Group #19147507 — subgroups

Subgroups — #19147507

Order 5504.

340 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 340 conjugacy classes of subgroups — too many to draw. Only its 133 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	Q₈×Dic₈₆	C₂	1	1	yes	maximal, characteristic, complemented
2	#14583609	C₂	1	1	yes	maximal, characteristic
3	#14583308	C₂	1	2	yes	maximal, complemented
4	#14583304	C₂	1	1	yes	maximal, characteristic, complemented
5	#14583207	C₂	1	2	yes	maximal, complemented
6	#14583195	C₂	1	1	yes	maximal, characteristic, complemented
7	#14583190	C₂	1	1	yes	maximal, characteristic
8	#14583180	C₂	1	2	yes	maximal
9	#14583001	C₂	1	2	yes	maximal
10	C₄×#10621873	C₂	1	1	yes	maximal, characteristic
11	C₄₃×#446	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#10621873	C₂²	1	1	yes	characteristic
13	#13063325	C₂²	1	1	yes	characteristic
14	#13063325	C₂²	1	1	yes	characteristic
15	#13063325	C₂²	1	2	yes	—
16	#13063324	—	2	1	no	—
17	#13063324	—	2	2	no	—
18	#13063317	C₂²	1	2	yes	—
19	#13063303	—	2	2	no	—
20	#13063301	—	2	1	no	—
21	Q₈×Dic₄₃	—	2	1	no	—
22	C₄×Dic₈₆	C₂²	1	1	yes	characteristic
23	C₄×Dic₈₆	C₂²	1	2	yes	—
24	C₄×D₁₇₂	C₂²	1	2	yes	—
25	C₄×D₁₇₂	C₂²	1	1	yes	characteristic
26	C₄⋊C₄×D₄₃	—	2	1	no	—
27	#13063259	C₂²	1	2	yes	—
28	#13063259	C₂²	1	2	yes	—
29	#13063259	C₂²	1	2	yes	—
30	#13063257	C₂²	1	1	yes	characteristic
31	#13063257	C₂²	1	2	yes	—
32	#13063250	C₂²	1	2	yes	—
33	#13063250	C₂²	1	1	yes	characteristic
34	#13063247	C₂²	1	1	yes	characteristic
35	#13063247	C₂²	1	2	yes	—
36	C₄×Q₈×C₄₃	C₂²	1	1	yes	characteristic
37	C₄⋊C₈×C₄₃	C₂²	1	2	yes	—
38	C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
39	#97×C₄₃	C₂²	1	2	yes	—
40	C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
41	C₂×Q₈×C₄₃	D₄	1	1	yes	characteristic
42	C₂×D₁₇₂	C₂³	1	1	yes	characteristic
43	C₂×C₄×D₄₃	—	2	1	no	—
44	C₂×C₄×D₄₃	—	2	2	no	—
45	C₂×Dic₈₆	—	2	1	no	—
46	C₂×Dic₈₆	—	2	2	no	—
47	C₂×Dic₈₆	—	2	1	no	—
48	C₂×Dic₈₆	C₂³	1	1	yes	characteristic
49	C₂×C₈×C₄₃	C₂³	1	1	yes	characteristic
50	C₂×C₈×C₄₃	C₂³	1	2	yes	—
51	C₂×C₈×C₄₃	C₂³	1	1	yes	characteristic
52	C₄⋊C₄×C₄₃	D₄	1	1	yes	characteristic
53	C₄⋊C₄×C₄₃	D₄	1	2	yes	—
54	C₄²×C₄₃	C₂³	1	1	yes	characteristic
55	C₄²×C₄₃	C₂³	1	2	yes	—
56	(C₂×D₄₃)⋊C₄	—	2	2	no	—
57	(C₂×D₄₃)⋊C₄	—	2	1	no	—
58	C₄⋊Dic₄₃	—	2	1	no	—
