Group #22621586 — subgroups

Subgroups — #22621586

Order 9344.

476 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 476 conjugacy classes of subgroups — too many to draw. Only its 121 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×#14556620	C₂	1	2	yes	maximal, complemented
2	#17989245	C₂	1	2	yes	maximal, complemented
3	#17988830	C₂	1	2	yes	maximal, complemented
4	#17988806	C₂	1	2	yes	maximal, complemented
5	#17988741	C₂	1	2	yes	maximal, complemented
6	#17988729	C₂	1	2	yes	maximal, complemented
7	C₄×Dic₂₉₂	C₂	1	1	yes	maximal, characteristic, complemented
8	#17988666	C₂	1	1	yes	maximal, characteristic, complemented
9	#495×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#11924027	C₂²	1	2	yes	—
11	C₂×Q₈×D₇₃	C₂²	1	2	yes	—
12	#14556620	—	2	8	no	—
13	C₂×Dic₂₉₂	C₂²	1	1	yes	characteristic
14	C₂×#11924018	C₂²	1	2	yes	—
15	C₂×#11924016	C₂²	1	2	yes	—
16	C₂×#11924011	C₂²	1	2	yes	—
17	#14556577	—	2	2	no	—
18	#14556568	—	2	2	no	—
19	#14556567	C₂²	1	2	yes	—
20	#14556564	—	2	2	no	—
21	#14556562	C₂²	1	2	yes	—
22	C₄×Dic₁₄₆	C₂²	1	2	yes	—
23	C₄×D₂₉₂	C₂²	1	1	yes	characteristic
24	#14556551	—	2	2	no	—
25	#14556525	C₂²	1	1	yes	characteristic
26	C₄⋊#10596831	C₂²	1	1	yes	characteristic
27	#14556516	C₂²	1	2	yes	—
28	#14556515	C₂²	1	2	yes	—
29	#14556512	C₂²	1	2	yes	—
30	#14556503	C₂²	1	2	yes	—
31	C₂×Q₁₆×C₇₃	C₂²	1	1	yes	characteristic
32	C₂×SD₁₆×C₇₃	C₂²	1	2	yes	—
33	C₂×D₈×C₇₃	C₂²	1	1	yes	characteristic
34	#124×C₇₃	C₂²	1	2	yes	—
35	C₄×C₈×C₇₃	C₂²	1	1	yes	characteristic
36	#11924027	—	2	4	no	—
37	#11924027	—	4	2	no	—
38	C₂×Dic₁₄₆	—	2	2	no	—
39	C₂×Dic₁₄₆	C₂³	1	2	yes	—
40	Q₈×D₇₃	—	2	4	no	—
41	Q₈×D₇₃	—	4	2	no	—
42	C₂×D₂₉₂	D₄	1	1	yes	characteristic
43	C₂×C₂²⋊D₇₃	—	2	2	no	—
44	C₂×C₂²⋊D₇₃	—	2	2	no	—
45	C₂²×Dic₇₃	—	2	2	no	—
46	C₂×C₄×D₇₃	—	2	2	no	—
47	C₂×C₄×D₇₃	C₂³	1	2	yes	—
48	Dic₂₉₂	D₄	1	4	yes	complemented
49	#11924018	—	2	4	no	—
50	#11924016	—	2	4	no	—
51	#11924011	—	2	4	no	—
52	C₂×#10596831	C₂³	1	2	yes	—
53	C₄⋊Dic₇₃	D₄	1	1	yes	characteristic
54	C₄⋊Dic₇₃	C₂³	1	2	yes	—
55	#11924007	—	2	2	no	—
56	#11924007	—	2	2	no	—
57	C₂²⋊Dic₇₃	—	2	2	no	—
58	#11924005	—	2	2	no	—
59	#11924005	D₄	1	2	yes	—
60	C₄×Dic₇₃	—	2	2	no	—
61	C₂×Q₈×C₇₃	C₂³	1	2	yes	—
62	C₂×D₄×C₇₃	C₂³	1	2	yes	—
63	Q₁₆×C₇₃	—	4	1	no	—
