Group #27283992 — subgroups

Subgroups — #27283992

Order 13568.

422 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 422 conjugacy classes of subgroups — too many to draw. Only its 131 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	#20285301	C₂	1	1	yes	maximal, characteristic
2	#20275692	C₂	1	2	yes	maximal
3	#20273474	C₂	1	1	yes	maximal, characteristic
4	#20273171	C₂	1	2	yes	maximal
5	C₅₃×#1744	C₂	1	1	yes	maximal, characteristic
6	#16811180	C₂²	1	2	yes	—
7	#16811028	C₄	1	1	yes	characteristic, complemented
8	#16811003	C₄	1	1	yes	characteristic, complemented
9	#16810974	C₄	1	2	yes	complemented
10	#16810864	—	2	2	no	—
11	C₄×Dic₂₁₂	—	2	2	no	—
12	#16810647	C₂²	1	2	yes	—
13	#16810383	—	2	4	no	—
14	#16810376	—	2	2	no	—
15	#16810355	—	2	4	no	—
16	C₂×C₄×C₈×C₅₃	C₂²	1	1	yes	characteristic
17	C₂×C₄×C₈×C₅₃	C₂²	1	1	yes	characteristic
18	C₄³×C₅₃	C₂²	1	1	yes	characteristic
19	C₅₃×#336	—	2	2	no	—
20	C₂×Dic₂₁₂	—	2	2	no	—
21	C₂×#11719917	—	2	2	no	—
22	#13133217	C₂×C₄	1	2	yes	—
23	#13133217	C₂×C₄	1	2	yes	—
24	#13133209	—	2	2	no	—
25	#13133196	—	2	2	no	—
26	#13133196	—	2	2	no	—
27	C₄×Dic₁₀₆	—	2	2	no	—
28	C₄×Dic₁₀₆	—	2	2	no	—
29	#13133176	—	2	2	no	—
30	#13133151	—	2	2	no	—
31	C₄⋊#88322	—	2	2	no	—
32	C₄⋊#88322	—	2	2	no	—
33	#13133142	—	2	4	no	—
34	C₂²×C₈×C₅₃	—	2	1	no	—
35	C₂²×C₈×C₅₃	D₄	1	2	yes	—
36	C₂×C₄²×C₅₃	—	2	1	no	—
37	C₂×C₄²×C₅₃	—	2	1	no	—
38	C₂×C₄²×C₅₃	D₄	1	2	yes	—
39	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
40	C₄×C₈×C₅₃	—	2	1	no	—
41	C₄×C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
42	C₄×C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
43	C₄×C₈×C₅₃	D₄	1	2	yes	—
44	C₄×C₈×C₅₃	D₄	1	2	yes	—
45	C₂²×C₄×C₅₃	—	2	2	no	—
46	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
47	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
48	C₂²×C₄×C₅₃	#41	1	1	yes	characteristic
49	C₂×Dic₁₀₆	—	2	2	no	—
50	C₂×Dic₁₀₆	—	2	2	no	—
51	C₂×C₈×C₅₃	—	2	2	no	—
52	C₂×C₈×C₅₃	—	4	2	no	—
53	C₂×C₈×C₅₃	—	4	2	no	—
54	C₂×C₈×C₅₃	C₂²⋊C₄	1	2	yes	—
55	C₂×C₈×C₅₃	C₂²⋊C₄	1	2	yes	—
56	C₄²×C₅₃	—	2	2	no	—
57	C₄²×C₅₃	—	4	2	no	—
58	C₄²×C₅₃	—	4	2	no	—
59	C₄²×C₅₃	Q₁₆	1	4	yes	complemented
60	C₄²×C₅₃	C₂²×C₄	1	1	yes	characteristic
61	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
62	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
63	C₄²×C₅₃	#41	1	1	yes	characteristic
64	C₂²⋊Dic₅₃	—	4	2	no	—
