Group #36448898 — subgroups

Subgroups — #36448898

Order 22784.

476 conjugacy classes of subgroups; only the 155 normal subgroups are shown.

normal subgroups only

This group has 476 conjugacy classes of subgroups — too many to draw. Only its 155 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	#26021055	C₂	1	1	yes	maximal, characteristic
2	#26021010	C₂	1	2	yes	maximal
3	C₂×#19151347	C₂	1	1	yes	maximal, characteristic
4	#26018093	C₂	1	2	yes	maximal
5	C₈₉×#2369	C₂	1	1	yes	maximal, characteristic
6	C₂×#15667945	—	2	2	no	—
7	C₂×C₄⋊#10623494	C₂²	1	2	yes	—
8	C₂×#15667936	—	2	2	no	—
9	C₂×C₄×#10623494	C₂²	1	1	yes	characteristic
10	#19151468	C₂²	1	1	yes	characteristic
11	#19151360	—	2	2	no	—
12	#19151347	C₄	1	4	yes	complemented
13	C₂×C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
14	#391×C₈₉	—	2	2	no	—
15	#389×C₈₉	—	2	2	no	—
16	C₄×C₄⋊C₄×C₈₉	—	2	2	no	—
17	C₄×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
18	C₂²×#10623494	—	2	2	no	—
19	C₂²×#10623494	—	2	1	no	—
20	C₂×C₄⋊Dic₈₉	—	2	2	no	—
21	C₂×C₄⋊Dic₈₉	—	2	1	no	—
22	#15667945	—	4	4	no	—
23	C₄⋊#10623494	—	2	2	no	—
24	C₄⋊#10623494	C₂×C₄	1	4	yes	—
25	#15667936	—	4	4	no	—
26	C₄×#10623494	—	2	2	no	—
27	C₂²×Q₈×C₈₉	D₄	1	2	yes	—
28	C₄⋊Q₈×C₈₉	—	2	2	no	—
29	C₄⋊Q₈×C₈₉	C₂×C₄	1	2	yes	—
30	C₄⋊Q₈×C₈₉	Q₈	1	2	yes	—
31	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
32	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
33	C₂×C₄⋊C₄×C₈₉	D₄	1	2	yes	—
34	C₂×C₄⋊C₄×C₈₉	D₄	1	2	yes	—
35	C₂×C₄²×C₈₉	—	2	2	no	—
36	C₂×C₄²×C₈₉	—	2	2	no	—
37	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
38	#95×C₈₉	—	2	4	no	—
39	#95×C₈₉	—	2	2	no	—
40	C₂²×Dic₈₉	—	4	1	no	—
41	C₂×#10623494	—	2	2	no	—
42	C₂×#10623494	—	2	4	no	—
43	C₂×#10623494	—	4	1	no	—
44	C₂×#10623494	—	4	1	no	—
45	C₂×#10623494	—	4	2	no	—
46	C₂×#10623494	—	4	2	no	—
47	C₄⋊Dic₈₉	—	4	2	no	—
48	C₄⋊Dic₈₉	—	4	2	no	—
49	C₄⋊Dic₈₉	—	4	2	no	—
50	C₂×Q₈×C₈₉	—	2	2	no	—
51	C₂×Q₈×C₈₉	—	4	2	no	—
52	C₂×Q₈×C₈₉	—	4	2	no	—
53	C₂×Q₈×C₈₉	C₄⋊C₄	1	4	yes	—
54	C₂²×C₄×C₈₉	—	2	2	no	—
55	C₂²×C₄×C₈₉	—	2	2	no	—
56	C₂²×C₄×C₈₉	—	2	2	no	—
57	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
58	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
59	C₄⋊C₄×C₈₉	—	2	4	no	—
60	C₄⋊C₄×C₈₉	—	2	4	no	—
61	C₄⋊C₄×C₈₉	—	2	2	no	—
62	C₄⋊C₄×C₈₉	—	2	2	no	—
63	C₄⋊C₄×C₈₉	—	2	2	no	—
64	C₄⋊C₄×C₈₉	—	8	2	no	—
65	C₄⋊C₄×C₈₉	Q₁₆	1	4	yes	—
66	C₄²×C₈₉	—	4	2	no	—