59	C₄⋊Dic₄₃	—	2	2	no	—
60	C₄⋊Dic₄₃	—	2	1	no	—
61	C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
62	C₄⋊Dic₄₃	C₂³	1	2	yes	—
63	C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
64	C₄⋊Dic₄₃	C₂³	1	2	yes	—
65	Dic₄₃⋊C₄	—	2	2	no	—
66	Dic₄₃⋊C₄	—	2	2	no	—
67	Dic₄₃⋊C₄	—	2	1	no	—
68	Dic₄₃⋊C₄	—	2	2	no	—
69	C₄×Dic₄₃	—	2	2	no	—
70	C₄×Dic₄₃	—	2	1	no	—
71	#10621873	Q₈	1	4	yes	complemented
72	C₂²×D₄₃	—	2	1	no	—
73	Q₈×C₄₃	—	2	2	no	—
74	C₂×C₄×C₄₃	C₂×D₄	1	2	yes	—
75	C₂×C₄×C₄₃	C₂×D₄	1	2	yes	—
76	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
77	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
78	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
79	C₂×Dic₄₃	—	2	1	no	—
80	C₂×Dic₄₃	—	2	2	no	—
81	C₂×Dic₄₃	—	2	1	no	—
82	C₂×Dic₄₃	—	2	1	no	—
83	C₂×Dic₄₃	—	2	2	no	—
84	D₁₇₂	—	2	1	no	—
85	D₁₇₂	C₂×Q₈	1	2	yes	—
86	C₄×D₄₃	—	4	2	no	—
87	C₄×D₄₃	—	8	2	no	—
88	Dic₈₆	—	2	1	no	—
89	Dic₈₆	—	8	1	no	—
90	Dic₈₆	—	8	2	no	—
91	Dic₈₆	—	8	1	no	—
92	Dic₈₆	C₂×Q₈	1	2	yes	—
93	C₈×C₄₃	—	2	1	no	—
94	C₈×C₄₃	—	2	2	no	—
95	C₈×C₄₃	C₂×Q₈	1	2	yes	—
96	C₂²×C₄₃	C₂²×D₄	1	1	yes	characteristic
97	C₂×D₄₃	—	2	2	no	—
98	C₂×D₄₃	—	4	1	no	—
99	C₂×D₄₃	—	4	1	no	—
100	C₄×C₄₃	—	2	2	no	—
101	C₄×C₄₃	—	2	1	no	—
102	C₄×C₄₃	—	2	2	no	—
103	C₄×C₄₃	#137	1	2	yes	—
104	C₄×C₄₃	C₂²×Q₈	1	1	yes	characteristic
105	C₄×C₄₃	2₋¹⁺⁴	1	1	yes	characteristic
106	Dic₄₃	—	2	2	no	—
107	Dic₄₃	—	4	1	no	—
108	Dic₄₃	—	4	2	no	—
109	Dic₄₃	—	4	1	no	—
110	Dic₄₃	—	4	2	no	—
111	#3385	—	43	1	no	maximal, Sylow
112	C₂×C₄₃	D₄×Q₈	1	1	yes	characteristic
113	C₂×C₄₃	C₂×#137	1	1	yes	characteristic
114	C₂×C₄₃	#576	1	1	yes	characteristic
115	D₄₃	—	4	2	no	—
116	Q₈²	—	43	1	no	—
117	#554	—	43	1	no	—
118	#501	—	43	2	no	—
119	#500	—	43	1	no	—
120	#479	—	43	2	no	—
121	#477	—	43	1	no	—
122	#476	—	43	1	no	—
123	#474	—	43	2	no	—
124	#446	D₄₃	1	1	yes	characteristic, complemented
125	#440	—	43	2	no	—
126	C₄×SD₁₆	—	43	1	no	—
127	C₄₃	#3385	1	1	yes	characteristic, complemented, Sylow
128	C₂×SD₁₆	—	43	1	no	—
129	C₄⋊Q₈	—	43	1	no	—
130	C₄⋊Q₈	—	43	2	no	—
131	C₄⋊Q₈	—	43	1	no	—
132	C₄⋊Q₈	—	86	1	no	—
133	C₄⋊Q₈	—	86	2	no	—
134	#125	—	43	2	no	—
135	C₂²⋊Q₈	—	86	1	no	—
136	C₂²⋊Q₈	—	86	2	no	—
137	C₄×Q₈	—	43	1	no	—
138	C₄×Q₈	—	43	2	no	—
139	C₄×Q₈	—	86	1	no	—
140	C₄×Q₈	C₂×D₄₃	1	1	yes	characteristic
141	C₄×D₄	—	43	1	no	—
142	C₄×D₄	—	43	2	no	—
