Group #25014051 — subgroups

Subgroups — #25014051

Order 11008.

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

normal subgroups only

This group has 458 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	#19144250	C₂	1	1	yes	maximal, characteristic
2	#19136316	C₂	1	2	yes	maximal, complemented
3	#19134641	C₂	1	1	yes	maximal, characteristic
4	#19132697	C₂	1	2	yes	maximal, complemented
5	C₄₃×#3407	C₂	1	1	yes	maximal, characteristic
6	C₂²×Dic₁₇₂	C₂²	1	1	yes	characteristic
7	#14583470	—	2	1	no	—
8	#14583157	C₄	1	4	yes	complemented
9	#14583140	—	2	2	no	—
10	#14582937	C₂²	1	2	yes	—
11	#14582937	C₂²	1	1	yes	characteristic
12	#14582909	—	2	1	no	—
13	#14582873	—	2	1	no	—
14	#14582704	—	2	4	no	—
15	#14582656	—	2	1	no	—
16	C₂×#131×C₄₃	C₂²	1	1	yes	characteristic
17	C₄₃×#504	—	2	4	no	—
18	C₂×M₃₂×C₄₃	—	2	2	no	—
19	C₂×M₃₂×C₄₃	C₂²	1	2	yes	—
20	C₂²×Dic₈₆	—	2	1	no	—
21	C₂×Dic₁₇₂	—	2	2	no	—
22	C₂×Dic₁₇₂	—	2	2	no	—
23	C₂×Dic₁₇₂	—	2	1	no	—
24	C₂×Dic₁₇₂	C₂×C₄	1	2	yes	—
25	#13063323	—	4	1	no	—
26	#13063312	—	4	1	no	—
27	#13063306	—	4	2	no	—
28	#13063304	—	2	4	no	—
29	#13063284	—	2	1	no	—
30	#13063284	—	2	2	no	—
31	#13063259	—	2	1	no	—
32	#13063259	—	2	2	no	—
33	#13063257	—	2	2	no	—
34	#13063257	C₂×C₄	1	2	yes	—
35	#13063250	—	2	4	no	—
36	#13063240	—	4	2	no	—
37	C₂×#41×C₄₃	D₄	1	1	yes	characteristic
38	#131×C₄₃	—	2	2	no	—
39	#131×C₄₃	—	2	2	no	—
40	C₂×M₁₆×C₄₃	C₂×C₄	1	2	yes	—
41	C₂×M₁₆×C₄₃	D₄	1	1	yes	characteristic
42	C₂²×C₈×C₄₃	D₄	1	2	yes	—
43	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
44	M₃₂×C₄₃	—	2	4	no	—
45	M₃₂×C₄₃	—	2	2	no	—
46	M₃₂×C₄₃	—	2	2	no	—
47	C₂×C₁₆×C₄₃	—	2	4	no	—
48	C₂×C₁₆×C₄₃	D₄	1	4	yes	—
49	#41×C₄₃	—	2	2	no	—
50	#41×C₄₃	—	2	2	no	—
51	C₂×Q₈×C₄₃	SD₁₆	1	1	yes	characteristic
52	C₂×D₄×C₄₃	D₈	1	2	yes	—
53	C₂×D₄×C₄₃	SD₁₆	1	1	yes	characteristic
54	C₂²×C₄×C₄₃	C₂²⋊C₄	1	2	yes	—
55	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
56	C₂²×Dic₄₃	—	4	1	no	—
57	C₂×Dic₈₆	—	2	2	no	—
58	C₂×Dic₈₆	—	4	2	no	—
59	C₂×Dic₈₆	—	4	2	no	—
60	C₂×Dic₈₆	—	4	1	no	—
61	M₁₆×C₄₃	—	2	2	no	—
62	M₁₆×C₄₃	—	2	4	no	—
63	C₂×C₈×C₄₃	—	2	2	no	—
64	C₂×C₈×C₄₃	—	2	2	no	—
65	C₂×C₈×C₄₃	C₂²⋊C₄	1	2	yes	—
66	C₂×C₈×C₄₃	C₂²×C₄	1	1	yes	characteristic
67	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
68	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
69	C₂×C₈×C₄₃	#41	1	2	yes	—