67	C₄²×C₈₉	—	4	2	no	—
68	C₄²×C₈₉	—	8	2	no	—
69	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
70	C₄²×C₈₉	C₂×Q₈	1	1	yes	characteristic
71	C₄²×C₈₉	#41	1	2	yes	—
72	C₂³×C₈₉	#120	1	1	yes	characteristic
73	Q₈×C₈₉	—	4	4	no	—
74	Q₈×C₈₉	—	8	2	no	—
75	C₂×C₄×C₈₉	—	2	1	no	—
76	C₂×C₄×C₈₉	—	2	1	no	—
77	C₂×C₄×C₈₉	—	2	4	no	—
78	C₂×C₄×C₈₉	—	2	4	no	—
79	C₂×C₄×C₈₉	—	4	2	no	—
80	C₂×C₄×C₈₉	—	4	2	no	—
81	C₂×C₄×C₈₉	—	4	2	no	—
82	C₂×C₄×C₈₉	—	4	2	no	—
83	C₂×C₄×C₈₉	—	4	2	no	—
84	C₂×C₄×C₈₉	—	4	2	no	—
85	C₂×C₄×C₈₉	—	4	2	no	—
86	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
87	C₂×C₄×C₈₉	C₄×D₄	1	2	yes	—
88	C₂×C₄×C₈₉	C₂²⋊Q₈	1	2	yes	—
89	C₂×C₄×C₈₉	#123	1	1	yes	characteristic
90	C₂×C₄×C₈₉	C₂×Q₁₆	1	2	yes	—
91	C₂×C₄×C₈₉	#135	1	2	yes	—
92	C₂×C₄×C₈₉	AGL(1,ℤ/8)	1	2	yes	—
93	C₂×C₄×C₈₉	#137	1	2	yes	—
94	C₂×Dic₈₉	—	8	2	no	—
95	C₂×Dic₈₉	—	8	1	no	—
96	#10623494	—	4	2	no	—
97	#10623494	—	4	4	no	—
98	C₂²×C₈₉	#385	1	1	yes	characteristic
99	C₂²×C₈₉	#449	1	2	yes	—
100	C₂²×C₈₉	#451	1	2	yes	—
101	C₂²×C₈₉	#453	1	1	yes	characteristic
102	C₂²×C₈₉	#455	1	1	yes	characteristic
103	C₄×C₈₉	—	2	1	no	—
104	C₄×C₈₉	—	2	1	no	—
105	C₄×C₈₉	—	4	4	no	—
106	C₄×C₈₉	—	4	4	no	—
107	C₄×C₈₉	—	8	2	no	—
108	C₄×C₈₉	C₄×Q₁₆	1	2	yes	—
109	C₄×C₈₉	#440	1	2	yes	—
110	C₄×C₈₉	#477	1	2	yes	—
111	C₄×C₈₉	#479	1	2	yes	—
112	Dic₈₉	—	16	1	no	—
113	#8929	—	89	1	no	maximal, Sylow
114	C₂×C₈₉	#1624	1	1	yes	characteristic
115	C₂×C₈₉	#1633	1	1	yes	characteristic
116	C₂×C₈₉	#1644	1	2	yes	—
117	C₂×C₈₉	#1856	1	1	yes	characteristic
118	C₂×C₈₉	#1863	1	2	yes	—
119	#2369	D₈₉	1	1	yes	characteristic
120	#1956	—	89	1	no	—
121	#1947	—	89	2	no	—
122	C₂×#333	—	89	1	no	—
123	#1279	—	89	2	no	—
124	C₈₉	#8929	1	1	yes	characteristic, complemented, Sylow
125	C₂×C₄⋊Q₈	C₂×D₈₉	1	1	yes	characteristic
126	C₂×#107	—	178	2	no	—
127	C₂×C₄⋊C₈	—	89	2	no	—
128	C₂×#103	—	178	2	no	—
129	C₂×C₄×C₈	—	89	1	no	—
130	#391	—	2	2	no	—
131	#389	—	2	2	no	—
132	#384	—	89	1	no	—
133	C₄×C₄⋊C₄	—	2	2	no	—
134	C₄×C₄⋊C₄	C₂×D₈₉	1	2	yes	—
135	#340	—	178	2	no	—
136	#333	—	89	4	no	—
137	C₂²×Q₈	C₂²⋊D₈₉	1	2	yes	—
138	C₂²×C₈	—	178	2	no	—
139	C₂²×C₈	—	178	1	no	—
140	C₄⋊Q₈	—	2	2	no	—
141	C₄⋊Q₈	Dic₁₇₈	1	2	yes	—
142	C₄⋊Q₈	C₄×D₈₉	1	2	yes	—
143	C₂×C₄⋊C₄	—	2	2	no	—
144	C₂×C₄⋊C₄	—	2	2	no	—
145	C₂×C₄⋊C₄	—	178	2	no	—
146	C₂×C₄⋊C₄	—	178	1	no	—
147	C₂×C₄⋊C₄	C₂²⋊D₈₉	1	2	yes	—
148	C₂×C₄⋊C₄	C₂²⋊D₈₉	1	2	yes	—
149	C₂×C₄²	—	2	2	no	—
