Group #36708928 — subgroups

Subgroups — #36708928

Order 22784.

650 conjugacy classes of subgroups; only the 171 normal subgroups are shown.

normal subgroups only

This group has 650 conjugacy classes of subgroups — too many to draw. Only its 171 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	C₂×#19152014	C₂	1	1	yes	maximal, characteristic
2	#26029903	C₂	1	2	yes	maximal
3	#26022357	C₂	1	4	yes	maximal, complemented
4	#26022340	C₂	1	4	yes	maximal, complemented
5	#26022036	C₂	1	1	yes	maximal, characteristic, complemented
6	#26021972	C₂	1	2	yes	maximal, complemented
7	C₂²×Q₃₂×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#15668018	C₂²	1	1	yes	characteristic
9	#19152172	—	2	2	no	—
10	#19152014	—	2	4	no	—
11	C₂×#15667952	C₂²	1	1	yes	characteristic
12	C₂×#15667951	C₂²	1	2	yes	—
13	C₂×C₁₆×D₈₉	C₂²	1	2	yes	—
14	#19151853	—	2	4	no	—
15	#19151836	C₂²	1	8	yes	—
16	#19151636	C₂²	1	2	yes	—
17	#19151607	—	2	2	no	—
18	#19151426	C₂²	1	2	yes	—
19	#19151424	C₂²	1	2	yes	—
20	#19151402	C₂²	1	8	yes	—
21	C₂²×Q₁₆×C₈₉	C₂²	1	2	yes	—
22	C₂×Q₃₂×C₈₉	—	2	4	no	—
23	C₂×Q₃₂×C₈₉	C₂²	1	2	yes	—
24	C₂×Q₃₂×C₈₉	C₂²	1	2	yes	—
25	C₂²×C₁₆×C₈₉	C₂²	1	1	yes	characteristic
26	C₂×#13083574	D₄	1	1	yes	characteristic
27	#15668018	—	2	2	no	—
28	#15668018	—	2	2	no	—
29	C₂×#13083558	D₄	1	1	yes	characteristic
30	C₂×#13083557	D₄	1	2	yes	—
31	C₂×C₈×D₈₉	C₂³	1	2	yes	—
32	#15668010	—	4	2	no	—
33	#15668001	—	4	2	no	—
34	#15667995	—	4	4	no	—
35	#15667988	—	2	8	no	—
36	#15667971	—	2	2	no	—
37	#15667952	—	2	2	no	—
38	#15667951	—	2	4	no	—
39	C₂×#13083549	C₂³	1	2	yes	—
40	C₁₆×D₈₉	—	2	4	no	—
41	#15667946	C₂³	1	4	yes	—
42	#15667944	—	2	2	no	—
43	#15667936	—	2	8	no	—
44	C₂²×Q₈×C₈₉	—	2	2	no	—
45	C₂×Q₁₆×C₈₉	—	2	4	no	—
46	C₂×Q₁₆×C₈₉	—	2	2	no	—
47	C₂×Q₁₆×C₈₉	—	2	4	no	—
48	C₂×Q₁₆×C₈₉	C₂³	1	4	yes	—
49	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
50	Q₃₂×C₈₉	—	2	4	no	—
51	Q₃₂×C₈₉	—	2	4	no	—
52	C₂×C₁₆×C₈₉	D₄	1	4	yes	—
53	C₂×C₁₆×C₈₉	C₂³	1	1	yes	characteristic
54	C₂×C₁₆×C₈₉	C₂³	1	1	yes	characteristic
55	#13083574	—	2	2	no	—
56	#13083574	—	2	2	no	—
57	C₂×Dic₁₇₈	D₈	1	1	yes	characteristic
58	C₂×D₃₅₆	D₈	1	1	yes	characteristic
59	C₂×C₂²⋊D₈₉	D₈	1	2	yes	—
60	C₂×C₄×D₈₉	C₂×D₄	1	2	yes	—
61	#13083558	—	2	2	no	—
62	#13083557	—	2	4	no	—
63	C₂×#10623494	C₂×D₄	1	2	yes	—
64	C₈×D₈₉	—	2	2	no	—
65	C₈×D₈₉	—	2	2	no	—
66	C₄⋊Dic₈₉	—	2	4	no	—
67	#13083553	—	4	8	no	—
68	C₂²⋊Dic₈₉	—	4	2	no	—
69	#13083551	—	4	8	no	—
70	C₄×Dic₈₉	—	4	2	no	—
71	#13083549	—	2	2	no	—
