Group #28305590 — subgroups

Subgroups — #28305590

Order 13568.

382 conjugacy classes of subgroups; only the 140 normal subgroups are shown.

normal subgroups only

This group has 382 conjugacy classes of subgroups — too many to draw. Only its 140 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	#20290813	C₂	1	2	yes	maximal
2	C₂×#16811486	C₂	1	1	yes	maximal, characteristic
3	C₂×#16811464	C₂	1	1	yes	maximal, characteristic
4	#20289551	C₂	1	2	yes	maximal
5	#106×Dic₅₃	C₂	1	1	yes	maximal, characteristic
6	C₂×#13133284	—	2	2	no	—
7	C₂×C₄⋊#88324	C₂²	1	2	yes	—
8	C₂×C₄×#88324	C₂²	1	1	yes	characteristic
9	C₂×C₄×#88324	C₂²	1	1	yes	characteristic
10	#16811489	—	2	2	no	—
11	#16811486	—	2	2	no	—
12	#16811464	—	2	2	no	—
13	C₂×#13133149	C₄	1	1	yes	characteristic
14	C₂×C₈×Dic₅₃	C₂²	1	1	yes	characteristic
15	C₄⋊C₄×Dic₅₃	C₂²	1	2	yes	—
16	#16810385	C₄	1	2	yes	—
17	C₂×#106×C₅₃	C₄	1	1	yes	characteristic
18	C₂²×#88324	—	2	1	no	—
19	C₂²×#88324	—	2	2	no	—
20	C₂²×#88324	D₄	1	1	yes	characteristic
21	C₂²×#88324	D₄	1	1	yes	characteristic
22	#13133284	—	4	4	no	—
23	C₄⋊#88324	—	2	2	no	—
24	C₄⋊#88324	—	2	2	no	—
25	C₄×#88324	—	2	1	no	—
26	C₄×#88324	—	2	1	no	—
27	C₄×#88324	—	2	1	no	—
28	C₄×#88324	Q₈	1	2	yes	—
29	C₂²×#88322	C₂×C₄	1	1	yes	characteristic
30	C₂×C₄⋊Dic₅₃	C₂×C₄	1	2	yes	—
31	C₂×C₄×Dic₅₃	—	2	2	no	—
32	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
33	#13133149	C₈	1	4	yes	complemented
34	C₈×Dic₅₃	D₄	1	2	yes	—
35	C₈×Dic₅₃	Q₈	1	2	yes	—
36	#13133124	—	2	2	no	—
37	C₂²×C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
38	C₂×C₄⋊C₄×C₅₃	C₂×C₄	1	2	yes	—
39	#106×C₅₃	—	2	2	no	—
40	C₂²×C₄×C₅₃	—	2	2	no	—
41	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
42	C₂²×Dic₅₃	—	2	2	no	—
43	C₂²×Dic₅₃	C₂×D₄	1	1	yes	characteristic
44	C₂²×Dic₅₃	#41	1	1	yes	characteristic
45	C₂×#88324	—	2	1	no	—
46	C₂×#88324	—	2	1	no	—
47	C₂×#88324	—	2	2	no	—
48	C₂×#88324	—	2	2	no	—
49	C₂×#88324	—	2	2	no	—
50	C₂×#88324	—	4	2	no	—
51	C₂×#88324	—	4	2	no	—
52	C₂×#88324	—	4	2	no	—
53	C₂×#88324	—	4	2	no	—
54	C₂×C₈×C₅₃	C₄⋊C₄	1	2	yes	—
55	C₂×C₈×C₅₃	C₂×C₈	1	2	yes	—
56	C₂×C₈×C₅₃	M₁₆	1	2	yes	—
57	C₄⋊C₄×C₅₃	—	2	2	no	—
58	C₄⋊C₄×C₅₃	—	2	2	no	—
59	C₄⋊Dic₅₃	—	2	2	no	—
60	C₄⋊Dic₅₃	C₂×C₈	1	4	yes	—
61	C₄×Dic₅₃	—	4	2	no	—
62	C₄×Dic₅₃	—	4	2	no	—
63	C₄×Dic₅₃	C₂×D₄	1	1	yes	characteristic
64	C₄×Dic₅₃	C₂×Q₈	1	1	yes	characteristic
65	C₄×Dic₅₃	C₂×Q₈	1	1	yes	characteristic
66	C₄×Dic₅₃	#41	1	1	yes	characteristic