64	SD₁₆×C₇₃	—	2	4	no	—
65	D₈×C₇₃	—	4	1	no	—
66	C₂×C₈×C₇₃	C₂³	1	1	yes	characteristic
67	C₂×C₈×C₇₃	C₂³	1	1	yes	characteristic
68	C₂²⋊C₄×C₇₃	—	2	2	no	—
69	C₂²⋊C₄×C₇₃	—	2	2	no	—
70	C₄²×C₇₃	C₂³	1	1	yes	characteristic
71	C₂³×C₇₃	—	2	2	no	—
72	C₂²×D₇₃	C₂×D₄	1	2	yes	—
73	Q₈×C₇₃	—	2	2	no	—
74	Q₈×C₇₃	—	2	2	no	—
75	D₄×C₇₃	—	2	2	no	—
76	D₄×C₇₃	—	2	2	no	—
77	C₂×C₄×C₇₃	—	2	2	no	—
78	C₂×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
79	C₂×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
80	C₂×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
81	C₂²⋊D₇₃	—	4	4	no	—
82	C₂²⋊D₇₃	—	4	4	no	—
83	C₂×Dic₇₃	—	2	2	no	—
84	C₂×Dic₇₃	—	2	2	no	—
85	C₂×Dic₇₃	—	4	4	no	—
86	C₂×Dic₇₃	C₂×D₄	1	2	yes	—
87	D₂₉₂	—	4	1	no	—
88	C₄×D₇₃	—	2	2	no	—
89	C₄×D₇₃	—	2	2	no	—
90	C₄×D₇₃	—	4	4	no	—
91	Dic₁₄₆	—	2	2	no	—
92	Dic₁₄₆	—	4	4	no	—
93	Dic₁₄₆	C₂×D₄	1	4	yes	—
94	C₈×C₇₃	—	2	1	no	—
95	C₈×C₇₃	C₂×D₄	1	2	yes	—
96	#10596831	—	2	2	no	—
97	C₂²×C₇₃	—	4	2	no	—
98	C₂²×C₇₃	—	4	2	no	—
99	C₂²×C₇₃	—	4	2	no	—
100	C₂²×C₇₃	C₂²×D₄	1	1	yes	characteristic
101	C₂×D₇₃	—	2	2	no	—
102	C₂×D₇₃	—	2	2	no	—
103	C₂×D₇₃	—	2	2	no	—
104	C₄×C₇₃	—	2	1	no	—
105	C₄×C₇₃	—	2	1	no	—
106	C₄×C₇₃	—	4	2	no	—
107	C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
108	C₄×C₇₃	H(5,𝔽₂)	1	1	yes	characteristic
109	Dic₇₃	—	2	4	no	—
110	Dic₇₃	—	2	2	no	—
111	Dic₇₃	—	4	2	no	—
112	C₂×C₇₃	—	8	2	no	—
113	C₂×C₇₃	D₄²	1	1	yes	characteristic
114	C₂×C₇₃	#575	1	1	yes	characteristic
115	C₂×C₇₃	#578	1	1	yes	characteristic
116	D₇₃	—	4	2	no	—
117	#3277	—	73	1	no	maximal, Sylow
118	C₇₃	#3277	1	1	yes	characteristic, complemented, Sylow
119	C₂×#137	—	73	2	no	—
120	#548	—	73	2	no	—
121	#495	D₇₃	1	1	yes	characteristic, complemented
122	#468	—	73	2	no	—
123	#464	—	73	2	no	—
124	#451	—	73	2	no	—
125	#449	—	73	2	no	—
126	C₄×Q₁₆	—	73	1	no	—
127	#436	—	73	1	no	—
128	C₂×#41	—	73	2	no	—
129	C₂²×Q₈	—	73	2	no	—
130	#137	—	146	8	no	—
131	C₂×Q₁₆	—	73	2	no	—
132	C₂×Q₁₆	—	73	1	no	—
133	C₂×Q₁₆	C₂×D₇₃	1	1	yes	characteristic
134	C₂×SD₁₆	—	73	2	no	—
135	C₂×SD₁₆	C₂×D₇₃	1	2	yes	—
136	C₂×D₈	C₂×D₇₃	1	1	yes	characteristic
137	C₂×M₁₆	—	73	2	no	—
138	#124	—	146	2	no	—
139	#124	C₂×D₇₃	1	2	yes	—
140	C₂²⋊Q₈	—	73	2	no	—
141	C₂²⋊Q₈	—	146	2	no	—
142	#121	—	73	2	no	—
143	#121	—	146	2	no	—
144	C₄×Q₈	—	73	2	no	—
