Group #24990185 — subgroups

Subgroups — #24990185

Order 11008.

378 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 378 conjugacy classes of subgroups — too many to draw. Only its 107 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	#19137560	C₂	1	1	yes	maximal, characteristic
2	#19132919	C₂	1	1	yes	maximal, characteristic
3	#19132496	C₂	1	2	yes	maximal
4	#19132455	C₂	1	2	yes	maximal
5	C₄₃×#1801	C₂	1	1	yes	maximal, characteristic
6	#14582952	C₂²	1	2	yes	—
7	#14582806	—	2	1	no	—
8	#14582785	—	2	2	no	—
9	#14582767	C₄	1	2	yes	—
10	#14582765	C₂²	1	1	yes	characteristic
11	C₄⋊C₄×Dic₄₃	—	2	1	no	—
12	C₄×C₄⋊Dic₄₃	C₂²	1	1	yes	characteristic
13	#14582745	C₄	1	2	yes	—
14	#14582625	—	2	2	no	—
15	C₂×C₄×Q₈×C₄₃	C₂²	1	1	yes	characteristic
16	C₄₃×#423	C₂²	1	2	yes	—
17	C₂×#101×C₄₃	—	2	1	no	—
18	C₄₃×#343	—	2	1	no	—
19	C₂×C₄⋊Dic₄₃	—	2	1	no	—
20	C₂×C₄⋊Dic₄₃	—	2	1	no	—
21	C₂×C₄×Dic₄₃	—	2	2	no	—
22	C₂×C₄×Dic₄₃	—	2	1	no	—
23	C₄⋊(C₄₃⋊C₈)	—	2	2	no	—
24	C₂²⋊(C₄₃⋊C₈)	—	2	2	no	—
25	C₄×C₄₃⋊C₈	—	2	2	no	—
26	C₄₃⋊#95	—	2	2	no	—
27	C₄₃⋊#95	—	2	2	no	—
28	C₄₃⋊#95	—	2	2	no	—
29	C₄₃⋊#95	—	2	1	no	—
30	C₄₃⋊#95	C₂×C₄	1	1	yes	characteristic
31	C₄₃⋊#95	C₂×C₄	1	2	yes	—
32	C₄₃⋊#95	C₂×C₄	1	1	yes	characteristic
33	C₂²×Q₈×C₄₃	D₄	1	1	yes	characteristic
34	C₂×M₁₆×C₄₃	—	2	2	no	—
35	C₄×Q₈×C₄₃	—	2	2	no	—
36	C₄×Q₈×C₄₃	—	2	2	no	—
37	C₂×C₄⋊C₄×C₄₃	D₄	1	2	yes	—
38	C₂×C₄⋊C₄×C₄₃	D₄	1	1	yes	characteristic
39	C₂×C₄²×C₄₃	C₂×C₄	1	2	yes	—
40	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
41	C₄⋊C₈×C₄₃	—	2	2	no	—
42	C₄⋊C₈×C₄₃	—	2	2	no	—
43	#101×C₄₃	—	4	2	no	—
44	C₂×Q₈×C₄₃	—	2	2	no	—
45	C₂×Q₈×C₄₃	—	2	2	no	—
46	C₂×Q₈×C₄₃	—	2	1	no	—
47	C₂×Q₈×C₄₃	—	2	1	no	—
48	C₂²×C₄×C₄₃	C₂²⋊C₄	1	2	yes	—
49	C₂²×C₄×C₄₃	C₂²⋊C₄	1	2	yes	—
50	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
51	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
52	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
53	C₂²×Dic₄₃	—	2	1	no	—
54	C₂²×Dic₄₃	—	2	2	no	—
55	C₂²×Dic₄₃	—	2	1	no	—
56	M₁₆×C₄₃	—	4	2	no	—
57	M₁₆×C₄₃	—	4	2	no	—
58	C₂×C₈×C₄₃	—	4	2	no	—
59	C₄⋊C₄×C₄₃	—	2	2	no	—
60	C₄⋊C₄×C₄₃	—	2	4	no	—
61	C₄²×C₄₃	—	2	2	no	—
62	C₄²×C₄₃	—	2	2	no	—
63	C₄²×C₄₃	#41	1	2	yes	—
64	C₄²×C₄₃	#41	1	2	yes	—
65	C₄⋊Dic₄₃	—	4	2	no	—
66	C₄⋊Dic₄₃	—	4	1	no	—
67	C₄⋊Dic₄₃	—	4	1	no	—
68	C₄×Dic₄₃	—	4	4	no	—
69	C₄×Dic₄₃	—	4	2	no	—
70	C₂×C₄₃⋊C₈	—	4	2	no	—