143	C₂×C₄⋊C₄	—	86	1	no	—
144	#107	—	43	2	no	—
145	#107	—	43	2	no	—
146	#107	—	43	2	no	—
147	#106	—	43	1	no	—
148	#106	—	43	2	no	—
149	C₄⋊C₈	C₂×D₄₃	1	2	yes	—
150	C₄⋊C₈	C₂×D₄₃	1	1	yes	characteristic
151	#103	—	43	1	no	—
152	#103	—	43	2	no	—
153	#102	—	43	1	no	—
154	#102	—	43	2	no	—
155	#97	C₂×D₄₃	1	2	yes	—
156	C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
157	C₂×Q₈	—	43	1	no	—
158	C₂×Q₈	—	86	1	no	—
159	C₂×Q₈	—	86	1	no	—
160	C₂×Q₈	—	86	2	no	—
161	C₂×Q₈	D₁₇₂	1	1	yes	characteristic
162	C₂×D₄	—	43	1	no	—
163	C₂²×C₄	—	86	2	no	—
164	C₂²×C₄	—	86	1	no	—
165	SD₁₆	—	43	4	no	—
166	C₂×C₈	C₂²×D₄₃	1	1	yes	characteristic
167	C₂×C₈	C₂²×D₄₃	1	2	yes	—
168	C₂×C₈	C₂²×D₄₃	1	1	yes	characteristic
169	C₄⋊C₄	—	43	1	no	—
170	C₄⋊C₄	—	43	2	no	—
171	C₄⋊C₄	—	43	1	no	—
172	C₄⋊C₄	—	43	2	no	—
173	C₄⋊C₄	—	86	2	no	—
174	C₄⋊C₄	—	86	1	no	—
175	C₄⋊C₄	—	86	1	no	—
176	C₄⋊C₄	—	86	2	no	—
177	C₄⋊C₄	—	86	2	no	—
178	C₄⋊C₄	—	86	1	no	—
179	C₄⋊C₄	—	86	2	no	—
180	C₄⋊C₄	D₁₇₂	1	1	yes	characteristic
181	C₄⋊C₄	D₁₇₂	1	2	yes	—
182	C₂²⋊C₄	—	86	1	no	—
183	C₂²⋊C₄	—	86	2	no	—
184	C₄²	—	86	2	no	—
185	C₄²	—	86	1	no	—
186	C₄²	C₂²×D₄₃	1	1	yes	characteristic
187	C₄²	C₂²×D₄₃	1	2	yes	—
188	C₂³	—	86	1	no	—
189	Q₈	—	2	2	no	—
190	Q₈	—	43	2	no	—
191	Q₈	—	86	1	no	—
192	Q₈	—	344	2	no	—
193	Q₈	—	344	1	no	—
194	Q₈	—	344	1	no	—
195	D₄	—	43	2	no	—
196	D₄	—	86	1	no	—
197	C₂×C₄	—	86	1	no	—
198	C₂×C₄	—	86	2	no	—
199	C₂×C₄	—	86	1	no	—
200	C₂×C₄	—	86	1	no	—
201	C₂×C₄	—	86	2	no	—
202	C₂×C₄	—	344	2	no	—
203	C₂×C₄	—	172	2	no	—
204	C₂×C₄	C₂×D₁₇₂	1	2	yes	—
205	C₂×C₄	C₂×D₁₇₂	1	1	yes	characteristic
206	C₂×C₄	C₂×D₁₇₂	1	2	yes	—
207	C₂×C₄	C₂×D₁₇₂	1	1	yes	characteristic
208	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
209	C₈	—	2	1	no	—
210	C₈	—	2	2	no	—
211	C₈	Q₈×D₄₃	1	2	yes	—
212	C₂²	—	86	2	no	—
213	C₂²	—	172	1	no	—
214	C₂²	—	172	1	no	—
215	C₂²	C₂²×D₁₇₂	1	1	yes	characteristic
216	C₄	—	2	2	no	—
217	C₄	—	2	2	no	—
218	C₄	—	2	1	no	—
219	C₄	—	86	2	no	—
220	C₄	—	172	1	no	—
221	C₄	—	172	2	no	—
222	C₄	—	172	1	no	—
223	C₄	—	172	2	no	—
224	C₄	#13063358	1	2	yes	—
225	C₄	C₂×Q₈×D₄₃	1	1	yes	characteristic
226	C₄	#13063372	1	1	yes	characteristic
227	C₂	—	172	2	no	—
228	C₂	Q₈×D₁₇₂	1	1	yes	characteristic
229	C₂	C₂×#13063358	1	1	yes	characteristic
230	C₂	#14583704	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

