Group #26031494 — subgroups

Subgroups — #26031494

Order 11392.

328 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 328 conjugacy classes of subgroups — too many to draw. Only its 117 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	#19152155	C₂	1	1	yes	maximal, characteristic, complemented
2	#19152132	C₂	1	1	yes	maximal, characteristic
3	#19152007	C₂	1	1	yes	maximal, characteristic, complemented
4	#19152007	C₂	1	1	yes	maximal, characteristic, complemented
5	#19151958	C₂	1	1	yes	maximal, characteristic, complemented
6	#19151958	C₂	1	1	yes	maximal, characteristic, complemented
7	#19151940	C₂	1	2	yes	maximal, complemented
8	#19151923	C₂	1	2	yes	maximal
9	#19151906	C₂	1	2	yes	maximal, complemented
10	#19151899	C₂	1	2	yes	maximal, complemented
11	#432×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
12	#15668012	C₂²	1	1	yes	characteristic
13	#15668012	C₂²	1	1	yes	characteristic
14	#15668006	—	2	1	no	—
15	#15668004	C₂²	1	1	yes	characteristic
16	#15668004	C₂²	1	2	yes	—
17	#15668000	C₂²	1	1	yes	characteristic
18	#15667995	—	2	1	no	—
19	#15667991	—	2	1	no	—
20	#15667991	—	2	1	no	—
21	#15667991	C₂²	1	1	yes	characteristic
22	#15667986	C₂²	1	1	yes	characteristic
23	C₄×Dic₁₇₈	—	2	1	no	—
24	C₄×Dic₁₇₈	—	2	1	no	—
25	C₄×Dic₁₇₈	C₂²	1	1	yes	characteristic
26	C₄×D₃₅₆	C₂²	1	1	yes	characteristic
27	C₄×C₂²⋊D₈₉	—	2	1	no	—
28	#15667971	C₂²	1	2	yes	—
29	#15667969	—	2	1	no	—
30	#15667946	C₂²	1	2	yes	—
31	#15667946	C₂²	1	2	yes	—
32	#15667944	C₂²	1	2	yes	—
33	#15667944	C₂²	1	2	yes	—
34	#15667937	C₂²	1	2	yes	—
35	#15667937	C₂²	1	2	yes	—
36	#15667934	C₂²	1	2	yes	—
37	#15667934	C₂²	1	2	yes	—
38	C₂×C₄²×C₈₉	C₂²	1	1	yes	characteristic
39	C₄⋊C₈×C₈₉	C₂²	1	2	yes	—
40	C₂²⋊C₈×C₈₉	C₂²	1	2	yes	—
41	#97×C₈₉	C₂²	1	1	yes	characteristic
42	#97×C₈₉	C₂²	1	1	yes	characteristic
43	C₂×Dic₁₇₈	—	2	1	no	—
44	C₂×Dic₁₇₈	—	2	1	no	—
45	C₂×Dic₁₇₈	C₂³	1	1	yes	characteristic
46	C₂×D₃₅₆	C₂³	1	1	yes	characteristic
47	C₂×C₂²⋊D₈₉	—	2	1	no	—
48	C₂×C₄×D₈₉	—	2	1	no	—
49	C₄⋊Dic₈₉	—	2	1	no	—
50	C₄⋊Dic₈₉	—	2	1	no	—
51	C₄⋊Dic₈₉	C₂³	1	2	yes	—
52	C₄⋊Dic₈₉	C₂³	1	2	yes	—
53	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
54	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
55	#13083553	—	2	1	no	—
56	#13083553	—	2	1	no	—
57	#13083553	—	2	1	no	—
58	#13083553	—	2	2	no	—
59	#13083553	—	2	2	no	—
60	#13083553	—	2	1	no	—
61	C₂²⋊Dic₈₉	—	2	2	no	—
62	C₂²⋊Dic₈₉	—	2	1	no	—
63	#13083551	—	2	1	no	—
64	#13083551	—	2	1	no	—
65	#13083551	—	2	1	no	—
66	#13083551	—	2	1	no	—
67	C₄×Dic₈₉	—	2	1	no	—