70	C₂²⋊Dic₄₃	—	4	4	no	—
71	C₂²⋊Dic₄₃	—	4	1	no	—
72	C₂²⋊Dic₄₃	—	4	2	no	—
73	C₄⋊Dic₄₃	—	2	2	no	—
74	C₄⋊Dic₄₃	—	4	2	no	—
75	Dic₄₃⋊C₄	—	4	4	no	—
76	C₄×Dic₄₃	—	4	1	no	—
77	C₄×Dic₄₃	—	4	2	no	—
78	Dic₁₇₂	—	2	4	no	—
79	Dic₁₇₂	—	4	1	no	—
80	Dic₁₇₂	—	4	1	no	—
81	C₁₆×C₄₃	—	2	4	no	—
82	C₂³×C₄₃	#102	1	2	yes	—
83	C₂³×C₄₃	C₂×D₈	1	1	yes	characteristic
84	Q₈×C₄₃	—	2	2	no	—
85	D₄×C₄₃	—	2	4	no	—
86	D₄×C₄₃	—	2	2	no	—
87	C₂×C₄×C₄₃	—	2	2	no	—
88	C₂×C₄×C₄₃	—	2	2	no	—
89	C₂×C₄×C₄₃	#102	1	2	yes	—
90	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
91	C₂×C₄×C₄₃	#121	1	2	yes	—
92	C₂×C₄×C₄₃	C₂×SD₁₆	1	1	yes	characteristic
93	C₂×C₄×C₄₃	#135	1	2	yes	—
94	C₂×Dic₄₃	—	4	2	no	—
95	C₂×Dic₄₃	—	4	2	no	—
96	C₂×Dic₄₃	—	8	2	no	—
97	C₂×Dic₄₃	—	8	2	no	—
98	Dic₈₆	—	4	2	no	—
99	Dic₈₆	—	4	2	no	—
100	Dic₈₆	—	8	2	no	—
101	C₈×C₄₃	—	2	2	no	—
102	C₈×C₄₃	C₄×D₄	1	2	yes	—
103	C₈×C₄₃	#120	1	1	yes	characteristic
104	C₈×C₄₃	#123	1	1	yes	characteristic
105	#13075	—	43	1	no	maximal, Sylow
106	C₂²×C₄₃	—	2	2	no	—
107	C₂²×C₄₃	—	4	1	no	—
108	C₂²×C₄₃	—	4	2	no	—
109	C₂²×C₄₃	C₂×#102	1	1	yes	characteristic
110	C₂²×C₄₃	#466	1	2	yes	—
111	C₄×C₄₃	—	2	2	no	—
112	C₄×C₄₃	#386	1	1	yes	characteristic
113	C₄×C₄₃	#416	1	1	yes	characteristic
114	C₄×C₄₃	#465	1	2	yes	—
115	Dic₄₃	—	8	2	no	—
116	Dic₄₃	—	8	2	no	—
117	Dic₄₃	—	16	2	no	—
118	#3407	D₄₃	1	1	yes	characteristic
119	#3059	—	43	1	no	—
120	#2141	—	43	2	no	—
121	#1812	—	43	1	no	—
122	#1384	—	43	2	no	—
123	C₂×C₄₃	—	2	1	no	—
124	C₂×C₄₃	—	2	2	no	—
125	C₂×C₄₃	—	4	2	no	—
126	C₂×C₄₃	#1893	1	1	yes	characteristic
127	C₂²×Q₁₆	—	43	1	no	—
128	C₂×#131	C₂×D₄₃	1	1	yes	characteristic
129	#536	—	86	1	no	—
130	#504	—	2	4	no	—
131	C₂×M₃₂	—	2	2	no	—
132	C₂×M₃₂	C₂×D₄₃	1	2	yes	—
133	#470	—	43	4	no	—
134	#467	—	86	2	no	—
135	#427	—	43	1	no	—
136	#427	—	43	2	no	—
137	#419	—	86	1	no	—
138	#410	—	86	1	no	—
139	#358	—	86	4	no	—
140	H(3,ℤ/4)	—	86	1	no	—
141	C₄₃	#13075	1	1	yes	characteristic, complemented, Sylow
142	C₂×#41	D₁₇₂	1	1	yes	characteristic
143	C₂²×Q₈	—	86	1	no	—
144	C₂×Q₁₆	—	43	2	no	—
145	C₂×Q₁₆	—	86	2	no	—
146	C₂×Q₁₆	—	86	2	no	—
147	C₂×Q₁₆	—	86	1	no	—
148	#131	—	2	2	no	—
149	#131	—	2	2	no	—
150	C₂×M₁₆	C₄×D₄₃	1	2	yes	—
151	C₂×M₁₆	D₁₇₂	1	1	yes	characteristic
152	C₂²×C₈	C₂²⋊D₄₃	1	2	yes	—
153	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
154	C₄⋊Q₈	—	172	1	no	—
155	#124	—	172	1	no	—
156	#123	—	172	2	no	—