67	C₂×#88322	—	2	1	no	—
68	C₂×#88322	—	2	1	no	—
69	C₂×#88322	C₄⋊C₄	1	2	yes	—
70	C₂³×C₅₃	C₄×D₄	1	1	yes	characteristic
71	C₂×C₄×C₅₃	—	4	2	no	—
72	C₂×C₄×C₅₃	—	4	2	no	—
73	C₂×C₄×C₅₃	—	4	2	no	—
74	C₂×C₄×C₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
75	C₂×C₄×C₅₃	C₄×Q₈	1	1	yes	characteristic
76	C₂×C₄×C₅₃	C₂²×C₈	1	1	yes	characteristic
77	C₂×C₄×C₅₃	C₂×M₁₆	1	1	yes	characteristic
78	C₂×C₄×C₅₃	#131	1	1	yes	characteristic
79	C₂×C₄×C₅₃	#131	1	1	yes	characteristic
80	C₂×Dic₅₃	—	2	2	no	—
81	C₂×Dic₅₃	—	2	4	no	—
82	C₂×Dic₅₃	—	4	2	no	—
83	C₂×Dic₅₃	—	4	2	no	—
84	C₂×Dic₅₃	#121	1	1	yes	characteristic
85	C₂×Dic₅₃	C₂²⋊Q₈	1	1	yes	characteristic
86	C₂×Dic₅₃	#125	1	1	yes	characteristic
87	C₂×Dic₅₃	C₄⋊Q₈	1	1	yes	characteristic
88	C₂×Dic₅₃	AGL(1,ℤ/8)	1	2	yes	—
89	C₂×Dic₅₃	#137	1	2	yes	—
90	#88324	—	4	2	no	—
91	#88324	—	4	1	no	—
92	#88324	—	4	1	no	—
93	#88324	—	8	2	no	—
94	C₈×C₅₃	C₄⋊C₈	1	4	yes	complemented
95	#88322	—	2	2	no	—
96	#9596	—	53	1	no	maximal, Sylow
97	C₂²×C₅₃	#389	1	1	yes	characteristic
98	C₂²×C₅₃	C₈×D₄	1	1	yes	characteristic
99	C₂²×C₅₃	#436	1	1	yes	characteristic
100	C₂²×C₅₃	#440	1	2	yes	—
101	C₂²×C₅₃	#444	1	2	yes	—
102	C₄×C₅₃	—	8	2	no	—
103	C₄×C₅₃	C₂×C₄⋊C₈	1	1	yes	characteristic
104	C₄×C₅₃	#424	1	1	yes	characteristic
105	C₄×C₅₃	C₈×Q₈	1	1	yes	characteristic
106	C₄×C₅₃	#446	1	1	yes	characteristic
107	Dic₅₃	—	2	1	no	—
108	Dic₅₃	—	2	1	no	—
109	Dic₅₃	—	4	4	no	—
110	Dic₅₃	#469	1	1	yes	characteristic
111	Dic₅₃	#470	1	1	yes	characteristic
112	Dic₅₃	#501	1	2	yes	—
113	#1939	—	53	2	no	—
114	C₄×#106	—	53	1	no	—
115	C₂×#335	—	53	1	no	—
116	C₂×#322	—	53	1	no	—
117	#1279	—	53	2	no	—
118	C₂×C₅₃	SD₁₆⋊C₈	1	2	yes	—
119	C₂×C₅₃	#1592	1	2	yes	—
120	C₂×C₅₃	#1939	1	1	yes	characteristic
121	C₂×C₅₃	#1944	1	1	yes	characteristic
122	C₂×C₅₃	#1946	1	1	yes	characteristic
123	C₂×#106	—	53	1	no	—
124	C₂×#106	#6157	1	1	yes	characteristic
125	C₂×C₄⋊C₈	—	53	2	no	—
126	C₂×C₄⋊C₈	—	106	2	no	—
127	C₂×C₄×C₈	—	53	1	no	—
128	C₂×C₄×C₈	—	53	1	no	—
129	C₂×C₄×C₈	—	53	1	no	—
130	C₄×C₄⋊C₄	—	53	2	no	—
131	#340	—	53	2	no	—
132	#336	—	106	2	no	—
133	#335	—	106	2	no	—
134	#322	—	106	2	no	—
135	C₅₃	#9596	1	1	yes	characteristic, complemented, Sylow
136	C₂²×C₈	—	53	1	no	—
137	C₂²×C₈	—	53	1	no	—
138	C₂²×C₈	—	53	1	no	—
139	C₂²×C₈	—	106	1	no	—
140	C₂²×C₈	—	106	2	no	—
141	C₂²×C₈	C₂×#6157	1	1	yes	characteristic
142	C₂×C₄⋊C₄	—	53	2	no	—
143	C₂×C₄⋊C₄	C₂×#6157	1	2	yes	—
144	C₂×C₄²	—	53	1	no	—
145	C₂×C₄²	—	106	2	no	—