71	C₂³×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
72	Q₈×C₄₃	—	4	2	no	—
73	Q₈×C₄₃	—	4	2	no	—
74	C₂×C₄×C₄₃	—	2	2	no	—
75	C₂×C₄×C₄₃	—	2	2	no	—
76	C₂×C₄×C₄₃	—	2	2	no	—
77	C₂×C₄×C₄₃	—	2	2	no	—
78	C₂×C₄×C₄₃	—	4	1	no	—
79	C₂×C₄×C₄₃	—	4	1	no	—
80	C₂×C₄×C₄₃	—	4	2	no	—
81	C₂×C₄×C₄₃	#117	1	1	yes	characteristic
82	C₂×C₄×C₄₃	#117	1	1	yes	characteristic
83	C₂×C₄×C₄₃	#123	1	2	yes	—
84	C₂×C₄×C₄₃	#123	1	2	yes	—
85	C₂×C₄×C₄₃	#135	1	2	yes	—
86	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	1	yes	characteristic
87	C₂×C₄×C₄₃	#137	1	1	yes	characteristic
88	C₂×Dic₄₃	—	2	2	no	—
89	C₂×Dic₄₃	—	4	1	no	—
90	C₂×Dic₄₃	—	4	1	no	—
91	C₂×Dic₄₃	—	4	2	no	—
92	C₂×Dic₄₃	—	4	1	no	—
93	C₂×Dic₄₃	—	4	1	no	—
94	C₂×Dic₄₃	—	4	2	no	—
95	C₂×Dic₄₃	—	4	1	no	—
96	C₂×Dic₄₃	—	4	2	no	—
97	C₈×C₄₃	—	8	2	no	—
98	C₄₃⋊C₈	—	8	2	no	—
99	#8769	—	43	1	no	maximal, Sylow
100	C₂²×C₄₃	—	2	1	no	—
101	C₂²×C₄₃	—	2	1	no	—
102	C₂²×C₄₃	#381	1	1	yes	characteristic
103	C₂²×C₄₃	#416	1	1	yes	characteristic
104	C₂²×C₄₃	#417	1	1	yes	characteristic
105	C₄×C₄₃	—	2	2	no	—
106	C₄×C₄₃	—	2	1	no	—
107	C₄×C₄₃	—	2	1	no	—
108	C₄×C₄₃	—	4	2	no	—
109	C₄×C₄₃	—	4	2	no	—
110	C₄×C₄₃	#482	1	2	yes	—
111	C₄×C₄₃	#485	1	2	yes	—
112	Dic₄₃	—	4	2	no	—
113	Dic₄₃	—	8	1	no	—
114	Dic₄₃	—	8	2	no	—
115	#2356	—	43	1	no	—
116	#1801	D₄₃	1	1	yes	characteristic
117	#1461	—	43	1	no	—
118	#1303	—	43	2	no	—
119	#1286	—	43	2	no	—
120	C₂×C₄₃	—	2	1	no	—
121	C₂×C₄₃	—	2	1	no	—
122	C₂×C₄₃	#1825	1	1	yes	characteristic
123	C₂×C₄₃	#1827	1	1	yes	characteristic
124	C₂×C₄₃	#1830	1	1	yes	characteristic
125	C₂×C₄×Q₈	C₂×D₄₃	1	1	yes	characteristic
126	#431	—	43	2	no	—
127	#423	C₂×D₄₃	1	2	yes	—
128	C₂×#101	—	2	1	no	—
129	#391	—	86	1	no	—
130	#387	—	86	2	no	—
131	#383	—	43	2	no	—
132	#382	—	43	1	no	—
133	C₄×C₄⋊C₄	—	43	1	no	—
134	C₄×C₄⋊C₄	—	86	1	no	—
135	#376	—	43	2	no	—
136	#343	—	2	1	no	—
137	#324	—	86	2	no	—
138	C₄₃	#8769	1	1	yes	characteristic, complemented, Sylow
139	C₂²×Q₈	C₂²⋊D₄₃	1	1	yes	characteristic
140	C₂×M₁₆	—	2	2	no	—
141	C₄×Q₈	—	2	2	no	—
142	C₄×Q₈	—	2	2	no	—
143	C₂×C₄⋊C₄	—	86	1	no	—
144	C₂×C₄⋊C₄	—	86	1	no	—
145	C₂×C₄⋊C₄	D₁₇₂	1	2	yes	—
146	C₂×C₄⋊C₄	C₂²⋊D₄₃	1	1	yes	characteristic
147	C₂×C₄²	—	86	2	no	—
148	C₂×C₄²	—	86	1	no	—
149	C₂×C₄²	C₄×D₄₃	1	2	yes	—
150	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
151	C₄⋊C₈	—	2	2	no	—