72	C₂×Q₈×C₈₉	—	2	4	no	—
73	C₂×Q₈×C₈₉	—	4	2	no	—
74	C₂×Q₈×C₈₉	—	4	4	no	—
75	C₂×Q₈×C₈₉	—	4	4	no	—
76	C₂²×C₄×C₈₉	—	4	2	no	—
77	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
78	Q₁₆×C₈₉	—	2	4	no	—
79	Q₁₆×C₈₉	—	2	4	no	—
80	Q₁₆×C₈₉	—	4	4	no	—
81	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
82	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
83	C₂×C₈×C₈₉	#41	1	2	yes	—
84	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
85	C₁₆×C₈₉	C₂×D₄	1	2	yes	—
86	C₁₆×C₈₉	C₂×D₄	1	2	yes	—
87	C₂³×C₈₉	C₂×D₈	1	1	yes	characteristic
88	C₂²×D₈₉	C₂×D₈	1	2	yes	—
89	Q₈×C₈₉	—	4	4	no	—
90	Q₈×C₈₉	—	4	4	no	—
91	Q₈×C₈₉	—	8	4	no	—
92	C₂×C₄×C₈₉	—	4	4	no	—
93	C₂×C₄×C₈₉	—	8	4	no	—
94	C₂×C₄×C₈₉	#121	1	2	yes	—
95	C₂×C₄×C₈₉	C₂×D₈	1	1	yes	characteristic
96	C₂×C₄×C₈₉	#135	1	2	yes	—
97	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
98	C₂²⋊D₈₉	—	2	4	no	—
99	C₂×Dic₈₉	—	4	4	no	—
100	C₂×Dic₈₉	C₂×D₈	1	2	yes	—
101	D₃₅₆	—	2	2	no	—
102	C₄×D₈₉	—	2	2	no	—
103	C₄×D₈₉	—	2	2	no	—
104	Dic₁₇₈	—	2	2	no	—
105	C₈×C₈₉	#121	1	2	yes	—
106	C₈×C₈₉	C₂²×D₄	1	1	yes	characteristic
107	C₈×C₈₉	C₂×#41	1	1	yes	characteristic
108	#10623494	—	2	2	no	—
109	C₂²×C₈₉	—	2	2	no	—
110	C₂²×C₈₉	#466	1	2	yes	—
111	C₂²×C₈₉	C₂²×D₈	1	1	yes	characteristic
112	C₂×D₈₉	—	2	4	no	—
113	C₂×D₈₉	—	2	2	no	—
114	C₄×C₈₉	—	8	4	no	—
115	C₄×C₈₉	#466	1	2	yes	—
116	C₄×C₈₉	C₂×#121	1	1	yes	characteristic
117	C₄×C₈₉	C₂×#135	1	1	yes	characteristic
118	Dic₈₉	—	2	2	no	—
119	Dic₈₉	—	8	4	no	—
120	#33608	—	89	1	no	maximal, Sylow
121	C₂×C₈₉	—	2	2	no	—
122	C₂×C₈₉	C₂×#466	1	1	yes	characteristic
123	C₂×C₈₉	#3417	1	2	yes	—
124	D₈₉	—	4	2	no	—
125	C₂²×Q₃₂	D₈₉	1	1	yes	characteristic, complemented
126	C₂×#504	—	89	1	no	—
127	#3059	—	89	2	no	—
128	#2219	—	89	4	no	—
129	#2216	—	89	4	no	—
130	#2158	—	89	1	no	—
131	#2141	—	89	2	no	—
132	C₈₉	#33608	1	1	yes	characteristic, complemented, Sylow
133	C₂²×Q₁₆	C₂×D₈₉	1	2	yes	—
134	C₂×#131	—	89	1	no	—
135	#536	—	178	2	no	—
136	C₂×Q₃₂	—	2	4	no	—
137	C₂×Q₃₂	C₂×D₈₉	1	2	yes	—
138	C₂×Q₃₂	C₂×D₈₉	1	2	yes	—
139	#504	—	178	4	no	—
140	C₂×M₃₂	—	89	1	no	—
141	C₂×M₃₂	—	89	2	no	—
142	C₂²×C₁₆	—	89	2	no	—
143	C₂²×C₁₆	C₂×D₈₉	1	1	yes	characteristic
144	#470	—	178	4	no	—
145	#467	—	89	8	no	—
146	#427	—	89	2	no	—
147	#419	—	178	2	no	—
148	#367	—	89	2	no	—
149	#366	—	89	2	no	—
150	#358	—	89	8	no	—
151	C₂×#41	—	89	1	no	—
152	C₂²×Q₈	—	2	2	no	—
153	C₂×Q₁₆	—	2	2	no	—
154	C₂×Q₁₆	—	2	4	no	—
155	C₂×Q₁₆	—	2	4	no	—
156	C₂×Q₁₆	C₂²×D₈₉	1	4	yes	—
