Group #27303201 — subgroups

Subgroups — #27303201

Order 13568.

402 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 402 conjugacy classes of subgroups — too many to draw. Only its 97 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	C₂×#16811021	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#16810434	C₂	1	2	yes	maximal
3	#20275603	C₂	1	1	yes	maximal, characteristic
4	#20272814	C₂	1	2	yes	maximal, complemented
5	C₅₃×#1376	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#13133239	C₂²	1	1	yes	characteristic
7	C₂×#13133217	—	2	1	no	—
8	#16811021	—	2	4	no	—
9	C₂×#13133153	C₂²	1	1	yes	characteristic
10	C₂×#13133149	—	2	1	no	—
11	C₂×#13133149	C₂²	1	2	yes	—
12	C₂×#13133145	—	2	1	no	—
13	#16810589	—	2	1	no	—
14	#16810434	—	2	4	no	—
15	C₂×M₃₂×C₅₃	C₂²	1	2	yes	—
16	C₂×C₄×C₈×C₅₃	C₂²	1	1	yes	characteristic
17	C₂×#11719945	—	2	1	no	—
18	C₂²×Dic₁₀₆	—	4	1	no	—
19	#13133239	—	2	2	no	—
20	#13133239	—	2	2	no	—
21	C₂×Dic₂₁₂	Q₈	1	1	yes	characteristic, complemented
22	C₂×#11719913	—	2	1	no	—
23	C₂×D₄₂₄	Q₈	1	1	yes	characteristic, complemented
24	C₂×#11719917	—	2	1	no	—
25	#13133217	—	2	4	no	—
26	#13133217	—	4	2	no	—
27	C₂×C₄⋊Dic₅₃	—	2	2	no	—
28	C₂×C₄⋊Dic₅₃	—	4	1	no	—
29	#13133153	—	2	2	no	—
30	#13133149	—	2	4	no	—
31	#13133149	—	2	2	no	—
32	#13133149	D₄	1	4	yes	—
33	#13133145	—	4	2	no	—
34	#13133129	—	4	2	no	—
35	C₂²×C₈×C₅₃	D₄	1	1	yes	characteristic
36	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
37	C₂×C₄²×C₅₃	D₄	1	1	yes	characteristic
38	M₃₂×C₅₃	—	2	2	no	—
39	M₃₂×C₅₃	—	2	2	no	—
40	C₂×C₁₆×C₅₃	—	2	2	no	—
41	C₄×C₈×C₅₃	—	2	2	no	—
42	C₂²×C₄×C₅₃	—	2	1	no	—
43	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
44	C₂×C₂²⋊D₅₃	—	4	1	no	—
45	C₂²×Dic₅₃	—	4	2	no	—
46	#11719945	—	4	1	no	—
47	#11719945	—	4	1	no	—
48	#11719945	—	4	1	no	—
49	#11719945	—	4	1	no	—
50	C₂×D₂₁₂	—	2	1	no	—
51	C₂×C₄×D₅₃	—	4	1	no	—
52	C₂×Dic₁₀₆	—	2	1	no	—
53	C₂×Dic₁₀₆	—	4	4	no	—
54	C₂×Dic₁₀₆	—	8	4	no	—
55	C₂×C₈×C₅₃	—	2	1	no	—
56	C₂×C₈×C₅₃	—	2	1	no	—
57	C₂×C₈×C₅₃	SD₁₆	1	2	yes	—
58	C₂×C₈×C₅₃	C₂×D₄	1	2	yes	—
59	C₂×C₈×C₅₃	C₂×Q₈	1	1	yes	characteristic
60	C₂×C₈×C₅₃	#41	1	2	yes	—
61	C₂×C₈×C₅₃	#41	1	1	yes	characteristic
62	C₄²×C₅₃	—	2	1	no	—
63	C₄²×C₅₃	D₈	1	2	yes	—
64	C₄⋊Dic₅₃	—	2	4	no	—
65	C₄⋊Dic₅₃	—	4	4	no	—
66	C₄⋊Dic₅₃	—	4	2	no	—
67	#11719917	—	4	1	no	—
68	#11719917	—	4	1	no	—
