Group #20254107 — subgroups

Subgroups — #20254107

Order 6016.

402 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 402 conjugacy classes of subgroups — too many to draw. Only its 129 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	#15689673	C₂	1	1	yes	maximal, characteristic
2	#15689526	C₂	1	1	yes	maximal, characteristic, complemented
3	#15689497	C₂	1	1	yes	maximal, characteristic, complemented
4	#15689473	C₂	1	1	yes	maximal, characteristic, complemented
5	#15689471	C₂	1	1	yes	maximal, characteristic, complemented
6	#15689371	C₂	1	4	yes	maximal, complemented
7	#15689221	C₂	1	4	yes	maximal, complemented
8	C₄×#10625329	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₇×#533	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#10625350	—	2	1	no	—
11	C₂×#10625336	C₂²	1	4	yes	—
12	C₂×#10625329	C₂²	1	2	yes	—
13	#13094024	C₂²	1	1	yes	characteristic
14	#13094021	C₂²	1	1	yes	characteristic
15	#13094012	—	2	1	no	—
16	#13093998	—	2	1	no	—
17	#13093998	C₂²	1	2	yes	—
18	C₄×D₁₈₈	—	2	1	no	—
19	C₄×D₁₈₈	C₂²	1	2	yes	—
20	#13093957	C₂²	1	4	yes	—
21	#13093948	C₂²	1	4	yes	—
22	#13093944	C₂²	1	4	yes	—
23	#13093935	C₂²	1	2	yes	—
24	C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
25	C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
26	C₄⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
27	C₄⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
28	#125×C₄₇	—	2	1	no	—
29	C₂²⋊Q₈×C₄₇	—	2	1	no	—
30	C₂²⋊Q₈×C₄₇	C₂²	1	2	yes	—
31	C₄×Q₈×C₄₇	—	2	1	no	—
32	C₄×Q₈×C₄₇	C₂²	1	2	yes	—
33	#117×C₄₇	—	2	1	no	—
34	C₂×C₄²×C₄₇	C₂²	1	1	yes	characteristic
35	C₂×Q₈×C₄₇	—	2	1	no	—
36	C₂×Q₈×C₄₇	C₂³	1	2	yes	—
37	C₂²×C₄×C₄₇	D₄	1	1	yes	characteristic
38	C₂²×C₄×C₄₇	D₄	1	1	yes	characteristic
39	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
40	C₂×C₂²⋊D₄₇	—	2	2	no	—
41	#10625350	—	4	4	no	—
42	C₂×D₁₈₈	—	2	1	no	—
43	C₂×D₁₈₈	—	2	1	no	—
44	C₂×D₁₈₈	C₂³	1	2	yes	—
45	C₂×C₄×D₄₇	—	2	2	no	—
46	C₂×Dic₉₄	—	2	1	no	—
47	C₄⋊C₄×C₄₇	—	2	1	no	—
48	C₄⋊C₄×C₄₇	—	2	1	no	—
49	C₄⋊C₄×C₄₇	—	2	1	no	—
50	C₄⋊C₄×C₄₇	—	2	2	no	—
51	C₄⋊C₄×C₄₇	—	2	2	no	—
52	C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
53	C₂²⋊C₄×C₄₇	—	2	2	no	—
54	C₄²×C₄₇	—	2	2	no	—
55	C₄²×C₄₇	D₄	1	1	yes	characteristic
56	C₄²×C₄₇	D₄	1	1	yes	characteristic
57	C₄²×C₄₇	C₂³	1	1	yes	characteristic
58	C₄²×C₄₇	C₂³	1	1	yes	characteristic
59	#10625336	—	2	8	no	—
