Group #24989598 — subgroups

Subgroups — #24989598

Order 11008.

320 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 320 conjugacy classes of subgroups — too many to draw. Only its 103 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	#19143529	C₂	1	1	yes	maximal, characteristic
2	#19133358	C₂	1	1	yes	maximal, characteristic
3	#19133232	C₂	1	2	yes	maximal
4	#19132505	C₂	1	2	yes	maximal
5	C₄₃×#1568	C₂	1	1	yes	maximal, characteristic
6	#14583456	C₂²	1	1	yes	characteristic
7	#14583029	—	2	1	no	—
8	#14583029	—	2	1	no	—
9	C₈×Dic₈₆	—	2	1	no	—
10	C₈×Dic₈₆	—	2	1	no	—
11	#14582956	C₂²	1	2	yes	—
12	#14582925	C₄	1	2	yes	—
13	#14582923	C₂²	1	1	yes	characteristic
14	#14582854	C₄	1	2	yes	—
15	#14582652	—	2	1	no	—
16	#14582650	—	2	1	no	—
17	#14582640	—	2	4	no	—
18	C₄₃×#432	C₂²	1	2	yes	—
19	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
20	C₄₃×#335	—	2	1	no	—
21	C₄₃×#334	—	2	1	no	—
22	C₂×#10621877	C₂×C₄	1	2	yes	—
23	#13063325	Q₈	1	1	yes	characteristic
24	#13063325	Q₈	1	1	yes	characteristic
25	#13063317	D₄	1	2	yes	—
26	#13063304	—	2	1	no	—
27	#13063304	—	2	1	no	—
28	C₄×Dic₈₆	—	2	1	no	—
29	C₄×Dic₈₆	—	2	1	no	—
30	#13063284	C₂×C₄	1	2	yes	—
31	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
32	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
33	C₄⋊(C₄₃⋊C₈)	—	2	2	no	—
34	Dic₄₃⋊C₈	—	2	2	no	—
35	Dic₄₃⋊C₈	—	2	2	no	—
36	C₂²⋊(C₄₃⋊C₈)	—	2	2	no	—
37	#13063236	—	2	2	no	—
38	#13063235	—	2	2	no	—
39	C₈×Dic₄₃	—	2	2	no	—
40	C₂²×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
41	C₂²×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
42	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
43	C₄⋊C₈×C₄₃	—	2	2	no	—
44	C₂²⋊C₈×C₄₃	—	2	2	no	—
45	#97×C₄₃	—	2	2	no	—
46	C₄×C₈×C₄₃	D₄	1	1	yes	characteristic
47	C₄×C₈×C₄₃	D₄	1	1	yes	characteristic
48	C₄×C₈×C₄₃	D₄	1	1	yes	characteristic
49	C₄×C₈×C₄₃	D₄	1	1	yes	characteristic
50	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
51	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
52	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
53	C₂×Dic₈₆	—	2	1	no	—
54	C₂×Dic₈₆	—	2	1	no	—
55	C₂×C₈×C₄₃	—	2	2	no	—
56	C₂×C₈×C₄₃	—	4	1	no	—
57	C₂×C₈×C₄₃	—	4	2	no	—
58	C₂×C₈×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
59	C₂×C₈×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
60	C₂×C₈×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
61	C₂×C₈×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
62	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
63	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
64	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
65	C₄²×C₄₃	C₂×Q₈	1	1	yes	characteristic
66	C₂²⋊Dic₄₃	—	2	2	no	—
67	C₄⋊Dic₄₃	—	2	1	no	—
68	C₄⋊Dic₄₃	—	2	1	no	—
69	C₄⋊Dic₄₃	C₄⋊C₄	1	2	yes	—
70	C₄⋊Dic₄₃	C₄⋊C₄	1	2	yes	—
71	Dic₄₃⋊C₄	—	2	2	no	—
72	Dic₄₃⋊C₄	—	2	2	no	—
73	C₄×Dic₄₃	—	2	2	no	—
74	#10621877	—	4	2	no	—
75	C₂×C₄₃⋊C₈	—	2	2	no	—
76	C₂×C₄₃⋊C₈	—	4	2	no	—
77	C₂³×C₄₃	#117	1	1	yes	characteristic
78	C₂×C₄×C₄₃	—	2	1	no	—
79	C₂×C₄×C₄₃	—	2	1	no	—
80	C₂×C₄×C₄₃	—	4	1	no	—
81	C₂×C₄×C₄₃	—	4	1	no	—
82	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
83	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
84	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
85	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
86	C₂×C₄×C₄₃	C₂²⋊Q₈	1	1	yes	characteristic
87	C₂×C₄×C₄₃	C₂²⋊Q₈	1	1	yes	characteristic
88	C₂×Dic₄₃	—	2	2	no	—
89	C₂×Dic₄₃	—	2	2	no	—
90	Dic₈₆	—	4	2	no	—
91	Dic₈₆	—	4	2	no	—
92	C₈×C₄₃	—	2	1	no	—
93	C₈×C₄₃	—	2	1	no	—
94	C₈×C₄₃	—	2	1	no	—
95	C₈×C₄₃	—	8	2	no	—
96	C₈×C₄₃	#101	1	2	yes	—
97	C₄₃⋊C₈	—	4	2	no	—
98	C₄₃⋊C₈	—	8	2	no	—
99	#8633	—	43	1	no	maximal, Sylow
100	C₂²×C₄₃	—	2	1	no	—
101	C₂²×C₄₃	—	2	1	no	—
102	C₂²×C₄₃	—	2	1	no	—
103	C₂²×C₄₃	#380	1	1	yes	characteristic
104	C₄×C₄₃	—	2	1	no	—