65	C₄⋊Dic₅₃	—	2	2	no	—
66	C₄⋊Dic₅₃	—	2	2	no	—
67	C₄⋊Dic₅₃	—	2	2	no	—
68	C₄⋊Dic₅₃	—	2	2	no	—
69	#11719919	—	4	2	no	—
70	#11719919	—	4	2	no	—
71	C₄×Dic₅₃	—	4	2	no	—
72	#11719917	—	4	4	no	—
73	C₂×#88322	—	4	2	no	—
74	Dic₂₁₂	—	4	4	no	—
75	C₂³×C₅₃	#121	1	1	yes	characteristic
76	C₂×C₄×C₅₃	—	2	2	no	—
77	C₂×C₄×C₅₃	—	2	2	no	—
78	C₂×C₄×C₅₃	—	2	4	no	—
79	C₂×C₄×C₅₃	—	4	2	no	—
80	C₂×C₄×C₅₃	—	4	2	no	—
81	C₂×C₄×C₅₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
82	C₂×C₄×C₅₃	C₄×D₄	1	1	yes	characteristic
83	C₂×C₄×C₅₃	C₄×D₄	1	1	yes	characteristic
84	C₂×C₄×C₅₃	#121	1	1	yes	characteristic
85	C₂×C₄×C₅₃	#124	1	1	yes	characteristic
86	C₂×C₄×C₅₃	#127	1	1	yes	characteristic
87	C₂×C₄×C₅₃	C₂×Q₁₆	1	2	yes	—
88	C₂×C₄×C₅₃	#135	1	2	yes	—
89	C₂×Dic₅₃	—	4	2	no	—
90	C₂×Dic₅₃	—	4	2	no	—
91	Dic₁₀₆	—	4	4	no	—
92	Dic₁₀₆	—	4	4	no	—
93	C₈×C₅₃	—	2	2	no	—
94	C₈×C₅₃	—	2	2	no	—
95	C₈×C₅₃	—	4	2	no	—
96	#88322	—	8	2	no	—
97	#9848	—	53	1	no	maximal, Sylow
98	C₂²×C₅₃	—	2	1	no	—
99	C₂²×C₅₃	—	2	1	no	—
100	C₂²×C₅₃	#390	1	1	yes	characteristic
101	C₂²×C₅₃	#467	1	2	yes	—
102	C₄×C₅₃	—	2	1	no	—
103	C₄×C₅₃	—	2	1	no	—
104	C₄×C₅₃	—	4	4	no	—
105	C₄×C₅₃	#421	1	2	yes	—
106	C₄×C₅₃	C₄×Q₁₆	1	2	yes	—
107	C₄×C₅₃	#444	1	2	yes	—
108	C₄×C₅₃	#494	1	1	yes	characteristic
109	C₄×C₅₃	#495	1	1	yes	characteristic
110	Dic₅₃	—	8	2	no	—
111	Dic₅₃	—	8	2	no	—
112	#3170	—	53	1	no	—
113	#1994	—	53	2	no	—
114	#1744	D₅₃	1	1	yes	characteristic
115	#1567	—	53	1	no	—
116	#1493	—	53	2	no	—
117	C₂×C₅₃	—	2	2	no	—
118	C₂×C₅₃	#1963	1	1	yes	characteristic
119	C₂×C₅₃	#1969	1	1	yes	characteristic
120	C₂×C₅₃	#1975	1	1	yes	characteristic
121	#533	—	53	2	no	—
122	#500	—	53	1	no	—
123	#494	—	53	1	no	—
124	#487	—	53	2	no	—
125	#467	—	106	2	no	—
126	C₄×Q₁₆	—	106	2	no	—
127	#423	—	53	2	no	—
128	C₂×C₄×C₈	C₂×D₅₃	1	1	yes	characteristic
129	C₂×C₄×C₈	C₂×D₅₃	1	1	yes	characteristic
130	C₄³	C₂×D₅₃	1	1	yes	characteristic
131	#339	—	106	4	no	—
132	#336	—	2	2	no	—
133	#335	—	106	2	no	—
134	Q₈⋊C₈	—	106	4	no	—
135	C₅₃	#9848	1	1	yes	characteristic, complemented, Sylow
136	C₂×Q₁₆	—	106	2	no	—
137	C₂×M₁₆	—	106	2	no	—
138	C₂²×C₈	—	2	1	no	—
139	C₂²×C₈	C₂²⋊D₅₃	1	2	yes	—
140	C₄⋊Q₈	—	53	2	no	—
141	C₄⋊Q₈	—	53	2	no	—
142	#125	—	106	2	no	—
143	C₂²⋊Q₈	—	106	2	no	—
144	C₂²⋊Q₈	—	106	2	no	—
145	C₄×Q₈	—	106	2	no	—
146	C₄×Q₈	—	106	2	no	—
147	#117	—	106	2	no	—
148	C₂×C₄²	—	2	1	no	—
149	C₂×C₄²	—	2	1	no	—
