Group #31902480 — subgroups

Subgroups — #31902480

Order 18176.

296 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 296 conjugacy classes of subgroups — too many to draw. Only its 89 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	#22589321	C₂	1	1	yes	maximal, characteristic
2	#22587114	C₂	1	1	yes	maximal, characteristic
3	#22587110	C₂	1	1	yes	maximal, characteristic
4	#22586742	C₂	1	1	yes	maximal, characteristic
5	#22586742	C₂	1	1	yes	maximal, characteristic
6	#22586169	C₂	1	1	yes	maximal, characteristic
7	C₇₁×#1832	C₂	1	1	yes	maximal, characteristic
8	#17986556	C₂²	1	1	yes	characteristic
9	#17986052	C₂²	1	1	yes	characteristic
10	#17986052	C₂²	1	1	yes	characteristic
11	#17986023	C₂²	1	1	yes	characteristic
12	#17985759	—	2	2	no	—
13	#17985751	—	2	2	no	—
14	#17985749	—	2	2	no	—
15	#17985729	—	2	2	no	—
16	#17985729	—	2	2	no	—
17	C₂×C₄⋊C₈×C₇₁	C₂²	1	1	yes	characteristic
18	C₂×C₄⋊C₈×C₇₁	C₂²	1	1	yes	characteristic
19	#376×C₇₁	C₂²	1	1	yes	characteristic
20	#336×C₇₁	—	2	2	no	—
21	C₂×#11765849	—	2	1	no	—
22	#14556128	Q₈	1	1	yes	characteristic
23	#14556128	Q₈	1	1	yes	characteristic
24	#14556120	—	2	1	no	—
25	#14556107	—	2	1	no	—
26	#14556107	—	2	1	no	—
27	C₄×Dic₁₄₂	—	2	1	no	—
28	C₄×Dic₁₄₂	—	2	1	no	—
29	#14556087	—	2	1	no	—
30	C₄⋊(C₇₁⋊C₈)	—	2	1	no	—
31	C₄⋊(C₇₁⋊C₈)	—	2	1	no	—
32	C₄⋊(C₇₁⋊C₈)	—	2	1	no	—
33	C₄⋊(C₇₁⋊C₈)	—	2	1	no	—
34	C₂²⋊(C₇₁⋊C₈)	—	2	1	no	—
35	C₂²⋊(C₇₁⋊C₈)	—	2	1	no	—
36	C₄×C₇₁⋊C₈	D₄	1	2	yes	—
37	C₄×C₇₁⋊C₈	D₄	1	2	yes	—
38	C₂²×C₈×C₇₁	—	2	1	no	—
39	C₂²×C₈×C₇₁	—	2	1	no	—
40	C₂×C₄²×C₇₁	D₄	1	2	yes	—
41	C₂×C₄²×C₇₁	C₂³	1	1	yes	characteristic
42	C₄⋊C₈×C₇₁	—	2	1	no	—
43	C₄⋊C₈×C₇₁	—	2	1	no	—
44	C₄⋊C₈×C₇₁	—	2	1	no	—
45	C₄⋊C₈×C₇₁	—	2	1	no	—
46	#95×C₇₁	—	2	1	no	—
47	#95×C₇₁	—	2	1	no	—
48	C₂×Dic₁₄₂	—	2	1	no	—
49	C₂×Dic₁₄₂	—	2	1	no	—
50	#11765849	—	4	2	no	—
51	C₂×C₇₁⋊C₈	—	2	2	no	—
52	C₂×C₇₁⋊C₈	—	2	2	no	—
53	C₂×C₇₁⋊C₈	—	4	1	no	—
54	C₄⋊Dic₇₁	—	2	1	no	—
55	C₄⋊Dic₇₁	—	2	1	no	—
56	C₄⋊Dic₇₁	—	2	1	no	—
57	C₄⋊Dic₇₁	—	2	1	no	—
58	Dic₇₁⋊C₄	—	4	1	no	—
59	Dic₇₁⋊C₄	—	4	1	no	—
60	C₂²⋊Dic₇₁	—	4	1	no	—
61	C₄×Dic₇₁	—	4	1	no	—
62	C₂²×C₄×C₇₁	—	2	2	no	—
63	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
64	C₂²×C₄×C₇₁	#41	1	1	yes	characteristic
65	C₂²×C₄×C₇₁	#41	1	1	yes	characteristic
66	C₂×C₈×C₇₁	—	4	1	no	—
67	C₂×C₈×C₇₁	—	4	1	no	—
68	C₂×C₈×C₇₁	—	4	2	no	—
