Group #36447668 — subgroups

Subgroups — #36447668

Order 22784.

350 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 350 conjugacy classes of subgroups — too many to draw. Only its 115 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	#26029186	C₂	1	1	yes	maximal, characteristic
2	#26020383	C₂	1	1	yes	maximal, characteristic
3	#26018817	C₂	1	2	yes	maximal
4	#26018111	C₂	1	2	yes	maximal
5	C₈₉×#1564	C₂	1	1	yes	maximal, characteristic
6	#19152155	C₂²	1	1	yes	characteristic
7	#19151728	—	2	1	no	—
8	#19151728	C₄	1	2	yes	complemented
9	C₈×Dic₁₇₈	—	2	1	no	—
10	C₈×Dic₁₇₈	C₄	1	2	yes	complemented
11	#19151624	—	2	1	no	—
12	#19151622	C₂²	1	1	yes	characteristic
13	#19151553	—	2	1	no	—
14	#19151464	C₂²	1	2	yes	—
15	#19151361	—	2	1	no	—
16	#19151361	—	2	1	no	—
17	#19151336	—	2	4	no	—
18	#431×C₈₉	C₂²	1	2	yes	—
19	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
20	#335×C₈₉	—	2	1	no	—
21	#334×C₈₉	—	2	1	no	—
22	C₂×#13083558	—	2	1	no	—
23	#15668012	Q₈	1	1	yes	characteristic
24	#15668012	Q₈	1	1	yes	characteristic
25	#15668004	—	2	1	no	—
26	#15667991	—	2	1	no	—
27	#15667991	D₄	1	2	yes	—
28	C₄×Dic₁₇₈	—	2	1	no	—
29	C₄×Dic₁₇₈	C₂×C₄	1	2	yes	—
30	#15667971	—	2	1	no	—
31	C₂×C₄⋊Dic₈₉	—	2	2	no	—
32	C₄⋊#10623494	—	2	1	no	—
33	C₄⋊#10623494	C₂×C₄	1	2	yes	—
34	#15667941	—	2	2	no	—
35	#15667941	—	2	2	no	—
36	#15667922	—	2	2	no	—
37	C₈×Dic₈₉	—	2	2	no	—
38	#15667919	—	2	2	no	—
39	#15667919	—	2	2	no	—
40	C₂²×C₈×C₈₉	D₄	1	1	yes	characteristic
41	C₂²×C₈×C₈₉	D₄	1	1	yes	characteristic
42	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
43	C₄⋊C₈×C₈₉	—	2	2	no	—
44	C₂²⋊C₈×C₈₉	—	2	2	no	—
45	C₄×C₈×C₈₉	—	2	2	no	—
46	C₄×C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
47	C₄×C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
48	C₄×C₈×C₈₉	D₄	1	1	yes	characteristic
49	C₄×C₈×C₈₉	D₄	1	1	yes	characteristic
50	C₂×Dic₁₇₈	—	2	1	no	—
51	C₂×Dic₁₇₈	C₄⋊C₄	1	2	yes	—
52	C₂²×Dic₈₉	—	4	2	no	—
53	#13083558	—	4	2	no	—
54	C₂×#10623494	—	2	2	no	—
55	C₄⋊Dic₈₉	—	2	1	no	—
56	C₄⋊Dic₈₉	—	2	1	no	—
57	C₄⋊Dic₈₉	—	2	1	no	—
58	C₄⋊Dic₈₉	—	4	2	no	—
59	C₄⋊Dic₈₉	—	4	2	no	—
60	C₄⋊Dic₈₉	C₄⋊C₄	1	2	yes	—
61	#13083553	—	2	2	no	—
62	#13083553	—	2	2	no	—
63	C₂²⋊Dic₈₉	—	2	2	no	—
64	C₄×Dic₈₉	—	2	2	no	—
65	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
66	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
67	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
68	C₂×C₈×C₈₉	—	2	2	no	—
69	C₂×C₈×C₈₉	—	2	2	no	—
70	C₂×C₈×C₈₉	—	4	2	no	—
71	C₂×C₈×C₈₉	C₂²⋊C₄	1	1	yes	characteristic
72	C₂×C₈×C₈₉	C₂²⋊C₄	1	1	yes	characteristic