152	C₄⋊C₈	—	2	2	no	—
153	C₄⋊C₈	—	86	2	no	—
154	#101	—	4	2	no	—
155	C₂²⋊C₈	—	86	2	no	—
156	C₄×C₈	—	86	2	no	—
157	#95	—	43	1	no	—
158	#95	—	43	2	no	—
159	#95	—	43	1	no	—
160	#95	—	86	2	no	—
161	#95	—	86	2	no	—
162	#95	—	86	2	no	—
163	#95	—	86	1	no	—
164	C₂×Q₈	—	2	2	no	—
165	C₂×Q₈	—	2	2	no	—
166	C₂×Q₈	—	2	1	no	—
167	C₂×Q₈	—	2	1	no	—
168	C₂²×C₄	—	86	1	no	—
169	C₂²×C₄	—	86	2	no	—
170	C₂²×C₄	—	86	1	no	—
171	C₂²×C₄	(C₂×D₄₃)⋊C₄	1	2	yes	—
172	C₂²×C₄	(C₂×D₄₃)⋊C₄	1	2	yes	—
173	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
174	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
175	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
176	M₁₆	—	4	2	no	—
177	M₁₆	—	4	2	no	—
178	C₂×C₈	—	4	2	no	—
179	C₂×C₈	—	172	2	no	—
180	C₄⋊C₄	—	2	2	no	—
181	C₄⋊C₄	—	2	4	no	—
182	C₄⋊C₄	—	172	2	no	—
183	C₄⋊C₄	—	172	1	no	—
184	C₄⋊C₄	—	172	1	no	—
185	C₄²	—	2	2	no	—
186	C₄²	—	2	2	no	—
187	C₄²	—	172	4	no	—
188	C₄²	—	172	2	no	—
189	C₄²	#10621900	1	2	yes	—
190	C₄²	#10621900	1	2	yes	—
191	C₂³	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
192	Q₈	—	4	2	no	—
193	Q₈	—	4	2	no	—
194	C₂×C₄	—	2	2	no	—
195	C₂×C₄	—	2	2	no	—
196	C₂×C₄	—	2	2	no	—
197	C₂×C₄	—	2	2	no	—
198	C₂×C₄	—	4	1	no	—
199	C₂×C₄	—	4	1	no	—
200	C₂×C₄	—	4	2	no	—
201	C₂×C₄	—	86	2	no	—
202	C₂×C₄	—	172	2	no	—
203	C₂×C₄	—	172	1	no	—
204	C₂×C₄	—	172	2	no	—
205	C₂×C₄	—	172	1	no	—
206	C₂×C₄	—	172	1	no	—
207	C₂×C₄	—	172	2	no	—
208	C₂×C₄	—	172	1	no	—
209	C₂×C₄	—	172	1	no	—
210	C₂×C₄	#13063281	1	1	yes	characteristic
211	C₂×C₄	#13063281	1	1	yes	characteristic
212	C₂×C₄	#13063306	1	2	yes	—
213	C₂×C₄	#13063309	1	2	yes	—
214	C₂×C₄	#13063345	1	2	yes	—
215	C₂×C₄	#13063351	1	1	yes	characteristic
216	C₂×C₄	#13063356	1	1	yes	characteristic
217	C₈	—	8	2	no	—
218	C₈	—	344	2	no	—
219	C₂²	—	2	1	no	—
220	C₂²	—	2	1	no	—
221	C₂²	#14582760	1	1	yes	characteristic
222	C₂²	#14582893	1	1	yes	characteristic
223	C₂²	#14582898	1	1	yes	characteristic
224	C₄	—	2	2	no	—
225	C₄	—	2	1	no	—
226	C₄	—	2	1	no	—
227	C₄	—	4	2	no	—
228	C₄	—	4	2	no	—
229	C₄	—	344	2	no	—
230	C₄	—	344	1	no	—
231	C₄	—	172	2	no	—
232	C₄	#14583220	1	2	yes	—
233	C₄	#14583237	1	2	yes	—
234	C₂	—	2	1	no	—
235	C₂	—	2	1	no	—
236	C₂	#19134687	1	1	yes	characteristic
237	C₂	#19134700	1	1	yes	characteristic
238	C₂	#19134707	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#19137560

