Group #25008196 — subgroups

Subgroups — #25008196

Order 11008.

262 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 115 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	#19136393	C₂	1	2	yes	maximal
2	C₈²×D₄₃	C₂	1	1	yes	maximal, characteristic
3	#19132665	C₂	1	1	yes	maximal, characteristic, complemented
4	#19132658	C₂	1	2	yes	maximal, complemented
5	C₄₃×#1370	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄×C₈×D₄₃	C₄	1	1	yes	characteristic
7	C₄×C₈×D₄₃	C₄	1	1	yes	characteristic
8	C₄×C₈×D₄₃	C₂²	1	1	yes	characteristic
9	C₄⋊(C₄₃⋊C₁₆)	C₂²	1	2	yes	—
10	(C₂×D₄₃)⋊C₁₆	—	2	2	no	—
11	C₁₆×Dic₄₃	—	2	2	no	—
12	C₈×C₄₃⋊C₈	C₄	1	1	yes	characteristic
13	C₈×C₄₃⋊C₈	C₄	1	1	yes	characteristic
14	C₈×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
15	C₄₃×C₄⋊C₁₆	C₂²	1	2	yes	—
16	C₈²×C₄₃	C₂²	1	1	yes	characteristic
17	C₂×C₈×D₄₃	—	2	1	no	—
18	C₂×C₈×D₄₃	C₈	1	1	yes	characteristic
19	C₂×C₈×D₄₃	C₈	1	1	yes	characteristic
20	C₂×C₈×D₄₃	D₄	1	1	yes	characteristic
21	C₂×C₈×D₄₃	Q₈	1	1	yes	characteristic
22	C₄²×D₄₃	C₂×C₄	1	1	yes	characteristic
23	C₂×C₄₃⋊C₁₆	—	2	2	no	—
24	C₄×C₄₃⋊C₈	C₂×C₄	1	1	yes	characteristic
25	C₄×C₄₃⋊C₈	C₂×C₄	1	1	yes	characteristic
26	C₄×C₄₃⋊C₈	C₂×C₄	1	1	yes	characteristic
27	C₈×Dic₄₃	—	2	1	no	—
28	C₈×Dic₄₃	C₈	1	1	yes	characteristic
29	C₈×Dic₄₃	C₈	1	1	yes	characteristic
30	C₈×Dic₄₃	D₄	1	1	yes	characteristic
31	C₈×Dic₄₃	Q₈	1	1	yes	characteristic
32	C₂×C₁₆×C₄₃	—	2	2	no	—
33	C₄×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
34	C₄×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
35	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
36	C₂×C₄×D₄₃	C₄⋊C₄	1	1	yes	characteristic
37	C₂×C₄×D₄₃	C₂×C₈	1	1	yes	characteristic
38	C₂×C₄×D₄₃	M₁₆	1	1	yes	characteristic
39	C₂×C₈×C₄₃	—	2	1	no	—
40	C₂×C₈×C₄₃	C₂×C₈	1	1	yes	characteristic
41	C₂×C₈×C₄₃	C₂×C₈	1	1	yes	characteristic
42	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
43	C₂×C₈×C₄₃	C₂×Q₈	1	1	yes	characteristic
44	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
45	C₄×Dic₄₃	C₄⋊C₄	1	1	yes	characteristic
46	C₄×Dic₄₃	C₂×C₈	1	1	yes	characteristic
47	C₄×Dic₄₃	M₁₆	1	1	yes	characteristic
48	C₂×C₄₃⋊C₈	—	2	1	no	—
49	C₂×C₄₃⋊C₈	C₄⋊C₄	1	1	yes	characteristic
