Group #27397982 — subgroups

Subgroups — #27397982

Order 13568.

810 conjugacy classes of subgroups; only the 211 normal subgroups are shown.

normal subgroups only

This group has 810 conjugacy classes of subgroups — too many to draw. Only its 211 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	#20285143	C₂	1	1	yes	maximal, characteristic
2	#20283434	C₂	1	2	yes	maximal, complemented
3	#20275547	C₂	1	2	yes	maximal, complemented
4	#20275041	C₂	1	8	yes	maximal, complemented
5	#20274853	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅₃×#1746	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#13133239	C₂²	1	4	yes	—
8	C₂×#13133223	C₂²	1	4	yes	—
9	#16811173	C₂²	1	2	yes	—
10	#16811007	C₄	1	4	yes	complemented
11	#16811003	C₄	1	1	yes	characteristic, complemented
12	#16811000	C₄	1	1	yes	characteristic, complemented
13	#16810996	C₄	1	2	yes	complemented
14	#16810696	—	2	8	no	—
15	#16810647	C₂²	1	2	yes	—
16	C₂×#13133145	C₂²	1	8	yes	—
17	#16810589	C₂²	1	4	yes	—
18	#16810388	C₂²	1	4	yes	—
19	C₂×#97×C₅₃	C₂²	1	1	yes	characteristic
20	C₂×C₄×C₈×C₅₃	C₂²	1	1	yes	characteristic
21	C₅₃×#376	C₂²	1	1	yes	characteristic
22	C₅₃×#336	C₂²	1	4	yes	—
23	C₂×#11719945	C₂³	1	4	yes	—
24	#13133239	—	4	8	no	—
25	C₂×Dic₂₁₂	C₂×C₄	1	4	yes	—
26	C₂×#11719913	C₂×C₄	1	8	yes	—
27	C₂×D₄₂₄	C₂×C₄	1	4	yes	—
28	#13133223	—	4	8	no	—
29	C₂×#11719917	C₂³	1	4	yes	—
30	C₂×#11719912	—	2	4	no	—
31	C₂×C₈×D₅₃	—	2	4	no	—
32	#13133217	C₂×C₄	1	2	yes	—
33	#13133214	C₂×C₄	1	2	yes	—
34	#13133205	C₂×C₄	1	4	yes	—
35	#13133191	—	2	4	no	—
36	C₄×D₂₁₂	—	2	4	no	—
37	C₄⋊#88322	—	2	4	no	—
38	#13133145	—	4	8	no	—
39	#13133129	—	2	8	no	—
40	C₂²×C₈×C₅₃	C₂³	1	2	yes	—
41	C₂²×C₈×C₅₃	C₂³	1	2	yes	—
42	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
43	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
44	#97×C₅₃	D₄	1	4	yes	—
45	C₄×C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
46	C₄×C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
47	C₄×C₈×C₅₃	C₂×C₄	1	2	yes	—
48	#95×C₅₃	—	2	2	no	—
49	C₂²×C₄×C₅₃	—	2	2	no	—
50	C₂²×C₄×C₅₃	#41	1	2	yes	—
51	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
52	C₂×C₂²⋊D₅₃	—	2	4	no	—
53	#11719945	—	2	8	no	—
54	#11719945	—	2	8	no	—
55	C₂×D₂₁₂	—	2	4	no	—
56	C₂×D₂₁₂	C₂²×C₄	1	4	yes	—
57	C₂×C₄×D₅₃	—	2	4	no	—
