Group #27275049 — subgroups

Subgroups — #27275049

Order 13568.

516 conjugacy classes of subgroups; only the 183 normal subgroups are shown.

normal subgroups only

This group has 516 conjugacy classes of subgroups — too many to draw. Only its 183 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	#20274568	C₂	1	2	yes	maximal
2	C₂×#16810372	C₂	1	2	yes	maximal
3	#20272598	C₂	1	2	yes	maximal
4	C₄×C₄⋊Q₈×C₅₃	C₂	1	1	yes	maximal, characteristic
5	C₂×C₄⋊#88322	C₂²	1	4	yes	—
6	C₂×#13133128	—	2	2	no	—
7	#16810378	—	2	2	no	—
8	#16810372	C₄	1	8	yes	complemented
9	C₂×C₄⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
10	C₂×C₄×Q₈×C₅₃	C₄	1	2	yes	—
11	C₅₃×#391	C₄	1	2	yes	—
12	C₅₃×#389	—	2	2	no	—
13	C₅₃×#384	C₂²	1	1	yes	characteristic
14	C₄×C₄⋊C₄×C₅₃	—	2	2	no	—
15	C₄³×C₅₃	C₂²	1	1	yes	characteristic
16	C₂²×#88322	—	2	4	no	—
17	C₄⋊#88322	—	2	4	no	—
18	C₄⋊#88322	C₂×C₄	1	8	yes	—
19	#13133128	—	4	4	no	—
20	C₂²×Q₈×C₅₃	C₂×C₄	1	2	yes	—
21	C₄⋊Q₈×C₅₃	—	2	2	no	—
22	C₄⋊Q₈×C₅₃	C₂×C₄	1	4	yes	—
23	C₄×Q₈×C₅₃	—	4	4	no	—
24	C₂×C₄⋊C₄×C₅₃	—	2	2	no	—
25	C₂×C₄⋊C₄×C₅₃	—	2	2	no	—
26	C₂×C₄⋊C₄×C₅₃	—	2	2	no	—
27	C₂×C₄⋊C₄×C₅₃	C₂×C₄	1	2	yes	—
28	C₂×C₄²×C₅₃	—	2	2	no	—
29	C₂×C₄²×C₅₃	C₂×C₄	1	1	yes	characteristic
30	C₂×C₄²×C₅₃	C₂×C₄	1	1	yes	characteristic
31	C₂×C₄²×C₅₃	D₄	1	2	yes	—
32	C₂×C₄²×C₅₃	D₄	1	2	yes	—
33	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
34	#95×C₅₃	—	2	4	no	—
35	C₂×Q₈×C₅₃	—	2	2	no	—
36	C₂×Q₈×C₅₃	—	4	2	no	—
37	C₂×Q₈×C₅₃	—	4	2	no	—
38	C₂×Q₈×C₅₃	C₄²	1	4	yes	—
39	C₂²×C₄×C₅₃	—	2	2	no	—
40	C₂²×C₄×C₅₃	—	2	2	no	—
41	C₂²×C₄×C₅₃	C₂²⋊C₄	1	2	yes	—
42	C₂²×C₄×C₅₃	C₂²⋊C₄	1	1	yes	characteristic
43	C₂²×C₄×C₅₃	C₂²⋊C₄	1	1	yes	characteristic
44	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
45	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
46	C₄⋊C₄×C₅₃	—	2	8	no	—
47	C₄⋊C₄×C₅₃	—	4	4	no	—
48	C₄⋊C₄×C₅₃	—	4	2	no	—
49	C₄⋊C₄×C₅₃	—	4	2	no	—
50	C₄⋊C₄×C₅₃	—	4	2	no	—
51	C₄²×C₅₃	—	2	2	no	—
52	C₄²×C₅₃	—	2	2	no	—
53	C₄²×C₅₃	—	2	4	no	—
54	C₄²×C₅₃	—	2	2	no	—
55	C₄²×C₅₃	—	4	1	no	—
56	C₄²×C₅₃	—	4	4	no	—
57	C₄²×C₅₃	C₂²×C₄	1	2	yes	—
58	C₄²×C₅₃	#41	1	2	yes	—
59	C₂×#88322	—	2	8	no	—
