Group #30759960 — subgroups

Subgroups — #30759960

Order 17152.

402 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 402 conjugacy classes of subgroups — too many to draw. Only its 95 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	#22571554	C₂	1	1	yes	maximal, characteristic
2	#22561185	C₂	1	2	yes	maximal
3	#22560360	C₂	1	1	yes	maximal, characteristic
4	#22558900	C₂	1	2	yes	maximal
5	C₆₇×#1292	C₂	1	1	yes	maximal, characteristic
6	#16863953	C₂²	1	2	yes	—
7	#16863692	—	2	2	no	—
8	#16863637	—	2	2	no	—
9	#16863607	—	2	2	no	—
10	C₂×C₄⋊(C₆₇⋊C₈)	C₂²	1	1	yes	characteristic
11	C₂×Dic₆₇⋊C₈	—	2	2	no	—
12	C₄²×Dic₆₇	C₂²	1	1	yes	characteristic
13	#16863157	—	2	2	no	—
14	#16863157	—	2	2	no	—
15	#16863144	—	2	2	no	—
16	#16863141	—	2	2	no	—
17	#423×C₆₇	C₂²	1	2	yes	—
18	C₂×C₄⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
19	C₂×Dic₂₆₈	—	2	2	no	—
20	C₂²×C₆₇⋊C₈	—	2	1	no	—
21	#14524043	D₄	1	2	yes	—
22	#14524043	D₄	1	2	yes	—
23	#14524035	—	2	2	no	—
24	#14524022	—	2	2	no	—
25	#14524022	—	2	2	no	—
26	C₄×Dic₁₃₄	—	2	2	no	—
27	C₄×Dic₁₃₄	—	2	2	no	—
28	#14524002	—	2	2	no	—
29	C₂×C₄×Dic₆₇	—	2	1	no	—
30	C₂×C₄×Dic₆₇	—	2	1	no	—
31	C₂×C₄×Dic₆₇	D₄	1	1	yes	characteristic
32	C₂×C₄×Dic₆₇	D₄	1	1	yes	characteristic
33	#14523977	—	2	2	no	—
34	C₄⋊(C₆₇⋊C₈)	—	2	2	no	—
35	Dic₆₇⋊C₈	—	4	4	no	—
36	#14523968	—	2	4	no	—
37	C₂×M₁₆×C₆₇	—	2	2	no	—
38	C₂²×C₈×C₆₇	D₄	1	2	yes	—
39	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
40	C₄⋊C₈×C₆₇	—	2	2	no	—
41	C₄⋊C₈×C₆₇	—	2	2	no	—
42	C₄⋊C₈×C₆₇	—	2	2	no	—
43	C₂×Dic₁₃₄	—	2	2	no	—
44	C₂×Dic₁₃₄	—	2	2	no	—
45	C₂²×Dic₆₇	—	2	1	no	—
46	C₂²×Dic₆₇	—	2	1	no	—
47	Dic₂₆₈	—	8	2	no	—
48	C₂×C₆₇⋊C₈	—	4	2	no	—
49	C₂×C₆₇⋊C₈	—	4	1	no	—
50	C₄⋊Dic₆₇	—	2	2	no	—
51	C₄⋊Dic₆₇	—	2	2	no	—
52	C₄⋊Dic₆₇	—	2	2	no	—
53	C₄⋊Dic₆₇	—	2	2	no	—
54	Dic₆₇⋊C₄	—	4	2	no	—
55	Dic₆₇⋊C₄	—	4	2	no	—
56	C₂²⋊Dic₆₇	—	4	2	no	—
57	C₄×Dic₆₇	—	2	2	no	—
58	C₄×Dic₆₇	—	2	2	no	—
59	C₄×Dic₆₇	—	2	1	no	—
60	C₄×Dic₆₇	—	2	2	no	—
61	C₄×Dic₆₇	—	4	2	no	—
62	C₄×Dic₆₇	—	4	2	no	—
63	C₄×Dic₆₇	Q₁₆	1	2	yes	complemented
64	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
65	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
66	C₂²×C₄×C₆₇	#41	1	1	yes	characteristic
67	M₁₆×C₆₇	—	4	2	no	—
68	M₁₆×C₆₇	—	4	2	no	—
69	C₂×C₈×C₆₇	—	2	2	no	—
70	C₂×C₈×C₆₇	—	4	2	no	—