157	C₂²⋊Q₈	—	86	4	no	—
158	#117	—	86	1	no	—
159	#117	—	86	2	no	—
160	M₃₂	—	2	4	no	—
161	M₃₂	—	2	2	no	—
162	M₃₂	—	2	2	no	—
163	C₂×C₁₆	—	2	4	no	—
164	C₂×C₁₆	C₂²⋊D₄₃	1	4	yes	—
165	#107	—	86	1	no	—
166	#107	—	86	2	no	—
167	#106	—	43	2	no	—
168	#106	—	86	2	no	—
169	#103	—	86	4	no	—
170	#99	—	172	2	no	—
171	#41	—	2	2	no	—
172	#41	—	2	2	no	—
173	C₂×Q₈	—	86	2	no	—
174	C₂×Q₈	—	172	2	no	—
175	C₂×Q₈	—	172	2	no	—
176	C₂×Q₈	—	172	1	no	—
177	C₂×Q₈	#10621873	1	1	yes	characteristic
178	C₂×D₄	#10621873	1	1	yes	characteristic
179	C₂×D₄	D₃₄₄	1	2	yes	—
180	C₂²×C₄	—	172	1	no	—
181	C₂²×C₄	(C₂×D₄₃)⋊C₄	1	2	yes	—
182	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
183	Q₁₆	—	86	4	no	—
184	Q₁₆	—	172	1	no	—
185	Q₁₆	—	172	1	no	—
186	M₁₆	—	2	2	no	—
187	M₁₆	—	2	4	no	—
188	C₂×C₈	—	2	2	no	—
189	C₂×C₈	—	2	2	no	—
190	C₂×C₈	(C₂×D₄₃)⋊C₄	1	2	yes	—
191	C₂×C₈	C₂×C₄×D₄₃	1	1	yes	characteristic
192	C₂×C₈	#10621898	1	2	yes	—
193	C₂×C₈	C₂×C₂²⋊D₄₃	1	2	yes	—
194	C₂×C₈	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
195	C₄⋊C₄	—	86	2	no	—
196	C₄⋊C₄	—	172	2	no	—
197	C₄⋊C₄	—	172	4	no	—
198	C₂²⋊C₄	—	172	2	no	—
199	C₂²⋊C₄	—	172	4	no	—
200	C₂²⋊C₄	—	172	1	no	—
201	C₄²	—	172	2	no	—
202	C₄²	—	172	1	no	—
203	C₁₆	—	2	4	no	—
204	C₂³	#13063247	1	2	yes	—
205	C₂³	C₂×D₃₄₄	1	1	yes	characteristic
206	Q₈	—	2	2	no	—
207	Q₈	—	344	2	no	—
208	Q₈	—	172	2	no	—
209	Q₈	—	172	2	no	—
210	D₄	—	2	4	no	—
211	D₄	—	2	2	no	—
212	C₂×C₄	—	2	2	no	—
213	C₂×C₄	—	2	2	no	—
214	C₂×C₄	—	344	2	no	—
215	C₂×C₄	—	344	2	no	—
216	C₂×C₄	—	172	2	no	—
217	C₂×C₄	—	172	2	no	—
218	C₂×C₄	#13063247	1	2	yes	—
219	C₂×C₄	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
220	C₂×C₄	#13063299	1	2	yes	—
221	C₂×C₄	C₂×#10621873	1	1	yes	characteristic
222	C₂×C₄	#13063347	1	2	yes	—
223	C₈	—	2	2	no	—
224	C₈	C₄×C₂²⋊D₄₃	1	2	yes	—
225	C₈	#13063294	1	1	yes	characteristic
226	C₈	#13063308	1	1	yes	characteristic
227	C₂²	—	2	2	no	—
228	C₂²	—	4	1	no	—
229	C₂²	—	4	2	no	—
230	C₂²	C₂×#13063247	1	1	yes	characteristic
231	C₂²	#14583135	1	2	yes	—
232	C₄	—	2	2	no	—
233	C₄	—	344	2	no	—
234	C₄	—	344	2	no	—
235	C₄	—	688	2	no	—
236	C₄	#14582778	1	1	yes	characteristic
237	C₄	#14582896	1	1	yes	characteristic
238	C₄	#14583128	1	2	yes	—
239	C₂	—	2	1	no	—
240	C₂	—	2	2	no	—
241	C₂	—	4	2	no	—
242	C₂	#19135023	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#19144250