69	C₂×#88322	—	4	1	no	—
70	Dic₂₁₂	—	2	2	no	—
71	D₄₂₄	—	2	2	no	—
72	#11719913	—	4	2	no	—
73	C₁₆×C₅₃	—	4	2	no	—
74	C₂³×C₅₃	AGL(1,ℤ/8)	1	1	yes	characteristic
75	C₂²×D₅₃	—	4	1	no	—
76	C₂×C₄×C₅₃	—	2	4	no	—
77	C₂×C₄×C₅₃	—	2	2	no	—
78	C₂×C₄×C₅₃	#120	1	1	yes	characteristic
79	C₂×C₄×C₅₃	C₂²⋊Q₈	1	1	yes	characteristic
80	C₂×C₄×C₅₃	#124	1	1	yes	characteristic
81	C₂×C₄×C₅₃	C₂×D₈	1	1	yes	characteristic
82	C₂×C₄×C₅₃	C₂×SD₁₆	1	1	yes	characteristic
83	C₂×C₄×C₅₃	#137	1	1	yes	characteristic
84	C₂²⋊D₅₃	—	8	1	no	—
85	C₂²⋊D₅₃	—	8	1	no	—
86	C₂×Dic₅₃	—	4	4	no	—
87	C₂×Dic₅₃	—	4	1	no	—
88	C₂×Dic₅₃	—	8	4	no	—
89	D₂₁₂	—	4	1	no	—
90	D₂₁₂	—	4	1	no	—
91	C₄×D₅₃	—	8	1	no	—
92	C₄×D₅₃	—	8	1	no	—
93	Dic₁₀₆	—	4	1	no	—
94	Dic₁₀₆	—	4	1	no	—
95	Dic₁₀₆	—	8	8	no	—
96	C₈×C₅₃	—	2	2	no	—
97	C₈×C₅₃	C₂²⋊Q₈	1	2	yes	—
98	C₈×C₅₃	#124	1	2	yes	—
99	#88322	—	8	1	no	—
100	#13371	—	53	1	no	maximal, Sylow
101	C₂²×C₅₃	—	2	2	no	—
102	C₂²×C₅₃	#447	1	1	yes	characteristic
103	C₂²×C₅₃	#476	1	1	yes	characteristic
104	C₂²×C₅₃	#489	1	1	yes	characteristic
105	C₂×D₅₃	—	8	2	no	—
106	C₂×D₅₃	—	8	1	no	—
107	C₄×C₅₃	—	2	4	no	—
108	C₄×C₅₃	#393	1	1	yes	characteristic
109	C₄×C₅₃	#448	1	1	yes	characteristic
110	C₄×C₅₃	#474	1	1	yes	characteristic
111	C₄×C₅₃	#486	1	1	yes	characteristic
112	Dic₅₃	—	8	4	no	—
113	Dic₅₃	—	8	1	no	—
114	C₂×#498	—	53	1	no	—
115	C₂×#360	—	53	2	no	—
116	#1974	—	53	1	no	—
117	#1383	—	53	2	no	—
118	#1376	D₅₃	1	1	yes	characteristic, complemented
119	C₂×C₅₃	—	2	1	no	—
120	C₂×C₅₃	—	2	1	no	—
121	C₂×C₅₃	#2023	1	1	yes	characteristic
122	C₂×C₅₃	#2230	1	2	yes	—
123	D₅₃	—	16	1	no	—
124	C₂×#135	—	53	1	no	—
125	C₂×C₄⋊Q₈	—	106	1	no	—
126	C₂×M₃₂	C₂×D₅₃	1	2	yes	—
127	#498	—	106	4	no	—
128	C₂×#108	—	53	1	no	—
129	C₂×#106	—	53	2	no	—
130	C₂×#106	—	106	1	no	—
131	C₂×#104	—	106	1	no	—
132	#408	—	106	1	no	—
133	C₂×C₄×C₈	C₂×D₅₃	1	1	yes	characteristic
134	#360	—	106	4	no	—
135	C₅₃	#13371	1	1	yes	characteristic, complemented, Sylow
136	C₂×#41	—	106	1	no	—
137	C₂²×Q₈	—	212	1	no	—
138	#135	—	106	2	no	—
139	#135	—	106	2	no	—
140	C₂×Q₁₆	—	53	1	no	—
141	C₂×SD₁₆	—	106	1	no	—
142	C₂×D₈	—	53	1	no	—
143	C₂×M₁₆	—	106	1	no	—
144	C₂²×C₈	D₂₁₂	1	1	yes	characteristic
145	C₂²×C₈	C₂²×D₅₃	1	1	yes	characteristic
146	C₄⋊Q₈	—	106	4	no	—
147	C₄⋊Q₈	—	212	2	no	—
148	C₂×C₄⋊C₄	—	106	2	no	—
149	C₂×C₄⋊C₄	—	212	1	no	—
150	C₂×C₄²	D₂₁₂	1	1	yes	characteristic