145	C₄×D₄	—	73	1	no	—
146	C₄×D₄	—	146	2	no	—
147	#107	—	73	1	no	—
148	C₄⋊C₈	—	73	1	no	—
149	#103	—	73	2	no	—
150	#103	—	73	2	no	—
151	#102	—	73	2	no	—
152	C₂²⋊C₈	—	73	2	no	—
153	C₄×C₈	C₂×D₇₃	1	1	yes	characteristic
154	#41	—	292	2	no	—
155	#41	—	146	4	no	—
156	C₂×Q₈	—	292	2	no	—
157	C₂×Q₈	—	73	2	no	—
158	C₂×Q₈	—	146	2	no	—
159	C₂×Q₈	—	146	4	no	—
160	C₂×Q₈	C₂²×D₇₃	1	2	yes	—
161	C₂×D₄	—	73	1	no	—
162	C₂×D₄	—	146	2	no	—
163	C₂×D₄	—	146	2	no	—
164	C₂×D₄	C₂²×D₇₃	1	2	yes	—
165	C₂²×C₄	—	73	2	no	—
166	C₂²×C₄	—	146	2	no	—
167	C₂²×C₄	—	146	2	no	—
168	Q₁₆	—	4	1	no	—
169	Q₁₆	—	73	4	no	—
170	Q₁₆	—	146	4	no	—
171	SD₁₆	—	2	4	no	—
172	SD₁₆	—	146	4	no	—
173	D₈	—	4	1	no	—
174	M₁₆	—	146	4	no	—
175	C₂×C₈	—	73	2	no	—
176	C₂×C₈	C₂²×D₇₃	1	1	yes	characteristic
177	C₂×C₈	C₂²×D₇₃	1	1	yes	characteristic
178	C₄⋊C₄	—	73	1	no	—
179	C₄⋊C₄	—	73	2	no	—
180	C₄⋊C₄	—	146	2	no	—
181	C₄⋊C₄	—	146	2	no	—
182	C₂²⋊C₄	—	2	2	no	—
183	C₂²⋊C₄	—	2	2	no	—
184	C₂²⋊C₄	—	73	2	no	—
185	C₂²⋊C₄	—	146	2	no	—
186	C₂²⋊C₄	—	146	2	no	—
187	C₄²	—	146	2	no	—
188	C₄²	C₂²×D₇₃	1	1	yes	characteristic
189	C₂³	—	2	2	no	—
190	C₂³	—	73	2	no	—
191	Q₈	—	2	2	no	—
192	Q₈	—	2	2	no	—
193	Q₈	—	292	4	no	—
194	Q₈	—	73	4	no	—
195	Q₈	—	146	2	no	—
196	D₄	—	2	2	no	—
197	D₄	—	2	2	no	—
198	D₄	—	292	1	no	—
199	D₄	—	292	4	no	—
200	D₄	—	292	4	no	—
201	C₂×C₄	—	2	2	no	—
202	C₂×C₄	—	292	4	no	—
203	C₂×C₄	—	292	4	no	—
204	C₂×C₄	—	73	2	no	—
205	C₂×C₄	—	146	2	no	—
206	C₂×C₄	—	146	2	no	—
207	C₂×C₄	—	146	2	no	—
208	C₂×C₄	—	146	2	no	—
209	C₂×C₄	D₄×D₇₃	1	1	yes	characteristic
210	C₂×C₄	D₄×D₇₃	1	1	yes	characteristic
211	C₂×C₄	C₂³×D₇₃	1	1	yes	characteristic
212	C₈	—	2	1	no	—
213	C₈	—	146	2	no	—
214	C₈	D₄×D₇₃	1	2	yes	—
215	C₂²	—	4	2	no	—
216	C₂²	—	4	2	no	—
217	C₂²	—	4	2	no	—
218	C₂²	—	146	2	no	—
219	C₂²	—	146	2	no	—
220	C₂²	—	146	2	no	—
221	C₂²	C₂×D₄×D₇₃	1	1	yes	characteristic
222	C₄	—	2	1	no	—
223	C₄	—	2	1	no	—
224	C₄	—	4	2	no	—
225	C₄	—	292	2	no	—
226	C₄	—	146	2	no	—
227	C₄	—	146	4	no	—
228	C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
229	C₄	#14556636	1	1	yes	characteristic
230	C₂	—	8	2	no	—
231	C₂	—	292	2	no	—
232	C₂	#17989222	1	1	yes	characteristic
233	C₂	#17989384	1	1	yes	characteristic
234	C₂	#17989401	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14556620

