Group #36465785 — subgroups

Subgroups — #36465785

Order 22784.

306 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 306 conjugacy classes of subgroups — too many to draw. Only its 85 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	#26030836	C₂	1	1	yes	maximal, characteristic
2	#26022054	C₂	1	1	yes	maximal, characteristic
3	#335×D₈₉	C₂	1	1	yes	maximal, characteristic
4	#26018308	C₂	1	1	yes	maximal, characteristic, complemented
5	#26018306	C₂	1	1	yes	maximal, characteristic, complemented
6	#26018301	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈₉×#1362	C₂	1	1	yes	maximal, characteristic, complemented
8	#19152153	—	2	1	no	—
9	#19152003	C₂²	1	1	yes	characteristic
10	#19151948	—	2	1	no	—
11	#19151836	—	2	1	no	—
12	#19151836	C₄	1	2	yes	—
13	Q₁₆×Dic₈₉	—	2	1	no	—
14	Q₁₆×Dic₈₉	C₄	1	2	yes	—
15	C₄⋊C₈×D₈₉	—	2	1	no	—
16	C₄×C₈×D₈₉	C₂²	1	1	yes	characteristic
17	C₄⋊#13083549	C₂²	1	1	yes	characteristic
18	#19151377	—	2	1	no	—
19	#19151373	—	2	1	no	—
20	#19151351	C₂²	1	1	yes	characteristic
21	#19151350	—	2	1	no	—
22	#494×C₈₉	C₂²	1	1	yes	characteristic
23	C₄⋊C₁₆×C₈₉	C₂²	1	1	yes	characteristic
24	#335×C₈₉	C₂²	1	1	yes	characteristic
25	C₂×C₈×D₈₉	—	4	1	no	—
26	C₂×C₈×D₈₉	C₂×C₄	1	1	yes	characteristic
27	C₂×C₈×D₈₉	D₄	1	1	yes	characteristic
28	#15668012	—	2	1	no	—
29	#15668003	—	4	1	no	—
30	#15667992	—	4	1	no	—
31	#15667988	—	2	2	no	—
32	Q₈×Dic₈₉	—	2	2	no	—
33	#15667977	—	4	1	no	—
34	#15667970	—	4	1	no	—
35	C₄²×D₈₉	D₄	1	1	yes	characteristic
36	C₂×#13083549	—	2	1	no	—
37	#15667946	—	2	1	no	—
38	#15667946	C₂×C₄	1	2	yes	—
39	C₄⋊#10623494	—	2	1	no	—
40	#15667941	—	4	1	no	—
41	#15667936	—	2	2	no	—
42	#15667936	—	2	2	no	—
43	C₄×#10623494	D₄	1	1	yes	characteristic
44	C₈×Dic₈₉	C₂×C₄	1	1	yes	characteristic
45	C₈×Dic₈₉	D₄	1	1	yes	characteristic
46	C₂×Q₁₆×C₈₉	—	2	1	no	—
47	C₂×Q₁₆×C₈₉	C₂×C₄	1	2	yes	—
48	C₄⋊Q₈×C₈₉	—	2	1	no	—
49	C₂×C₁₆×C₈₉	—	2	1	no	—
50	C₄⋊C₈×C₈₉	—	2	1	no	—
51	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
52	C₂×Dic₁₇₈	—	4	1	no	—
53	C₂×C₄×D₈₉	C₂²⋊C₄	1	1	yes	characteristic
54	C₂×C₄×D₈₉	D₈	1	1	yes	characteristic
55	C₂×C₄×D₈₉	SD₁₆	1	1	yes	characteristic
56	C₂×#10623494	—	4	1	no	—
57	C₂×#10623494	C₂²⋊C₄	1	1	yes	characteristic
58	C₂×#10623494	C₂²⋊C₄	1	1	yes	characteristic
59	C₈×D₈₉	—	2	1	no	—
60	C₈×D₈₉	—	2	1	no	—
61	C₈×D₈₉	—	4	1	no	—
62	C₈×D₈₉	—	8	2	no	—
63	C₄⋊Dic₈₉	—	2	2	no	—
64	C₄⋊Dic₈₉	—	4	1	no	—
65	C₄⋊Dic₈₉	—	4	2	no	—
66	#13083553	—	4	2	no	—
67	#13083551	—	4	2	no	—
68	C₄×Dic₈₉	—	4	2	no	—
69	C₄×Dic₈₉	C₂²⋊C₄	1	1	yes	characteristic
70	C₄×Dic₈₉	D₈	1	1	yes	characteristic