60	C₂×#88322	—	4	4	no	—
61	C₂×#88322	—	4	4	no	—
62	C₂³×C₅₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
63	Q₈×C₅₃	—	4	4	no	—
64	Q₈×C₅₃	—	4	4	no	—
65	C₂×C₄×C₅₃	—	2	1	no	—
66	C₂×C₄×C₅₃	—	2	1	no	—
67	C₂×C₄×C₅₃	—	2	2	no	—
68	C₂×C₄×C₅₃	—	2	4	no	—
69	C₂×C₄×C₅₃	—	2	1	no	—
70	C₂×C₄×C₅₃	—	2	2	no	—
71	C₂×C₄×C₅₃	—	2	2	no	—
72	C₂×C₄×C₅₃	—	2	2	no	—
73	C₂×C₄×C₅₃	—	2	2	no	—
74	C₂×C₄×C₅₃	—	4	2	no	—
75	C₂×C₄×C₅₃	—	4	2	no	—
76	C₂×C₄×C₅₃	—	4	2	no	—
77	C₂×C₄×C₅₃	—	4	4	no	—
78	C₂×C₄×C₅₃	#100	1	2	yes	—
79	C₂×C₄×C₅₃	C₂×C₄²	1	1	yes	characteristic
80	C₂×C₄×C₅₃	#117	1	1	yes	characteristic
81	C₂×C₄×C₅₃	C₄×D₄	1	4	yes	—
82	C₂×C₄×C₅₃	AGL(1,ℤ/8)	1	2	yes	—
83	C₂×C₄×C₅₃	#137	1	2	yes	—
84	C₂×C₄×C₅₃	#137	1	4	yes	—
85	#88322	—	4	8	no	—
86	#8232	—	53	1	no	maximal, Sylow
87	C₂²×C₅₃	C₄×C₂²⋊C₄	1	1	yes	characteristic
88	C₂²×C₅₃	C₂×#100	1	1	yes	characteristic
89	C₂²×C₅₃	#413	1	1	yes	characteristic
90	C₂²×C₅₃	#417	1	2	yes	—
91	C₂²×C₅₃	#419	1	2	yes	—
92	C₄×C₅₃	—	2	2	no	—
93	C₄×C₅₃	—	2	1	no	—
94	C₄×C₅₃	—	2	1	no	—
95	C₄×C₅₃	—	4	2	no	—
96	C₄×C₅₃	—	4	1	no	—
97	C₄×C₅₃	—	4	4	no	—
98	C₄×C₅₃	—	8	2	no	—
99	C₄×C₅₃	#440	1	4	yes	—
100	C₄×C₅₃	#441	1	4	yes	—
101	C₄×C₄⋊Q₈	D₅₃	1	1	yes	characteristic
102	#1767	—	53	2	no	—
103	C₂×#333	—	53	2	no	—
104	#1296	—	53	2	no	—
105	C₂×C₅₃	#1558	1	1	yes	characteristic
106	C₂×C₅₃	#1559	1	2	yes	—
107	C₂×C₅₃	#1560	1	1	yes	characteristic
108	C₂×C₅₃	C₄×#100	1	1	yes	characteristic
109	C₂×C₅₃	#1763	1	2	yes	—
110	C₂×C₄⋊Q₈	C₂×D₅₃	1	1	yes	characteristic
111	C₂×C₄×Q₈	Dic₅₃	1	2	yes	—
112	C₂×C₄⋊C₈	—	53	4	no	—
113	C₂×#97	—	106	2	no	—
114	#391	Dic₅₃	1	2	yes	—
115	#389	—	2	2	no	—
116	#384	C₂×D₅₃	1	1	yes	characteristic
117	C₄×C₄⋊C₄	—	2	2	no	—
118	C₄³	C₂×D₅₃	1	1	yes	characteristic
119	#336	—	106	2	no	—
120	#333	—	53	8	no	—
121	C₅₃	#8232	1	1	yes	characteristic, complemented, Sylow
122	C₂²×Q₈	C₂×Dic₅₃	1	2	yes	—
123	C₂²×C₈	—	106	4	no	—
124	C₄⋊Q₈	—	2	2	no	—
125	C₄⋊Q₈	C₄×D₅₃	1	4	yes	—
126	C₄×Q₈	—	4	4	no	—
127	C₂×C₄⋊C₄	—	2	2	no	—
128	C₂×C₄⋊C₄	—	2	2	no	—
129	C₂×C₄⋊C₄	—	2	2	no	—
130	C₂×C₄⋊C₄	C₂×Dic₅₃	1	2	yes	—
131	C₂×C₄²	—	2	2	no	—
132	C₂×C₄²	C₂×Dic₅₃	1	1	yes	characteristic
133	C₂×C₄²	C₂×Dic₅₃	1	1	yes	characteristic