146	#106	—	2	2	no	—
147	#106	—	53	4	no	—
148	C₄⋊C₈	—	106	2	no	—
149	C₄⋊C₈	—	106	2	no	—
150	C₄⋊C₈	—	212	4	no	—
151	C₄×C₈	—	53	2	no	—
152	C₄×C₈	—	53	2	no	—
153	C₄×C₈	—	53	2	no	—
154	C₄×C₈	—	106	1	no	—
155	C₄×C₈	—	106	1	no	—
156	C₄×C₈	—	106	1	no	—
157	#95	—	106	2	no	—
158	C₂²×C₄	—	2	2	no	—
159	C₂²×C₄	—	53	1	no	—
160	C₂²×C₄	—	53	1	no	—
161	C₂²×C₄	—	106	2	no	—
162	C₂²×C₄	C₂²×#6157	1	1	yes	characteristic
163	C₂×C₈	—	53	2	no	—
164	C₂×C₈	—	106	1	no	—
165	C₂×C₈	—	106	1	no	—
166	C₂×C₈	—	106	2	no	—
167	C₂×C₈	—	106	1	no	—
168	C₂×C₈	—	106	1	no	—
169	C₂×C₈	—	106	2	no	—
170	C₂×C₈	—	106	2	no	—
171	C₂×C₈	—	212	2	no	—
172	C₂×C₈	—	212	2	no	—
173	C₂×C₈	—	212	2	no	—
174	C₂×C₈	—	212	2	no	—
175	C₂×C₈	D₅₃⋊C₈	1	2	yes	—
176	C₂×C₈	C₄⋊#6157	1	2	yes	—
177	C₂×C₈	#11719940	1	2	yes	—
178	C₄⋊C₄	—	2	2	no	—
179	C₄⋊C₄	—	2	2	no	—
180	C₄⋊C₄	—	53	4	no	—
181	C₄⋊C₄	—	106	2	no	—
182	C₄²	—	53	1	no	—
183	C₄²	—	53	1	no	—
184	C₄²	—	53	1	no	—
185	C₄²	—	53	1	no	—
186	C₄²	—	212	2	no	—
187	C₄²	—	212	2	no	—
188	C₂³	D₄×#6157	1	1	yes	characteristic
189	C₂×C₄	—	4	2	no	—
190	C₂×C₄	—	4	2	no	—
191	C₂×C₄	—	4	2	no	—
192	C₂×C₄	—	53	1	no	—
193	C₂×C₄	—	53	1	no	—
194	C₂×C₄	—	53	2	no	—
195	C₂×C₄	—	53	2	no	—
196	C₂×C₄	—	53	1	no	—
197	C₂×C₄	—	53	1	no	—
198	C₂×C₄	—	106	2	no	—
199	C₂×C₄	—	106	4	no	—
200	C₂×C₄	—	212	2	no	—
201	C₂×C₄	—	212	2	no	—
202	C₂×C₄	C₂×C₄⋊#6157	1	1	yes	characteristic
203	C₂×C₄	Q₈×#6157	1	1	yes	characteristic
204	C₂×C₄	C₂×D₅₃⋊C₈	1	1	yes	characteristic
205	C₂×C₄	C₂×#11719940	1	1	yes	characteristic
206	C₂×C₄	#13133304	1	1	yes	characteristic
207	C₂×C₄	#13133305	1	1	yes	characteristic
208	C₈	—	106	2	no	—
209	C₈	—	424	2	no	—
210	C₈	—	212	1	no	—
211	C₈	—	212	1	no	—
212	C₈	—	212	2	no	—
213	C₈	#13133284	1	4	yes	complemented
214	C₂²	#16811574	1	1	yes	characteristic
215	C₂²	#16811651	1	1	yes	characteristic
216	C₂²	#16811658	1	1	yes	characteristic
217	C₂²	#16811662	1	2	yes	—
218	C₂²	#16811668	1	2	yes	—
219	C₄	—	8	2	no	—
220	C₄	—	53	1	no	—
221	C₄	—	53	1	no	—
222	C₄	—	53	2	no	—
223	C₄	—	106	1	no	—
224	C₄	—	106	1	no	—
225	C₄	—	212	4	no	—
226	C₄	C₂×#13133284	1	1	yes	characteristic
227	C₄	#16811630	1	1	yes	characteristic
228	C₄	#16811672	1	1	yes	characteristic
229	C₄	#16811674	1	1	yes	characteristic
230	C₂	#20290307	1	2	yes	—
231	C₂	#20290358	1	2	yes	—
232	C₂	#20290813	1	1	yes	characteristic
233	C₂	#20290821	1	1	yes	characteristic
234	C₂	#20290825	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#20290813

