Group #30755739 — subgroups

Subgroups — #30755739

Order 17152.

454 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 454 conjugacy classes of subgroups — too many to draw. Only its 127 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	#22570795	C₂	1	1	yes	maximal, characteristic
2	#22561185	C₂	1	2	yes	maximal
3	C₄×#14523953	C₂	1	1	yes	maximal, characteristic
4	#22558663	C₂	1	2	yes	maximal
5	C₆₇×#1566	C₂	1	1	yes	maximal, characteristic
6	#16863953	C₂²	1	2	yes	—
7	#16863801	C₄	1	1	yes	characteristic, complemented
8	#16863776	C₄	1	1	yes	characteristic, complemented
9	#16863747	C₄	1	2	yes	complemented
10	#16863637	—	2	2	no	—
11	C₄×Dic₂₆₈	—	2	2	no	—
12	C₂×#14523953	—	2	2	no	—
13	C₂×C₄×C₆₇⋊C₈	C₂²	1	1	yes	characteristic
14	C₄²×Dic₆₇	C₂²	1	1	yes	characteristic
15	#16863157	—	2	4	no	—
16	#16863126	—	2	4	no	—
17	#423×C₆₇	C₂²	1	2	yes	—
18	C₂×C₄×C₈×C₆₇	C₂²	1	1	yes	characteristic
19	#334×C₆₇	—	2	2	no	—
20	C₂×Dic₂₆₈	—	2	2	no	—
21	C₂²×C₆₇⋊C₈	—	2	1	no	—
22	#14524043	C₂×C₄	1	2	yes	—
23	#14524043	C₂×C₄	1	2	yes	—
24	#14524035	—	2	2	no	—
25	#14524022	—	2	2	no	—
26	#14524022	—	2	2	no	—
27	C₄×Dic₁₃₄	—	2	2	no	—
28	C₄×Dic₁₃₄	—	2	2	no	—
29	#14524002	—	2	2	no	—
30	C₂×C₄×Dic₆₇	—	2	1	no	—
31	C₂×C₄×Dic₆₇	—	2	1	no	—
32	C₂×C₄×Dic₆₇	D₄	1	2	yes	—
33	#14523977	—	2	2	no	—
34	#14523968	—	2	4	no	—
35	#14523953	—	2	8	no	—
36	C₄×C₆₇⋊C₈	—	2	1	no	—
37	C₄×C₆₇⋊C₈	D₄	1	2	yes	—
38	C₂×M₁₆×C₆₇	—	2	2	no	—
39	C₂²×C₈×C₆₇	D₄	1	2	yes	—
40	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
41	C₄⋊C₈×C₆₇	—	2	2	no	—
42	C₄⋊C₈×C₆₇	—	2	2	no	—
43	C₄×C₈×C₆₇	C₂×C₄	1	1	yes	characteristic
44	C₄×C₈×C₆₇	C₂×C₄	1	1	yes	characteristic
45	C₄×C₈×C₆₇	D₄	1	2	yes	—
46	C₂×Dic₁₃₄	—	2	2	no	—
47	C₂×Dic₁₃₄	—	2	2	no	—
48	C₂²×Dic₆₇	—	2	2	no	—
49	Dic₂₆₈	—	4	4	no	—
50	C₂×C₆₇⋊C₈	—	2	4	no	—
51	C₂×C₆₇⋊C₈	—	2	2	no	—
52	C₄⋊Dic₆₇	—	2	2	no	—
53	C₄⋊Dic₆₇	—	2	2	no	—
54	C₄⋊Dic₆₇	—	2	2	no	—
55	C₄⋊Dic₆₇	—	2	2	no	—
56	Dic₆₇⋊C₄	—	4	2	no	—
57	Dic₆₇⋊C₄	—	4	2	no	—
58	C₂²⋊Dic₆₇	—	4	2	no	—
59	C₄×Dic₆₇	—	2	4	no	—
60	C₄×Dic₆₇	—	2	4	no	—
61	C₄×Dic₆₇	—	4	2	no	—
62	C₄×Dic₆₇	—	4	2	no	—
63	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
64	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
65	C₂²×C₄×C₆₇	#41	1	1	yes	characteristic
66	M₁₆×C₆₇	—	4	4	no	—
67	C₂×C₈×C₆₇	—	2	4	no	—
68	C₂×C₈×C₆₇	—	4	2	no	—
69	C₂×C₈×C₆₇	C₂²⋊C₄	1	2	yes	—
