Group #27537395 — subgroups

Subgroups — C₂×#20276591 #27537395

Order 13568.

798 conjugacy classes of subgroups; only the 267 normal subgroups are shown.

normal subgroups only

This group has 798 conjugacy classes of subgroups — too many to draw. Only its 267 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×D₈×Dic₅₃	C₂	1	2	yes	maximal, complemented
2	#20276591	C₂	1	8	yes	maximal, direct product factor
3	C₂×#16810451	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#16810424	C₂	1	2	yes	maximal, complemented
5	C₂×#16810398	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×D₁₆×C₅₃	C₂	1	1	yes	maximal, characteristic
7	C₂×D₄×Dic₅₃	—	2	2	no	—
8	C₂²×#11719908	C₂²	1	1	yes	characteristic
9	D₈×Dic₅₃	—	2	4	no	—
10	D₈×Dic₅₃	C₂²	1	8	yes	complemented
11	C₂×#13133151	C₂²	1	2	yes	—
12	C₂×#13133138	—	2	2	no	—
13	C₂×C₈×Dic₅₃	C₂²	1	1	yes	characteristic
14	#16810451	C₂²	1	4	yes	complemented
15	#16810424	C₂²	1	8	yes	complemented
16	#16810398	C₂²	1	4	yes	complemented
17	C₂²×D₈×C₅₃	C₂²	1	2	yes	—
18	C₂×D₁₆×C₅₃	C₄	1	8	yes	complemented
19	C₂×D₁₆×C₅₃	C₂²	1	4	yes	—
20	C₂²×C₁₆×C₅₃	C₂²	1	1	yes	characteristic
21	C₂³×Dic₅₃	—	4	2	no	—
22	C₂²×#88322	D₄	1	1	yes	characteristic
23	D₄×Dic₅₃	—	2	8	no	—
24	D₄×Dic₅₃	—	4	4	no	—
25	C₂×C₄⋊Dic₅₃	—	2	2	no	—
26	C₂×C₂²⋊Dic₅₃	—	4	2	no	—
27	C₂×C₄×Dic₅₃	D₄	1	1	yes	characteristic
28	C₂×#11719908	—	2	2	no	—
29	C₂×#11719908	C₂³	1	2	yes	—
30	#13133151	—	2	2	no	—
31	#13133151	C₂³	1	4	yes	—
32	#13133138	—	2	8	no	—
33	C₈×Dic₅₃	D₄	1	2	yes	—
34	C₈×Dic₅₃	C₂³	1	2	yes	—
35	C₂²×D₄×C₅₃	—	2	2	no	—
36	C₂×D₈×C₅₃	—	2	2	no	—
37	C₂×D₈×C₅₃	—	2	4	no	—
38	C₂×D₈×C₅₃	C₂×C₄	1	8	yes	complemented
39	C₂×D₈×C₅₃	C₂³	1	4	yes	—
40	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
41	D₁₆×C₅₃	C₂×C₄	1	16	yes	complemented
42	C₂×C₁₆×C₅₃	C₂×C₄	1	4	yes	complemented
43	C₂×C₁₆×C₅₃	C₂³	1	2	yes	—
44	C₂⁴×C₅₃	—	4	2	no	—
45	C₂×D₄×C₅₃	—	2	8	no	—
46	C₂×D₄×C₅₃	—	2	4	no	—
47	C₂×D₄×C₅₃	—	4	2	no	—
48	C₂×D₄×C₅₃	—	4	4	no	—
49	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
50	C₂²×Dic₅₃	—	4	2	no	—
51	C₂²×Dic₅₃	—	4	8	no	—
52	C₂²×Dic₅₃	—	8	8	no	—
53	C₂²×Dic₅₃	D₈	1	2	yes	—
54	D₈×C₅₃	—	2	8	no	—
55	D₈×C₅₃	—	2	4	no	—
56	D₈×C₅₃	C₂²×C₄	1	8	yes	complemented
57	C₂×C₈×C₅₃	C₂²×C₄	1	2	yes	—
