Group #30774592 — subgroups

Subgroups — #30774592

Order 17152.

516 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 516 conjugacy classes of subgroups — too many to draw. Only its 99 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×#16863668	C₂	1	2	yes	maximal
2	C₂×#16863212	C₂	1	2	yes	maximal, complemented
3	#22561822	C₂	1	1	yes	maximal, characteristic
4	#22558303	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×Q₃₂×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#14524074	—	2	2	no	—
7	C₂×#14524049	C₂²	1	1	yes	characteristic
8	C₂×#14523983	C₂²	1	1	yes	characteristic
9	#16863668	—	2	4	no	—
10	#16863668	—	2	4	no	—
11	C₂×#14523979	C₂²	1	2	yes	—
12	C₂×#14523962	—	2	2	no	—
13	#16863212	—	2	4	no	—
14	(C₂×D₆₇)⋊C₁₆	—	2	2	no	—
15	C₂²×Q₁₆×C₆₇	C₂²	1	2	yes	—
16	C₂×Q₃₂×C₆₇	—	2	4	no	—
17	C₂×Q₃₂×C₆₇	—	2	2	no	—
18	C₂²×C₁₆×C₆₇	C₂²	1	1	yes	characteristic
19	C₂×#11761628	D₄	1	1	yes	characteristic
20	#14524074	—	2	8	no	—
21	#14524074	—	4	4	no	—
22	C₂×#11761618	—	4	2	no	—
23	C₂×#11761615	—	4	2	no	—
24	#14524049	—	2	2	no	—
25	#14524049	—	2	2	no	—
26	C₂×#11761612	—	2	2	no	—
27	C₂×#11761612	D₄	1	1	yes	characteristic
28	C₂×#11761611	—	2	1	no	—
29	C₂×C₈×D₆₇	—	2	1	no	—
30	#14523983	—	2	2	no	—
31	C₂×C₆₇⋊C₁₆	—	2	1	no	—
32	#14523979	—	2	2	no	—
33	#14523979	D₄	1	4	yes	—
34	#14523962	—	2	8	no	—
35	C₂²×Q₈×C₆₇	—	2	2	no	—
36	C₂×Q₁₆×C₆₇	—	2	2	no	—
37	C₂×Q₁₆×C₆₇	—	2	2	no	—
38	C₂×Q₁₆×C₆₇	—	2	2	no	—
39	C₂×Q₁₆×C₆₇	—	2	2	no	—
40	C₂×Q₁₆×C₆₇	—	2	2	no	—
41	C₂×Q₁₆×C₆₇	D₄	1	4	yes	—
42	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
43	Q₃₂×C₆₇	—	2	8	no	—
44	C₂×C₁₆×C₆₇	—	2	2	no	—
45	C₂×C₁₆×C₆₇	D₄	1	2	yes	—
46	#11761628	—	2	2	no	—
47	#11761628	—	2	2	no	—
48	C₂×Dic₁₃₄	D₈	1	1	yes	characteristic
49	C₂×D₂₆₈	D₈	1	1	yes	characteristic
50	C₂×C₂²⋊D₆₇	—	2	1	no	—
51	C₂×C₄×D₆₇	—	2	1	no	—
52	#11761618	—	4	8	no	—
53	#11761615	—	4	8	no	—
54	#11761612	—	2	2	no	—
55	#11761612	—	2	4	no	—
56	#11761612	—	4	2	no	—
57	#11761611	—	4	2	no	—
58	C₂×C₆₇⋊C₈	—	2	1	no	—
59	C₂×C₆₇⋊C₈	—	4	2	no	—
60	C₈×D₆₇	—	4	1	no	—
61	C₈×D₆₇	—	4	1	no	—
62	C₆₇⋊C₁₆	—	4	1	no	—
63	C₂×Q₈×C₆₇	—	2	4	no	—
64	C₂×Q₈×C₆₇	—	4	2	no	—
65	C₂×Q₈×C₆₇	—	4	2	no	—
66	C₂×Q₈×C₆₇	—	4	2	no	—
67	C₂×Q₈×C₆₇	—	4	2	no	—
68	C₂×Q₈×C₆₇	—	4	2	no	—
69	C₂²×C₄×C₆₇	—	4	2	no	—
