Group #24999686 — subgroups

Subgroups — #24999686

Order 11008.

454 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 454 conjugacy classes of subgroups — too many to draw. Only its 97 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	#19142973	C₂	1	1	yes	maximal, characteristic, complemented
2	#19135423	C₂	1	1	yes	maximal, characteristic
3	#19133156	C₂	1	2	yes	maximal
4	#19132454	C₂	1	2	yes	maximal, complemented
5	C₄₃×#1276	C₂	1	1	yes	maximal, characteristic, complemented
6	#14583449	C₂²	1	1	yes	characteristic
7	C₂×#13063325	—	2	1	no	—
8	#14582923	C₂²	1	1	yes	characteristic
9	C₂×#13063253	—	2	1	no	—
10	C₂×#13063253	—	2	1	no	—
11	#14582805	—	2	4	no	—
12	#14582765	—	2	1	no	—
13	#14582765	C₂²	1	2	yes	—
14	#14582634	—	2	4	no	—
15	C₄₃×#431	C₂²	1	2	yes	—
16	C₄³×C₄₃	C₂²	1	1	yes	characteristic
17	C₂×#10621898	—	2	1	no	—
18	C₂²×Dic₈₆	—	2	2	no	—
19	C₂×#10621877	—	2	1	no	—
20	#13063325	—	4	2	no	—
21	#13063325	—	4	2	no	—
22	#13063325	Q₈	1	1	yes	characteristic, complemented
23	#13063322	Q₈	1	1	yes	characteristic, complemented
24	#13063313	—	2	1	no	—
25	#13063299	—	2	2	no	—
26	C₄×D₁₇₂	—	2	2	no	—
27	C₂×C₄⋊Dic₄₃	—	2	2	no	—
28	C₂×C₄⋊Dic₄₃	—	2	2	no	—
29	C₄⋊(C₄₃⋊C₈)	—	2	2	no	—
30	#13063253	—	4	2	no	—
31	#13063253	—	4	2	no	—
32	C₄₃⋊#95	—	2	4	no	—
33	C₄₃⋊#95	—	2	2	no	—
34	C₄₃⋊#95	D₄	1	4	yes	—
35	C₂×C₄²×C₄₃	—	2	2	no	—
36	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
37	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
38	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
39	C₄⋊C₈×C₄₃	—	2	2	no	—
40	C₂²⋊C₈×C₄₃	—	2	2	no	—
41	C₄×C₈×C₄₃	—	2	2	no	—
42	C₂²×C₄×C₄₃	—	2	1	no	—
43	C₂²×C₄×C₄₃	—	2	1	no	—
44	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
45	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
46	C₂×C₂²⋊D₄₃	—	4	1	no	—
47	C₂²×Dic₄₃	—	2	4	no	—
48	#10621898	—	4	1	no	—
49	#10621898	—	4	1	no	—
50	#10621898	—	4	1	no	—
51	#10621898	—	4	1	no	—
52	C₂×D₁₇₂	—	2	1	no	—
53	C₂×D₁₇₂	—	2	2	no	—
54	C₂×C₄×D₄₃	—	4	1	no	—
55	C₂×Dic₈₆	—	2	1	no	—
56	C₂×Dic₈₆	—	4	4	no	—
57	C₂×Dic₈₆	—	4	8	no	—
58	C₂×C₈×C₄₃	—	4	2	no	—
59	C₄²×C₄₃	—	2	1	no	—
60	C₄²×C₄₃	—	2	1	no	—
61	C₄²×C₄₃	—	4	4	no	—
62	C₄²×C₄₃	D₈	1	2	yes	—
63	C₄²×C₄₃	SD₁₆	1	2	yes	—
64	C₄²×C₄₃	C₂×Q₈	1	1	yes	characteristic
65	C₄²×C₄₃	#41	1	2	yes	—
66	C₄²×C₄₃	#41	1	1	yes	characteristic
67	(C₂×D₄₃)⋊C₄	—	4	2	no	—
68	C₄⋊Dic₄₃	—	2	2	no	—
69	C₄⋊Dic₄₃	—	4	4	no	—
70	C₄⋊Dic₄₃	—	4	2	no	—
71	C₄⋊Dic₄₃	—	4	2	no	—
72	#10621877	—	4	1	no	—
73	#10621877	—	4	1	no	—