58	C₂×C₈×C₅₃	C₂×D₄	1	1	yes	characteristic
59	C₂×C₈×C₅₃	#41	1	2	yes	—
60	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
61	C₂²⋊Dic₅₃	—	4	8	no	—
62	C₄⋊Dic₅₃	—	2	4	no	—
63	C₄⋊Dic₅₃	—	4	2	no	—
64	C₄×Dic₅₃	D₈	1	2	yes	—
65	C₄×Dic₅₃	C₂×D₄	1	2	yes	—
66	C₂×#88322	—	2	2	no	—
67	C₂×#88322	C₂×D₄	1	2	yes	—
68	C₁₆×C₅₃	C₂²×C₄	1	4	yes	complemented
69	#11719908	—	2	2	no	—
70	C₂³×C₅₃	—	4	4	no	—
71	C₂³×C₅₃	—	4	8	no	—
72	C₂³×C₅₃	—	8	4	no	—
73	C₂³×C₅₃	—	8	4	no	—
74	C₂³×C₅₃	C₂×D₈	1	1	yes	characteristic
75	D₄×C₅₃	—	2	8	no	—
76	D₄×C₅₃	—	4	4	no	—
77	D₄×C₅₃	—	4	8	no	—
78	C₂×C₄×C₅₃	C₄×D₄	1	2	yes	—
79	C₂×C₄×C₅₃	C₂×D₈	1	1	yes	characteristic
80	C₂×C₄×C₅₃	#135	1	2	yes	—
81	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
82	C₂×Dic₅₃	—	2	4	no	—
83	C₂×Dic₅₃	—	4	4	no	—
84	C₂×Dic₅₃	—	8	16	no	—
85	C₂×Dic₅₃	—	8	4	no	—
86	C₂×Dic₅₃	C₂×D₈	1	4	yes	—
87	C₈×C₅₃	C₄×D₄	1	2	yes	—
88	C₈×C₅₃	C₂³×C₄	1	1	yes	characteristic
89	C₈×C₅₃	C₂×#41	1	1	yes	characteristic
90	#88322	—	2	2	no	—
91	C₂×#2177	—	53	1	no	maximal, Sylow
92	C₂²×C₅₃	—	4	8	no	—
93	C₂²×C₅₃	—	8	4	no	—
94	C₂²×C₅₃	—	8	4	no	—
95	C₂²×C₅₃	—	8	16	no	—
96	C₂²×C₅₃	C₄×D₈	1	2	yes	—
97	C₂²×C₅₃	#509	1	4	yes	—
98	C₂²×C₅₃	C₂²×D₈	1	1	yes	characteristic
99	C₄×C₅₃	C₄×D₈	1	2	yes	—
100	C₄×C₅₃	C₂×C₄×D₄	1	1	yes	characteristic
101	C₄×C₅₃	C₂×#135	1	1	yes	characteristic
102	Dic₅₃	—	2	4	no	—
103	Dic₅₃	—	8	4	no	—
104	C₂²×D₁₆	D₅₃	1	1	yes	characteristic
105	C₂×C₄×D₈	—	53	2	no	—
106	#2177	—	53	8	no	—
107	C₂×#367	—	53	1	no	—
108	C₂×#357	—	53	2	no	—
109	C₂×#346	—	53	1	no	—
110	C₂×C₅₃	—	8	8	no	—
111	C₂×C₅₃	#2177	1	4	yes	complemented
112	C₂×C₅₃	C₂×C₄×D₈	1	1	yes	characteristic
113	C₂×C₅₃	C₂×#509	1	2	yes	—
114	C₂²×D₈	C₂×D₅₃	1	2	yes	—
115	C₂×C₄×D₄	—	106	2	no	—
116	C₂×D₁₆	Dic₅₃	1	8	yes	complemented
117	C₂×D₁₆	C₂×D₅₃	1	4	yes	—
118	C₂²×C₁₆	—	53	1	no	—
119	C₂²×C₁₆	C₂×D₅₃	1	1	yes	characteristic
120	C₄×D₈	—	53	8	no	—
121	C₄×D₈	—	106	4	no	—
122	C₂×#107	—	53	2	no	—
123	C₂×#102	—	106	2	no	—
124	C₂×C₄×C₈	—	53	1	no	—
125	#367	—	53	4	no	—
126	#357	—	53	8	no	—
127	#346	—	53	4	no	—
128	C₅₃	C₂×#2177	1	1	yes	characteristic, complemented, Sylow
129	C₂²×D₄	—	2	2	no	—
130	C₂³×C₄	—	212	2	no	—
131	C₂×D₈	—	2	2	no	—
132	C₂×D₈	—	2	4	no	—
133	C₂×D₈	C₂×Dic₅₃	1	8	yes	complemented
134	C₂×D₈	C₂²×D₅₃	1	4	yes	—