151	M₃₂	—	2	2	no	—
152	M₃₂	—	2	2	no	—
153	C₂×C₁₆	—	2	2	no	—
154	#108	—	106	2	no	—
155	#106	—	53	4	no	—
156	#106	—	106	4	no	—
157	#106	—	106	2	no	—
158	#104	—	212	2	no	—
159	C₂²⋊C₈	—	212	2	no	—
160	C₄×C₈	—	2	2	no	—
161	#41	—	212	1	no	—
162	#41	—	212	1	no	—
163	#41	—	212	1	no	—
164	#41	—	212	1	no	—
165	C₂×Q₈	—	106	1	no	—
166	C₂×Q₈	—	424	4	no	—
167	C₂×Q₈	—	212	4	no	—
168	C₂×D₄	—	106	1	no	—
169	C₂×D₄	—	212	1	no	—
170	C₂²×C₄	—	2	1	no	—
171	C₂²×C₄	—	212	2	no	—
172	C₂²×C₄	—	212	1	no	—
173	C₂²×C₄	C₂×D₂₁₂	1	1	yes	characteristic
174	Q₁₆	—	106	2	no	—
175	SD₁₆	—	212	2	no	—
176	D₈	—	106	2	no	—
177	M₁₆	—	212	1	no	—
178	M₁₆	—	212	1	no	—
179	C₂×C₈	—	2	1	no	—
180	C₂×C₈	—	2	1	no	—
181	C₂×C₈	—	212	1	no	—
182	C₂×C₈	#11719913	1	2	yes	—
183	C₂×C₈	#11719945	1	2	yes	—
184	C₂×C₈	D₄×D₅₃	1	2	yes	—
185	C₂×C₈	#11719947	1	1	yes	characteristic
186	C₂×C₈	Q₈×D₅₃	1	1	yes	characteristic
187	C₄⋊C₄	—	106	4	no	—
188	C₄⋊C₄	—	212	4	no	—
189	C₄⋊C₄	—	212	2	no	—
190	C₄²	—	2	1	no	—
191	C₄²	D₄₂₄	1	2	yes	—
192	C₁₆	—	4	2	no	—
193	C₂³	—	212	1	no	—
194	C₂³	#13133245	1	1	yes	characteristic
195	Q₈	—	424	8	no	—
196	Q₈	—	212	1	no	—
197	Q₈	—	212	1	no	—
198	D₄	—	424	1	no	—
199	D₄	—	424	1	no	—
200	D₄	—	212	1	no	—
201	D₄	—	212	1	no	—
202	C₂×C₄	—	2	4	no	—
203	C₂×C₄	—	2	2	no	—
204	C₂×C₄	—	424	4	no	—
205	C₂×C₄	—	424	1	no	—
206	C₂×C₄	—	424	1	no	—
207	C₂×C₄	—	212	4	no	—
208	C₂×C₄	—	212	1	no	—
209	C₂×C₄	#13133187	1	1	yes	characteristic
210	C₂×C₄	#13133197	1	1	yes	characteristic
211	C₂×C₄	#13133205	1	1	yes	characteristic
212	C₂×C₄	C₂×D₄₂₄	1	1	yes	characteristic
213	C₂×C₄	C₂×#11719913	1	1	yes	characteristic
214	C₂×C₄	#13133250	1	1	yes	characteristic
215	C₈	—	2	2	no	—
216	C₈	—	424	1	no	—
217	C₈	#13133195	1	2	yes	—
218	C₈	#13133203	1	2	yes	—
219	C₂²	—	2	2	no	—
220	C₂²	—	424	1	no	—
221	C₂²	—	424	2	no	—
222	C₂²	#16810759	1	1	yes	characteristic
223	C₂²	#16810914	1	1	yes	characteristic
224	C₂²	#16810983	1	1	yes	characteristic
225	C₄	—	2	4	no	—
226	C₄	—	424	4	no	—
227	C₄	—	424	1	no	—
228	C₄	#16810536	1	1	yes	characteristic
229	C₄	#16810764	1	1	yes	characteristic
230	C₄	#16810904	1	1	yes	characteristic
231	C₄	#16810970	1	1	yes	characteristic
232	C₂	—	2	1	no	—
233	C₂	—	2	1	no	—
234	C₂	—	848	1	no	—
235	C₂	#20275852	1	1	yes	characteristic
236	C₂	#20276887	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#16811021