58	C₂×Dic₁₀₆	C₂²×C₄	1	4	yes	—
59	C₂×C₈×C₅₃	—	2	4	no	—
60	C₂×C₈×C₅₃	—	2	4	no	—
61	C₂×C₈×C₅₃	C₂²×C₄	1	2	yes	—
62	C₂×C₈×C₅₃	C₂²×C₄	1	2	yes	—
63	C₂×C₈×C₅₃	C₂×D₄	1	4	yes	—
64	C₄²×C₅₃	—	2	4	no	—
65	C₄²×C₅₃	C₂²×C₄	1	1	yes	characteristic
66	C₄²×C₅₃	C₂²×C₄	1	1	yes	characteristic
67	C₄²×C₅₃	C₂×D₄	1	2	yes	—
68	#11719921	—	2	8	no	—
69	C₄⋊Dic₅₃	—	2	4	no	—
70	#11719917	—	2	8	no	—
71	C₂×#88322	—	2	4	no	—
72	Dic₂₁₂	—	4	4	no	—
73	D₄₂₄	—	4	4	no	—
74	#11719913	—	4	8	no	—
75	#11719912	—	4	8	no	—
76	C₈×D₅₃	—	4	8	no	—
77	C₂³×C₅₃	C₂×#41	1	1	yes	characteristic
78	C₂²×D₅₃	—	2	4	no	—
79	C₂×C₄×C₅₃	—	4	2	no	—
80	C₂×C₄×C₅₃	—	4	4	no	—
81	C₂×C₄×C₅₃	—	4	2	no	—
82	C₂×C₄×C₅₃	C₄×D₄	1	2	yes	—
83	C₂×C₄×C₅₃	C₄×D₄	1	2	yes	—
84	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
85	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
86	C₂×C₄×C₅₃	H(5,𝔽₂)	1	4	yes	—
87	C₂²⋊D₅₃	—	4	8	no	—
88	C₂×Dic₅₃	—	2	4	no	—
89	D₂₁₂	—	2	8	no	—
90	D₂₁₂	—	8	4	no	—
91	C₄×D₅₃	—	4	4	no	—
92	C₄×D₅₃	—	4	4	no	—
93	Dic₁₀₆	—	2	8	no	—
94	C₈×C₅₃	—	2	2	no	—
95	C₈×C₅₃	—	2	2	no	—
96	C₈×C₅₃	—	2	4	no	—
97	#88322	—	4	4	no	—
98	#22282	—	53	1	no	maximal, Sylow
99	C₂²×C₅₃	—	2	2	no	—
100	C₂²×C₅₃	C₂×C₄×D₄	1	1	yes	characteristic
101	C₂²×C₅₃	#540	1	2	yes	—
102	C₂×D₅₃	—	4	4	no	—
103	C₂×D₅₃	—	4	8	no	—
104	C₄×C₅₃	—	2	2	no	—
105	C₄×C₅₃	—	2	2	no	—
106	C₄×C₅₃	—	8	2	no	—
107	C₄×C₅₃	#518	1	2	yes	—
108	C₄×C₅₃	#535	1	2	yes	—
109	Dic₅₃	—	4	4	no	—
110	#3147	—	53	1	no	—
111	#2932	—	53	2	no	—
112	#1963	—	53	2	no	—
113	#1876	—	53	8	no	—
114	#1837	—	53	1	no	—
115	#1746	D₅₃	1	1	yes	characteristic, complemented
116	C₂×C₅₃	—	2	2	no	—
117	C₂×C₅₃	#2328	1	1	yes	characteristic
118	C₂×C₅₃	#2957	1	2	yes	—
119	D₅₃	—	8	4	no	—
120	C₂×#135	—	53	4	no	—
121	C₂×#131	—	53	4	no	—
122	#532	—	53	2	no	—
123	#495	—	53	4	no	—
124	#494	—	53	1	no	—
125	#493	—	53	1	no	—
126	#492	—	53	2	no	—
127	#435	—	106	8	no	—
128	#423	—	53	2	no	—
129	C₂×#104	—	53	8	no	—
130	#408	—	53	4	no	—
131	C₂×#97	C₂×D₅₃	1	1	yes	characteristic
132	C₂×C₄×C₈	C₂×D₅₃	1	1	yes	characteristic
133	#376	C₂×D₅₃	1	1	yes	characteristic
134	#341	—	53	4	no	—
135	#336	C₂×D₅₃	1	4	yes	—
136	C₅₃	#22282	1	1	yes	characteristic, complemented, Sylow
137	C₂×#41	—	53	4	no	—
138	#135	—	212	8	no	—
139	C₂×Q₁₆	—	53	4	no	—
140	C₂×SD₁₆	—	53	8	no	—
141	C₂×D₈	—	53	4	no	—