50	C₂×C₄₃⋊C₈	C₄⋊C₄	1	1	yes	characteristic
51	C₂×C₄₃⋊C₈	C₂×C₈	1	1	yes	characteristic
52	C₂×C₄₃⋊C₈	C₂×C₈	1	1	yes	characteristic
53	C₈×D₄₃	—	2	4	no	—
54	C₈×D₄₃	—	2	2	no	—
55	C₈×D₄₃	—	2	1	no	—
56	C₈×D₄₃	—	2	1	no	—
57	C₈×D₄₃	—	2	2	no	—
58	C₈×D₄₃	C₁₆	1	4	yes	complemented
59	C₁₆×C₄₃	—	4	2	no	—
60	C₄₃⋊C₁₆	—	4	2	no	—
61	C₂²×D₄₃	C₄⋊C₈	1	1	yes	characteristic
62	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
63	C₂×C₄×C₄₃	C₂²×C₈	1	1	yes	characteristic
64	C₂×C₄×C₄₃	C₂×M₁₆	1	1	yes	characteristic
65	C₂×Dic₄₃	C₄⋊C₈	1	1	yes	characteristic
66	C₂×Dic₄₃	C₄⋊C₈	1	1	yes	characteristic
67	C₂×Dic₄₃	C₄⋊C₈	1	1	yes	characteristic
68	C₄×D₄₃	—	2	1	no	—
69	C₄×D₄₃	—	2	1	no	—
70	C₄×D₄₃	—	2	2	no	—
71	C₄×D₄₃	C₂×C₁₆	1	2	yes	—
72	C₄×D₄₃	M₃₂	1	2	yes	—
73	C₈×C₄₃	—	2	2	no	—
74	C₈×C₄₃	—	2	1	no	—
75	C₈×C₄₃	—	2	1	no	—
76	C₈×C₄₃	C₂×C₁₆	1	2	yes	—
77	C₈×C₄₃	#135	1	1	yes	characteristic
78	C₈×C₄₃	#135	1	1	yes	characteristic
79	C₄₃⋊C₈	—	2	2	no	—
80	C₄₃⋊C₈	—	2	1	no	—
81	C₄₃⋊C₈	—	2	1	no	—
82	C₄₃⋊C₈	#108	1	2	yes	—
83	C₄₃⋊C₈	C₂×C₁₆	1	2	yes	—
84	#12012	—	43	1	no	maximal, Sylow
85	C₂²×C₄₃	C₂×C₄⋊C₈	1	1	yes	characteristic
86	C₂×D₄₃	—	2	1	no	—
87	C₂×D₄₃	—	2	1	no	—
88	C₂×D₄₃	C₄⋊C₁₆	1	2	yes	—
89	C₄×C₄₃	—	2	1	no	—
90	C₄×C₄₃	#427	1	1	yes	characteristic
91	C₄×C₄₃	C₂×#108	1	1	yes	characteristic
92	C₄×C₄₃	C₂²×C₁₆	1	1	yes	characteristic
93	C₄×C₄₃	C₂×M₃₂	1	1	yes	characteristic
94	Dic₄₃	—	2	1	no	—
95	Dic₄₃	C₄⋊C₁₆	1	2	yes	—
96	Dic₄₃	#364	1	2	yes	—
97	#2162	—	43	2	no	—
98	C₂×C₈²	—	43	1	no	—
99	#1370	—	43	1	no	—
100	#1370	D₄₃	1	1	yes	characteristic, complemented
101	#1367	—	43	2	no	—
102	C₂×C₄₃	#1564	1	1	yes	characteristic
103	C₂×C₄₃	C₂×C₄⋊C₁₆	1	1	yes	characteristic
104	C₂×C₄₃	C₂×#364	1	1	yes	characteristic
105	D₄₃	—	2	2	no	—
106	C₂×C₄×C₈	—	43	1	no	—
107	C₂×C₄×C₈	—	43	1	no	—
108	C₂×C₄×C₈	—	43	1	no	—
109	C₄⋊C₁₆	—	43	2	no	—
110	C₄⋊C₁₆	C₂×D₄₃	1	2	yes	—
111	C₂²⋊C₁₆	—	86	2	no	—
112	C₄×C₁₆	—	86	2	no	—
113	C₈²	—	43	1	no	—
114	C₈²	—	43	1	no	—
115	C₈²	—	43	1	no	—
116	C₈²	C₂×D₄₃	1	1	yes	characteristic
117	C₄₃	#12012	1	1	yes	characteristic, complemented, Sylow
118	C₂²×C₈	—	43	1	no	—
119	C₂²×C₈	—	43	1	no	—
120	C₂²×C₈	—	43	1	no	—
121	C₂²×C₈	—	43	1	no	—