Q₈×Dic₈₆

C₂

yes

maximal, characteristic, complemented

#14583609

C₂

yes

maximal, characteristic

#14583308

C₂

yes

maximal, complemented

#14583304

C₂

yes

maximal, characteristic, complemented

#14583207

C₂

yes

maximal, complemented

#14583195

C₂

yes

maximal, characteristic, complemented

#14583190

C₂

yes

maximal, characteristic

#14583180

C₂

yes

maximal

#14583001

C₂

yes

maximal

C₄×#10621873

C₂

yes

maximal, characteristic

C₄₃×#446

C₂

yes

maximal, characteristic, complemented

C₂×#10621873

C₂²

yes

characteristic

#13063325

C₂²

yes

characteristic

#13063325

C₂²

yes

characteristic

#13063325

C₂²

yes

—

#13063324

—

#13063324

—

#13063317

C₂²

yes

—

#13063303

—

#13063301

—

Q₈×Dic₄₃

—

C₄×Dic₈₆

C₂²

yes

characteristic

C₄×Dic₈₆

C₂²

yes

—

C₄×D₁₇₂

C₂²

yes

—

C₄×D₁₇₂

C₂²

yes

characteristic

C₄⋊C₄×D₄₃

—

#13063259

C₂²

yes

—

#13063259

C₂²

yes

—

#13063259

C₂²

yes

—

#13063257

C₂²

yes

characteristic

#13063257

C₂²

yes

—

#13063250

C₂²

yes

—

#13063250

C₂²

yes

characteristic

#13063247

C₂²

yes

characteristic

#13063247

C₂²

yes

—

C₄×Q₈×C₄₃

C₂²

yes

characteristic

C₄⋊C₈×C₄₃

C₂²

yes

—

C₄⋊C₈×C₄₃

C₂²

yes

characteristic

#97×C₄₃

C₂²

yes

—

C₄×C₈×C₄₃

C₂²

yes

characteristic

C₂×Q₈×C₄₃

D₄

yes

characteristic

C₂×D₁₇₂

C₂³

yes

characteristic

C₂×C₄×D₄₃

—

C₂×C₄×D₄₃

—

C₂×Dic₈₆

—

C₂×Dic₈₆

—

C₂×Dic₈₆

—

C₂×Dic₈₆

C₂³

yes

characteristic

C₂×C₈×C₄₃

C₂³

yes

characteristic

C₂×C₈×C₄₃

C₂³

yes

—

C₂×C₈×C₄₃

C₂³

yes

characteristic

C₄⋊C₄×C₄₃

D₄

yes

characteristic

C₄⋊C₄×C₄₃

D₄

yes

—

C₄²×C₄₃

C₂³

yes

characteristic

C₄²×C₄₃

C₂³

yes

—

(C₂×D₄₃)⋊C₄

—

(C₂×D₄₃)⋊C₄

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

C₂³

yes

characteristic

C₄⋊Dic₄₃

C₂³

yes

—

C₄⋊Dic₄₃

C₂³

yes

characteristic

C₄⋊Dic₄₃

C₂³

yes

—

Dic₄₃⋊C₄

—

Dic₄₃⋊C₄

—

Dic₄₃⋊C₄

—

Dic₄₃⋊C₄

—

C₄×Dic₄₃

—

C₄×Dic₄₃

—

#10621873

Q₈

yes

complemented

C₂²×D₄₃

—

Q₈×C₄₃

—

C₂×C₄×C₄₃

C₂×D₄

yes

—

C₂×C₄×C₄₃

C₂×D₄

yes

—

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂×C₄×C₄₃