C₂

yes

maximal, complemented

#17989245

C₂

yes

maximal, complemented

#17988830

C₂

yes

maximal, complemented

#17988806

C₂

yes

maximal, complemented

#17988741

C₂

yes

maximal, complemented

#17988729

C₂

yes

maximal, complemented

C₄×Dic₂₉₂

C₂

yes

maximal, characteristic, complemented

#17988666

C₂

yes

maximal, characteristic, complemented

#495×C₇₃

C₂

yes

maximal, characteristic, complemented

C₂×#11924027

C₂²

yes

—

C₂×Q₈×D₇₃

C₂²

yes

—

#14556620

—

C₂×Dic₂₉₂

C₂²

yes

characteristic

C₂×#11924018

C₂²

yes

—

C₂×#11924016

C₂²

yes

—

C₂×#11924011

C₂²

yes

—

#14556577

—

#14556568

—

#14556567

C₂²

yes

—

#14556564

—

#14556562

C₂²

yes

—

C₄×Dic₁₄₆

C₂²

yes

—

C₄×D₂₉₂

C₂²

yes

characteristic

#14556551

—

#14556525

C₂²

yes

characteristic

C₄⋊#10596831

C₂²

yes

characteristic

#14556516

C₂²

yes

—

#14556515

C₂²

yes

—

#14556512

C₂²

yes

—

#14556503

C₂²

yes

—

C₂×Q₁₆×C₇₃

C₂²

yes

characteristic

C₂×SD₁₆×C₇₃

C₂²

yes

—

C₂×D₈×C₇₃

C₂²

yes

characteristic

#124×C₇₃

C₂²

yes

—

C₄×C₈×C₇₃

C₂²

yes

characteristic

#11924027

—

#11924027

—

C₂×Dic₁₄₆

—

C₂×Dic₁₄₆

C₂³

yes

—

Q₈×D₇₃

—

Q₈×D₇₃

—

C₂×D₂₉₂

D₄

yes

characteristic

C₂×C₂²⋊D₇₃

—

C₂×C₂²⋊D₇₃

—

C₂²×Dic₇₃

—

C₂×C₄×D₇₃

—

C₂×C₄×D₇₃

C₂³

yes

—

Dic₂₉₂

D₄

yes

—

—

—

C₂³

yes

—

C₄⋊Dic₇₃

D₄

yes

characteristic

C₄⋊Dic₇₃

C₂³

yes

—

#11924007

—

#11924007

—

C₂²⋊Dic₇₃

—

#11924005

—

#11924005

D₄

yes

—

C₄×Dic₇₃

—

C₂×Q₈×C₇₃

C₂³

yes

—

C₂×D₄×C₇₃

C₂³

yes

—

Q₁₆×C₇₃

—

SD₁₆×C₇₃

—

D₈×C₇₃

—

C₂×C₈×C₇₃

C₂³

yes

characteristic

C₂×C₈×C₇₃

C₂³

yes

characteristic

C₂²⋊C₄×C₇₃

—

C₂²⋊C₄×C₇₃

—

C₄²×C₇₃

C₂³

yes

characteristic

C₂³×C₇₃

—

C₂²×D₇₃

C₂×D₄

yes

—

Q₈×C₇₃

—

Q₈×C₇₃

—

D₄×C₇₃

—

D₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₂×D₄

yes

characteristic

C₂×C₄×C₇₃

C₂×D₄

yes

characteristic

C₂×C₄×C₇₃

C₂⁴

yes

characteristic

C₂²⋊D₇₃

—

C₂²⋊D₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

C₂×D₄

yes

—

D₂₉₂

—

C₄×D₇₃

—

C₄×D₇₃

—

C₄×D₇₃

—

Dic₁₄₆

—

Dic₁₄₆

—

Dic₁₄₆

C₂×D₄

yes

—

C₈×C₇₃

—

C₈×C₇₃

C₂×D₄

yes

—

#10596831

—

C₂²×C₇₃

—

C₂²×C₇₃

—

C₂²×C₇₃

—

100

C₂²×C₇₃

C₂²×D₄

yes

characteristic

101

C₂×D₇₃

—

102

C₂×D₇₃

—

103

C₂×D₇₃

—

104

C₄×C₇₃

—

105

C₄×C₇₃

—

106

C₄×C₇₃

—

107

C₄×C₇₃

C₂²×D₄

yes

characteristic

108

C₄×C₇₃

H(5,𝔽₂)