157	#131	—	178	2	no	—
158	#131	—	178	2	no	—
159	C₂×M₁₆	—	89	1	no	—
160	C₂×M₁₆	—	89	2	no	—
161	C₂²×C₈	—	89	2	no	—
162	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
163	C₄⋊Q₈	—	356	2	no	—
164	#124	—	356	2	no	—
165	#123	—	356	4	no	—
166	C₂²⋊Q₈	—	178	8	no	—
167	#117	—	178	2	no	—
168	Q₃₂	—	2	4	no	—
169	Q₃₂	—	2	4	no	—
170	M₃₂	—	178	2	no	—
171	M₃₂	—	178	4	no	—
172	C₂×C₁₆	—	89	2	no	—
173	C₂×C₁₆	—	178	4	no	—
174	C₂×C₁₆	C₂²⋊D₈₉	1	4	yes	—
175	C₂×C₁₆	C₂²×D₈₉	1	1	yes	characteristic
176	C₂×C₁₆	C₂²×D₈₉	1	1	yes	characteristic
177	#107	—	89	4	no	—
178	#106	—	178	2	no	—
179	#103	—	178	8	no	—
180	#41	—	178	2	no	—
181	#41	—	178	2	no	—
182	C₂×Q₈	—	2	4	no	—
183	C₂×Q₈	—	4	2	no	—
184	C₂×Q₈	—	4	4	no	—
185	C₂×Q₈	—	4	4	no	—
186	C₂×Q₈	—	89	1	no	—
187	C₂×D₄	—	89	2	no	—
188	C₂×D₄	—	89	1	no	—
189	C₂²×C₄	—	4	2	no	—
190	C₂²×C₄	—	89	2	no	—
191	C₂²×C₄	D₄×D₈₉	1	1	yes	characteristic
192	Q₁₆	—	2	4	no	—
193	Q₁₆	—	2	4	no	—
194	Q₁₆	—	4	4	no	—
195	M₁₆	—	178	2	no	—
196	M₁₆	—	178	4	no	—
197	C₂×C₈	—	89	2	no	—
198	C₂×C₈	—	178	2	no	—
199	C₂×C₈	—	178	2	no	—
200	C₂×C₈	D₄×D₈₉	1	1	yes	characteristic
201	C₂×C₈	C₂×C₂²⋊D₈₉	1	2	yes	—
202	C₂×C₈	#13083573	1	2	yes	—
203	C₂×C₈	C₂³×D₈₉	1	1	yes	characteristic
204	C₄⋊C₄	—	356	8	no	—
205	C₄⋊C₄	—	178	4	no	—
206	C₂²⋊C₄	—	356	8	no	—
207	C₂²⋊C₄	—	356	2	no	—
208	C₄²	—	356	2	no	—
209	C₁₆	—	178	2	no	—
210	C₁₆	C₂×C₂²⋊D₈₉	1	2	yes	—
211	C₁₆	C₂×C₂²⋊D₈₉	1	2	yes	—
212	C₂³	—	89	2	no	—
213	C₂³	D₈×D₈₉	1	1	yes	characteristic
214	Q₈	—	4	4	no	—
215	Q₈	—	4	4	no	—
216	Q₈	—	8	4	no	—
217	Q₈	—	178	2	no	—
218	D₄	—	178	4	no	—
219	D₄	—	178	2	no	—
220	C₂×C₄	—	4	4	no	—
221	C₂×C₄	—	8	4	no	—
222	C₂×C₄	—	89	2	no	—
223	C₂×C₄	—	356	4	no	—
224	C₂×C₄	—	178	2	no	—
225	C₂×C₄	—	178	2	no	—
226	C₂×C₄	#15667983	1	2	yes	—
227	C₂×C₄	D₈×D₈₉	1	1	yes	characteristic
228	C₂×C₄	#15668031	1	2	yes	—
229	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
230	C₈	—	178	2	no	—
231	C₈	#15667983	1	2	yes	—
232	C₈	C₂²×C₂²⋊D₈₉	1	1	yes	characteristic
233	C₈	C₂×#13083573	1	1	yes	characteristic
234	C₂²	—	2	2	no	—
235	C₂²	—	178	2	no	—
236	C₂²	—	178	4	no	—
237	C₂²	#19151831	1	2	yes	—
238	C₂²	C₂×D₈×D₈₉	1	1	yes	characteristic
239	C₄	—	8	4	no	—
240	C₄	—	178	2	no	—
241	C₄	—	712	4	no	—
242	C₄	#19151831	1	2	yes	—
243	C₄	C₂×#15667983	1	1	yes	characteristic
244	C₄	C₂×#15668031	1	1	yes	characteristic
245	C₂	—	2	2	no	—
246	C₂	—	356	2	no	—
247	C₂	C₂×#19151831	1	1	yes	characteristic
248	C₂	#26033401	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#19152014

