Group #26110154 — subgroups

Subgroups — #26110154

Order 12032.

386 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 386 conjugacy classes of subgroups — too many to draw. Only its 119 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	#20252473	C₂	1	1	yes	maximal, characteristic
2	C₄×#13093943	C₂	1	1	yes	maximal, characteristic
3	#20242138	C₂	1	2	yes	maximal
4	#20241225	C₂	1	2	yes	maximal
5	C₄₇×#1984	C₂	1	1	yes	maximal, characteristic
6	#15689254	—	2	2	no	—
7	#15689254	—	2	2	no	—
8	#15689180	—	2	2	no	—
9	#15689176	C₂²	1	2	yes	—
10	C₂×#13093943	C₄	1	2	yes	—
11	C₄×#10625329	C₂²	1	2	yes	—
12	#15688892	C₄	1	1	yes	characteristic
13	#15688892	C₄	1	1	yes	characteristic
14	#15688875	—	2	2	no	—
15	#15688873	—	2	2	no	—
16	C₂×C₄×Q₈×C₄₇	C₂²	1	1	yes	characteristic
17	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
18	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
19	C₄₇×#336	—	2	2	no	—
20	C₂×#10625329	C₂×C₄	1	2	yes	—
21	C₂×#10625329	C₂×C₄	1	2	yes	—
22	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
23	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
24	C₄⋊(C₄₇⋊C₈)	D₄	1	2	yes	—
25	C₄⋊(C₄₇⋊C₈)	D₄	1	2	yes	—
26	#13093943	—	2	4	no	—
27	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
28	#13093935	—	2	4	no	—
29	#13093935	—	2	2	no	—
30	C₄×C₄₇⋊C₈	—	2	2	no	—
31	C₄×C₄₇⋊C₈	—	2	2	no	—
32	C₂²×Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
33	C₂²×C₈×C₄₇	—	2	1	no	—
34	C₂²×C₈×C₄₇	—	2	1	no	—
35	C₄×Q₈×C₄₇	—	2	2	no	—
36	C₄×Q₈×C₄₇	—	2	2	no	—
37	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
38	C₂×C₄⋊C₄×C₄₇	Q₈	1	2	yes	—
39	C₂×C₄²×C₄₇	D₄	1	2	yes	—
40	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
41	C₄⋊C₈×C₄₇	—	2	2	no	—
42	C₄×C₈×C₄₇	—	2	2	no	—
43	C₂×Q₈×C₄₇	—	2	2	no	—
44	C₂×Q₈×C₄₇	—	2	2	no	—
45	C₂×Q₈×C₄₇	—	2	1	no	—
46	C₂×Q₈×C₄₇	—	2	1	no	—
47	C₂²×C₄×C₄₇	C₄⋊C₄	1	2	yes	—
48	C₂²×C₄×C₄₇	C₄⋊C₄	1	2	yes	—
49	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
50	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
51	C₂²×C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
52	C₂×C₈×C₄₇	—	2	2	no	—
53	C₂×C₈×C₄₇	—	4	1	no	—
54	C₂×C₈×C₄₇	—	4	1	no	—
55	C₂×C₈×C₄₇	—	4	2	no	—
56	C₂×C₈×C₄₇	—	4	1	no	—
57	C₄⋊C₄×C₄₇	—	2	2	no	—
58	C₄⋊C₄×C₄₇	—	2	4	no	—
59	C₄²×C₄₇	—	2	2	no	—
60	C₄²×C₄₇	—	2	2	no	—
61	C₄²×C₄₇	C₂×D₄	1	2	yes	—
62	C₄²×C₄₇	#41	1	2	yes	—