yes

characteristic

109

Dic₇₃

—

110

Dic₇₃

—

111

Dic₇₃

—

112

C₂×C₇₃

—

113

C₂×C₇₃

D₄²

yes

characteristic

114

C₂×C₇₃

#575

yes

characteristic

115

C₂×C₇₃

#578

yes

characteristic

116

D₇₃

—

117

#3277

—

maximal, Sylow

118

C₇₃

#3277

yes

characteristic, complemented, Sylow

119

C₂×#137

—

120

#548

—

121

#495

D₇₃

yes

characteristic, complemented

122

#468

—

123

#464

—

124

#451

—

125

#449

—

126

C₄×Q₁₆

—

127

#436

—

128

C₂×#41

—

129

C₂²×Q₈

—

130

#137

—

146

—

131

C₂×Q₁₆

—

132

C₂×Q₁₆

—

133

C₂×Q₁₆

C₂×D₇₃

yes

characteristic

134

C₂×SD₁₆

—

135

C₂×SD₁₆

C₂×D₇₃

yes

—

136

C₂×D₈

C₂×D₇₃

yes

characteristic

137

C₂×M₁₆

—

138

#124

—

146

—

139

#124

C₂×D₇₃

yes

—

140

C₂²⋊Q₈

—

141

C₂²⋊Q₈

—

146

—

142

#121

—

143

#121

—

146

—

144

C₄×Q₈

—

145

C₄×D₄

—

146

C₄×D₄

—

146

—

147

#107

—

148

C₄⋊C₈

—

149

#103

—

150

#103

—

151

#102

—

152

C₂²⋊C₈

—

153

C₄×C₈

C₂×D₇₃

yes

characteristic

154

#41

—

292

—

155

#41

—

146

—

156

C₂×Q₈

—

292

—

157

C₂×Q₈

—

158

C₂×Q₈

—

146

—

159

C₂×Q₈

—

146

—

160

C₂×Q₈

C₂²×D₇₃

yes

—

161

C₂×D₄

—

162

C₂×D₄

—

146

—

163

C₂×D₄

—

146

—

164

C₂×D₄

C₂²×D₇₃

yes

—

165

C₂²×C₄

—

166

C₂²×C₄

—

146

—

167

C₂²×C₄

—

146

—

168

Q₁₆

—

169

Q₁₆

—

170

Q₁₆

—

146

—

171

SD₁₆

—

172

SD₁₆

—

146

—

173

D₈

—

174

M₁₆

—

146

—

175

C₂×C₈

—

176

C₂×C₈

C₂²×D₇₃

yes

characteristic

177

C₂×C₈

C₂²×D₇₃

yes

characteristic

178

C₄⋊C₄

—

179

C₄⋊C₄

—

180

C₄⋊C₄

—

146

—

181

C₄⋊C₄

—

146

—

182

C₂²⋊C₄

—

183

C₂²⋊C₄

—

184

C₂²⋊C₄

—

185

C₂²⋊C₄

—

146

—

186

C₂²⋊C₄

—

146

—

187

C₄²

—

146

—

188

C₄²

C₂²×D₇₃

yes

characteristic

189

C₂³

—

190

C₂³

—

191

Q₈

—

192

Q₈

—

193

Q₈

—

292

—

194

Q₈

—

195

Q₈

—

146

—

196

D₄

—

197

D₄

—

198

D₄

—

292

—

199

D₄

—

292

—

200

D₄

—

292

—

201

C₂×C₄

—

202

C₂×C₄

—

292

—

203