105	C₄×C₄₃	—	2	1	no	—
106	C₄×C₄₃	—	2	1	no	—
107	C₄×C₄₃	—	2	1	no	—
108	C₄×C₄₃	—	2	1	no	—
109	C₄×C₄₃	C₂×#101	1	1	yes	characteristic
110	C₄×C₄₃	#413	1	1	yes	characteristic
111	Dic₄₃	—	4	2	no	—
112	Dic₄₃	—	4	2	no	—
113	#2960	—	43	1	no	—
114	#1568	—	43	1	no	—
115	#1568	D₄₃	1	1	yes	characteristic
116	#1537	—	43	2	no	—
117	#1307	—	43	2	no	—
118	C₂×C₄₃	—	4	1	no	—
119	C₂×C₄₃	#1801	1	1	yes	characteristic
120	C₂×C₄₃	#1814	1	1	yes	characteristic
121	C₂×C₄₃	#1814	1	1	yes	characteristic
122	#533	—	43	1	no	—
123	#446	—	86	1	no	—
124	#446	—	86	1	no	—
125	C₈×Q₈	—	86	1	no	—
126	C₈×Q₈	—	86	1	no	—
127	#432	—	43	2	no	—
128	#432	C₂×D₄₃	1	2	yes	—
129	#424	—	43	2	no	—
130	#423	—	43	1	no	—
131	#405	—	43	2	no	—
132	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
133	#335	—	2	1	no	—
134	#335	—	86	1	no	—
135	#334	—	2	1	no	—
136	#334	—	86	1	no	—
137	#330	—	86	4	no	—
138	C₄₃	#8633	1	1	yes	characteristic, complemented, Sylow
139	C₂×M₁₆	—	43	2	no	—
140	C₂²×C₈	C₄×D₄₃	1	1	yes	characteristic
141	C₂²×C₈	C₄×D₄₃	1	1	yes	characteristic
142	C₄⋊Q₈	—	43	1	no	—
143	C₄⋊Q₈	—	43	1	no	—
144	#125	—	43	2	no	—
145	C₂²⋊Q₈	—	86	1	no	—
146	C₂²⋊Q₈	—	86	1	no	—
147	C₄×Q₈	—	86	1	no	—
148	C₄×Q₈	—	86	1	no	—
149	#117	—	43	2	no	—
150	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
151	C₄⋊C₈	—	2	2	no	—
152	C₄⋊C₈	—	86	2	no	—
153	C₄⋊C₈	—	86	2	no	—
154	C₄⋊C₈	—	86	1	no	—
155	C₄⋊C₈	—	86	2	no	—
156	C₄⋊C₈	—	86	1	no	—
157	C₂²⋊C₈	—	2	2	no	—
158	C₂²⋊C₈	—	86	2	no	—
159	#97	—	2	2	no	—
160	#97	—	86	2	no	—
161	#97	—	86	2	no	—
162	C₄×C₈	—	86	2	no	—
163	C₄×C₈	D₁₇₂	1	1	yes	characteristic
164	C₄×C₈	D₁₇₂	1	1	yes	characteristic
165	C₄×C₈	C₂²⋊D₄₃	1	1	yes	characteristic
166	C₄×C₈	C₂²⋊D₄₃	1	1	yes	characteristic
167	C₂×Q₈	—	86	1	no	—
168	C₂×Q₈	—	86	1	no	—
169	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
170	C₂²×C₄	#10621900	1	1	yes	characteristic
171	C₂²×C₄	#10621902	1	1	yes	characteristic
172	M₁₆	—	172	2	no	—
173	C₂×C₈	—	2	2	no	—
174	C₂×C₈	—	4	1	no	—
175	C₂×C₈	—	4	2	no	—
176	C₂×C₈	—	86	2	no	—
177	C₂×C₈	—	172	2	no	—
178	C₂×C₈	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
179	C₂×C₈	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
180	C₂×C₈	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
181	C₂×C₈	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
182	C₄⋊C₄	—	43	2	no	—
183	C₄⋊C₄	—	43	2	no	—
184	C₄⋊C₄	—	86	2	no	—
185	C₄⋊C₄	—	86	2	no	—
186	C₄⋊C₄	—	86	1	no	—
187	C₄⋊C₄	—	86	1	no	—
188	C₂²⋊C₄	—	86	2	no	—
189	C₄²	—	86	2	no	—
190	C₄²	C₂×D₁₇₂	1	1	yes	characteristic
191	C₄²	D₄×D₄₃	1	1	yes	characteristic
192	C₄²	Q₈×D₄₃	1	1	yes	characteristic
193	C₄²	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
194	C₂³	#13063283	1	1	yes	characteristic
195	Q₈	—	172	2	no	—
196	Q₈	—	172	2	no	—
197	C₂×C₄	—	2	1	no	—
198	C₂×C₄	—	2	1	no	—
199	C₂×C₄	—	4	1	no	—
200	C₂×C₄	—	4	1	no	—
201	C₂×C₄	—	86	2	no	—
202	C₂×C₄	—	86	2	no	—
203	C₂×C₄	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
204	C₂×C₄	C₄⋊C₄×D₄₃	1	1	yes	characteristic
205	C₂×C₄	#13063296	1	1	yes	characteristic
206	C₂×C₄	#13063300	1	1	yes	characteristic
207	C₂×C₄	#13063301	1	1	yes	characteristic
208	C₂×C₄	#13063305	1	1	yes	characteristic
209	C₈	—	2	1	no	—
210	C₈	—	2	1	no	—
211	C₈	—	2	1	no	—
212	C₈	—	8	2	no	—
213	C₈	—	344	2	no	—
214	C₈	—	172	2	no	—
215	C₈	#13063243	1	2	yes	—
216	C₂²	—	2	1	no	—
217	C₂²	—	2	1	no	—
218	C₂²	—	2	1	no	—
219	C₂²	#14582756	1	1	yes	characteristic
220	C₄	—	2	1	no	—
221	C₄	—	2	1	no	—
222	C₄	—	2	1	no	—
223	C₄	—	2	1	no	—
224	C₄	—	2	1	no	—
225	C₄	—	172	2	no	—
226	C₄	—	172	2	no	—
227	C₄	C₂×#13063243	1	1	yes	characteristic
228	C₄	#14582881	1	1	yes	characteristic
229	C₂	—	4	1	no	—
230	C₂	#19134588	1	1	yes	characteristic
231	C₂	#19134646	1	1	yes	characteristic
232	C₂	#19134650	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#19143529