74	C₂×C₄₃⋊C₈	—	4	1	no	—
75	C₂³×C₄₃	#120	1	1	yes	characteristic
76	C₂²×D₄₃	—	4	1	no	—
77	C₂×C₄×C₄₃	—	2	4	no	—
78	C₂×C₄×C₄₃	—	2	2	no	—
79	C₂×C₄×C₄₃	—	2	2	no	—
80	C₂×C₄×C₄₃	—	4	2	no	—
81	C₂×C₄×C₄₃	—	4	2	no	—
82	C₂×C₄×C₄₃	C₂²⋊Q₈	1	2	yes	—
83	C₂×C₄×C₄₃	C₂²⋊Q₈	1	1	yes	characteristic
84	C₂×C₄×C₄₃	#124	1	2	yes	—
85	C₂×C₄×C₄₃	#124	1	1	yes	characteristic
86	C₂×C₄×C₄₃	C₂×D₈	1	1	yes	characteristic
87	C₂×C₄×C₄₃	C₂×SD₁₆	1	1	yes	characteristic
88	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	1	yes	characteristic
89	C₂×C₄×C₄₃	#137	1	1	yes	characteristic
90	C₂²⋊D₄₃	—	8	1	no	—
91	C₂²⋊D₄₃	—	8	1	no	—
92	C₂×Dic₄₃	—	4	8	no	—
93	C₂×Dic₄₃	—	4	1	no	—
94	C₂×Dic₄₃	—	4	4	no	—
95	D₁₇₂	—	4	1	no	—
96	D₁₇₂	—	4	1	no	—
97	D₁₇₂	—	8	2	no	—
98	C₄×D₄₃	—	8	1	no	—
99	C₄×D₄₃	—	8	1	no	—
100	Dic₈₆	—	4	1	no	—
101	Dic₈₆	—	4	1	no	—
102	Dic₈₆	—	8	8	no	—
103	C₈×C₄₃	—	8	2	no	—
104	C₄₃⋊C₈	—	8	1	no	—
105	#10362	—	43	1	no	maximal, Sylow
106	C₂²×C₄₃	—	2	2	no	—
107	C₂²×C₄₃	#393	1	1	yes	characteristic
108	C₂²×C₄₃	#447	1	1	yes	characteristic
109	C₂²×C₄₃	#448	1	1	yes	characteristic
110	C₂×D₄₃	—	8	1	no	—
111	C₂×D₄₃	—	8	2	no	—
112	C₄×C₄₃	—	2	4	no	—
113	C₄×C₄₃	—	2	2	no	—
114	C₄×C₄₃	—	2	2	no	—
115	C₄×C₄₃	—	4	2	no	—
116	C₄×C₄₃	#474	1	1	yes	characteristic
117	C₄×C₄₃	#476	1	1	yes	characteristic
118	C₄×C₄₃	#486	1	1	yes	characteristic
119	C₄×C₄₃	#489	1	1	yes	characteristic
120	Dic₄₃	—	8	4	no	—
121	Dic₄₃	—	8	1	no	—
122	#2862	—	43	1	no	—
123	#1962	—	43	1	no	—
124	#1517	—	43	2	no	—
125	#1286	—	43	2	no	—
126	#1276	D₄₃	1	1	yes	characteristic, complemented
127	C₂×C₄₃	—	2	1	no	—
128	C₂×C₄₃	—	2	1	no	—
129	C₂×C₄₃	#2023	1	1	yes	characteristic
130	C₂×C₄₃	#2031	1	2	yes	—
131	D₄₃	—	16	1	no	—
132	#532	—	43	1	no	—
133	C₂×C₄⋊Q₈	—	86	1	no	—
134	#431	C₂×D₄₃	1	2	yes	—
135	#423	—	43	1	no	—
136	C₂×#104	—	86	1	no	—
137	C₂×#104	—	86	1	no	—
138	#391	—	86	4	no	—
139	#382	—	43	2	no	—
140	#382	—	86	1	no	—
141	C₄³	C₂×D₄₃	1	1	yes	characteristic
142	#327	—	86	4	no	—
143	C₄₃	#10362	1	1	yes	characteristic, complemented, Sylow
144	C₂×#41	—	86	1	no	—
145	C₂²×Q₈	—	86	2	no	—
146	C₂×M₁₆	—	86	1	no	—
147	C₄⋊Q₈	—	43	1	no	—
148	C₄⋊Q₈	—	172	2	no	—
149	C₄⋊Q₈	—	172	2	no	—
150	#127	—	43	1	no	—
151	#124	—	86	1	no	—
152	#121	—	86	2	no	—
153	C₄×D₄	—	86	2	no	—
154	C₂×C₄⋊C₄	—	86	2	no	—
155	C₂×C₄⋊C₄	—	86	2	no	—
156	C₂×C₄²	—	2	2	no	—
157	C₂×C₄²	D₁₇₂	1	1	yes	characteristic
158	C₂×C₄²	D₁₇₂	1	1	yes	characteristic
159	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
160	C₄⋊C₈	—	2	2	no	—