150	C₂×C₄²	—	2	2	no	—
151	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
152	#107	—	356	4	no	—
153	C₄⋊C₈	—	89	4	no	—
154	C₄⋊C₈	—	178	2	no	—
155	#103	—	356	4	no	—
156	C₄×C₈	—	178	2	no	—
157	#95	—	2	4	no	—
158	#95	—	2	2	no	—
159	C₂×Q₈	—	2	2	no	—
160	C₂×Q₈	—	4	2	no	—
161	C₂×Q₈	—	4	2	no	—
162	C₂×Q₈	#13083553	1	4	yes	—
163	C₂²×C₄	—	2	2	no	—
164	C₂²×C₄	—	2	2	no	—
165	C₂²×C₄	—	2	2	no	—
166	C₂²×C₄	—	356	1	no	—
167	C₂²×C₄	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
168	C₂²×C₄	C₂×C₂²⋊D₈₉	1	2	yes	—
169	C₂×C₈	—	356	1	no	—
170	C₂×C₈	—	356	1	no	—
171	C₂×C₈	—	356	2	no	—
172	C₂×C₈	—	356	2	no	—
173	C₂×C₈	—	178	2	no	—
174	C₂×C₈	—	178	4	no	—
175	C₄⋊C₄	—	2	4	no	—
176	C₄⋊C₄	—	2	4	no	—
177	C₄⋊C₄	—	2	2	no	—
178	C₄⋊C₄	—	2	2	no	—
179	C₄⋊C₄	—	2	2	no	—
180	C₄⋊C₄	—	8	2	no	—
181	C₄⋊C₄	—	356	2	no	—
182	C₄⋊C₄	—	356	2	no	—
183	C₄⋊C₄	—	356	2	no	—
184	C₄⋊C₄	#13083564	1	4	yes	—
185	C₄²	—	4	2	no	—
186	C₄²	—	4	2	no	—
187	C₄²	—	8	2	no	—
188	C₄²	C₂×C₄×D₈₉	1	1	yes	characteristic
189	C₄²	C₂×Dic₁₇₈	1	1	yes	characteristic
190	C₄²	#13083574	1	2	yes	—
191	C₂³	#15667981	1	1	yes	characteristic
192	Q₈	—	4	4	no	—
193	Q₈	—	8	2	no	—
194	C₂×C₄	—	2	1	no	—
195	C₂×C₄	—	2	1	no	—
196	C₂×C₄	—	2	4	no	—
197	C₂×C₄	—	2	4	no	—
198	C₂×C₄	—	4	2	no	—
199	C₂×C₄	—	4	2	no	—
200	C₂×C₄	—	4	2	no	—
201	C₂×C₄	—	4	2	no	—
202	C₂×C₄	—	4	2	no	—
203	C₂×C₄	—	4	2	no	—
204	C₂×C₄	—	4	2	no	—
205	C₂×C₄	—	712	2	no	—
206	C₂×C₄	—	712	1	no	—
207	C₂×C₄	C₂×#13083553	1	1	yes	characteristic
208	C₂×C₄	C₄×C₂²⋊D₈₉	1	2	yes	—
209	C₂×C₄	#15667991	1	2	yes	—
210	C₂×C₄	#15667995	1	1	yes	characteristic
211	C₂×C₄	C₂×#13083564	1	2	yes	—
212	C₂×C₄	#15668032	1	2	yes	—
213	C₂×C₄	#15668037	1	2	yes	—
214	C₂×C₄	#15668043	1	2	yes	—
215	C₈	—	356	2	no	—
216	C₈	—	356	4	no	—
217	C₂²	#19151471	1	1	yes	characteristic
218	C₂²	#19151743	1	2	yes	—
219	C₂²	#19151754	1	2	yes	—
220	C₂²	#19151766	1	1	yes	characteristic
221	C₂²	#19151776	1	1	yes	characteristic
222	C₄	—	2	1	no	—
223	C₄	—	2	1	no	—
224	C₄	—	4	4	no	—
225	C₄	—	4	4	no	—
226	C₄	—	8	2	no	—
227	C₄	—	1424	1	no	—
228	C₄	C₄×#13083564	1	2	yes	—
229	C₄	#19151696	1	2	yes	—
230	C₄	#19151893	1	2	yes	—
231	C₄	#19151905	1	2	yes	—
232	C₂	#26019335	1	1	yes	characteristic
233	C₂	#26019392	1	1	yes	characteristic
234	C₂	#26019466	1	2	yes	—
235	C₂	#26020462	1	1	yes	characteristic
236	C₂	#26020506	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#26021055