C₂

yes

maximal, characteristic

#19133358

C₂

yes

maximal, characteristic

#19133232

C₂

yes

maximal

#19132505

C₂

yes

maximal

C₄₃×#1568

C₂

yes

maximal, characteristic

#14583456

C₂²

yes

characteristic

#14583029

—

#14583029

—

C₈×Dic₈₆

—

C₈×Dic₈₆

—

#14582956

C₂²

yes

—

#14582925

C₄

yes

—

#14582923

C₂²

yes

characteristic

#14582854

C₄

yes

—

#14582652

—

#14582650

—

#14582640

—

C₄₃×#432

C₂²

yes

—

C₂×C₄×C₈×C₄₃

C₂²

yes

characteristic

C₄₃×#335

—

C₄₃×#334

—

C₂×#10621877

C₂×C₄

yes

—

#13063325

Q₈

yes

characteristic

#13063325

Q₈

yes

characteristic

#13063317

D₄

yes

—

#13063304

—

#13063304

—

C₄×Dic₈₆

—

C₄×Dic₈₆

—

#13063284

C₂×C₄

yes

—

C₄⋊(C₄₃⋊C₈)

—

C₄⋊(C₄₃⋊C₈)

—

C₄⋊(C₄₃⋊C₈)

—

Dic₄₃⋊C₈

—

Dic₄₃⋊C₈

—

C₂²⋊(C₄₃⋊C₈)