134	C₂×C₄²	C₂²⋊D₅₃	1	2	yes	—
135	C₂×C₄²	C₂²⋊D₅₃	1	2	yes	—
136	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
137	C₄⋊C₈	—	53	8	no	—
138	C₄⋊C₈	—	106	4	no	—
139	#97	—	212	4	no	—
140	#95	—	2	4	no	—
141	C₂×Q₈	—	2	2	no	—
142	C₂×Q₈	—	4	2	no	—
143	C₂×Q₈	—	4	2	no	—
144	C₂×Q₈	C₄×Dic₅₃	1	4	yes	—
145	C₂²×C₄	—	2	2	no	—
146	C₂²×C₄	—	2	2	no	—
147	C₂²×C₄	C₂²⋊Dic₅₃	1	2	yes	—
148	C₂²×C₄	C₂²⋊Dic₅₃	1	1	yes	characteristic
149	C₂²×C₄	C₂²⋊Dic₅₃	1	1	yes	characteristic
150	C₂²×C₄	C₂²×Dic₅₃	1	1	yes	characteristic
151	C₂²×C₄	C₂×C₂²⋊D₅₃	1	2	yes	—
152	C₂×C₈	—	106	8	no	—
153	C₂×C₈	—	212	4	no	—
154	C₂×C₈	—	212	4	no	—
155	C₄⋊C₄	—	2	8	no	—
156	C₄⋊C₄	—	4	2	no	—
157	C₄⋊C₄	—	4	4	no	—
158	C₄⋊C₄	—	4	2	no	—
159	C₄⋊C₄	—	4	2	no	—
160	C₄²	—	2	2	no	—
161	C₄²	—	2	2	no	—
162	C₄²	—	2	2	no	—
163	C₄²	—	2	4	no	—
164	C₄²	—	4	1	no	—
165	C₄²	—	4	4	no	—
166	C₄²	C₂×C₄×D₅₃	1	2	yes	—
167	C₄²	#11719945	1	2	yes	—
168	C₂³	C₂×C₂²⋊Dic₅₃	1	1	yes	characteristic
169	Q₈	—	4	4	no	—
170	Q₈	—	4	4	no	—
171	C₂×C₄	—	2	1	no	—
172	C₂×C₄	—	2	1	no	—
173	C₂×C₄	—	2	2	no	—
174	C₂×C₄	—	2	1	no	—
175	C₂×C₄	—	2	2	no	—
176	C₂×C₄	—	2	2	no	—
177	C₂×C₄	—	2	2	no	—
178	C₂×C₄	—	2	2	no	—
179	C₂×C₄	—	2	4	no	—
180	C₂×C₄	—	4	2	no	—
181	C₂×C₄	—	4	2	no	—
182	C₂×C₄	—	4	2	no	—
183	C₂×C₄	—	4	4	no	—
184	C₂×C₄	#13133134	1	2	yes	—
185	C₂×C₄	C₂×C₄×Dic₅₃	1	1	yes	characteristic
186	C₂×C₄	#13133176	1	1	yes	characteristic
187	C₂×C₄	C₄×C₂²⋊D₅₃	1	4	yes	—
188	C₂×C₄	#13133242	1	2	yes	—
189	C₂×C₄	#13133247	1	2	yes	—
190	C₂×C₄	#13133248	1	4	yes	—
191	C₈	—	212	8	no	—
192	C₂²	C₄×C₂²⋊Dic₅₃	1	1	yes	characteristic
193	C₂²	C₂×#13133134	1	1	yes	characteristic
194	C₂²	#16810607	1	1	yes	characteristic
195	C₂²	#16810624	1	2	yes	—
196	C₂²	#16810632	1	2	yes	—
197	C₄	—	2	2	no	—
198	C₄	—	2	1	no	—
199	C₄	—	2	1	no	—
200	C₄	—	4	2	no	—
201	C₄	—	4	1	no	—
202	C₄	—	4	4	no	—
203	C₄	—	8	2	no	—
204	C₄	#16810721	1	4	yes	—
205	C₄	#16810728	1	4	yes	—
206	C₂	#20273441	1	1	yes	characteristic
207	C₂	#20273445	1	2	yes	—
208	C₂	#20273450	1	1	yes	characteristic
209	C₂	C₄×#13133134	1	1	yes	characteristic
210	C₂	#20274545	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#20274568

