Group #32997516 — subgroups

Subgroups — #32997516

Order 18688.

412 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 412 conjugacy classes of subgroups — too many to draw. Only its 87 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	#22611743	C₂	1	2	yes	maximal, complemented
2	#22607972	C₂	1	2	yes	maximal, complemented
3	#22607968	C₂	1	2	yes	maximal, complemented
4	C₇₃×#3151	C₂	1	1	yes	maximal, characteristic
5	#17988408	C₂²	1	4	yes	complemented
6	#17988369	—	2	2	no	—
7	#17988365	—	2	2	no	—
8	C₂×AGL(1,ℤ/8)×C₇₃	—	2	2	no	—
9	#532×C₇₃	C₄	1	1	yes	characteristic
10	C₂×#127×C₇₃	C₄	1	1	yes	characteristic
11	#496×C₇₃	—	2	2	no	—
12	#493×C₇₃	C₄	1	1	yes	characteristic
13	#493×C₇₃	C₂²	1	1	yes	characteristic
14	#492×C₇₃	C₄	1	1	yes	characteristic
15	#492×C₇₃	C₂²	1	1	yes	characteristic
16	C₄×M₁₆×C₇₃	C₂²	1	1	yes	characteristic
17	#14556531	—	2	4	no	—
18	C₂×#41×C₇₃	—	2	1	no	—
19	C₂²×D₄×C₇₃	—	2	1	no	—
20	C₂²×D₄×C₇₃	—	4	1	no	—
21	AGL(1,ℤ/8)×C₇₃	—	4	8	no	—
22	C₂×SD₁₆×C₇₃	—	2	2	no	—
23	C₂×SD₁₆×C₇₃	—	2	2	no	—
24	C₂×D₈×C₇₃	—	2	2	no	—
25	C₂×D₈×C₇₃	—	2	2	no	—
26	C₂×M₁₆×C₇₃	D₄	1	2	yes	—
27	C₄⋊Q₈×C₇₃	C₂×C₄	1	1	yes	characteristic
28	#127×C₇₃	—	2	1	no	—
29	#127×C₇₃	—	4	1	no	—
30	#127×C₇₃	C₂×C₄	1	1	yes	characteristic
31	#127×C₇₃	C₂×C₄	1	1	yes	characteristic
32	#127×C₇₃	C₂×C₄	1	1	yes	characteristic
33	#124×C₇₃	—	2	1	no	—
34	#121×C₇₃	—	4	1	no	—
35	C₄×D₄×C₇₃	—	4	1	no	—
36	C₂×C₄²×C₇₃	C₂×C₄	1	1	yes	characteristic
37	#97×C₇₃	D₄	1	2	yes	—
38	C₄×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
39	C₄×C₈×C₇₃	C₂³	1	1	yes	characteristic
40	#11924003	—	4	4	no	—
41	C₂⁴×C₇₃	—	4	1	no	—
42	#41×C₇₃	—	4	4	no	—
43	C₂×Q₈×C₇₃	—	2	1	no	—
44	C₂×D₄×C₇₃	—	2	1	no	—
45	C₂×D₄×C₇₃	—	2	1	no	—
46	C₂×D₄×C₇₃	—	2	1	no	—
47	C₂×D₄×C₇₃	—	4	4	no	—
48	C₂×D₄×C₇₃	—	4	1	no	—
49	C₂×D₄×C₇₃	—	4	1	no	—
50	C₂×D₄×C₇₃	—	4	1	no	—
51	C₂×D₄×C₇₃	—	4	2	no	—
52	C₂×D₄×C₇₃	—	4	1	no	—
53	C₂×D₄×C₇₃	—	4	1	no	—
54	C₂×D₄×C₇₃	—	8	4	no	—
55	C₂²×C₄×C₇₃	—	2	1	no	—
56	C₂²×C₄×C₇₃	—	4	1	no	—
57	C₂²×C₄×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
58	SD₁₆×C₇₃	—	4	4	no	—
59	SD₁₆×C₇₃	—	4	4	no	—
60	D₈×C₇₃	—	4	4	no	—
61	D₈×C₇₃	—	4	4	no	—
62	M₁₆×C₇₃	—	2	4	no	—
63	C₂×C₈×C₇₃	C₂²⋊C₄	1	2	yes	—
64	C₂×C₈×C₇₃	C₂×D₄	1	2	yes	—