—

#13063236

—

#13063235

—

C₈×Dic₄₃

—

C₂²×C₈×C₄₃

C₂×C₄

yes

characteristic

C₂²×C₈×C₄₃

C₂×C₄

yes

characteristic

C₂×C₄²×C₄₃

C₂³

yes

characteristic

C₄⋊C₈×C₄₃

—

C₂²⋊C₈×C₄₃

—

#97×C₄₃

—

C₄×C₈×C₄₃

D₄

yes

characteristic

C₄×C₈×C₄₃

D₄

yes

characteristic

C₄×C₈×C₄₃

D₄

yes

characteristic

C₄×C₈×C₄₃

D₄

yes

characteristic

C₂²×C₄×C₄₃

C₂²×C₄

yes

C₂²×C₄×C₄₃

yes

C₂²×C₄×C₄₃

yes

C₂×Dic₈₆

—

C₂×Dic₈₆

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₄₃

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₄₃

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₄₃

C₂²⋊C₄

yes

characteristic

C₄²×C₄₃

C₂×D₄

yes

characteristic

C₄²×C₄₃

C₂×D₄

yes

characteristic

C₄²×C₄₃

C₂×D₄

yes

characteristic

C₄²×C₄₃

C₂×Q₈

yes

characteristic

C₂²⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

C₄⋊C₄

yes

—

C₄⋊Dic₄₃

C₄⋊C₄

yes

—

Dic₄₃⋊C₄

—

Dic₄₃⋊C₄

—

C₄×Dic₄₃

—

#10621877

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂³×C₄₃

#117

yes

characteristic

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₄₃

C₂×C₄⋊C₄

yes

C₂×C₄×C₄₃

yes

C₂×C₄×C₄₃

yes

C₂×C₄×C₄₃

C₂²⋊Q₈

yes

characteristic

C₂×C₄×C₄₃

C₂²⋊Q₈

yes

characteristic

C₂×Dic₄₃

—

C₂×Dic₄₃

—

Dic₈₆

—

Dic₈₆

—

C₈×C₄₃

—

C₈×C₄₃

—

C₈×C₄₃

—

C₈×C₄₃

—

C₈×C₄₃

#101

yes

—

C₄₃⋊C₈

—

C₄₃⋊C₈

—

#8633

—

maximal, Sylow

100

C₂²×C₄₃

—

101

C₂²×C₄₃

—

102

C₂²×C₄₃

—

103

C₂²×C₄₃

#380

yes

characteristic

104

C₄×C₄₃

—

105

C₄×C₄₃

—

106

C₄×C₄₃

—

107

C₄×C₄₃

—

108

C₄×C₄₃

—

109

C₄×C₄₃

C₂×#101

yes

characteristic

110

C₄×C₄₃

#413

yes

characteristic

111

Dic₄₃

—

112

Dic₄₃

—

113

#2960

—

114

#1568

—

115

#1568

D₄₃

yes

characteristic

116

#1537

—

117

#1307

—

118

C₂×C₄₃

—

119

C₂×C₄₃

#1801

yes

characteristic

120

C₂×C₄₃

#1814

yes

characteristic

121

C₂×C₄₃

#1814

yes

characteristic

122

#533

—

123

#446

—

124

#446

—

125

C₈×Q₈

—

126

C₈×Q₈

—

127

#432

—

128

#432

C₂×D₄₃

yes

—

129

#424

—

130

#423

—

131

#405

—

132

C₂×C₄×C₈

C₂×D₄₃

yes

characteristic

133

#335

—

134

#335

—

135

#334

—

136

#334

—

137

#330

—

138

C₄₃

#8633

yes

characteristic, complemented, Sylow

139

C₂×M₁₆

—

140

C₂²×C₈

C₄×D₄₃

yes

characteristic

141

C₂²×C₈

C₄×D₄₃

yes

characteristic

142

C₄⋊Q₈

—

143

C₄⋊Q₈

—

144

#125

—

145

C₂²⋊Q₈

—

146

C₂²⋊Q₈

—

147

C₄×Q₈

—

148

C₄×Q₈

—

149

#117

—

150

C₂×C₄²

C₂²×D₄₃

yes

characteristic

151

C₄⋊C₈

—

152

C₄⋊C₈

—

153

C₄⋊C₈

—

154

C₄⋊C₈

—

155

C₄⋊C₈

—

156

C₄⋊C₈

—

157

C₂²⋊C₈

—

158

C₂²⋊C₈

—

159

#97

—

160

#97

—

161

#97

—

162

C₄×C₈

—

163

C₄×C₈

D₁₇₂

yes

characteristic

164

C₄×C₈

D₁₇₂

yes