161	C₄⋊C₈	—	86	2	no	—
162	#104	—	172	2	no	—
163	#104	—	172	2	no	—
164	C₂²⋊C₈	—	2	2	no	—
165	C₄×C₈	—	2	2	no	—
166	#95	—	43	4	no	—
167	#95	—	86	4	no	—
168	#95	—	86	2	no	—
169	#41	—	172	1	no	—
170	#41	—	172	1	no	—
171	#41	—	172	1	no	—
172	#41	—	172	1	no	—
173	C₂×Q₈	—	86	1	no	—
174	C₂×Q₈	—	172	4	no	—
175	C₂×Q₈	—	172	8	no	—
176	C₂×D₄	—	86	2	no	—
177	C₂×D₄	—	86	1	no	—
178	C₂×D₄	—	172	1	no	—
179	C₂²×C₄	—	2	1	no	—
180	C₂²×C₄	—	2	1	no	—
181	C₂²×C₄	—	86	4	no	—
182	C₂²×C₄	—	172	1	no	—
183	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
184	C₂²×C₄	D₄×D₄₃	1	2	yes	—
185	M₁₆	—	172	1	no	—
186	M₁₆	—	172	1	no	—
187	C₂×C₈	—	4	2	no	—
188	C₂×C₈	—	172	1	no	—
189	C₄⋊C₄	—	86	2	no	—
190	C₄⋊C₄	—	172	4	no	—
191	C₄⋊C₄	—	172	2	no	—
192	C₄⋊C₄	—	172	2	no	—
193	C₂²⋊C₄	—	172	2	no	—
194	C₄²	—	2	1	no	—
195	C₄²	—	2	1	no	—
196	C₄²	—	4	4	no	—
197	C₄²	#10621873	1	2	yes	—
198	C₄²	D₃₄₄	1	2	yes	—
199	C₄²	#10621898	1	2	yes	—
200	C₄²	#10621900	1	1	yes	characteristic
201	C₄²	Q₈×D₄₃	1	1	yes	characteristic
202	C₂³	—	172	1	no	—
203	C₂³	#13063295	1	1	yes	characteristic
204	Q₈	—	344	8	no	—
205	Q₈	—	172	1	no	—
206	Q₈	—	172	1	no	—
207	D₄	—	344	2	no	—
208	D₄	—	344	1	no	—
209	D₄	—	344	1	no	—
210	D₄	—	172	1	no	—
211	D₄	—	172	1	no	—
212	C₂×C₄	—	2	4	no	—
213	C₂×C₄	—	2	2	no	—
214	C₂×C₄	—	2	2	no	—
215	C₂×C₄	—	4	2	no	—
216	C₂×C₄	—	4	2	no	—
217	C₂×C₄	—	344	1	no	—
218	C₂×C₄	—	344	1	no	—
219	C₂×C₄	—	172	8	no	—
220	C₂×C₄	—	172	1	no	—
221	C₂×C₄	—	172	4	no	—
222	C₂×C₄	#13063303	1	2	yes	—
223	C₂×C₄	#13063305	1	1	yes	characteristic
224	C₂×C₄	#13063311	1	2	yes	—
225	C₂×C₄	#13063313	1	1	yes	characteristic
226	C₂×C₄	C₂×D₃₄₄	1	1	yes	characteristic
227	C₂×C₄	C₂×#10621873	1	1	yes	characteristic
228	C₂×C₄	#13063353	1	1	yes	characteristic
229	C₂×C₄	#13063358	1	1	yes	characteristic
230	C₈	—	8	2	no	—
231	C₈	—	344	1	no	—
232	C₂²	—	2	2	no	—
233	C₂²	—	344	2	no	—
234	C₂²	—	344	1	no	—
235	C₂²	#14582812	1	1	yes	characteristic
236	C₂²	#14583035	1	1	yes	characteristic
237	C₂²	#14583040	1	1	yes	characteristic
238	C₄	—	2	4	no	—
239	C₄	—	2	2	no	—
240	C₄	—	2	2	no	—
241	C₄	—	4	2	no	—
242	C₄	—	344	4	no	—
243	C₄	—	344	1	no	—
244	C₄	#14583180	1	1	yes	characteristic
245	C₄	#14583190	1	1	yes	characteristic
246	C₄	#14583246	1	1	yes	characteristic
247	C₄	#14583259	1	1	yes	characteristic
248	C₂	—	2	1	no	—
249	C₂	—	2	1	no	—
250	C₂	—	688	1	no	—
251	C₂	#19135732	1	1	yes	characteristic
252	C₂	#19135768	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#19142973

