#16811663	1	2	yes	—
239	C₄	#16811664	1	2	yes	—
240	C₂	—	53	2	no	—
241	C₂	—	53	2	no	—
242	C₂	#20290842	1	1	yes	characteristic
243	C₂	#20290863	1	1	yes	characteristic
244	C₂	#20290864	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#20290896

C₂

yes

maximal

#20290842

C₂

yes

maximal

#20290650

C₂

yes

maximal, characteristic

#20289909

C₂

yes

maximal, characteristic

#500×D₅₃

C₂

yes

maximal, characteristic

C₂×#13133285

—

C₂×#13133280

—

C₄×D₅₃⋊C₈

C₂²

yes

characteristic

C₄×D₅₃⋊C₈

C₂²

yes

characteristic

#16811569

C₂²

yes

—

#16811496

—

#16811464

—

C₄⋊Q₈×D₅₃

C₂²

yes

—

#16811028

C₄

yes

characteristic, complemented

#16811027

—

#16811026

C₄

yes

complemented

#107×D₅₃

—

C₄×C₈×D₅₃

C₂²

yes

characteristic

C₅₃×#500

C₄

yes

characteristic, complemented

C₂×D₅₃⋊C₈

D₄

yes

—

C₂×D₅₃⋊C₈

D₄

yes

—

C₂×C₄⋊#6157

—

C₂×C₄⋊#6157

—

C₂×C₄⋊#6157

—

—

—

—

—

—

—

C₂×Q₈×D₅₃

—

C₂×C₈×D₅₃

D₄

yes

—

#13133217

C₂×C₄

yes

—

#13133216

—

#13133216

—

#13133215

—

C₄⋊C₄×D₅₃

—

C₄⋊C₄×D₅₃

—

C₄²×D₅₃

C₂³

yes

—

—

C₂×C₄

yes

characteristic

C₈×Dic₅₃

D₄

yes

—

C₄⋊Q₈×C₅₃

C₂×C₄

yes

—

#107×C₅₃

—

C₄×C₈×C₅₃

C₂×C₄

yes

characteristic

C₂²×#6157

—

C₂×Q₈×C₅₃

—

Q₈×D₅₃

—

Q₈×D₅₃

—

C₂×C₄×D₅₃

—

C₂×C₄×D₅₃

C₂×D₄

yes

characteristic

C₂×C₄×D₅₃

C₂×D₄

yes

characteristic

C₂×C₄×D₅₃

C₂×D₄

yes

characteristic

C₂×Dic₁₀₆

—

C₂×Dic₁₀₆

—

—

—

—

—

—

D₅₃⋊C₈

—

D₅₃⋊C₈

—

C₂×C₈×C₅₃

C₂²⋊C₄

yes

—

C₄⋊C₄×C₅₃

—

C₄⋊C₄×C₅₃

—

C₄²×C₅₃

C₂²×C₄

yes

characteristic

C₄⋊Dic₅₃

—

C₄⋊Dic₅₃

—

#11719919

—

#11719919

—

C₄×Dic₅₃

C₂×D₄

yes

C₄×Dic₅₃

yes

C₄×Dic₅₃

yes

C₂²⋊C₄

yes

—

C₈×D₅₃

SD₁₆

yes

—

C₈×D₅₃

Q₁₆

yes

—

C₂²×D₅₃

yes

—

—

—

Q₈×C₅₃

—

C₂×C₄×C₅₃

—

C₂×C₄×C₅₃

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₅₃

C₄×D₄

yes

characteristic

C₂×C₄×C₅₃

C₄×D₄

yes

characteristic

C₂×Dic₅₃

—

C₂×Dic₅₃

yes

C₂×Dic₅₃

yes

C₂×Dic₅₃

yes

C₄×D₅₃

—

C₄×D₅₃

—

C₄×D₅₃

C₂×SD₁₆

yes

—

C₄×D₅₃

C₂×Q₁₆

yes

—

C₄×D₅₃

AGL(1,ℤ/8)