135	C₂²×C₈	—	53	1	no	—
136	C₂²×C₈	C₂²×D₅₃	1	1	yes	characteristic
137	C₄×D₄	—	106	8	no	—
138	C₄×D₄	—	212	4	no	—
139	C₂×C₄⋊C₄	—	106	2	no	—
140	C₂×C₂²⋊C₄	—	212	2	no	—
141	C₂×C₄²	—	53	1	no	—
142	D₁₆	C₂×Dic₅₃	1	16	yes	complemented
143	C₂×C₁₆	—	53	2	no	—
144	C₂×C₁₆	—	106	2	no	—
145	C₂×C₁₆	C₂×Dic₅₃	1	4	yes	complemented
146	C₂×C₁₆	C₂²×D₅₃	1	2	yes	—
147	#107	—	53	4	no	—
148	#107	—	106	2	no	—
149	#102	—	106	8	no	—
150	C₄×C₈	—	53	2	no	—
151	C₄×C₈	—	53	2	no	—
152	C₂⁴	—	4	2	no	—
153	C₂×D₄	—	2	8	no	—
154	C₂×D₄	—	2	4	no	—
155	C₂×D₄	—	4	2	no	—
156	C₂×D₄	—	4	4	no	—
157	C₂²×C₄	—	53	2	no	—
158	C₂²×C₄	—	424	8	no	—
159	C₂²×C₄	—	212	8	no	—
160	C₂²×C₄	—	212	2	no	—
161	C₂²×C₄	D₄×D₅₃	1	1	yes	characteristic
162	D₈	—	2	8	no	—
163	D₈	—	2	4	no	—
164	D₈	C₂²×Dic₅₃	1	8	yes	complemented
165	C₂×C₈	—	53	2	no	—
166	C₂×C₈	—	106	2	no	—
167	C₂×C₈	D₄×D₅₃	1	1	yes	characteristic
168	C₂×C₈	#11719947	1	2	yes	—
169	C₂×C₈	C₂²×Dic₅₃	1	2	yes	—
170	C₂×C₈	C₂³×D₅₃	1	1	yes	characteristic
171	C₄⋊C₄	—	106	4	no	—
172	C₄⋊C₄	—	212	2	no	—
173	C₂²⋊C₄	—	212	8	no	—
174	C₄²	—	53	2	no	—
175	C₄²	—	53	2	no	—
176	C₁₆	—	106	2	no	—
177	C₁₆	C₂²×Dic₅₃	1	4	yes	complemented
178	C₂³	—	4	4	no	—
179	C₂³	—	4	8	no	—
180	C₂³	—	8	4	no	—
181	C₂³	—	8	4	no	—
182	C₂³	D₈×D₅₃	1	1	yes	characteristic
183	D₄	—	2	8	no	—
184	D₄	—	4	4	no	—
185	D₄	—	4	8	no	—
186	C₂×C₄	—	53	4	no	—
187	C₂×C₄	—	106	4	no	—
188	C₂×C₄	—	424	16	no	—
189	C₂×C₄	—	424	4	no	—
190	C₂×C₄	—	212	4	no	—
191	C₂×C₄	D₄×Dic₅₃	1	2	yes	—
192	C₂×C₄	D₈×D₅₃	1	1	yes	characteristic
193	C₂×C₄	#13133236	1	2	yes	—
194	C₂×C₄	C₂×D₄×D₅₃	1	1	yes	characteristic
195	C₈	—	106	2	no	—
196	C₈	D₄×Dic₅₃	1	2	yes	—
197	C₈	C₂³×Dic₅₃	1	1	yes	characteristic
198	C₈	C₂×#11719947	1	1	yes	characteristic
199	C₂²	—	4	8	no	—
200	C₂²	—	8	4	no	—
201	C₂²	—	8	4	no	—
202	C₂²	—	8	16	no	—
203	C₂²	D₈×Dic₅₃	1	2	yes	—
204	C₂²	#16811057	1	4	yes	—
205	C₂²	C₂×D₈×D₅₃	1	1	yes	characteristic
206	C₄	—	106	4	no	—
207	C₄	—	424	4	no	—
208	C₄	D₈×Dic₅₃	1	2	yes	—
209	C₄	C₂×D₄×Dic₅₃	1	1	yes	characteristic
210	C₄	C₂×#13133236	1	1	yes	characteristic
211	C₂	—	8	8	no	—
212	C₂	#20276591	1	4	yes	direct product factor
213	C₂	C₂×D₈×Dic₅₃	1	1	yes	characteristic
214	C₂	C₂×#16811057	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×D₈×Dic₅₃