C₂

yes

maximal, characteristic

#19136316

C₂

yes

maximal, complemented

#19134641

C₂

yes

maximal, characteristic

#19132697

C₂

yes

maximal, complemented

C₄₃×#3407

C₂

yes

maximal, characteristic

C₂²×Dic₁₇₂

C₂²

yes

characteristic

#14583470

—

#14583157

C₄

yes

complemented

#14583140

—

#14582937

C₂²

yes

—

#14582937

C₂²

yes

—

—

—

—

C₂×#131×C₄₃

C₂²

yes

characteristic

C₄₃×#504

—

C₂×M₃₂×C₄₃

—

C₂×M₃₂×C₄₃

C₂²

yes

—

C₂²×Dic₈₆

—

C₂×Dic₁₇₂

—

C₂×Dic₁₇₂

—

C₂×Dic₁₇₂

—

C₂×Dic₁₇₂

C₂×C₄

yes

—

—

—

—

—

—

—

—

—

—

C₂×C₄

yes

—

#13063250

—

#13063240

—

C₂×#41×C₄₃

D₄

yes

characteristic

#131×C₄₃

—

#131×C₄₃

—

C₂×M₁₆×C₄₃

C₂×C₄

yes

—

C₂×M₁₆×C₄₃

D₄

yes

characteristic

C₂²×C₈×C₄₃

D₄

yes

—

C₂²×C₈×C₄₃

C₂³

yes

characteristic

M₃₂×C₄₃

—

M₃₂×C₄₃

—

M₃₂×C₄₃

—

C₂×C₁₆×C₄₃

—

C₂×C₁₆×C₄₃

D₄

yes

—

#41×C₄₃

—

#41×C₄₃

—

C₂×Q₈×C₄₃

SD₁₆

yes

characteristic

C₂×D₄×C₄₃

D₈

yes

—

C₂×D₄×C₄₃

SD₁₆

yes

characteristic

C₂²×C₄×C₄₃

C₂²⋊C₄

yes

—

C₂²×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂²×Dic₄₃

—

C₂×Dic₈₆

—

C₂×Dic₈₆

—

C₂×Dic₈₆

—

C₂×Dic₈₆

—

M₁₆×C₄₃

—

M₁₆×C₄₃

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

C₂²⋊C₄

yes

—

C₂×C₈×C₄₃

C₂²×C₄

yes

characteristic

C₂×C₈×C₄₃

C₂×D₄

yes

—

C₂×C₈×C₄₃

C₂×D₄

yes

characteristic

C₂×C₈×C₄₃

#41

yes

—

C₂²⋊Dic₄₃

—

C₂²⋊Dic₄₃

—

C₂²⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

Dic₄₃⋊C₄

—

C₄×Dic₄₃

—

C₄×Dic₄₃

—

Dic₁₇₂

—

Dic₁₇₂

—

Dic₁₇₂

—

C₁₆×C₄₃

—

C₂³×C₄₃

#102

yes

—

C₂³×C₄₃

C₂×D₈

yes

characteristic

Q₈×C₄₃

—

D₄×C₄₃

—

D₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

#102

yes

—

C₂×C₄×C₄₃

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₄₃

#121

yes

—

C₂×C₄×C₄₃

C₂×SD₁₆

yes

characteristic

C₂×C₄×C₄₃

#135

yes

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

Dic₈₆

—

Dic₈₆

—

100

Dic₈₆

—

101

C₈×C₄₃

—

102

C₈×C₄₃

C₄×D₄

yes

—

103

C₈×C₄₃

#120

yes

characteristic

104

C₈×C₄₃

yes

105

—

106

C₂²×C₄₃

—

107

C₂²×C₄₃

—

108

C₂²×C₄₃

—

109

C₂²×C₄₃

C₂×#102

yes

characteristic

110

C₂²×C₄₃

#466

yes

—

111

C₄×C₄₃

—

112

C₄×C₄₃

#386

yes

characteristic

113

C₄×C₄₃

#416

yes

characteristic

114

C₄×C₄₃

#465

yes

—

115

Dic₄₃

—

116

Dic₄₃

—

117

Dic₄₃

—

118

#3407

D₄₃

yes

characteristic

119

#3059

—

120

#2141

—

121

#1812

—

122

#1384

—

123

C₂×C₄₃

—

124

C₂×C₄₃

—

125

C₂×C₄₃

—

126

C₂×C₄₃

#1893

yes

characteristic

127

C₂²×Q₁₆

—

128

C₂×#131

C₂×D₄₃

yes

characteristic

129

#536

—

130

#504

—

131

C₂×M₃₂

—

132

C₂×M₃₂

C₂×D₄₃

yes

—

133

#470

—

134

#467

—

135

#427

—

136

#427

—

137

#419

—

138

#410

—

139

#358

—

140

H(3,ℤ/4)