122	C₂²×C₈	—	86	1	no	—
123	C₂×C₄²	—	43	1	no	—
124	C₂×C₁₆	—	2	2	no	—
125	C₂×C₁₆	—	86	2	no	—
126	C₄×C₈	—	43	1	no	—
127	C₄×C₈	—	43	1	no	—
128	C₄×C₈	—	43	1	no	—
129	C₄×C₈	—	43	1	no	—
130	C₄×C₈	—	43	1	no	—
131	C₄×C₈	—	43	1	no	—
132	C₄×C₈	—	43	1	no	—
133	C₄×C₈	—	86	1	no	—
134	C₄×C₈	C₄×D₄₃	1	1	yes	characteristic
135	C₄×C₈	C₄×D₄₃	1	1	yes	characteristic
136	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
137	C₂²×C₄	—	43	1	no	—
138	C₂²×C₄	—	43	1	no	—
139	C₂²×C₄	—	43	1	no	—
140	C₂×C₈	—	2	1	no	—
141	C₂×C₈	—	43	1	no	—
142	C₂×C₈	—	43	1	no	—
143	C₂×C₈	—	43	4	no	—
144	C₂×C₈	—	43	1	no	—
145	C₂×C₈	—	43	1	no	—
146	C₂×C₈	—	86	2	no	—
147	C₂×C₈	—	86	2	no	—
148	C₂×C₈	—	86	4	no	—
149	C₂×C₈	—	86	1	no	—
150	C₂×C₈	—	86	1	no	—
151	C₂×C₈	—	86	1	no	—
152	C₂×C₈	C₈×D₄₃	1	1	yes	characteristic
153	C₂×C₈	C₈×D₄₃	1	1	yes	characteristic
154	C₂×C₈	D₄×D₄₃	1	1	yes	characteristic
155	C₂×C₈	Q₈×D₄₃	1	1	yes	characteristic
156	C₄²	—	43	1	no	—
157	C₄²	—	43	1	no	—
158	C₄²	—	43	1	no	—
159	C₄²	C₂×C₄×D₄₃	1	1	yes	characteristic
160	C₁₆	—	4	2	no	—
161	C₁₆	—	172	2	no	—
162	C₂³	—	43	1	no	—
163	C₂×C₄	—	43	1	no	—
164	C₂×C₄	—	43	1	no	—
165	C₂×C₄	—	43	2	no	—
166	C₂×C₄	—	43	2	no	—
167	C₂×C₄	—	43	1	no	—
168	C₂×C₄	—	86	2	no	—
169	C₂×C₄	—	86	1	no	—
170	C₂×C₄	—	86	1	no	—
171	C₂×C₄	C₄⋊C₄×D₄₃	1	1	yes	characteristic
172	C₂×C₄	C₂×C₈×D₄₃	1	1	yes	characteristic
173	C₂×C₄	M₁₆×D₄₃	1	1	yes	characteristic
174	C₈	—	2	2	no	—
175	C₈	—	2	1	no	—
176	C₈	—	2	1	no	—
177	C₈	—	43	2	no	—
178	C₈	—	43	2	no	—
179	C₈	—	86	2	no	—
180	C₈	—	86	1	no	—
181	C₈	—	86	1	no	—
182	C₈	C₁₆×D₄₃	1	2	yes	—
183	C₈	#13063344	1	1	yes	characteristic
184	C₈	#13063348	1	1	yes	characteristic
185	C₂²	—	43	2	no	—
186	C₂²	—	86	1	no	—
187	C₂²	—	86	1	no	—
188	C₂²	C₄⋊C₈×D₄₃	1	1	yes	characteristic
189	C₄	—	2	1	no	—
190	C₄	—	43	2	no	—
191	C₄	—	43	2	no	—
192	C₄	—	86	1	no	—
193	C₄	#14582936	1	1	yes	characteristic
194	C₄	#108×D₄₃	1	1	yes	characteristic
195	C₄	C₂×C₁₆×D₄₃	1	1	yes	characteristic
196	C₄	M₃₂×D₄₃	1	1	yes	characteristic
197	C₂	—	86	2	no	—
198	C₂	#19133342	1	1	yes	characteristic
199	C₂	C₄⋊C₁₆×D₄₃	1	1	yes	characteristic
200	C₂	#364×D₄₃	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#19136393