142	#131	—	212	8	no	—
143	C₂×M₁₆	—	53	4	no	—
144	C₂×M₁₆	—	106	4	no	—
145	C₂²×C₈	—	106	4	no	—
146	C₂²×C₈	C₂²×D₅₃	1	2	yes	—
147	C₂²×C₈	C₂²×D₅₃	1	2	yes	—
148	C₄⋊Q₈	—	53	2	no	—
149	#127	—	53	2	no	—
150	#124	—	53	4	no	—
151	#121	—	106	4	no	—
152	C₄×D₄	—	106	4	no	—
153	C₂×C₄²	C₂²×D₅₃	1	2	yes	—
154	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
155	C₄⋊C₈	—	106	4	no	—
156	#104	—	212	8	no	—
157	C₂²⋊C₈	—	106	8	no	—
158	#97	D₂₁₂	1	4	yes	—
159	C₄×C₈	C₄×D₅₃	1	1	yes	characteristic
160	C₄×C₈	C₄×D₅₃	1	1	yes	characteristic
161	C₄×C₈	C₄×D₅₃	1	2	yes	—
162	#95	—	2	2	no	—
163	#41	—	106	8	no	—
164	#41	—	106	8	no	—
165	C₂×Q₈	—	53	4	no	—
166	C₂×D₄	—	53	4	no	—
167	C₂×D₄	—	106	4	no	—
168	C₂×D₄	—	106	4	no	—
169	C₂²×C₄	—	2	2	no	—
170	C₂²×C₄	—	106	4	no	—
171	C₂²×C₄	#11719945	1	2	yes	—
172	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
173	Q₁₆	—	212	4	no	—
174	SD₁₆	—	212	8	no	—
175	D₈	—	212	4	no	—
176	M₁₆	—	106	8	no	—
177	M₁₆	—	212	8	no	—
178	C₂×C₈	—	2	4	no	—
179	C₂×C₈	—	2	4	no	—
180	C₂×C₈	—	106	4	no	—
181	C₂×C₈	—	212	8	no	—
182	C₂×C₈	C₂×C₄×D₅₃	1	2	yes	—
183	C₂×C₈	C₂×C₄×D₅₃	1	2	yes	—
184	C₂×C₈	C₂×D₂₁₂	1	4	yes	—
185	C₄⋊C₄	—	106	4	no	—
186	C₂²⋊C₄	—	106	8	no	—
187	C₄²	—	2	4	no	—
188	C₄²	C₂×C₄×D₅₃	1	1	yes	characteristic
189	C₄²	C₂×C₄×D₅₃	1	1	yes	characteristic
190	C₄²	C₂×D₂₁₂	1	2	yes	—
191	C₂³	—	106	4	no	—
192	C₂³	C₂×#11719945	1	1	yes	characteristic
193	Q₈	—	106	8	no	—
194	D₄	—	106	8	no	—
195	D₄	—	424	4	no	—
196	D₄	—	212	8	no	—
197	C₂×C₄	—	4	2	no	—
198	C₂×C₄	—	4	4	no	—
199	C₂×C₄	—	4	2	no	—
200	C₂×C₄	—	106	4	no	—
201	C₂×C₄	—	212	4	no	—
202	C₂×C₄	—	212	4	no	—
203	C₂×C₄	C₄×D₂₁₂	1	2	yes	—
204	C₂×C₄	C₄×D₂₁₂	1	2	yes	—
205	C₂×C₄	C₂²×C₄×D₅₃	1	1	yes	characteristic
206	C₂×C₄	C₂²×D₂₁₂	1	1	yes	characteristic
207	C₂×C₄	#13133263	1	4	yes	—
208	C₈	—	2	2	no	—
209	C₈	—	2	2	no	—
210	C₈	—	2	4	no	—
211	C₈	—	212	4	no	—
212	C₂²	—	2	2	no	—
213	C₂²	—	212	4	no	—
214	C₂²	—	212	8	no	—
215	C₂²	C₂×C₄×D₂₁₂	1	1	yes	characteristic
216	C₂²	#16811228	1	2	yes	—
217	C₄	—	2	2	no	—
218	C₄	—	2	2	no	—
219	C₄	—	8	2	no	—
220	C₄	—	212	4	no	—
221	C₄	#16811097	1	2	yes	—
222	C₄	#16811192	1	2	yes	—
223	C₂	—	2	2	no	—
224	C₂	—	424	4	no	—
225	C₂	#20277440	1	1	yes	characteristic
226	C₂	#20283633	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#20285143