68	C₄×Dic₈₉	—	2	2	no	—
69	C₂²×C₄×C₈₉	D₄	1	1	yes	characteristic
70	C₂²×C₄×C₈₉	D₄	1	1	yes	characteristic
71	C₂²×C₄×C₈₉	C₂³	1	1	yes	characteristic
72	C₂×C₈×C₈₉	C₂³	1	2	yes	—
73	C₂×C₈×C₈₉	C₂³	1	2	yes	—
74	C₄²×C₈₉	D₄	1	1	yes	characteristic
75	C₄²×C₈₉	D₄	1	1	yes	characteristic
76	C₄²×C₈₉	C₂³	1	1	yes	characteristic
77	C₄²×C₈₉	C₂³	1	1	yes	characteristic
78	C₂³×C₈₉	C₂×D₄	1	1	yes	characteristic
79	C₂²×D₈₉	—	2	1	no	—
80	C₂×C₄×C₈₉	—	2	2	no	—
81	C₂×C₄×C₈₉	—	4	1	no	—
82	C₂×C₄×C₈₉	—	4	1	no	—
83	C₂×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
84	C₂×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
85	C₂×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
86	C₂×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
87	C₂×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
88	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
89	C₂²⋊D₈₉	—	4	2	no	—
90	C₂×Dic₈₉	—	2	1	no	—
91	C₂×Dic₈₉	—	2	1	no	—
92	C₂×Dic₈₉	—	2	2	no	—
93	C₂×Dic₈₉	—	2	2	no	—
94	C₂×Dic₈₉	—	2	1	no	—
95	D₃₅₆	—	2	2	no	—
96	C₄×D₈₉	—	4	2	no	—
97	Dic₁₇₈	—	2	2	no	—
98	Dic₁₇₈	—	4	2	no	—
99	Dic₁₇₈	—	4	2	no	—
100	C₈×C₈₉	—	2	2	no	—
101	C₈×C₈₉	—	2	2	no	—
102	C₂²×C₈₉	—	2	1	no	—
103	C₂²×C₈₉	—	2	1	no	—
104	C₂²×C₈₉	—	2	1	no	—
105	C₂²×C₈₉	C₂²×D₄	1	1	yes	characteristic
106	C₂×D₈₉	—	4	1	no	—
107	C₂×D₈₉	—	4	1	no	—
108	C₂×D₈₉	—	4	1	no	—
109	C₄×C₈₉	—	2	1	no	—
110	C₄×C₈₉	—	2	1	no	—
111	C₄×C₈₉	—	2	1	no	—
112	C₄×C₈₉	—	2	1	no	—
113	C₄×C₈₉	—	2	1	no	—
114	C₄×C₈₉	2₋¹⁺⁴	1	2	yes	—
115	Dic₈₉	—	4	1	no	—
116	Dic₈₉	—	4	2	no	—
117	Dic₈₉	—	4	2	no	—
118	Dic₈₉	—	4	1	no	—
119	Dic₈₉	—	4	1	no	—
120	C₂×C₈₉	—	4	1	no	—
121	C₂×C₈₉	#536	1	1	yes	characteristic
122	C₂×C₈₉	#575	1	1	yes	characteristic
123	C₂×C₈₉	#575	1	1	yes	characteristic
124	D₈₉	—	8	1	no	—
125	#3240	—	89	1	no	maximal, Sylow
126	C₈₉	#3240	1	1	yes	characteristic, complemented, Sylow
127	#533	—	89	1	no	—
128	#529	—	89	1	no	—
129	#501	—	89	1	no	—
130	#501	—	89	1	no	—
131	#489	—	89	1	no	—
132	#489	—	89	1	no	—
133	#485	—	89	2	no	—
134	#482	—	89	2	no	—
135	#479	—	89	2	no	—
136	#478	—	89	2	no	—
137	#432	D₈₉	1	1	yes	characteristic, complemented
138	C₄⋊Q₈	—	89	1	no	—
139	C₄⋊Q₈	—	89	1	no	—
140	#126	—	178	1	no	—
141	#125	—	89	1	no	—
142	#125	—	89	2	no	—
143	#124	—	89	1	no	—
144	#123	—	178	1	no	—
145	C₂²⋊Q₈	—	89	1	no	—
146	C₂²⋊Q₈	—	178	1	no	—
147	C₂²⋊Q₈	—	178	1	no	—
148	#121	—	89	1	no	—
149	C₄×Q₈	—	89	1	no	—
150	C₄×Q₈	—	178	1	no	—
151	C₄×Q₈	—	178	1	no	—
152	C₄×D₄	—	89	1	no	—
153	C₄×D₄	—	178	1	no	—
154	#117	—	89	2	no	—
155	#117	—	178	1	no	—
156	C₂×C₄²	C₂×D₈₉	1	1	yes	characteristic