C₂

yes

maximal, characteristic, complemented

C₂×#16810434

C₂

yes

maximal

#20275603

C₂

yes

maximal, characteristic

#20272814

C₂

yes

maximal, complemented

C₅₃×#1376

C₂

yes

maximal, characteristic, complemented

C₂×#13133239

C₂²

yes

—

—

C₂²

yes

characteristic

C₂×#13133149

—

C₂×#13133149

C₂²

yes

—

C₂×#13133145

—

#16810589

—

#16810434

—

C₂×M₃₂×C₅₃

C₂²

yes

—

C₂×C₄×C₈×C₅₃

C₂²

yes

characteristic

C₂×#11719945

—

C₂²×Dic₁₀₆

—

#13133239

—

#13133239

—

C₂×Dic₂₁₂

Q₈

yes

characteristic, complemented

C₂×#11719913

—

C₂×D₄₂₄

Q₈

yes

characteristic, complemented

C₂×#11719917

—

#13133217

—

#13133217

—

C₂×C₄⋊Dic₅₃

—

C₂×C₄⋊Dic₅₃

—

—

—

—

D₄

yes

—

#13133145

—

#13133129

—

C₂²×C₈×C₅₃

D₄

yes

characteristic

C₂²×C₈×C₅₃

C₂³

yes

characteristic

C₂×C₄²×C₅₃

D₄

yes

characteristic

M₃₂×C₅₃

—

M₃₂×C₅₃

—

C₂×C₁₆×C₅₃

—

C₄×C₈×C₅₃

—

C₂²×C₄×C₅₃

—

C₂²×C₄×C₅₃

C₂×D₄

yes

characteristic

C₂×C₂²⋊D₅₃

—

C₂²×Dic₅₃

—

—

—

—

—

C₂×D₂₁₂

—

C₂×C₄×D₅₃

—

C₂×Dic₁₀₆

—

C₂×Dic₁₀₆

—

C₂×Dic₁₀₆

—

C₂×C₈×C₅₃

—

C₂×C₈×C₅₃

—

C₂×C₈×C₅₃

SD₁₆

yes

—

C₂×C₈×C₅₃

C₂×D₄

yes

—

C₂×C₈×C₅₃

C₂×Q₈

yes

characteristic

C₂×C₈×C₅₃

#41

yes

—

C₂×C₈×C₅₃

#41

yes

characteristic

C₄²×C₅₃

—

C₄²×C₅₃

D₈

yes

—

C₄⋊Dic₅₃

—

C₄⋊Dic₅₃

—

C₄⋊Dic₅₃

—

#11719917

—

#11719917

—

C₂×#88322

—

Dic₂₁₂

—

D₄₂₄

—

#11719913

—

C₁₆×C₅₃

—

C₂³×C₅₃

AGL(1,ℤ/8)