C₂

yes

maximal, characteristic

#20283434

C₂

yes

maximal, complemented

#20275547

C₂

yes

maximal, complemented

#20275041

C₂

yes

maximal, complemented

#20274853

C₂

yes

maximal, characteristic, complemented

C₅₃×#1746

C₂

yes

maximal, characteristic, complemented

C₂×#13133239

C₂²

yes

—

C₂×#13133223

C₂²

yes

—

#16811173

C₂²

yes

—

#16811007

C₄

yes

complemented

#16811003

C₄

yes

characteristic, complemented

#16811000

C₄

yes

characteristic, complemented

#16810996

C₄

yes

complemented

#16810696

—

#16810647

C₂²

yes

—

C₂×#13133145

C₂²

yes

—

#16810589

C₂²

yes

—

#16810388

C₂²

yes

—

C₂×#97×C₅₃

C₂²

yes

characteristic

C₂×C₄×C₈×C₅₃

C₂²

yes

characteristic

C₅₃×#376

C₂²

yes

characteristic

C₅₃×#336

C₂²

yes

—

C₂×#11719945

C₂³

yes

—

#13133239

—

C₂×Dic₂₁₂

C₂×C₄

yes

—

C₂×#11719913

C₂×C₄

yes

—

C₂×D₄₂₄

C₂×C₄

yes

—

#13133223

—

C₂×#11719917

C₂³

yes

—

C₂×#11719912

—

C₂×C₈×D₅₃

—

#13133217

C₂×C₄

yes

—

#13133214

C₂×C₄

yes

—

#13133205

C₂×C₄

yes

—

#13133191

—

C₄×D₂₁₂

—

C₄⋊#88322

—

#13133145

—

#13133129

—

C₂²×C₈×C₅₃

C₂³

yes

—

C₂²×C₈×C₅₃

C₂³

yes

—

C₂×C₄²×C₅₃

C₂³

yes

—

C₂×C₄²×C₅₃

C₂³

yes

characteristic

#97×C₅₃

D₄

yes

—

C₄×C₈×C₅₃

C₂×C₄

yes

characteristic

C₄×C₈×C₅₃

C₂×C₄

yes

characteristic

C₄×C₈×C₅₃

C₂×C₄

yes

—

#95×C₅₃

—

C₂²×C₄×C₅₃

—

C₂²×C₄×C₅₃

#41

yes

—

C₂²×C₄×C₅₃

C₂⁴

yes

characteristic

C₂×C₂²⋊D₅₃

—

#11719945

—

#11719945

—

C₂×D₂₁₂

—

C₂×D₂₁₂

C₂²×C₄

yes

—

C₂×C₄×D₅₃

—

C₂×Dic₁₀₆

C₂²×C₄

yes

—

C₂×C₈×C₅₃

—

C₂×C₈×C₅₃

—

C₂×C₈×C₅₃

C₂²×C₄

yes

—

C₂×C₈×C₅₃

C₂²×C₄

yes

—

C₂×C₈×C₅₃

C₂×D₄

yes

—

C₄²×C₅₃

—

C₄²×C₅₃

C₂²×C₄

yes

characteristic

C₄²×C₅₃

C₂²×C₄

yes

characteristic

C₄²×C₅₃

C₂×D₄

yes

—

#11719921

—

C₄⋊Dic₅₃

—

#11719917

—

C₂×#88322

—

Dic₂₁₂

—

D₄₂₄

—

#11719913

—

#11719912

—

C₈×D₅₃

—

C₂³×C₅₃

C₂×#41

yes

characteristic

C₂²×D₅₃

—

C₂×C₄×C₅₃

—

C₂×C₄×C₅₃

—

C₂×C₄×C₅₃

—

C₂×C₄×C₅₃

C₄×D₄

yes

—

C₂×C₄×C₅₃

C₄×D₄

yes

—

C₂×C₄×C₅₃

C₂³×C₄

yes

characteristic

C₂×C₄×C₅₃

C₂²×D₄

yes

characteristic

C₂×C₄×C₅₃

H(5,𝔽₂)