70	C₂×C₈×C₆₇	C₂²⋊C₄	1	2	yes	—
71	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
72	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
73	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
74	C₄²×C₆₇	#41	1	1	yes	characteristic
75	C₂³×C₆₇	#121	1	1	yes	characteristic
76	C₂×C₄×C₆₇	—	2	2	no	—
77	C₂×C₄×C₆₇	—	2	2	no	—
78	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
79	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
80	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
81	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
82	C₂×C₄×C₆₇	#124	1	1	yes	characteristic
83	C₂×C₄×C₆₇	#127	1	1	yes	characteristic
84	C₂×C₄×C₆₇	#137	1	4	yes	—
85	C₂×Dic₆₇	—	2	4	no	—
86	C₂×Dic₆₇	—	4	2	no	—
87	C₂×Dic₆₇	—	4	2	no	—
88	C₂×Dic₆₇	—	4	2	no	—
89	C₂×Dic₆₇	—	4	2	no	—
90	Dic₁₃₄	—	4	4	no	—
91	Dic₁₃₄	—	4	4	no	—
92	C₈×C₆₇	—	2	2	no	—
93	C₈×C₆₇	—	8	2	no	—
94	C₈×C₆₇	#104	1	4	yes	—
95	C₆₇⋊C₈	—	2	4	no	—
96	C₂²×C₆₇	—	2	1	no	—
97	C₂²×C₆₇	—	2	1	no	—
98	C₂²×C₆₇	#390	1	1	yes	characteristic
99	C₂²×C₆₇	#470	1	2	yes	—
100	C₄×C₆₇	—	2	1	no	—
101	C₄×C₆₇	—	2	1	no	—
102	C₄×C₆₇	C₂×#104	1	2	yes	—
103	C₄×C₆₇	#441	1	2	yes	—
104	C₄×C₆₇	#444	1	2	yes	—
105	C₄×C₆₇	#497	1	2	yes	—
106	Dic₆₇	—	4	4	no	—
107	Dic₆₇	—	8	2	no	—
108	Dic₆₇	—	8	2	no	—
109	#9850	—	67	1	no	maximal, Sylow
110	C₂×C₆₇	—	2	2	no	—
111	C₂×C₆₇	#1962	1	1	yes	characteristic
112	C₂×C₆₇	#1971	1	1	yes	characteristic
113	C₂×C₆₇	#1975	1	1	yes	characteristic
114	#3170	—	67	1	no	—
115	#1994	—	67	2	no	—
116	C₄×#97	—	67	1	no	—
117	#1566	D₆₇	1	1	yes	characteristic
118	#1493	—	67	2	no	—
119	C₆₇	#9850	1	1	yes	characteristic, complemented, Sylow
120	#533	—	67	2	no	—
121	#500	—	67	1	no	—
122	#494	—	67	1	no	—
123	#487	—	67	2	no	—
124	#467	—	134	2	no	—
125	C₄×Q₁₆	—	134	2	no	—
126	#423	C₂×D₆₇	1	2	yes	—
127	C₂×#97	—	134	2	no	—
128	C₂×C₄×C₈	—	67	1	no	—
129	C₂×C₄×C₈	C₂×D₆₇	1	1	yes	characteristic
130	C₄³	—	67	1	no	—
131	#339	—	134	4	no	—
132	#334	—	2	2	no	—
133	Q₈⋊C₈	—	134	4	no	—
134	C₂×Q₁₆	—	134	2	no	—
135	C₂×M₁₆	—	2	2	no	—
136	C₂²×C₈	—	134	1	no	—
137	C₂²×C₈	D₂₆₈	1	2	yes	—
138	C₄⋊Q₈	—	67	2	no	—
139	C₄⋊Q₈	—	67	2	no	—
140	#125	—	134	2	no	—
141	C₂²⋊Q₈	—	134	2	no	—
142	C₂²⋊Q₈	—	134	2	no	—
143	C₄×Q₈	—	134	2	no	—
144	C₄×Q₈	—	134	2	no	—
145	#117	—	134	2	no	—
146	C₂×C₄²	—	67	2	no	—
147	C₂×C₄²	—	134	1	no	—
148	C₂×C₄²	—	134	1	no	—