65	C₄⋊C₄×C₇₃	—	4	1	no	—
66	C₂²⋊C₄×C₇₃	—	4	2	no	—
67	C₄²×C₇₃	—	2	1	no	—
68	C₄²×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
69	C₄²×C₇₃	C₂²×C₄	1	1	yes	characteristic
70	C₂³×C₇₃	—	4	1	no	—
71	C₂³×C₇₃	—	4	1	no	—
72	C₂³×C₇₃	—	4	1	no	—
73	C₂³×C₇₃	—	8	2	no	—
74	C₂³×C₇₃	—	8	4	no	—
75	C₂³×C₇₃	#100	1	1	yes	characteristic
76	Q₈×C₇₃	—	4	2	no	—
77	D₄×C₇₃	—	4	2	no	—
78	D₄×C₇₃	—	4	2	no	—
79	D₄×C₇₃	—	4	2	no	—
80	D₄×C₇₃	—	8	2	no	—
81	D₄×C₇₃	—	8	2	no	—
82	D₄×C₇₃	—	8	2	no	—
83	D₄×C₇₃	—	8	2	no	—
84	D₄×C₇₃	—	8	4	no	—
85	D₄×C₇₃	—	8	2	no	—
86	C₂×C₄×C₇₃	—	2	1	no	—
87	C₂×C₄×C₇₃	—	2	2	no	—
88	C₂×C₄×C₇₃	—	2	1	no	—
89	C₂×C₄×C₇₃	—	4	2	no	—
90	C₂×C₄×C₇₃	—	4	1	no	—
91	C₂×C₄×C₇₃	—	8	2	no	—
92	C₂×C₄×C₇₃	#100	1	1	yes	characteristic
93	C₂×C₄×C₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
94	C₈×C₇₃	—	2	2	no	—
95	C₈×C₇₃	AGL(1,ℤ/8)	1	4	yes	—
96	C₂²×C₇₃	—	2	1	no	—
97	C₂²×C₇₃	—	4	1	no	—
98	C₂²×C₇₃	—	8	2	no	—
99	C₂²×C₇₃	—	8	2	no	—
100	C₂²×C₇₃	—	8	2	no	—
101	C₂²×C₇₃	—	8	1	no	—
102	C₂²×C₇₃	—	8	1	no	—
103	C₂²×C₇₃	—	8	1	no	—
104	C₂²×C₇₃	—	16	4	no	—
105	C₂²×C₇₃	C₂×#100	1	1	yes	characteristic
106	C₄×C₇₃	—	2	2	no	—
107	C₄×C₇₃	—	2	1	no	—
108	C₄×C₇₃	—	4	1	no	—
109	C₄×C₇₃	—	8	1	no	—
110	C₄×C₇₃	#418	1	2	yes	—
111	#11992	—	73	1	no	maximal, Sylow
112	C₂×C₇₃	—	2	1	no	—
113	C₂×C₇₃	—	4	1	no	—
114	C₂×C₇₃	—	16	1	no	—
115	C₂×C₇₃	—	16	1	no	—
116	C₂×C₇₃	—	16	1	no	—
117	C₂×C₇₃	#1555	1	1	yes	characteristic
118	#3151	D₇₃	1	1	yes	characteristic
119	#2165	—	73	2	no	—
120	#1359	—	73	2	no	—
121	#1357	—	73	2	no	—
122	C₇₃	#11992	1	1	yes	characteristic, complemented, Sylow
123	C₂×AGL(1,ℤ/8)	—	2	2	no	—
124	#532	Dic₇₃	1	1	yes	characteristic
125	C₂×#127	Dic₇₃	1	1	yes	characteristic
126	#496	—	2	2	no	—
127	#493	Dic₇₃	1	1	yes	characteristic
128	#493	C₂×D₇₃	1	1	yes	characteristic
129	#492	Dic₇₃	1	1	yes	characteristic
130	#492	C₂×D₇₃	1	1	yes	characteristic
131	C₄×M₁₆	C₂×D₇₃	1	1	yes	characteristic
132	#364	—	73	4	no	—
133	#349	—	146	2	no	—
134	#347	—	146	2	no	—
135	C₂×#41	—	2	1	no	—
136	C₂²×D₄	—	2	1	no	—
137	C₂²×D₄	—	4	1	no	—
138	AGL(1,ℤ/8)	—	4	8	no	—
139	C₂×SD₁₆	—	2	2	no	—
140	C₂×SD₁₆	—	2	2	no	—
141	C₂×D₈	—	2	2	no	—
142	C₂×D₈	—	2	2	no	—
143	C₂×M₁₆	C₂²⋊D₇₃	1	2	yes	—
144	C₄⋊Q₈	C₂×Dic₇₃	1	1	yes	characteristic