C₂

yes

maximal, characteristic

#26021010

C₂

yes

maximal

C₂×#19151347

C₂

yes

maximal, characteristic

#26018093

C₂

yes

maximal

C₈₉×#2369

C₂

yes

maximal, characteristic

C₂×#15667945

—

C₂×C₄⋊#10623494

C₂²

yes

—

C₂×#15667936

—

C₂×C₄×#10623494

C₂²

yes

characteristic

#19151468

C₂²

yes

characteristic

#19151360

—

#19151347

C₄

yes

complemented

C₂×C₄⋊Q₈×C₈₉

C₂²

yes

characteristic

#391×C₈₉

—

#389×C₈₉

—

C₄×C₄⋊C₄×C₈₉

—

C₄×C₄⋊C₄×C₈₉

C₂²

yes

—

C₂²×#10623494

—

C₂²×#10623494

—

C₂×C₄⋊Dic₈₉

—

C₂×C₄⋊Dic₈₉

—

#15667945

—

C₄⋊#10623494

—

C₄⋊#10623494

C₂×C₄

yes

—

#15667936

—

C₄×#10623494

—

C₂²×Q₈×C₈₉

D₄

yes

—

C₄⋊Q₈×C₈₉

—

C₄⋊Q₈×C₈₉

C₂×C₄

yes

—

C₄⋊Q₈×C₈₉

Q₈

yes

—

C₂×C₄⋊C₄×C₈₉

—

C₂×C₄⋊C₄×C₈₉

—

C₂×C₄⋊C₄×C₈₉

D₄

yes

—

C₂×C₄⋊C₄×C₈₉

D₄

yes

—

C₂×C₄²×C₈₉

—

C₂×C₄²×C₈₉

—

C₂×C₄²×C₈₉

C₂³

yes

characteristic

#95×C₈₉

—

#95×C₈₉

—

C₂²×Dic₈₉

—

—

—

—

—

—

—

C₄⋊Dic₈₉

—

C₄⋊Dic₈₉

—

C₄⋊Dic₈₉

—

C₂×Q₈×C₈₉

—

C₂×Q₈×C₈₉

—

C₂×Q₈×C₈₉

—

C₂×Q₈×C₈₉

C₄⋊C₄

yes

—

C₂²×C₄×C₈₉

—

C₂²×C₄×C₈₉

—

C₂²×C₄×C₈₉

—

C₂²×C₄×C₈₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₈₉

C₂×D₄

yes

—

C₄⋊C₄×C₈₉

—

C₄⋊C₄×C₈₉

—

C₄⋊C₄×C₈₉

—

C₄⋊C₄×C₈₉

—

C₄⋊C₄×C₈₉

—

C₄⋊C₄×C₈₉

—

C₄⋊C₄×C₈₉

Q₁₆

yes

—

C₄²×C₈₉

—

C₄²×C₈₉

—

C₄²×C₈₉

—

C₄²×C₈₉

C₂²×C₄

yes

characteristic

C₄²×C₈₉

C₂×Q₈

yes

characteristic

C₄²×C₈₉

#41

yes

—

C₂³×C₈₉

#120

yes

characteristic

Q₈×C₈₉

—

Q₈×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

C₂×C₄⋊C₄

yes

characteristic

C₂×C₄×C₈₉

C₄×D₄

yes

—

C₂×C₄×C₈₉

C₂²⋊Q₈

yes

—

C₂×C₄×C₈₉

#123

yes

characteristic

C₂×C₄×C₈₉

C₂×Q₁₆

yes

—

C₂×C₄×C₈₉

#135

yes

—

C₂×C₄×C₈₉

AGL(1,ℤ/8)