C₂

yes

maximal

C₈²×D₄₃

C₂

yes

maximal, characteristic

#19132665

C₂

yes

maximal, characteristic, complemented

#19132658

C₂

yes

maximal, complemented

C₄₃×#1370

C₂

yes

maximal, characteristic, complemented

C₄×C₈×D₄₃

C₄

yes

characteristic

C₄×C₈×D₄₃

C₄

yes

characteristic

C₄×C₈×D₄₃

C₂²

yes

characteristic

C₄⋊(C₄₃⋊C₁₆)

C₂²

yes

—

(C₂×D₄₃)⋊C₁₆

—

C₁₆×Dic₄₃

—

C₈×C₄₃⋊C₈

C₄

yes

characteristic

C₈×C₄₃⋊C₈

C₄

yes

characteristic

C₈×C₄₃⋊C₈

C₂²

yes

characteristic

C₄₃×C₄⋊C₁₆

C₂²

yes

—

C₈²×C₄₃

C₂²

yes

characteristic

C₂×C₈×D₄₃

—

C₂×C₈×D₄₃

C₈

yes

characteristic

C₂×C₈×D₄₃

C₈

yes

characteristic

C₂×C₈×D₄₃

D₄

yes

characteristic

C₂×C₈×D₄₃

Q₈

yes

characteristic

C₄²×D₄₃

C₂×C₄

yes

characteristic

C₂×C₄₃⋊C₁₆

—

C₄×C₄₃⋊C₈

C₂×C₄

yes

characteristic

C₄×C₄₃⋊C₈

C₂×C₄

yes

characteristic

C₄×C₄₃⋊C₈

C₂×C₄

yes

characteristic

C₈×Dic₄₃

—

C₈×Dic₄₃

C₈

yes

characteristic

C₈×Dic₄₃

C₈

yes

characteristic

C₈×Dic₄₃

D₄

yes

characteristic

C₈×Dic₄₃

Q₈

yes

characteristic

C₂×C₁₆×C₄₃

—

C₄×C₈×C₄₃

C₂×C₄

yes

characteristic

C₄×C₈×C₄₃

C₂×C₄

yes

characteristic

C₄×C₈×C₄₃

C₂³

yes

characteristic

C₂×C₄×D₄₃

C₄⋊C₄

yes

characteristic

C₂×C₄×D₄₃

C₂×C₈

yes

characteristic

C₂×C₄×D₄₃

M₁₆

yes

characteristic

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

C₂×C₈

yes

characteristic

C₂×C₈×C₄₃

C₂×C₈

yes

characteristic

C₂×C₈×C₄₃

C₂×D₄

yes

characteristic

C₂×C₈×C₄₃

C₂×Q₈

yes

characteristic

C₄²×C₄₃

C₂²×C₄

yes

characteristic

C₄×Dic₄₃

C₄⋊C₄

yes

characteristic

C₄×Dic₄₃

C₂×C₈

yes

characteristic

C₄×Dic₄₃

M₁₆

yes

characteristic

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

C₄⋊C₄

yes

characteristic

C₂×C₄₃⋊C₈

C₄⋊C₄

yes

characteristic

C₂×C₄₃⋊C₈

C₂×C₈

yes

characteristic

C₂×C₄₃⋊C₈

C₂×C₈

yes

characteristic

C₈×D₄₃

—

C₈×D₄₃

—

C₈×D₄₃

—

C₈×D₄₃

—

C₈×D₄₃

—

C₈×D₄₃

C₁₆

yes

complemented

C₁₆×C₄₃

—

C₄₃⋊C₁₆

—

C₂²×D₄₃

C₄⋊C₈

yes

characteristic

C₂×C₄×C₄₃

C₂×C₄⋊C₄

yes

characteristic

C₂×C₄×C₄₃

C₂²×C₈

yes

characteristic

C₂×C₄×C₄₃