145	#127	—	2	1	no	—
146	#127	—	4	1	no	—
147	#127	C₂×Dic₇₃	1	1	yes	characteristic
148	#127	C₂×Dic₇₃	1	1	yes	characteristic
149	#127	C₂×Dic₇₃	1	1	yes	characteristic
150	#124	—	2	1	no	—
151	#121	—	4	1	no	—
152	C₄×D₄	—	4	1	no	—
153	C₂×C₄²	C₂×Dic₇₃	1	1	yes	characteristic
154	M₃₂	—	146	4	no	—
155	#97	C₂²⋊D₇₃	1	2	yes	—
156	C₄×C₈	C₂×Dic₇₃	1	1	yes	characteristic
157	C₄×C₈	C₂²×D₇₃	1	1	yes	characteristic
158	C₂⁴	—	4	1	no	—
159	#41	—	4	4	no	—
160	C₂×Q₈	—	2	1	no	—
161	C₂×D₄	—	2	1	no	—
162	C₂×D₄	—	2	1	no	—
163	C₂×D₄	—	2	1	no	—
164	C₂×D₄	—	4	4	no	—
165	C₂×D₄	—	4	1	no	—
166	C₂×D₄	—	4	1	no	—
167	C₂×D₄	—	4	1	no	—
168	C₂×D₄	—	4	2	no	—
169	C₂×D₄	—	4	1	no	—
170	C₂×D₄	—	4	1	no	—
171	C₂×D₄	—	8	4	no	—
172	C₂²×C₄	—	2	1	no	—
173	C₂²×C₄	—	4	1	no	—
174	C₂²×C₄	C₂²⋊Dic₇₃	1	1	yes	characteristic
175	SD₁₆	—	4	4	no	—
176	SD₁₆	—	4	4	no	—
177	D₈	—	4	4	no	—
178	D₈	—	4	4	no	—
179	M₁₆	—	2	4	no	—
180	C₂×C₈	C₂²⋊Dic₇₃	1	2	yes	—
181	C₂×C₈	C₂×C₂²⋊D₇₃	1	2	yes	—
182	C₄⋊C₄	—	4	1	no	—
183	C₂²⋊C₄	—	4	2	no	—
184	C₄²	—	2	1	no	—
185	C₄²	C₂²⋊Dic₇₃	1	1	yes	characteristic
186	C₄²	C₂²×Dic₇₃	1	1	yes	characteristic
187	C₁₆	—	292	4	no	—
188	C₂³	—	4	1	no	—
189	C₂³	—	4	1	no	—
190	C₂³	—	4	1	no	—
191	C₂³	—	8	2	no	—
192	C₂³	—	8	4	no	—
193	C₂³	#14556508	1	1	yes	characteristic
194	Q₈	—	4	2	no	—
195	D₄	—	4	2	no	—
196	D₄	—	4	2	no	—
197	D₄	—	4	2	no	—
198	D₄	—	8	2	no	—
199	D₄	—	8	2	no	—
200	D₄	—	8	2	no	—
201	D₄	—	8	2	no	—
202	D₄	—	8	4	no	—
203	D₄	—	8	2	no	—
204	C₂×C₄	—	2	1	no	—
205	C₂×C₄	—	2	2	no	—
206	C₂×C₄	—	2	1	no	—
207	C₂×C₄	—	4	2	no	—
208	C₂×C₄	—	4	1	no	—
209	C₂×C₄	—	8	2	no	—
210	C₂×C₄	#14556508	1	1	yes	characteristic
211	C₂×C₄	C₂×C₂²⋊Dic₇₃	1	1	yes	characteristic
212	C₈	—	2	2	no	—
213	C₈	#14556617	1	4	yes	—
214	C₂²	—	2	1	no	—
215	C₂²	—	4	1	no	—
216	C₂²	—	8	2	no	—
217	C₂²	—	8	2	no	—
218	C₂²	—	8	2	no	—
219	C₂²	—	8	1	no	—
220	C₂²	—	8	1	no	—
221	C₂²	—	8	1	no	—
222	C₂²	—	16	4	no	—
223	C₂²	C₂×#14556508	1	1	yes	characteristic
224	C₄	—	2	2	no	—
225	C₄	—	2	1	no	—
226	C₄	—	4	1	no	—
227	C₄	—	8	1	no	—
228	C₄	#17988592	1	2	yes	—
229	C₂	—	2	1	no	—
230	C₂	—	4	1	no	—
231	C₂	—	16	1	no	—
232	C₂	—	16	1	no	—
233	C₂	—	16	1	no	—
234	C₂	#22608645	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#22611743

