Group #32985671 — subgroups

Subgroups — #32985671

Order 18688.

602 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 602 conjugacy classes of subgroups — too many to draw. Only its 127 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×#17988964	C₂	1	1	yes	maximal, characteristic
2	#22610770	C₂	1	2	yes	maximal, complemented
3	#22608600	C₂	1	2	yes	maximal, complemented
4	#22608220	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇₃×#1566	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×D₅₈₄	C₄	1	4	yes	—
7	C₂×#14556588	C₂²	1	2	yes	—
8	#17988964	—	2	1	no	—
9	#17988964	—	2	1	no	—
10	#17988964	—	2	2	no	—
11	#17988640	C₂²	1	1	yes	characteristic
12	C₂×#14556507	—	2	4	no	—
13	C₄×#11924012	C₂²	1	1	yes	characteristic
14	#17988330	—	2	4	no	—
15	#17988309	—	2	1	no	—
16	#17988308	—	2	1	no	—
17	#423×C₇₃	C₂²	1	2	yes	—
18	C₂×C₄×C₈×C₇₃	C₂²	1	1	yes	characteristic
19	#334×C₇₃	—	2	2	no	—
20	C₂²×D₂₉₂	—	2	2	no	—
21	C₂²×D₂₉₂	—	2	2	no	—
22	C₂²×D₂₉₂	C₂×C₄	1	4	yes	—
23	C₂×D₅₈₄	—	2	4	no	—
24	C₂×D₅₈₄	—	2	4	no	—
25	C₂×D₅₈₄	—	4	8	no	—
26	C₂×#11924012	D₄	1	2	yes	—
27	#14556588	—	2	2	no	—
28	#14556588	—	2	2	no	—
29	#14556588	—	2	2	no	—
30	#14556588	—	2	2	no	—
31	C₄⋊#10596831	D₄	1	2	yes	—
32	#14556507	—	4	8	no	—
33	C₂²⋊#10596831	—	2	1	no	—
34	#14556502	—	2	1	no	—
35	C₄×#10596831	—	2	1	no	—
36	C₄×#10596831	—	2	1	no	—
37	C₂×M₁₆×C₇₃	—	2	2	no	—
38	C₂²×C₈×C₇₃	C₂×C₄	1	2	yes	—
39	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
40	C₄⋊C₈×C₇₃	—	2	2	no	—
41	C₄⋊C₈×C₇₃	—	2	2	no	—
42	C₄×C₈×C₇₃	D₄	1	1	yes	characteristic
43	C₄×C₈×C₇₃	D₄	1	1	yes	characteristic
44	C₄×C₈×C₇₃	D₄	1	2	yes	—
45	C₂³×D₇₃	—	2	4	no	—
46	C₂×D₂₉₂	—	2	4	no	—
47	C₂×D₂₉₂	—	2	4	no	—
48	C₂×D₂₉₂	—	4	8	no	—
49	C₂×D₂₉₂	—	4	2	no	—
50	C₂×D₂₉₂	—	4	2	no	—
51	C₂×D₂₉₂	—	4	2	no	—
52	C₂×D₂₉₂	—	4	2	no	—
53	C₂×D₂₉₂	—	4	4	no	—
54	C₂×D₂₉₂	—	4	4	no	—
55	C₂×D₂₉₂	—	8	4	no	—
56	D₅₈₄	—	4	8	no	—
57	D₅₈₄	—	4	8	no	—
58	#11924012	—	2	4	no	—
59	C₂×#10596831	—	2	2	no	—
60	C₂×#10596831	—	2	2	no	—
61	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
62	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
63	C₂²×C₄×C₇₃	#41	1	1	yes	characteristic
64	M₁₆×C₇₃	—	4	4	no	—
65	C₂×C₈×C₇₃	—	2	4	no	—
66	C₂×C₈×C₇₃	—	4	2	no	—
67	C₂×C₈×C₇₃	C₂²⋊C₄	1	2	yes	—
68	C₂×C₈×C₇₃	C₂²⋊C₄	1	2	yes	—
69	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