yes

—

C₂×C₄×C₈₉

#137

yes

—

C₂×Dic₈₉

—

C₂×Dic₈₉

—

#10623494

—

#10623494

—

C₂²×C₈₉

#385

yes

characteristic

C₂²×C₈₉

#449

yes

—

100

C₂²×C₈₉

#451

yes

—

101

C₂²×C₈₉

#453

yes

characteristic

102

C₂²×C₈₉

#455

yes

characteristic

103

C₄×C₈₉

—

104

C₄×C₈₉

—

105

C₄×C₈₉

—

106

C₄×C₈₉

—

107

C₄×C₈₉

—

108

C₄×C₈₉

C₄×Q₁₆

yes

—

109

C₄×C₈₉

#440

yes

—

110

C₄×C₈₉

#477

yes

—

111

C₄×C₈₉

#479

yes

—

112

Dic₈₉

—

113

#8929

—

maximal, Sylow

114

C₂×C₈₉

#1624

yes

characteristic

115

C₂×C₈₉

#1633

yes

characteristic

116

C₂×C₈₉

#1644

yes

—

117

C₂×C₈₉

#1856

yes

characteristic

118

C₂×C₈₉

#1863

yes

—

119

#2369

D₈₉

yes

characteristic

120

#1956

—

121

#1947

—

122

C₂×#333

—

123

#1279

—

124

C₈₉

#8929

yes

characteristic, complemented, Sylow

125

C₂×C₄⋊Q₈

C₂×D₈₉

yes

characteristic

126

C₂×#107

—

178

—

127

C₂×C₄⋊C₈

—

128

C₂×#103

—

178

—

129

C₂×C₄×C₈

—

130

#391

—

131

#389

—

132

#384

—

133

C₄×C₄⋊C₄

—

134

C₄×C₄⋊C₄

C₂×D₈₉

yes

—

135

#340

—

178

—

136

#333

—

137

C₂²×Q₈

C₂²⋊D₈₉

yes

—

138

C₂²×C₈

—

178

—

139

C₂²×C₈

—

178

—

140

C₄⋊Q₈

—

141

C₄⋊Q₈

Dic₁₇₈

yes

—

142

C₄⋊Q₈

C₄×D₈₉

yes

—

143

C₂×C₄⋊C₄

—

144

C₂×C₄⋊C₄

—

145

C₂×C₄⋊C₄

—

178

—

146

C₂×C₄⋊C₄

—

178

—

147

C₂×C₄⋊C₄

C₂²⋊D₈₉

yes

—

148

C₂×C₄⋊C₄

C₂²⋊D₈₉

yes

—

149

C₂×C₄²

—

150

C₂×C₄²

—

151

C₂×C₄²

C₂²×D₈₉

yes

characteristic

152

#107

—

356

—

153

C₄⋊C₈

—

154

C₄⋊C₈

—

178

—

155

#103

—

356

—

156

C₄×C₈

—

178

—

157

#95

—

158

#95

—

159

C₂×Q₈

—

160

C₂×Q₈

—

161

C₂×Q₈

—

162

C₂×Q₈

#13083553

yes

—

163

C₂²×C₄

—

164

C₂²×C₄

—

165

C₂²×C₄

—

166

C₂²×C₄

—

356

—

167

C₂²×C₄

C₂×C₂²⋊D₈₉

yes

characteristic

168

C₂²×C₄

C₂×C₂²⋊D₈₉

yes

—

169

C₂×C₈

—

356

—

170

C₂×C₈

—

356

—

171

C₂×C₈

—

356

—

172

C₂×C₈

—

356

—

173

C₂×C₈

—

178

—

174

C₂×C₈

—

178

—

175

C₄⋊C₄

—

176

C₄⋊C₄

—

177

C₄⋊C₄

—

178

C₄⋊C₄

—

179

C₄⋊C₄

—

180

C₄⋊C₄

—

181

C₄⋊C₄

—

356

—

182

C₄⋊C₄

—

356

—

183

C₄⋊C₄

—

356

—

184

C₄⋊C₄

#13083564

yes

—

185

C₄²

—

186

C₄²

—

187

C₄²

—

188

C₄²

C₂×C₄×D₈₉

yes

characteristic

189