C₂

yes

maximal

C₂×#16811486

C₂

yes

maximal, characteristic

C₂×#16811464

C₂

yes

maximal, characteristic

#20289551

C₂

yes

maximal

#106×Dic₅₃

C₂

yes

maximal, characteristic

C₂×#13133284

—

C₂×C₄⋊#88324

C₂²

yes

—

C₂×C₄×#88324

C₂²

yes

characteristic

C₂×C₄×#88324

C₂²

yes

—

—

—

C₄

yes

characteristic

C₂×C₈×Dic₅₃

C₂²

yes

characteristic

C₄⋊C₄×Dic₅₃

C₂²

yes

—

#16810385

C₄

yes

—

C₂×#106×C₅₃

C₄

yes

characteristic

C₂²×#88324

—

C₂²×#88324

—

C₂²×#88324

D₄

yes

characteristic

C₂²×#88324

D₄

yes

—

—

—

—

—

—

Q₈

yes

—

C₂²×#88322

C₂×C₄

yes

characteristic

C₂×C₄⋊Dic₅₃

C₂×C₄

yes

—

C₂×C₄×Dic₅₃

—

C₂×C₄×Dic₅₃

C₂³

yes

characteristic

#13133149

C₈

yes

complemented

C₈×Dic₅₃

D₄

yes

—

C₈×Dic₅₃

Q₈

yes

—

#13133124

—

C₂²×C₈×C₅₃

C₂×C₄

yes

characteristic

C₂×C₄⋊C₄×C₅₃

C₂×C₄

yes

—

#106×C₅₃

—

C₂²×C₄×C₅₃

—

C₂²×C₄×C₅₃

C₂²×C₄

yes

characteristic

C₂²×Dic₅₃

—

C₂²×Dic₅₃

C₂×D₄

yes

C₂²×Dic₅₃

yes

—

—

—

—

—

—

—

—

—

C₂×C₈×C₅₃

C₄⋊C₄

yes

—

C₂×C₈×C₅₃

C₂×C₈

yes

—

C₂×C₈×C₅₃

M₁₆

yes

—

C₄⋊C₄×C₅₃

—

C₄⋊C₄×C₅₃

—

C₄⋊Dic₅₃

—

C₄⋊Dic₅₃

C₂×C₈

yes

—

C₄×Dic₅₃

—

C₄×Dic₅₃

—

C₄×Dic₅₃

C₂×D₄

yes

characteristic

C₄×Dic₅₃

C₂×Q₈

yes

characteristic

C₄×Dic₅₃

C₂×Q₈

yes

C₄×Dic₅₃

yes

—

—

C₄⋊C₄

yes

—

C₂³×C₅₃

C₄×D₄

yes

characteristic

C₂×C₄×C₅₃

—

C₂×C₄×C₅₃

—

C₂×C₄×C₅₃

—

C₂×C₄×C₅₃

C₂×C₄⋊C₄

yes

characteristic

C₂×C₄×C₅₃

C₄×Q₈

yes

characteristic

C₂×C₄×C₅₃

C₂²×C₈

yes

characteristic

C₂×C₄×C₅₃

C₂×M₁₆

yes

C₂×C₄×C₅₃

yes

C₂×C₄×C₅₃

yes

C₂×Dic₅₃

—

C₂×Dic₅₃

—

C₂×Dic₅₃

—

C₂×Dic₅₃

—

C₂×Dic₅₃

#121

yes

characteristic

C₂×Dic₅₃

C₂²⋊Q₈

yes

characteristic

C₂×Dic₅₃

#125

yes

characteristic

C₂×Dic₅₃

C₄⋊Q₈

yes

characteristic

C₂×Dic₅₃

AGL(1,ℤ/8)