70	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
71	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
72	C₄²×C₇₃	#41	1	1	yes	characteristic
73	C₂³×C₇₃	C₄×D₄	1	1	yes	characteristic
74	C₂²×D₇₃	—	4	4	no	—
75	C₂²×D₇₃	—	4	8	no	—
76	C₂²×D₇₃	—	8	4	no	—
77	C₂²×D₇₃	—	8	4	no	—
78	C₂×C₄×C₇₃	—	2	2	no	—
79	C₂×C₄×C₇₃	—	2	2	no	—
80	C₂×C₄×C₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
81	C₂×C₄×C₇₃	C₄×D₄	1	1	yes	characteristic
82	C₂×C₄×C₇₃	#121	1	1	yes	characteristic
83	C₂×C₄×C₇₃	#121	1	1	yes	characteristic
84	C₂×C₄×C₇₃	#124	1	1	yes	characteristic
85	C₂×C₄×C₇₃	#127	1	1	yes	characteristic
86	C₂×C₄×C₇₃	AGL(1,ℤ/8)	1	4	yes	—
87	D₂₉₂	—	4	8	no	—
88	D₂₉₂	—	8	4	no	—
89	D₂₉₂	—	8	4	no	—
90	D₂₉₂	—	8	4	no	—
91	D₂₉₂	—	8	4	no	—
92	D₂₉₂	—	8	2	no	—
93	D₂₉₂	—	8	2	no	—
94	C₈×C₇₃	—	2	2	no	—
95	C₈×C₇₃	—	8	2	no	—
96	C₈×C₇₃	#100	1	4	yes	complemented
97	#10596831	—	4	2	no	—
98	#10596831	—	4	2	no	—
99	C₂²×C₇₃	—	2	1	no	—
100	C₂²×C₇₃	—	2	1	no	—
101	C₂²×C₇₃	#390	1	1	yes	characteristic
102	C₂²×C₇₃	#442	1	2	yes	—
103	C₂×D₇₃	—	8	4	no	—
104	C₂×D₇₃	—	8	4	no	—
105	C₂×D₇₃	—	8	4	no	—
106	C₂×D₇₃	—	16	8	no	—
107	C₄×C₇₃	—	2	1	no	—
108	C₄×C₇₃	—	2	1	no	—
109	C₄×C₇₃	C₂×#100	1	2	yes	—
110	C₄×C₇₃	#469	1	2	yes	—
111	C₄×C₇₃	#472	1	2	yes	—
112	C₄×C₇₃	#496	1	2	yes	—
113	#9811	—	73	1	no	maximal, Sylow
114	C₂×C₇₃	—	2	2	no	—
115	C₂×C₇₃	#1965	1	1	yes	characteristic
116	C₂×C₇₃	#1972	1	1	yes	characteristic
117	C₂×C₇₃	#1978	1	1	yes	characteristic
118	D₇₃	—	16	4	no	—
119	C₂×#493	—	73	1	no	—
120	#1965	—	73	2	no	—
121	#1566	D₇₃	1	1	yes	characteristic, complemented
122	#1545	—	73	2	no	—
123	#1451	—	73	1	no	—
124	C₇₃	#9811	1	1	yes	characteristic, complemented, Sylow
125	C₂²×D₈	—	73	4	no	—
126	C₂×#127	—	73	2	no	—
127	#493	—	146	1	no	—
128	#493	—	146	1	no	—
129	#493	—	146	2	no	—
130	#431	—	73	1	no	—
131	#423	C₂×D₇₃	1	2	yes	—
132	C₂×#100	—	146	4	no	—
133	C₄×M₁₆	—	73	1	no	—
134	C₂×C₄×C₈	C₂×D₇₃	1	1	yes	characteristic
135	#334	—	2	2	no	—
136	#331	—	146	4	no	—
137	#322	—	146	1	no	—
138	#322	—	146	1	no	—
139	C₂²×D₄	—	73	4	no	—
140	C₂²×D₄	—	146	2	no	—
141	C₂²×D₄	—	146	2	no	—
142	C₂×D₈	—	292	8	no	—
143	C₂×D₈	—	146	4	no	—
144	C₂×D₈	—	146	4	no	—
145	C₂×M₁₆	—	2	2	no	—
146	C₂×M₁₆	—	73	2	no	—
147	C₂²×C₈	C₄×D₇₃	1	2	yes	—
148	#127	—	146	2	no	—
149	#127	—	146	2	no	—
150	#127	—	146	2	no	—
151	#127	—	146	2	no	—
152	C₂×C₄²	C₂²×D₇₃	1	1	yes	characteristic
153	C₄⋊C₈	—	2	2	no	—