—

141

C₄₃

#13075

yes

characteristic, complemented, Sylow

142

C₂×#41

D₁₇₂

yes

characteristic

143

C₂²×Q₈

—

144

C₂×Q₁₆

—

145

C₂×Q₁₆

—

146

C₂×Q₁₆

—

147

C₂×Q₁₆

—

148

#131

—

149

#131

—

150

C₂×M₁₆

C₄×D₄₃

yes

—

151

C₂×M₁₆

D₁₇₂

yes

characteristic

152

C₂²×C₈

C₂²⋊D₄₃

yes

—

153

C₂²×C₈

C₂²×D₄₃

yes

characteristic

154

C₄⋊Q₈

—

172

—

155

#124

—

172

—

156

#123

—

172

—

157

C₂²⋊Q₈

—

158

#117

—

159

#117

—

160

M₃₂

—

161

M₃₂

—

162

M₃₂

—

163

C₂×C₁₆

—

164

C₂×C₁₆

C₂²⋊D₄₃

yes

—

165

#107

—

166

#107

—

167

#106

—

168

#106

—

169

#103

—

170

#99

—

172

—

171

#41

—

172

#41

—

173

C₂×Q₈

—

174

C₂×Q₈

—

172

—

175

C₂×Q₈

—

172

—

176

C₂×Q₈

—

172

—

177

C₂×Q₈

#10621873

yes

characteristic

178

C₂×D₄

#10621873

yes

characteristic

179

C₂×D₄

D₃₄₄

yes

—

180

C₂²×C₄

—

172

—

181

C₂²×C₄

(C₂×D₄₃)⋊C₄

yes

—

182

C₂²×C₄

C₂×D₁₇₂

yes

characteristic

183

Q₁₆

—

184

Q₁₆

—

172

—

185

Q₁₆

—

172

—

186

M₁₆

—

187

M₁₆

—

188

C₂×C₈

—

189

C₂×C₈

—

190

C₂×C₈

(C₂×D₄₃)⋊C₄

yes

—

191

C₂×C₈

C₂×C₄×D₄₃

yes

characteristic

192

C₂×C₈

#10621898

yes

—

193

C₂×C₈

C₂×C₂²⋊D₄₃

yes

—

194

C₂×C₈

C₂×C₂²⋊D₄₃

yes

characteristic

195

C₄⋊C₄

—

196

C₄⋊C₄

—

172

—

197

C₄⋊C₄

—

172

—

198

C₂²⋊C₄

—

172

—

199

C₂²⋊C₄

—

172

—

200

C₂²⋊C₄

—

172

—

201

C₄²

—

172

—

202

C₄²

—

172

—

203

C₁₆

—

204

C₂³

#13063247

yes

—

205

C₂³

C₂×D₃₄₄

yes

characteristic

206

Q₈

—

207

Q₈

—

344

—

208

Q₈

—

172

—

209

Q₈

—

172

—

210

D₄

—

211

D₄

—

212

C₂×C₄

—

213

C₂×C₄

—

214

C₂×C₄

—

344

—

215

C₂×C₄

—

344

—

216

C₂×C₄

—

172

—

217

C₂×C₄

—

172

—

218

C₂×C₄

#13063247

yes

—

219