71	C₄×Dic₈₉	SD₁₆	1	1	yes	characteristic
72	#13083549	—	4	1	no	—
73	C₂×Q₈×C₈₉	—	2	2	no	—
74	Q₁₆×C₈₉	—	4	2	no	—
75	Q₁₆×C₈₉	—	4	1	no	—
76	Q₁₆×C₈₉	—	4	1	no	—
77	C₂×C₈×C₈₉	—	4	1	no	—
78	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
79	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
80	C₄⋊C₄×C₈₉	—	4	1	no	—
81	C₄⋊C₄×C₈₉	—	4	1	no	—
82	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
83	C₁₆×C₈₉	—	4	1	no	—
84	C₂²×D₈₉	#102	1	1	yes	characteristic
85	Q₈×C₈₉	—	4	2	no	—
86	Q₈×C₈₉	—	4	2	no	—
87	C₂×C₄×C₈₉	—	4	2	no	—
88	C₂×C₄×C₈₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
89	C₂×C₄×C₈₉	C₂×D₈	1	1	yes	characteristic
90	C₂×C₄×C₈₉	C₂×SD₁₆	1	1	yes	characteristic
91	C₂×Dic₈₉	—	4	2	no	—
92	C₂×Dic₈₉	#102	1	1	yes	characteristic
93	C₂×Dic₈₉	#102	1	1	yes	characteristic
94	C₂×Dic₈₉	#102	1	1	yes	characteristic
95	C₄×D₈₉	—	2	2	no	—
96	C₄×D₈₉	—	2	1	no	—
97	C₄×D₈₉	—	2	1	no	—
98	C₄×D₈₉	—	2	1	no	—
99	C₄×D₈₉	—	2	1	no	—
100	Dic₁₇₈	—	8	1	no	—
101	Dic₁₇₈	—	8	1	no	—
102	C₈×C₈₉	—	2	1	no	—
103	C₈×C₈₉	—	8	1	no	—
104	C₈×C₈₉	#135	1	1	yes	characteristic
105	C₈×C₈₉	#135	1	1	yes	characteristic
106	#10623494	—	2	1	no	—
107	#10623494	—	2	1	no	—
108	#10623494	—	8	1	no	—
109	C₂²×C₈₉	C₂×#102	1	1	yes	characteristic
110	C₂×D₈₉	—	2	1	no	—
111	C₂×D₈₉	—	2	1	no	—
112	C₂×D₈₉	#362	1	2	yes	—
113	C₄×C₈₉	—	2	1	no	—
114	C₄×C₈₉	—	8	2	no	—
115	C₄×C₈₉	#413	1	1	yes	characteristic
116	C₄×C₈₉	#416	1	1	yes	characteristic
117	C₄×C₈₉	#509	1	1	yes	characteristic
118	C₄×C₈₉	#510	1	1	yes	characteristic
119	Dic₈₉	—	2	1	no	—
120	Dic₈₉	—	2	1	no	—
121	Dic₈₉	—	2	1	no	—
122	Dic₈₉	—	8	2	no	—
123	#11954	—	89	1	no	maximal, Sylow
124	C₂×C₈₉	#1540	1	1	yes	characteristic
125	C₂×C₈₉	#2139	1	1	yes	characteristic
126	C₂×C₈₉	C₂×#362	1	1	yes	characteristic
127	D₈₉	—	2	2	no	—
128	#3170	—	89	1	no	—
129	#2163	—	89	1	no	—
130	C₂×#335	—	89	1	no	—
131	#1364	—	89	1	no	—
132	#1364	—	89	1	no	—
133	#1362	—	89	1	no	—
134	#1362	D₈₉	1	1	yes	characteristic, complemented
135	C₈₉	#11954	1	1	yes	characteristic, complemented, Sylow
136	#533	—	178	1	no	—
137	#500	—	89	1	no	—
138	#494	C₂×D₈₉	1	1	yes	characteristic
139	#487	—	178	1	no	—
140	#467	—	89	2	no	—
141	#467	—	178	1	no	—
142	C₄×Q₁₆	—	89	2	no	—
143	C₄×Q₁₆	—	178	1	no	—
144	C₂×C₄⋊C₈	—	178	1	no	—
145	C₂×C₄×C₈	—	89	1	no	—
146	C₄⋊C₁₆	—	89	1	no	—
147	C₄⋊C₁₆	C₂×D₈₉	1	1	yes	characteristic
148	C₂²⋊C₁₆	—	178	1	no	—
149	#346	—	178	1	no	—
150	#335	—	89	1	no	—
151	#335	—	178	1	no	—
152	#335	C₂×D₈₉	1	1	yes	characteristic
153	C₂×Q₁₆	—	2	1	no	—
154	C₂×Q₁₆	C₄×D₈₉	1	2	yes	—
155	C₂²×C₈	—	89	1	no	—