C₄²

C₂×Dic₁₇₈

yes

characteristic

190

C₄²

#13083574

yes

—

191

C₂³

#15667981

yes

characteristic

192

Q₈

—

193

Q₈

—

194

C₂×C₄

—

195

C₂×C₄

—

196

C₂×C₄

—

197

C₂×C₄

—

198

C₂×C₄

—

199

C₂×C₄

—

200

C₂×C₄

—

201

C₂×C₄

—

202

C₂×C₄

—

203

C₂×C₄

—

204

C₂×C₄

—

205

C₂×C₄

—

712

—

206

C₂×C₄

—

712

—

207

C₂×C₄

C₂×#13083553

yes

characteristic

208

C₂×C₄

C₄×C₂²⋊D₈₉

yes

—

209

C₂×C₄

#15667991

yes

—

210

C₂×C₄

#15667995

yes

characteristic

211

C₂×C₄

C₂×#13083564

yes

—

212

C₂×C₄

#15668032

yes

—

213

C₂×C₄

#15668037

yes

—

214

C₂×C₄

#15668043

yes

—

215

C₈

—

356

—

216

C₈

—

356

—

217

C₂²

#19151471

yes

characteristic

218

C₂²

#19151743

yes

—

219

C₂²

#19151754

yes

—

220

C₂²

#19151766

yes

characteristic

221

C₂²

#19151776

yes

characteristic

222

C₄

—

223

C₄

—

224

C₄

—

225

C₄

—

226

C₄

—

227

C₄

—

1424

—

228

C₄

C₄×#13083564

yes

—

229

C₄

#19151696

yes

—

230

C₄

#19151893

yes

—

231

C₄

#19151905

yes

—

232

C₂

#26019335

yes

characteristic

233

C₂

#26019392

yes

characteristic

234

C₂

#26019466

yes

—

235

C₂

#26020462

yes

characteristic

236

C₂

#26020506

yes

—

	subgroup	G/H
center	C₂³	#15667981
commutator	C₄²×C₈₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₈₉
Fitting	C₈₉×#2369	C₂
socle, prime radical	C₂³×C₈₉	#120
cosocle	C₂×C₄²×C₈₉	C₂³
hypercenter	#2369	D₈₉
hypocenter	C₈₉	#8929
LCS	G ▷ C₄²×C₈₉ ▷ C₂²×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #2369

subgroup

G/H

center

C₂³

#15667981

commutator

C₄²×C₈₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₈₉

Fitting

C₈₉×#2369

C₂

socle, prime radical

C₂³×C₈₉

#120

cosocle

C₂×C₄²×C₈₉

C₂³

D₈₉

C₈₉

G ▷ C₄²×C₈₉ ▷ C₂²×C₈₉ ▷ C₈₉

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #2369

N	H ≅ G/N	type
12. #19151347	C₄	semidirect
124. C₈₉	#8929	semidirect

H ≅ G/N

type

12. #19151347

C₄

semidirect

124. C₈₉

#8929

semidirect

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

subgroup	index
#26021055	2
#26021010	2
C₂×#19151347	2
#26018093	2
C₈₉×#2369	2
#8929	89

subgroup

index

C₈₉×#2369

Subgroups — #36448898

Conjugacy classes of subgroups

Complements

Maximal subgroups