Group #25001629 — subgroups

Subgroups — #25001629

Order 11008.

316 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 95 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	#19135577	C₂	1	1	yes	maximal, characteristic
2	#19134748	C₂	1	1	yes	maximal, characteristic
3	#19133366	C₂	1	1	yes	maximal, characteristic
4	#19133365	C₂	1	1	yes	maximal, characteristic
5	#19132998	C₂	1	1	yes	maximal, characteristic
6	#19132423	C₂	1	1	yes	maximal, characteristic
7	C₄₃×#1481	C₂	1	1	yes	maximal, characteristic
8	#14582952	C₂²	1	1	yes	characteristic
9	#14582923	C₂²	1	1	yes	characteristic
10	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
11	C₂×Dic₄₃⋊C₈	—	2	2	no	—
12	#14582745	C₂²	1	1	yes	characteristic
13	#14582658	—	2	2	no	—
14	#14582650	—	2	2	no	—
15	#14582649	—	2	2	no	—
16	Q₈⋊(C₄₃⋊C₈)	—	2	2	no	—
17	C₄₃×#533	C₂²	1	1	yes	characteristic
18	C₄₃×#431	C₂²	1	1	yes	characteristic
19	C₂×C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
20	C₄₃×Q₈⋊C₈	—	2	2	no	—
21	C₂×#10621877	—	2	1	no	—
22	C₂²×C₄₃⋊C₈	—	2	1	no	—
23	C₂×C₄×Dic₄₃	D₄	1	2	yes	—
24	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
25	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
26	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
27	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
28	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
29	Dic₄₃⋊C₈	—	4	4	no	—
30	C₂²⋊(C₄₃⋊C₈)	—	2	1	no	—
31	C₄×C₄₃⋊C₈	D₄	1	2	yes	—
32	C₄₃⋊#95	—	2	1	no	—
33	C₄₃⋊#95	—	2	1	no	—
34	C₂²×C₈×C₄₃	—	2	1	no	—
35	C₄⋊Q₈×C₄₃	Q₈	1	1	yes	characteristic
36	C₄⋊Q₈×C₄₃	Q₈	1	1	yes	characteristic
37	#125×C₄₃	—	2	1	no	—
38	C₂²⋊Q₈×C₄₃	—	2	1	no	—
39	C₂²⋊Q₈×C₄₃	—	2	1	no	—
40	C₄×Q₈×C₄₃	—	2	1	no	—
41	C₄×Q₈×C₄₃	—	2	1	no	—
42	#117×C₄₃	—	2	1	no	—
43	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
44	C₄⋊C₈×C₄₃	—	2	1	no	—
45	C₄⋊C₈×C₄₃	—	2	1	no	—
46	C₄⋊C₈×C₄₃	—	2	1	no	—
47	C₂²⋊C₈×C₄₃	—	2	1	no	—
48	C₄×C₈×C₄₃	D₄	1	2	yes	—
49	C₂×Q₈×C₄₃	—	2	1	no	—
50	C₂×Q₈×C₄₃	—	2	1	no	—
51	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
52	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
53	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
54	C₂²×Dic₄₃	—	2	2	no	—
55	C₂×C₈×C₄₃	—	2	2	no	—
56	C₂×C₈×C₄₃	—	4	1	no	—
57	C₂×C₈×C₄₃	—	4	2	no	—
58	C₄⋊C₄×C₄₃	—	2	1	no	—
59	C₄⋊C₄×C₄₃	—	2	1	no	—
60	C₄⋊C₄×C₄₃	—	2	1	no	—
61	C₄⋊C₄×C₄₃	—	2	1	no	—
62	C₄⋊C₄×C₄₃	—	4	1	no	—
63	C₄⋊C₄×C₄₃	—	4	1	no	—
64	C₂²⋊C₄×C₄₃	—	4	1	no	—