71	C₂×C₈×C₆₇	—	4	2	no	—
72	C₄²×C₆₇	C₂×D₄	1	2	yes	—
73	C₄²×C₆₇	#41	1	2	yes	—
74	C₂³×C₆₇	#121	1	1	yes	characteristic
75	C₂×C₄×C₆₇	—	2	1	no	—
76	C₂×C₄×C₆₇	—	2	1	no	—
77	C₂×C₄×C₆₇	—	4	1	no	—
78	C₂×C₄×C₆₇	#120	1	1	yes	characteristic
79	C₂×C₄×C₆₇	#121	1	2	yes	—
80	C₂×C₄×C₆₇	#123	1	2	yes	—
81	C₂×C₄×C₆₇	#124	1	1	yes	characteristic
82	C₂×C₄×C₆₇	C₂×Q₁₆	1	1	yes	characteristic
83	C₂×C₄×C₆₇	#135	1	1	yes	characteristic
84	C₂×C₄×C₆₇	#137	1	2	yes	—
85	C₂×Dic₆₇	—	2	2	no	—
86	C₂×Dic₆₇	—	2	2	no	—
87	C₂×Dic₆₇	—	2	2	no	—
88	C₂×Dic₆₇	—	2	2	no	—
89	C₂×Dic₆₇	—	4	1	no	—
90	C₂×Dic₆₇	—	4	1	no	—
91	C₂×Dic₆₇	—	4	2	no	—
92	C₂×Dic₆₇	—	4	2	no	—
93	Dic₁₃₄	—	4	2	no	—
94	Dic₁₃₄	—	4	2	no	—
95	Dic₁₃₄	—	8	2	no	—
96	C₈×C₆₇	—	4	2	no	—
97	C₈×C₆₇	—	8	2	no	—
98	C₆₇⋊C₈	—	8	1	no	—
99	C₂²×C₆₇	—	2	1	no	—
100	C₂²×C₆₇	—	2	1	no	—
101	C₂²×C₆₇	#394	1	1	yes	characteristic
102	C₂²×C₆₇	#467	1	1	yes	characteristic
103	C₂²×C₆₇	#470	1	1	yes	characteristic
104	C₄×C₆₇	—	2	2	no	—
105	C₄×C₆₇	—	2	1	no	—
106	C₄×C₆₇	#453	1	1	yes	characteristic
107	C₄×C₆₇	#456	1	1	yes	characteristic
108	C₄×C₆₇	#462	1	2	yes	—
109	C₄×C₆₇	#464	1	2	yes	—
110	Dic₆₇	—	2	4	no	—
111	Dic₆₇	—	4	2	no	—
112	Dic₆₇	—	8	2	no	—
113	Dic₆₇	—	8	2	no	—
114	#10522	—	67	1	no	maximal, Sylow
115	C₂×C₆₇	—	2	1	no	—
116	C₂×C₆₇	—	2	1	no	—
117	C₂×C₆₇	#2039	1	1	yes	characteristic
118	C₂×C₆₇	#2050	1	1	yes	characteristic
119	C₂×C₆₇	#2056	1	1	yes	characteristic
120	#3249	—	67	1	no	—
121	#1994	—	67	2	no	—
122	#1842	—	67	1	no	—
123	#1550	—	67	2	no	—
124	#1292	D₆₇	1	1	yes	characteristic
125	C₆₇	#10522	1	1	yes	characteristic, complemented, Sylow
126	#533	—	67	2	no	—
127	#477	—	134	2	no	—
128	#467	—	134	2	no	—
129	#462	—	134	2	no	—
130	#423	C₂×D₆₇	1	2	yes	—
131	C₂×C₄⋊C₈	—	67	1	no	—
132	C₂×C₄⋊C₈	—	134	2	no	—
133	C₂×C₄⋊C₈	C₂×D₆₇	1	1	yes	characteristic
134	C₄³	—	67	1	no	—
135	#339	—	134	2	no	—
136	#339	—	134	2	no	—
137	#333	—	134	2	no	—
138	#332	—	134	2	no	—
139	C₂×Q₁₆	—	134	2	no	—
140	C₂×M₁₆	—	2	2	no	—
141	C₂²×C₈	—	134	1	no	—
142	C₂²×C₈	D₂₆₈	1	2	yes	—
143	C₄⋊Q₈	—	67	2	no	—
144	C₄⋊Q₈	—	67	2	no	—
145	#125	—	134	2	no	—
146	C₂²⋊Q₈	—	134	2	no	—
147	C₂²⋊Q₈	—	134	2	no	—
148	C₄×Q₈	—	134	2	no	—
149	C₄×Q₈	—	134	2	no	—
150	#117	—	134	2	no	—
151	C₂×C₄²	—	67	1	no	—
152	C₂×C₄²	—	67	1	no	—
153	C₂×C₄²	—	134	1	no	—
154	C₂×C₄²	—	134	1	no	—