60	(C₂×D₄₇)⋊C₄	—	2	2	no	—
61	(C₂×D₄₇)⋊C₄	—	2	2	no	—
62	C₄⋊Dic₄₇	—	2	1	no	—
63	C₄⋊Dic₄₇	C₂³	1	2	yes	—
64	#10625329	—	2	4	no	—
65	C₂×C₄₇⋊C₈	C₂³	1	2	yes	—
66	C₂×C₄₇⋊C₈	C₂³	1	2	yes	—
67	C₂³×C₄₇	C₂×D₄	1	1	yes	characteristic
68	C₂²×D₄₇	—	2	2	no	—
69	Q₈×C₄₇	—	2	4	no	—
70	Q₈×C₄₇	—	4	2	no	—
71	C₂×C₄×C₄₇	—	2	2	no	—
72	C₂×C₄×C₄₇	—	2	2	no	—
73	C₂×C₄×C₄₇	—	2	2	no	—
74	C₂×C₄×C₄₇	—	2	2	no	—
75	C₂×C₄×C₄₇	—	2	2	no	—
76	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
77	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
78	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
79	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
80	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
81	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
82	C₂²⋊D₄₇	—	4	4	no	—
83	C₂×Dic₄₇	—	2	2	no	—
84	D₁₈₈	—	2	4	no	—
85	D₁₈₈	—	4	2	no	—
86	D₁₈₈	—	4	2	no	—
87	C₄×D₄₇	—	4	4	no	—
88	Dic₉₄	—	4	2	no	—
89	C₄₇⋊C₈	—	2	2	no	—
90	C₄₇⋊C₈	#41	1	4	yes	complemented
91	C₂²×C₄₇	—	2	1	no	—
92	C₂²×C₄₇	—	2	1	no	—
93	C₂²×C₄₇	—	2	1	no	—
94	C₂²×C₄₇	C₂²×D₄	1	1	yes	characteristic
95	C₂×D₄₇	—	4	2	no	—
96	C₂×D₄₇	—	4	2	no	—
97	C₂×D₄₇	—	4	2	no	—
98	C₄×C₄₇	—	2	1	no	—
99	C₄×C₄₇	—	2	1	no	—
100	C₄×C₄₇	—	2	1	no	—
101	C₄×C₄₇	—	4	2	no	—
102	C₄×C₄₇	—	4	2	no	—
103	C₄×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
104	C₄×C₄₇	#137	1	2	yes	—
105	C₄×C₄₇	C₂×#41	1	2	yes	—
106	Dic₄₇	—	4	2	no	—
107	#3182	—	47	1	no	maximal, Sylow
108	C₂×C₄₇	—	4	1	no	—
109	C₂×C₄₇	#532	1	1	yes	characteristic
110	C₂×C₄₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
111	C₂×C₄₇	C₂×#137	1	1	yes	characteristic
112	D₄₇	—	8	2	no	—
113	#533	D₄₇	1	1	yes	characteristic, complemented
114	#532	—	47	1	no	—
115	#500	—	47	1	no	—
116	#492	—	47	1	no	—
117	#487	—	47	1	no	—
118	#486	—	47	1	no	—
119	#468	—	47	4	no	—
120	#440	—	47	4	no	—
121	C₄×M₁₆	—	47	1	no	—
122	C₄₇	#3182	1	1	yes	characteristic, complemented, Sylow
123	C₂×#41	—	94	1	no	—
124	C₂×SD₁₆	—	47	4	no	—
125	C₂×M₁₆	—	47	2	no	—
126	C₄⋊Q₈	—	47	1	no	—
127	C₄⋊Q₈	C₂×D₄₇	1	1	yes	characteristic
128	C₄⋊Q₈	C₂×D₄₇	1	1	yes	characteristic
129	#127	—	47	1	no	—
130	#125	—	2	1	no	—
131	#124	—	94	1	no	—
132	C₂²⋊Q₈	—	2	1	no	—
133	C₂²⋊Q₈	C₂×D₄₇	1	2	yes	—
134	#121	—	47	2	no	—
135	#121	—	94	1	no	—
136	C₄×Q₈	—	2	1	no	—
137	C₄×Q₈	C₂×D₄₇	1	2	yes	—
138	C₄×D₄	—	47	2	no	—
139	C₄×D₄	—	94	1	no	—
140	#117	—	2	1	no	—
141	C₂×C₄²	C₂×D₄₇	1	1	yes	characteristic
142	#107	—	47	4	no	—