C₂

yes

maximal

C₂×#16810372

C₂

yes

maximal

#20272598

C₂

yes

maximal

C₄×C₄⋊Q₈×C₅₃

C₂

yes

maximal, characteristic

C₂×C₄⋊#88322

C₂²

yes

—

C₂×#13133128

—

#16810378

—

#16810372

C₄

yes

complemented

C₂×C₄⋊Q₈×C₅₃

C₂²

yes

characteristic

C₂×C₄×Q₈×C₅₃

C₄

yes

—

C₅₃×#391

C₄

yes

—

C₅₃×#389

—

C₅₃×#384

C₂²

yes

characteristic

C₄×C₄⋊C₄×C₅₃

—

C₄³×C₅₃

C₂²

yes

characteristic

C₂²×#88322

—

C₄⋊#88322

—

C₄⋊#88322

C₂×C₄

yes

—

#13133128

—

C₂²×Q₈×C₅₃

C₂×C₄

yes

—

C₄⋊Q₈×C₅₃

—

C₄⋊Q₈×C₅₃

C₂×C₄

yes

—

C₄×Q₈×C₅₃

—

C₂×C₄⋊C₄×C₅₃

—

C₂×C₄⋊C₄×C₅₃

—

C₂×C₄⋊C₄×C₅₃

—

C₂×C₄⋊C₄×C₅₃

C₂×C₄

yes

—

C₂×C₄²×C₅₃

—

C₂×C₄²×C₅₃

C₂×C₄

yes

characteristic

C₂×C₄²×C₅₃

C₂×C₄

yes

characteristic

C₂×C₄²×C₅₃

D₄

yes

—

C₂×C₄²×C₅₃

D₄

yes

—

C₂×C₄²×C₅₃

C₂³

yes

characteristic

#95×C₅₃

—

C₂×Q₈×C₅₃

—

C₂×Q₈×C₅₃

—

C₂×Q₈×C₅₃

—

C₂×Q₈×C₅₃

C₄²

yes

—

C₂²×C₄×C₅₃

—

C₂²×C₄×C₅₃

—

C₂²×C₄×C₅₃

C₂²⋊C₄

yes

—

C₂²×C₄×C₅₃

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₅₃

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₅₃

C₂²×C₄

yes

characteristic

C₂²×C₄×C₅₃

C₂×D₄

yes

—

C₄⋊C₄×C₅₃

—

C₄⋊C₄×C₅₃

—

C₄⋊C₄×C₅₃

—

C₄⋊C₄×C₅₃

—

C₄⋊C₄×C₅₃

—

C₄²×C₅₃

—

C₄²×C₅₃

—

C₄²×C₅₃

—

C₄²×C₅₃

—

C₄²×C₅₃

—

C₄²×C₅₃

—

C₄²×C₅₃

C₂²×C₄

yes

—

C₄²×C₅₃

#41

yes

—

C₂×#88322

—

C₂×#88322

—

C₂×#88322

—

C₂³×C₅₃

C₂×C₂²⋊C₄

yes

characteristic

Q₈×C₅₃

—

Q₈×C₅₃

—

C₂×C₄×C₅₃

—

C₂×C₄×C₅₃

—

C₂×C₄×C₅₃

—

C₂×C₄×C₅₃

—

C₂×C₄×C₅₃

—

C₂×C₄×C₅₃

—

C₂×C₄×C₅₃

—

C₂×C₄×C₅₃

—

C₂×C₄×C₅₃

—

C₂×C₄×C₅₃

—

C₂×C₄×C₅₃

—

C₂×C₄×C₅₃

—

C₂×C₄×C₅₃

—

C₂×C₄×C₅₃

#100

yes

—

C₂×C₄×C₅₃

C₂×C₄²

yes

characteristic

C₂×C₄×C₅₃

#117

yes

characteristic

C₂×C₄×C₅₃

C₄×D₄

yes

—

C₂×C₄×C₅₃

AGL(1,ℤ/8)