yes

—

C₂×Dic₅₃

#137

yes

—

—

—

—

—

C₈×C₅₃

C₄⋊C₈

yes

—

—

C₂²×C₅₃

yes

C₂²×C₅₃

C₈×D₄

yes

characteristic

C₂²×C₅₃

#436

yes

characteristic

100

C₂²×C₅₃

#440

yes

—

101

C₂²×C₅₃

#444

yes

—

102

C₄×C₅₃

—

103

C₄×C₅₃

C₂×C₄⋊C₈

yes

characteristic

104

C₄×C₅₃

#424

yes

characteristic

105

C₄×C₅₃

C₈×Q₈

yes

characteristic

106

C₄×C₅₃

#446

yes

characteristic

107

Dic₅₃

—

108

Dic₅₃

—

109

Dic₅₃

—

110

Dic₅₃

#469

yes

characteristic

111

Dic₅₃

#470

yes

characteristic

112

Dic₅₃

#501

yes

—

113

#1939

—

114

C₄×#106

—

115

C₂×#335

—

116

C₂×#322

—

117

#1279

—

118

C₂×C₅₃

SD₁₆⋊C₈

yes

—

119

C₂×C₅₃

#1592

yes

—

120

C₂×C₅₃

#1939

yes

characteristic

121

C₂×C₅₃

#1944

yes

characteristic

122

C₂×C₅₃

#1946

yes

characteristic

123

C₂×#106

—

124

C₂×#106

#6157

yes

characteristic

125

C₂×C₄⋊C₈

—

126

C₂×C₄⋊C₈

—

106

—

127

C₂×C₄×C₈

—

128

C₂×C₄×C₈

—

129

C₂×C₄×C₈

—

130

C₄×C₄⋊C₄

—

131

#340

—

132

#336

—

106

—

133

#335

—

106

—

134

#322

—

106

—

135

C₅₃

#9596

yes

characteristic, complemented, Sylow

136

C₂²×C₈

—

137

C₂²×C₈

—

138

C₂²×C₈

—

139

C₂²×C₈

—

106

—

140

C₂²×C₈

—

106

—

141

C₂²×C₈

C₂×#6157

yes

characteristic

142

C₂×C₄⋊C₄

—

143

C₂×C₄⋊C₄

C₂×#6157

yes

—

144

C₂×C₄²

—

145

C₂×C₄²

—

106

—

146

#106

—

147

#106

—

148

C₄⋊C₈

—

106

—

149

C₄⋊C₈

—

106

—

150

C₄⋊C₈

—

212

—

151

C₄×C₈

—

152

C₄×C₈

—

153

C₄×C₈

—

154

C₄×C₈

—

106

—

155

C₄×C₈

—

106

—

156

C₄×C₈

—

106

—

157

#95

—

106

—

158

C₂²×C₄

—

159

C₂²×C₄

—

160

C₂²×C₄

—

161

C₂²×C₄

—

106

—

162

C₂²×C₄

C₂²×#6157

yes

characteristic

163

C₂×C₈

—

164

C₂×C₈

—

106

—

165

C₂×C₈

—

106

—

166

C₂×C₈

—

106

—

167

C₂×C₈

—

106

—

168

C₂×C₈

—

106

—

169

C₂×C₈

—

106

—

170

C₂×C₈

—

106

—

171

C₂×C₈

—

212

—

172

C₂×C₈

—

212

—

173

C₂×C₈

—

212

—

174

C₂×C₈

—

212

—

175

C₂×C₈

D₅₃⋊C₈

yes

—

176

C₂×C₈

C₄⋊#6157

yes

—

177

C₂×C₈

#11719940

yes

—

178

C₄⋊C₄

—

179

C₄⋊C₄

—

180

C₄⋊C₄

—

181

C₄⋊C₄

—

106

—

182

C₄²

—

183

C₄²

—

184

C₄²

—

185

C₄²

—

186

C₄²

—

212

—

187

C₄²

—

212

—

188

C₂³

D₄×#6157

yes

characteristic

189

C₂×C₄

—

190

C₂×C₄

—

191

C₂×C₄

—

192

C₂×C₄

—

193

C₂×C₄

—

