Group #28312338 — subgroups

Subgroups — #28312338

Order 13568.

330 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 330 conjugacy classes of subgroups — too many to draw. Only its 106 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×#16811556	C₂	1	2	yes	maximal, complemented
2	#20289829	C₂	1	2	yes	maximal, complemented
3	C₂²⋊#13133267	C₂	1	2	yes	maximal, complemented
4	C₂²×C₁₆×D₅₃	C₂	1	1	yes	maximal, characteristic
5	#16811556	—	2	4	no	—
6	C₂×#13133267	C₂²	1	4	yes	complemented
7	C₂²×C₈×D₅₃	C₄	1	1	yes	characteristic
8	C₂²×#11719908	C₂²	1	1	yes	characteristic
9	C₂×C₁₆×D₅₃	—	2	4	no	—
10	C₂×C₁₆×D₅₃	C₄	1	1	yes	characteristic
11	C₂×C₁₆×D₅₃	C₄	1	1	yes	characteristic
12	C₂×C₁₆×D₅₃	C₂²	1	1	yes	characteristic
13	C₂×C₁₆×D₅₃	C₂²	1	1	yes	characteristic
14	C₂²×C₁₆×C₅₃	C₄	1	1	yes	characteristic
15	#13133267	—	2	4	no	—
16	C₂²×C₄×D₅₃	C₈	1	1	yes	characteristic
17	C₂²×#88322	C₈	1	1	yes	characteristic
18	C₂×C₈×D₅₃	—	2	2	no	—
19	C₂×C₈×D₅₃	—	2	2	no	—
20	C₂×C₈×D₅₃	C₈	1	1	yes	characteristic
21	C₂×C₈×D₅₃	C₈	1	1	yes	characteristic
22	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
23	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
24	C₂×#11719908	—	2	2	no	—
25	C₂×#11719908	C₂×C₄	1	1	yes	characteristic
26	C₂×#11719908	C₂³	1	1	yes	characteristic
27	C₁₆×D₅₃	—	2	2	no	—
28	C₁₆×D₅₃	—	2	2	no	—
29	C₁₆×D₅₃	—	2	2	no	—
30	C₁₆×D₅₃	D₄	1	4	yes	—
31	C₂²×C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
32	C₂×C₁₆×C₅₃	—	2	2	no	—
33	C₂×C₁₆×C₅₃	C₂×C₄	1	1	yes	characteristic
34	C₂×C₁₆×C₅₃	C₂×C₄	1	1	yes	characteristic
35	C₂³×D₅₃	C₁₆	1	1	yes	characteristic
36	C₂²×C₄×C₅₃	C₂×C₈	1	1	yes	characteristic
37	C₂²×Dic₅₃	C₁₆	1	1	yes	characteristic
38	C₂×C₄×D₅₃	—	2	2	no	—
39	C₂×C₄×D₅₃	—	2	2	no	—
40	C₂×C₄×D₅₃	C₁₆	1	1	yes	characteristic
41	C₂×C₄×D₅₃	C₁₆	1	1	yes	characteristic
42	C₂×C₄×D₅₃	C₂×C₈	1	1	yes	characteristic
43	C₂×C₄×D₅₃	C₂×C₈	1	1	yes	characteristic
44	C₂×C₈×C₅₃	—	2	1	no	—
45	C₂×C₈×C₅₃	—	2	1	no	—
46	C₂×C₈×C₅₃	C₂×C₈	1	1	yes	characteristic
47	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
48	C₂×#88322	—	2	2	no	—
49	C₂×#88322	C₂×C₈	1	1	yes	characteristic
50	C₂×#88322	C₂×C₈	1	1	yes	characteristic
51	C₈×D₅₃	—	2	2	no	—
52	C₈×D₅₃	—	2	1	no	—
53	C₈×D₅₃	—	2	1	no	—