73	C₂×C₈×C₈₉	C₂²⋊C₄	1	1	yes	characteristic
74	C₂×C₈×C₈₉	C₂²⋊C₄	1	1	yes	characteristic
75	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
76	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
77	C₄²×C₈₉	C₂×Q₈	1	1	yes	characteristic
78	C₄²×C₈₉	#41	1	1	yes	characteristic
79	C₂³×C₈₉	#121	1	1	yes	characteristic
80	C₂×C₄×C₈₉	—	4	1	no	—
81	C₂×C₄×C₈₉	—	4	1	no	—
82	C₂×C₄×C₈₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
83	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
84	C₂×C₄×C₈₉	#117	1	1	yes	characteristic
85	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
86	C₂×C₄×C₈₉	C₂²⋊Q₈	1	1	yes	characteristic
87	C₂×C₄×C₈₉	C₂²⋊Q₈	1	1	yes	characteristic
88	C₂×C₄×C₈₉	#135	1	2	yes	—
89	C₂×C₄×C₈₉	#137	1	2	yes	—
90	C₂×Dic₈₉	—	2	2	no	—
91	C₂×Dic₈₉	—	2	2	no	—
92	C₂×Dic₈₉	—	8	2	no	—
93	C₂×Dic₈₉	—	8	2	no	—
94	C₂×Dic₈₉	—	8	2	no	—
95	Dic₁₇₈	—	4	2	no	—
96	Dic₁₇₈	—	4	2	no	—
97	C₈×C₈₉	—	2	1	no	—
98	C₈×C₈₉	—	2	1	no	—
99	C₈×C₈₉	—	2	1	no	—
100	C₈×C₈₉	—	2	1	no	—
101	C₈×C₈₉	—	8	2	no	—
102	#10623494	—	4	2	no	—
103	C₂²×C₈₉	—	2	1	no	—
104	C₂²×C₈₉	—	2	1	no	—
105	C₂²×C₈₉	#380	1	1	yes	characteristic
106	C₂²×C₈₉	#464	1	2	yes	—
107	C₄×C₈₉	—	2	1	no	—
108	C₄×C₈₉	—	2	1	no	—
109	C₄×C₈₉	—	2	1	no	—
110	C₄×C₈₉	—	2	1	no	—
111	C₄×C₈₉	#416	1	1	yes	characteristic
112	C₄×C₈₉	#419	1	1	yes	characteristic
113	C₄×C₈₉	#479	1	2	yes	—
114	Dic₈₉	—	4	2	no	—
115	Dic₈₉	—	4	2	no	—
116	Dic₈₉	—	16	2	no	—
117	#8681	—	89	1	no	maximal, Sylow
118	C₂×C₈₉	—	2	2	no	—
119	C₂×C₈₉	#1805	1	1	yes	characteristic
120	C₂×C₈₉	#1812	1	1	yes	characteristic
121	C₂×C₈₉	#1814	1	1	yes	characteristic
122	#2960	—	89	1	no	—
123	#1835	—	89	1	no	—
124	#1564	D₈₉	1	1	yes	characteristic
125	#1518	—	89	2	no	—
126	#1286	—	89	2	no	—
127	C₈₉	#8681	1	1	yes	characteristic, complemented, Sylow
128	#533	—	89	1	no	—
129	#446	—	89	2	no	—
130	#446	—	178	1	no	—
131	C₈×Q₈	—	89	2	no	—
132	C₈×Q₈	—	178	1	no	—
133	#431	C₂×D₈₉	1	2	yes	—
134	#424	—	178	1	no	—
135	#423	—	89	1	no	—
136	#405	—	178	1	no	—
137	C₂×C₄×C₈	C₂×D₈₉	1	1	yes	characteristic
138	#382	—	89	2	no	—
139	#340	—	178	1	no	—
140	#340	—	178	1	no	—
141	#335	—	2	1	no	—
142	#334	—	2	1	no	—
143	#328	—	178	4	no	—
144	C₂×M₁₆	—	178	1	no	—
145	C₂²×C₈	D₃₅₆	1	1	yes	characteristic
146	C₂²×C₈	D₃₅₆	1	1	yes	characteristic
147	C₄⋊Q₈	—	89	1	no	—
148	C₄⋊Q₈	—	89	1	no	—
149	#125	—	178	1	no	—
150	C₂²⋊Q₈	—	89	2	no	—
151	C₂²⋊Q₈	—	178	1	no	—
152	C₄×Q₈	—	89	2	no	—
153	C₄×Q₈	—	178	1	no	—
154	#117	—	178	1	no	—
155	C₂×C₄⋊C₄	—	178	2	no	—
156	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