yes

characteristic

C₂²×D₅₃

—

C₂×C₄×C₅₃

—

C₂×C₄×C₅₃

—

C₂×C₄×C₅₃

#120

yes

characteristic

C₂×C₄×C₅₃

C₂²⋊Q₈

yes

characteristic

C₂×C₄×C₅₃

#124

yes

characteristic

C₂×C₄×C₅₃

C₂×D₈

yes

characteristic

C₂×C₄×C₅₃

C₂×SD₁₆

yes

characteristic

C₂×C₄×C₅₃

#137

yes

characteristic

C₂²⋊D₅₃

—

C₂²⋊D₅₃

—

C₂×Dic₅₃

—

C₂×Dic₅₃

—

C₂×Dic₅₃

—

D₂₁₂

—

D₂₁₂

—

C₄×D₅₃

—

C₄×D₅₃

—

Dic₁₀₆

—

Dic₁₀₆

—

Dic₁₀₆

—

C₈×C₅₃

—

C₈×C₅₃

C₂²⋊Q₈

yes

—

C₈×C₅₃

#124

yes

—

#88322

—

100

#13371

—

maximal, Sylow

101

C₂²×C₅₃

—

102

C₂²×C₅₃

#447

yes

characteristic

103

C₂²×C₅₃

#476

yes

characteristic

104

C₂²×C₅₃

#489

yes

characteristic

105

C₂×D₅₃

—

106

C₂×D₅₃

—

107

C₄×C₅₃

—

108

C₄×C₅₃

#393

yes

characteristic

109

C₄×C₅₃

#448

yes

characteristic

110

C₄×C₅₃

#474

yes

characteristic

111

C₄×C₅₃

#486

yes

characteristic

112

Dic₅₃

—

113

Dic₅₃

—

114

C₂×#498

—

115

C₂×#360

—

116

#1974

—

117

#1383

—

118

#1376

D₅₃

yes

characteristic, complemented

119

C₂×C₅₃

—

120

C₂×C₅₃

—

121

C₂×C₅₃

#2023

yes

characteristic

122

C₂×C₅₃

#2230

yes

—

123

D₅₃

—

124

C₂×#135

—

125

C₂×C₄⋊Q₈

—

106

—

126

C₂×M₃₂

C₂×D₅₃

yes

—

127

#498

—

106

—

128

C₂×#108

—

129

C₂×#106

—

130

C₂×#106

—

106

—

131

C₂×#104

—

106

—

132

#408

—

106

—

133

C₂×C₄×C₈

C₂×D₅₃

yes

characteristic

134

#360

—

106

—

135

C₅₃

#13371

yes

characteristic, complemented, Sylow

136

C₂×#41

—

106

—

137

C₂²×Q₈

—

212

—

138

#135

—

106

—

139

#135

—

106

—

140

C₂×Q₁₆

—

141

C₂×SD₁₆

—

106

—

142

C₂×D₈

—

143

C₂×M₁₆

—

106

—

144

C₂²×C₈

D₂₁₂

yes

characteristic

145

C₂²×C₈

C₂²×D₅₃

yes

characteristic

146

C₄⋊Q₈

—

106

—

147

C₄⋊Q₈

—

212

—

148

C₂×C₄⋊C₄

—

106

—

149

C₂×C₄⋊C₄

—

212

—

150

C₂×C₄²

D₂₁₂

yes

characteristic

151

M₃₂

—

152

M₃₂

—

153

C₂×C₁₆

—

154

#108

—

106

—

155

#106

—

156

#106

—

106

—

157

#106

—

106

—

158

#104

—

212

—

159

C₂²⋊C₈

—

212

—

160

C₄×C₈

—

161

#41

—

212

—

162

#41

—

212

—

163

#41

—

212

—

164

#41

—

212

—

165

C₂×Q₈

—

106

—

166

C₂×Q₈

—

424

—

167

C₂×Q₈

—

212

—

168

C₂×D₄

—

106

—

169

C₂×D₄

—

212

—

170

C₂²×C₄

—

171

C₂²×C₄

—

212

—

172

C₂²×C₄

—

212

—

173

C₂²×C₄

C₂×D₂₁₂

yes

characteristic

174

Q₁₆

—

106

—

175

SD₁₆

—

212

—

176

D₈

—

106

—

177

M₁₆

—

212

—

178

M₁₆

—

212

—

179

C₂×C₈

—

180

C₂×C₈

—

181

C₂×C₈

—

212

—

182

C₂×C₈

#11719913

yes

—

183

C₂×C₈

#11719945

yes

—

184

C₂×C₈

D₄×D₅₃

yes

—

185

C₂×C₈

#11719947

yes