154	C₄⋊C₈	—	2	2	no	—
155	C₄⋊C₈	—	73	2	no	—
156	#100	—	292	8	no	—
157	C₂²⋊C₈	—	146	1	no	—
158	#97	—	146	1	no	—
159	C₄×C₈	—	146	1	no	—
160	C₄×C₈	—	146	1	no	—
161	C₄×C₈	D₂₉₂	1	1	yes	characteristic
162	C₄×C₈	D₂₉₂	1	1	yes	characteristic
163	C₄×C₈	C₂²⋊D₇₃	1	2	yes	—
164	C₂⁴	—	146	4	no	—
165	C₂×D₄	—	292	8	no	—
166	C₂×D₄	—	292	2	no	—
167	C₂×D₄	—	292	2	no	—
168	C₂×D₄	—	292	2	no	—
169	C₂×D₄	—	292	2	no	—
170	C₂×D₄	—	292	4	no	—
171	C₂×D₄	—	292	4	no	—
172	C₂×D₄	—	584	4	no	—
173	C₂×D₄	—	146	4	no	—
174	C₂×D₄	—	146	4	no	—
175	C₂²×C₄	C₂×C₄×D₇₃	1	1	yes	characteristic
176	C₂²×C₄	D₄×D₇₃	1	1	yes	characteristic
177	C₂²×C₄	#11924029	1	1	yes	characteristic
178	D₈	—	292	8	no	—
179	D₈	—	292	8	no	—
180	M₁₆	—	4	4	no	—
181	M₁₆	—	146	4	no	—
182	C₂×C₈	—	2	4	no	—
183	C₂×C₈	—	4	2	no	—
184	C₂×C₈	—	146	2	no	—
185	C₂×C₈	—	146	2	no	—
186	C₂×C₈	#11924005	1	2	yes	—
187	C₂×C₈	#11924005	1	2	yes	—
188	C₄²	D₄×D₇₃	1	1	yes	characteristic
189	C₄²	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
190	C₄²	C₂×D₂₉₂	1	1	yes	characteristic
191	C₄²	#11924029	1	1	yes	characteristic
192	C₂³	—	292	4	no	—
193	C₂³	—	292	8	no	—
194	C₂³	—	584	4	no	—
195	C₂³	—	584	4	no	—
196	C₂³	#14556553	1	1	yes	characteristic
197	D₄	—	292	8	no	—
198	D₄	—	584	4	no	—
199	D₄	—	584	4	no	—
200	D₄	—	584	2	no	—
201	D₄	—	584	2	no	—
202	D₄	—	584	4	no	—
203	D₄	—	584	4	no	—
204	C₂×C₄	—	2	2	no	—
205	C₂×C₄	—	2	2	no	—
206	C₂×C₄	C₂×#11924005	1	1	yes	characteristic
207	C₂×C₄	#14556553	1	1	yes	characteristic
208	C₂×C₄	#14556566	1	1	yes	characteristic
209	C₂×C₄	#14556566	1	1	yes	characteristic
210	C₂×C₄	#14556580	1	1	yes	characteristic
211	C₂×C₄	#14556587	1	1	yes	characteristic
212	C₂×C₄	#14556618	1	4	yes	—
213	C₈	—	2	2	no	—
214	C₈	—	8	2	no	—
215	C₈	—	292	2	no	—
216	C₈	—	292	2	no	—
217	C₈	#14556507	1	4	yes	complemented
218	C₂²	—	2	1	no	—
219	C₂²	—	2	1	no	—
220	C₂²	—	584	4	no	—
221	C₂²	—	584	4	no	—
222	C₂²	—	584	4	no	—
223	C₂²	—	1168	8	no	—
224	C₂²	#17988488	1	1	yes	characteristic
225	C₂²	#17988698	1	2	yes	—
226	C₄	—	2	1	no	—
227	C₄	—	2	1	no	—
228	C₄	C₂×#14556507	1	2	yes	—
229	C₄	#17988841	1	2	yes	—
230	C₄	#17988858	1	2	yes	—
231	C₄	#17988973	1	2	yes	—
232	C₂	—	2	2	no	—
233	C₂	—	1168	4	no	—
234	C₂	#22610770	1	1	yes	characteristic
235	C₂	#22610805	1	1	yes	characteristic
236	C₂	#22610839	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#17988964