C₂

yes

maximal, characteristic

#19132919

C₂

yes

maximal, characteristic

#19132496

C₂

yes

maximal

#19132455

C₂

yes

maximal

C₄₃×#1801

C₂

yes

maximal, characteristic

#14582952

C₂²

yes

—

#14582806

—

#14582785

—

#14582767

C₄

yes

—

#14582765

C₂²

yes

characteristic

C₄⋊C₄×Dic₄₃

—

C₄×C₄⋊Dic₄₃

C₂²

yes

characteristic

#14582745

C₄

yes

—

#14582625

—

C₂×C₄×Q₈×C₄₃

C₂²

yes

characteristic

C₄₃×#423

C₂²

yes

—

C₂×#101×C₄₃

—

C₄₃×#343

—

C₂×C₄⋊Dic₄₃

—

C₂×C₄⋊Dic₄₃

—

C₂×C₄×Dic₄₃

—

C₂×C₄×Dic₄₃

—

C₄⋊(C₄₃⋊C₈)

—

C₂²⋊(C₄₃⋊C₈)

—

C₄×C₄₃⋊C₈

—

C₄₃⋊#95

—

C₄₃⋊#95

—

C₄₃⋊#95

—

C₄₃⋊#95

—

C₄₃⋊#95

C₂×C₄

yes

characteristic

C₄₃⋊#95

C₂×C₄

yes

—

C₄₃⋊#95

C₂×C₄

yes

characteristic

C₂²×Q₈×C₄₃

D₄

yes

characteristic

C₂×M₁₆×C₄₃

—

C₄×Q₈×C₄₃

—

C₄×Q₈×C₄₃

—

C₂×C₄⋊C₄×C₄₃

D₄

yes

—

C₂×C₄⋊C₄×C₄₃

D₄

yes

characteristic

C₂×C₄²×C₄₃

C₂×C₄

yes

—

C₂×C₄²×C₄₃

C₂³

yes

characteristic

C₄⋊C₈×C₄₃

—

C₄⋊C₈×C₄₃

—

#101×C₄₃

—

C₂×Q₈×C₄₃

—

C₂×Q₈×C₄₃

—

C₂×Q₈×C₄₃

—

C₂×Q₈×C₄₃

—

C₂²×C₄×C₄₃

C₂²⋊C₄

yes

—

C₂²×C₄×C₄₃

C₂²⋊C₄

yes

—

C₂²×C₄×C₄₃

C₂²×C₄

yes

characteristic

C₂²×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂²×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂²×Dic₄₃