54	C₈×D₅₃	—	2	2	no	—
55	C₈×D₅₃	C₂²⋊C₄	1	2	yes	—
56	C₈×D₅₃	M₁₆	1	2	yes	—
57	C₁₆×C₅₃	—	2	1	no	—
58	C₁₆×C₅₃	C₂²⋊C₄	1	2	yes	—
59	#11719908	—	2	1	no	—
60	#11719908	C₂×D₄	1	2	yes	—
61	C₂³×C₅₃	C₂×C₁₆	1	1	yes	characteristic
62	C₂²×D₅₃	—	2	2	no	—
63	C₂²×D₅₃	—	2	2	no	—
64	C₂²×D₅₃	—	2	2	no	—
65	C₂²×D₅₃	C₂×C₁₆	1	1	yes	characteristic
66	C₂²×D₅₃	C₂×C₁₆	1	1	yes	characteristic
67	C₂×C₄×C₅₃	—	2	1	no	—
68	C₂×C₄×C₅₃	—	2	1	no	—
69	C₂×C₄×C₅₃	C₂×C₁₆	1	1	yes	characteristic
70	C₂×C₄×C₅₃	C₂²×C₈	1	1	yes	characteristic
71	C₂×Dic₅₃	—	2	2	no	—
72	C₂×Dic₅₃	C₂×C₁₆	1	1	yes	characteristic
73	C₂×Dic₅₃	C₂×C₁₆	1	1	yes	characteristic
74	C₄×D₅₃	—	2	2	no	—
75	C₄×D₅₃	—	2	1	no	—
76	C₄×D₅₃	—	2	1	no	—
77	C₄×D₅₃	—	2	2	no	—
78	C₄×D₅₃	C₂²⋊C₈	1	2	yes	—
79	C₄×D₅₃	M₃₂	1	2	yes	—
80	C₈×C₅₃	—	2	1	no	—
81	C₈×C₅₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
82	C₈×C₅₃	C₂×M₁₆	1	1	yes	characteristic
83	#88322	—	2	1	no	—
84	#88322	C₂²⋊C₈	1	2	yes	—
85	#13553	—	53	1	no	maximal, Sylow
86	C₂²×C₅₃	—	2	1	no	—
87	C₂²×C₅₃	—	2	1	no	—
88	C₂²×C₅₃	M₆₄	1	2	yes	complemented
89	C₂²×C₅₃	C₂²×C₁₆	1	1	yes	characteristic
90	C₂×D₅₃	—	2	8	no	—
91	C₂×D₅₃	—	2	1	no	—
92	C₂×D₅₃	—	2	1	no	—
93	C₂×D₅₃	—	2	1	no	—
94	C₂×D₅₃	—	2	1	no	—
95	C₂×D₅₃	C₂²⋊C₁₆	1	2	yes	—
96	C₂×D₅₃	M₆₄	1	2	yes	complemented
97	C₄×C₅₃	—	2	1	no	—
98	C₄×C₅₃	C₂×C₂²⋊C₈	1	1	yes	characteristic
99	C₄×C₅₃	C₂×M₃₂	1	1	yes	characteristic
100	Dic₅₃	—	2	1	no	—
101	Dic₅₃	C₂²⋊C₁₆	1	2	yes	—
102	C₂³×C₁₆	—	53	1	no	—
103	C₂×M₆₄	—	53	2	no	—
104	C₂²⋊C₃₂	—	53	2	no	—
105	C₂²⋊C₃₂	—	53	2	no	—
106	C₂×C₅₃	—	2	2	no	—
107	C₂×C₅₃	C₂×C₂²⋊C₁₆	1	1	yes	characteristic
108	C₂×C₅₃	C₂×M₆₄	1	1	yes	characteristic
109	C₂×C₅₃	C₂×M₆₄	1	1	yes	characteristic
110	D₅₃	—	2	2	no	—
111	D₅₃	—	2	2	no	—
112	C₂³×C₈	—	53	1	no	—
113	C₂²×C₁₆	—	53	1	no	—
114	C₂²×C₁₆	—	53	1	no	—
115	C₂²×C₁₆	—	53	1	no	—
116	C₂²×C₁₆	—	53	1	no	—
117	C₂²×C₁₆	—	53	1	no	—
118	C₂²×C₁₆	—	106	4	no	—
119	C₂²×C₁₆	#6157	1	1	yes	characteristic
120	M₆₄	—	106	4	no	—
121	C₂×C₃₂	—	53	4	no	—
122	C₅₃	#13553	1	1	yes	characteristic, complemented, Sylow
123	C₂³×C₄	—	53	1	no	—
124	C₂²×C₈	—	53	1	no	—
125	C₂²×C₈	—	53	1	no	—
126	C₂²×C₈	—	53	1	no	—
127	C₂²×C₈	—	53	1	no	—
128	C₂²×C₈	—	53	1	no	—
129	C₂²×C₈	—	106	2	no	—
130	C₂²×C₈	—	106	2	no	—
131	C₂²×C₈	C₂×#6157	1	1	yes	characteristic