63	#10625329	—	2	2	no	—
64	#10625329	—	2	2	no	—
65	#10625329	—	2	2	no	—
66	#10625329	M₁₆	1	4	yes	—
67	C₂×C₄₇⋊C₈	—	2	2	no	—
68	C₂×C₄₇⋊C₈	—	2	2	no	—
69	C₂×C₄₇⋊C₈	—	2	2	no	—
70	C₂×C₄₇⋊C₈	—	2	2	no	—
71	C₂³×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
72	Q₈×C₄₇	—	4	2	no	—
73	Q₈×C₄₇	—	4	2	no	—
74	C₂×C₄×C₄₇	—	2	1	no	—
75	C₂×C₄×C₄₇	—	2	1	no	—
76	C₂×C₄×C₄₇	—	2	2	no	—
77	C₂×C₄×C₄₇	—	2	2	no	—
78	C₂×C₄×C₄₇	—	2	2	no	—
79	C₂×C₄×C₄₇	—	2	2	no	—
80	C₂×C₄×C₄₇	—	4	1	no	—
81	C₂×C₄×C₄₇	—	4	2	no	—
82	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
83	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
84	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
85	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
86	C₂×C₄×C₄₇	C₂×M₁₆	1	2	yes	—
87	C₂×C₄×C₄₇	#131	1	1	yes	characteristic
88	C₂×C₄×C₄₇	#131	1	1	yes	characteristic
89	C₈×C₄₇	—	4	2	no	—
90	C₈×C₄₇	—	8	1	no	—
91	C₄₇⋊C₈	—	2	4	no	—
92	C₄₇⋊C₈	—	4	2	no	—
93	C₄₇⋊C₈	—	4	2	no	—
94	C₄₇⋊C₈	—	4	2	no	—
95	#8838	—	47	1	no	maximal, Sylow
96	C₂²×C₄₇	—	2	1	no	—
97	C₂²×C₄₇	—	2	1	no	—
98	C₂²×C₄₇	#385	1	1	yes	characteristic
99	C₂²×C₄₇	#423	1	1	yes	characteristic
100	C₂²×C₄₇	#424	1	1	yes	characteristic
101	C₄×C₄₇	—	2	1	no	—
102	C₄×C₄₇	—	2	2	no	—
103	C₄×C₄₇	—	4	2	no	—
104	C₄×C₄₇	—	4	2	no	—
105	C₄×C₄₇	#435	1	2	yes	—
106	C₄×C₄₇	#436	1	2	yes	—
107	C₄×C₄₇	#454	1	1	yes	characteristic
108	C₄×C₄₇	#456	1	1	yes	characteristic
109	#2983	—	47	1	no	—
110	#1984	D₄₇	1	1	yes	characteristic
111	C₄×#101	—	47	1	no	—
112	#1565	—	47	2	no	—
113	#1278	—	47	2	no	—
114	C₂×C₄₇	—	2	1	no	—
115	C₂×C₄₇	—	2	1	no	—
116	C₂×C₄₇	#1851	1	1	yes	characteristic
117	C₂×C₄₇	#1857	1	1	yes	characteristic
118	C₂×C₄₇	#1858	1	1	yes	characteristic
119	C₂×C₄×Q₈	C₂×D₄₇	1	1	yes	characteristic
120	#446	—	94	2	no	—
121	#446	—	94	2	no	—
122	#432	—	94	2	no	—
123	#431	—	47	2	no	—
124	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
125	C₂×#101	—	47	2	no	—
126	C₄×M₁₆	—	47	2	no	—
127	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
128	#343	—	47	1	no	—
129	#343	—	47	1	no	—
130	#336	—	2	2	no	—
131	#335	—	94	2	no	—
132	#334	—	94	2	no	—
133	C₄₇	#8838	1	1	yes	characteristic, complemented, Sylow
134	C₂²×Q₈	C₄×D₄₇	1	1	yes	characteristic
135	C₂×M₁₆	—	47	2	no	—
136	C₂×M₁₆	—	47	2	no	—
137	C₂²×C₈	—	2	1	no	—
138	C₂²×C₈	—	2	1	no	—
139	C₄×Q₈	—	2	2	no	—
140	C₄×Q₈	—	2	2	no	—
141	C₂×C₄⋊C₄	Dic₉₄	1	2	yes	—