70	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
71	Q₁₆×C₆₇	—	2	4	no	—
72	Q₁₆×C₆₇	—	2	4	no	—
73	Q₁₆×C₆₇	—	4	2	no	—
74	Q₁₆×C₆₇	—	4	2	no	—
75	C₂×C₈×C₆₇	C₂×D₄	1	2	yes	—
76	C₂×C₈×C₆₇	C₂×D₄	1	2	yes	—
77	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
78	C₂×C₈×C₆₇	#41	1	1	yes	characteristic
79	C₁₆×C₆₇	—	2	2	no	—
80	C₂³×C₆₇	#135	1	1	yes	characteristic
81	C₂²×D₆₇	—	2	1	no	—
82	Q₈×C₆₇	—	4	4	no	—
83	Q₈×C₆₇	—	4	4	no	—
84	Q₈×C₆₇	—	8	2	no	—
85	Q₈×C₆₇	—	8	2	no	—
86	C₂×C₄×C₆₇	—	4	4	no	—
87	C₂×C₄×C₆₇	—	8	2	no	—
88	C₂×C₄×C₆₇	—	8	2	no	—
89	C₂×C₄×C₆₇	#120	1	2	yes	—
90	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
91	C₂×C₄×C₆₇	C₂×D₈	1	1	yes	characteristic
92	C₂×C₄×C₆₇	AGL(1,ℤ/8)	1	2	yes	—
93	C₂²⋊D₆₇	—	4	2	no	—
94	C₂×Dic₆₇	—	2	1	no	—
95	D₂₆₈	—	2	2	no	—
96	C₄×D₆₇	—	4	1	no	—
97	C₄×D₆₇	—	4	1	no	—
98	Dic₁₃₄	—	2	2	no	—
99	C₈×C₆₇	#120	1	1	yes	characteristic
100	C₈×C₆₇	#121	1	2	yes	—
101	C₈×C₆₇	#127	1	1	yes	characteristic
102	C₆₇⋊C₈	—	4	1	no	—
103	C₆₇⋊C₈	—	4	4	no	—
104	C₂²×C₆₇	—	2	2	no	—
105	C₂²×C₆₇	#449	1	2	yes	—
106	C₂²×C₆₇	#466	1	1	yes	characteristic
107	C₂×D₆₇	—	4	2	no	—
108	C₂×D₆₇	—	4	1	no	—
109	C₄×C₆₇	—	8	4	no	—
110	C₄×C₆₇	#392	1	1	yes	characteristic
111	C₄×C₆₇	#447	1	2	yes	—
112	C₄×C₆₇	#469	1	1	yes	characteristic
113	Dic₆₇	—	4	1	no	—
114	#13315	—	67	1	no	maximal, Sylow
115	C₂×C₆₇	—	2	2	no	—
116	C₂×C₆₇	#1999	1	1	yes	characteristic
117	C₂×C₆₇	#2222	1	2	yes	—
118	D₆₇	—	8	1	no	—
119	C₂²×Q₃₂	D₆₇	1	1	yes	characteristic, complemented
120	C₂×#473	—	67	2	no	—
121	C₂×#362	—	67	2	no	—
122	#2113	—	67	1	no	—
123	#1381	—	67	1	no	—
124	C₆₇	#13315	1	1	yes	characteristic, complemented, Sylow
125	C₂×#137	—	134	2	no	—
126	C₂²×Q₁₆	C₂×D₆₇	1	2	yes	—
127	C₂×#131	—	67	1	no	—
128	C₂×Q₃₂	—	2	4	no	—
129	C₂×Q₃₂	—	2	2	no	—
130	C₂×M₃₂	—	67	1	no	—
131	C₂²×C₁₆	C₂×D₆₇	1	1	yes	characteristic
132	#473	—	134	4	no	—
133	#473	—	134	4	no	—
134	C₂×#108	—	67	2	no	—
135	C₂×#101	—	134	2	no	—
136	#362	—	134	4	no	—
137	C₂²⋊C₁₆	—	134	2	no	—
138	C₂×#41	—	67	1	no	—
139	C₂²×Q₈	—	2	2	no	—
140	#137	—	268	4	no	—
141	#137	—	134	8	no	—
142	C₂×Q₁₆	—	2	2	no	—
143	C₂×Q₁₆	—	2	2	no	—
144	C₂×Q₁₆	—	2	2	no	—
145	C₂×Q₁₆	—	2	2	no	—
146	C₂×Q₁₆	—	2	2	no	—
147	C₂×Q₁₆	—	268	2	no	—
148	C₂×Q₁₆	C₂²⋊D₆₇	1	4	yes	—
149	C₂×SD₁₆	—	268	2	no	—
150	#131	—	134	2	no	—
