Group #26033160 — subgroups

Subgroups — #26033160

Order 11392.

340 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 340 conjugacy classes of subgroups — too many to draw. Only its 133 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	Q₈×Dic₁₇₈	C₂	1	1	yes	maximal, characteristic, complemented
2	#19152305	C₂	1	1	yes	maximal, characteristic
3	#19152005	C₂	1	2	yes	maximal, complemented
4	#19152003	C₂	1	1	yes	maximal, characteristic, complemented
5	#19151907	C₂	1	2	yes	maximal, complemented
6	#19151893	C₂	1	1	yes	maximal, characteristic, complemented
7	#19151888	C₂	1	1	yes	maximal, characteristic
8	#19151876	C₂	1	2	yes	maximal
9	#19151728	C₂	1	1	yes	maximal, characteristic, complemented
10	#19151699	C₂	1	2	yes	maximal
11	C₄×SD₁₆×C₈₉	C₂	1	1	yes	maximal, characteristic
12	#15668012	—	2	1	no	—
13	#15668012	C₂²	1	1	yes	characteristic
14	#15668012	C₂²	1	1	yes	characteristic
15	#15668011	—	2	2	no	—
16	#15668011	C₂²	1	2	yes	—
17	#15668003	C₂²	1	2	yes	—
18	#15667991	—	2	1	no	—
19	#15667989	—	2	2	no	—
20	Q₈×Dic₈₉	C₂²	1	2	yes	—
21	C₄×Dic₁₇₈	—	2	1	no	—
22	C₄×Dic₁₇₈	C₂²	1	1	yes	characteristic
23	D₄×Dic₈₉	C₂²	1	2	yes	—
24	C₂×C₄⋊Dic₈₉	—	2	1	no	—
25	#15667946	C₂²	1	2	yes	—
26	#15667946	C₂²	1	2	yes	—
27	#15667945	C₂²	1	2	yes	—
28	#15667943	C₂²	1	2	yes	—
29	C₄⋊#10623494	C₂²	1	1	yes	characteristic
30	#15667941	C₂²	1	2	yes	—
31	#15667936	C₂²	1	2	yes	—
32	#15667933	C₂²	1	2	yes	—
33	#15667922	C₂²	1	2	yes	—
34	C₂×SD₁₆×C₈₉	C₂²	1	1	yes	characteristic
35	C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
36	C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
37	#106×C₈₉	C₂²	1	1	yes	characteristic
38	#103×C₈₉	C₂²	1	1	yes	characteristic
39	#102×C₈₉	C₂²	1	1	yes	characteristic
40	C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
41	C₂×Dic₁₇₈	—	2	1	no	—
42	C₂×Dic₁₇₈	—	2	1	no	—
43	C₂×Dic₁₇₈	—	2	2	no	—
44	C₂×Dic₁₇₈	D₄	1	1	yes	characteristic
45	C₂²×Dic₈₉	—	2	2	no	—
46	C₂×#10623494	C₂³	1	2	yes	—
47	C₄⋊Dic₈₉	—	2	1	no	—
48	C₄⋊Dic₈₉	—	2	1	no	—
49	C₄⋊Dic₈₉	—	2	2	no	—
50	C₄⋊Dic₈₉	—	2	2	no	—
51	C₄⋊Dic₈₉	D₄	1	1	yes	characteristic
52	C₄⋊Dic₈₉	C₂³	1	2	yes	—
53	C₄⋊Dic₈₉	C₂³	1	2	yes	—
54	#13083553	—	2	2	no	—
55	#13083553	—	2	2	no	—
56	#13083553	D₄	1	2	yes	—
57	C₂²⋊Dic₈₉	—	2	2	no	—
58	C₄×Dic₈₉	—	2	2	no	—
59	C₄×Dic₈₉	C₂³	1	2	yes	—
60	C₂×Q₈×C₈₉	C₂³	1	1	yes	characteristic
61	C₂×D₄×C₈₉	C₂³	1	1	yes	characteristic