C₂×M₁₆

yes

characteristic

C₂×Dic₄₃

C₄⋊C₈

yes

characteristic

C₂×Dic₄₃

C₄⋊C₈

yes

characteristic

C₂×Dic₄₃

C₄⋊C₈

yes

characteristic

C₄×D₄₃

—

C₄×D₄₃

—

C₄×D₄₃

—

C₄×D₄₃

C₂×C₁₆

yes

—

C₄×D₄₃

M₃₂

yes

—

C₈×C₄₃

—

C₈×C₄₃

—

C₈×C₄₃

—

C₈×C₄₃

C₂×C₁₆

yes

—

C₈×C₄₃

yes

C₈×C₄₃

yes

C₄₃⋊C₈

—

C₄₃⋊C₈

—

C₄₃⋊C₈

—

C₄₃⋊C₈

#108

yes

—

C₄₃⋊C₈

C₂×C₁₆

yes

—

#12012

—

maximal, Sylow

C₂²×C₄₃

C₂×C₄⋊C₈

yes

characteristic

C₂×D₄₃

—

C₂×D₄₃

—

C₂×D₄₃

C₄⋊C₁₆

yes

—

C₄×C₄₃

—

C₄×C₄₃

yes

C₄×C₄₃

yes

C₄×C₄₃

C₂²×C₁₆

yes

characteristic

C₄×C₄₃

C₂×M₃₂

yes

characteristic

Dic₄₃

—

Dic₄₃

C₄⋊C₁₆

yes

—

Dic₄₃

#364

yes

—

#2162

—

C₂×C₈²

—

#1370

—

100

#1370

D₄₃

yes

characteristic, complemented

101

#1367

—

102

C₂×C₄₃

#1564

yes

characteristic

103

C₂×C₄₃

C₂×C₄⋊C₁₆

yes

characteristic

104

C₂×C₄₃

C₂×#364

yes

characteristic

105

D₄₃

—

106

C₂×C₄×C₈

—

107

C₂×C₄×C₈

—

108

C₂×C₄×C₈

—

109

C₄⋊C₁₆

—

110

C₄⋊C₁₆

C₂×D₄₃

yes

—

111

C₂²⋊C₁₆

—

112

C₄×C₁₆

—

113

C₈²

—

114

C₈²

—

115

C₈²

—

116

C₈²

C₂×D₄₃

yes

characteristic

117

C₄₃

#12012

yes

characteristic, complemented, Sylow

118

C₂²×C₈

—

119

C₂²×C₈

—

120

C₂²×C₈

—

121

C₂²×C₈

—

122

C₂²×C₈

—

123

C₂×C₄²

—

124

C₂×C₁₆

—

125

C₂×C₁₆

—

126

C₄×C₈

—

127

C₄×C₈

—

128

C₄×C₈

—

129

C₄×C₈

—

130

C₄×C₈

—

131

C₄×C₈

—

132

C₄×C₈

—

133

C₄×C₈

—

134

C₄×C₈

C₄×D₄₃

yes

characteristic

135

C₄×C₈

C₄×D₄₃

yes

characteristic

136

C₄×C₈

C₂²×D₄₃

yes

characteristic

137

C₂²×C₄

—

138

C₂²×C₄

—

139

C₂²×C₄

—

140

C₂×C₈

—

141

C₂×C₈

—

142

C₂×C₈

—

143

C₂×C₈

—

144

C₂×C₈

—

145

C₂×C₈

—

146

C₂×C₈

—

147

C₂×C₈

—

148

C₂×C₈

—

149

C₂×C₈

—

150

C₂×C₈

—

151

C₂×C₈

—

152

C₂×C₈

C₈×D₄₃

yes

characteristic

153

C₂×C₈

C₈×D₄₃

yes

characteristic

154

C₂×C₈

D₄×D₄₃

yes

characteristic

155

C₂×C₈

Q₈×D₄₃

yes

characteristic

156

C₄²

—

157

C₄²

—

158

C₄²

—

159

C₄²

C₂×C₄×D₄₃

yes

characteristic

160

C₁₆

—

161

C₁₆

—

172

—

162

C₂³

—

163

C₂×C₄

—