yes

—

C₂²⋊D₅₃

—

C₂×Dic₅₃

—

D₂₁₂

—

D₂₁₂

—

C₄×D₅₃

—

C₄×D₅₃

—

Dic₁₀₆

—

C₈×C₅₃

—

C₈×C₅₃

—

C₈×C₅₃

—

#88322

—

#22282

—

maximal, Sylow

C₂²×C₅₃

—

100

C₂²×C₅₃

C₂×C₄×D₄

yes

characteristic

101

C₂²×C₅₃

#540

yes

—

102

C₂×D₅₃

—

103

C₂×D₅₃

—

104

C₄×C₅₃

—

105

C₄×C₅₃

—

106

C₄×C₅₃

—

107

C₄×C₅₃

#518

yes

—

108

C₄×C₅₃

#535

yes

—

109

Dic₅₃

—

110

#3147

—

111

#2932

—

112

#1963

—

113

#1876

—

114

#1837

—

115

#1746

D₅₃

yes

characteristic, complemented

116

C₂×C₅₃

—

117

C₂×C₅₃

#2328

yes

characteristic

118

C₂×C₅₃

#2957

yes

—

119

D₅₃

—

120

C₂×#135

—

121

C₂×#131

—

122

#532

—

123

#495

—

124

#494

—

125

#493

—

126

#492

—

127

#435

—

106

—

128

#423

—

129

C₂×#104

—

130

#408

—

131

C₂×#97

C₂×D₅₃

yes

characteristic

132

C₂×C₄×C₈

C₂×D₅₃

yes

characteristic

133

#376

C₂×D₅₃

yes

characteristic

134

#341

—

135

#336

C₂×D₅₃

yes

—

136

C₅₃

#22282

yes

characteristic, complemented, Sylow

137

C₂×#41

—

138

#135

—

212

—

139

C₂×Q₁₆

—

140

C₂×SD₁₆

—

141

C₂×D₈

—

142

#131

—

212

—

143

C₂×M₁₆

—

144

C₂×M₁₆

—

106

—

145

C₂²×C₈

—

106

—

146

C₂²×C₈

C₂²×D₅₃

yes

—

147

C₂²×C₈

C₂²×D₅₃

yes

—

148

C₄⋊Q₈

—

149

#127

—

150

#124

—

151

#121

—

106

—

152

C₄×D₄

—

106

—

153

C₂×C₄²

C₂²×D₅₃

yes

—

154

C₂×C₄²

C₂²×D₅₃

yes

characteristic

155

C₄⋊C₈

—

106

—

156

#104

—

212

—

157

C₂²⋊C₈

—

106

—

158

#97

D₂₁₂

yes

—

159

C₄×C₈

C₄×D₅₃

yes

characteristic

160

C₄×C₈

C₄×D₅₃

yes

characteristic

161

C₄×C₈

C₄×D₅₃

yes

—

162

#95

—

163

#41

—

106

—

164

#41

—

106

—

165

C₂×Q₈

—

166

C₂×D₄

—

167

C₂×D₄

—

106

—

168

C₂×D₄

—

106

—

169

C₂²×C₄

—

170

C₂²×C₄

—

106

—

171

C₂²×C₄

#11719945

yes

—

172

C₂²×C₄

C₂³×D₅₃

yes

characteristic

173

Q₁₆

—

212

—

174

SD₁₆

—

212

—

175

D₈

—

212

—

176

M₁₆

—

106

—

177

M₁₆

—

212

—

178

C₂×C₈

—

179

C₂×C₈

—

180

C₂×C₈

—

106

—

181

C₂×C₈

—

212

—

182

C₂×C₈

C₂×C₄×D₅₃

yes

—

183

C₂×C₈

C₂×C₄×D₅₃

yes

—

184

C₂×C₈

C₂×D₂₁₂

yes

—

185

C₄⋊C₄

—

106

—

186

C₂²⋊C₄

—

106

—

187

C₄²

—

188

C₄²

C₂×C₄×D₅₃

yes

characteristic

189

C₄²

C₂×C₄×D₅₃

yes

characteristic

190

C₄²

C₂×D₂₁₂

yes

—

191

C₂³

—

106

—

192

C₂³

C₂×#11719945

yes