62	C₂²×C₄×C₈₉	—	2	1	no	—
63	SD₁₆×C₈₉	Q₈	1	4	yes	complemented
64	C₂×C₈×C₈₉	C₂³	1	1	yes	characteristic
65	C₂×C₈×C₈₉	C₂³	1	1	yes	characteristic
66	C₄⋊C₄×C₈₉	—	2	1	no	—
67	C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
68	C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
69	C₂²⋊C₄×C₈₉	—	2	1	no	—
70	C₄²×C₈₉	—	2	1	no	—
71	C₄²×C₈₉	C₂³	1	1	yes	characteristic
72	C₂³×C₈₉	—	2	1	no	—
73	Q₈×C₈₉	—	2	1	no	—
74	Q₈×C₈₉	C₂×Q₈	1	2	yes	—
75	D₄×C₈₉	—	2	1	no	—
76	D₄×C₈₉	C₂×Q₈	1	2	yes	—
77	C₂×C₄×C₈₉	—	2	1	no	—
78	C₂×C₄×C₈₉	—	2	1	no	—
79	C₂×C₄×C₈₉	—	2	1	no	—
80	C₂×C₄×C₈₉	—	4	2	no	—
81	C₂×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
82	C₂×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
83	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
84	C₂×Dic₈₉	—	2	2	no	—
85	C₂×Dic₈₉	—	2	2	no	—
86	C₂×Dic₈₉	—	8	2	no	—
87	C₂×Dic₈₉	C₂×D₄	1	2	yes	—
88	C₂×Dic₈₉	C₂×D₄	1	2	yes	—
89	Dic₁₇₈	—	2	2	no	—
90	Dic₁₇₈	—	8	2	no	—
91	Dic₁₇₈	—	8	1	no	—
92	Dic₁₇₈	—	8	1	no	—
93	C₈×C₈₉	—	2	1	no	—
94	C₈×C₈₉	C₂×Q₈	1	2	yes	—
95	#10623494	—	2	2	no	—
96	C₂²×C₈₉	—	2	2	no	—
97	C₂²×C₈₉	—	4	1	no	—
98	C₂²×C₈₉	—	4	1	no	—
99	C₂²×C₈₉	C₂²×D₄	1	1	yes	characteristic
100	C₄×C₈₉	—	2	2	no	—
101	C₄×C₈₉	—	2	1	no	—
102	C₄×C₈₉	—	4	1	no	—
103	C₄×C₈₉	—	4	1	no	—
104	C₄×C₈₉	#137	1	2	yes	—
105	C₄×C₈₉	C₂²×Q₈	1	1	yes	characteristic
106	C₄×C₈₉	2₋¹⁺⁴	1	1	yes	characteristic
107	Dic₈₉	—	2	2	no	—
108	Dic₈₉	—	2	2	no	—
109	Dic₈₉	—	4	2	no	—
110	Dic₈₉	—	4	2	no	—
111	C₂×C₈₉	—	4	2	no	—
112	C₂×C₈₉	D₄×Q₈	1	1	yes	characteristic
113	C₂×C₈₉	C₂×#137	1	1	yes	characteristic
114	C₂×C₈₉	#576	1	1	yes	characteristic
115	#3385	—	89	1	no	maximal, Sylow
116	C₈₉	#3385	1	1	yes	characteristic, complemented, Sylow
117	Q₈²	—	89	1	no	—
118	#554	—	89	1	no	—
119	#501	—	89	2	no	—
120	#500	—	89	1	no	—
121	#479	—	89	2	no	—
122	#477	—	89	1	no	—
123	#476	—	89	1	no	—
124	#474	—	89	2	no	—
125	#446	—	89	1	no	—
126	#440	—	89	2	no	—
127	C₄×SD₁₆	D₈₉	1	1	yes	characteristic
128	C₂×SD₁₆	C₂×D₈₉	1	1	yes	characteristic
129	C₄⋊Q₈	—	89	2	no	—
130	C₄⋊Q₈	—	89	1	no	—
131	C₄⋊Q₈	—	89	1	no	—
132	C₄⋊Q₈	—	178	1	no	—
133	C₄⋊Q₈	—	178	2	no	—
134	#125	—	89	2	no	—
135	C₂²⋊Q₈	—	178	2	no	—
136	C₂²⋊Q₈	—	178	1	no	—
137	C₄×Q₈	—	89	1	no	—
138	C₄×Q₈	—	89	2	no	—
139	C₄×Q₈	—	178	1	no	—
140	C₄×Q₈	C₂×D₈₉	1	1	yes	characteristic
141	C₄×D₄	—	89	2	no	—
142	C₄×D₄	C₂×D₈₉	1	1	yes	characteristic
143	C₂×C₄⋊C₄	—	178	1	no	—