C₂

yes

maximal, characteristic, complemented

#19135423

C₂

yes

maximal, characteristic

#19133156

C₂

yes

maximal

#19132454

C₂

yes

maximal, complemented

C₄₃×#1276

C₂

yes

maximal, characteristic, complemented

#14583449

C₂²

yes

characteristic

C₂×#13063325

—

#14582923

C₂²

yes

—

—

—

—

C₂²

yes

—

#14582634

—

C₄₃×#431

C₂²

yes

—

C₄³×C₄₃

C₂²

yes

characteristic

C₂×#10621898

—

C₂²×Dic₈₆

—

—

—

—

Q₈

yes

characteristic, complemented

#13063322

Q₈

yes

characteristic, complemented

#13063313

—

#13063299

—

C₄×D₁₇₂

—

C₂×C₄⋊Dic₄₃

—

C₂×C₄⋊Dic₄₃

—

C₄⋊(C₄₃⋊C₈)

—

#13063253

—

#13063253

—

C₄₃⋊#95

—

C₄₃⋊#95

—

C₄₃⋊#95

D₄

yes

—

C₂×C₄²×C₄₃

—

C₂×C₄²×C₄₃

D₄

yes

characteristic

C₂×C₄²×C₄₃

D₄

yes

characteristic

C₂×C₄²×C₄₃

C₂³

yes

characteristic

C₄⋊C₈×C₄₃

—

C₂²⋊C₈×C₄₃

—

C₄×C₈×C₄₃

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂²×C₄×C₄₃

C₂×D₄

yes

—

C₂×C₂²⋊D₄₃

—

C₂²×Dic₄₃

—

—

—

—

—

C₂×D₁₇₂

—

C₂×D₁₇₂

—

C₂×C₄×D₄₃

—

C₂×Dic₈₆

—

C₂×Dic₈₆

—

C₂×Dic₈₆

—

C₂×C₈×C₄₃

—

C₄²×C₄₃

—

C₄²×C₄₃

—

C₄²×C₄₃

—

C₄²×C₄₃

D₈

yes

—

C₄²×C₄₃

SD₁₆

yes

—

C₄²×C₄₃

C₂×Q₈

yes

characteristic

C₄²×C₄₃

#41

yes

—

C₄²×C₄₃

#41

yes

characteristic

(C₂×D₄₃)⋊C₄

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

#10621877

—

#10621877

—

C₂×C₄₃⋊C₈

—

C₂³×C₄₃

#120

yes

characteristic

C₂²×D₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂²⋊Q₈

yes

—

C₂×C₄×C₄₃

C₂²⋊Q₈

yes

characteristic

C₂×C₄×C₄₃

#124

yes

—

C₂×C₄×C₄₃

#124

yes

characteristic

C₂×C₄×C₄₃

C₂×D₈

yes

characteristic

C₂×C₄×C₄₃

C₂×SD₁₆

yes

C₂×C₄×C₄₃

yes

C₂×C₄×C₄₃

yes

C₂²⋊D₄₃

—

C₂²⋊D₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

D₁₇₂

—

D₁₇₂

—

D₁₇₂

—

C₄×D₄₃

—

C₄×D₄₃

—

100

Dic₈₆

—

101

Dic₈₆

—

102

Dic₈₆

—

103

C₈×C₄₃

—

104

C₄₃⋊C₈

—

105

#10362

—

maximal, Sylow

106

C₂²×C₄₃

—

107

C₂²×C₄₃

#393

yes

characteristic

108

C₂²×C₄₃

#447

yes

characteristic

109

C₂²×C₄₃

#448

yes

characteristic

110

C₂×D₄₃

—

111

C₂×D₄₃

—

112

C₄×C₄₃

—

113

C₄×C₄₃

—

114

C₄×C₄₃

—

115

C₄×C₄₃

—

116

C₄×C₄₃

#474

yes

characteristic

117