C₂

yes

maximal, characteristic

#26029903

C₂

yes

maximal

#26022357

C₂

yes

maximal, complemented

#26022340

C₂

yes

maximal, complemented

#26022036

C₂

yes

maximal, characteristic, complemented

#26021972

C₂

yes

maximal, complemented

C₂²×Q₃₂×C₈₉

C₂

yes

maximal, characteristic, complemented

C₂×#15668018

C₂²

yes

—

—

C₂²

yes

characteristic

C₂×#15667951

C₂²

yes

—

C₂×C₁₆×D₈₉

C₂²

yes

—

#19151853

—

#19151836

C₂²

yes

—

#19151636

C₂²

yes

—

#19151607

—

#19151426

C₂²

yes

—

#19151424

C₂²

yes

—

#19151402

C₂²

yes

—

C₂²×Q₁₆×C₈₉

C₂²

yes

—

C₂×Q₃₂×C₈₉

—

C₂×Q₃₂×C₈₉

C₂²

yes

—

C₂×Q₃₂×C₈₉

C₂²

yes

—

C₂²×C₁₆×C₈₉

C₂²

yes

characteristic

C₂×#13083574

D₄

yes

—

—

D₄

yes

characteristic

C₂×#13083557

D₄

yes

—

C₂×C₈×D₈₉

C₂³

yes

—

—

—

—

—

—

—

—

C₂³

yes

—

C₁₆×D₈₉

—

#15667946

C₂³

yes

—

#15667944

—

#15667936

—

C₂²×Q₈×C₈₉

—

C₂×Q₁₆×C₈₉

—

C₂×Q₁₆×C₈₉

—

C₂×Q₁₆×C₈₉

—

C₂×Q₁₆×C₈₉

C₂³

yes

—

C₂²×C₈×C₈₉

C₂³

yes

characteristic

Q₃₂×C₈₉

—

Q₃₂×C₈₉

—

C₂×C₁₆×C₈₉

D₄

yes

—

C₂×C₁₆×C₈₉

C₂³

yes

characteristic

C₂×C₁₆×C₈₉

C₂³

yes

characteristic

#13083574

—

#13083574

—

C₂×Dic₁₇₈

D₈

yes

characteristic

C₂×D₃₅₆

D₈

yes

characteristic

C₂×C₂²⋊D₈₉

D₈

yes

—

C₂×C₄×D₈₉

C₂×D₄

yes

—

#13083558

—

#13083557

—

C₂×#10623494

C₂×D₄

yes

—

C₈×D₈₉

—

C₈×D₈₉

—

C₄⋊Dic₈₉

—

#13083553

—

C₂²⋊Dic₈₉

—

#13083551

—

C₄×Dic₈₉

—

#13083549

—

C₂×Q₈×C₈₉

—

C₂×Q₈×C₈₉

—

C₂×Q₈×C₈₉

—

C₂×Q₈×C₈₉

—

C₂²×C₄×C₈₉

—

C₂²×C₄×C₈₉

C₂×D₄

yes

characteristic

Q₁₆×C₈₉

—

Q₁₆×C₈₉

—

Q₁₆×C₈₉

—

C₂×C₈×C₈₉

C₂×D₄

yes

characteristic

C₂×C₈×C₈₉

C₂×D₄

yes

—

C₂×C₈×C₈₉

#41

yes

—

C₂×C₈×C₈₉

C₂⁴

yes

characteristic

C₁₆×C₈₉

C₂×D₄

yes

—

C₁₆×C₈₉

C₂×D₄

yes

—

C₂³×C₈₉

C₂×D₈

yes

characteristic

C₂²×D₈₉

C₂×D₈

yes

—

Q₈×C₈₉

—

Q₈×C₈₉

—

Q₈×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

#121

yes

—

C₂×C₄×C₈₉

C₂×D₈

yes

characteristic

C₂×C₄×C₈₉

#135

yes

—

C₂×C₄×C₈₉

C₂²×D₄

yes

characteristic

C₂²⋊D₈₉

—

C₂×Dic₈₉

—

100

C₂×Dic₈₉

C₂×D₈

yes

—

101

D₃₅₆

—

102

C₄×D₈₉

—

103

C₄×D₈₉

—

104

Dic₁₇₈

—

105

C₈×C₈₉

#121

yes

—

106

C₈×C₈₉

C₂²×D₄

yes

characteristic

107

C₈×C₈₉

C₂×#41

yes

characteristic

108

#10623494

—

109

C₂²×C₈₉