C₂

yes

maximal, complemented

#22607972

C₂

yes

maximal, complemented

#22607968

C₂

yes

maximal, complemented

C₇₃×#3151

C₂

yes

maximal, characteristic

#17988408

C₂²

yes

complemented

#17988369

—

#17988365

—

C₂×AGL(1,ℤ/8)×C₇₃

—

#532×C₇₃

C₄

yes

characteristic

C₂×#127×C₇₃

C₄

yes

characteristic

#496×C₇₃

—

#493×C₇₃

C₄

yes

characteristic

#493×C₇₃

C₂²

yes

characteristic

#492×C₇₃

C₄

yes

characteristic

#492×C₇₃

C₂²

yes

characteristic

C₄×M₁₆×C₇₃

C₂²

yes

characteristic

#14556531

—

C₂×#41×C₇₃

—

C₂²×D₄×C₇₃

—

C₂²×D₄×C₇₃

—

AGL(1,ℤ/8)×C₇₃

—

C₂×SD₁₆×C₇₃

—

C₂×SD₁₆×C₇₃

—

C₂×D₈×C₇₃

—

C₂×D₈×C₇₃

—

C₂×M₁₆×C₇₃

D₄

yes

—

C₄⋊Q₈×C₇₃

C₂×C₄

yes

characteristic

#127×C₇₃

—

#127×C₇₃

—

#127×C₇₃

C₂×C₄

yes

characteristic

#127×C₇₃

C₂×C₄

yes

characteristic

#127×C₇₃

C₂×C₄

yes

characteristic

#124×C₇₃

—

#121×C₇₃

—

C₄×D₄×C₇₃

—

C₂×C₄²×C₇₃

C₂×C₄

yes

characteristic

#97×C₇₃

D₄

yes

—

C₄×C₈×C₇₃

C₂×C₄

yes

characteristic

C₄×C₈×C₇₃

C₂³

yes

characteristic

#11924003

—

C₂⁴×C₇₃

—

#41×C₇₃

—

C₂×Q₈×C₇₃

—

C₂×D₄×C₇₃

—

C₂×D₄×C₇₃

—

C₂×D₄×C₇₃

—

C₂×D₄×C₇₃

—

C₂×D₄×C₇₃

—

C₂×D₄×C₇₃

—

C₂×D₄×C₇₃

—

C₂×D₄×C₇₃

—

C₂×D₄×C₇₃

—

C₂×D₄×C₇₃

—

C₂×D₄×C₇₃

—

C₂²×C₄×C₇₃

—

C₂²×C₄×C₇₃

—

C₂²×C₄×C₇₃

C₂²⋊C₄

yes

characteristic

SD₁₆×C₇₃

—

SD₁₆×C₇₃

—

D₈×C₇₃

—

D₈×C₇₃

—

M₁₆×C₇₃

—

C₂×C₈×C₇₃

C₂²⋊C₄

yes

—

C₂×C₈×C₇₃

C₂×D₄

yes

—

C₄⋊C₄×C₇₃

—

C₂²⋊C₄×C₇₃

—