65	C₄²×C₄₃	—	4	1	no	—
66	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
67	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
68	C₄²×C₄₃	C₂×Q₈	1	1	yes	characteristic
69	C₄²×C₄₃	#41	1	1	yes	characteristic
70	C₄×Dic₄₃	—	2	2	no	—
71	C₄×Dic₄₃	SD₁₆	1	4	yes	—
72	#10621877	—	4	2	no	—
73	C₂×C₄₃⋊C₈	—	2	2	no	—
74	C₂×C₄₃⋊C₈	—	4	1	no	—
75	C₂×C₄₃⋊C₈	—	4	1	no	—
76	C₂×C₄₃⋊C₈	—	4	2	no	—
77	C₂³×C₄₃	#123	1	1	yes	characteristic
78	Q₈×C₄₃	—	4	2	no	—
79	Q₈×C₄₃	—	4	2	no	—
80	C₂×C₄×C₄₃	—	4	1	no	—
81	C₂×C₄×C₄₃	—	4	1	no	—
82	C₂×C₄×C₄₃	—	4	1	no	—
83	C₂×C₄×C₄₃	—	4	1	no	—
84	C₂×C₄×C₄₃	C₂²⋊Q₈	1	1	yes	characteristic
85	C₂×C₄×C₄₃	C₂²⋊Q₈	1	1	yes	characteristic
86	C₂×C₄×C₄₃	C₂²⋊Q₈	1	1	yes	characteristic
87	C₂×C₄×C₄₃	#123	1	1	yes	characteristic
88	C₂×C₄×C₄₃	#123	1	1	yes	characteristic
89	C₂×C₄×C₄₃	#127	1	1	yes	characteristic
90	C₂×C₄×C₄₃	C₂×SD₁₆	1	2	yes	—
91	C₂×C₄×C₄₃	#137	1	2	yes	—
92	C₂×Dic₄₃	—	2	4	no	—
93	C₂×Dic₄₃	—	4	2	no	—
94	C₂×Dic₄₃	—	4	2	no	—
95	C₈×C₄₃	—	4	2	no	—
96	C₈×C₄₃	—	8	1	no	—
97	C₄₃⋊C₈	—	4	2	no	—
98	C₄₃⋊C₈	—	8	1	no	—
99	C₄₃⋊C₈	—	8	1	no	—
100	#10670	—	43	1	no	maximal, Sylow
101	C₂²×C₄₃	—	2	1	no	—
102	C₂²×C₄₃	—	2	1	no	—
103	C₂²×C₄₃	#399	1	1	yes	characteristic
104	C₂²×C₄₃	#483	1	2	yes	—
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	—	8	1	no	—
110	C₄×C₄₃	—	8	1	no	—
111	C₄×C₄₃	#475	1	2	yes	—
112	C₄×C₄₃	#492	1	1	yes	characteristic
113	C₄×C₄₃	#497	1	1	yes	characteristic
114	Dic₄₃	—	4	4	no	—
115	#1995	—	43	1	no	—
116	#1843	—	43	1	no	—
117	#1570	—	43	1	no	—
118	#1570	—	43	1	no	—
119	#1481	—	43	1	no	—
120	#1481	D₄₃	1	1	yes	characteristic
121	#1274	—	43	1	no	—
122	C₂×C₄₃	—	2	2	no	—
123	C₂×C₄₃	#2096	1	1	yes	characteristic
124	C₂×C₄₃	#2098	1	1	yes	characteristic
125	C₂×C₄₃	#2098	1	1	yes	characteristic
126	#533	C₂×D₄₃	1	1	yes	characteristic
127	#431	—	43	1	no	—
128	#431	C₂×D₄₃	1	1	yes	characteristic
129	#423	—	43	1	no	—
130	C₂×C₄⋊C₈	—	43	1	no	—
131	C₂×C₄⋊C₈	—	86	2	no	—
132	C₂×C₄⋊C₈	C₂×D₄₃	1	1	yes	characteristic
133	#376	—	43	1	no	—
134	#339	—	86	2	no	—
135	#334	—	86	2	no	—
136	#334	—	86	2	no	—
137	Q₈⋊C₈	—	2	2	no	—
138	Q₈⋊C₈	—	86	2	no	—
139	C₄₃	#10670	1	1	yes	characteristic, complemented, Sylow
140	C₂×M₁₆	—	86	1	no	—
141	C₂²×C₈	—	2	1	no	—
142	C₂²×C₈	—	86	1	no	—
143	C₄⋊Q₈	Dic₈₆	1	1	yes	characteristic
144	C₄⋊Q₈	Dic₈₆	1	1	yes	characteristic
145	#125	—	2	1	no	—
146	C₂²⋊Q₈	—	2	1	no	—
147	C₂²⋊Q₈	—	2	1	no	—
148	C₄×Q₈	—	2	1	no	—
149	C₄×Q₈	—	2	1	no	—