151	#131	—	134	2	no	—
152	C₂×M₁₆	—	67	1	no	—
153	C₂×M₁₆	—	134	2	no	—
154	C₂×M₁₆	—	134	1	no	—
155	C₂²×C₈	—	134	1	no	—
156	C₂²×C₈	C₂²×D₆₇	1	1	yes	characteristic
157	Q₃₂	—	2	8	no	—
158	M₃₂	—	134	2	no	—
159	C₂×C₁₆	—	2	2	no	—
160	C₂×C₁₆	—	134	1	no	—
161	C₂×C₁₆	C₂²⋊D₆₇	1	2	yes	—
162	#108	—	67	4	no	—
163	#108	—	134	2	no	—
164	#101	—	134	8	no	—
165	#41	—	134	2	no	—
166	#41	—	134	2	no	—
167	C₂×Q₈	—	2	4	no	—
168	C₂×Q₈	—	4	2	no	—
169	C₂×Q₈	—	4	2	no	—
170	C₂×Q₈	—	4	2	no	—
171	C₂×Q₈	—	4	2	no	—
172	C₂×Q₈	—	4	2	no	—
173	C₂×Q₈	—	67	1	no	—
174	C₂×D₄	—	67	1	no	—
175	C₂×D₄	—	134	1	no	—
176	C₂²×C₄	—	4	2	no	—
177	C₂²×C₄	—	134	1	no	—
178	C₂²×C₄	D₄×D₆₇	1	1	yes	characteristic
179	Q₁₆	—	2	4	no	—
180	Q₁₆	—	2	4	no	—
181	Q₁₆	—	4	2	no	—
182	Q₁₆	—	4	2	no	—
183	Q₁₆	—	268	8	no	—
184	SD₁₆	—	268	8	no	—
185	M₁₆	—	268	2	no	—
186	M₁₆	—	268	2	no	—
187	M₁₆	—	134	2	no	—
188	M₁₆	—	134	4	no	—
189	C₂×C₈	—	268	2	no	—
190	C₂×C₈	—	268	1	no	—
191	C₂×C₈	—	268	1	no	—
192	C₂×C₈	—	134	1	no	—
193	C₂×C₈	D₄×D₆₇	1	2	yes	—
194	C₂×C₈	C₂×C₂²⋊D₆₇	1	2	yes	—
195	C₂×C₈	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
196	C₂×C₈	#11761627	1	1	yes	characteristic
197	C₁₆	—	2	2	no	—
198	C₁₆	—	268	1	no	—
199	C₂³	—	134	1	no	—
200	C₂³	#14524062	1	1	yes	characteristic
201	Q₈	—	4	4	no	—
202	Q₈	—	4	4	no	—
203	Q₈	—	8	2	no	—
204	Q₈	—	8	2	no	—
205	Q₈	—	134	2	no	—
206	D₄	—	268	2	no	—
207	D₄	—	134	2	no	—
208	C₂×C₄	—	4	4	no	—
209	C₂×C₄	—	8	2	no	—
210	C₂×C₄	—	8	2	no	—
211	C₂×C₄	—	268	1	no	—
212	C₂×C₄	—	268	1	no	—
213	C₂×C₄	—	134	1	no	—
214	C₂×C₄	#14524011	1	2	yes	—
215	C₂×C₄	#14524014	1	1	yes	characteristic
216	C₂×C₄	D₈×D₆₇	1	1	yes	characteristic
217	C₂×C₄	#14524067	1	2	yes	—
218	C₈	—	268	4	no	—
219	C₈	—	268	1	no	—
220	C₈	#14524012	1	1	yes	characteristic
221	C₈	#14524015	1	2	yes	—
222	C₈	#14524039	1	1	yes	characteristic
223	C₂²	—	2	2	no	—
224	C₂²	—	268	2	no	—
225	C₂²	—	268	1	no	—
226	C₂²	#16863538	1	2	yes	—
227	C₂²	#16863629	1	1	yes	characteristic
228	C₄	—	8	4	no	—
229	C₄	—	268	1	no	—
230	C₄	#16863304	1	1	yes	characteristic
231	C₄	#16863528	1	2	yes	—
232	C₄	#16863646	1	1	yes	characteristic
233	C₂	—	2	2	no	—
234	C₂	—	536	1	no	—
235	C₂	#22561204	1	1	yes	characteristic
236	C₂	#22562331	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#16863668