157	#107	—	89	2	no	—
158	#107	—	89	2	no	—
159	#106	—	89	2	no	—
160	#106	—	89	2	no	—
161	C₄⋊C₈	C₂×D₈₉	1	2	yes	—
162	#103	—	89	2	no	—
163	#103	—	89	2	no	—
164	#102	—	89	2	no	—
165	#102	—	89	2	no	—
166	C₂²⋊C₈	C₂×D₈₉	1	2	yes	—
167	#97	C₂×D₈₉	1	1	yes	characteristic
168	#97	C₂×D₈₉	1	1	yes	characteristic
169	C₂×Q₈	—	89	1	no	—
170	C₂×Q₈	—	178	1	no	—
171	C₂×Q₈	—	178	1	no	—
172	C₂×D₄	—	89	1	no	—
173	C₂×D₄	—	178	1	no	—
174	C₂²×C₄	—	178	1	no	—
175	C₂²×C₄	D₃₅₆	1	1	yes	characteristic
176	C₂²×C₄	D₃₅₆	1	1	yes	characteristic
177	C₂²×C₄	C₂²×D₈₉	1	1	yes	characteristic
178	C₂×C₈	C₂²×D₈₉	1	2	yes	—
179	C₂×C₈	C₂²×D₈₉	1	2	yes	—
180	C₄⋊C₄	—	89	2	no	—
181	C₄⋊C₄	—	89	2	no	—
182	C₄⋊C₄	—	89	1	no	—
183	C₄⋊C₄	—	89	1	no	—
184	C₄⋊C₄	—	178	1	no	—
185	C₄⋊C₄	—	178	1	no	—
186	C₄⋊C₄	—	178	1	no	—
187	C₄⋊C₄	—	178	1	no	—
188	C₄⋊C₄	—	178	2	no	—
189	C₄⋊C₄	—	178	2	no	—
190	C₄⋊C₄	—	178	1	no	—
191	C₄⋊C₄	—	178	1	no	—
192	C₂²⋊C₄	—	178	2	no	—
193	C₂²⋊C₄	—	178	1	no	—
194	C₂²⋊C₄	—	178	1	no	—
195	C₂²⋊C₄	—	178	1	no	—
196	C₂²⋊C₄	—	178	1	no	—
197	C₂²⋊C₄	—	178	1	no	—
198	C₄²	—	178	2	no	—
199	C₄²	—	178	1	no	—
200	C₄²	D₃₅₆	1	1	yes	characteristic
201	C₄²	D₃₅₆	1	1	yes	characteristic
202	C₄²	C₂²×D₈₉	1	1	yes	characteristic
203	C₄²	C₂²×D₈₉	1	1	yes	characteristic
204	C₂³	—	178	1	no	—
205	C₂³	C₂×D₃₅₆	1	1	yes	characteristic
206	Q₈	—	356	2	no	—
207	Q₈	—	356	2	no	—
208	Q₈	—	178	2	no	—
209	D₄	—	356	2	no	—
210	D₄	—	178	2	no	—
211	C₂×C₄	—	2	2	no	—
212	C₂×C₄	—	4	1	no	—
213	C₂×C₄	—	4	1	no	—
214	C₂×C₄	—	356	2	no	—
215	C₂×C₄	—	178	1	no	—
216	C₂×C₄	—	178	1	no	—
217	C₂×C₄	—	178	2	no	—
218	C₂×C₄	—	178	2	no	—
219	C₂×C₄	—	178	1	no	—
220	C₂×C₄	C₂×D₃₅₆	1	1	yes	characteristic
221	C₂×C₄	C₂×D₃₅₆	1	1	yes	characteristic
222	C₂×C₄	C₂×D₃₅₆	1	1	yes	characteristic
223	C₂×C₄	C₂×D₃₅₆	1	1	yes	characteristic
224	C₂×C₄	C₂×D₃₅₆	1	1	yes	characteristic
225	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
226	C₈	—	2	2	no	—
227	C₈	—	2	2	no	—
228	C₂²	—	2	1	no	—
229	C₂²	—	2	1	no	—
230	C₂²	—	2	1	no	—
231	C₂²	—	356	1	no	—
232	C₂²	—	356	1	no	—
233	C₂²	—	356	1	no	—
234	C₂²	C₂²×D₃₅₆	1	1	yes	characteristic
235	C₄	—	2	1	no	—
236	C₄	—	2	1	no	—
237	C₄	—	2	1	no	—
238	C₄	—	2	1	no	—
239	C₄	—	2	1	no	—
240	C₄	—	356	1	no	—
241	C₄	—	356	1	no	—
242	C₄	—	356	2	no	—
243	C₄	—	356	2	no	—
244	C₄	—	356	1	no	—
245	C₄	#15668059	1	2	yes	—
246	C₂	—	4	1	no	—
247	C₂	—	712	1	no	—
248	C₂	#19152174	1	1	yes	characteristic
249	C₂	#19152398	1	1	yes	characteristic
250	C₂	#19152398	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#19152155