C₂

yes

maximal, complemented

#20276591

C₂

yes

maximal, direct product factor

C₂×#16810451

C₂

yes

maximal, characteristic, complemented

C₂×#16810424

C₂

yes

maximal, complemented

C₂×#16810398

C₂

yes

maximal, characteristic, complemented

C₂²×D₁₆×C₅₃

C₂

yes

maximal, characteristic

C₂×D₄×Dic₅₃

—

C₂²×#11719908

C₂²

yes

characteristic

D₈×Dic₅₃

—

D₈×Dic₅₃

C₂²

yes

complemented

C₂×#13133151

C₂²

yes

—

C₂×#13133138

—

C₂×C₈×Dic₅₃

C₂²

yes

characteristic

#16810451

C₂²

yes

complemented

#16810424

C₂²

yes

complemented

#16810398

C₂²

yes

complemented

C₂²×D₈×C₅₃

C₂²

yes

—

C₂×D₁₆×C₅₃

C₄

yes

complemented

C₂×D₁₆×C₅₃

C₂²

yes

—

C₂²×C₁₆×C₅₃

C₂²

yes

characteristic

C₂³×Dic₅₃

—

C₂²×#88322

D₄

yes

characteristic

D₄×Dic₅₃

—

D₄×Dic₅₃

—

C₂×C₄⋊Dic₅₃

—

C₂×C₂²⋊Dic₅₃

—

C₂×C₄×Dic₅₃

D₄

yes

characteristic

C₂×#11719908

—

C₂×#11719908

C₂³

yes

—

#13133151

—

#13133151

C₂³

yes

—

#13133138

—

C₈×Dic₅₃

D₄

yes

—

C₈×Dic₅₃

C₂³

yes

—

C₂²×D₄×C₅₃

—

C₂×D₈×C₅₃

—

C₂×D₈×C₅₃

—

C₂×D₈×C₅₃

C₂×C₄

yes

complemented

C₂×D₈×C₅₃

C₂³

yes

—

C₂²×C₈×C₅₃

C₂³

yes

characteristic

D₁₆×C₅₃

C₂×C₄

yes

complemented

C₂×C₁₆×C₅₃

C₂×C₄

yes

complemented

C₂×C₁₆×C₅₃

C₂³

yes

—

C₂⁴×C₅₃

—

C₂×D₄×C₅₃

—

C₂×D₄×C₅₃

—

C₂×D₄×C₅₃

—

C₂×D₄×C₅₃

—

C₂²×C₄×C₅₃

C₂×D₄

yes

characteristic

C₂²×Dic₅₃

—

C₂²×Dic₅₃

—

C₂²×Dic₅₃

—

C₂²×Dic₅₃

D₈

yes

—

D₈×C₅₃

—

D₈×C₅₃

—

D₈×C₅₃

C₂²×C₄

yes

complemented

C₂×C₈×C₅₃

C₂²×C₄

yes

—

C₂×C₈×C₅₃

C₂×D₄

yes

characteristic

C₂×C₈×C₅₃

#41

yes

—

C₂×C₈×C₅₃

C₂⁴

yes

characteristic

C₂²⋊Dic₅₃

—

C₄⋊Dic₅₃

—

C₄⋊Dic₅₃

—

C₄×Dic₅₃

D₈

yes

—

C₄×Dic₅₃

C₂×D₄

yes

—

C₂×#88322

—

C₂×#88322

C₂×D₄

yes

—

C₁₆×C₅₃

C₂²×C₄

yes

complemented

#11719908

—

C₂³×C₅₃

—

C₂³×C₅₃

—

C₂³×C₅₃

—

C₂³×C₅₃

—

C₂³×C₅₃