150	#117	—	2	1	no	—
151	C₂×C₄²	—	43	2	no	—
152	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
153	C₄⋊C₈	—	2	1	no	—
154	C₄⋊C₈	—	2	1	no	—
155	C₄⋊C₈	—	2	1	no	—
156	C₄⋊C₈	—	86	1	no	—
157	C₄⋊C₈	—	86	1	no	—
158	C₄⋊C₈	—	86	1	no	—
159	C₄⋊C₈	—	86	1	no	—
160	C₄⋊C₈	—	86	1	no	—
161	C₄⋊C₈	—	172	4	no	—
162	C₂²⋊C₈	—	2	1	no	—
163	C₂²⋊C₈	—	86	1	no	—
164	C₄×C₈	—	43	2	no	—
165	C₄×C₈	C₂²⋊D₄₃	1	2	yes	—
166	#95	—	86	1	no	—
167	#95	—	86	1	no	—
168	C₂×Q₈	—	2	1	no	—
169	C₂×Q₈	—	2	1	no	—
170	C₂²×C₄	—	86	2	no	—
171	C₂²×C₄	#10621898	1	1	yes	characteristic
172	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
173	C₂²×C₄	#10621900	1	1	yes	characteristic
174	M₁₆	—	172	2	no	—
175	C₂×C₈	—	2	2	no	—
176	C₂×C₈	—	4	1	no	—
177	C₂×C₈	—	4	2	no	—
178	C₂×C₈	—	86	2	no	—
179	C₂×C₈	—	172	1	no	—
180	C₂×C₈	—	172	1	no	—
181	C₂×C₈	—	172	2	no	—
182	C₄⋊C₄	—	2	1	no	—
183	C₄⋊C₄	—	2	1	no	—
184	C₄⋊C₄	—	2	1	no	—
185	C₄⋊C₄	—	2	1	no	—
186	C₄⋊C₄	—	4	1	no	—
187	C₄⋊C₄	—	4	1	no	—
188	C₂²⋊C₄	—	4	1	no	—
189	C₄²	—	4	1	no	—
190	C₄²	—	43	4	no	—
191	C₄²	—	86	2	no	—
192	C₄²	C₂×Dic₈₆	1	1	yes	characteristic
193	C₄²	D₄×D₄₃	1	1	yes	characteristic
194	C₄²	#10621900	1	1	yes	characteristic
195	C₄²	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
196	C₂³	#13063307	1	1	yes	characteristic
197	Q₈	—	4	2	no	—
198	Q₈	—	4	2	no	—
199	C₂×C₄	—	4	1	no	—
200	C₂×C₄	—	4	1	no	—
201	C₂×C₄	—	4	1	no	—
202	C₂×C₄	—	4	1	no	—
203	C₂×C₄	—	86	4	no	—
204	C₂×C₄	—	172	2	no	—
205	C₂×C₄	—	172	2	no	—
206	C₂×C₄	#13063302	1	1	yes	characteristic
207	C₂×C₄	#13063302	1	1	yes	characteristic
208	C₂×C₄	#13063304	1	1	yes	characteristic
209	C₂×C₄	#13063306	1	1	yes	characteristic
210	C₂×C₄	#13063307	1	1	yes	characteristic
211	C₂×C₄	#13063321	1	1	yes	characteristic
212	C₂×C₄	SD₁₆×D₄₃	1	2	yes	—
213	C₂×C₄	#13063357	1	2	yes	—
214	C₈	—	4	2	no	—
215	C₈	—	8	1	no	—
216	C₈	—	344	1	no	—
217	C₈	—	344	1	no	—
218	C₈	—	172	2	no	—
219	C₂²	—	2	1	no	—
220	C₂²	—	2	1	no	—
221	C₂²	#14582835	1	1	yes	characteristic
222	C₂²	#14583228	1	2	yes	—
223	C₄	—	2	1	no	—
224	C₄	—	2	1	no	—
225	C₄	—	2	1	no	—
226	C₄	—	2	1	no	—
227	C₄	—	8	1	no	—
228	C₄	—	8	1	no	—
229	C₄	—	172	4	no	—
230	C₄	#14583182	1	2	yes	—
231	C₄	#14583270	1	1	yes	characteristic
232	C₄	#14583292	1	1	yes	characteristic
233	C₂	—	2	2	no	—
234	C₂	#19136136	1	1	yes	characteristic
235	C₂	#19136148	1	1	yes	characteristic
236	C₂	#19136150	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#19135577