C₂

yes

maximal

C₂×#16863212

C₂

yes

maximal, complemented

#22561822

C₂

yes

maximal, characteristic

#22558303

C₂

yes

maximal, characteristic, complemented

C₂²×Q₃₂×C₆₇

C₂

yes

maximal, characteristic, complemented

C₂×#14524074

—

C₂×#14524049

C₂²

yes

characteristic

C₂×#14523983

C₂²

yes

—

—

C₂²

yes

—

C₂×#14523962

—

#16863212

—

(C₂×D₆₇)⋊C₁₆

—

C₂²×Q₁₆×C₆₇

C₂²

yes

—

C₂×Q₃₂×C₆₇

—

C₂×Q₃₂×C₆₇

—

C₂²×C₁₆×C₆₇

C₂²

yes

characteristic

C₂×#11761628

D₄

yes

—

—

—

—

—

—

—

D₄

yes

characteristic

C₂×#11761611

—

C₂×C₈×D₆₇

—

#14523983

—

C₂×C₆₇⋊C₁₆

—

#14523979

—

#14523979

D₄

yes

—

#14523962

—

C₂²×Q₈×C₆₇

—

C₂×Q₁₆×C₆₇

—

C₂×Q₁₆×C₆₇

—

C₂×Q₁₆×C₆₇

—

C₂×Q₁₆×C₆₇

—

C₂×Q₁₆×C₆₇

—

C₂×Q₁₆×C₆₇

D₄

yes

—

C₂²×C₈×C₆₇

C₂³

yes

characteristic

Q₃₂×C₆₇

—

C₂×C₁₆×C₆₇

—

C₂×C₁₆×C₆₇

D₄

yes

—

#11761628

—

#11761628

—

C₂×Dic₁₃₄

D₈

yes

characteristic

C₂×D₂₆₈

D₈

yes

characteristic

C₂×C₂²⋊D₆₇

—

C₂×C₄×D₆₇

—

—

—

—

—

—

—

C₂×C₆₇⋊C₈

—

C₂×C₆₇⋊C₈

—

C₈×D₆₇

—

C₈×D₆₇

—

C₆₇⋊C₁₆

—

C₂×Q₈×C₆₇

—

C₂×Q₈×C₆₇

—

C₂×Q₈×C₆₇

—

C₂×Q₈×C₆₇

—

C₂×Q₈×C₆₇

—

C₂×Q₈×C₆₇

—

C₂²×C₄×C₆₇

—

C₂²×C₄×C₆₇

C₂×D₄

yes

characteristic

Q₁₆×C₆₇

—

Q₁₆×C₆₇

—

Q₁₆×C₆₇

—

Q₁₆×C₆₇

—

C₂×C₈×C₆₇

C₂×D₄

yes

—

C₂×C₈×C₆₇

C₂×D₄

yes

—

C₂×C₈×C₆₇

C₂×D₄

yes

characteristic

C₂×C₈×C₆₇

#41

yes

characteristic

C₁₆×C₆₇

—

C₂³×C₆₇

#135

yes

characteristic

C₂²×D₆₇

—

Q₈×C₆₇

—

Q₈×C₆₇

—

Q₈×C₆₇

—

Q₈×C₆₇

—

C₂×C₄×C₆₇

—

C₂×C₄×C₆₇

—

C₂×C₄×C₆₇

—

C₂×C₄×C₆₇

#120

yes

—

C₂×C₄×C₆₇

#121

yes

characteristic

C₂×C₄×C₆₇

C₂×D₈

yes

characteristic

C₂×C₄×C₆₇

AGL(1,ℤ/8)