C₂×D₈

yes

characteristic

D₄×C₅₃

—

D₄×C₅₃

—

D₄×C₅₃

—

C₂×C₄×C₅₃

C₄×D₄

yes

—

C₂×C₄×C₅₃

C₂×D₈

yes

characteristic

C₂×C₄×C₅₃

#135

yes

—

C₂×C₄×C₅₃

C₂²×D₄

yes

characteristic

C₂×Dic₅₃

—

C₂×Dic₅₃

—

C₂×Dic₅₃

—

C₂×Dic₅₃

—

C₂×Dic₅₃

C₂×D₈

yes

—

C₈×C₅₃

C₄×D₄

yes

—

C₈×C₅₃

C₂³×C₄

yes

characteristic

C₈×C₅₃

C₂×#41

yes

—

—

C₂²×C₅₃

—

C₂²×C₅₃

—

C₂²×C₅₃

—

C₂²×C₅₃

—

C₂²×C₅₃

C₄×D₈

yes

—

C₂²×C₅₃

#509

yes

—

C₂²×C₅₃

C₂²×D₈

yes

characteristic

C₄×C₅₃

C₄×D₈

yes

—

100

C₄×C₅₃

C₂×C₄×D₄

yes

characteristic

101

C₄×C₅₃

C₂×#135

yes

characteristic

102

Dic₅₃

—

103

Dic₅₃

—

104

C₂²×D₁₆

D₅₃

yes

characteristic

105

C₂×C₄×D₈

—

106

#2177

—

107

C₂×#367

—

108

C₂×#357

—

109

C₂×#346

—

110

C₂×C₅₃

—

111

C₂×C₅₃

#2177

yes

complemented

112

C₂×C₅₃

C₂×C₄×D₈

yes

characteristic

113

C₂×C₅₃

C₂×#509

yes

—

114

C₂²×D₈

C₂×D₅₃

yes

—

115

C₂×C₄×D₄

—

106

—

116

C₂×D₁₆

Dic₅₃

yes

complemented

117

C₂×D₁₆

C₂×D₅₃

yes

—

118

C₂²×C₁₆

—

119

C₂²×C₁₆

C₂×D₅₃

yes

characteristic

120

C₄×D₈

—

121

C₄×D₈

—

106

—

122

C₂×#107

—

123

C₂×#102

—

106

—

124

C₂×C₄×C₈

—

125

#367

—

126

#357

—

127

#346

—

128

C₅₃

C₂×#2177

yes

characteristic, complemented, Sylow

129

C₂²×D₄

—

130

C₂³×C₄

—

212

—

131

C₂×D₈

—

132

C₂×D₈

—

133

C₂×D₈

C₂×Dic₅₃

yes

complemented

134

C₂×D₈

C₂²×D₅₃

yes

—

135

C₂²×C₈

—

136

C₂²×C₈

C₂²×D₅₃

yes

characteristic

137

C₄×D₄

—

106

—

138

C₄×D₄

—

212

—

139

C₂×C₄⋊C₄

—

106

—

140

C₂×C₂²⋊C₄

—

212

—

141

C₂×C₄²

—

142

D₁₆

C₂×Dic₅₃

yes

complemented

143

C₂×C₁₆

—

144

C₂×C₁₆

—

106

—

145

C₂×C₁₆

C₂×Dic₅₃

yes

complemented

146

C₂×C₁₆

C₂²×D₅₃

yes

—

147

#107

—

148

#107

—

106

—

149

#102

—

106

—

150

C₄×C₈

—

151

C₄×C₈

—

152

C₂⁴