149	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
150	#107	—	134	2	no	—
151	C₄⋊C₈	—	2	2	no	—
152	C₄⋊C₈	—	2	2	no	—
153	#103	—	134	4	no	—
154	#97	—	134	8	no	—
155	C₄×C₈	—	67	2	no	—
156	C₄×C₈	—	134	1	no	—
157	C₄×C₈	C₄×D₆₇	1	1	yes	characteristic
158	C₄×C₈	C₄×D₆₇	1	1	yes	characteristic
159	C₄×C₈	C₂²⋊D₆₇	1	2	yes	—
160	C₂×Q₈	—	134	2	no	—
161	C₂×Q₈	—	134	2	no	—
162	C₂²×C₄	—	134	2	no	—
163	C₂²×C₄	D₄×D₆₇	1	1	yes	characteristic
164	C₂²×C₄	C₂×D₂₆₈	1	1	yes	characteristic
165	C₂²×C₄	#11761629	1	1	yes	characteristic
166	Q₁₆	—	268	4	no	—
167	M₁₆	—	4	4	no	—
168	C₂×C₈	—	2	4	no	—
169	C₂×C₈	—	4	2	no	—
170	C₂×C₈	—	134	4	no	—
171	C₂×C₈	—	134	2	no	—
172	C₂×C₈	(C₂×D₆₇)⋊C₄	1	2	yes	—
173	C₂×C₈	(C₂×D₆₇)⋊C₄	1	2	yes	—
174	C₄⋊C₄	—	268	2	no	—
175	C₄⋊C₄	—	268	2	no	—
176	C₄⋊C₄	—	134	2	no	—
177	C₄⋊C₄	—	134	2	no	—
178	C₄⋊C₄	—	134	2	no	—
179	C₄⋊C₄	—	134	2	no	—
180	C₂²⋊C₄	—	268	2	no	—
181	C₄²	—	268	2	no	—
182	C₄²	—	268	2	no	—
183	C₄²	—	134	4	no	—
184	C₄²	—	134	4	no	—
185	C₄²	C₂×C₄×D₆₇	1	1	yes	characteristic
186	C₄²	D₄×D₆₇	1	1	yes	characteristic
187	C₄²	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
188	C₄²	#11761629	1	1	yes	characteristic
189	C₂³	#14524018	1	1	yes	characteristic
190	Q₈	—	268	4	no	—
191	Q₈	—	268	4	no	—
192	C₂×C₄	—	2	2	no	—
193	C₂×C₄	—	2	2	no	—
194	C₂×C₄	—	268	2	no	—
195	C₂×C₄	—	268	2	no	—
196	C₂×C₄	—	268	2	no	—
197	C₂×C₄	—	268	2	no	—
198	C₂×C₄	—	134	4	no	—
199	C₂×C₄	C₂×(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
200	C₂×C₄	#14524005	1	1	yes	characteristic
201	C₂×C₄	#14524005	1	1	yes	characteristic
202	C₂×C₄	#14524018	1	1	yes	characteristic
203	C₂×C₄	#14524032	1	1	yes	characteristic
204	C₂×C₄	#14524039	1	1	yes	characteristic
205	C₂×C₄	#14524072	1	4	yes	—
206	C₈	—	2	2	no	—
207	C₈	—	8	2	no	—
208	C₈	—	134	4	no	—
209	C₈	#14523969	1	4	yes	—
210	C₂²	—	2	1	no	—
211	C₂²	—	2	1	no	—
212	C₂²	#16863297	1	1	yes	characteristic
213	C₂²	#16863655	1	2	yes	—
214	C₄	—	2	1	no	—
215	C₄	—	2	1	no	—
216	C₄	—	268	4	no	—
217	C₄	—	536	2	no	—
218	C₄	—	536	2	no	—
219	C₄	C₂×#14523969	1	2	yes	—
220	C₄	#16863502	1	2	yes	—
221	C₄	#16863517	1	2	yes	—
222	C₄	#16863787	1	2	yes	—
223	C₂	—	2	2	no	—
224	C₂	#22561036	1	1	yes	characteristic
225	C₂	#22561078	1	1	yes	characteristic
226	C₂	#22561100	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#22570795