155	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
156	#107	—	134	2	no	—
157	C₄⋊C₈	—	2	2	no	—
158	C₄⋊C₈	—	2	2	no	—
159	C₄⋊C₈	—	2	2	no	—
160	C₄⋊C₈	—	268	4	no	—
161	C₄⋊C₈	—	134	2	no	—
162	#103	—	134	4	no	—
163	C₂×Q₈	—	134	2	no	—
164	C₂×Q₈	—	134	2	no	—
165	C₂²×C₄	—	134	1	no	—
166	C₂²×C₄	—	134	1	no	—
167	C₂²×C₄	D₄×D₆₇	1	1	yes	characteristic
168	C₂²×C₄	C₂×D₂₆₈	1	1	yes	characteristic
169	C₂²×C₄	#11761629	1	1	yes	characteristic
170	Q₁₆	—	536	2	no	—
171	M₁₆	—	4	2	no	—
172	M₁₆	—	4	2	no	—
173	C₂×C₈	—	2	2	no	—
174	C₂×C₈	—	4	2	no	—
175	C₂×C₈	—	4	2	no	—
176	C₂×C₈	—	268	2	no	—
177	C₂×C₈	—	268	1	no	—
178	C₄⋊C₄	—	268	2	no	—
179	C₄⋊C₄	—	268	2	no	—
180	C₄⋊C₄	—	134	2	no	—
181	C₄⋊C₄	—	134	2	no	—
182	C₄⋊C₄	—	134	2	no	—
183	C₄⋊C₄	—	134	2	no	—
184	C₂²⋊C₄	—	268	2	no	—
185	C₄²	—	268	2	no	—
186	C₄²	—	268	2	no	—
187	C₄²	—	67	2	no	—
188	C₄²	—	134	2	no	—
189	C₄²	—	134	2	no	—
190	C₄²	—	134	2	no	—
191	C₄²	—	134	1	no	—
192	C₄²	D₄×D₆₇	1	2	yes	—
193	C₄²	#11761628	1	2	yes	—
194	C₂³	#14524018	1	1	yes	characteristic
195	Q₈	—	268	2	no	—
196	Q₈	—	268	2	no	—
197	Q₈	—	536	2	no	—
198	C₂×C₄	—	2	1	no	—
199	C₂×C₄	—	2	1	no	—
200	C₂×C₄	—	4	1	no	—
201	C₂×C₄	—	268	1	no	—
202	C₂×C₄	—	268	1	no	—
203	C₂×C₄	—	268	2	no	—
204	C₂×C₄	—	268	2	no	—
205	C₂×C₄	—	134	2	no	—
206	C₂×C₄	—	134	2	no	—
207	C₂×C₄	—	134	2	no	—
208	C₂×C₄	—	134	2	no	—
209	C₂×C₄	#14524013	1	1	yes	characteristic
210	C₂×C₄	#14524016	1	2	yes	—
211	C₂×C₄	#14524028	1	2	yes	—
212	C₂×C₄	#14524031	1	1	yes	characteristic
213	C₂×C₄	Q₁₆×D₆₇	1	1	yes	characteristic
214	C₂×C₄	#14524062	1	1	yes	characteristic
215	C₂×C₄	#14524072	1	2	yes	—
216	C₈	—	4	2	no	—
217	C₈	—	8	2	no	—
218	C₈	—	536	1	no	—
219	C₂²	—	2	1	no	—
220	C₂²	—	2	1	no	—
221	C₂²	#16863314	1	1	yes	characteristic
222	C₂²	#16863638	1	1	yes	characteristic
223	C₂²	#16863655	1	1	yes	characteristic
224	C₄	—	2	1	no	—
225	C₄	—	2	2	no	—
226	C₄	—	268	2	no	—
227	C₄	—	536	2	no	—
228	C₄	—	536	2	no	—
229	C₄	—	134	4	no	—
230	C₄	#16863566	1	1	yes	characteristic
231	C₄	#16863581	1	1	yes	characteristic
232	C₄	#16863605	1	2	yes	—
233	C₄	#16863617	1	2	yes	—
234	C₂	—	2	1	no	—
235	C₂	—	2	1	no	—
236	C₂	#22561434	1	1	yes	characteristic
237	C₂	#22561497	1	1	yes	characteristic
238	C₂	#22561533	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#22571554