132	C₂×C₁₆	—	2	2	no	—
133	C₂×C₁₆	—	53	1	no	—
134	C₂×C₁₆	—	53	4	no	—
135	C₂×C₁₆	—	53	1	no	—
136	C₂×C₁₆	—	106	2	no	—
137	C₂×C₁₆	—	106	2	no	—
138	C₂×C₁₆	—	106	2	no	—
139	C₂×C₁₆	—	106	2	no	—
140	C₂×C₁₆	C₂×#6157	1	1	yes	characteristic
141	C₂×C₁₆	C₂×#6157	1	1	yes	characteristic
142	C₃₂	—	106	4	no	—
143	C₂⁴	—	53	1	no	—
144	C₂²×C₄	—	53	1	no	—
145	C₂²×C₄	—	53	1	no	—
146	C₂²×C₄	—	53	1	no	—
147	C₂²×C₄	—	53	1	no	—
148	C₂²×C₄	—	53	1	no	—
149	C₂²×C₄	—	106	2	no	—
150	C₂²×C₄	—	106	2	no	—
151	C₂²×C₄	D₅₃⋊C₈	1	1	yes	characteristic
152	C₂×C₈	—	2	1	no	—
153	C₂×C₈	—	2	1	no	—
154	C₂×C₈	—	53	1	no	—
155	C₂×C₈	—	53	2	no	—
156	C₂×C₈	—	53	2	no	—
157	C₂×C₈	—	53	1	no	—
158	C₂×C₈	—	106	2	no	—
159	C₂×C₈	—	106	2	no	—
160	C₂×C₈	—	106	2	no	—
161	C₂×C₈	—	106	1	no	—
162	C₂×C₈	—	106	1	no	—
163	C₂×C₈	D₅₃⋊C₈	1	1	yes	characteristic
164	C₂×C₈	C₂²×#6157	1	1	yes	characteristic
165	C₁₆	—	2	1	no	—
166	C₁₆	—	53	2	no	—
167	C₁₆	—	106	1	no	—
168	C₁₆	C₂²⋊#6157	1	2	yes	—
169	C₂³	—	53	1	no	—
170	C₂³	—	53	1	no	—
171	C₂³	—	106	2	no	—
172	C₂³	—	106	2	no	—
173	C₂³	—	106	2	no	—
174	C₂³	D₅₃⋊C₁₆	1	1	yes	characteristic
175	C₂×C₄	—	2	1	no	—
176	C₂×C₄	—	2	1	no	—
177	C₂×C₄	—	53	1	no	—
178	C₂×C₄	—	53	2	no	—
179	C₂×C₄	—	53	2	no	—
180	C₂×C₄	—	53	1	no	—
181	C₂×C₄	—	106	2	no	—
182	C₂×C₄	—	106	2	no	—
183	C₂×C₄	—	106	2	no	—
184	C₂×C₄	—	106	1	no	—
185	C₂×C₄	—	106	1	no	—
186	C₂×C₄	D₅₃⋊C₁₆	1	1	yes	characteristic
187	C₂×C₄	C₂×D₅₃⋊C₈	1	1	yes	characteristic
188	C₈	—	2	1	no	—
189	C₈	—	53	2	no	—
190	C₈	—	106	1	no	—
191	C₈	C₂×C₂²⋊#6157	1	1	yes	characteristic
192	C₈	D₅₃⋊M₁₆	1	1	yes	characteristic
193	C₂²	—	2	1	no	—
194	C₂²	—	2	1	no	—
195	C₂²	—	53	2	no	—
196	C₂²	—	53	2	no	—
197	C₂²	—	106	8	no	—
198	C₂²	—	106	1	no	—
199	C₂²	—	106	1	no	—
200	C₂²	—	106	1	no	—
201	C₂²	—	106	1	no	—
202	C₂²	#16811556	1	2	yes	complemented
203	C₂²	C₂×D₅₃⋊C₁₆	1	1	yes	characteristic
204	C₄	—	2	1	no	—
205	C₄	—	53	2	no	—
206	C₄	—	106	1	no	—
207	C₄	D₅₃⋊(C₂²⋊C₈)	1	1	yes	characteristic
208	C₄	D₅₃⋊M₃₂	1	1	yes	characteristic
209	C₂	—	2	2	no	—
210	C₂	—	106	2	no	—
211	C₂	—	106	2	no	—
212	C₂	D₅₃⋊(C₂²⋊C₁₆)	1	1	yes	characteristic
213	C₂	D₅₃⋊M₆₄	1	1	yes	characteristic
214	C₂	C₂×#16811556	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#16811556