—

110

C₂²×C₈₉

#466

yes

—

111

C₂²×C₈₉

C₂²×D₈

yes

characteristic

112

C₂×D₈₉

—

113

C₂×D₈₉

—

114

C₄×C₈₉

—

115

C₄×C₈₉

#466

yes

—

116

C₄×C₈₉

C₂×#121

yes

characteristic

117

C₄×C₈₉

C₂×#135

yes

characteristic

118

Dic₈₉

—

119

Dic₈₉

—

120

#33608

—

maximal, Sylow

121

C₂×C₈₉

—

122

C₂×C₈₉

C₂×#466

yes

characteristic

123

C₂×C₈₉

#3417

yes

—

124

D₈₉

—

125

C₂²×Q₃₂

D₈₉

yes

characteristic, complemented

126

C₂×#504

—

127

#3059

—

128

#2219

—

129

#2216

—

130

#2158

—

131

#2141

—

132

C₈₉

#33608

yes

characteristic, complemented, Sylow

133

C₂²×Q₁₆

C₂×D₈₉

yes

—

134

C₂×#131

—

135

#536

—

178

—

136

C₂×Q₃₂

—

137

C₂×Q₃₂

C₂×D₈₉

yes

—

138

C₂×Q₃₂

C₂×D₈₉

yes

—

139

#504

—

178

—

140

C₂×M₃₂

—

141

C₂×M₃₂

—

142

C₂²×C₁₆

—

143

C₂²×C₁₆

C₂×D₈₉

yes

characteristic

144

#470

—

178

—

145

#467

—

146

#427

—

147

#419

—

178

—

148

#367

—

149

#366

—

150

#358

—

151

C₂×#41

—

152

C₂²×Q₈

—

153

C₂×Q₁₆

—

154

C₂×Q₁₆

—

155

C₂×Q₁₆

—

156

C₂×Q₁₆

C₂²×D₈₉

yes

—

157

#131

—

178

—

158

#131

—

178

—

159

C₂×M₁₆

—

160

C₂×M₁₆

—

161

C₂²×C₈

—

162

C₂²×C₈

C₂²×D₈₉

yes

characteristic

163

C₄⋊Q₈

—

356

—

164

#124

—

356

—

165

#123

—

356

—

166

C₂²⋊Q₈

—

178

—

167

#117

—

178

—

168

Q₃₂

—

169

Q₃₂

—

170

M₃₂

—

178

—

171

M₃₂

—

178

—

172

C₂×C₁₆

—

173

C₂×C₁₆

—

178

—

174

C₂×C₁₆

C₂²⋊D₈₉

yes

—

175

C₂×C₁₆

C₂²×D₈₉

yes

characteristic

176

C₂×C₁₆

C₂²×D₈₉

yes

characteristic

177

#107

—

178

#106

—

178

—

179

#103

—

178

—

180

#41

—

178

—

181

#41

—

178

—

182

C₂×Q₈

—

183

C₂×Q₈

—

184

C₂×Q₈

—

185

C₂×Q₈

—

186

C₂×Q₈

—

187

C₂×D₄

—

188

C₂×D₄

—

189

C₂²×C₄

—

190

C₂²×C₄

—

191

C₂²×C₄

D₄×D₈₉

yes

characteristic

192

Q₁₆

—

193

Q₁₆

—

194

Q₁₆

—

195

M₁₆

—

178

—

196

M₁₆

—

178

—

197

C₂×C₈

—

198

C₂×C₈

—

178

—

199

C₂×C₈

—

178

—

200

C₂×C₈

D₄×D₈₉

yes

characteristic

201

C₂×C₈

C₂×C₂²⋊D₈₉

yes

—

202

C₂×C₈

#13083573

yes

—

203

C₂×C₈

C₂³×D₈₉

yes

characteristic

204

C₄⋊C₄

—

356

—

205

C₄⋊C₄

—

178

—

206

C₂²⋊C₄

—

356

—

207

C₂²⋊C₄

—

356

—

208

C₄²

—

356

—

209

C₁₆

—

178

—

210

C₁₆

C₂×C₂²⋊D₈₉

yes

—

211

C₁₆