C₂

yes

maximal, characteristic

#22561185

C₂

yes

maximal

#22560360

C₂

yes

maximal, characteristic

#22558900

C₂

yes

maximal

C₆₇×#1292

C₂

yes

maximal, characteristic

#16863953

C₂²

yes

—

#16863692

—

#16863637

—

#16863607

—

C₂×C₄⋊(C₆₇⋊C₈)

C₂²

yes

characteristic

C₂×Dic₆₇⋊C₈

—

C₄²×Dic₆₇

C₂²

yes

—

—

—

—

#423×C₆₇

C₂²

yes

—

C₂×C₄⋊C₈×C₆₇

C₂²

yes

characteristic

C₂×Dic₂₆₈

—

C₂²×C₆₇⋊C₈

—

#14524043

D₄

yes

—

#14524043

D₄

yes

—

#14524035

—

#14524022

—

#14524022

—

C₄×Dic₁₃₄

—

C₄×Dic₁₃₄

—

#14524002

—

C₂×C₄×Dic₆₇

—

C₂×C₄×Dic₆₇

—

C₂×C₄×Dic₆₇

D₄

yes

characteristic

C₂×C₄×Dic₆₇

D₄

yes

characteristic

#14523977

—

C₄⋊(C₆₇⋊C₈)

—

Dic₆₇⋊C₈

—

#14523968

—

C₂×M₁₆×C₆₇

—

C₂²×C₈×C₆₇

D₄

yes

—

C₂×C₄²×C₆₇

C₂³

yes

characteristic

C₄⋊C₈×C₆₇

—

C₄⋊C₈×C₆₇

—

C₄⋊C₈×C₆₇

—

C₂×Dic₁₃₄

—

C₂×Dic₁₃₄

—

C₂²×Dic₆₇

—

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

—

C₄×Dic₆₇

—

C₄×Dic₆₇

—

C₄×Dic₆₇

Q₁₆

yes

complemented

C₂²×C₄×C₆₇

C₂×D₄

yes

characteristic

C₂²×C₄×C₆₇

C₂×D₄

yes

characteristic

C₂²×C₄×C₆₇

#41

yes

characteristic

M₁₆×C₆₇

—

M₁₆×C₆₇

—

C₂×C₈×C₆₇

—

C₂×C₈×C₆₇

—

C₂×C₈×C₆₇

—

C₄²×C₆₇

C₂×D₄

yes

—

C₄²×C₆₇

#41

yes

—

C₂³×C₆₇

#121

yes

characteristic

C₂×C₄×C₆₇

—

C₂×C₄×C₆₇

—

C₂×C₄×C₆₇

—

C₂×C₄×C₆₇

#120

yes

characteristic

C₂×C₄×C₆₇

#121

yes

—

C₂×C₄×C₆₇

#123

yes

—

C₂×C₄×C₆₇

#124

yes

characteristic

C₂×C₄×C₆₇

C₂×Q₁₆

yes

C₂×C₄×C₆₇

yes

C₂×C₄×C₆₇

yes

—

C₂×Dic₆₇

—

C₂×Dic₆₇

—

C₂×Dic₆₇

—

C₂×Dic₆₇

—

C₂×Dic₆₇

—

C₂×Dic₆₇

—

C₂×Dic₆₇

—

C₂×Dic₆₇

—

Dic₁₃₄

—

Dic₁₃₄

—

Dic₁₃₄

—

C₈×C₆₇

—

C₈×C₆₇

—

C₆₇⋊C₈

—

C₂²×C₆₇

—

100

C₂²×C₆₇

—

101

C₂²×C₆₇

#394

yes

characteristic

102

C₂²×C₆₇

#467

yes

characteristic

103

C₂²×C₆₇

#470

yes

characteristic

104

C₄×C₆₇

—

105

C₄×C₆₇

—

106

C₄×C₆₇

#453

yes

characteristic

107

C₄×C₆₇

#456

yes

characteristic

108

C₄×C₆₇

#462

yes

—

109

C₄×C₆₇

#464

yes

—

110

Dic₆₇

—

111

Dic₆₇