C₂

yes

maximal, complemented

#20289829

C₂

yes

maximal, complemented

C₂²⋊#13133267

C₂

yes

maximal, complemented

C₂²×C₁₆×D₅₃

C₂

yes

maximal, characteristic

#16811556

—

C₂×#13133267

C₂²

yes

complemented

C₂²×C₈×D₅₃

C₄

yes

characteristic

C₂²×#11719908

C₂²

yes

characteristic

C₂×C₁₆×D₅₃

—

C₂×C₁₆×D₅₃

C₄

yes

characteristic

C₂×C₁₆×D₅₃

C₄

yes

characteristic

C₂×C₁₆×D₅₃

C₂²

yes

characteristic

C₂×C₁₆×D₅₃

C₂²

yes

characteristic

C₂²×C₁₆×C₅₃

C₄

yes

characteristic

#13133267

—

C₂²×C₄×D₅₃

C₈

yes

characteristic

C₂²×#88322

C₈

yes

characteristic

C₂×C₈×D₅₃

—

C₂×C₈×D₅₃

—

C₂×C₈×D₅₃

C₈

yes

characteristic

C₂×C₈×D₅₃

C₈

yes

characteristic

C₂×C₈×D₅₃

C₂×C₄

yes

characteristic

C₂×C₈×D₅₃

C₂×C₄

yes

characteristic

C₂×#11719908

—

C₂×#11719908

C₂×C₄

yes

characteristic

C₂×#11719908

C₂³

yes

characteristic

C₁₆×D₅₃

—

C₁₆×D₅₃

—

C₁₆×D₅₃

—

C₁₆×D₅₃

D₄

yes

—

C₂²×C₈×C₅₃

C₂×C₄

yes

characteristic

C₂×C₁₆×C₅₃

—

C₂×C₁₆×C₅₃

C₂×C₄

yes

characteristic

C₂×C₁₆×C₅₃

C₂×C₄

yes

characteristic

C₂³×D₅₃

C₁₆

yes

characteristic

C₂²×C₄×C₅₃

C₂×C₈

yes

characteristic

C₂²×Dic₅₃

C₁₆

yes

characteristic

C₂×C₄×D₅₃

—

C₂×C₄×D₅₃

—

C₂×C₄×D₅₃

C₁₆

yes

characteristic

C₂×C₄×D₅₃

C₁₆

yes

characteristic

C₂×C₄×D₅₃

C₂×C₈

yes

characteristic

C₂×C₄×D₅₃

C₂×C₈

yes

characteristic

C₂×C₈×C₅₃

—

C₂×C₈×C₅₃

—

C₂×C₈×C₅₃

C₂×C₈

yes

characteristic

C₂×C₈×C₅₃

C₂²×C₄

yes

characteristic

C₂×#88322

—

C₂×#88322

C₂×C₈

yes

characteristic

C₂×#88322

C₂×C₈

yes

characteristic

C₈×D₅₃

—

C₈×D₅₃

—

C₈×D₅₃

—

C₈×D₅₃

—

C₈×D₅₃

C₂²⋊C₄

yes

—

C₈×D₅₃

M₁₆

yes

—

C₁₆×C₅₃

—

C₁₆×C₅₃

C₂²⋊C₄

yes

—

#11719908

—

#11719908

C₂×D₄

yes

—

C₂³×C₅₃

C₂×C₁₆

yes

characteristic

C₂²×D₅₃

—

C₂²×D₅₃

—

C₂²×D₅₃

—

C₂²×D₅₃

C₂×C₁₆

yes

characteristic

C₂²×D₅₃

C₂×C₁₆

yes

characteristic

C₂×C₄×C₅₃

—

C₂×C₄×C₅₃

—

C₂×C₄×C₅₃

C₂×C₁₆

yes

characteristic

C₂×C₄×C₅₃

C₂²×C₈

yes

characteristic

C₂×Dic₅₃

—

C₂×Dic₅₃

C₂×C₁₆

yes

characteristic

C₂×Dic₅₃

C₂×C₁₆

yes

characteristic

C₄×D₅₃

—

C₄×D₅₃

—

C₄×D₅₃

—

C₄×D₅₃

—

C₄×D₅₃

C₂²⋊C₈

yes

—

C₄×D₅₃

M₃₂

yes

—

C₈×C₅₃

—