C₂

yes

maximal, characteristic, complemented

#19152132

C₂

yes

maximal, characteristic

#19152007

C₂

yes

maximal, characteristic, complemented

#19152007

C₂

yes

maximal, characteristic, complemented

#19151958

C₂

yes

maximal, characteristic, complemented

#19151958

C₂

yes

maximal, characteristic, complemented

#19151940

C₂

yes

maximal, complemented

#19151923

C₂

yes

maximal

#19151906

C₂

yes

maximal, complemented

#19151899

C₂

yes

maximal, complemented

#432×C₈₉

C₂

yes

maximal, characteristic, complemented

#15668012

C₂²

yes

characteristic

#15668012

C₂²

yes

characteristic

#15668006

—

#15668004

C₂²

yes

characteristic

#15668004

C₂²

yes

—

#15668000

C₂²

yes

—

—

—

C₂²

yes

characteristic

#15667986

C₂²

yes

characteristic

C₄×Dic₁₇₈

—

C₄×Dic₁₇₈

—

C₄×Dic₁₇₈

C₂²

yes

characteristic

C₄×D₃₅₆

C₂²

yes

characteristic

C₄×C₂²⋊D₈₉

—

#15667971

C₂²

yes

—

#15667969

—

#15667946

C₂²

yes

—

#15667946

C₂²

yes

—

#15667944

C₂²

yes

—

#15667944

C₂²

yes

—

#15667937

C₂²

yes

—

#15667937

C₂²

yes

—

#15667934

C₂²

yes

—

#15667934

C₂²

yes

—

C₂×C₄²×C₈₉

C₂²

yes

characteristic

C₄⋊C₈×C₈₉

C₂²

yes

—

C₂²⋊C₈×C₈₉

C₂²

yes

—

#97×C₈₉

C₂²

yes

characteristic

#97×C₈₉

C₂²

yes

characteristic

C₂×Dic₁₇₈

—

C₂×Dic₁₇₈

—

C₂×Dic₁₇₈

C₂³

yes

characteristic

C₂×D₃₅₆

C₂³

yes

characteristic

C₂×C₂²⋊D₈₉

—

C₂×C₄×D₈₉

—

C₄⋊Dic₈₉

—

C₄⋊Dic₈₉

—

C₄⋊Dic₈₉

C₂³

yes

—

C₄⋊Dic₈₉

C₂³

yes

—

C₄⋊Dic₈₉

C₂³

yes

characteristic

C₄⋊Dic₈₉

C₂³

yes

—

—

—

—

—

—

C₂²⋊Dic₈₉

—

C₂²⋊Dic₈₉

—

—

—

—

—

C₄×Dic₈₉

—

C₄×Dic₈₉

—

C₂²×C₄×C₈₉

D₄

yes

characteristic

C₂²×C₄×C₈₉

D₄

yes

characteristic

C₂²×C₄×C₈₉

C₂³

yes

characteristic

C₂×C₈×C₈₉

C₂³

yes

—

C₂×C₈×C₈₉

C₂³

yes

—

C₄²×C₈₉

D₄

yes

characteristic

C₄²×C₈₉

D₄

yes

characteristic

C₄²×C₈₉

C₂³

yes

characteristic

C₄²×C₈₉

C₂³

yes

characteristic

C₂³×C₈₉

C₂×D₄

yes

characteristic

C₂²×D₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

C₂×D₄

yes

characteristic

C₂×C₄×C₈₉

C₂×D₄

yes

characteristic

C₂×C₄×C₈₉

C₂×D₄

yes

characteristic

C₂×C₄×C₈₉

C₂×D₄

yes

characteristic

C₂×C₄×C₈₉

C₂×D₄

yes

characteristic

C₂×C₄×C₈₉

C₂⁴

yes

characteristic

C₂²⋊D₈₉

—

C₂×Dic₈₉

—

C₂×Dic₈₉

—

C₂×Dic₈₉

—

C₂×Dic₈₉

—

C₂×Dic₈₉

—

D₃₅₆

—

C₄×D₈₉

—

Dic₁₇₈

—

Dic₁₇₈

—

Dic₁₇₈

—

100

C₈×C₈₉

—

101

C₈×C₈₉