142	C₂×C₄⋊C₄	C₄×D₄₇	1	1	yes	characteristic
143	C₂×C₄²	C₂²⋊D₄₇	1	2	yes	—
144	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
145	C₄⋊C₈	—	2	2	no	—
146	C₄⋊C₈	—	47	2	no	—
147	C₄⋊C₈	—	47	2	no	—
148	C₄⋊C₈	—	94	2	no	—
149	C₄⋊C₈	—	94	2	no	—
150	#101	—	94	4	no	—
151	C₂²⋊C₈	—	94	2	no	—
152	#97	—	94	4	no	—
153	#97	—	94	2	no	—
154	C₄×C₈	—	2	2	no	—
155	C₄×C₈	—	94	2	no	—
156	C₄×C₈	—	94	2	no	—
157	C₂×Q₈	—	2	2	no	—
158	C₂×Q₈	—	2	2	no	—
159	C₂×Q₈	—	2	1	no	—
160	C₂×Q₈	—	2	1	no	—
161	C₂²×C₄	Dic₄₇⋊C₄	1	2	yes	—
162	C₂²×C₄	Dic₄₇⋊C₄	1	2	yes	—
163	C₂²×C₄	C₂×Dic₉₄	1	1	yes	characteristic
164	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
165	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
166	M₁₆	—	47	4	no	—
167	M₁₆	—	94	2	no	—
168	M₁₆	—	94	2	no	—
169	M₁₆	—	94	2	no	—
170	C₂×C₈	—	2	2	no	—
171	C₂×C₈	—	4	1	no	—
172	C₂×C₈	—	4	1	no	—
173	C₂×C₈	—	4	2	no	—
174	C₂×C₈	—	4	1	no	—
175	C₂×C₈	—	94	2	no	—
176	C₂×C₈	—	94	2	no	—
177	C₂×C₈	—	94	2	no	—
178	C₂×C₈	—	94	2	no	—
179	C₄⋊C₄	—	2	2	no	—
180	C₄⋊C₄	—	2	4	no	—
181	C₄²	—	2	2	no	—
182	C₄²	—	2	2	no	—
183	C₄²	D₄×D₄₇	1	2	yes	—
184	C₄²	#10625352	1	2	yes	—
185	C₂³	C₂×Dic₄₇⋊C₄	1	1	yes	characteristic
186	Q₈	—	4	2	no	—
187	Q₈	—	4	2	no	—
188	C₂×C₄	—	2	1	no	—
189	C₂×C₄	—	2	1	no	—
190	C₂×C₄	—	2	2	no	—
191	C₂×C₄	—	2	2	no	—
192	C₂×C₄	—	2	2	no	—
193	C₂×C₄	—	2	2	no	—
194	C₂×C₄	—	4	1	no	—
195	C₂×C₄	—	4	2	no	—
196	C₂×C₄	(C₂²⋊D₄₇)⋊C₄	1	2	yes	—
197	C₂×C₄	#13093992	1	1	yes	characteristic
198	C₂×C₄	#13094001	1	2	yes	—
199	C₂×C₄	#13094005	1	1	yes	characteristic
200	C₂×C₄	M₁₆×D₄₇	1	2	yes	—
201	C₂×C₄	#13094030	1	1	yes	characteristic
202	C₂×C₄	#13094030	1	1	yes	characteristic
203	C₈	—	4	2	no	—
204	C₈	—	8	1	no	—
205	C₈	—	94	4	no	—
206	C₈	—	188	2	no	—
207	C₈	—	188	2	no	—
208	C₈	—	188	2	no	—
209	C₂²	—	2	1	no	—
210	C₂²	—	2	1	no	—
211	C₂²	#15688995	1	1	yes	characteristic
212	C₂²	#15689146	1	1	yes	characteristic
213	C₂²	#15689149	1	1	yes	characteristic
214	C₄	—	2	1	no	—
215	C₄	—	2	2	no	—
216	C₄	—	4	2	no	—
217	C₄	—	4	2	no	—
218	C₄	#15689197	1	2	yes	—
219	C₄	#15689198	1	2	yes	—
220	C₄	#15689295	1	1	yes	characteristic
221	C₄	#15689305	1	1	yes	characteristic
222	C₂	—	2	1	no	—
223	C₂	—	2	1	no	—
224	C₂	#20243570	1	1	yes	characteristic
225	C₂	#20243602	1	1	yes	characteristic
226	C₂	#20243607	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#20252473