143	#103	—	47	4	no	—
144	#102	—	47	4	no	—
145	#97	—	47	2	no	—
146	C₄×C₈	—	47	1	no	—
147	C₄×C₈	—	47	1	no	—
148	#41	—	188	4	no	—
149	C₂×Q₈	—	2	1	no	—
150	C₂×Q₈	—	94	1	no	—
151	C₂×Q₈	C₂²×D₄₇	1	2	yes	—
152	C₂×D₄	—	47	2	no	—
153	C₂×D₄	—	94	2	no	—
154	C₂×D₄	—	94	1	no	—
155	C₂×D₄	—	94	1	no	—
156	C₂²×C₄	—	94	2	no	—
157	C₂²×C₄	C₂²⋊D₄₇	1	1	yes	characteristic
158	C₂²×C₄	C₂²⋊D₄₇	1	1	yes	characteristic
159	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
160	SD₁₆	—	94	8	no	—
161	M₁₆	—	94	4	no	—
162	C₂×C₈	—	47	2	no	—
163	C₂×C₈	—	47	2	no	—
164	C₄⋊C₄	—	2	1	no	—
165	C₄⋊C₄	—	2	1	no	—
166	C₄⋊C₄	—	2	1	no	—
167	C₄⋊C₄	—	2	2	no	—
168	C₄⋊C₄	—	2	2	no	—
169	C₄⋊C₄	—	47	2	no	—
170	C₄⋊C₄	—	94	1	no	—
171	C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
172	C₂²⋊C₄	—	2	2	no	—
173	C₂²⋊C₄	—	94	2	no	—
174	C₂²⋊C₄	—	94	2	no	—
175	C₄²	—	2	2	no	—
176	C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
177	C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
178	C₄²	C₂²×D₄₇	1	1	yes	characteristic
179	C₄²	C₂²×D₄₇	1	1	yes	characteristic
180	C₂³	—	94	2	no	—
181	C₂³	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
182	Q₈	—	2	4	no	—
183	Q₈	—	4	2	no	—
184	Q₈	—	188	2	no	—
185	D₄	—	94	4	no	—
186	D₄	—	188	4	no	—
187	D₄	—	188	2	no	—
188	D₄	—	188	2	no	—
189	C₂×C₄	—	2	2	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	—	94	2	no	—
195	C₂×C₄	—	188	4	no	—
196	C₂×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
197	C₂×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
198	C₂×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
199	C₂×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
200	C₂×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
201	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
202	C₈	—	47	4	no	—
203	C₈	—	94	2	no	—
204	C₂²	—	2	1	no	—
205	C₂²	—	2	1	no	—
206	C₂²	—	2	1	no	—
207	C₂²	—	188	2	no	—
208	C₂²	—	188	2	no	—
209	C₂²	—	188	2	no	—
210	C₂²	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
211	C₄	—	2	1	no	—
212	C₄	—	2	1	no	—
213	C₄	—	2	1	no	—
214	C₄	—	4	2	no	—
215	C₄	—	4	2	no	—
216	C₄	—	188	2	no	—
217	C₄	#13094049	1	2	yes	—
218	C₄	#13094055	1	2	yes	—
219	C₄	#41×D₄₇	1	2	yes	—
220	C₂	—	4	1	no	—
221	C₂	—	376	2	no	—
222	C₂	#15689669	1	1	yes	characteristic
223	C₂	C₂×#13094049	1	1	yes	characteristic
224	C₂	C₂×#13094055	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#15689673