yes

—

C₂×C₄×C₅₃

#137

yes

—

C₂×C₄×C₅₃

#137

yes

—

#88322

—

#8232

—

maximal, Sylow

C₂²×C₅₃

C₄×C₂²⋊C₄

yes

C₂²×C₅₃

yes

C₂²×C₅₃

yes

C₂²×C₅₃

yes

—

C₂²×C₅₃

#419

yes

—

C₄×C₅₃

—

C₄×C₅₃

—

C₄×C₅₃

—

C₄×C₅₃

—

C₄×C₅₃

—

C₄×C₅₃

—

C₄×C₅₃

—

C₄×C₅₃

#440

yes

—

100

C₄×C₅₃

#441

yes

—

101

C₄×C₄⋊Q₈

D₅₃

yes

characteristic

102

#1767

—

103

C₂×#333

—

104

#1296

—

105

C₂×C₅₃

#1558

yes

characteristic

106

C₂×C₅₃

#1559

yes

—

107

C₂×C₅₃

#1560

yes

characteristic

108

C₂×C₅₃

C₄×#100

yes

characteristic

109

C₂×C₅₃

#1763

yes

—

110

C₂×C₄⋊Q₈

C₂×D₅₃

yes

characteristic

111

C₂×C₄×Q₈

Dic₅₃

yes

—

112

C₂×C₄⋊C₈

—

113

C₂×#97

—

106

—

114

#391

Dic₅₃

yes

—

115

#389

—

116

#384

C₂×D₅₃

yes

characteristic

117

C₄×C₄⋊C₄

—

118

C₄³

C₂×D₅₃

yes

characteristic

119

#336

—

106

—

120

#333

—

121

C₅₃

#8232

yes

characteristic, complemented, Sylow

122

C₂²×Q₈

C₂×Dic₅₃

yes

—

123

C₂²×C₈

—

106

—

124

C₄⋊Q₈

—

125

C₄⋊Q₈

C₄×D₅₃

yes

—

126

C₄×Q₈

—

127

C₂×C₄⋊C₄

—

128

C₂×C₄⋊C₄

—

129

C₂×C₄⋊C₄

—

130

C₂×C₄⋊C₄

C₂×Dic₅₃

yes

—

131

C₂×C₄²

—

132

C₂×C₄²

C₂×Dic₅₃

yes

characteristic

133

C₂×C₄²

C₂×Dic₅₃

yes

characteristic

134

C₂×C₄²

C₂²⋊D₅₃

yes

—

135

C₂×C₄²

C₂²⋊D₅₃

yes

—

136

C₂×C₄²

C₂²×D₅₃

yes

characteristic

137

C₄⋊C₈

—

138

C₄⋊C₈

—

106

—

139

#97

—

212

—

140

#95

—

141

C₂×Q₈

—

142

C₂×Q₈

—

143

C₂×Q₈

—

144

C₂×Q₈

C₄×Dic₅₃

yes

—

145

C₂²×C₄

—

146

C₂²×C₄

—

147

C₂²×C₄

C₂²⋊Dic₅₃

yes

—

148

C₂²×C₄

C₂²⋊Dic₅₃

yes

characteristic

149

C₂²×C₄

C₂²⋊Dic₅₃

yes

characteristic

150

C₂²×C₄

C₂²×Dic₅₃

yes

characteristic

151

C₂²×C₄

C₂×C₂²⋊D₅₃

yes

—

152

C₂×C₈

—

106

—

153

C₂×C₈

—

212

—

154

C₂×C₈

—

212

—

155

C₄⋊C₄

—

156

C₄⋊C₄

—

157

C₄⋊C₄

—

158

C₄⋊C₄

—

159

C₄⋊C₄

—

160

C₄²

—

161

C₄²

—

162

C₄²

—

163

C₄²

—

164

C₄²

—

165

C₄²

—

166

C₄²

C₂×C₄×D₅₃

yes

—

167

C₄²

#11719945

yes

—

168

C₂³

C₂×C₂²⋊Dic₅₃

yes