C₂×C₄

—

292

—

204

C₂×C₄

—

205

C₂×C₄

—

146

—

206

C₂×C₄

—

146

—

207

C₂×C₄

—

146

—

208

C₂×C₄

—

146

—

209

C₂×C₄

D₄×D₇₃

yes

characteristic

210

C₂×C₄

D₄×D₇₃

yes

characteristic

211

C₂×C₄

C₂³×D₇₃

yes

characteristic

212

C₈

—

213

C₈

—

146

—

214

C₈

D₄×D₇₃

yes

—

215

C₂²

—

216

C₂²

—

217

C₂²

—

218

C₂²

—

146

—

219

C₂²

—

146

—

220

C₂²

—

146

—

221

C₂²

C₂×D₄×D₇₃

yes

characteristic

222

C₄

—

223

C₄

—

224

C₄

—

225

C₄

—

292

—

226

C₄

—

146

—

227

C₄

—

146

—

228

C₄

C₂×D₄×D₇₃

yes

characteristic

229

C₄

#14556636

yes

characteristic

230

C₂

—

231

C₂

—

292

—

232

C₂

#17989222

yes

characteristic

233

C₂

#17989384

yes

characteristic

234

C₂

#17989401

yes

characteristic

	subgroup	G/H
center	C₂²	C₂×D₄×D₇₃
commutator	C₂×C₄×C₇₃	C₂⁴
Frattini	C₂×C₄	C₂³×D₇₃
Fitting	#495×C₇₃	C₂
socle	C₂²×C₇₃	C₂²×D₄
hypercenter	#495	D₇₃
hypocenter	C₇₃	#3277
LCS	G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #495

subgroup

G/H

center

C₂²

C₂×D₄×D₇₃

commutator

C₂×C₄×C₇₃

C₂⁴

Frattini

C₂×C₄

C₂³×D₇₃

Fitting

#495×C₇₃

C₂

socle

C₂²×C₇₃

C₂²×D₄

D₇₃

C₇₃

G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #495

N	H ≅ G/N	type
1. C₂×#14556620	C₂	semidirect
2. #17989245	C₂	semidirect
3. #17988830	C₂	semidirect
4. #17988806	C₂	semidirect
5. #17988741	C₂	semidirect
6. #17988729	C₂	semidirect
7. C₄×Dic₂₉₂	C₂	semidirect
8. #17988666	C₂	semidirect
9. #495×C₇₃	C₂	semidirect
48. Dic₂₉₂	D₄	semidirect
118. C₇₃	#3277	semidirect
121. #495	D₇₃	semidirect

H ≅ G/N

type

1. C₂×#14556620

C₂

semidirect

2. #17989245

C₂

semidirect

3. #17988830

C₂

semidirect

4. #17988806

C₂

semidirect

5. #17988741

C₂

semidirect

6. #17988729

C₂

semidirect

7. C₄×Dic₂₉₂

C₂

semidirect

8. #17988666

C₂

semidirect

9. #495×C₇₃

C₂

semidirect

48. Dic₂₉₂

D₄

semidirect

118. C₇₃

#3277

semidirect

121. #495

D₇₃

semidirect

Subgroups — #22621586

Conjugacy classes of subgroups

Complements