—

C₂²×Dic₄₃

—

C₂²×Dic₄₃

—

M₁₆×C₄₃

—

M₁₆×C₄₃

—

C₂×C₈×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄²×C₄₃

—

C₄²×C₄₃

—

C₄²×C₄₃

#41

yes

—

C₄²×C₄₃

#41

yes

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄×Dic₄₃

—

C₄×Dic₄₃

—

C₂×C₄₃⋊C₈

—

C₂³×C₄₃

C₂×C₂²⋊C₄

yes

characteristic

Q₈×C₄₃

—

Q₈×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

yes

C₂×C₄×C₄₃

yes

C₂×C₄×C₄₃

yes

—

C₂×C₄×C₄₃

#123

yes

—

C₂×C₄×C₄₃

#135

yes

—

C₂×C₄×C₄₃

yes

C₂×C₄×C₄₃

yes

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₈×C₄₃

—

C₄₃⋊C₈

—

#8769

—

maximal, Sylow

100

C₂²×C₄₃

—

101

C₂²×C₄₃

—

102

C₂²×C₄₃

#381

yes

characteristic

103

C₂²×C₄₃

#416

yes

characteristic

104

C₂²×C₄₃

#417

yes

characteristic

105

C₄×C₄₃

—

106

C₄×C₄₃

—

107

C₄×C₄₃

—

108

C₄×C₄₃

—

109

C₄×C₄₃

—

110

C₄×C₄₃

#482

yes

—

111

C₄×C₄₃

#485

yes

—

112

Dic₄₃

—

113

Dic₄₃

—

114

Dic₄₃

—

115

#2356

—

116

#1801

D₄₃

yes

characteristic

117

#1461

—

118

#1303

—

119

#1286

—

120

C₂×C₄₃

—

121

C₂×C₄₃

—

122

C₂×C₄₃

#1825

yes

characteristic

123

C₂×C₄₃

#1827

yes

characteristic

124

C₂×C₄₃

#1830

yes

characteristic

125

C₂×C₄×Q₈

C₂×D₄₃

yes

characteristic

126

#431

—

127

#423

C₂×D₄₃

yes

—

128

C₂×#101

—

129

#391

—

130

#387

—

131

#383

—

132

#382

—

133

C₄×C₄⋊C₄

—

134

C₄×C₄⋊C₄

—

135

#376

—

136

#343

—

137

#324

—

138

C₄₃

#8769

yes

characteristic, complemented, Sylow

139

C₂²×Q₈

C₂²⋊D₄₃

yes

characteristic

140

C₂×M₁₆

—

141

C₄×Q₈

—

142

C₄×Q₈

—

143

C₂×C₄⋊C₄

—

144

C₂×C₄⋊C₄

—

145

C₂×C₄⋊C₄

D₁₇₂

yes

—

146

C₂×C₄⋊C₄

C₂²⋊D₄₃

yes

characteristic

147

C₂×C₄²

—

148

C₂×C₄²

—

149

C₂×C₄²

C₄×D₄₃

yes

—

150

C₂×C₄²

C₂²×D₄₃

yes

characteristic

151

C₄⋊C₈

—

152

C₄⋊C₈

—

153

C₄⋊C₈

—

154

#101

—

155

C₂²⋊C₈

—

156

C₄×C₈

—

157

#95

—

158

#95

—

159

#95

—

160

#95

—

161

#95

—

162

#95

—

163

#95

—

164

C₂×Q₈

—

165

C₂×Q₈

—

166

C₂×Q₈

—

167

C₂×Q₈

—

168

C₂²×C₄

—

169

C₂²×C₄

—

170

C₂²×C₄

—

171

C₂²×C₄

(C₂×D₄₃)⋊C₄

yes

—

172

C₂²×C₄

(C₂×D₄₃)⋊C₄

yes

—

173

C₂²×C₄

C₂×C₄×D₄₃

yes

characteristic

174

C₂²×C₄

C₂×D₁₇₂

yes

characteristic

175

C₂²×C₄

C₂×C₂²⋊D₄₃

yes

characteristic

176

M₁₆

—

177

M₁₆

—

178

C₂×C₈

—

179

C₂×C₈

—

172

—