69	C₂×C₈×C₇₁	—	4	2	no	—
70	C₄²×C₇₁	—	2	2	no	—
71	C₄²×C₇₁	—	2	2	no	—
72	C₄²×C₇₁	C₂×D₄	1	1	yes	characteristic
73	C₄²×C₇₁	C₂×D₄	1	1	yes	characteristic
74	C₄²×C₇₁	C₂×Q₈	1	1	yes	characteristic
75	C₄²×C₇₁	#41	1	1	yes	characteristic
76	C₂³×C₇₁	#123	1	1	yes	characteristic
77	C₂×C₄×C₇₁	—	4	1	no	—
78	C₂×C₄×C₇₁	—	4	1	no	—
79	C₂×C₄×C₇₁	—	4	2	no	—
80	C₂×C₄×C₇₁	—	4	2	no	—
81	C₂×C₄×C₇₁	—	4	2	no	—
82	C₂×C₄×C₇₁	C₂²⋊Q₈	1	1	yes	characteristic
83	C₂×C₄×C₇₁	C₂²⋊Q₈	1	1	yes	characteristic
84	C₂×C₄×C₇₁	C₂²⋊Q₈	1	1	yes	characteristic
85	C₂×C₄×C₇₁	#123	1	1	yes	characteristic
86	C₂×C₄×C₇₁	#123	1	1	yes	characteristic
87	C₂×C₄×C₇₁	#127	1	1	yes	characteristic
88	C₂×C₄×C₇₁	#135	1	2	yes	—
89	C₂×C₄×C₇₁	#137	1	2	yes	—
90	C₂×Dic₇₁	—	4	1	no	—
91	C₂×Dic₇₁	—	4	1	no	—
92	Dic₁₄₂	—	4	2	no	—
93	Dic₁₄₂	—	4	2	no	—
94	C₈×C₇₁	—	8	1	no	—
95	C₈×C₇₁	—	8	1	no	—
96	C₇₁⋊C₈	—	4	2	no	—
97	C₇₁⋊C₈	—	4	2	no	—
98	C₇₁⋊C₈	—	8	1	no	—
99	C₂²×C₇₁	—	2	1	no	—
100	C₂²×C₇₁	—	2	1	no	—
101	C₂²×C₇₁	#399	1	1	yes	characteristic
102	C₂²×C₇₁	#485	1	2	yes	—
103	C₄×C₇₁	—	2	1	no	—
104	C₄×C₇₁	—	2	1	no	—
105	C₄×C₇₁	—	2	1	no	—
106	C₄×C₇₁	—	2	1	no	—
107	C₄×C₇₁	—	8	2	no	—
108	C₄×C₇₁	#479	1	2	yes	—
109	C₄×C₇₁	#495	1	1	yes	characteristic
110	C₄×C₇₁	#497	1	1	yes	characteristic
111	Dic₇₁	—	8	1	no	—
112	Dic₇₁	—	8	1	no	—
113	#10669	—	71	1	no	maximal, Sylow
114	C₂×C₇₁	—	2	2	no	—
115	C₂×C₇₁	#2097	1	1	yes	characteristic
116	C₂×C₇₁	#2098	1	1	yes	characteristic
117	C₂×C₇₁	#2098	1	1	yes	characteristic
118	#1995	—	71	1	no	—
119	#1832	D₇₁	1	1	yes	characteristic
120	#1571	—	71	1	no	—
121	#1570	—	71	1	no	—
122	#1481	—	71	1	no	—
123	#1481	—	71	1	no	—
124	#1274	—	71	1	no	—
125	C₇₁	#10669	1	1	yes	characteristic, complemented, Sylow
126	#533	—	71	1	no	—
127	#431	—	71	1	no	—
128	#431	—	71	1	no	—
129	#423	—	71	1	no	—
130	C₂×C₄⋊C₈	C₂×D₇₁	1	1	yes	characteristic
131	C₂×C₄⋊C₈	C₂×D₇₁	1	1	yes	characteristic
132	#376	C₂×D₇₁	1	1	yes	characteristic
133	#339	—	142	2	no	—
134	#336	—	2	2	no	—
135	#335	—	142	2	no	—
136	#334	—	142	2	no	—
137	Q₈⋊C₈	—	142	2	no	—
138	Q₈⋊C₈	—	142	2	no	—
139	C₂×M₁₆	—	142	1	no	—
140	C₂²×C₈	—	2	1	no	—
141	C₂²×C₈	—	2	1	no	—
142	C₄⋊Q₈	—	71	1	no	—
143	C₄⋊Q₈	—	71	1	no	—
144	#125	—	142	1	no	—
145	C₂²⋊Q₈	—	142	1	no	—
146	C₂²⋊Q₈	—	142	1	no	—
147	C₄×Q₈	—	142	1	no	—
148	C₄×Q₈	—	142	1	no	—
149	#117	—	142	1	no	—
150	C₂×C₄²	C₂²⋊D₇₁	1	2	yes	—