yes

—

C₄×D₅₃

#137

yes

—

Dic₁₀₆

—

Dic₁₀₆

—

#88324

—

100

#88324

—

101

C₈×C₅₃

yes

102

yes

103

—

104

C₂²×C₅₃

#390

yes

characteristic

105

C₂×D₅₃

#492

yes

characteristic

106

C₂×D₅₃

#494

yes

characteristic

107

C₂×D₅₃

#496

yes

—

108

C₂×D₅₃

#497

yes

—

109

#6157

—

110

C₄×C₅₃

—

111

C₄×C₅₃

C₂×#103

yes

—

112

C₄×C₅₃

#441

yes

—

113

C₄×C₅₃

#442

yes

—

114

Dic₅₃

—

115

Dic₅₃

#469

yes

—

116

Dic₅₃

#470

yes

—

117

Dic₅₃

#487

yes

—

118

C₂×#500

—

119

#1990

—

120

#1956

—

121

#1844

—

122

C₂×#322

—

123

C₂×C₅₃

#1956

yes

characteristic

124

C₂×C₅₃

#1971

yes

characteristic

125

C₂×C₅₃

#1972

yes

characteristic

126

D₅₃

#1714

yes

—

127

D₅₃

#1723

yes

—

128

C₂×C₄⋊Q₈

—

129

#500

—

130

#500

—

131

#500

—

106

—

132

#500

#6157

yes

characteristic, complemented

133

C₂×#107

—

106

—

134

C₂×#106

—

106

—

135

C₂×#103

—

106

—

136

C₂×C₄×C₈

—

137

C₂×C₄×C₈

—

138

C₂×C₄×C₈

—

139

#384

—

140

#340

—

106

—

141

#322

—

106

—

142

C₅₃

#9836

yes

characteristic, complemented, Sylow

143

C₂²×Q₈

—

106

—

144

C₂²×C₈

—

145

C₂²×C₈

—

146

C₂²×C₈

—

147

C₄⋊Q₈

—

148

C₄⋊Q₈

—

106

—

149

C₄⋊Q₈

—

106

—

150

C₄⋊Q₈

—

106

—

151

C₄⋊Q₈

C₂×#6157

yes

—

152

C₂×C₄⋊C₄

—

106

—

153

C₂×C₄⋊C₄

—

106

—

154

C₂×C₄⋊C₄

—

106

—

155

C₂×C₄⋊C₄

—

106

—

156

C₂×C₄⋊C₄

—

106

—

157

C₂×C₄²

—

158

#107

—

159

#107

—

106

—

160

#107

—

106

—

161

#106

—

212

—

162

#103

—

212

—

163

C₄×C₈

—

164

C₄×C₈

—

165

C₄×C₈

—

106

—

166

C₄×C₈

—

106

—

167

C₄×C₈

—

106

—

168

C₄×C₈

—

106

—

169

C₄×C₈

C₂×#6157

yes

characteristic

170

C₂×Q₈

—

171

C₂×Q₈

—

106

—

172

C₂×Q₈

—

212

—

173

C₂×Q₈

—

212

—

174

C₂×Q₈

—

212

—

175

C₂²×C₄

—

176

C₂²×C₄

—

177

C₂²×C₄

—

178

C₂²×C₄

—

212

—

179

C₂²×C₄

—

212

—

180

C₂×C₈

—

181

C₂×C₈

—

182

C₂×C₈

—

183

C₂×C₈

—

106

—

184

C₂×C₈

—

106

—

185

C₂×C₈

—

106

—

186

C₂×C₈

—

106

—

187

C₂×C₈

C₂²⋊#6157

yes

—

188

C₄⋊C₄

—

189

C₄⋊C₄

—

190

C₄⋊C₄

—

106

—

191

C₄⋊C₄

—

106

—

192

C₄⋊C₄

—

212

—

193

C₄⋊C₄

—

212

—

194

C₄⋊C₄

—

212

—

195

C₄⋊C₄

—

212

—

196

C₄⋊C₄

—

212

—

197

C₄²

—

198

C₄²

—

199

C₄²

—

200

C₄²

C₂²×#6157

yes

characteristic

201

C₂³

—

202

Q₈

—

203

Q₈

—

424

—

204

Q₈

—

212

—

205

C₂×C₄

—

206

C₂×C₄

—

207

C₂×C₄

—

208

C₂×C₄

—

209

C₂×C₄

—

210

C₂×C₄

—

211

C₂×C₄

—

212

C₂×C₄

—

213

C₂×C₄

—

424

—

214

C₂×C₄

—

424

—

215

C₂×C₄

—

424

—

216

C₂×C₄

—

424

—

217

C₂×C₄

—

424

—

218

C₂×C₄

—

212

—

219

C₂×C₄

C₂×C₂²⋊#6157

yes

characteristic

220

C₂×C₄

D₄×#6157

yes

characteristic

221

C₂×C₄

D₄×#6157

yes

characteristic

222

C₈

—

223

C₈

—

212

—

224

C₈

—

212

—

225

C₈

#13133280

yes

complemented

226

C₂²

—

227

C₂²

—

228

C₂²

—

229

C₂²

—

230

C₂²

#16811575

yes

characteristic

231

C₄

—

232

C₄

—

233

C₄

—

234

C₄

—

235

C₄

—

848

—

236

C₄

—

424

—

237

C₄

C₂×#13133280

yes

—

238

C₄

#16811663

yes

—

239

C₄

#16811664

yes

—

240

C₂

—

241

C₂

—

242

C₂

#20290842

yes

characteristic

243

C₂

#20290863

yes

characteristic

244

C₂

#20290864

yes

characteristic

	subgroup	G/H
center	C₂²	#16811575
commutator	C₄²×C₅₃	C₂²×C₄
Frattini	C₄²	C₂²×#6157
Fitting	C₅₃×#500	C₄
socle	C₂²×C₅₃	#390
prime radical	C₂²×D₅₃	#127
cosocle	C₄²×D₅₃	C₂³
hypercenter	#500	#6157
hypocenter	C₅₃	#9836
LCS	G ▷ C₄²×C₅₃ ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #500

subgroup

G/H

center

C₂²

#16811575

commutator

C₄²×C₅₃

C₂²×C₄

Frattini

C₄²

C₂²×#6157

Fitting

C₅₃×#500

C₄

C₂²×C₅₃

C₂²×D₅₃

C₄²×D₅₃

C₂³

C₅₃

G ▷ C₄²×C₅₃ ▷ C₂²×C₅₃ ▷ C₅₃

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #500

N	H ≅ G/N	type
14. #16811028	C₄	semidirect
16. #16811026	C₄	semidirect
19. C₅₃×#500	C₄	semidirect
101. C₈×C₅₃	#103	semidirect
102. #88322	#103	semidirect
132. #500	#6157	semidirect
142. C₅₃	#9836	semidirect
225. C₈	#13133280	semidirect

H ≅ G/N

type

14. #16811028

C₄

semidirect

16. #16811026

C₄

semidirect

19. C₅₃×#500

C₄

semidirect

101. C₈×C₅₃

#103

semidirect

102. #88322

#103

semidirect

132. #500

#6157

semidirect

142. C₅₃

#9836

semidirect

225. C₈

#13133280

semidirect

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

subgroup	index
#20290896	2
#20290842	2
#20290650	2
#20289909	2
#500×D₅₃	2
#9836	53

subgroup

index

#500×D₅₃

Subgroups — #28306129

Conjugacy classes of subgroups

Complements

Maximal subgroups