194

C₂×C₄

—

195

C₂×C₄

—

196

C₂×C₄

—

197

C₂×C₄

—

198

C₂×C₄

—

106

—

199

C₂×C₄

—

106

—

200

C₂×C₄

—

212

—

201

C₂×C₄

—

212

—

202

C₂×C₄

C₂×C₄⋊#6157

yes

characteristic

203

C₂×C₄

Q₈×#6157

yes

characteristic

204

C₂×C₄

C₂×D₅₃⋊C₈

yes

characteristic

205

C₂×C₄

C₂×#11719940

yes

characteristic

206

C₂×C₄

#13133304

yes

characteristic

207

C₂×C₄

#13133305

yes

characteristic

208

C₈

—

106

—

209

C₈

—

424

—

210

C₈

—

212

—

211

C₈

—

212

—

212

C₈

—

212

—

213

C₈

#13133284

yes

complemented

214

C₂²

#16811574

yes

characteristic

215

C₂²

#16811651

yes

characteristic

216

C₂²

#16811658

yes

characteristic

217

C₂²

#16811662

yes

—

218

C₂²

#16811668

yes

—

219

C₄

—

220

C₄

—

221

C₄

—

222

C₄

—

223

C₄

—

106

—

224

C₄

—

106

—

225

C₄

—

212

—

226

C₄

C₂×#13133284

yes

characteristic

227

C₄

#16811630

yes

characteristic

228

C₄

#16811672

yes

characteristic

229

C₄

#16811674

yes

characteristic

230

C₂

#20290307

yes

—

231

C₂

#20290358

yes

—

232

C₂

#20290813

yes

characteristic

233

C₂

#20290821

yes

characteristic

234

C₂

#20290825

yes

characteristic

	subgroup	G/H
center	C₂³	D₄×#6157
commutator	C₂×C₄×C₅₃	C₂²×C₈
Frattini	C₂²×C₄	C₂²×#6157
Fitting	C₂×#106×C₅₃	C₄
socle, prime radical	C₂³×C₅₃	C₄×D₄
cosocle	C₂×C₄×Dic₅₃	C₂³
hypercenter	C₂×#106	#6157
hypocenter	C₅₃	#9596
LCS	G ▷ C₂×C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂×#106

subgroup

G/H

center

C₂³

D₄×#6157

commutator

C₂×C₄×C₅₃

C₂²×C₈

Frattini

C₂²×C₄

C₂²×#6157

Fitting

C₂×#106×C₅₃

C₄

socle, prime radical

C₂³×C₅₃

C₄×D₄

cosocle

C₂×C₄×Dic₅₃

C₂³

C₅₃

G ▷ C₂×C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃

UCS

C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂×#106

N	H ≅ G/N	type
33. #13133149	C₈	semidirect
94. C₈×C₅₃	C₄⋊C₈	semidirect
135. C₅₃	#9596	semidirect
213. C₈	#13133284	semidirect

H ≅ G/N

type

33. #13133149

C₈

semidirect

94. C₈×C₅₃

C₄⋊C₈

semidirect

135. C₅₃

#9596

semidirect

213. C₈

#13133284

semidirect

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

subgroup	index
#20290813	2
C₂×#16811486	2
C₂×#16811464	2
#20289551	2
#106×Dic₅₃	2
#9596	53

subgroup

index

#106×Dic₅₃

Subgroups — #28305590

Conjugacy classes of subgroups

Complements

Maximal subgroups