C₂

yes

maximal, characteristic

#15689526

C₂

yes

maximal, characteristic, complemented

#15689497

C₂

yes

maximal, characteristic, complemented

#15689473

C₂

yes

maximal, characteristic, complemented

#15689471

C₂

yes

maximal, characteristic, complemented

#15689371

C₂

yes

maximal, complemented

#15689221

C₂

yes

maximal, complemented

C₄×#10625329

C₂

yes

maximal, characteristic, complemented

C₄₇×#533

C₂

yes

maximal, characteristic, complemented

C₂×#10625350

—

C₂×#10625336

C₂²

yes

—

C₂×#10625329

C₂²

yes

—

#13094024

C₂²

yes

characteristic

#13094021

C₂²

yes

—

—

C₂²

yes

—

C₄×D₁₈₈

—

C₄×D₁₈₈

C₂²

yes

—

#13093957

C₂²

yes

—

#13093948

C₂²

yes

—

#13093944

C₂²

yes

—

#13093935

C₂²

yes

—

C₄×C₄₇⋊C₈

C₂²

yes

characteristic

C₄×C₄₇⋊C₈

C₂²

yes

characteristic

C₄⋊Q₈×C₄₇

C₂²

yes

characteristic

C₄⋊Q₈×C₄₇

C₂²

yes

characteristic

#125×C₄₇

—

C₂²⋊Q₈×C₄₇

—

C₂²⋊Q₈×C₄₇

C₂²

yes

—

C₄×Q₈×C₄₇

—

C₄×Q₈×C₄₇

C₂²

yes

—

#117×C₄₇

—

C₂×C₄²×C₄₇

C₂²

yes

characteristic

C₂×Q₈×C₄₇

—

C₂×Q₈×C₄₇

C₂³

yes

—

C₂²×C₄×C₄₇

D₄

yes

characteristic

C₂²×C₄×C₄₇

D₄

yes

characteristic

C₂²×C₄×C₄₇

C₂³

yes

characteristic

C₂×C₂²⋊D₄₇

—

#10625350

—

C₂×D₁₈₈

—

C₂×D₁₈₈

—

C₂×D₁₈₈

C₂³

yes

—

C₂×C₄×D₄₇

—

C₂×Dic₉₄

—

C₄⋊C₄×C₄₇

—

C₄⋊C₄×C₄₇

—

C₄⋊C₄×C₄₇

—

C₄⋊C₄×C₄₇

—

C₄⋊C₄×C₄₇

—

C₄⋊C₄×C₄₇

C₂³

yes

—

C₂²⋊C₄×C₄₇

—

C₄²×C₄₇

—

C₄²×C₄₇

D₄

yes

characteristic

C₄²×C₄₇

D₄

yes

characteristic

C₄²×C₄₇

C₂³

yes

characteristic

C₄²×C₄₇

C₂³

yes

characteristic

#10625336

—

(C₂×D₄₇)⋊C₄

—

(C₂×D₄₇)⋊C₄

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

C₂³

yes

—

#10625329

—

C₂×C₄₇⋊C₈

C₂³

yes

—

C₂×C₄₇⋊C₈

C₂³

yes

—

C₂³×C₄₇

C₂×D₄

yes

characteristic

C₂²×D₄₇

—

Q₈×C₄₇

—

Q₈×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂×C₄×C₄₇

C₂⁴

yes

characteristic

C₂²⋊D₄₇

—

C₂×Dic₄₇

—

D₁₈₈

—

D₁₈₈

—

D₁₈₈

—

C₄×D₄₇

—

Dic₉₄

—

C₄₇⋊C₈

—

C₄₇⋊C₈

#41

yes

complemented

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

C₂²×D₄

yes

characteristic

C₂×D₄₇

—

C₂×D₄₇

—

C₂×D₄₇

—

C₄×C₄₇

—

C₄×C₄₇

—

100

C₄×C₄₇

—

101

C₄×C₄₇

—

102

C₄×C₄₇

—

103

C₄×C₄₇

AGL(1,ℤ/8)

yes

—

104

C₄×C₄₇

#137

yes

—

105

C₄×C₄₇

C₂×#41

yes

—

106

Dic₄₇

—

107

#3182

—

maximal, Sylow

108

C₂×C₄₇

—

109

C₂×C₄₇

#532

yes

characteristic

110

C₂×C₄₇

C₂×AGL(1,ℤ/8)