157	C₄⋊C₈	—	2	2	no	—
158	C₄⋊C₈	—	89	2	no	—
159	C₄⋊C₈	—	178	2	no	—
160	C₄⋊C₈	—	178	2	no	—
161	C₄⋊C₈	—	178	1	no	—
162	C₂²⋊C₈	—	2	2	no	—
163	#97	—	178	2	no	—
164	C₄×C₈	—	2	2	no	—
165	C₄×C₈	—	178	2	no	—
166	C₄×C₈	C₄×D₈₉	1	1	yes	characteristic
167	C₄×C₈	C₄×D₈₉	1	1	yes	characteristic
168	C₄×C₈	C₂²⋊D₈₉	1	1	yes	characteristic
169	C₄×C₈	C₂²⋊D₈₉	1	1	yes	characteristic
170	#95	—	178	2	no	—
171	#95	—	178	2	no	—
172	C₂×Q₈	—	89	2	no	—
173	C₂×Q₈	—	178	1	no	—
174	C₂²×C₄	—	356	2	no	—
175	C₂²×C₄	D₄×D₈₉	1	1	yes	characteristic
176	C₂²×C₄	C₂×D₃₅₆	1	1	yes	characteristic
177	C₂²×C₄	#13083575	1	1	yes	characteristic
178	M₁₆	—	356	2	no	—
179	C₂×C₈	—	2	2	no	—
180	C₂×C₈	—	2	2	no	—
181	C₂×C₈	—	4	2	no	—
182	C₂×C₈	—	178	2	no	—
183	C₂×C₈	#13083551	1	1	yes	characteristic
184	C₂×C₈	#13083551	1	1	yes	characteristic
185	C₂×C₈	#13083551	1	1	yes	characteristic
186	C₂×C₈	#13083551	1	1	yes	characteristic
187	C₄⋊C₄	—	89	2	no	—
188	C₄⋊C₄	—	356	2	no	—
189	C₄⋊C₄	—	356	2	no	—
190	C₄⋊C₄	—	178	2	no	—
191	C₄⋊C₄	—	178	2	no	—
192	C₄⋊C₄	—	178	1	no	—
193	C₄⋊C₄	—	178	1	no	—
194	C₄⋊C₄	—	178	1	no	—
195	C₂²⋊C₄	—	178	2	no	—
196	C₄²	—	178	2	no	—
197	C₄²	C₂×C₄×D₈₉	1	1	yes	characteristic
198	C₄²	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
199	C₄²	Q₈×D₈₉	1	1	yes	characteristic
200	C₄²	#13083573	1	1	yes	characteristic
201	C₂³	#15667987	1	1	yes	characteristic
202	Q₈	—	356	2	no	—
203	Q₈	—	356	2	no	—
204	C₂×C₄	—	4	1	no	—
205	C₂×C₄	—	4	1	no	—
206	C₂×C₄	—	178	2	no	—
207	C₂×C₄	—	178	2	no	—
208	C₂×C₄	—	712	2	no	—
209	C₂×C₄	—	712	2	no	—
210	C₂×C₄	—	712	2	no	—
211	C₂×C₄	C₂×#13083551	1	1	yes	characteristic
212	C₂×C₄	C₄⋊C₄×D₈₉	1	1	yes	characteristic
213	C₂×C₄	#15667970	1	1	yes	characteristic
214	C₂×C₄	#15667983	1	1	yes	characteristic
215	C₂×C₄	#15667988	1	1	yes	characteristic
216	C₂×C₄	#15667992	1	1	yes	characteristic
217	C₂×C₄	#15668034	1	2	yes	—
218	C₂×C₄	#15668045	1	2	yes	—
219	C₈	—	2	1	no	—
220	C₈	—	2	1	no	—
221	C₈	—	2	1	no	—
222	C₈	—	2	1	no	—
223	C₈	—	8	2	no	—
224	C₈	—	356	2	no	—
225	C₂²	—	2	1	no	—
226	C₂²	—	2	1	no	—
227	C₂²	#19151455	1	1	yes	characteristic
228	C₂²	#19151821	1	2	yes	—
229	C₄	—	2	1	no	—
230	C₄	—	2	1	no	—
231	C₄	—	2	1	no	—
232	C₄	—	2	1	no	—
233	C₄	—	356	2	no	—
234	C₄	—	356	2	no	—
235	C₄	—	1424	2	no	—
236	C₄	#19151595	1	1	yes	characteristic
237	C₄	#19151608	1	1	yes	characteristic
238	C₄	#19151906	1	2	yes	—
239	C₂	—	2	2	no	—
240	C₂	#26020268	1	1	yes	characteristic
241	C₂	#26020295	1	1	yes	characteristic
242	C₂	#26020307	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#26029186