C₂

yes

maximal, characteristic

#22610770

C₂

yes

maximal, complemented

#22608600

C₂

yes

maximal, complemented

#22608220

C₂

yes

maximal, characteristic, complemented

C₇₃×#1566

C₂

yes

maximal, characteristic, complemented

C₂²×D₅₈₄

C₄

yes

—

C₂×#14556588

C₂²

yes

—

—

—

—

C₂²

yes

characteristic

C₂×#14556507

—

C₄×#11924012

C₂²

yes

—

—

—

#423×C₇₃

C₂²

yes

—

C₂×C₄×C₈×C₇₃

C₂²

yes

characteristic

#334×C₇₃

—

C₂²×D₂₉₂

—

C₂²×D₂₉₂

—

C₂²×D₂₉₂

C₂×C₄

yes

—

C₂×D₅₈₄

—

C₂×D₅₈₄

—

C₂×D₅₈₄

—

C₂×#11924012

D₄

yes

—

—

—

—

—

D₄

yes

—

—

—

—

—

—

C₂×M₁₆×C₇₃

—

C₂²×C₈×C₇₃

C₂×C₄

yes

—

C₂×C₄²×C₇₃

C₂³

yes

characteristic

C₄⋊C₈×C₇₃

—

C₄⋊C₈×C₇₃

—

C₄×C₈×C₇₃

D₄

yes

characteristic

C₄×C₈×C₇₃

D₄

yes

characteristic

C₄×C₈×C₇₃

D₄

yes

—

C₂³×D₇₃

—

C₂×D₂₉₂

—

C₂×D₂₉₂

—

C₂×D₂₉₂

—

C₂×D₂₉₂

—

C₂×D₂₉₂

—

C₂×D₂₉₂

—

C₂×D₂₉₂

—

C₂×D₂₉₂

—

C₂×D₂₉₂

—

C₂×D₂₉₂

—

D₅₈₄

—

D₅₈₄

—

#11924012

—

C₂×#10596831

—

C₂×#10596831

—

C₂²×C₄×C₇₃

C₂²×C₄

yes

characteristic

C₂²×C₄×C₇₃

C₂×D₄

yes

characteristic

C₂²×C₄×C₇₃

#41

yes

characteristic

M₁₆×C₇₃

—

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

C₂²⋊C₄

yes

—

C₂×C₈×C₇₃

C₂²⋊C₄

yes

—

C₄²×C₇₃

C₂×D₄

yes

characteristic

C₄²×C₇₃

C₂×D₄

yes

characteristic

C₄²×C₇₃

C₂×D₄

yes

characteristic

C₄²×C₇₃

#41

yes

characteristic

C₂³×C₇₃

C₄×D₄

yes

characteristic

C₂²×D₇₃

—

C₂²×D₇₃

—

C₂²×D₇₃

—

C₂²×D₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₇₃

C₄×D₄

yes

C₂×C₄×C₇₃

yes

C₂×C₄×C₇₃

yes

C₂×C₄×C₇₃

yes

C₂×C₄×C₇₃

yes

C₂×C₄×C₇₃

yes

—

D₂₉₂

—

D₂₉₂

—

D₂₉₂

—

D₂₉₂

—

D₂₉₂

—

D₂₉₂

—

D₂₉₂

—

C₈×C₇₃

—

C₈×C₇₃

—

C₈×C₇₃

yes

—

—

C₂²×C₇₃

—

100

C₂²×C₇₃

—

101

C₂²×C₇₃

#390

yes

characteristic

102

C₂²×C₇₃

#442

yes

—

103

C₂×D₇₃

—

104

C₂×D₇₃

—

105

C₂×D₇₃

—

106

C₂×D₇₃

—

107

C₄×C₇₃

—

108

C₄×C₇₃

—

109

C₄×C₇₃

C₂×#100

yes

—

110

C₄×C₇₃

#469

yes

—

111

C₄×C₇₃

#472

yes

—

112

C₄×C₇₃

#496

yes

—

113

#9811

—

maximal, Sylow

114

C₂×C₇₃

—

115

C₂×C₇₃

#1965

yes

characteristic

116

C₂×C₇₃

#1972

yes

characteristic

117

C₂×C₇₃

#1978

yes