C₂

yes

maximal, characteristic

#22561185

C₂

yes

maximal

C₄×#14523953

C₂

yes

maximal, characteristic

#22558663

C₂

yes

maximal

C₆₇×#1566

C₂

yes

maximal, characteristic

#16863953

C₂²

yes

—

#16863801

C₄

yes

characteristic, complemented

#16863776

C₄

yes

characteristic, complemented

#16863747

C₄

yes

complemented

#16863637

—

C₄×Dic₂₆₈

—

C₂×#14523953

—

C₂×C₄×C₆₇⋊C₈

C₂²

yes

characteristic

C₄²×Dic₆₇

C₂²

yes

characteristic

#16863157

—

#16863126

—

#423×C₆₇

C₂²

yes

—

C₂×C₄×C₈×C₆₇

C₂²

yes

characteristic

#334×C₆₇

—

C₂×Dic₂₆₈

—

C₂²×C₆₇⋊C₈

—

#14524043

C₂×C₄

yes

—

#14524043

C₂×C₄

yes

—

#14524035

—

#14524022

—

#14524022

—

C₄×Dic₁₃₄

—

C₄×Dic₁₃₄

—

#14524002

—

C₂×C₄×Dic₆₇

—

C₂×C₄×Dic₆₇

—

C₂×C₄×Dic₆₇

D₄

yes

—

#14523977

—

#14523968

—

#14523953

—

C₄×C₆₇⋊C₈

—

C₄×C₆₇⋊C₈

D₄

yes

—

C₂×M₁₆×C₆₇

—

C₂²×C₈×C₆₇

D₄

yes

—

C₂×C₄²×C₆₇

C₂³

yes

characteristic

C₄⋊C₈×C₆₇

—

C₄⋊C₈×C₆₇

—

C₄×C₈×C₆₇

C₂×C₄

yes

characteristic

C₄×C₈×C₆₇

C₂×C₄

yes

characteristic

C₄×C₈×C₆₇

D₄

yes

—

C₂×Dic₁₃₄

—

C₂×Dic₁₃₄

—

C₂²×Dic₆₇

—

Dic₂₆₈

—

C₂×C₆₇⋊C₈

—

C₂×C₆₇⋊C₈

—

C₄⋊Dic₆₇

—

C₄⋊Dic₆₇

—

C₄⋊Dic₆₇

—

C₄⋊Dic₆₇

—

Dic₆₇⋊C₄

—

Dic₆₇⋊C₄

—

C₂²⋊Dic₆₇

—

C₄×Dic₆₇

—

C₄×Dic₆₇

—

C₄×Dic₆₇

—

C₄×Dic₆₇

—

C₂²×C₄×C₆₇

C₂×D₄

yes

characteristic

C₂²×C₄×C₆₇

C₂×D₄

yes

characteristic

C₂²×C₄×C₆₇

#41

yes

characteristic

M₁₆×C₆₇

—

C₂×C₈×C₆₇

—

C₂×C₈×C₆₇

—

C₂×C₈×C₆₇

C₂²⋊C₄

yes

—

C₂×C₈×C₆₇

C₂²⋊C₄

yes

—

C₄²×C₆₇

C₂²×C₄

yes

characteristic

C₄²×C₆₇

C₂×D₄

yes

characteristic

C₄²×C₆₇

C₂×D₄

yes

C₄²×C₆₇

yes

C₂³×C₆₇

yes

C₂×C₄×C₆₇

—

C₂×C₄×C₆₇

—

C₂×C₄×C₆₇

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₆₇

C₄×D₄

yes

characteristic

C₂×C₄×C₆₇

C₄×D₄

yes

C₂×C₄×C₆₇

yes

C₂×C₄×C₆₇

yes

C₂×C₄×C₆₇

yes

C₂×C₄×C₆₇

yes

—

C₂×Dic₆₇

—

C₂×Dic₆₇

—

C₂×Dic₆₇

—

C₂×Dic₆₇

—

C₂×Dic₆₇

—

Dic₁₃₄

—

Dic₁₃₄

—

C₈×C₆₇

—

C₈×C₆₇

—

C₈×C₆₇

#104

yes

—

C₆₇⋊C₈

—

C₂²×C₆₇

—

C₂²×C₆₇

—

C₂²×C₆₇

#390

yes

characteristic

C₂²×C₆₇

#470

yes

—

100

C₄×C₆₇

—

101

C₄×C₆₇

—

102

C₄×C₆₇

C₂×#104

yes

—

103