C₂

yes

maximal, characteristic

#19134748

C₂

yes

maximal, characteristic

#19133366

C₂

yes

maximal, characteristic

#19133365

C₂

yes

maximal, characteristic

#19132998

C₂

yes

maximal, characteristic

#19132423

C₂

yes

maximal, characteristic

C₄₃×#1481

C₂

yes

maximal, characteristic

#14582952

C₂²

yes

characteristic

#14582923

C₂²

yes

characteristic

C₂×C₄⋊(C₄₃⋊C₈)

C₂²

yes

characteristic

C₂×Dic₄₃⋊C₈

—

#14582745

C₂²

yes

—

—

—

Q₈⋊(C₄₃⋊C₈)

—

C₄₃×#533

C₂²

yes

characteristic

C₄₃×#431

C₂²

yes

characteristic

C₂×C₄⋊C₈×C₄₃

C₂²

yes

characteristic

C₄₃×Q₈⋊C₈

—

C₂×#10621877

—

C₂²×C₄₃⋊C₈

—

C₂×C₄×Dic₄₃

D₄

yes

—

C₄⋊(C₄₃⋊C₈)

—

C₄⋊(C₄₃⋊C₈)

—

C₄⋊(C₄₃⋊C₈)

—

C₄⋊(C₄₃⋊C₈)

—

C₄⋊(C₄₃⋊C₈)

—

Dic₄₃⋊C₈

—

C₂²⋊(C₄₃⋊C₈)