characteristic

118

D₇₃

—

119

C₂×#493

—

120

#1965

—

121

#1566

D₇₃

yes

characteristic, complemented

122

#1545

—

123

#1451

—

124

C₇₃

#9811

yes

characteristic, complemented, Sylow

125

C₂²×D₈

—

126

C₂×#127

—

127

#493

—

146

—

128

#493

—

146

—

129

#493

—

146

—

130

#431

—

131

#423

C₂×D₇₃

yes

—

132

C₂×#100

—

146

—

133

C₄×M₁₆

—

134

C₂×C₄×C₈

C₂×D₇₃

yes

characteristic

135

#334

—

136

#331

—

146

—

137

#322

—

146

—

138

#322

—

146

—

139

C₂²×D₄

—

140

C₂²×D₄

—

146

—

141

C₂²×D₄

—

146

—

142

C₂×D₈

—

292

—

143

C₂×D₈

—

146

—

144

C₂×D₈

—

146

—

145

C₂×M₁₆

—

146

C₂×M₁₆

—

147

C₂²×C₈

C₄×D₇₃

yes

—

148

#127

—

146

—

149

#127

—

146

—

150

#127

—

146

—

151

#127

—

146

—

152

C₂×C₄²

C₂²×D₇₃

yes

characteristic

153

C₄⋊C₈

—

154

C₄⋊C₈

—

155

C₄⋊C₈

—

156

#100

—

292

—

157

C₂²⋊C₈

—

146

—

158

#97

—

146

—

159

C₄×C₈

—

146

—

160

C₄×C₈

—

146

—

161

C₄×C₈

D₂₉₂

yes

characteristic

162

C₄×C₈

D₂₉₂

yes

characteristic

163

C₄×C₈

C₂²⋊D₇₃

yes

—

164

C₂⁴

—

146

—

165

C₂×D₄

—

292

—

166

C₂×D₄

—

292

—

167

C₂×D₄

—

292

—

168

C₂×D₄

—

292

—

169

C₂×D₄

—

292

—

170

C₂×D₄

—

292

—

171

C₂×D₄

—

292

—

172

C₂×D₄

—

584

—

173

C₂×D₄

—

146

—

174

C₂×D₄

—

146

—

175

C₂²×C₄

C₂×C₄×D₇₃

yes

characteristic

176

C₂²×C₄

D₄×D₇₃

yes

characteristic

177

C₂²×C₄

#11924029

yes

characteristic

178

D₈

—

292

—

179

D₈

—

292

—

180

M₁₆

—

181

M₁₆

—

146

—

182

C₂×C₈

—

183

C₂×C₈

—

184

C₂×C₈

—

146

—

185

C₂×C₈

—

146

—

186

C₂×C₈

#11924005

yes

—

187

C₂×C₈

#11924005

yes

—

188

C₄²

D₄×D₇₃

yes

characteristic

189

C₄²

C₂×C₂²⋊D₇₃

yes

characteristic

190

C₄²

C₂×D₂₉₂

yes

characteristic

191

C₄²

#11924029

yes

characteristic

192

C₂³

—

292

—

193

C₂³

—

292

—

194

C₂³

—

584

—

195

C₂³

—

584

—

196

C₂³

#14556553

yes

characteristic

197

D₄

—

292

—

198

D₄

—

584

—

199

D₄

—

584

—

200

D₄

—

584

—

201

D₄

—

584

—

202

D₄

—

584

—

203

D₄

—

584

—

204

C₂×C₄

—

205

C₂×C₄

—

206

C₂×C₄

C₂×#11924005

yes