144	#107	—	89	2	no	—
145	#107	—	89	2	no	—
146	#107	—	89	2	no	—
147	#106	—	89	2	no	—
148	#106	C₂×D₈₉	1	1	yes	characteristic
149	C₄⋊C₈	—	89	2	no	—
150	C₄⋊C₈	—	89	1	no	—
151	#103	—	89	2	no	—
152	#103	C₂×D₈₉	1	1	yes	characteristic
153	#102	—	89	2	no	—
154	#102	C₂×D₈₉	1	1	yes	characteristic
155	#97	—	89	2	no	—
156	C₄×C₈	C₂×D₈₉	1	1	yes	characteristic
157	C₂×Q₈	—	89	1	no	—
158	C₂×Q₈	—	178	2	no	—
159	C₂×Q₈	—	178	1	no	—
160	C₂×Q₈	—	178	1	no	—
161	C₂×Q₈	C₂²×D₈₉	1	1	yes	characteristic
162	C₂×D₄	C₂²×D₈₉	1	1	yes	characteristic
163	C₂²×C₄	—	2	1	no	—
164	C₂²×C₄	—	178	2	no	—
165	SD₁₆	Dic₁₇₈	1	4	yes	complemented
166	C₂×C₈	—	89	2	no	—
167	C₂×C₈	C₂²×D₈₉	1	1	yes	characteristic
168	C₂×C₈	C₂²×D₈₉	1	1	yes	characteristic
169	C₄⋊C₄	—	2	1	no	—
170	C₄⋊C₄	—	89	1	no	—
171	C₄⋊C₄	—	89	2	no	—
172	C₄⋊C₄	—	89	2	no	—
173	C₄⋊C₄	—	89	2	no	—
174	C₄⋊C₄	—	178	2	no	—
175	C₄⋊C₄	—	178	2	no	—
176	C₄⋊C₄	—	178	2	no	—
177	C₄⋊C₄	—	178	2	no	—
178	C₄⋊C₄	—	178	1	no	—
179	C₄⋊C₄	—	178	1	no	—
180	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
181	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
182	C₂²⋊C₄	—	2	1	no	—
183	C₂²⋊C₄	—	178	2	no	—
184	C₄²	—	2	1	no	—
185	C₄²	—	89	2	no	—
186	C₄²	—	178	2	no	—
187	C₄²	C₂²×D₈₉	1	1	yes	characteristic
188	C₂³	—	2	1	no	—
189	Q₈	—	2	1	no	—
190	Q₈	—	178	2	no	—
191	Q₈	—	712	1	no	—
192	Q₈	—	712	1	no	—
193	Q₈	—	712	2	no	—
194	Q₈	C₂×Dic₁₇₈	1	2	yes	—
195	D₄	—	2	1	no	—
196	D₄	C₂×Dic₁₇₈	1	2	yes	—
197	C₂×C₄	—	2	1	no	—
198	C₂×C₄	—	2	1	no	—
199	C₂×C₄	—	2	1	no	—
200	C₂×C₄	—	4	2	no	—
201	C₂×C₄	—	89	2	no	—
202	C₂×C₄	—	89	2	no	—
203	C₂×C₄	—	178	2	no	—
204	C₂×C₄	—	178	2	no	—
205	C₂×C₄	—	712	2	no	—
206	C₂×C₄	D₄×D₈₉	1	1	yes	characteristic
207	C₂×C₄	D₄×D₈₉	1	1	yes	characteristic
208	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
209	C₈	—	2	1	no	—
210	C₈	—	178	2	no	—
211	C₈	C₂×Dic₁₇₈	1	2	yes	—
212	C₂²	—	2	2	no	—
213	C₂²	—	4	1	no	—
214	C₂²	—	4	1	no	—
215	C₂²	C₂×D₄×D₈₉	1	1	yes	characteristic
216	C₄	—	2	1	no	—
217	C₄	—	2	2	no	—
218	C₄	—	4	1	no	—
219	C₄	—	4	1	no	—
220	C₄	—	356	2	no	—
221	C₄	—	356	2	no	—
222	C₄	—	178	2	no	—
223	C₄	—	178	2	no	—
224	C₄	#15668041	1	2	yes	—
225	C₄	C₂²×Dic₁₇₈	1	1	yes	characteristic
226	C₄	#15668059	1	1	yes	characteristic
227	C₂	—	4	2	no	—
228	C₂	D₄×Dic₁₇₈	1	1	yes	characteristic
229	C₂	C₂×#15668041	1	1	yes	characteristic
230	C₂	#19152400	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