—

153

C₂×D₄

—

154

C₂×D₄

—

155

C₂×D₄

—

156

C₂×D₄

—

157

C₂²×C₄

—

158

C₂²×C₄

—

424

—

159

C₂²×C₄

—

212

—

160

C₂²×C₄

—

212

—

161

C₂²×C₄

D₄×D₅₃

yes

characteristic

162

D₈

—

163

D₈

—

164

D₈

C₂²×Dic₅₃

yes

complemented

165

C₂×C₈

—

166

C₂×C₈

—

106

—

167

C₂×C₈

D₄×D₅₃

yes

characteristic

168

C₂×C₈

#11719947

yes

—

169

C₂×C₈

C₂²×Dic₅₃

yes

—

170

C₂×C₈

C₂³×D₅₃

yes

characteristic

171

C₄⋊C₄

—

106

—

172

C₄⋊C₄

—

212

—

173

C₂²⋊C₄

—

212

—

174

C₄²

—

175

C₄²

—

176

C₁₆

—

106

—

177

C₁₆

C₂²×Dic₅₃

yes

complemented

178

C₂³

—

179

C₂³

—

180

C₂³

—

181

C₂³

—

182

C₂³

D₈×D₅₃

yes

characteristic

183

D₄

—

184

D₄

—

185

D₄

—

186

C₂×C₄

—

187

C₂×C₄

—

106

—

188

C₂×C₄

—

424

—

189

C₂×C₄

—

424

—

190

C₂×C₄

—

212

—

191

C₂×C₄

D₄×Dic₅₃

yes

—

192

C₂×C₄

D₈×D₅₃

yes

characteristic

193

C₂×C₄

#13133236

yes

—

194

C₂×C₄

C₂×D₄×D₅₃

yes

characteristic

195

C₈

—

106

—

196

C₈

D₄×Dic₅₃

yes

—

197

C₈

C₂³×Dic₅₃

yes

characteristic

198

C₈

C₂×#11719947

yes

characteristic

199

C₂²

—

200

C₂²

—

201

C₂²

—

202

C₂²

—

203

C₂²

D₈×Dic₅₃

yes

—

204

C₂²

#16811057

yes

—

205

C₂²

C₂×D₈×D₅₃

yes

characteristic

206

C₄

—

106

—

207

C₄

—

424

—

208

C₄

D₈×Dic₅₃

yes

—

209

C₄

C₂×D₄×Dic₅₃

yes

characteristic

210

C₄

C₂×#13133236

yes

characteristic

211

C₂

—

212

C₂

#20276591

yes

direct product factor

213

C₂

C₂×D₈×Dic₅₃

yes

characteristic

214

C₂

C₂×#16811057

yes

—

	subgroup	G/H
center	C₂³	D₈×D₅₃
commutator	C₈×C₅₃	C₂³×C₄
Frattini	C₂×C₈	C₂³×D₅₃
Fitting, prime radical	C₂²×D₁₆×C₅₃	C₂
socle	C₂³×C₅₃	C₂×D₈
cosocle	C₂×C₈×C₅₃	C₂⁴
hypercenter	C₂²×D₁₆	D₅₃
hypocenter	C₅₃	C₂×#2177
LCS	G ▷ C₈×C₅₃ ▷ C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂²×D₁₆