C₂×C₂²⋊D₈₉

yes

—

212

C₂³

—

213

C₂³

D₈×D₈₉

yes

characteristic

214

Q₈

—

215

Q₈

—

216

Q₈

—

217

Q₈

—

178

—

218

D₄

—

178

—

219

D₄

—

178

—

220

C₂×C₄

—

221

C₂×C₄

—

222

C₂×C₄

—

223

C₂×C₄

—

356

—

224

C₂×C₄

—

178

—

225

C₂×C₄

—

178

—

226

C₂×C₄

#15667983

yes

—

227

C₂×C₄

D₈×D₈₉

yes

characteristic

228

C₂×C₄

#15668031

yes

—

229

C₂×C₄

C₂×D₄×D₈₉

yes

characteristic

230

C₈

—

178

—

231

C₈

#15667983

yes

—

232

C₈

C₂²×C₂²⋊D₈₉

yes

characteristic

233

C₈

C₂×#13083573

yes

characteristic

234

C₂²

—

235

C₂²

—

178

—

236

C₂²

—

178

—

237

C₂²

#19151831

yes

—

238

C₂²

C₂×D₈×D₈₉

yes

characteristic

239

C₄

—

240

C₄

—

178

—

241

C₄

—

712

—

242

C₄

#19151831

yes

—

243

C₄

C₂×#15667983

yes

characteristic

244

C₄

C₂×#15668031

yes

characteristic

245

C₂

—

246

C₂

—

356

—

247

C₂

C₂×#19151831

yes

characteristic

248

C₂

#26033401

yes

—

	subgroup	G/H
center	C₂²	C₂×D₈×D₈₉
commutator, cosocle	C₂×C₈×C₈₉	C₂⁴
Frattini	C₂×C₈	C₂³×D₈₉
Fitting	C₂²×Q₃₂×C₈₉	C₂
socle	C₂²×C₈₉	C₂²×D₈
prime radical	C₂×#13083574	D₄
hypercenter	C₂²×Q₃₂	D₈₉
hypocenter	C₈₉	#33608
LCS	G ▷ C₂×C₈×C₈₉ ▷ C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂²×Q₃₂

subgroup

G/H

center

C₂²

C₂×D₈×D₈₉

commutator, cosocle

C₂×C₈×C₈₉

C₂⁴

Frattini

C₂×C₈

C₂³×D₈₉

Fitting

C₂²×Q₃₂×C₈₉

C₂

socle

C₂²×C₈₉

C₂²×D₈

prime radical

C₂×#13083574

D₄

hypercenter

C₂²×Q₃₂

D₈₉

hypocenter

C₈₉

#33608

LCS

G ▷ C₂×C₈×C₈₉ ▷ C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂²×Q₃₂

N	H ≅ G/N	type
3. #26022357	C₂	semidirect
4. #26022340	C₂	semidirect
5. #26022036	C₂	semidirect
6. #26021972	C₂	semidirect
7. C₂²×Q₃₂×C₈₉	C₂	semidirect
125. C₂²×Q₃₂	D₈₉	semidirect
132. C₈₉	#33608	semidirect

H ≅ G/N

type

3. #26022357

C₂

semidirect

4. #26022340

C₂

semidirect

5. #26022036

C₂

semidirect

6. #26021972

C₂

semidirect

7. C₂²×Q₃₂×C₈₉

C₂

semidirect

125. C₂²×Q₃₂

D₈₉

semidirect

132. C₈₉

#33608

semidirect

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

subgroup	index
C₂×#19152014	2
#26029903	2
#26022357	2
#26022340	2
#26022036	2
#26021972	2
C₂²×Q₃₂×C₈₉	2
#33608	89

subgroup

index

C₂²×Q₃₂×C₈₉

Subgroups — #36708928

Conjugacy classes of subgroups

Complements

Maximal subgroups