C₂

yes

maximal, characteristic

#26020383

C₂

yes

maximal, characteristic

#26018817

C₂

yes

maximal

#26018111

C₂

yes

maximal

C₈₉×#1564

C₂

yes

maximal, characteristic

#19152155

C₂²

yes

characteristic

#19151728

—

#19151728

C₄

yes

complemented

C₈×Dic₁₇₈

—

C₈×Dic₁₇₈

C₄

yes

complemented

#19151624

—

#19151622

C₂²

yes

characteristic

#19151553

—

#19151464

C₂²

yes

—

#19151361

—

#19151361

—

#19151336

—

#431×C₈₉

C₂²

yes

—

C₂×C₄×C₈×C₈₉

C₂²

yes

characteristic

#335×C₈₉

—

#334×C₈₉

—

C₂×#13083558

—

#15668012

Q₈

yes

characteristic

#15668012

Q₈

yes

—

—

D₄

yes

—

C₄×Dic₁₇₈

—

C₄×Dic₁₇₈

C₂×C₄

yes

—

#15667971

—

C₂×C₄⋊Dic₈₉

—

C₄⋊#10623494

—

C₄⋊#10623494

C₂×C₄

yes

—

#15667941

—

#15667941

—

#15667922

—

C₈×Dic₈₉

—

#15667919

—

#15667919

—

C₂²×C₈×C₈₉

D₄

yes

characteristic

C₂²×C₈×C₈₉

D₄

yes

characteristic

C₂×C₄²×C₈₉

C₂³

yes

characteristic

C₄⋊C₈×C₈₉

—

C₂²⋊C₈×C₈₉

—

C₄×C₈×C₈₉

—

C₄×C₈×C₈₉

C₂×C₄

yes

characteristic

C₄×C₈×C₈₉

C₂×C₄

yes

characteristic

C₄×C₈×C₈₉

D₄

yes

characteristic

C₄×C₈×C₈₉

D₄

yes

characteristic

C₂×Dic₁₇₈

—

C₂×Dic₁₇₈

C₄⋊C₄

yes

—

C₂²×Dic₈₉

—

#13083558

—

C₂×#10623494

—

C₄⋊Dic₈₉

—

C₄⋊Dic₈₉

—

C₄⋊Dic₈₉

—

C₄⋊Dic₈₉

—

C₄⋊Dic₈₉

—

C₄⋊Dic₈₉

C₄⋊C₄

yes

—

#13083553

—

#13083553

—

C₂²⋊Dic₈₉

—

C₄×Dic₈₉

—

C₂²×C₄×C₈₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₈₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₈₉