156	C₂²×C₈	—	89	1	no	—
157	C₂²×C₈	—	356	1	no	—
158	C₄⋊Q₈	—	2	1	no	—
159	C₄⋊Q₈	—	178	1	no	—
160	#125	—	356	1	no	—
161	C₂²⋊Q₈	—	356	1	no	—
162	C₂²⋊Q₈	—	178	2	no	—
163	C₄×Q₈	—	356	1	no	—
164	C₄×Q₈	—	178	2	no	—
165	#117	—	356	1	no	—
166	C₂×C₄²	—	89	1	no	—
167	C₂×C₁₆	—	2	1	no	—
168	C₂×C₁₆	—	178	1	no	—
169	#107	—	89	2	no	—
170	#107	—	178	1	no	—
171	C₄⋊C₈	—	2	1	no	—
172	C₄⋊C₈	—	356	1	no	—
173	C₄⋊C₈	—	178	1	no	—
174	#103	—	178	2	no	—
175	#103	—	178	2	no	—
176	C₄×C₈	—	89	1	no	—
177	C₄×C₈	—	89	1	no	—
178	C₄×C₈	—	89	1	no	—
179	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
180	C₂×Q₈	—	2	2	no	—
181	C₂×Q₈	—	356	1	no	—
182	C₂²×C₄	—	89	1	no	—
183	C₂²×C₄	—	89	1	no	—
184	C₂²×C₄	—	89	1	no	—
185	Q₁₆	—	4	2	no	—
186	Q₁₆	—	4	1	no	—
187	Q₁₆	—	4	1	no	—
188	C₂×C₈	—	4	1	no	—
189	C₂×C₈	—	89	1	no	—
190	C₂×C₈	—	89	1	no	—
191	C₂×C₈	—	356	1	no	—
192	C₂×C₈	—	356	1	no	—
193	C₂×C₈	—	178	1	no	—
194	C₂×C₈	—	178	1	no	—
195	C₂×C₈	—	712	2	no	—
196	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
197	C₂×C₈	D₄×D₈₉	1	1	yes	characteristic
198	C₄⋊C₄	—	4	1	no	—
199	C₄⋊C₄	—	4	1	no	—
200	C₄⋊C₄	—	356	2	no	—
201	C₄⋊C₄	—	356	2	no	—
202	C₄⋊C₄	—	356	1	no	—
203	C₄⋊C₄	—	178	2	no	—
204	C₂²⋊C₄	—	356	2	no	—
205	C₄²	—	89	1	no	—
206	C₄²	—	89	1	no	—
207	C₄²	—	89	1	no	—
208	C₄²	—	356	2	no	—
209	C₄²	D₄×D₈₉	1	1	yes	characteristic
210	C₁₆	—	4	1	no	—
211	C₁₆	—	356	1	no	—
212	C₂³	—	89	1	no	—
213	Q₈	—	4	2	no	—
214	Q₈	—	4	2	no	—
215	Q₈	—	712	1	no	—
216	Q₈	—	712	1	no	—
217	C₂×C₄	—	4	2	no	—
218	C₂×C₄	—	89	1	no	—
219	C₂×C₄	—	89	1	no	—
220	C₂×C₄	—	89	1	no	—
221	C₂×C₄	—	356	2	no	—
222	C₂×C₄	—	178	2	no	—
223	C₂×C₄	—	178	1	no	—
224	C₂×C₄	—	178	1	no	—
225	C₂×C₄	—	178	1	no	—
226	C₂×C₄	—	178	1	no	—
227	C₂×C₄	C₂²⋊C₄×D₈₉	1	1	yes	characteristic
228	C₂×C₄	D₈×D₈₉	1	1	yes	characteristic
229	C₂×C₄	SD₁₆×D₈₉	1	1	yes	characteristic
230	C₈	—	2	1	no	—
231	C₈	—	8	1	no	—
232	C₈	—	178	1	no	—
233	C₈	—	178	1	no	—
234	C₈	—	712	1	no	—
235	C₈	#15668031	1	1	yes	characteristic
236	C₈	#15668033	1	1	yes	characteristic
237	C₂²	—	89	2	no	—
238	C₂²	—	178	1	no	—
239	C₂²	—	178	1	no	—
240	C₂²	#102×D₈₉	1	1	yes	characteristic
241	C₄	—	2	1	no	—
242	C₄	—	8	2	no	—
243	C₄	—	178	1	no	—
244	C₄	—	178	1	no	—
245	C₄	—	178	1	no	—
246	C₄	—	712	2	no	—
247	C₄	#19151579	1	1	yes	characteristic
248	C₄	#19151591	1	1	yes	characteristic
249	C₄	#19152035	1	1	yes	characteristic
250	C₄	#19152040	1	1	yes	characteristic
251	C₂	—	178	2	no	—
252	C₂	#26018898	1	1	yes	characteristic
253	C₂	#26021963	1	1	yes	characteristic
254	C₂	#362×D₈₉	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#26030836