C₈×C₅₃

C₂×C₂²⋊C₄

yes

characteristic

C₈×C₅₃

C₂×M₁₆

yes

characteristic

#88322

—

#88322

C₂²⋊C₈

yes

—

#13553

—

maximal, Sylow

C₂²×C₅₃

—

C₂²×C₅₃

—

C₂²×C₅₃

M₆₄

yes

complemented

C₂²×C₅₃

C₂²×C₁₆

yes

characteristic

C₂×D₅₃

—

C₂×D₅₃

—

C₂×D₅₃

—

C₂×D₅₃

—

C₂×D₅₃

—

C₂×D₅₃

C₂²⋊C₁₆

yes

—

C₂×D₅₃

M₆₄

yes

complemented

C₄×C₅₃

—

C₄×C₅₃

C₂×C₂²⋊C₈

yes

characteristic

C₄×C₅₃

C₂×M₃₂

yes

characteristic

100

Dic₅₃

—

101

Dic₅₃

C₂²⋊C₁₆

yes

—

102

C₂³×C₁₆

—

103

C₂×M₆₄

—

104

C₂²⋊C₃₂

—

105

C₂²⋊C₃₂

—

106

C₂×C₅₃

—

107

C₂×C₅₃

C₂×C₂²⋊C₁₆

yes

characteristic

108

C₂×C₅₃

C₂×M₆₄

yes

characteristic

109

C₂×C₅₃

C₂×M₆₄

yes

characteristic

110

D₅₃

—

111

D₅₃

—

112

C₂³×C₈

—

113

C₂²×C₁₆

—

114

C₂²×C₁₆

—

115

C₂²×C₁₆

—

116

C₂²×C₁₆

—

117

C₂²×C₁₆

—

118

C₂²×C₁₆

—

106

—

119

C₂²×C₁₆

#6157

yes

characteristic

120

M₆₄

—

106

—

121

C₂×C₃₂

—

122

C₅₃

#13553

yes

characteristic, complemented, Sylow

123

C₂³×C₄

—

124

C₂²×C₈

—

125

C₂²×C₈

—

126

C₂²×C₈

—

127

C₂²×C₈

—

128

C₂²×C₈

—

129

C₂²×C₈

—

106

—

130

C₂²×C₈

—

106

—

131

C₂²×C₈

C₂×#6157

yes

characteristic

132

C₂×C₁₆

—

133

C₂×C₁₆

—

134

C₂×C₁₆

—

135

C₂×C₁₆

—

136

C₂×C₁₆

—

106

—

137

C₂×C₁₆

—

106

—

138

C₂×C₁₆

—

106

—

139

C₂×C₁₆

—

106

—

140

C₂×C₁₆

C₂×#6157

yes

characteristic

141

C₂×C₁₆

C₂×#6157

yes

characteristic

142

C₃₂

—

106

—

143

C₂⁴

—

144

C₂²×C₄

—

145

C₂²×C₄

—

146

C₂²×C₄

—

147

C₂²×C₄

—

148

C₂²×C₄

—

149

C₂²×C₄

—

106

—

150

C₂²×C₄

—

106

—

151

C₂²×C₄

D₅₃⋊C₈

yes

characteristic

152

C₂×C₈

—

153

C₂×C₈

—

154

C₂×C₈

—

155

C₂×C₈

—

156

C₂×C₈

—

157

C₂×C₈

—

158

C₂×C₈

—

106

—

159

C₂×C₈

—

106

—

160

C₂×C₈

—

106

—

161

C₂×C₈

—

106

—

162

C₂×C₈

—

106

—

163

C₂×C₈

D₅₃⋊C₈

yes

characteristic

164

C₂×C₈

C₂²×#6157

yes

characteristic

165

C₁₆

—

166

C₁₆

—

167

C₁₆

—

106

—

168

C₁₆

C₂²⋊#6157

yes

—

169

C₂³

—

170

C₂³

—

171

C₂³

—

106

—

172

C₂³

—

106

—

173

C₂³

—

106

—

174

C₂³

D₅₃⋊C₁₆

yes

characteristic

175

C₂×C₄

—

176

C₂×C₄

—

177

C₂×C₄

—