151	C₂×C₄²	C₂²×D₇₁	1	1	yes	characteristic
152	C₄⋊C₈	—	2	1	no	—
153	C₄⋊C₈	—	2	1	no	—
154	C₄⋊C₈	—	2	1	no	—
155	C₄⋊C₈	—	2	1	no	—
156	C₄⋊C₈	—	142	1	no	—
157	C₄⋊C₈	—	142	1	no	—
158	C₄⋊C₈	—	142	1	no	—
159	C₄⋊C₈	—	142	1	no	—
160	C₂²⋊C₈	—	142	1	no	—
161	C₂²⋊C₈	—	142	1	no	—
162	C₄×C₈	—	71	2	no	—
163	C₄×C₈	—	71	2	no	—
164	#95	—	2	1	no	—
165	#95	—	2	1	no	—
166	C₂×Q₈	—	142	1	no	—
167	C₂×Q₈	—	142	1	no	—
168	C₂²×C₄	—	2	2	no	—
169	C₂²×C₄	C₂×C₂²⋊D₇₁	1	1	yes	characteristic
170	C₂²×C₄	#11765865	1	1	yes	characteristic
171	C₂²×C₄	#11765865	1	1	yes	characteristic
172	M₁₆	—	284	2	no	—
173	C₂×C₈	—	4	1	no	—
174	C₂×C₈	—	4	1	no	—
175	C₂×C₈	—	4	2	no	—
176	C₂×C₈	—	4	2	no	—
177	C₂×C₈	—	284	1	no	—
178	C₂×C₈	—	142	2	no	—
179	C₂×C₈	—	142	2	no	—
180	C₄⋊C₄	—	284	1	no	—
181	C₄⋊C₄	—	284	1	no	—
182	C₄⋊C₄	—	142	1	no	—
183	C₄⋊C₄	—	142	1	no	—
184	C₄⋊C₄	—	142	1	no	—
185	C₄⋊C₄	—	142	1	no	—
186	C₂²⋊C₄	—	284	1	no	—
187	C₄²	—	2	2	no	—
188	C₄²	—	2	2	no	—
189	C₄²	—	284	1	no	—
190	C₄²	D₄×D₇₁	1	1	yes	characteristic
191	C₄²	D₄×D₇₁	1	1	yes	characteristic
192	C₄²	Q₈×D₇₁	1	1	yes	characteristic
193	C₄²	#11765866	1	1	yes	characteristic
194	C₂³	#14556111	1	1	yes	characteristic
195	Q₈	—	284	2	no	—
196	Q₈	—	284	2	no	—
197	C₂×C₄	—	4	1	no	—
198	C₂×C₄	—	4	1	no	—
199	C₂×C₄	—	4	2	no	—
200	C₂×C₄	—	4	2	no	—
201	C₂×C₄	—	4	2	no	—
202	C₂×C₄	—	284	1	no	—
203	C₂×C₄	—	284	1	no	—
204	C₂×C₄	#14556104	1	1	yes	characteristic
205	C₂×C₄	#14556106	1	1	yes	characteristic
206	C₂×C₄	#14556106	1	1	yes	characteristic
207	C₂×C₄	#14556113	1	1	yes	characteristic
208	C₂×C₄	#14556113	1	1	yes	characteristic
209	C₂×C₄	#14556124	1	1	yes	characteristic
210	C₂×C₄	#14556148	1	2	yes	—
211	C₂×C₄	#14556158	1	2	yes	—
212	C₈	—	8	1	no	—
213	C₈	—	8	1	no	—
214	C₈	—	284	2	no	—
215	C₈	—	284	2	no	—
216	C₈	—	568	1	no	—
217	C₂²	—	2	1	no	—
218	C₂²	—	2	1	no	—
219	C₂²	#17985934	1	1	yes	characteristic
220	C₂²	#17986340	1	2	yes	—
221	C₄	—	2	1	no	—
222	C₄	—	2	1	no	—
223	C₄	—	2	1	no	—
224	C₄	—	2	1	no	—
225	C₄	—	8	2	no	—
226	C₄	—	568	1	no	—
227	C₄	—	568	1	no	—
228	C₄	#17986303	1	2	yes	—
229	C₄	#17986381	1	1	yes	characteristic
230	C₄	#17986394	1	1	yes	characteristic
231	C₂	—	2	2	no	—
232	C₂	#22589891	1	1	yes	characteristic
233	C₂	#22589896	1	1	yes	characteristic
234	C₂	#22589896	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#22589321