subgroup

G/H

center

C₂³

D₈×D₅₃

commutator

C₈×C₅₃

C₂³×C₄

Frattini

C₂×C₈

C₂³×D₅₃

Fitting, prime radical

C₂²×D₁₆×C₅₃

C₂

socle

C₂³×C₅₃

C₂×D₈

cosocle

C₂×C₈×C₅₃

C₂⁴

hypercenter

C₂²×D₁₆

D₅₃

hypocenter

C₅₃

C₂×#2177

LCS

G ▷ C₈×C₅₃ ▷ C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃

UCS

C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂²×D₁₆

N	H ≅ G/N	type
1. C₂×D₈×Dic₅₃	C₂	semidirect
2. #20276591	C₂	direct (N × H)
3. C₂×#16810451	C₂	semidirect
4. C₂×#16810424	C₂	semidirect
5. C₂×#16810398	C₂	semidirect
10. D₈×Dic₅₃	C₂²	semidirect
14. #16810451	C₂²	semidirect
15. #16810424	C₂²	semidirect
16. #16810398	C₂²	semidirect
18. C₂×D₁₆×C₅₃	C₄	semidirect
38. C₂×D₈×C₅₃	C₂×C₄	semidirect
41. D₁₆×C₅₃	C₂×C₄	semidirect
42. C₂×C₁₆×C₅₃	C₂×C₄	semidirect
56. D₈×C₅₃	C₂²×C₄	semidirect
68. C₁₆×C₅₃	C₂²×C₄	semidirect
111. C₂×C₅₃	#2177	semidirect
116. C₂×D₁₆	Dic₅₃	semidirect
128. C₅₃	C₂×#2177	semidirect
133. C₂×D₈	C₂×Dic₅₃	semidirect
142. D₁₆	C₂×Dic₅₃	semidirect
145. C₂×C₁₆	C₂×Dic₅₃	semidirect
164. D₈	C₂²×Dic₅₃	semidirect
177. C₁₆	C₂²×Dic₅₃	semidirect
212. C₂	#20276591	direct (N × H)

H ≅ G/N

type

1. C₂×D₈×Dic₅₃

C₂

semidirect

2. #20276591

C₂

direct (N × H)

3. C₂×#16810451

C₂

semidirect

4. C₂×#16810424

C₂

semidirect

5. C₂×#16810398

C₂

semidirect

10. D₈×Dic₅₃

C₂²

semidirect

14. #16810451

C₂²

semidirect

15. #16810424

C₂²

semidirect

16. #16810398

C₂²

semidirect

18. C₂×D₁₆×C₅₃

C₄

semidirect

38. C₂×D₈×C₅₃

C₂×C₄

semidirect

41. D₁₆×C₅₃

C₂×C₄

semidirect

42. C₂×C₁₆×C₅₃

C₂×C₄

semidirect

56. D₈×C₅₃

C₂²×C₄

semidirect

68. C₁₆×C₅₃

C₂²×C₄

semidirect

111. C₂×C₅₃

#2177

semidirect

116. C₂×D₁₆

Dic₅₃

semidirect

128. C₅₃

C₂×#2177

semidirect

133. C₂×D₈

C₂×Dic₅₃

semidirect

142. D₁₆

C₂×Dic₅₃

semidirect

145. C₂×C₁₆

C₂×Dic₅₃

semidirect

164. D₈

C₂²×Dic₅₃

semidirect

177. C₁₆

C₂²×Dic₅₃

semidirect

212. C₂

#20276591

direct (N × H)

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

subgroup	index
C₂×D₈×Dic₅₃	2
#20276591	2
C₂×#16810451	2
C₂×#16810424	2
C₂×#16810398	2
C₂²×D₁₆×C₅₃	2
C₂×#2177	53

subgroup

index

C₂×D₈×Dic₅₃

C₂²×D₁₆×C₅₃

Subgroups — C₂×#20276591 #27537395

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C2×#20276591 #27537395

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20276591 #27537395