Q₈×Dic₁₇₈

C₂

yes

maximal, characteristic, complemented

#19152305

C₂

yes

maximal, characteristic

#19152005

C₂

yes

maximal, complemented

#19152003

C₂

yes

maximal, characteristic, complemented

#19151907

C₂

yes

maximal, complemented

#19151893

C₂

yes

maximal, characteristic, complemented

#19151888

C₂

yes

maximal, characteristic

#19151876

C₂

yes

maximal

#19151728

C₂

yes

maximal, characteristic, complemented

#19151699

C₂

yes

maximal

C₄×SD₁₆×C₈₉

C₂

yes

maximal, characteristic

#15668012

—

#15668012

C₂²

yes

characteristic

#15668012

C₂²

yes

characteristic

#15668011

—

#15668011

C₂²

yes

—

#15668003

C₂²

yes

—

#15667991

—

#15667989

—

Q₈×Dic₈₉

C₂²

yes

—

C₄×Dic₁₇₈

—

C₄×Dic₁₇₈

C₂²

yes

characteristic

D₄×Dic₈₉

C₂²

yes

—

C₂×C₄⋊Dic₈₉

—

#15667946

C₂²

yes

—

#15667946

C₂²

yes

—

#15667945

C₂²

yes

—

#15667943

C₂²

yes

—

C₄⋊#10623494

C₂²

yes

characteristic

#15667941

C₂²

yes

—

#15667936

C₂²

yes

—

#15667933

C₂²

yes

—

#15667922

C₂²

yes

—

C₂×SD₁₆×C₈₉

C₂²

yes

characteristic

C₄×Q₈×C₈₉

C₂²

yes

characteristic

C₄×D₄×C₈₉

C₂²

yes

characteristic

#106×C₈₉

C₂²

yes

characteristic

#103×C₈₉

C₂²

yes

characteristic

#102×C₈₉

C₂²

yes

characteristic

C₄×C₈×C₈₉

C₂²

yes

characteristic

C₂×Dic₁₇₈

—

C₂×Dic₁₇₈

—

C₂×Dic₁₇₈

—

C₂×Dic₁₇₈

D₄

yes

characteristic

C₂²×Dic₈₉

—

C₂×#10623494

C₂³

yes

—

C₄⋊Dic₈₉

—

C₄⋊Dic₈₉

—

C₄⋊Dic₈₉

—

C₄⋊Dic₈₉

—

C₄⋊Dic₈₉

D₄

yes

characteristic

C₄⋊Dic₈₉

C₂³

yes

—

C₄⋊Dic₈₉

C₂³

yes

—

#13083553

—

#13083553

—

#13083553

D₄

yes

—

C₂²⋊Dic₈₉

—

C₄×Dic₈₉

—

C₄×Dic₈₉

C₂³

yes

—

C₂×Q₈×C₈₉

C₂³

yes

characteristic

C₂×D₄×C₈₉

C₂³

yes

characteristic

C₂²×C₄×C₈₉

—

SD₁₆×C₈₉

Q₈

yes

complemented

C₂×C₈×C₈₉

C₂³

yes

characteristic

C₂×C₈×C₈₉

C₂³

yes

characteristic

C₄⋊C₄×C₈₉

—

C₄⋊C₄×C₈₉

C₂³

yes

characteristic

C₄⋊C₄×C₈₉

C₂³

yes

characteristic

C₂²⋊C₄×C₈₉

—

C₄²×C₈₉

—

C₄²×C₈₉

C₂³

yes

characteristic

C₂³×C₈₉

—

Q₈×C₈₉

—

Q₈×C₈₉

C₂×Q₈

yes

—

D₄×C₈₉

—

D₄×C₈₉

C₂×Q₈

yes

—

C₂×C₄×C₈₉

—

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

C₂⁴

yes

characteristic

C₂×Dic₈₉

—

C₂×Dic₈₉

—

C₂×Dic₈₉

—

C₂×Dic₈₉

C₂×D₄

yes

—

C₂×Dic₈₉

C₂×D₄

yes

—

Dic₁₇₈

—

Dic₁₇₈

—

Dic₁₇₈

—