characteristic

165

C₄×C₈

C₂²⋊D₄₃

yes

characteristic

166

C₄×C₈

C₂²⋊D₄₃

yes

characteristic

167

C₂×Q₈

—

168

C₂×Q₈

—

169

C₂²×C₄

C₂×C₄×D₄₃

yes

characteristic

170

C₂²×C₄

#10621900

yes

characteristic

171

C₂²×C₄

#10621902

yes

characteristic

172

M₁₆

—

172

—

173

C₂×C₈

—

174

C₂×C₈

—

175

C₂×C₈

—

176

C₂×C₈

—

177

C₂×C₈

—

172

—

178

C₂×C₈

(C₂×D₄₃)⋊C₄

yes

characteristic

179

C₂×C₈

(C₂×D₄₃)⋊C₄

yes

characteristic

180

C₂×C₈

(C₂×D₄₃)⋊C₄

yes

characteristic

181

C₂×C₈

(C₂×D₄₃)⋊C₄

yes

characteristic

182

C₄⋊C₄

—

183

C₄⋊C₄

—

184

C₄⋊C₄

—

185

C₄⋊C₄

—

186

C₄⋊C₄

—

187

C₄⋊C₄

—

188

C₂²⋊C₄

—

189

C₄²

—

190

C₄²

C₂×D₁₇₂

yes

characteristic

191

C₄²

D₄×D₄₃

yes

characteristic

192

C₄²

Q₈×D₄₃

yes

characteristic

193

C₄²

C₂×C₂²⋊D₄₃

yes

characteristic

194

C₂³

#13063283

yes

characteristic

195

Q₈

—

172

—

196

Q₈

—

172

—

197

C₂×C₄

—

198

C₂×C₄

—

199

C₂×C₄

—

200

C₂×C₄

—

201

C₂×C₄

—

202

C₂×C₄

—

203

C₂×C₄

C₂×(C₂×D₄₃)⋊C₄

yes

characteristic

204

C₂×C₄

C₄⋊C₄×D₄₃

yes

characteristic

205

C₂×C₄

#13063296

yes

characteristic

206

C₂×C₄

#13063300

yes

characteristic

207

C₂×C₄

#13063301

yes

characteristic

208

C₂×C₄

#13063305

yes

characteristic

209

C₈

—

210

C₈

—

211

C₈

—

212

C₈

—

213

C₈

—

344

—

214

C₈

—

172

—

215

C₈

#13063243

yes

—

216

C₂²

—

217

C₂²

—

218

C₂²

—

219

C₂²

#14582756

yes

characteristic

220

C₄

—

221

C₄

—

222

C₄

—

223

C₄

—

224

C₄

—

225

C₄

—

172

—

226

C₄

—

172

—

227

C₄

C₂×#13063243

yes

characteristic

228

C₄

#14582881

yes

characteristic

229

C₂

—

230

C₂

#19134588

yes

characteristic

231

C₂

#19134646

yes

characteristic

232

C₂

#19134650

yes

characteristic

	subgroup	G/H
center	C₂²	#14582756
commutator	C₂²×C₄×C₄₃	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₄₃
Fitting	C₄₃×#1568	C₂
socle	C₂²×C₄₃	#380
prime radical	C₂³×C₄₃	#117
cosocle	C₂×C₄²×C₄₃	C₂³
hypercenter	#1568	D₄₃
hypocenter	C₄₃	#8633
LCS	G ▷ C₂²×C₄×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1568

subgroup

G/H

center

C₂²

#14582756

commutator

C₂²×C₄×C₄₃

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₄₃

Fitting

C₄₃×#1568

C₂

C₂²×C₄₃

C₂³×C₄₃

C₂×C₄²×C₄₃

C₂³

D₄₃

C₄₃

G ▷ C₂²×C₄×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1568

N	H ≅ G/N	type
138. C₄₃	#8633	semidirect

H ≅ G/N

type

138. C₄₃

#8633

semidirect

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

subgroup	index
#19143529	2
#19133358	2
#19133232	2
#19132505	2
C₄₃×#1568	2
#8633	43

subgroup

index

C₄₃×#1568

Subgroups — #24989598

Conjugacy classes of subgroups

Complements

Maximal subgroups