—

C₄×C₄₃⋊C₈

D₄

yes

—

C₄₃⋊#95

—

C₄₃⋊#95

—

C₂²×C₈×C₄₃

—

C₄⋊Q₈×C₄₃

Q₈

yes

characteristic

C₄⋊Q₈×C₄₃

Q₈

yes

characteristic

#125×C₄₃

—

C₂²⋊Q₈×C₄₃

—

C₂²⋊Q₈×C₄₃

—

C₄×Q₈×C₄₃

—

C₄×Q₈×C₄₃

—

#117×C₄₃

—

C₂×C₄²×C₄₃

C₂³

yes

characteristic

C₄⋊C₈×C₄₃

—

C₄⋊C₈×C₄₃

—

C₄⋊C₈×C₄₃

—

C₂²⋊C₈×C₄₃

—

C₄×C₈×C₄₃

D₄

yes

—

C₂×Q₈×C₄₃

—

C₂×Q₈×C₄₃

—

C₂²×C₄×C₄₃

C₂×D₄

yes

C₂²×C₄×C₄₃

yes

C₂²×C₄×C₄₃

yes

C₂²×Dic₄₃

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

C₂²⋊C₄×C₄₃

—

C₄²×C₄₃

—

C₄²×C₄₃

C₂×D₄

yes

characteristic

C₄²×C₄₃

C₂×D₄

yes

characteristic

C₄²×C₄₃

C₂×Q₈

yes

characteristic

C₄²×C₄₃

#41

yes

characteristic

C₄×Dic₄₃

—

C₄×Dic₄₃

SD₁₆

yes

—

#10621877

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂³×C₄₃

#123

yes

characteristic

Q₈×C₄₃

—

Q₈×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂²⋊Q₈

yes

characteristic

C₂×C₄×C₄₃

C₂²⋊Q₈

yes

characteristic

C₂×C₄×C₄₃

C₂²⋊Q₈

yes

C₂×C₄×C₄₃

yes

C₂×C₄×C₄₃

yes

C₂×C₄×C₄₃

yes

C₂×C₄×C₄₃

C₂×SD₁₆

yes

—

C₂×C₄×C₄₃

#137

yes

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₈×C₄₃

—

C₈×C₄₃

—

C₄₃⋊C₈

—

C₄₃⋊C₈

—

C₄₃⋊C₈

—

100

#10670

—

maximal, Sylow

101

C₂²×C₄₃

—

102

C₂²×C₄₃

—

103

C₂²×C₄₃

#399

yes

characteristic

104

C₂²×C₄₃

#483

yes

—

105

C₄×C₄₃

—

106

C₄×C₄₃

—

107

C₄×C₄₃

—

108

C₄×C₄₃

—

109

C₄×C₄₃

—

110

C₄×C₄₃

—

111

C₄×C₄₃

#475

yes

—

112

C₄×C₄₃

#492

yes

characteristic

113

C₄×C₄₃

#497

yes

characteristic

114

Dic₄₃

—

115

#1995

—

116

#1843

—

117

#1570

—

118

#1570

—

119

#1481

—

120

#1481

D₄₃

yes

characteristic

121

#1274

—

122

C₂×C₄₃

—

123

C₂×C₄₃

#2096

yes

characteristic

124

C₂×C₄₃

#2098

yes

characteristic

125

C₂×C₄₃

#2098

yes

characteristic

126

#533

C₂×D₄₃

yes

characteristic

127

#431

—

128

#431

C₂×D₄₃

yes

characteristic

129

#423

—

130

C₂×C₄⋊C₈

—

131

C₂×C₄⋊C₈

—

132

C₂×C₄⋊C₈

C₂×D₄₃

yes

characteristic

133

#376

—

134

#339

—

135

#334

—

136

#334

—

137

Q₈⋊C₈

—

138

Q₈⋊C₈

—

139

C₄₃

#10670

yes

characteristic, complemented, Sylow

140

C₂×M₁₆

—

141

C₂²×C₈

—

142

C₂²×C₈

—

143

C₄⋊Q₈

Dic₈₆

yes

characteristic

144

C₄⋊Q₈

Dic₈₆

yes

characteristic

145

#125

—

146

C₂²⋊Q₈

—

147

C₂²⋊Q₈

—

148

C₄×Q₈

—

149

C₄×Q₈

—

150

#117

—

151

C₂×C₄²

—

152

C₂×C₄²

C₂²×D₄₃

yes

characteristic

153

C₄⋊C₈

—

154

C₄⋊C₈

—

155

C₄⋊C₈

—

156

C₄⋊C₈

—

157

C₄⋊C₈

—

158

C₄⋊C₈

—

159

C₄⋊C₈

—

160

C₄⋊C₈

—

161

C₄⋊C₈

—

172

—

162

C₂²⋊C₈