—

112

Dic₆₇

—

113

Dic₆₇

—

114

#10522

—

maximal, Sylow

115

C₂×C₆₇

—

116

C₂×C₆₇

—

117

C₂×C₆₇

#2039

yes

characteristic

118

C₂×C₆₇

#2050

yes

characteristic

119

C₂×C₆₇

#2056

yes

characteristic

120

#3249

—

121

#1994

—

122

#1842

—

123

#1550

—

124

#1292

D₆₇

yes

characteristic

125

C₆₇

#10522

yes

characteristic, complemented, Sylow

126

#533

—

127

#477

—

134

—

128

#467

—

134

—

129

#462

—

134

—

130

#423

C₂×D₆₇

yes

—

131

C₂×C₄⋊C₈

—

132

C₂×C₄⋊C₈

—

134

—

133

C₂×C₄⋊C₈

C₂×D₆₇

yes

characteristic

134

C₄³

—

135

#339

—

134

—

136

#339

—

134

—

137

#333

—

134

—

138

#332

—

134

—

139

C₂×Q₁₆

—

134

—

140

C₂×M₁₆

—

141

C₂²×C₈

—

134

—

142

C₂²×C₈

D₂₆₈

yes

—

143

C₄⋊Q₈

—

144

C₄⋊Q₈

—

145

#125

—

134

—

146

C₂²⋊Q₈

—

134

—

147

C₂²⋊Q₈

—

134

—

148

C₄×Q₈

—

134

—

149

C₄×Q₈

—

134

—

150

#117

—

134

—

151

C₂×C₄²

—

152

C₂×C₄²

—

153

C₂×C₄²

—

134

—

154

C₂×C₄²

—

134

—

155

C₂×C₄²

C₂²×D₆₇

yes

characteristic

156

#107

—

134

—

157

C₄⋊C₈

—

158

C₄⋊C₈

—

159

C₄⋊C₈

—

160

C₄⋊C₈

—

268

—

161

C₄⋊C₈

—

134

—

162

#103

—

134

—

163

C₂×Q₈

—

134

—

164

C₂×Q₈

—

134

—

165

C₂²×C₄

—

134

—

166

C₂²×C₄

—

134

—

167

C₂²×C₄

D₄×D₆₇

yes

characteristic

168

C₂²×C₄

C₂×D₂₆₈

yes

characteristic

169

C₂²×C₄

#11761629

yes

characteristic

170

Q₁₆

—

536

—

171

M₁₆

—

172

M₁₆

—

173

C₂×C₈

—

174

C₂×C₈

—

175

C₂×C₈

—

176

C₂×C₈

—

268

—

177

C₂×C₈

—

268

—

178

C₄⋊C₄

—

268

—

179

C₄⋊C₄

—

268

—

180

C₄⋊C₄

—

134

—

181

C₄⋊C₄

—

134

—

182

C₄⋊C₄

—

134

—

183

C₄⋊C₄

—

134

—

184

C₂²⋊C₄

—

268

—

185

C₄²

—

268

—

186

C₄²

—

268

—

187

C₄²

—

188

C₄²

—

134

—

189

C₄²

—

134

—

190

C₄²

—

134

—

191

C₄²

—

134

—

192

C₄²

D₄×D₆₇

yes

—

193

C₄²

#11761628

yes

—

194

C₂³

#14524018

yes

characteristic

195

Q₈

—

268

—

196

Q₈

—

268

—

197

Q₈

—

536

—

198