C₄²×C₇₃

—

C₄²×C₇₃

C₂²⋊C₄

yes

characteristic

C₄²×C₇₃

C₂²×C₄

yes

characteristic

C₂³×C₇₃

—

C₂³×C₇₃

—

C₂³×C₇₃

—

C₂³×C₇₃

—

C₂³×C₇₃

—

C₂³×C₇₃

#100

yes

characteristic

Q₈×C₇₃

—

D₄×C₇₃

—

D₄×C₇₃

—

D₄×C₇₃

—

D₄×C₇₃

—

D₄×C₇₃

—

D₄×C₇₃

—

D₄×C₇₃

—

D₄×C₇₃

—

D₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

#100

yes

characteristic

C₂×C₄×C₇₃

C₂×C₂²⋊C₄

yes

characteristic

C₈×C₇₃

—

C₈×C₇₃

AGL(1,ℤ/8)

yes

—

C₂²×C₇₃

—

C₂²×C₇₃

—

C₂²×C₇₃

—

C₂²×C₇₃

—

100

C₂²×C₇₃

—

101

C₂²×C₇₃

—

102

C₂²×C₇₃

—

103

C₂²×C₇₃

—

104

C₂²×C₇₃

—

105

C₂²×C₇₃

C₂×#100

yes

characteristic

106

C₄×C₇₃

—

107

C₄×C₇₃

—

108

C₄×C₇₃

—

109

C₄×C₇₃

—

110

C₄×C₇₃

#418

yes

—

111

#11992

—

maximal, Sylow

112

C₂×C₇₃

—

113

C₂×C₇₃

—

114

C₂×C₇₃

—

115

C₂×C₇₃

—

116

C₂×C₇₃

—

117

C₂×C₇₃

#1555

yes

characteristic

118

#3151

D₇₃

yes

characteristic

119

#2165

—

120

#1359

—

121

#1357

—

122

C₇₃

#11992

yes

characteristic, complemented, Sylow

123

C₂×AGL(1,ℤ/8)

—

124

#532

Dic₇₃

yes

characteristic

125

C₂×#127

Dic₇₃

yes

characteristic

126

#496

—

127

#493

Dic₇₃

yes

characteristic

128

#493

C₂×D₇₃

yes

characteristic

129

#492

Dic₇₃

yes

characteristic

130

#492

C₂×D₇₃

yes

characteristic

131

C₄×M₁₆

C₂×D₇₃

yes

characteristic

132

#364

—

133

#349

—

146

—

134

#347

—

146

—

135

C₂×#41

—

136

C₂²×D₄

—

137

C₂²×D₄

—

138

AGL(1,ℤ/8)