C₂

yes

maximal, characteristic

#26022054

C₂

yes

maximal, characteristic

#335×D₈₉

C₂

yes

maximal, characteristic

#26018308

C₂

yes

maximal, characteristic, complemented

#26018306

C₂

yes

maximal, characteristic, complemented

#26018301

C₂

yes

maximal, characteristic, complemented

C₈₉×#1362

C₂

yes

maximal, characteristic, complemented

#19152153

—

#19152003

C₂²

yes

—

—

C₄

yes

—

Q₁₆×Dic₈₉

—

Q₁₆×Dic₈₉

C₄

yes

—

C₄⋊C₈×D₈₉

—

C₄×C₈×D₈₉

C₂²

yes

characteristic

C₄⋊#13083549

C₂²

yes

—

—

C₂²

yes

characteristic

#19151350

—

#494×C₈₉

C₂²

yes

characteristic

C₄⋊C₁₆×C₈₉

C₂²

yes

characteristic

#335×C₈₉

C₂²

yes

characteristic

C₂×C₈×D₈₉

—

C₂×C₈×D₈₉

C₂×C₄

yes

characteristic

C₂×C₈×D₈₉

D₄

yes

—

—

—

—

Q₈×Dic₈₉

—

#15667977

—

#15667970

—

C₄²×D₈₉

D₄

yes

—

—

C₂×C₄

yes

—

—

—

—

—

D₄

yes

characteristic

C₈×Dic₈₉

C₂×C₄

yes

characteristic

C₈×Dic₈₉

D₄

yes

characteristic

C₂×Q₁₆×C₈₉

—

C₂×Q₁₆×C₈₉

C₂×C₄

yes

—

C₄⋊Q₈×C₈₉

—

C₂×C₁₆×C₈₉

—

C₄⋊C₈×C₈₉

—

C₄×C₈×C₈₉

C₂³

yes

characteristic

C₂×Dic₁₇₈

—

C₂×C₄×D₈₉

C₂²⋊C₄

yes

characteristic

C₂×C₄×D₈₉

D₈

yes

characteristic

C₂×C₄×D₈₉

SD₁₆

yes

characteristic

C₂×#10623494

—

C₂×#10623494

C₂²⋊C₄

yes

characteristic

C₂×#10623494

C₂²⋊C₄

yes

characteristic

C₈×D₈₉

—

C₈×D₈₉

—

C₈×D₈₉

—

C₈×D₈₉

—

C₄⋊Dic₈₉

—

C₄⋊Dic₈₉

—

C₄⋊Dic₈₉

—

#13083553

—

#13083551

—

C₄×Dic₈₉

—

C₄×Dic₈₉

C₂²⋊C₄

yes

characteristic

C₄×Dic₈₉

D₈

yes

characteristic

C₄×Dic₈₉

SD₁₆

yes

characteristic

#13083549

—

C₂×Q₈×C₈₉

—

Q₁₆×C₈₉

—

Q₁₆×C₈₉

—

Q₁₆×C₈₉

—

C₂×C₈×C₈₉

—

C₂×C₈×C₈₉

C₂²×C₄

yes

characteristic

C₂×C₈×C₈₉

C₂×D₄

yes

characteristic

C₄⋊C₄×C₈₉

—

C₄⋊C₄×C₈₉

—

C₄²×C₈₉

C₂×D₄

yes

characteristic

C₁₆×C₈₉

—

C₂²×D₈₉

#102

yes

characteristic

Q₈×C₈₉

—

Q₈×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₈₉

C₂×D₈

yes

characteristic

C₂×C₄×C₈₉

C₂×SD₁₆

yes

characteristic

C₂×Dic₈₉

—

C₂×Dic₈₉

yes

C₂×Dic₈₉

yes

C₂×Dic₈₉

yes

C₄×D₈₉

—

C₄×D₈₉

—

C₄×D₈₉

—

C₄×D₈₉

—

C₄×D₈₉

—

100

Dic₁₇₈

—

101

Dic₁₇₈

—

102

C₈×C₈₉

—

103

C₈×C₈₉

—

104

C₈×C₈₉

#135

yes

characteristic

105

C₈×C₈₉

#135

yes

characteristic

106

#10623494

—

107

#10623494

—

108

#10623494

—

109

C₂²×C₈₉

C₂×#102