178

C₂×C₄

—

179

C₂×C₄

—

180

C₂×C₄

—

181

C₂×C₄

—

106

—

182

C₂×C₄

—

106

—

183

C₂×C₄

—

106

—

184

C₂×C₄

—

106

—

185

C₂×C₄

—

106

—

186

C₂×C₄

D₅₃⋊C₁₆

yes

characteristic

187

C₂×C₄

C₂×D₅₃⋊C₈

yes

characteristic

188

C₈

—

189

C₈

—

190

C₈

—

106

—

191

C₈

C₂×C₂²⋊#6157

yes

characteristic

192

C₈

D₅₃⋊M₁₆

yes

characteristic

193

C₂²

—

194

C₂²

—

195

C₂²

—

196

C₂²

—

197

C₂²

—

106

—

198

C₂²

—

106

—

199

C₂²

—

106

—

200

C₂²

—

106

—

201

C₂²

—

106

—

202

C₂²

#16811556

yes

complemented

203

C₂²

C₂×D₅₃⋊C₁₆

yes

characteristic

204

C₄

—

205

C₄

—

206

C₄

—

106

—

207

C₄

D₅₃⋊(C₂²⋊C₈)

yes

characteristic

208

C₄

D₅₃⋊M₃₂

yes

characteristic

209

C₂

—

210

C₂

—

106

—

211

C₂

—

106

—

212

C₂

D₅₃⋊(C₂²⋊C₁₆)

yes

characteristic

213

C₂

D₅₃⋊M₆₄

yes

characteristic

214

C₂

C₂×#16811556

yes

characteristic

	subgroup	G/H
center, Frattini	C₂×C₈	C₂²×#6157
commutator, socle	C₂²×C₅₃	C₂²×C₁₆
Fitting	C₂²×C₁₆×C₅₃	C₄
prime radical	C₂³×D₅₃	C₁₆
cosocle	C₂×#11719908	C₂³
hypercenter	C₂²×C₁₆	#6157
hypocenter	C₅₃	#13553
LCS	G ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂×C₈ ◁ C₂²×C₁₆

subgroup

G/H

center, Frattini

C₂×C₈

C₂²×#6157

commutator, socle

C₂²×C₅₃

C₂²×C₁₆

Fitting

C₂²×C₁₆×C₅₃

C₄

prime radical

C₂³×D₅₃

C₁₆

C₂³

C₂²×C₁₆

C₅₃

G ▷ C₂²×C₅₃ ▷ C₅₃

C₁ ◁ C₂×C₈ ◁ C₂²×C₁₆

N	H ≅ G/N	type
1. C₂×#16811556	C₂	semidirect
2. #20289829	C₂	semidirect
3. C₂²⋊#13133267	C₂	semidirect
6. C₂×#13133267	C₂²	semidirect
88. C₂²×C₅₃	M₆₄	semidirect
96. C₂×D₅₃	M₆₄	semidirect
122. C₅₃	#13553	semidirect
202. C₂²	#16811556	semidirect

H ≅ G/N

type

1. C₂×#16811556

C₂

semidirect

2. #20289829

C₂

semidirect

3. C₂²⋊#13133267

C₂

semidirect

6. C₂×#13133267

C₂²

semidirect

88. C₂²×C₅₃

M₆₄

semidirect

96. C₂×D₅₃

M₆₄

semidirect

122. C₅₃

#13553

semidirect

202. C₂²

#16811556

semidirect

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

subgroup	index
C₂×#16811556	2
#20289829	2
C₂²⋊#13133267	2
C₂²×C₁₆×D₅₃	2
#13553	53

subgroup

index

C₂²×C₁₆×D₅₃

Subgroups — #28312338

Conjugacy classes of subgroups

Complements

Maximal subgroups