yes

—

C₂²⋊D₆₇

—

C₂×Dic₆₇

—

D₂₆₈

—

C₄×D₆₇

—

C₄×D₆₇

—

Dic₁₃₄

—

C₈×C₆₇

#120

yes

characteristic

100

C₈×C₆₇

#121

yes

—

101

C₈×C₆₇

#127

yes

characteristic

102

C₆₇⋊C₈

—

103

C₆₇⋊C₈

—

104

C₂²×C₆₇

—

105

C₂²×C₆₇

#449

yes

—

106

C₂²×C₆₇

#466

yes

characteristic

107

C₂×D₆₇

—

108

C₂×D₆₇

—

109

C₄×C₆₇

—

110

C₄×C₆₇

#392

yes

characteristic

111

C₄×C₆₇

#447

yes

—

112

C₄×C₆₇

#469

yes

characteristic

113

Dic₆₇

—

114

#13315

—

maximal, Sylow

115

C₂×C₆₇

—

116

C₂×C₆₇

#1999

yes

characteristic

117

C₂×C₆₇

#2222

yes

—

118

D₆₇

—

119

C₂²×Q₃₂

D₆₇

yes

characteristic, complemented

120

C₂×#473

—

121

C₂×#362

—

122

#2113

—

123

#1381

—

124

C₆₇

#13315

yes

characteristic, complemented, Sylow

125

C₂×#137

—

134

—

126

C₂²×Q₁₆

C₂×D₆₇

yes

—

127

C₂×#131

—

128

C₂×Q₃₂

—

129

C₂×Q₃₂

—

130

C₂×M₃₂

—

131

C₂²×C₁₆

C₂×D₆₇

yes

characteristic

132

#473

—

134

—

133

#473

—

134

—

134

C₂×#108

—

135

C₂×#101

—

134

—

136

#362

—

134

—

137

C₂²⋊C₁₆

—

134

—

138

C₂×#41

—

139

C₂²×Q₈

—

140

#137

—

268

—

141

#137

—

134

—

142

C₂×Q₁₆

—

143

C₂×Q₁₆

—

144

C₂×Q₁₆

—

145

C₂×Q₁₆

—

146

C₂×Q₁₆

—

147

C₂×Q₁₆

—

268

—

148

C₂×Q₁₆

C₂²⋊D₆₇

yes

—

149

C₂×SD₁₆

—

268

—

150

#131

—

134

—

151

#131

—

134

—

152

C₂×M₁₆

—

153

C₂×M₁₆

—

134

—

154

C₂×M₁₆

—

134

—

155

C₂²×C₈

—

134

—

156

C₂²×C₈

C₂²×D₆₇

yes

characteristic

157

Q₃₂

—

158

M₃₂

—

134

—

159

C₂×C₁₆

—

160

C₂×C₁₆

—

134

—

161

C₂×C₁₆

C₂²⋊D₆₇

yes

—

162

#108

—

163

#108

—

134

—

164

#101

—

134

—

165

#41

—

134

—

166

#41

—

134

—

167

C₂×Q₈

—

168

C₂×Q₈

—

169

C₂×Q₈

—

170

C₂×Q₈

—

171

C₂×Q₈

—

172

C₂×Q₈

—

173

C₂×Q₈

—

174

C₂×D₄

—

175

C₂×D₄

—

134

—

176

C₂²×C₄

—

177

C₂²×C₄

—

134

—

178

C₂²×C₄

D₄×D₆₇

yes

characteristic

179

Q₁₆

—

180

Q₁₆

—

181

Q₁₆

—

182

Q₁₆

—

183

Q₁₆

—

268

—

184

SD₁₆

—

268

—

185

M₁₆

—

268

—

186

M₁₆

—

268

—

187

M₁₆

—

134

—

188

M₁₆

—

134

—

189

C₂×C₈

—

268

—

190

C₂×C₈

—

268

—

191

C₂×C₈

—

268

—

192

C₂×C₈

—

134

—

193

C₂×C₈

D₄×D₆₇

yes

—

194

C₂×C₈

C₂×C₂²⋊D₆₇