characteristic

207

C₂×C₄

#14556553

yes

characteristic

208

C₂×C₄

#14556566

yes

characteristic

209

C₂×C₄

#14556566

yes

characteristic

210

C₂×C₄

#14556580

yes

characteristic

211

C₂×C₄

#14556587

yes

characteristic

212

C₂×C₄

#14556618

yes

—

213

C₈

—

214

C₈

—

215

C₈

—

292

—

216

C₈

—

292

—

217

C₈

#14556507

yes

complemented

218

C₂²

—

219

C₂²

—

220

C₂²

—

584

—

221

C₂²

—

584

—

222

C₂²

—

584

—

223

C₂²

—

1168

—

224

C₂²

#17988488

yes

characteristic

225

C₂²

#17988698

yes

—

226

C₄

—

227

C₄

—

228

C₄

C₂×#14556507

yes

—

229

C₄

#17988841

yes

—

230

C₄

#17988858

yes

—

231

C₄

#17988973

yes

—

232

C₂

—

233

C₂

—

1168

—

234

C₂

#22610770

yes

characteristic

235

C₂

#22610805

yes

characteristic

236

C₂

#22610839

yes

characteristic

	subgroup	G/H
center	C₂²	#17988488
commutator	C₂²×C₄×C₇₃	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₇₃
Fitting	C₇₃×#1566	C₂
socle	C₂²×C₇₃	#390
prime radical	C₂×#17988964	C₂
cosocle	C₂×C₄²×C₇₃	C₂³
hypercenter	#1566	D₇₃
hypocenter	C₇₃	#9811
LCS	G ▷ C₂²×C₄×C₇₃ ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1566

subgroup

G/H

center

C₂²

#17988488

commutator

C₂²×C₄×C₇₃

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₇₃

Fitting

C₇₃×#1566

C₂

C₂²×C₇₃

C₂

C₂×C₄²×C₇₃

C₂³

D₇₃

C₇₃

G ▷ C₂²×C₄×C₇₃ ▷ C₂²×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1566

N	H ≅ G/N	type
2. #22610770	C₂	semidirect
3. #22608600	C₂	semidirect
4. #22608220	C₂	semidirect
5. C₇₃×#1566	C₂	semidirect
96. C₈×C₇₃	#100	semidirect
121. #1566	D₇₃	semidirect
124. C₇₃	#9811	semidirect
217. C₈	#14556507	semidirect

H ≅ G/N

type

2. #22610770

C₂

semidirect

3. #22608600

C₂

semidirect

4. #22608220

C₂

semidirect

5. C₇₃×#1566

C₂

semidirect

96. C₈×C₇₃

#100

semidirect

121. #1566

D₇₃

semidirect

124. C₇₃

#9811

semidirect

217. C₈

#14556507

semidirect

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

subgroup	index
C₂×#17988964	2
#22610770	2
#22608600	2
#22608220	2
C₇₃×#1566	2
#9811	73

subgroup

index

C₇₃×#1566

Subgroups — #32985671

Conjugacy classes of subgroups

Complements

Maximal subgroups