C₂

yes

maximal, characteristic

C₄×#13093943

C₂

yes

maximal, characteristic

#20242138

C₂

yes

maximal

#20241225

C₂

yes

maximal

C₄₇×#1984

C₂

yes

maximal, characteristic

—

—

—

C₂²

yes

—

C₂×#13093943

C₄

yes

—

C₄×#10625329

C₂²

yes

—

#15688892

C₄

yes

characteristic

#15688892

C₄

yes

characteristic

#15688875

—

#15688873

—

C₂×C₄×Q₈×C₄₇

C₂²

yes

characteristic

C₂×C₄⋊C₈×C₄₇

C₂²

yes

characteristic

C₂×C₄×C₈×C₄₇

C₂²

yes

characteristic

C₄₇×#336

—

C₂×#10625329

C₂×C₄

yes

—

C₂×#10625329

C₂×C₄

yes

—

C₄⋊(C₄₇⋊C₈)

—

C₄⋊(C₄₇⋊C₈)

—

C₄⋊(C₄₇⋊C₈)

D₄

yes

—

C₄⋊(C₄₇⋊C₈)

D₄

yes

—

#13093943

—

C₂²⋊(C₄₇⋊C₈)

—

#13093935

—

#13093935

—

C₄×C₄₇⋊C₈

—

C₄×C₄₇⋊C₈

—

C₂²×Q₈×C₄₇

C₂×C₄

yes

characteristic

C₂²×C₈×C₄₇

—

C₂²×C₈×C₄₇

—

C₄×Q₈×C₄₇

—

C₄×Q₈×C₄₇

—

C₂×C₄⋊C₄×C₄₇

C₂×C₄

yes

characteristic

C₂×C₄⋊C₄×C₄₇

Q₈

yes

—

C₂×C₄²×C₄₇

D₄

yes

—

C₂×C₄²×C₄₇

C₂³

yes

characteristic

C₄⋊C₈×C₄₇

—

C₄×C₈×C₄₇

—

C₂×Q₈×C₄₇

—

C₂×Q₈×C₄₇

—

C₂×Q₈×C₄₇

—

C₂×Q₈×C₄₇

—

C₂²×C₄×C₄₇

C₄⋊C₄

yes

—

C₂²×C₄×C₄₇

C₄⋊C₄

yes

—

C₂²×C₄×C₄₇

C₂²×C₄

yes

characteristic

C₂²×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂²×C₄×C₄₇

C₂×Q₈

yes

characteristic

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

—

C₄⋊C₄×C₄₇

—

C₄⋊C₄×C₄₇

—

C₄²×C₄₇

—

C₄²×C₄₇

—

C₄²×C₄₇

C₂×D₄

yes

—

C₄²×C₄₇

#41

yes

—

—

—

—

M₁₆

yes

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂³×C₄₇

C₂×C₄⋊C₄

yes

characteristic

Q₈×C₄₇

—

Q₈×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₄×D₄

yes

—

C₂×C₄×C₄₇

#120

yes

characteristic

C₂×C₄×C₄₇

C₂²⋊Q₈

yes

—

C₂×C₄×C₄₇

#123

yes

characteristic

C₂×C₄×C₄₇

C₂×M₁₆

yes

—

C₂×C₄×C₄₇

yes

C₂×C₄×C₄₇

yes

C₈×C₄₇

—

C₈×C₄₇

—

C₄₇⋊C₈

—

C₄₇⋊C₈

—

C₄₇⋊C₈

—

C₄₇⋊C₈

—

#8838

—

maximal, Sylow

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

yes

C₂²×C₄₇

yes

100

C₂²×C₄₇

#424

yes

characteristic

101

C₄×C₄₇

—

102

C₄×C₄₇

—

103

C₄×C₄₇

—

104

C₄×C₄₇

—

105

C₄×C₄₇

#435

yes

—

106

C₄×C₄₇

#436

yes

—

107

C₄×C₄₇

#454

yes

characteristic

108

C₄×C₄₇

#456

yes

characteristic

109

#2983

—

110

#1984

D₄₇

yes

characteristic

111

C₄×#101

—

112

#1565

—

113

#1278

—

114

C₂×C₄₇

—

115

C₂×C₄₇

—

116

C₂×C₄₇

#1851

yes

characteristic

117

C₂×C₄₇

#1857

yes

characteristic

118

C₂×C₄₇

#1858

yes

characteristic

119

C₂×C₄×Q₈

C₂×D₄₇

yes

characteristic

120

#446

—

121

#446

—

122

#432

—

123

#431

—

124

C₂×C₄⋊C₈

C₂×D₄₇

yes

characteristic

125

C₂×#101

—

126

C₄×M₁₆

—

127

C₂×C₄×C₈

C₂×D₄₇

yes

characteristic

128

#343

—

129

#343

—

130

#336

—

131

#335

—

132

#334

—

133

C₄₇

#8838

yes

characteristic, complemented, Sylow

134

C₂²×Q₈

C₄×D₄₇

yes

characteristic

135

C₂×M₁₆

—

136

C₂×M₁₆

—

137

C₂²×C₈

—

138

C₂²×C₈

—

139

C₄×Q₈

—

140

C₄×Q₈

—

141