164

C₂×C₄

—

165

C₂×C₄

—

166

C₂×C₄

—

167

C₂×C₄

—

168

C₂×C₄

—

169

C₂×C₄

—

170

C₂×C₄

—

171

C₂×C₄

C₄⋊C₄×D₄₃

yes

characteristic

172

C₂×C₄

C₂×C₈×D₄₃

yes

characteristic

173

C₂×C₄

M₁₆×D₄₃

yes

characteristic

174

C₈

—

175

C₈

—

176

C₈

—

177

C₈

—

178

C₈

—

179

C₈

—

180

C₈

—

181

C₈

—

182

C₈

C₁₆×D₄₃

yes

—

183

C₈

#13063344

yes

characteristic

184

C₈

#13063348

yes

characteristic

185

C₂²

—

186

C₂²

—

187

C₂²

—

188

C₂²

C₄⋊C₈×D₄₃

yes

characteristic

189

C₄

—

190

C₄

—

191

C₄

—

192

C₄

—

193

C₄

#14582936

yes

characteristic

194

C₄

#108×D₄₃

yes

characteristic

195

C₄

C₂×C₁₆×D₄₃

yes

characteristic

196

C₄

M₃₂×D₄₃

yes

characteristic

197

C₂

—

198

C₂

#19133342

yes

characteristic

199

C₂

C₄⋊C₁₆×D₄₃

yes

characteristic

200

C₂

#364×D₄₃

yes

characteristic

	subgroup	G/H
center	C₂×C₈	D₄×D₄₃
commutator	C₄×C₄₃	C₂²×C₁₆
Frattini	C₄×C₈	C₂²×D₄₃
Fitting	C₄₃×#1370	C₂
socle	C₂²×C₄₃	C₂×C₄⋊C₈
prime radical	C₂²×D₄₃	C₄⋊C₈
cosocle	C₄×C₈×C₄₃	C₂³
hypercenter	#1370	D₄₃
hypocenter	C₄₃	#12012
LCS	G ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₈ ◁ C₄×C₈ ◁ #1370

subgroup

G/H

center

C₂×C₈

D₄×D₄₃

commutator

C₄×C₄₃

C₂²×C₁₆

Frattini

C₄×C₈

C₂²×D₄₃

Fitting

C₄₃×#1370

C₂

socle

C₂²×C₄₃

C₂×C₄⋊C₈

prime radical

C₂²×D₄₃

C₄⋊C₈

cosocle

C₄×C₈×C₄₃

C₂³

D₄₃

C₄₃

G ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂×C₈ ◁ C₄×C₈ ◁ #1370

N	H ≅ G/N	type
3. #19132665	C₂	semidirect
4. #19132658	C₂	semidirect
5. C₄₃×#1370	C₂	semidirect
58. C₈×D₄₃	C₁₆	semidirect
100. #1370	D₄₃	semidirect
117. C₄₃	#12012	semidirect

H ≅ G/N

type

3. #19132665

C₂

semidirect

4. #19132658

C₂

semidirect

5. C₄₃×#1370

C₂

semidirect

58. C₈×D₄₃

C₁₆

semidirect

100. #1370

D₄₃

semidirect

117. C₄₃

#12012

semidirect

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

subgroup	index
#19136393	2
C₈²×D₄₃	2
#19132665	2
#19132658	2
C₄₃×#1370	2
#12012	43

subgroup

index

C₈²×D₄₃

C₄₃×#1370

Subgroups — #25008196

Conjugacy classes of subgroups

Complements

Maximal subgroups