#41

yes

characteristic

C₂×C₈×C₈₉

—

C₂×C₈×C₈₉

—

C₂×C₈×C₈₉

—

C₂×C₈×C₈₉

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₈₉

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₈₉

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₈₉

C₂²⋊C₄

yes

characteristic

C₄²×C₈₉

C₂²×C₄

yes

characteristic

C₄²×C₈₉

C₂×D₄

yes

characteristic

C₄²×C₈₉

C₂×Q₈

yes

C₄²×C₈₉

yes

C₂³×C₈₉

yes

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₈₉

C₂×C₄⋊C₄

yes

C₂×C₄×C₈₉

yes

C₂×C₄×C₈₉

yes

C₂×C₄×C₈₉

C₂²⋊Q₈

yes

characteristic

C₂×C₄×C₈₉

C₂²⋊Q₈

yes

characteristic

C₂×C₄×C₈₉

#135

yes

—

C₂×C₄×C₈₉

#137

yes

—

C₂×Dic₈₉

—

C₂×Dic₈₉

—

C₂×Dic₈₉

—

C₂×Dic₈₉

—

C₂×Dic₈₉

—

Dic₁₇₈

—

Dic₁₇₈

—

C₈×C₈₉

—

C₈×C₈₉

—

C₈×C₈₉

—

100

C₈×C₈₉

—

101

C₈×C₈₉

—

102

#10623494

—

103

C₂²×C₈₉

—

104

C₂²×C₈₉

—

105

C₂²×C₈₉

#380

yes

characteristic

106

C₂²×C₈₉

#464

yes

—

107

C₄×C₈₉

—

108

C₄×C₈₉

—

109

C₄×C₈₉

—

110

C₄×C₈₉

—

111

C₄×C₈₉

#416

yes

characteristic

112

C₄×C₈₉

#419

yes

characteristic

113

C₄×C₈₉

#479

yes

—

114

Dic₈₉

—

115

Dic₈₉

—

116

Dic₈₉

—

117

#8681

—

maximal, Sylow

118

C₂×C₈₉

—

119

C₂×C₈₉

#1805

yes

characteristic

120

C₂×C₈₉

#1812

yes

characteristic

121

C₂×C₈₉

#1814

yes

characteristic

122

#2960

—

123

#1835

—

124

#1564

D₈₉

yes

characteristic

125

#1518

—

126

#1286

—

127

C₈₉

#8681

yes

characteristic, complemented, Sylow

128

#533

—

129

#446

—

130

#446

—

178

—

131

C₈×Q₈

—

132

C₈×Q₈

—

178

—

133

#431

C₂×D₈₉

yes

—

134

#424

—

178

—

135

#423

—

136

#405

—

178

—

137

C₂×C₄×C₈

C₂×D₈₉

yes

characteristic

138

#382

—

139

#340

—

178

—

140

#340

—

178

—

141

#335

—

142

#334

—

143

#328

—

178

—

144

C₂×M₁₆

—

178

—

145

C₂²×C₈

D₃₅₆

yes

characteristic

146

C₂²×C₈

D₃₅₆

yes

characteristic

147

C₄⋊Q₈

—

148

C₄⋊Q₈

—

149

#125

—

178

—

150

C₂²⋊Q₈

—

151

C₂²⋊Q₈

—

178

—

152

C₄×Q₈

—

153

C₄×Q₈

—

178

—

154

#117

—

178

—

155

C₂×C₄⋊C₄

—

178

—

156

C₂×C₄²

C₂²×D₈₉

yes

characteristic

157

C₄⋊C₈

—

158

C₄⋊C₈

—

159

C₄⋊C₈

—

178

—

160

C₄⋊C₈

—

178

—

161

C₄⋊C₈

—

178

—

162

C₂²⋊C₈

—

163

#97

—

178

—

164

C₄×C₈

—

165

C₄×C₈

—

178

—

166

C₄×C₈

C₄×D₈₉

yes

characteristic

167

C₄×C₈

C₄×D₈₉

yes

characteristic

168

C₄×C₈

C₂²⋊D₈₉

yes

characteristic

169

C₄×C₈

C₂²⋊D₈₉

yes

characteristic

170

#95

—

178

—

171

#95

—

178

—

172

C₂×Q₈

—

173

C₂×Q₈

—

178

—

174

C₂²×C₄

—

356

—

175

C₂²×C₄

D₄×D₈₉

yes

characteristic

176

C₂²×C₄

C₂×D₃₅₆

yes

characteristic

177

C₂²×C₄

#13083575

yes

characteristic

178

M₁₆

—

356

—

179

C₂×C₈

—

180

C₂×C₈

—

181