C₂×C₄

C₂×(C₂×D₄₃)⋊C₄

yes

characteristic

220

C₂×C₄

#13063299

yes

—

221

C₂×C₄

C₂×#10621873

yes

characteristic

222

C₂×C₄

#13063347

yes

—

223

C₈

—

224

C₈

C₄×C₂²⋊D₄₃

yes

—

225

C₈

#13063294

yes

characteristic

226

C₈

#13063308

yes

characteristic

227

C₂²

—

228

C₂²

—

229

C₂²

—

230

C₂²

C₂×#13063247

yes

characteristic

231

C₂²

#14583135

yes

—

232

C₄

—

233

C₄

—

344

—

234

C₄

—

344

—

235

C₄

—

688

—

236

C₄

#14582778

yes

characteristic

237

C₄

#14582896

yes

characteristic

238

C₄

#14583128

yes

—

239

C₂

—

240

C₂

—

241

C₂

—

242

C₂

#19135023

yes

characteristic

	subgroup	G/H
center	C₂	#19135023
commutator	C₂×C₈×C₄₃	C₂²×C₄
Frattini	C₂²×C₈	C₂²×D₄₃
Fitting	C₄₃×#3407	C₂
socle	C₂×C₄₃	#1893
prime radical	C₂×#41×C₄₃	D₄
cosocle	C₂²×C₈×C₄₃	C₂³
hypercenter	#3407	D₄₃
hypocenter	C₄₃	#13075
LCS	G ▷ C₂×C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂ ◁ C₂²×C₄ ◁ C₂×#131 ◁ #3407

subgroup

G/H

center

C₂

#19135023

commutator

C₂×C₈×C₄₃

C₂²×C₄

Frattini

C₂²×C₈

C₂²×D₄₃

Fitting

C₄₃×#3407

C₂

socle

C₂×C₄₃

#1893

prime radical

C₂×#41×C₄₃

D₄

cosocle

C₂²×C₈×C₄₃

C₂³

D₄₃

C₄₃

G ▷ C₂×C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂ ◁ C₂²×C₄ ◁ C₂×#131 ◁ #3407

N	H ≅ G/N	type
2. #19136316	C₂	semidirect
4. #19132697	C₂	semidirect
8. #14583157	C₄	semidirect
141. C₄₃	#13075	semidirect

H ≅ G/N

type

2. #19136316

C₂

semidirect

4. #19132697

C₂

semidirect

8. #14583157

C₄

semidirect

141. C₄₃

#13075

semidirect

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

subgroup	index
#19144250	2
#19136316	2
#19134641	2
#19132697	2
C₄₃×#3407	2
#13075	43

subgroup

index

C₄₃×#3407

Subgroups — #25014051

Conjugacy classes of subgroups

Complements

Maximal subgroups