Dic₁₇₈

—

C₈×C₈₉

—

C₈×C₈₉

C₂×Q₈

yes

—

#10623494

—

C₂²×C₈₉

—

C₂²×C₈₉

—

C₂²×C₈₉

—

C₂²×C₈₉

C₂²×D₄

yes

characteristic

100

C₄×C₈₉

—

101

C₄×C₈₉

—

102

C₄×C₈₉

—

103

C₄×C₈₉

—

104

C₄×C₈₉

#137

yes

—

105

C₄×C₈₉

C₂²×Q₈

yes

characteristic

106

C₄×C₈₉

2₋¹⁺⁴

yes

characteristic

107

Dic₈₉

—

108

Dic₈₉

—

109

Dic₈₉

—

110

Dic₈₉

—

111

C₂×C₈₉

—

112

C₂×C₈₉

D₄×Q₈

yes

characteristic

113

C₂×C₈₉

C₂×#137

yes

characteristic

114

C₂×C₈₉

yes

115

—

116

C₈₉

#3385

yes

characteristic, complemented, Sylow

117

Q₈²

—

118

#554

—

119

#501

—

120

#500

—

121

#479

—

122

#477

—

123

#476

—

124

#474

—

125

#446

—

126

#440

—

127

C₄×SD₁₆

D₈₉

yes

characteristic

128

C₂×SD₁₆

C₂×D₈₉

yes

characteristic

129

C₄⋊Q₈

—

130

C₄⋊Q₈

—

131

C₄⋊Q₈

—

132

C₄⋊Q₈

—

178

—

133

C₄⋊Q₈

—

178

—

134

#125

—

135

C₂²⋊Q₈

—

178

—

136

C₂²⋊Q₈

—

178

—

137

C₄×Q₈

—

138

C₄×Q₈

—

139

C₄×Q₈

—

178

—

140

C₄×Q₈

C₂×D₈₉

yes

characteristic

141

C₄×D₄

—

142

C₄×D₄

C₂×D₈₉

yes

characteristic

143

C₂×C₄⋊C₄

—

178

—

144

#107

—

145

#107

—

146

#107

—

147

#106

—

148

#106

C₂×D₈₉

yes

characteristic

149

C₄⋊C₈

—

150

C₄⋊C₈

—

151

#103

—

152

#103

C₂×D₈₉

yes

characteristic

153

#102

—

154

#102

C₂×D₈₉

yes

characteristic

155

#97

—

156

C₄×C₈

C₂×D₈₉

yes

characteristic

157

C₂×Q₈

—

158

C₂×Q₈

—

178

—

159

C₂×Q₈

—

178

—

160

C₂×Q₈

—

178

—

161

C₂×Q₈

C₂²×D₈₉

yes

characteristic

162

C₂×D₄

C₂²×D₈₉

yes

characteristic

163

C₂²×C₄

—

164

C₂²×C₄

—

178

—

165

SD₁₆

Dic₁₇₈

yes

complemented

166

C₂×C₈

—

167

C₂×C₈

C₂²×D₈₉

yes

characteristic

168

C₂×C₈

C₂²×D₈₉

yes

characteristic

169

C₄⋊C₄

—

170

C₄⋊C₄

—

171

C₄⋊C₄

—

172

C₄⋊C₄

—

173

C₄⋊C₄

—

174

C₄⋊C₄

—

178

—

175

C₄⋊C₄

—

178

—

176

C₄⋊C₄

—

178

—

177

C₄⋊C₄

—

178

—

178

C₄⋊C₄

—

178

—

179

C₄⋊C₄

—

178

—

180

C₄⋊C₄

C₂²×D₈₉

yes

characteristic

181

C₄⋊C₄

C₂²×D₈₉

yes

characteristic

182

C₂²⋊C₄

—

183

C₂²⋊C₄

—

178

—

184

C₄²

—

185

C₄²

—

186

C₄²

—

178

—

187

C₄²

C₂²×D₈₉

yes

characteristic

188

C₂³

—

189

Q₈

—

190

Q₈

—

178

—

191

Q₈

—

712

—

192

Q₈

—

712

—

193

Q₈

—

712

—

194

Q₈

C₂×Dic₁₇₈

yes

—