—

139

C₂×SD₁₆

—

140

C₂×SD₁₆

—

141

C₂×D₈

—

142

C₂×D₈

—

143

C₂×M₁₆

C₂²⋊D₇₃

yes

—

144

C₄⋊Q₈

C₂×Dic₇₃

yes

characteristic

145

#127

—

146

#127

—

147

#127

C₂×Dic₇₃

yes

characteristic

148

#127

C₂×Dic₇₃

yes

characteristic

149

#127

C₂×Dic₇₃

yes

characteristic

150

#124

—

151

#121

—

152

C₄×D₄

—

153

C₂×C₄²

C₂×Dic₇₃

yes

characteristic

154

M₃₂

—

146

—

155

#97

C₂²⋊D₇₃

yes

—

156

C₄×C₈

C₂×Dic₇₃

yes

characteristic

157

C₄×C₈

C₂²×D₇₃

yes

characteristic

158

C₂⁴

—

159

#41

—

160

C₂×Q₈

—

161

C₂×D₄

—

162

C₂×D₄

—

163

C₂×D₄

—

164

C₂×D₄

—

165

C₂×D₄

—

166

C₂×D₄

—

167

C₂×D₄

—

168

C₂×D₄

—

169

C₂×D₄

—

170

C₂×D₄

—

171

C₂×D₄

—

172

C₂²×C₄

—

173

C₂²×C₄

—

174

C₂²×C₄

C₂²⋊Dic₇₃

yes

characteristic

175

SD₁₆

—

176

SD₁₆

—

177

D₈

—

178

D₈

—

179

M₁₆

—

180

C₂×C₈

C₂²⋊Dic₇₃

yes

—

181

C₂×C₈

C₂×C₂²⋊D₇₃

yes

—

182

C₄⋊C₄

—

183

C₂²⋊C₄

—

184

C₄²

—

185

C₄²

C₂²⋊Dic₇₃

yes

characteristic

186

C₄²

C₂²×Dic₇₃

yes

characteristic

187

C₁₆

—

292

—

188

C₂³

—

189

C₂³

—

190

C₂³

—

191

C₂³

—

192

C₂³

—

193

C₂³

#14556508

yes

characteristic

194

Q₈

—

195

D₄

—

196

D₄

—

197

D₄

—

198

D₄

—

199

D₄

—

200

D₄

—

201

D₄

—

202

D₄

—

203

D₄

—

204

C₂×C₄

—

205

C₂×C₄

—

206

C₂×C₄

—

207

C₂×C₄

—

208

C₂×C₄

—

209

C₂×C₄

—

210

C₂×C₄

#14556508

yes

characteristic

211

C₂×C₄

C₂×C₂²⋊Dic₇₃

yes

characteristic

212

C₈

—

213

C₈

#14556617

yes

—

214

C₂²

—

215

C₂²

—

216

C₂²

—

217

C₂²

—

218

C₂²

—

219

C₂²

—

220

C₂²

—

221

C₂²

—

222

C₂²

—

223

C₂²

C₂×#14556508

yes

characteristic

224

C₄

—

225

C₄

—

226

C₄

—

227

C₄

—

228

C₄

#17988592

yes

—

229

C₂

—

230

C₂

—

231

C₂

—

232

C₂

—

233

C₂

—

234

C₂

#22608645

yes

characteristic

	subgroup	G/H
center	C₂	#22608645
commutator	C₄²×C₇₃	C₂²×C₄
Frattini	C₄×C₈	C₂²×D₇₃
Fitting, prime radical	C₇₃×#3151	C₂
socle	C₂×C₇₃	#1555
cosocle	C₄×C₈×C₇₃	C₂³
hypercenter	#3151	D₇₃
hypocenter	C₇₃	#11992
LCS	G ▷ C₄²×C₇₃ ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₄×M₁₆ ◁ #3151

subgroup

G/H

center

C₂

#22608645

commutator

C₄²×C₇₃

C₂²×C₄

Frattini

C₄×C₈

C₂²×D₇₃

Fitting, prime radical

C₇₃×#3151

C₂

socle

C₂×C₇₃

#1555

cosocle

C₄×C₈×C₇₃

C₂³

D₇₃

C₇₃

G ▷ C₄²×C₇₃ ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₄×M₁₆ ◁ #3151

N	H ≅ G/N	type
1. #22611743	C₂	semidirect
2. #22607972	C₂	semidirect
3. #22607968	C₂	semidirect
5. #17988408	C₂²	semidirect
122. C₇₃	#11992	semidirect

H ≅ G/N

type

1. #22611743

C₂

semidirect

2. #22607972

C₂

semidirect

3. #22607968

C₂

semidirect

5. #17988408

C₂²

semidirect

122. C₇₃

#11992

semidirect

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

subgroup	index
#22611743	2
#22607972	2
#22607968	2
C₇₃×#3151	2
#11992	73

subgroup

index

C₇₃×#3151

Subgroups — #32997516

Conjugacy classes of subgroups

Complements

Maximal subgroups