C₂

yes

maximal, characteristic

#22587114

C₂

yes

maximal, characteristic

#22587110

C₂

yes

maximal, characteristic

#22586742

C₂

yes

maximal, characteristic

#22586742

C₂

yes

maximal, characteristic

#22586169

C₂

yes

maximal, characteristic

C₇₁×#1832

C₂

yes

maximal, characteristic

#17986556

C₂²

yes

characteristic

#17986052

C₂²

yes

characteristic

#17986052

C₂²

yes

characteristic

#17986023

C₂²

yes

—

—

—

—

—

C₂×C₄⋊C₈×C₇₁

C₂²

yes

characteristic

C₂×C₄⋊C₈×C₇₁

C₂²

yes

characteristic

#376×C₇₁

C₂²

yes

characteristic

#336×C₇₁

—

C₂×#11765849

—

#14556128

Q₈

yes

characteristic

#14556128

Q₈

yes

—

—

—

C₄×Dic₁₄₂

—

C₄×Dic₁₄₂

—

#14556087

—

C₄⋊(C₇₁⋊C₈)

—

C₄⋊(C₇₁⋊C₈)

—

C₄⋊(C₇₁⋊C₈)

—

C₄⋊(C₇₁⋊C₈)

—

C₂²⋊(C₇₁⋊C₈)

—

C₂²⋊(C₇₁⋊C₈)