yes

—

195

C₂×C₈

C₂×C₂²⋊D₆₇

yes

characteristic

196

C₂×C₈

#11761627

yes

characteristic

197

C₁₆

—

198

C₁₆

—

268

—

199

C₂³

—

134

—

200

C₂³

#14524062

yes

characteristic

201

Q₈

—

202

Q₈

—

203

Q₈

—

204

Q₈

—

205

Q₈

—

134

—

206

D₄

—

268

—

207

D₄

—

134

—

208

C₂×C₄

—

209

C₂×C₄

—

210

C₂×C₄

—

211

C₂×C₄

—

268

—

212

C₂×C₄

—

268

—

213

C₂×C₄

—

134

—

214

C₂×C₄

#14524011

yes

—

215

C₂×C₄

#14524014

yes

characteristic

216

C₂×C₄

D₈×D₆₇

yes

characteristic

217

C₂×C₄

#14524067

yes

—

218

C₈

—

268

—

219

C₈

—

268

—

220

C₈

#14524012

yes

characteristic

221

C₈

#14524015

yes

—

222

C₈

#14524039

yes

characteristic

223

C₂²

—

224

C₂²

—

268

—

225

C₂²

—

268

—

226

C₂²

#16863538

yes

—

227

C₂²

#16863629

yes

characteristic

228

C₄

—

229

C₄

—

268

—

230

C₄

#16863304

yes

characteristic

231

C₄

#16863528

yes

—

232

C₄

#16863646

yes

characteristic

233

C₂

—

234

C₂

—

536

—

235

C₂

#22561204

yes

characteristic

236

C₂

#22562331

yes

—

	subgroup	G/H
center	C₂²	#16863629
commutator, cosocle	C₂²×C₈×C₆₇	C₂³
Frattini	C₂²×C₈	C₂²×D₆₇
Fitting	C₂²×Q₃₂×C₆₇	C₂
socle	C₂²×C₆₇	#466
prime radical	C₂×#11761628	D₄
hypercenter	C₂²×Q₃₂	D₆₇
hypocenter	C₆₇	#13315
LCS	G ▷ C₂²×C₈×C₆₇ ▷ C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂²×Q₃₂

subgroup

G/H

center

C₂²

#16863629

commutator, cosocle

C₂²×C₈×C₆₇

C₂³

Frattini

C₂²×C₈

C₂²×D₆₇

Fitting

C₂²×Q₃₂×C₆₇

C₂

C₂²×C₆₇

D₄

C₂²×Q₃₂

D₆₇

hypocenter

C₆₇

#13315

LCS

G ▷ C₂²×C₈×C₆₇ ▷ C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂²×Q₃₂

N	H ≅ G/N	type
2. C₂×#16863212	C₂	semidirect
4. #22558303	C₂	semidirect
5. C₂²×Q₃₂×C₆₇	C₂	semidirect
119. C₂²×Q₃₂	D₆₇	semidirect
124. C₆₇	#13315	semidirect

H ≅ G/N

type

2. C₂×#16863212

C₂

semidirect

4. #22558303

C₂

semidirect

5. C₂²×Q₃₂×C₆₇

C₂

semidirect

119. C₂²×Q₃₂

D₆₇

semidirect

124. C₆₇

#13315

semidirect

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

subgroup	index
C₂×#16863668	2
C₂×#16863212	2
#22561822	2
#22558303	2
C₂²×Q₃₂×C₆₇	2
#13315	67

subgroup

index

C₂²×Q₃₂×C₆₇

Subgroups — #30774592

Conjugacy classes of subgroups

Complements

Maximal subgroups