C₂×C₈

—

182

C₂×C₈

—

178

—

183

C₂×C₈

#13083551

yes

characteristic

184

C₂×C₈

#13083551

yes

characteristic

185

C₂×C₈

#13083551

yes

characteristic

186

C₂×C₈

#13083551

yes

characteristic

187

C₄⋊C₄

—

188

C₄⋊C₄

—

356

—

189

C₄⋊C₄

—

356

—

190

C₄⋊C₄

—

178

—

191

C₄⋊C₄

—

178

—

192

C₄⋊C₄

—

178

—

193

C₄⋊C₄

—

178

—

194

C₄⋊C₄

—

178

—

195

C₂²⋊C₄

—

178

—

196

C₄²

—

178

—

197

C₄²

C₂×C₄×D₈₉

yes

characteristic

198

C₄²

C₂×C₂²⋊D₈₉

yes

characteristic

199

C₄²

Q₈×D₈₉

yes

characteristic

200

C₄²

#13083573

yes

characteristic

201

C₂³

#15667987

yes

characteristic

202

Q₈

—

356

—

203

Q₈

—

356

—

204

C₂×C₄

—

205

C₂×C₄

—

206

C₂×C₄

—

178

—

207

C₂×C₄

—

178

—

208

C₂×C₄

—

712

—

209

C₂×C₄

—

712

—

210

C₂×C₄

—

712

—

211

C₂×C₄

C₂×#13083551

yes

characteristic

212

C₂×C₄

C₄⋊C₄×D₈₉

yes

characteristic

213

C₂×C₄

#15667970

yes

characteristic

214

C₂×C₄

#15667983

yes

characteristic

215

C₂×C₄

#15667988

yes

characteristic

216

C₂×C₄

#15667992

yes

characteristic

217

C₂×C₄

#15668034

yes

—

218

C₂×C₄

#15668045

yes

—

219

C₈

—

220

C₈

—

221

C₈

—

222

C₈

—

223

C₈

—

224

C₈

—

356

—

225

C₂²

—

226

C₂²

—

227

C₂²

#19151455

yes

characteristic

228

C₂²

#19151821

yes

—

229

C₄

—

230

C₄

—

231

C₄

—

232

C₄

—

233

C₄

—

356

—

234

C₄

—

356

—

235

C₄

—

1424

—

236

C₄

#19151595

yes

characteristic

237

C₄

#19151608

yes

characteristic

238

C₄

#19151906

yes

—

239

C₂

—

240

C₂

#26020268

yes

characteristic

241

C₂

#26020295

yes

characteristic

242

C₂

#26020307

yes

characteristic

	subgroup	G/H
center	C₂²	#19151455
commutator	C₄²×C₈₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₈₉
Fitting	C₈₉×#1564	C₂
socle	C₂²×C₈₉	#380
prime radical	C₂³×C₈₉	#121
cosocle	C₂×C₄²×C₈₉	C₂³
hypercenter	#1564	D₈₉
hypocenter	C₈₉	#8681
LCS	G ▷ C₄²×C₈₉ ▷ C₂²×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1564

subgroup

G/H

center

C₂²

#19151455

commutator

C₄²×C₈₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₈₉

Fitting

C₈₉×#1564

C₂

C₂²×C₈₉

C₂³×C₈₉

C₂×C₄²×C₈₉

C₂³

D₈₉

C₈₉

G ▷ C₄²×C₈₉ ▷ C₂²×C₈₉ ▷ C₈₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1564

N	H ≅ G/N	type
8. #19151728	C₄	semidirect
10. C₈×Dic₁₇₈	C₄	semidirect
127. C₈₉	#8681	semidirect

H ≅ G/N

type

8. #19151728

C₄

semidirect

10. C₈×Dic₁₇₈

C₄

semidirect

127. C₈₉

#8681

semidirect

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

subgroup	index
#26029186	2
#26020383	2
#26018817	2
#26018111	2
C₈₉×#1564	2
#8681	89

subgroup

index

C₈₉×#1564

Subgroups — #36447668

Conjugacy classes of subgroups

Complements

Maximal subgroups