—

163

C₂²⋊C₈

—

164

C₄×C₈

—

165

C₄×C₈

C₂²⋊D₄₃

yes

—

166

#95

—

167

#95

—

168

C₂×Q₈

—

169

C₂×Q₈

—

170

C₂²×C₄

—

171

C₂²×C₄

#10621898

yes

characteristic

172

C₂²×C₄

D₄×D₄₃

yes

characteristic

173

C₂²×C₄

#10621900

yes

characteristic

174

M₁₆

—

172

—

175

C₂×C₈

—

176

C₂×C₈

—

177

C₂×C₈

—

178

C₂×C₈

—

179

C₂×C₈

—

172

—

180

C₂×C₈

—

172

—

181

C₂×C₈

—

172

—

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

—

191

C₄²

—

192

C₄²

C₂×Dic₈₆

yes

characteristic

193

C₄²

D₄×D₄₃

yes

characteristic

194

C₄²

#10621900

yes

characteristic

195

C₄²

C₂×C₂²⋊D₄₃

yes

characteristic

196

C₂³

#13063307

yes

characteristic

197

Q₈

—

198

Q₈

—

199

C₂×C₄

—

200

C₂×C₄

—

201

C₂×C₄

—

202

C₂×C₄

—

203

C₂×C₄

—

204

C₂×C₄

—

172

—

205

C₂×C₄

—

172

—

206

C₂×C₄

#13063302

yes

characteristic

207

C₂×C₄

#13063302

yes

characteristic

208

C₂×C₄

#13063304

yes

characteristic

209

C₂×C₄

#13063306

yes

characteristic

210

C₂×C₄

#13063307

yes

characteristic

211

C₂×C₄

#13063321

yes

characteristic

212

C₂×C₄

SD₁₆×D₄₃

yes

—

213

C₂×C₄

#13063357

yes

—

214

C₈

—

215

C₈

—

216

C₈

—

344

—

217

C₈

—

344

—

218

C₈

—

172

—

219

C₂²

—

220

C₂²

—

221

C₂²

#14582835

yes

characteristic

222

C₂²

#14583228

yes

—

223

C₄

—

224

C₄

—

225

C₄

—

226

C₄

—

227

C₄

—

228

C₄

—

229

C₄

—

172

—

230

C₄

#14583182

yes

—

231

C₄

#14583270

yes

characteristic

232

C₄

#14583292

yes

characteristic

233

C₂

—

234

C₂

#19136136

yes

characteristic

235

C₂

#19136148

yes

characteristic

236

C₂

#19136150

yes

characteristic

	subgroup	G/H
center	C₂×C₄	#13063321
commutator, cosocle	C₂×C₄²×C₄₃	C₂³
Frattini	C₂×C₄²	C₂²×D₄₃
Fitting	C₄₃×#1481	C₂
socle	C₂²×C₄₃	#399
prime radical	C₂³×C₄₃	#123
hypercenter	#1481	D₄₃
hypocenter	C₄₃	#10670
LCS	G ▷ C₂×C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1481

subgroup

G/H

center

C₂×C₄

#13063321

commutator, cosocle

C₂×C₄²×C₄₃

C₂³

Frattini

C₂×C₄²

C₂²×D₄₃

Fitting

C₄₃×#1481

C₂

C₂²×C₄₃

C₂³×C₄₃

D₄₃

C₄₃

G ▷ C₂×C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1481

N	H ≅ G/N	type
139. C₄₃	#10670	semidirect

H ≅ G/N

type

139. C₄₃

#10670

semidirect

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

subgroup	index
#19135577	2
#19134748	2
#19133366	2
#19133365	2
#19132998	2
#19132423	2
C₄₃×#1481	2
#10670	43

subgroup

index

C₄₃×#1481

Subgroups — #25001629

Conjugacy classes of subgroups

Complements

Maximal subgroups