C₄×C₄₃

#476

yes

characteristic

118

C₄×C₄₃

#486

yes

characteristic

119

C₄×C₄₃

#489

yes

characteristic

120

Dic₄₃

—

121

Dic₄₃

—

122

#2862

—

123

#1962

—

124

#1517

—

125

#1286

—

126

#1276

D₄₃

yes

characteristic, complemented

127

C₂×C₄₃

—

128

C₂×C₄₃

—

129

C₂×C₄₃

#2023

yes

characteristic

130

C₂×C₄₃

#2031

yes

—

131

D₄₃

—

132

#532

—

133

C₂×C₄⋊Q₈

—

134

#431

C₂×D₄₃

yes

—

135

#423

—

136

C₂×#104

—

137

C₂×#104

—

138

#391

—

139

#382

—

140

#382

—

141

C₄³

C₂×D₄₃

yes

characteristic

142

#327

—

143

C₄₃

#10362

yes

characteristic, complemented, Sylow

144

C₂×#41

—

145

C₂²×Q₈

—

146

C₂×M₁₆

—

147

C₄⋊Q₈

—

148

C₄⋊Q₈

—

172

—

149

C₄⋊Q₈

—

172

—

150

#127

—

151

#124

—

152

#121

—

153

C₄×D₄

—

154

C₂×C₄⋊C₄

—

155

C₂×C₄⋊C₄

—

156

C₂×C₄²

—

157

C₂×C₄²

D₁₇₂

yes

characteristic

158

C₂×C₄²

D₁₇₂

yes

characteristic

159

C₂×C₄²

C₂²×D₄₃

yes

characteristic

160

C₄⋊C₈

—

161

C₄⋊C₈

—

162

#104

—

172

—

163

#104

—

172

—

164

C₂²⋊C₈

—

165

C₄×C₈

—

166

#95

—

167

#95

—

168

#95

—

169

#41

—

172

—

170

#41

—

172

—

171

#41

—

172

—

172

#41

—

172

—

173

C₂×Q₈

—

174

C₂×Q₈

—

172

—

175

C₂×Q₈

—

172

—

176

C₂×D₄

—

177

C₂×D₄

—

178

C₂×D₄

—

172

—

179

C₂²×C₄

—

180

C₂²×C₄

—

181

C₂²×C₄

—

182

C₂²×C₄

—

172

—

183

C₂²×C₄

C₂×D₁₇₂

yes

characteristic

184

C₂²×C₄

D₄×D₄₃

yes

—

185

M₁₆

—

172

—

186

M₁₆

—

172

—

187

C₂×C₈

—

188

C₂×C₈

—

172

—

189

C₄⋊C₄

—

190

C₄⋊C₄

—

172

—

191

C₄⋊C₄

—

172

—

192

C₄⋊C₄

—

172

—

193

C₂²⋊C₄

—

172

—

194

C₄²

—

195

C₄²

—

196

C₄²

—

197

C₄²

#10621873

yes

—

198

C₄²

D₃₄₄

yes

—

199

C₄²

#10621898

yes

—

200

C₄²

#10621900

yes

characteristic

201

C₄²

Q₈×D₄₃

yes

characteristic

202

C₂³

—

172

—

203

C₂³

#13063295

yes

characteristic

204

Q₈

—

344

—

205

Q₈

—

172

—

206

Q₈

—

172

—

207

D₄

—

344

—

208

D₄

—

344

—

209

D₄

—

344

—

210

D₄

—

172

—

211

D₄

—

172

—

212

C₂×C₄

—

213

C₂×C₄

—

214

C₂×C₄

—

215

C₂×C₄

—

216

C₂×C₄

—

217

C₂×C₄

—

344

—

218