195

D₄

—

196

D₄

C₂×Dic₁₇₈

yes

—

197

C₂×C₄

—

198

C₂×C₄

—

199

C₂×C₄

—

200

C₂×C₄

—

201

C₂×C₄

—

202

C₂×C₄

—

203

C₂×C₄

—

178

—

204

C₂×C₄

—

178

—

205

C₂×C₄

—

712

—

206

C₂×C₄

D₄×D₈₉

yes

characteristic

207

C₂×C₄

D₄×D₈₉

yes

characteristic

208

C₂×C₄

C₂³×D₈₉

yes

characteristic

209

C₈

—

210

C₈

—

178

—

211

C₈

C₂×Dic₁₇₈

yes

—

212

C₂²

—

213

C₂²

—

214

C₂²

—

215

C₂²

C₂×D₄×D₈₉

yes

characteristic

216

C₄

—

217

C₄

—

218

C₄

—

219

C₄

—

220

C₄

—

356

—

221

C₄

—

356

—

222

C₄

—

178

—

223

C₄

—

178

—

224

C₄

#15668041

yes

—

225

C₄

C₂²×Dic₁₇₈

yes

characteristic

226

C₄

#15668059

yes

characteristic

227

C₂

—

228

C₂

D₄×Dic₁₇₈

yes

characteristic

229

C₂

C₂×#15668041

yes

characteristic

230

C₂

#19152400

yes

characteristic

	subgroup	G/H
center	C₂²	C₂×D₄×D₈₉
commutator, cosocle	C₂×C₄×C₈₉	C₂⁴
Frattini	C₂×C₄	C₂³×D₈₉
Fitting	C₄×SD₁₆×C₈₉	C₂
socle	C₂²×C₈₉	C₂²×D₄
prime radical	C₂×D₄×C₈₉	C₂³
hypercenter	C₄×SD₁₆	D₈₉
hypocenter	C₈₉	#3385
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×SD₁₆

subgroup

G/H

center

C₂²

C₂×D₄×D₈₉

commutator, cosocle

C₂×C₄×C₈₉

C₂⁴

Frattini

C₂×C₄

C₂³×D₈₉

Fitting

C₄×SD₁₆×C₈₉

C₂

socle

C₂²×C₈₉

C₂²×D₄

prime radical

C₂×D₄×C₈₉

C₂³

hypercenter

C₄×SD₁₆

D₈₉

hypocenter

C₈₉

#3385

LCS

G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ C₄×SD₁₆

N	H ≅ G/N	type
1. Q₈×Dic₁₇₈	C₂	semidirect
3. #19152005	C₂	semidirect
4. #19152003	C₂	semidirect
5. #19151907	C₂	semidirect
6. #19151893	C₂	semidirect
9. #19151728	C₂	semidirect
63. SD₁₆×C₈₉	Q₈	semidirect
116. C₈₉	#3385	semidirect
165. SD₁₆	Dic₁₇₈	semidirect

H ≅ G/N

type

1. Q₈×Dic₁₇₈

C₂

semidirect

3. #19152005

C₂

semidirect

4. #19152003

C₂

semidirect

5. #19151907

C₂

semidirect

6. #19151893

C₂

semidirect

9. #19151728

C₂

semidirect

63. SD₁₆×C₈₉

Q₈

semidirect

116. C₈₉

#3385

semidirect

165. SD₁₆

Dic₁₇₈

semidirect

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

subgroup	index
Q₈×Dic₁₇₈	2
#19152305	2
#19152005	2
#19152003	2
#19151907	2
#19151893	2
#19151888	2
#19151876	2
#19151728	2
#19151699	2
C₄×SD₁₆×C₈₉	2
#3385	89

subgroup

index

Q₈×Dic₁₇₈

C₄×SD₁₆×C₈₉

Subgroups — #26033160

Conjugacy classes of subgroups

Complements

Maximal subgroups