C₂×C₄

—

199

C₂×C₄

—

200

C₂×C₄

—

201

C₂×C₄

—

268

—

202

C₂×C₄

—

268

—

203

C₂×C₄

—

268

—

204

C₂×C₄

—

268

—

205

C₂×C₄

—

134

—

206

C₂×C₄

—

134

—

207

C₂×C₄

—

134

—

208

C₂×C₄

—

134

—

209

C₂×C₄

#14524013

yes

characteristic

210

C₂×C₄

#14524016

yes

—

211

C₂×C₄

#14524028

yes

—

212

C₂×C₄

#14524031

yes

characteristic

213

C₂×C₄

Q₁₆×D₆₇

yes

characteristic

214

C₂×C₄

#14524062

yes

characteristic

215

C₂×C₄

#14524072

yes

—

216

C₈

—

217

C₈

—

218

C₈

—

536

—

219

C₂²

—

220

C₂²

—

221

C₂²

#16863314

yes

characteristic

222

C₂²

#16863638

yes

characteristic

223

C₂²

#16863655

yes

characteristic

224

C₄

—

225

C₄

—

226

C₄

—

268

—

227

C₄

—

536

—

228

C₄

—

536

—

229

C₄

—

134

—

230

C₄

#16863566

yes

characteristic

231

C₄

#16863581

yes

characteristic

232

C₄

#16863605

yes

—

233

C₄

#16863617

yes

—

234

C₂

—

235

C₂

—

236

C₂

#22561434

yes

characteristic

237

C₂

#22561497

yes

characteristic

238

C₂

#22561533

yes

characteristic

	subgroup	G/H
center	C₂²	#16863314
commutator, cosocle	C₂×C₄²×C₆₇	C₂³
Frattini	C₂×C₄²	C₂²×D₆₇
Fitting	C₆₇×#1292	C₂
socle	C₂²×C₆₇	#394
prime radical	C₂³×C₆₇	#121
hypercenter	#1292	D₆₇
hypocenter	C₆₇	#10522
LCS	G ▷ C₂×C₄²×C₆₇ ▷ C₂²×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1292

subgroup

G/H

center

C₂²

#16863314

commutator, cosocle

C₂×C₄²×C₆₇

C₂³

Frattini

C₂×C₄²

C₂²×D₆₇

Fitting

C₆₇×#1292

C₂

C₂²×C₆₇

C₂³×C₆₇

D₆₇

C₆₇

G ▷ C₂×C₄²×C₆₇ ▷ C₂²×C₆₇ ▷ C₆₇

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1292

N	H ≅ G/N	type
63. C₄×Dic₆₇	Q₁₆	semidirect
125. C₆₇	#10522	semidirect

H ≅ G/N

type

63. C₄×Dic₆₇

Q₁₆

semidirect

125. C₆₇

#10522

semidirect

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

subgroup	index
#22571554	2
#22561185	2
#22560360	2
#22558900	2
C₆₇×#1292	2
#10522	67

subgroup

index

C₆₇×#1292

Subgroups — #30759960

Conjugacy classes of subgroups

Complements

Maximal subgroups