characteristic

186

C₂×C₈

Q₈×D₅₃

yes

characteristic

187

C₄⋊C₄

—

106

—

188

C₄⋊C₄

—

212

—

189

C₄⋊C₄

—

212

—

190

C₄²

—

191

C₄²

D₄₂₄

yes

—

192

C₁₆

—

193

C₂³

—

212

—

194

C₂³

#13133245

yes

characteristic

195

Q₈

—

424

—

196

Q₈

—

212

—

197

Q₈

—

212

—

198

D₄

—

424

—

199

D₄

—

424

—

200

D₄

—

212

—

201

D₄

—

212

—

202

C₂×C₄

—

203

C₂×C₄

—

204

C₂×C₄

—

424

—

205

C₂×C₄

—

424

—

206

C₂×C₄

—

424

—

207

C₂×C₄

—

212

—

208

C₂×C₄

—

212

—

209

C₂×C₄

#13133187

yes

characteristic

210

C₂×C₄

#13133197

yes

characteristic

211

C₂×C₄

#13133205

yes

characteristic

212

C₂×C₄

C₂×D₄₂₄

yes

characteristic

213

C₂×C₄

C₂×#11719913

yes

characteristic

214

C₂×C₄

#13133250

yes

characteristic

215

C₈

—

216

C₈

—

424

—

217

C₈

#13133195

yes

—

218

C₈

#13133203

yes

—

219

C₂²

—

220

C₂²

—

424

—

221

C₂²

—

424

—

222

C₂²

#16810759

yes

characteristic

223

C₂²

#16810914

yes

characteristic

224

C₂²

#16810983

yes

characteristic

225

C₄

—

226

C₄

—

424

—

227

C₄

—

424

—

228

C₄

#16810536

yes

characteristic

229

C₄

#16810764

yes

characteristic

230

C₄

#16810904

yes

characteristic

231

C₄

#16810970

yes

characteristic

232

C₂

—

233

C₂

—

234

C₂

—

848

—

235

C₂

#20275852

yes

characteristic

236

C₂

#20276887

yes

—

	subgroup	G/H
center	C₂²	#16810914
commutator, cosocle	C₂²×C₈×C₅₃	C₂³
Frattini	C₂²×C₈	C₂²×D₅₃
Fitting	C₅₃×#1376	C₂
socle	C₂²×C₅₃	#476
prime radical	C₂×#13133239	C₂²
hypercenter	#1376	D₅₃
hypocenter	C₅₃	#13371
LCS	G ▷ C₂²×C₈×C₅₃ ▷ C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×C₄×C₈ ◁ #1376

subgroup

G/H

center

C₂²

#16810914

commutator, cosocle

C₂²×C₈×C₅₃

C₂³

Frattini

C₂²×C₈

C₂²×D₅₃

Fitting

C₅₃×#1376

C₂

C₂²×C₅₃

C₂²

D₅₃

C₅₃

G ▷ C₂²×C₈×C₅₃ ▷ C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×C₄×C₈ ◁ #1376

N	H ≅ G/N	type
1. C₂×#16811021	C₂	semidirect
4. #20272814	C₂	semidirect
5. C₅₃×#1376	C₂	semidirect
21. C₂×Dic₂₁₂	Q₈	semidirect
23. C₂×D₄₂₄	Q₈	semidirect
118. #1376	D₅₃	semidirect
135. C₅₃	#13371	semidirect

H ≅ G/N

type

1. C₂×#16811021

C₂

semidirect

4. #20272814

C₂

semidirect

5. C₅₃×#1376

C₂

semidirect

21. C₂×Dic₂₁₂

Q₈

semidirect

23. C₂×D₄₂₄

Q₈

semidirect

118. #1376

D₅₃

semidirect

135. C₅₃

#13371

semidirect

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

subgroup	index
C₂×#16811021	2
C₂×#16810434	2
#20275603	2
#20272814	2
C₅₃×#1376	2
#13371	53

subgroup

index

C₅₃×#1376

Subgroups — #27303201

Conjugacy classes of subgroups

Complements

Maximal subgroups