C₂×C₄⋊C₄

Dic₉₄

yes

—

142

C₂×C₄⋊C₄

C₄×D₄₇

yes

characteristic

143

C₂×C₄²

C₂²⋊D₄₇

yes

—

144

C₂×C₄²

C₂²×D₄₇

yes

characteristic

145

C₄⋊C₈

—

146

C₄⋊C₈

—

147

C₄⋊C₈

—

148

C₄⋊C₈

—

149

C₄⋊C₈

—

150

#101

—

151

C₂²⋊C₈

—

152

#97

—

153

#97

—

154

C₄×C₈

—

155

C₄×C₈

—

156

C₄×C₈

—

157

C₂×Q₈

—

158

C₂×Q₈

—

159

C₂×Q₈

—

160

C₂×Q₈

—

161

C₂²×C₄

Dic₄₇⋊C₄

yes

—

162

C₂²×C₄

Dic₄₇⋊C₄

yes

—

163

C₂²×C₄

C₂×Dic₉₄

yes

characteristic

164

C₂²×C₄

C₂×C₄×D₄₇

yes

characteristic

165

C₂²×C₄

C₂×C₂²⋊D₄₇

yes

characteristic

166

M₁₆

—

167

M₁₆

—

168

M₁₆

—

169

M₁₆

—

170

C₂×C₈

—

171

C₂×C₈

—

172

C₂×C₈

—

173

C₂×C₈

—

174

C₂×C₈

—

175

C₂×C₈

—

176

C₂×C₈

—

177

C₂×C₈

—

178

C₂×C₈

—

179

C₄⋊C₄

—

180

C₄⋊C₄

—

181

C₄²

—

182

C₄²

—

183

C₄²

D₄×D₄₇

yes

—

184

C₄²

#10625352

yes

—

185

C₂³

C₂×Dic₄₇⋊C₄

yes

characteristic

186

Q₈

—

187

Q₈

—

188

C₂×C₄

—

189

C₂×C₄

—

190

C₂×C₄

—

191

C₂×C₄

—

192

C₂×C₄

—

193

C₂×C₄

—

194

C₂×C₄

—

195

C₂×C₄

—

196

C₂×C₄

(C₂²⋊D₄₇)⋊C₄

yes

—

197

C₂×C₄

#13093992

yes

characteristic

198

C₂×C₄

#13094001

yes

—

199

C₂×C₄

#13094005

yes

characteristic

200

C₂×C₄

M₁₆×D₄₇

yes

—

201

C₂×C₄

#13094030

yes

characteristic

202

C₂×C₄

#13094030

yes

characteristic

203

C₈

—

204

C₈

—

205

C₈

—

206

C₈

—

188

—

207

C₈

—

188

—

208

C₈

—

188

—

209

C₂²

—

210

C₂²

—

211

C₂²

#15688995

yes

characteristic

212

C₂²

#15689146

yes

characteristic

213

C₂²

#15689149

yes

characteristic

214

C₄

—

215

C₄

—

216

C₄

—

217

C₄

—

218

C₄

#15689197

yes

—

219

C₄

#15689198

yes

—

220

C₄

#15689295

yes

characteristic

221

C₄

#15689305

yes

characteristic

222

C₂

—

223

C₂

—

224

C₂

#20243570

yes

characteristic

225

C₂

#20243602

yes

characteristic

226

C₂

#20243607

yes

characteristic

	subgroup	G/H
center	C₂×C₄	#13093992
commutator	C₂²×C₄×C₄₇	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₄₇
Fitting	C₄₇×#1984	C₂
socle	C₂²×C₄₇	#385
prime radical	C₂³×C₄₇	C₂×C₄⋊C₄
cosocle	C₂×C₄²×C₄₇	C₂³
hypercenter	#1984	D₄₇
hypocenter	C₄₇	#8838
LCS	G ▷ C₂²×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1984

subgroup

G/H

center

C₂×C₄

#13093992

commutator

C₂²×C₄×C₄₇

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₄₇

Fitting

C₄₇×#1984

C₂

socle

C₂²×C₄₇

#385

prime radical

C₂³×C₄₇

C₂×C₄⋊C₄

cosocle

C₂×C₄²×C₄₇

C₂³

D₄₇

C₄₇

G ▷ C₂²×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1984

N	H ≅ G/N	type
133. C₄₇	#8838	semidirect

H ≅ G/N

type

133. C₄₇

#8838

semidirect

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

subgroup	index
#20252473	2
C₄×#13093943	2
#20242138	2
#20241225	2
C₄₇×#1984	2
#8838	47

subgroup

index

C₄₇×#1984

Subgroups — #26110154

Conjugacy classes of subgroups

Complements

Maximal subgroups