—

102

C₂²×C₈₉

—

103

C₂²×C₈₉

—

104

C₂²×C₈₉

—

105

C₂²×C₈₉

C₂²×D₄

yes

characteristic

106

C₂×D₈₉

—

107

C₂×D₈₉

—

108

C₂×D₈₉

—

109

C₄×C₈₉

—

110

C₄×C₈₉

—

111

C₄×C₈₉

—

112

C₄×C₈₉

—

113

C₄×C₈₉

—

114

C₄×C₈₉

2₋¹⁺⁴

yes

—

115

Dic₈₉

—

116

Dic₈₉

—

117

Dic₈₉

—

118

Dic₈₉

—

119

Dic₈₉

—

120

C₂×C₈₉

—

121

C₂×C₈₉

#536

yes

characteristic

122

C₂×C₈₉

#575

yes

characteristic

123

C₂×C₈₉

#575

yes

characteristic

124

D₈₉

—

125

#3240

—

maximal, Sylow

126

C₈₉

#3240

yes

characteristic, complemented, Sylow

127

#533

—

128

#529

—

129

#501

—

130

#501

—

131

#489

—

132

#489

—

133

#485

—

134

#482

—

135

#479

—

136

#478

—

137

#432

D₈₉

yes

characteristic, complemented

138

C₄⋊Q₈

—

139

C₄⋊Q₈

—

140

#126

—

178

—

141

#125

—

142

#125

—

143

#124

—

144

#123

—

178

—

145

C₂²⋊Q₈

—

146

C₂²⋊Q₈

—

178

—

147

C₂²⋊Q₈

—

178

—

148

#121

—

149

C₄×Q₈

—

150

C₄×Q₈

—

178

—

151

C₄×Q₈

—

178

—

152

C₄×D₄

—

153

C₄×D₄

—

178

—

154

#117

—

155

#117

—

178

—

156

C₂×C₄²

C₂×D₈₉

yes

characteristic

157

#107

—

158

#107

—

159

#106

—

160

#106

—

161

C₄⋊C₈

C₂×D₈₉

yes

—

162

#103

—

163

#103

—

164

#102

—

165

#102

—

166

C₂²⋊C₈

C₂×D₈₉

yes

—

167

#97

C₂×D₈₉

yes

characteristic

168

#97

C₂×D₈₉

yes

characteristic

169

C₂×Q₈

—

170

C₂×Q₈

—

178

—

171

C₂×Q₈

—

178

—

172

C₂×D₄

—

173

C₂×D₄

—

178

—

174

C₂²×C₄

—

178

—

175

C₂²×C₄

D₃₅₆

yes

characteristic

176

C₂²×C₄

D₃₅₆

yes

characteristic

177

C₂²×C₄

C₂²×D₈₉

yes

characteristic

178

C₂×C₈

C₂²×D₈₉

yes

—

179

C₂×C₈

C₂²×D₈₉

yes

—

180

C₄⋊C₄

—

181

C₄⋊C₄

—

182

C₄⋊C₄

—

183

C₄⋊C₄

—

184

C₄⋊C₄

—

178

—

185

C₄⋊C₄

—

178

—

186

C₄⋊C₄

—

178

—

187

C₄⋊C₄

—

178

—

188

C₄⋊C₄

—

178

—

189

C₄⋊C₄

—

178

—

190

C₄⋊C₄

—

178

—

191

C₄⋊C₄

—

178

—

192

C₂²⋊C₄

—

178

—

193

C₂²⋊C₄

—

178

—

194

C₂²⋊C₄

—

178

—

195

C₂²⋊C₄

—

178

—

196

C₂²⋊C₄

—

178

—

197

C₂²⋊C₄

—

178

—

198

C₄²

—

178

—

199

C₄²

—

178

—

200

C₄²

D₃₅₆

yes

characteristic

201

C₄²

D₃₅₆

yes

characteristic

202

C₄²

C₂²×D₈₉

yes

characteristic

203

C₄²

C₂²×D₈₉

yes

characteristic

204

C₂³

—

178

—

205

C₂³

C₂×D₃₅₆

yes

characteristic

206

Q₈

—

356

—

207

Q₈

—

356

—

208

Q₈

—

178

—

209

D₄

—

356