C₂⁴

yes

characteristic

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

D₁₇₂

—

D₁₇₂

C₂×Q₈

yes

—

C₄×D₄₃

—

C₄×D₄₃

—

Dic₈₆

—

Dic₈₆

—

Dic₈₆

—

Dic₈₆

—

Dic₈₆

C₂×Q₈

yes

—

C₈×C₄₃

—

C₈×C₄₃

—

C₈×C₄₃

C₂×Q₈

yes

—

C₂²×C₄₃

C₂²×D₄

yes

characteristic

C₂×D₄₃

—

C₂×D₄₃

—

C₂×D₄₃

—

100

C₄×C₄₃

—

101

C₄×C₄₃

—

102

C₄×C₄₃

—

103

C₄×C₄₃

#137

yes

—

104

C₄×C₄₃

C₂²×Q₈

yes

characteristic

105

C₄×C₄₃

2₋¹⁺⁴

yes

characteristic

106

Dic₄₃

—

107

Dic₄₃

—

108

Dic₄₃

—

109

Dic₄₃

—

110

Dic₄₃

—

111

#3385

—

maximal, Sylow

112

C₂×C₄₃

D₄×Q₈

yes

characteristic

113

C₂×C₄₃

C₂×#137

yes

characteristic

114

C₂×C₄₃

#576

yes

characteristic

115

D₄₃

—

116

Q₈²

—

117

#554

—

118

#501

—

119

#500

—

120

#479

—

121

#477

—

122

#476

—

123

#474

—

124

#446

D₄₃

yes

characteristic, complemented

125

#440

—

126

C₄×SD₁₆

—

127

C₄₃

#3385

yes

characteristic, complemented, Sylow

128

C₂×SD₁₆

—

129

C₄⋊Q₈

—

130

C₄⋊Q₈

—

131

C₄⋊Q₈

—

132

C₄⋊Q₈

—

133

C₄⋊Q₈

—

134

#125

—

135

C₂²⋊Q₈

—

136

C₂²⋊Q₈

—

137

C₄×Q₈

—

138

C₄×Q₈

—

139

C₄×Q₈

—

140

C₄×Q₈

C₂×D₄₃

yes

characteristic

141

C₄×D₄

—

142

C₄×D₄

—

143

C₂×C₄⋊C₄

—

144

#107

—

145

#107

—

146

#107

—

147

#106

—

148

#106

—

149

C₄⋊C₈

C₂×D₄₃

yes

—

150

C₄⋊C₈

C₂×D₄₃

yes

characteristic

151

#103

—

152

#103

—

153

#102

—

154

#102

—

155

#97

C₂×D₄₃

yes

—

156

C₄×C₈

C₂×D₄₃

yes

characteristic

157

C₂×Q₈

—

158

C₂×Q₈

—

159

C₂×Q₈

—

160

C₂×Q₈

—

161

C₂×Q₈

D₁₇₂

yes

characteristic

162

C₂×D₄

—

163

C₂²×C₄

—

164

C₂²×C₄

—

165

SD₁₆

—

166

C₂×C₈

C₂²×D₄₃

yes

characteristic

167

C₂×C₈

C₂²×D₄₃

yes

—

168

C₂×C₈

C₂²×D₄₃

yes

characteristic

169

C₄⋊C₄

—

170

C₄⋊C₄

—

171

C₄⋊C₄

—

172

C₄⋊C₄

—

173

C₄⋊C₄

—

174

C₄⋊C₄

—

175

C₄⋊C₄

—

176

C₄⋊C₄

—

177

C₄⋊C₄

—

178

C₄⋊C₄

—

179

C₄⋊C₄

—

180

C₄⋊C₄

D₁₇₂

yes

characteristic

181

C₄⋊C₄

D₁₇₂

yes

—

182

C₂²⋊C₄

—

183

C₂²⋊C₄

—

184

C₄²

—

185

C₄²

—