150	C₂×C₄²	D₂₁₂	1	2	yes	—
151	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
152	#107	—	106	2	no	—
153	C₄⋊C₈	—	106	2	no	—
154	C₄⋊C₈	—	106	2	no	—
155	#103	—	106	4	no	—
156	C₄×C₈	—	2	1	no	—
157	C₄×C₈	C₄×D₅₃	1	1	yes	characteristic
158	C₄×C₈	C₄×D₅₃	1	1	yes	characteristic
159	C₄×C₈	D₂₁₂	1	2	yes	—
160	C₄×C₈	D₂₁₂	1	2	yes	—
161	C₂×Q₈	—	106	2	no	—
162	C₂×Q₈	—	106	2	no	—
163	C₂²×C₄	—	2	2	no	—
164	C₂²×C₄	C₂×D₂₁₂	1	1	yes	characteristic
165	C₂²×C₄	#11719945	1	1	yes	characteristic
166	C₂²×C₄	C₂×C₂²⋊D₅₃	1	1	yes	characteristic
167	Q₁₆	—	212	4	no	—
168	M₁₆	—	212	4	no	—
169	C₂×C₈	—	2	2	no	—
170	C₂×C₈	—	4	2	no	—
171	C₂×C₈	—	4	2	no	—
172	C₂×C₈	—	212	2	no	—
173	C₂×C₈	#11719921	1	2	yes	—
174	C₂×C₈	#11719921	1	2	yes	—
175	C₄⋊C₄	—	106	2	no	—
176	C₄⋊C₄	—	106	2	no	—
177	C₄⋊C₄	—	106	2	no	—
178	C₄⋊C₄	—	106	2	no	—
179	C₄⋊C₄	—	212	2	no	—
180	C₄⋊C₄	—	212	2	no	—
181	C₂²⋊C₄	—	212	2	no	—
182	C₄²	—	2	2	no	—
183	C₄²	—	4	2	no	—
184	C₄²	—	4	2	no	—
185	C₄²	—	212	2	no	—
186	C₄²	Dic₂₁₂	1	4	yes	complemented
187	C₄²	C₂×C₄×D₅₃	1	1	yes	characteristic
188	C₄²	C₂×D₂₁₂	1	1	yes	characteristic
189	C₄²	C₂×D₂₁₂	1	1	yes	characteristic
190	C₄²	#11719945	1	1	yes	characteristic
191	C₂³	#13133191	1	1	yes	characteristic
192	Q₈	—	212	4	no	—
193	Q₈	—	212	4	no	—
194	C₂×C₄	—	2	2	no	—
195	C₂×C₄	—	2	2	no	—
196	C₂×C₄	—	2	4	no	—
197	C₂×C₄	—	4	2	no	—
198	C₂×C₄	—	4	2	no	—
199	C₂×C₄	—	212	2	no	—
200	C₂×C₄	—	212	2	no	—
201	C₂×C₄	C₂×#11719921	1	1	yes	characteristic
202	C₂×C₄	C₄×D₂₁₂	1	1	yes	characteristic
203	C₂×C₄	C₄×D₂₁₂	1	1	yes	characteristic
204	C₂×C₄	#13133191	1	1	yes	characteristic
205	C₂×C₄	#13133205	1	1	yes	characteristic
206	C₂×C₄	#13133214	1	1	yes	characteristic
207	C₂×C₄	C₂×Dic₂₁₂	1	2	yes	—
208	C₂×C₄	#13133239	1	2	yes	—
209	C₈	—	2	2	no	—
210	C₈	—	2	2	no	—
211	C₈	—	4	2	no	—
212	C₈	—	424	2	no	—
213	C₂²	—	2	1	no	—
214	C₂²	—	2	1	no	—
215	C₂²	#16810525	1	1	yes	characteristic
216	C₂²	#16810864	1	2	yes	—
217	C₄	—	2	1	no	—
218	C₄	—	2	1	no	—
219	C₄	—	4	4	no	—
220	C₄	—	424	2	no	—
221	C₄	—	424	2	no	—
222	C₄	#16810641	1	2	yes	—
223	C₄	C₄×Dic₂₁₂	1	2	yes	—
224	C₄	#16810746	1	2	yes	—
225	C₄	#16811003	1	1	yes	characteristic
226	C₄	#16811007	1	1	yes	characteristic
227	C₂	—	2	2	no	—
228	C₂	#20275547	1	1	yes	characteristic
229	C₂	#20275576	1	1	yes	characteristic
230	C₂	#20275608	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#20285301