yes

characteristic

111

C₂×C₄₇

C₂×#137

yes

characteristic

112

D₄₇

—

113

#533

D₄₇

yes

characteristic, complemented

114

#532

—

115

#500

—

116

#492

—

117

#487

—

118

#486

—

119

#468

—

120

#440

—

121

C₄×M₁₆

—

122

C₄₇

#3182

yes

characteristic, complemented, Sylow

123

C₂×#41

—

124

C₂×SD₁₆

—

125

C₂×M₁₆

—

126

C₄⋊Q₈

—

127

C₄⋊Q₈

C₂×D₄₇

yes

characteristic

128

C₄⋊Q₈

C₂×D₄₇

yes

characteristic

129

#127

—

130

#125

—

131

#124

—

132

C₂²⋊Q₈

—

133

C₂²⋊Q₈

C₂×D₄₇

yes

—

134

#121

—

135

#121

—

136

C₄×Q₈

—

137

C₄×Q₈

C₂×D₄₇

yes

—

138

C₄×D₄

—

139

C₄×D₄

—

140

#117

—

141

C₂×C₄²

C₂×D₄₇

yes

characteristic

142

#107

—

143

#103

—

144

#102

—

145

#97

—

146

C₄×C₈

—

147

C₄×C₈

—

148

#41

—

188

—

149

C₂×Q₈

—

150

C₂×Q₈

—

151

C₂×Q₈

C₂²×D₄₇

yes

—

152

C₂×D₄

—

153

C₂×D₄

—

154

C₂×D₄

—

155

C₂×D₄

—

156

C₂²×C₄

—

157

C₂²×C₄

C₂²⋊D₄₇

yes

characteristic

158

C₂²×C₄

C₂²⋊D₄₇

yes

characteristic

159

C₂²×C₄

C₂²×D₄₇

yes

characteristic

160

SD₁₆

—

161

M₁₆

—

162

C₂×C₈

—

163

C₂×C₈

—

164

C₄⋊C₄

—

165

C₄⋊C₄

—

166

C₄⋊C₄

—

167

C₄⋊C₄

—

168

C₄⋊C₄

—

169

C₄⋊C₄

—

170

C₄⋊C₄

—

171

C₄⋊C₄

C₂²×D₄₇

yes

—

172

C₂²⋊C₄

—

173

C₂²⋊C₄

—

174

C₂²⋊C₄

—

175

C₄²

—

176

C₄²

C₂²⋊D₄₇

yes

characteristic

177

C₄²

C₂²⋊D₄₇

yes

characteristic

178

C₄²

C₂²×D₄₇

yes

characteristic

179

C₄²

C₂²×D₄₇

yes

characteristic

180

C₂³

—

181

C₂³

C₂×C₂²⋊D₄₇

yes

characteristic

182

Q₈

—

183

Q₈

—

184

Q₈

—

188

—

185

D₄

—

186

D₄

—

188

—

187

D₄

—

188

—

188

D₄

—

188

—

189

C₂×C₄

—

190

C₂×C₄

—

191

C₂×C₄

—

192

C₂×C₄

—

193

C₂×C₄

—

194

C₂×C₄

—

195

C₂×C₄

—

188

—

196

C₂×C₄

C₂×C₂²⋊D₄₇

yes

characteristic

197

C₂×C₄

C₂×C₂²⋊D₄₇

yes

characteristic

198

C₂×C₄

C₂×C₂²⋊D₄₇

yes

characteristic

199

C₂×C₄

C₂×C₂²⋊D₄₇

yes

characteristic

200

C₂×C₄

C₂×C₂²⋊D₄₇

yes

characteristic

201

C₂×C₄

C₂³×D₄₇

yes

characteristic

202

C₈

—

203

C₈

—

204

C₂²

—

205

C₂²

—

206

C₂²

—

207

C₂²

—

188

—

208

C₂²

—

188

—

209

C₂²

—

188

—

210

C₂²

C₂²×C₂²⋊D₄₇

yes

characteristic

211

C₄

—

212

C₄

—

213

C₄

—

214

C₄

—

215

C₄

—

216

C₄

—

188

—

217

C₄

#13094049

yes

—

218

C₄

#13094055

yes

—

219

C₄

#41×D₄₇

yes

—

220

C₂

—

221

C₂

—

376

—

222

C₂

#15689669

yes

characteristic

223

C₂

C₂×#13094049

yes

characteristic

224

C₂

C₂×#13094055

yes

characteristic

	subgroup	G/H
center	C₂²	C₂²×C₂²⋊D₄₇
commutator	C₂×C₄×C₄₇	C₂⁴
Frattini	C₂×C₄	C₂³×D₄₇
Fitting	C₄₇×#533	C₂
socle	C₂²×C₄₇	C₂²×D₄
hypercenter	#533	D₄₇
hypocenter	C₄₇	#3182
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #533

subgroup

G/H

center

C₂²

C₂²×C₂²⋊D₄₇

commutator

C₂×C₄×C₄₇

C₂⁴

Frattini

C₂×C₄

C₂³×D₄₇

Fitting

C₄₇×#533

C₂

socle

C₂²×C₄₇

C₂²×D₄

D₄₇

C₄₇

G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #533

N	H ≅ G/N	type
2. #15689526	C₂	semidirect
3. #15689497	C₂	semidirect
4. #15689473	C₂	semidirect
5. #15689471	C₂	semidirect
6. #15689371	C₂	semidirect
7. #15689221	C₂	semidirect
8. C₄×#10625329	C₂	semidirect
9. C₄₇×#533	C₂	semidirect
90. C₄₇⋊C₈	#41	semidirect
113. #533	D₄₇	semidirect
122. C₄₇	#3182	semidirect

H ≅ G/N

type

2. #15689526

C₂

semidirect

3. #15689497

C₂

semidirect

4. #15689473

C₂

semidirect

5. #15689471

C₂

semidirect

6. #15689371

C₂

semidirect

7. #15689221

C₂

semidirect

8. C₄×#10625329

C₂

semidirect

9. C₄₇×#533

C₂

semidirect

90. C₄₇⋊C₈

#41

semidirect

113. #533

D₄₇

semidirect

122. C₄₇

#3182

semidirect

Subgroups — #20254107

Conjugacy classes of subgroups

Complements