—

C₄×C₇₁⋊C₈

D₄

yes

—

C₄×C₇₁⋊C₈

D₄

yes

—

C₂²×C₈×C₇₁

—

C₂²×C₈×C₇₁

—

C₂×C₄²×C₇₁

D₄

yes

—

C₂×C₄²×C₇₁

C₂³

yes

characteristic

C₄⋊C₈×C₇₁

—

C₄⋊C₈×C₇₁

—

C₄⋊C₈×C₇₁

—

C₄⋊C₈×C₇₁

—

#95×C₇₁

—

#95×C₇₁

—

C₂×Dic₁₄₂

—

C₂×Dic₁₄₂

—

#11765849

—

C₂×C₇₁⋊C₈

—

C₂×C₇₁⋊C₈

—

C₂×C₇₁⋊C₈

—

C₄⋊Dic₇₁

—

C₄⋊Dic₇₁

—

C₄⋊Dic₇₁

—

C₄⋊Dic₇₁

—

Dic₇₁⋊C₄

—

Dic₇₁⋊C₄

—

C₂²⋊Dic₇₁

—

C₄×Dic₇₁

—

C₂²×C₄×C₇₁

—

C₂²×C₄×C₇₁

C₂×D₄

yes

C₂²×C₄×C₇₁

yes

C₂²×C₄×C₇₁

yes

C₂×C₈×C₇₁

—

C₂×C₈×C₇₁

—

C₂×C₈×C₇₁

—

C₂×C₈×C₇₁

—

C₄²×C₇₁

—

C₄²×C₇₁

—

C₄²×C₇₁

C₂×D₄

yes

characteristic

C₄²×C₇₁

C₂×D₄

yes

characteristic

C₄²×C₇₁

C₂×Q₈

yes

C₄²×C₇₁

yes

C₂³×C₇₁

yes

C₂×C₄×C₇₁

—

C₂×C₄×C₇₁

—

C₂×C₄×C₇₁

—

C₂×C₄×C₇₁

—

C₂×C₄×C₇₁

—

C₂×C₄×C₇₁

C₂²⋊Q₈

yes

characteristic

C₂×C₄×C₇₁

C₂²⋊Q₈

yes

characteristic

C₂×C₄×C₇₁

C₂²⋊Q₈

yes

C₂×C₄×C₇₁

yes

C₂×C₄×C₇₁

yes

C₂×C₄×C₇₁

yes

C₂×C₄×C₇₁

yes

—

C₂×C₄×C₇₁

#137

yes

—

C₂×Dic₇₁

—

C₂×Dic₇₁

—

Dic₁₄₂

—

Dic₁₄₂

—

C₈×C₇₁

—

C₈×C₇₁

—

C₇₁⋊C₈

—

C₇₁⋊C₈

—

C₇₁⋊C₈

—

C₂²×C₇₁

—

100

C₂²×C₇₁

—

101

C₂²×C₇₁

#399

yes

characteristic

102

C₂²×C₇₁

#485

yes

—

103

C₄×C₇₁

—

104

C₄×C₇₁

—

105

C₄×C₇₁

—

106

C₄×C₇₁

—

107

C₄×C₇₁

—

108

C₄×C₇₁

#479

yes

—

109

C₄×C₇₁

#495

yes

characteristic

110

C₄×C₇₁

#497

yes

characteristic

111

Dic₇₁

—

112

Dic₇₁

—

113

#10669

—

maximal, Sylow

114

C₂×C₇₁

—

115

C₂×C₇₁

#2097

yes

characteristic

116

C₂×C₇₁

#2098

yes

characteristic

117

C₂×C₇₁

#2098

yes

characteristic

118

#1995

—

119

#1832

D₇₁

yes

characteristic

120

#1571

—

121

#1570

—

122

#1481

—

123

#1481

—

124

#1274

—

125

C₇₁

#10669

yes

characteristic, complemented, Sylow

126

#533

—

127

#431

—

128

#431

—

129

#423

—

130

C₂×C₄⋊C₈

C₂×D₇₁

yes

characteristic

131

C₂×C₄⋊C₈

C₂×D₇₁

yes

characteristic

132

#376

C₂×D₇₁

yes

characteristic

133

#339

—

142

—

134

#336

—

135

#335

—

142

—

136

#334

—

142

—

137

Q₈⋊C₈

—

142

—

138

Q₈⋊C₈

—

142

—

139

C₂×M₁₆

—

142

—

140

C₂²×C₈

—

141

C₂²×C₈

—

142

C₄⋊Q₈

—

143

C₄⋊Q₈

—

144

#125

—

142

—

145

C₂²⋊Q₈

—

142

—

146

C₂²⋊Q₈

—

142

—

147

C₄×Q₈

—

142

—

148

C₄×Q₈

—

142

—

149

#117

—

142

—

150

C₂×C₄²

C₂²⋊D₇₁

yes

—

151

C₂×C₄²

C₂²×D₇₁

yes

characteristic

152

C₄⋊C₈

—

153

C₄⋊C₈

—

154

C₄⋊C₈

—

155

C₄⋊C₈

—

156

C₄⋊C₈

—

142

—

157

C₄⋊C₈

—

142

—

158

C₄⋊C₈

—

142

—

159

C₄⋊C₈

—

142

—

160

C₂²⋊C₈

—

142

—

161

C₂²⋊C₈

—

142

—

162

C₄×C₈

—

163

C₄×C₈

—

164

#95

—

165

#95

—

166

C₂×Q₈

—

142

—

167

C₂×Q₈