C₂

yes

maximal, characteristic

#20275692

C₂

yes

maximal

#20273474

C₂

yes

maximal, characteristic

#20273171

C₂

yes

maximal

C₅₃×#1744

C₂

yes

maximal, characteristic

#16811180

C₂²

yes

—

#16811028

C₄

yes

characteristic, complemented

#16811003

C₄

yes

characteristic, complemented

#16810974

C₄

yes

complemented

#16810864

—

C₄×Dic₂₁₂

—

#16810647

C₂²

yes

—

#16810383

—

#16810376

—

#16810355

—

C₂×C₄×C₈×C₅₃

C₂²

yes

characteristic

C₂×C₄×C₈×C₅₃

C₂²

yes

characteristic

C₄³×C₅₃

C₂²

yes

characteristic

C₅₃×#336

—

C₂×Dic₂₁₂

—

C₂×#11719917

—

#13133217

C₂×C₄

yes

—

#13133217

C₂×C₄

yes

—

#13133209

—

#13133196

—

#13133196

—

C₄×Dic₁₀₆

—

C₄×Dic₁₀₆

—

—

—

—

—

—

C₂²×C₈×C₅₃

—

C₂²×C₈×C₅₃

D₄

yes

—

C₂×C₄²×C₅₃

—

C₂×C₄²×C₅₃

—

C₂×C₄²×C₅₃

D₄

yes

—

C₂×C₄²×C₅₃

C₂³

yes

characteristic

C₄×C₈×C₅₃

—

C₄×C₈×C₅₃

C₂×C₄

yes

characteristic

C₄×C₈×C₅₃

C₂×C₄

yes

characteristic

C₄×C₈×C₅₃

D₄

yes

—

C₄×C₈×C₅₃

D₄

yes

—

C₂²×C₄×C₅₃

—

C₂²×C₄×C₅₃

C₂×D₄

yes

characteristic

C₂²×C₄×C₅₃

C₂×D₄

yes

characteristic

C₂²×C₄×C₅₃

#41

yes

characteristic

C₂×Dic₁₀₆

—

C₂×Dic₁₀₆

—

C₂×C₈×C₅₃

—

C₂×C₈×C₅₃

—

C₂×C₈×C₅₃

—

C₂×C₈×C₅₃

C₂²⋊C₄

yes

—

C₂×C₈×C₅₃

C₂²⋊C₄

yes

—

C₄²×C₅₃

—

C₄²×C₅₃

—

C₄²×C₅₃

—

C₄²×C₅₃

Q₁₆

yes

complemented

C₄²×C₅₃

C₂²×C₄

yes

characteristic

C₄²×C₅₃

C₂×D₄

yes

characteristic

C₄²×C₅₃

C₂×D₄

yes

characteristic

C₄²×C₅₃

#41

yes

characteristic

C₂²⋊Dic₅₃

—

C₄⋊Dic₅₃

—

C₄⋊Dic₅₃

—

C₄⋊Dic₅₃

—

C₄⋊Dic₅₃

—

#11719919

—

#11719919

—

C₄×Dic₅₃

—

#11719917

—

C₂×#88322

—

Dic₂₁₂

—

C₂³×C₅₃

#121

yes

characteristic

C₂×C₄×C₅₃

—

C₂×C₄×C₅₃

—

C₂×C₄×C₅₃

—

C₂×C₄×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

C₂×C₄×C₅₃

yes

C₂×C₄×C₅₃

yes

C₂×C₄×C₅₃

yes

C₂×C₄×C₅₃

C₂×Q₁₆

yes

—

C₂×C₄×C₅₃

#135

yes

—

C₂×Dic₅₃

—

C₂×Dic₅₃

—

Dic₁₀₆

—

Dic₁₀₆

—

C₈×C₅₃

—

C₈×C₅₃

—

C₈×C₅₃

—

#88322

—

#9848

—

maximal, Sylow

C₂²×C₅₃

—

C₂²×C₅₃

—

100

C₂²×C₅₃

#390

yes

characteristic

101

C₂²×C₅₃

#467

yes

—

102

C₄×C₅₃

—

103

C₄×C₅₃

—

104

C₄×C₅₃

—

105

C₄×C₅₃

#421

yes

—

106

C₄×C₅₃

C₄×Q₁₆

yes

—

107

C₄×C₅₃

#444

yes

—