yes

characteristic

110

C₂×D₈₉

—

111

C₂×D₈₉

—

112

C₂×D₈₉

#362

yes

—

113

C₄×C₈₉

—

114

C₄×C₈₉

—

115

C₄×C₈₉

#413

yes

characteristic

116

C₄×C₈₉

#416

yes

characteristic

117

C₄×C₈₉

#509

yes

characteristic

118

C₄×C₈₉

#510

yes

characteristic

119

Dic₈₉

—

120

Dic₈₉

—

121

Dic₈₉

—

122

Dic₈₉

—

123

#11954

—

maximal, Sylow

124

C₂×C₈₉

#1540

yes

characteristic

125

C₂×C₈₉

#2139

yes

characteristic

126

C₂×C₈₉

C₂×#362

yes

characteristic

127

D₈₉

—

128

#3170

—

129

#2163

—

130

C₂×#335

—

131

#1364

—

132

#1364

—

133

#1362

—

134

#1362

D₈₉

yes

characteristic, complemented

135

C₈₉

#11954

yes

characteristic, complemented, Sylow

136

#533

—

178

—

137

#500

—

138

#494

C₂×D₈₉

yes

characteristic

139

#487

—

178

—

140

#467

—

141

#467

—

178

—

142

C₄×Q₁₆

—

143

C₄×Q₁₆

—

178

—

144

C₂×C₄⋊C₈

—

178

—

145

C₂×C₄×C₈

—

146

C₄⋊C₁₆

—

147

C₄⋊C₁₆

C₂×D₈₉

yes

characteristic

148

C₂²⋊C₁₆

—

178

—

149

#346

—

178

—

150

#335

—

151

#335

—

178

—

152

#335

C₂×D₈₉

yes

characteristic

153

C₂×Q₁₆

—

154

C₂×Q₁₆

C₄×D₈₉

yes

—

155

C₂²×C₈

—

156

C₂²×C₈

—

157

C₂²×C₈

—

356

—

158

C₄⋊Q₈

—

159

C₄⋊Q₈

—

178

—

160

#125

—

356

—

161

C₂²⋊Q₈

—

356

—

162

C₂²⋊Q₈

—

178

—

163

C₄×Q₈

—

356

—

164

C₄×Q₈

—

178

—

165

#117

—

356

—

166

C₂×C₄²

—

167

C₂×C₁₆

—

168

C₂×C₁₆

—

178

—

169

#107

—

170

#107

—

178

—

171

C₄⋊C₈

—

172

C₄⋊C₈

—

356

—

173

C₄⋊C₈

—

178

—

174

#103

—

178

—

175

#103

—

178

—

176

C₄×C₈

—

177

C₄×C₈

—

178

C₄×C₈

—

179

C₄×C₈

C₂²×D₈₉

yes

characteristic

180

C₂×Q₈

—

181

C₂×Q₈

—

356

—

182

C₂²×C₄

—

183

C₂²×C₄

—

184

C₂²×C₄

—

185

Q₁₆

—

186

Q₁₆

—

187

Q₁₆

—

188

C₂×C₈

—

189

C₂×C₈

—

190

C₂×C₈

—

191

C₂×C₈

—

356

—

192

C₂×C₈

—

356

—

193

C₂×C₈

—

178

—

194

C₂×C₈

—

178

—

195

C₂×C₈

—

712

—

196

C₂×C₈

C₂×C₄×D₈₉

yes

characteristic

197

C₂×C₈

D₄×D₈₉

yes

characteristic

198

C₄⋊C₄

—

199

C₄⋊C₄

—

200

C₄⋊C₄

—

356

—

201

C₄⋊C₄

—

356

—

202

C₄⋊C₄

—

356

—

203

C₄⋊C₄

—

178

—

204

C₂²⋊C₄

—

356

—

205

C₄²

—

206

C₄²

—

207

C₄²

—

208

C₄²

—

356

—

209

C₄²

D₄×D₈₉

yes

characteristic

210

C₁₆

—