C₂×C₄

—

344

—

219

C₂×C₄

—

172

—

220

C₂×C₄

—

172

—

221

C₂×C₄

—

172

—

222

C₂×C₄

#13063303

yes

—

223

C₂×C₄

#13063305

yes

characteristic

224

C₂×C₄

#13063311

yes

—

225

C₂×C₄

#13063313

yes

characteristic

226

C₂×C₄

C₂×D₃₄₄

yes

characteristic

227

C₂×C₄

C₂×#10621873

yes

characteristic

228

C₂×C₄

#13063353

yes

characteristic

229

C₂×C₄

#13063358

yes

characteristic

230

C₈

—

231

C₈

—

344

—

232

C₂²

—

233

C₂²

—

344

—

234

C₂²

—

344

—

235

C₂²

#14582812

yes

characteristic

236

C₂²

#14583035

yes

characteristic

237

C₂²

#14583040

yes

characteristic

238

C₄

—

239

C₄

—

240

C₄

—

241

C₄

—

242

C₄

—

344

—

243

C₄

—

344

—

244

C₄

#14583180

yes

characteristic

245

C₄

#14583190

yes

characteristic

246

C₄

#14583246

yes

characteristic

247

C₄

#14583259

yes

characteristic

248

C₂

—

249

C₂

—

250

C₂

—

688

—

251

C₂

#19135732

yes

characteristic

252

C₂

#19135768

yes

—

	subgroup	G/H
center	C₂²	#14582812
commutator, cosocle	C₂×C₄²×C₄₃	C₂³
Frattini	C₂×C₄²	C₂²×D₄₃
Fitting	C₄₃×#1276	C₂
socle	C₂²×C₄₃	#393
prime radical	#14583449	C₂²
hypercenter	#1276	D₄₃
hypocenter	C₄₃	#10362
LCS	G ▷ C₂×C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1276

subgroup

G/H

center

C₂²

#14582812

commutator, cosocle

C₂×C₄²×C₄₃

C₂³

Frattini

C₂×C₄²

C₂²×D₄₃

Fitting

C₄₃×#1276

C₂

C₂²×C₄₃

C₂²

D₄₃

C₄₃

G ▷ C₂×C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1276

N	H ≅ G/N	type
1. #19142973	C₂	semidirect
4. #19132454	C₂	semidirect
5. C₄₃×#1276	C₂	semidirect
22. #13063325	Q₈	semidirect
23. #13063322	Q₈	semidirect
126. #1276	D₄₃	semidirect
143. C₄₃	#10362	semidirect

H ≅ G/N

type

1. #19142973

C₂

semidirect

4. #19132454

C₂

semidirect

5. C₄₃×#1276

C₂

semidirect

22. #13063325

Q₈

semidirect

23. #13063322

Q₈

semidirect

126. #1276

D₄₃

semidirect

143. C₄₃

#10362

semidirect

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

subgroup	index
#19142973	2
#19135423	2
#19133156	2
#19132454	2
C₄₃×#1276	2
#10362	43

subgroup

index

C₄₃×#1276

Subgroups — #24999686

Conjugacy classes of subgroups

Complements

Maximal subgroups