108

C₄×C₅₃

#494

yes

characteristic

109

C₄×C₅₃

#495

yes

characteristic

110

Dic₅₃

—

111

Dic₅₃

—

112

#3170

—

113

#1994

—

114

#1744

D₅₃

yes

characteristic

115

#1567

—

116

#1493

—

117

C₂×C₅₃

—

118

C₂×C₅₃

#1963

yes

characteristic

119

C₂×C₅₃

#1969

yes

characteristic

120

C₂×C₅₃

#1975

yes

characteristic

121

#533

—

122

#500

—

123

#494

—

124

#487

—

125

#467

—

106

—

126

C₄×Q₁₆

—

106

—

127

#423

—

128

C₂×C₄×C₈

C₂×D₅₃

yes

characteristic

129

C₂×C₄×C₈

C₂×D₅₃

yes

characteristic

130

C₄³

C₂×D₅₃

yes

characteristic

131

#339

—

106

—

132

#336

—

133

#335

—

106

—

134

Q₈⋊C₈

—

106

—

135

C₅₃

#9848

yes

characteristic, complemented, Sylow

136

C₂×Q₁₆

—

106

—

137

C₂×M₁₆

—

106

—

138

C₂²×C₈

—

139

C₂²×C₈

C₂²⋊D₅₃

yes

—

140

C₄⋊Q₈

—

141

C₄⋊Q₈

—

142

#125

—

106

—

143

C₂²⋊Q₈

—

106

—

144

C₂²⋊Q₈

—

106

—

145

C₄×Q₈

—

106

—

146

C₄×Q₈

—

106

—

147

#117

—

106

—

148

C₂×C₄²

—

149

C₂×C₄²

—

150

C₂×C₄²

D₂₁₂

yes

—

151

C₂×C₄²

C₂²×D₅₃

yes

characteristic

152

#107

—

106

—

153

C₄⋊C₈

—

106

—

154

C₄⋊C₈

—

106

—

155

#103

—

106

—

156

C₄×C₈

—

157

C₄×C₈

C₄×D₅₃

yes

characteristic

158

C₄×C₈

C₄×D₅₃

yes

characteristic

159

C₄×C₈

D₂₁₂

yes

—

160

C₄×C₈

D₂₁₂

yes

—

161

C₂×Q₈

—

106

—

162

C₂×Q₈

—

106

—

163

C₂²×C₄

—

164

C₂²×C₄

C₂×D₂₁₂

yes

characteristic

165

C₂²×C₄

#11719945

yes

characteristic

166

C₂²×C₄

C₂×C₂²⋊D₅₃

yes

characteristic

167

Q₁₆

—

212

—

168

M₁₆

—

212

—

169

C₂×C₈

—

170

C₂×C₈

—

171

C₂×C₈

—

172

C₂×C₈

—

212

—

173

C₂×C₈

#11719921

yes

—

174

C₂×C₈

#11719921

yes

—

175

C₄⋊C₄

—

106

—

176

C₄⋊C₄

—

106

—

177

C₄⋊C₄

—

106

—

178

C₄⋊C₄

—

106

—

179

C₄⋊C₄

—

212

—

180

C₄⋊C₄

—

212

—

181

C₂²⋊C₄

—

212

—

182

C₄²

—

183

C₄²

—

184

C₄²

—

185

C₄²

—

212

—

186

C₄²

Dic₂₁₂

yes

complemented

187

C₄²

C₂×C₄×D₅₃

yes

characteristic

188

C₄²

C₂×D₂₁₂

yes

characteristic

189

C₄²

C₂×D₂₁₂

yes

characteristic

190

C₄²

#11719945

yes

characteristic

191

C₂³

#13133191

yes

characteristic

192

Q₈

—

212

—

193

Q₈

—

212