C₄×C₆₇

#441

yes

—

104

C₄×C₆₇

#444

yes

—

105

C₄×C₆₇

#497

yes

—

106

Dic₆₇

—

107

Dic₆₇

—

108

Dic₆₇

—

109

#9850

—

maximal, Sylow

110

C₂×C₆₇

—

111

C₂×C₆₇

#1962

yes

characteristic

112

C₂×C₆₇

#1971

yes

characteristic

113

C₂×C₆₇

#1975

yes

characteristic

114

#3170

—

115

#1994

—

116

C₄×#97

—

117

#1566

D₆₇

yes

characteristic

118

#1493

—

119

C₆₇

#9850

yes

characteristic, complemented, Sylow

120

#533

—

121

#500

—

122

#494

—

123

#487

—

124

#467

—

134

—

125

C₄×Q₁₆

—

134

—

126

#423

C₂×D₆₇

yes

—

127

C₂×#97

—

134

—

128

C₂×C₄×C₈

—

129

C₂×C₄×C₈

C₂×D₆₇

yes

characteristic

130

C₄³

—

131

#339

—

134

—

132

#334

—

133

Q₈⋊C₈

—

134

—

134

C₂×Q₁₆

—

134

—

135

C₂×M₁₆

—

136

C₂²×C₈

—

134

—

137

C₂²×C₈

D₂₆₈

yes

—

138

C₄⋊Q₈

—

139

C₄⋊Q₈

—

140

#125

—

134

—

141

C₂²⋊Q₈

—

134

—

142

C₂²⋊Q₈

—

134

—

143

C₄×Q₈

—

134

—

144

C₄×Q₈

—

134

—

145

#117

—

134

—

146

C₂×C₄²

—

147

C₂×C₄²

—

134

—

148

C₂×C₄²

—

134

—

149

C₂×C₄²

C₂²×D₆₇

yes

characteristic

150

#107

—

134

—

151

C₄⋊C₈

—

152

C₄⋊C₈

—

153

#103

—

134

—

154

#97

—

134

—

155

C₄×C₈

—

156

C₄×C₈

—

134

—

157

C₄×C₈

C₄×D₆₇

yes

characteristic

158

C₄×C₈

C₄×D₆₇

yes

characteristic

159

C₄×C₈

C₂²⋊D₆₇

yes

—

160

C₂×Q₈

—

134

—

161

C₂×Q₈

—

134

—

162

C₂²×C₄

—

134

—

163

C₂²×C₄

D₄×D₆₇

yes

characteristic

164

C₂²×C₄

C₂×D₂₆₈

yes

characteristic

165

C₂²×C₄

#11761629

yes

characteristic

166

Q₁₆

—

268

—

167

M₁₆

—

168

C₂×C₈

—

169

C₂×C₈

—

170

C₂×C₈

—

134

—

171

C₂×C₈

—

134

—

172

C₂×C₈

(C₂×D₆₇)⋊C₄

yes

—

173

C₂×C₈

(C₂×D₆₇)⋊C₄

yes

—

174

C₄⋊C₄

—

268

—

175

C₄⋊C₄

—

268

—

176

C₄⋊C₄

—

134

—

177

C₄⋊C₄

—

134

—

178

C₄⋊C₄

—

134

—

179

C₄⋊C₄

—

134

—

180

C₂²⋊C₄

—

268

—

181

C₄²

—

268

—

182

C₄²

—

268

—

183

C₄²

—

134

—

184

C₄²

—

134

—

185

C₄²

C₂×C₄×D₆₇

yes

characteristic

186

C₄²

D₄×D₆₇

yes

characteristic

187

C₄²

C₂×C₂²⋊D₆₇

yes

characteristic

188

C₄²

#11761629

yes

characteristic

189