—

142

—

168

C₂²×C₄

—

169

C₂²×C₄

C₂×C₂²⋊D₇₁

yes

characteristic

170

C₂²×C₄

#11765865

yes

characteristic

171

C₂²×C₄

#11765865

yes

characteristic

172

M₁₆

—

284

—

173

C₂×C₈

—

174

C₂×C₈

—

175

C₂×C₈

—

176

C₂×C₈

—

177

C₂×C₈

—

284

—

178

C₂×C₈

—

142

—

179

C₂×C₈

—

142

—

180

C₄⋊C₄

—

284

—

181

C₄⋊C₄

—

284

—

182

C₄⋊C₄

—

142

—

183

C₄⋊C₄

—

142

—

184

C₄⋊C₄

—

142

—

185

C₄⋊C₄

—

142

—

186

C₂²⋊C₄

—

284

—

187

C₄²

—

188

C₄²

—

189

C₄²

—

284

—

190

C₄²

D₄×D₇₁

yes

characteristic

191

C₄²

D₄×D₇₁

yes

characteristic

192

C₄²

Q₈×D₇₁

yes

characteristic

193

C₄²

#11765866

yes

characteristic

194

C₂³

#14556111

yes

characteristic

195

Q₈

—

284

—

196

Q₈

—

284

—

197

C₂×C₄

—

198

C₂×C₄

—

199

C₂×C₄

—

200

C₂×C₄

—

201

C₂×C₄

—

202

C₂×C₄

—

284

—

203

C₂×C₄

—

284

—

204

C₂×C₄

#14556104

yes

characteristic

205

C₂×C₄

#14556106

yes

characteristic

206

C₂×C₄

#14556106

yes

characteristic

207

C₂×C₄

#14556113

yes

characteristic

208

C₂×C₄

#14556113

yes

characteristic

209

C₂×C₄

#14556124

yes

characteristic

210

C₂×C₄

#14556148

yes

—

211

C₂×C₄

#14556158

yes

—

212

C₈

—

213

C₈

—

214

C₈

—

284

—

215

C₈

—

284

—

216

C₈

—

568

—

217

C₂²

—

218

C₂²

—

219

C₂²

#17985934

yes

characteristic

220

C₂²

#17986340

yes

—

221

C₄

—

222

C₄

—

223

C₄

—

224

C₄

—

225

C₄

—

226

C₄

—

568

—

227

C₄

—

568

—

228

C₄

#17986303

yes

—

229

C₄

#17986381

yes

characteristic

230

C₄

#17986394

yes

characteristic

231

C₂

—

232

C₂

#22589891

yes

characteristic

233

C₂

#22589896

yes

characteristic

234

C₂

#22589896

yes

characteristic

	subgroup	G/H
center	C₂×C₄	#14556124
commutator, cosocle	C₂×C₄²×C₇₁	C₂³
Frattini	C₂×C₄²	C₂²×D₇₁
Fitting	C₇₁×#1832	C₂
socle	C₂²×C₇₁	#399
prime radical	C₂³×C₇₁	#123
hypercenter	#1832	D₇₁
hypocenter	C₇₁	#10669
LCS	G ▷ C₂×C₄²×C₇₁ ▷ C₂²×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1832

subgroup

G/H

center

C₂×C₄

#14556124

commutator, cosocle

C₂×C₄²×C₇₁

C₂³

Frattini

C₂×C₄²

C₂²×D₇₁

Fitting

C₇₁×#1832

C₂

C₂²×C₇₁

C₂³×C₇₁

D₇₁

C₇₁

G ▷ C₂×C₄²×C₇₁ ▷ C₂²×C₇₁ ▷ C₇₁

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1832

N	H ≅ G/N	type
125. C₇₁	#10669	semidirect

H ≅ G/N

type

125. C₇₁

#10669

semidirect

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

subgroup	index
#22589321	2
#22587114	2
#22587110	2
#22586742	2
#22586169	2
C₇₁×#1832	2
#10669	71

subgroup

index

C₇₁×#1832

Subgroups — #31902480

Conjugacy classes of subgroups

Complements

Maximal subgroups