—

194

C₂×C₄

—

195

C₂×C₄

—

196

C₂×C₄

—

197

C₂×C₄

—

198

C₂×C₄

—

199

C₂×C₄

—

212

—

200

C₂×C₄

—

212

—

201

C₂×C₄

C₂×#11719921

yes

characteristic

202

C₂×C₄

C₄×D₂₁₂

yes

characteristic

203

C₂×C₄

C₄×D₂₁₂

yes

characteristic

204

C₂×C₄

#13133191

yes

characteristic

205

C₂×C₄

#13133205

yes

characteristic

206

C₂×C₄

#13133214

yes

characteristic

207

C₂×C₄

C₂×Dic₂₁₂

yes

—

208

C₂×C₄

#13133239

yes

—

209

C₈

—

210

C₈

—

211

C₈

—

212

C₈

—

424

—

213

C₂²

—

214

C₂²

—

215

C₂²

#16810525

yes

characteristic

216

C₂²

#16810864

yes

—

217

C₄

—

218

C₄

—

219

C₄

—

220

C₄

—

424

—

221

C₄

—

424

—

222

C₄

#16810641

yes

—

223

C₄

C₄×Dic₂₁₂

yes

—

224

C₄

#16810746

yes

—

225

C₄

#16811003

yes

characteristic

226

C₄

#16811007

yes

characteristic

227

C₂

—

228

C₂

#20275547

yes

characteristic

229

C₂

#20275576

yes

characteristic

230

C₂

#20275608

yes

characteristic

	subgroup	G/H
center	C₂×C₄	#13133214
commutator	C₄²×C₅₃	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₅₃
Fitting	C₅₃×#1744	C₂
socle	C₂²×C₅₃	#390
prime radical	C₂³×C₅₃	#121
cosocle	C₂×C₄²×C₅₃	C₂³
hypercenter	#1744	D₅₃
hypocenter	C₅₃	#9848
LCS	G ▷ C₄²×C₅₃ ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1744

subgroup

G/H

center

C₂×C₄

#13133214

commutator

C₄²×C₅₃

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₅₃

Fitting

C₅₃×#1744

C₂

C₂²×C₅₃

C₂³×C₅₃

C₂×C₄²×C₅₃

C₂³

D₅₃

C₅₃

G ▷ C₄²×C₅₃ ▷ C₂²×C₅₃ ▷ C₅₃

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1744

N	H ≅ G/N	type
7. #16811028	C₄	semidirect
8. #16811003	C₄	semidirect
9. #16810974	C₄	semidirect
59. C₄²×C₅₃	Q₁₆	semidirect
135. C₅₃	#9848	semidirect
186. C₄²	Dic₂₁₂	semidirect

H ≅ G/N

type

7. #16811028

C₄

semidirect

8. #16811003

C₄

semidirect

9. #16810974

C₄

semidirect

59. C₄²×C₅₃

Q₁₆

semidirect

135. C₅₃

#9848

semidirect

186. C₄²

Dic₂₁₂

semidirect

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

subgroup	index
#20285301	2
#20275692	2
#20273474	2
#20273171	2
C₅₃×#1744	2
#9848	53

subgroup

index

C₅₃×#1744

Subgroups — #27283992

Conjugacy classes of subgroups

Complements

Maximal subgroups