characteristic

169

Q₈

—

170

Q₈

—

171

C₂×C₄

—

172

C₂×C₄

—

173

C₂×C₄

—

174

C₂×C₄

—

175

C₂×C₄

—

176

C₂×C₄

—

177

C₂×C₄

—

178

C₂×C₄

—

179

C₂×C₄

—

180

C₂×C₄

—

181

C₂×C₄

—

182

C₂×C₄

—

183

C₂×C₄

—

184

C₂×C₄

#13133134

yes

—

185

C₂×C₄

C₂×C₄×Dic₅₃

yes

characteristic

186

C₂×C₄

#13133176

yes

characteristic

187

C₂×C₄

C₄×C₂²⋊D₅₃

yes

—

188

C₂×C₄

#13133242

yes

—

189

C₂×C₄

#13133247

yes

—

190

C₂×C₄

#13133248

yes

—

191

C₈

—

212

—

192

C₂²

C₄×C₂²⋊Dic₅₃

yes

characteristic

193

C₂²

C₂×#13133134

yes

characteristic

194

C₂²

#16810607

yes

characteristic

195

C₂²

#16810624

yes

—

196

C₂²

#16810632

yes

—

197

C₄

—

198

C₄

—

199

C₄

—

200

C₄

—

201

C₄

—

202

C₄

—

203

C₄

—

204

C₄

#16810721

yes

—

205

C₄

#16810728

yes

—

206

C₂

#20273441

yes

characteristic

207

C₂

#20273445

yes

—

208

C₂

#20273450

yes

characteristic

209

C₂

C₄×#13133134

yes

characteristic

210

C₂

#20274545

yes

—

	subgroup	G/H
center	C₂³	C₂×C₂²⋊Dic₅₃
commutator	C₂×C₄×C₅₃	C₂×C₄²
Frattini	C₂×C₄²	C₂²×D₅₃
Fitting	C₄×C₄⋊Q₈×C₅₃	C₂
socle, prime radical	C₂³×C₅₃	C₂×C₂²⋊C₄
cosocle	C₂×C₄²×C₅₃	C₂³
hypercenter	C₄×C₄⋊Q₈	D₅₃
hypocenter	C₅₃	#8232
LCS	G ▷ C₂×C₄×C₅₃ ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂³ ◁ C₄³ ◁ C₄×C₄⋊Q₈

subgroup

G/H

center

C₂³

C₂×C₂²⋊Dic₅₃

commutator

C₂×C₄×C₅₃

C₂×C₄²

Frattini

C₂×C₄²

C₂²×D₅₃

Fitting

C₄×C₄⋊Q₈×C₅₃

C₂

socle, prime radical

C₂³×C₅₃

C₂×C₂²⋊C₄

cosocle

C₂×C₄²×C₅₃

C₂³

hypercenter

C₄×C₄⋊Q₈

D₅₃

hypocenter

C₅₃

#8232

LCS

G ▷ C₂×C₄×C₅₃ ▷ C₂²×C₅₃ ▷ C₅₃

UCS

C₁ ◁ C₂³ ◁ C₄³ ◁ C₄×C₄⋊Q₈

N	H ≅ G/N	type
8. #16810372	C₄	semidirect
121. C₅₃	#8232	semidirect

H ≅ G/N

type

8. #16810372

C₄

semidirect

121. C₅₃

#8232

semidirect

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

subgroup	index
#20274568	2
C₂×#16810372	2
#20272598	2
C₄×C₄⋊Q₈×C₅₃	2
#8232	53

subgroup

index

C₄×C₄⋊Q₈×C₅₃

Subgroups — #27275049

Conjugacy classes of subgroups

Complements

Maximal subgroups