—

210

D₄

—

178

—

211

C₂×C₄

—

212

C₂×C₄

—

213

C₂×C₄

—

214

C₂×C₄

—

356

—

215

C₂×C₄

—

178

—

216

C₂×C₄

—

178

—

217

C₂×C₄

—

178

—

218

C₂×C₄

—

178

—

219

C₂×C₄

—

178

—

220

C₂×C₄

C₂×D₃₅₆

yes

characteristic

221

C₂×C₄

C₂×D₃₅₆

yes

characteristic

222

C₂×C₄

C₂×D₃₅₆

yes

characteristic

223

C₂×C₄

C₂×D₃₅₆

yes

characteristic

224

C₂×C₄

C₂×D₃₅₆

yes

characteristic

225

C₂×C₄

C₂³×D₈₉

yes

characteristic

226

C₈

—

227

C₈

—

228

C₂²

—

229

C₂²

—

230

C₂²

—

231

C₂²

—

356

—

232

C₂²

—

356

—

233

C₂²

—

356

—

234

C₂²

C₂²×D₃₅₆

yes

characteristic

235

C₄

—

236

C₄

—

237

C₄

—

238

C₄

—

239

C₄

—

240

C₄

—

356

—

241

C₄

—

356

—

242

C₄

—

356

—

243

C₄

—

356

—

244

C₄

—

356

—

245

C₄

#15668059

yes

—

246

C₂

—

247

C₂

—

712

—

248

C₂

#19152174

yes

characteristic

249

C₂

#19152398

yes

characteristic

250

C₂

#19152398

yes

characteristic

	subgroup	G/H
center	C₂²	C₂²×D₃₅₆
commutator, cosocle	C₂×C₄×C₈₉	C₂⁴
Frattini	C₂×C₄	C₂³×D₈₉
Fitting	#432×C₈₉	C₂
socle	C₂²×C₈₉	C₂²×D₄
prime radical	#15667986	C₂²
hypercenter	#432	D₈₉
hypocenter	C₈₉	#3240
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #432

subgroup

G/H

center

C₂²

C₂²×D₃₅₆

commutator, cosocle

C₂×C₄×C₈₉

C₂⁴

Frattini

C₂×C₄

C₂³×D₈₉

Fitting

#432×C₈₉

C₂

socle

C₂²×C₈₉

C₂²×D₄

C₂²

D₈₉

C₈₉

G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #432

N	H ≅ G/N	type
1. #19152155	C₂	semidirect
3. #19152007	C₂	semidirect
4. #19152007	C₂	semidirect
5. #19151958	C₂	semidirect
6. #19151958	C₂	semidirect
7. #19151940	C₂	semidirect
9. #19151906	C₂	semidirect
10. #19151899	C₂	semidirect
11. #432×C₈₉	C₂	semidirect
126. C₈₉	#3240	semidirect
137. #432	D₈₉	semidirect

H ≅ G/N

type

1. #19152155

C₂

semidirect

3. #19152007

C₂

semidirect

4. #19152007

C₂

semidirect

5. #19151958

C₂

semidirect

6. #19151958

C₂

semidirect

7. #19151940

C₂

semidirect

9. #19151906

C₂

semidirect

10. #19151899

C₂

semidirect

11. #432×C₈₉

C₂

semidirect

126. C₈₉

#3240

semidirect

137. #432

D₈₉

semidirect

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

subgroup	index
#19152155	2
#19152132	2
#19152007	2
#19151958	2
#19151940	2
#19151923	2
#19151906	2
#19151899	2
#432×C₈₉	2
#3240	89

subgroup

index

#432×C₈₉

Subgroups — #26031494

Conjugacy classes of subgroups

Complements

Maximal subgroups