186

C₄²

C₂²×D₄₃

yes

characteristic

187

C₄²

C₂²×D₄₃

yes

—

188

C₂³

—

189

Q₈

—

190

Q₈

—

191

Q₈

—

192

Q₈

—

344

—

193

Q₈

—

344

—

194

Q₈

—

344

—

195

D₄

—

196

D₄

—

197

C₂×C₄

—

198

C₂×C₄

—

199

C₂×C₄

—

200

C₂×C₄

—

201

C₂×C₄

—

202

C₂×C₄

—

344

—

203

C₂×C₄

—

172

—

204

C₂×C₄

C₂×D₁₇₂

yes

—

205

C₂×C₄

C₂×D₁₇₂

yes

characteristic

206

C₂×C₄

C₂×D₁₇₂

yes

—

207

C₂×C₄

C₂×D₁₇₂

yes

characteristic

208

C₂×C₄

C₂³×D₄₃

yes

characteristic

209

C₈

—

210

C₈

—

211

C₈

Q₈×D₄₃

yes

—

212

C₂²

—

213

C₂²

—

172

—

214

C₂²

—

172

—

215

C₂²

C₂²×D₁₇₂

yes

characteristic

216

C₄

—

217

C₄

—

218

C₄

—

219

C₄

—

220

C₄

—

172

—

221

C₄

—

172

—

222

C₄

—

172

—

223

C₄

—

172

—

224

C₄

#13063358

yes

—

225

C₄

C₂×Q₈×D₄₃

yes

characteristic

226

C₄

#13063372

yes

characteristic

227

C₂

—

172

—

228

C₂

Q₈×D₁₇₂

yes

characteristic

229

C₂

C₂×#13063358

yes

characteristic

230

C₂

#14583704

yes

characteristic

	subgroup	G/H
center	C₂²	C₂²×D₁₇₂
commutator	C₂×C₄×C₄₃	C₂⁴
Frattini	C₂×C₄	C₂³×D₄₃
Fitting	C₄₃×#446	C₂
socle	C₂²×C₄₃	C₂²×D₄
hypercenter	#446	D₄₃
hypocenter	C₄₃	#3385
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₄×Q₈ ◁ #446

subgroup

G/H

center

C₂²

C₂²×D₁₇₂

commutator

C₂×C₄×C₄₃

C₂⁴

Frattini

C₂×C₄

C₂³×D₄₃

Fitting

C₄₃×#446

C₂

socle

C₂²×C₄₃

C₂²×D₄

D₄₃

C₄₃

G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂² ◁ C₄×Q₈ ◁ #446

N	H ≅ G/N	type
1. Q₈×Dic₈₆	C₂	semidirect
3. #14583308	C₂	semidirect
4. #14583304	C₂	semidirect
5. #14583207	C₂	semidirect
6. #14583195	C₂	semidirect
11. C₄₃×#446	C₂	semidirect
71. #10621873	Q₈	semidirect
124. #446	D₄₃	semidirect
127. C₄₃	#3385	semidirect

H ≅ G/N

type

1. Q₈×Dic₈₆

C₂

semidirect

3. #14583308

C₂

semidirect

4. #14583304

C₂

semidirect

5. #14583207

C₂

semidirect

6. #14583195

C₂

semidirect

11. C₄₃×#446

C₂

semidirect

71. #10621873

Q₈

semidirect

124. #446

D₄₃

semidirect

127. C₄₃

#3385

semidirect

Subgroups — #19147507

Conjugacy classes of subgroups

Complements