180

C₄⋊C₄

—

181

C₄⋊C₄

—

182

C₄⋊C₄

—

172

—

183

C₄⋊C₄

—

172

—

184

C₄⋊C₄

—

172

—

185

C₄²

—

186

C₄²

—

187

C₄²

—

172

—

188

C₄²

—

172

—

189

C₄²

#10621900

yes

—

190

C₄²

#10621900

yes

—

191

C₂³

C₂×(C₂×D₄₃)⋊C₄

yes

characteristic

192

Q₈

—

193

Q₈

—

194

C₂×C₄

—

195

C₂×C₄

—

196

C₂×C₄

—

197

C₂×C₄

—

198

C₂×C₄

—

199

C₂×C₄

—

200

C₂×C₄

—

201

C₂×C₄

—

202

C₂×C₄

—

172

—

203

C₂×C₄

—

172

—

204

C₂×C₄

—

172

—

205

C₂×C₄

—

172

—

206

C₂×C₄

—

172

—

207

C₂×C₄

—

172

—

208

C₂×C₄

—

172

—

209

C₂×C₄

—

172

—

210

C₂×C₄

#13063281

yes

characteristic

211

C₂×C₄

#13063281

yes

characteristic

212

C₂×C₄

#13063306

yes

—

213

C₂×C₄

#13063309

yes

—

214

C₂×C₄

#13063345

yes

—

215

C₂×C₄

#13063351

yes

characteristic

216

C₂×C₄

#13063356

yes

characteristic

217

C₈

—

218

C₈

—

344

—

219

C₂²

—

220

C₂²

—

221

C₂²

#14582760

yes

characteristic

222

C₂²

#14582893

yes

characteristic

223

C₂²

#14582898

yes

characteristic

224

C₄

—

225

C₄

—

226

C₄

—

227

C₄

—

228

C₄

—

229

C₄

—

344

—

230

C₄

—

344

—

231

C₄

—

172

—

232

C₄

#14583220

yes

—

233

C₄

#14583237

yes

—

234

C₂

—

235

C₂

—

236

C₂

#19134687

yes

characteristic

237

C₂

#19134700

yes

characteristic

238

C₂

#19134707

yes

characteristic

	subgroup	G/H
center	C₂²	#14582760
commutator	C₂²×C₄×C₄₃	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₄₃
Fitting	C₄₃×#1801	C₂
socle	C₂²×C₄₃	#381
prime radical	C₂³×C₄₃	C₂×C₂²⋊C₄
cosocle	C₂×C₄²×C₄₃	C₂³
hypercenter	#1801	D₄₃
hypocenter	C₄₃	#8769
LCS	G ▷ C₂²×C₄×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1801

subgroup

G/H

center

C₂²

#14582760

commutator

C₂²×C₄×C₄₃

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₄₃

Fitting

C₄₃×#1801

C₂

socle

C₂²×C₄₃

#381

prime radical

C₂³×C₄₃

C₂×C₂²⋊C₄

cosocle

C₂×C₄²×C₄₃

C₂³

D₄₃

C₄₃

G ▷ C₂²×C₄×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1801

N	H ≅ G/N	type
138. C₄₃	#8769	semidirect

H ≅ G/N

type

138. C₄₃

#8769

semidirect

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

subgroup	index
#19137560	2
#19132919	2
#19132496	2
#19132455	2
C₄₃×#1801	2
#8769	43

subgroup

index

C₄₃×#1801

Subgroups — #24990185

Conjugacy classes of subgroups

Complements

Maximal subgroups