C₂³

#14524018

yes

characteristic

190

Q₈

—

268

—

191

Q₈

—

268

—

192

C₂×C₄

—

193

C₂×C₄

—

194

C₂×C₄

—

268

—

195

C₂×C₄

—

268

—

196

C₂×C₄

—

268

—

197

C₂×C₄

—

268

—

198

C₂×C₄

—

134

—

199

C₂×C₄

C₂×(C₂×D₆₇)⋊C₄

yes

characteristic

200

C₂×C₄

#14524005

yes

characteristic

201

C₂×C₄

#14524005

yes

characteristic

202

C₂×C₄

#14524018

yes

characteristic

203

C₂×C₄

#14524032

yes

characteristic

204

C₂×C₄

#14524039

yes

characteristic

205

C₂×C₄

#14524072

yes

—

206

C₈

—

207

C₈

—

208

C₈

—

134

—

209

C₈

#14523969

yes

—

210

C₂²

—

211

C₂²

—

212

C₂²

#16863297

yes

characteristic

213

C₂²

#16863655

yes

—

214

C₄

—

215

C₄

—

216

C₄

—

268

—

217

C₄

—

536

—

218

C₄

—

536

—

219

C₄

C₂×#14523969

yes

—

220

C₄

#16863502

yes

—

221

C₄

#16863517

yes

—

222

C₄

#16863787

yes

—

223

C₂

—

224

C₂

#22561036

yes

characteristic

225

C₂

#22561078

yes

characteristic

226

C₂

#22561100

yes

characteristic

	subgroup	G/H
center	C₂×C₄	#14524039
commutator	C₄²×C₆₇	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₆₇
Fitting	C₆₇×#1566	C₂
socle	C₂²×C₆₇	#390
prime radical	C₂³×C₆₇	#121
cosocle	C₂×C₄²×C₆₇	C₂³
hypercenter	#1566	D₆₇
hypocenter	C₆₇	#9850
LCS	G ▷ C₄²×C₆₇ ▷ C₂²×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1566

subgroup

G/H

center

C₂×C₄

#14524039

commutator

C₄²×C₆₇

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₆₇

Fitting

C₆₇×#1566

C₂

C₂²×C₆₇

C₂³×C₆₇

C₂×C₄²×C₆₇

C₂³

D₆₇

C₆₇

G ▷ C₄²×C₆₇ ▷ C₂²×C₆₇ ▷ C₆₇

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1566

N	H ≅ G/N	type
7. #16863801	C₄	semidirect
8. #16863776	C₄	semidirect
9. #16863747	C₄	semidirect
119. C₆₇	#9850	semidirect

H ≅ G/N

type

7. #16863801

C₄

semidirect

8. #16863776

C₄

semidirect

9. #16863747

C₄

semidirect

119. C₆₇

#9850

semidirect

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

subgroup	index
#22570795	2
#22561185	2
C₄×#14523953	2
#22558663	2
C₆₇×#1566	2
#9850	67

subgroup

index

C₆₇×#1566

Subgroups — #30755739

Conjugacy classes of subgroups

Complements

Maximal subgroups