211

C₁₆

—

356

—

212

C₂³

—

213

Q₈

—

214

Q₈

—

215

Q₈

—

712

—

216

Q₈

—

712

—

217

C₂×C₄

—

218

C₂×C₄

—

219

C₂×C₄

—

220

C₂×C₄

—

221

C₂×C₄

—

356

—

222

C₂×C₄

—

178

—

223

C₂×C₄

—

178

—

224

C₂×C₄

—

178

—

225

C₂×C₄

—

178

—

226

C₂×C₄

—

178

—

227

C₂×C₄

C₂²⋊C₄×D₈₉

yes

characteristic

228

C₂×C₄

D₈×D₈₉

yes

characteristic

229

C₂×C₄

SD₁₆×D₈₉

yes

characteristic

230

C₈

—

231

C₈

—

232

C₈

—

178

—

233

C₈

—

178

—

234

C₈

—

712

—

235

C₈

#15668031

yes

characteristic

236

C₈

#15668033

yes

characteristic

237

C₂²

—

238

C₂²

—

178

—

239

C₂²

—

178

—

240

C₂²

#102×D₈₉

yes

characteristic

241

C₄

—

242

C₄

—

243

C₄

—

178

—

244

C₄

—

178

—

245

C₄

—

178

—

246

C₄

—

712

—

247

C₄

#19151579

yes

characteristic

248

C₄

#19151591

yes

characteristic

249

C₄

#19152035

yes

characteristic

250

C₄

#19152040

yes

characteristic

251

C₂

—

178

—

252

C₂

#26018898

yes

characteristic

253

C₂

#26021963

yes

characteristic

254

C₂

#362×D₈₉

yes

characteristic

	subgroup	G/H
center	C₂²	#102×D₈₉
commutator	C₂×C₈×C₈₉	C₂²×C₄
Frattini	C₄×C₈	C₂²×D₈₉
Fitting	C₈₉×#1362	C₂
socle	C₂²×C₈₉	C₂×#102
prime radical	C₂²×D₈₉	#102
cosocle	C₄×C₈×C₈₉	C₂³
hypercenter	#1362	D₈₉
hypocenter	C₈₉	#11954
LCS	G ▷ C₂×C₈×C₈₉ ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #1362

subgroup

G/H

center

C₂²

#102×D₈₉

commutator

C₂×C₈×C₈₉

C₂²×C₄

Frattini

C₄×C₈

C₂²×D₈₉

Fitting

C₈₉×#1362

C₂

C₂²×C₈₉

C₂²×D₈₉

C₄×C₈×C₈₉

C₂³

D₈₉

C₈₉

G ▷ C₂×C₈×C₈₉ ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #1362

N	H ≅ G/N	type
4. #26018308	C₂	semidirect
5. #26018306	C₂	semidirect
6. #26018301	C₂	semidirect
7. C₈₉×#1362	C₂	semidirect
134. #1362	D₈₉	semidirect
135. C₈₉	#11954	semidirect

H ≅ G/N

type

4. #26018308

C₂

semidirect

5. #26018306

C₂

semidirect

6. #26018301

C₂

semidirect

7. C₈₉×#1362

C₂

semidirect

134. #1362

D₈₉

semidirect

135. C₈₉

#11954

semidirect

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

subgroup	index
#26030836	2
#26022054	2
#335×D₈₉	2
#26018308	2
#26018306	2
#26018301	2
C₈₉×#1362	2
#11954	89

subgroup

index

#335×D₈₉

C₈₉×#1362

Subgroups — #36465785

Conjugacy classes of subgroups

Complements

Maximal subgroups