characteristic

193

Q₈

—

106

—

194

D₄

—

106

—

195

D₄

—

424

—

196

D₄

—

212

—

197

C₂×C₄

—

198

C₂×C₄

—

199

C₂×C₄

—

200

C₂×C₄

—

106

—

201

C₂×C₄

—

212

—

202

C₂×C₄

—

212

—

203

C₂×C₄

C₄×D₂₁₂

yes

—

204

C₂×C₄

C₄×D₂₁₂

yes

—

205

C₂×C₄

C₂²×C₄×D₅₃

yes

characteristic

206

C₂×C₄

C₂²×D₂₁₂

yes

characteristic

207

C₂×C₄

#13133263

yes

—

208

C₈

—

209

C₈

—

210

C₈

—

211

C₈

—

212

—

212

C₂²

—

213

C₂²

—

212

—

214

C₂²

—

212

—

215

C₂²

C₂×C₄×D₂₁₂

yes

characteristic

216

C₂²

#16811228

yes

—

217

C₄

—

218

C₄

—

219

C₄

—

220

C₄

—

212

—

221

C₄

#16811097

yes

—

222

C₄

#16811192

yes

—

223

C₂

—

224

C₂

—

424

—

225

C₂

#20277440

yes

characteristic

226

C₂

#20283633

yes

—

	subgroup	G/H
center	C₂×C₄	C₂²×D₂₁₂
commutator	C₂×C₄×C₅₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₅₃
Fitting	C₅₃×#1746	C₂
socle	C₂²×C₅₃	C₂×C₄×D₄
prime radical	#20285143	C₂
cosocle	C₂²×C₄×C₅₃	C₂⁴
hypercenter	#1746	D₅₃
hypocenter	C₅₃	#22282
LCS	G ▷ C₂×C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×#97 ◁ #1746

subgroup

G/H

center

C₂×C₄

C₂²×D₂₁₂

commutator

C₂×C₄×C₅₃

C₂³×C₄

Frattini

C₂²×C₄

C₂³×D₅₃

Fitting

C₅₃×#1746

C₂

socle

C₂²×C₅₃

C₂×C₄×D₄

prime radical

#20285143

C₂

cosocle

C₂²×C₄×C₅₃

C₂⁴

D₅₃

C₅₃

G ▷ C₂×C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃

UCS

C₁ ◁ C₂×C₄ ◁ C₂×#97 ◁ #1746

N	H ≅ G/N	type
2. #20283434	C₂	semidirect
3. #20275547	C₂	semidirect
4. #20275041	C₂	semidirect
5. #20274853	C₂	semidirect
6. C₅₃×#1746	C₂	semidirect
10. #16811007	C₄	semidirect
11. #16811003	C₄	semidirect
12. #16811000	C₄	semidirect
13. #16810996	C₄	semidirect
115. #1746	D₅₃	semidirect
136. C₅₃	#22282	semidirect

H ≅ G/N

type

2. #20283434

C₂

semidirect

3. #20275547

C₂

semidirect

4. #20275041

C₂

semidirect

5. #20274853

C₂

semidirect

6. C₅₃×#1746

C₂

semidirect

10. #16811007

C₄

semidirect

11. #16811003

C₄

semidirect

12. #16811000

C₄

semidirect

13. #16810996

C₄

semidirect

115. #1746

D₅₃

semidirect

136. C₅₃

#22282

semidirect

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

subgroup	index
#20285143	2
#20283434	2
#20275547	2
#20275041	2
#20274853	2
C₅₃×#1746	2
#22282	53

subgroup

index

C₅₃×#1746

Subgroups — #27397982

Conjugacy classes of subgroups

Complements

Maximal subgroups