Finite Group Databasebeta

← #26023514

Subgroups — #26023514

Order 11392.

560 conjugacy classes of subgroups; only the 143 normal subgroups are shown.

normal subgroups only

This group has 560 conjugacy classes of subgroups — too many to draw. Only its 143 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15667972C211yesmaximal, characteristic
2C2×#15667970C211yesmaximal, characteristic, complemented
3#19151538C211yesmaximal, characteristic, complemented
4#19151534C211yesmaximal, characteristic, complemented
5#19151529C211yesmaximal, characteristic, complemented
6#19151527C212yesmaximal, complemented
7#19151513C212yesmaximal
8#19151449C212yesmaximal, complemented
9C22⋊C4×Dic89C212yesmaximal, complemented
10#19151445C211yesmaximal, characteristic, complemented
11#397×C89C211yesmaximal, characteristic, complemented
12C22×C22⋊D89C2211yescharacteristic
13C23×Dic89C2211yescharacteristic
14C22×C4×D89C2211yescharacteristic
15#15667972—24no—
16#15667970—24no—
17C2×C4⋊Dic89C2211yescharacteristic
18C2×#13083553C2212yes—
19C2×#13083553C2212yes—
20C2×#13083553C2211yescharacteristic
21C2×C22⋊Dic89C2212yes—
22C2×#13083551C2212yes—
23C2×#13083551C2212yes—
24C2×#13083551C2211yescharacteristic
25C2×C4×Dic89C2212yes—
26C2×C4×Dic89C2212yes—
27C2×C4×Dic89C2211yescharacteristic
28#15667919C2211yescharacteristic
29#15667919C2212yes—
30#15667919C2212yes—
31#15667919C2212yes—
32C2×C4⋊C4×C89C2211yescharacteristic
33C2×C22⋊C4×C89C2212yes—
34C2×C22⋊C4×C89C2211yescharacteristic
35#95×C89C2211yescharacteristic
36#95×C89C2212yes—
37C23×D89C2311yescharacteristic
38C2×C22⋊D89—22no—
39C2×C22⋊D89—22no—
40C2×C22⋊D89—22no—
41C22×Dic89—22no—
42C22×Dic89—24no—
43C22×Dic89C2311yescharacteristic
44C22×Dic89C2312yes—
45C22×Dic89C2311yescharacteristic
46C22×Dic89C2312yes—
47C22×Dic89C2311yescharacteristic
48C2×C4×D89—24no—
49C2×C4×D89D414yes—
50C4⋊Dic89—22no—
51#13083553—22no—
52#13083553—24no—
53#13083553—24no—
54C22⋊Dic89—24no—
55#13083551—24no—
56#13083551—22no—
57#13083551—24no—
58C4×Dic89—24no—
59C4×Dic89—22no—
60C4×Dic89—24no—
61C24×C89C2311yescharacteristic
62C22×C4×C89C2312yes—
63C22×C4×C89C2311yescharacteristic
64C22×C4×C89C2312yes—
65C22×C4×C89C2311yescharacteristic
66C4⋊C4×C89—22no—
67C22⋊C4×C89—24no—
68C22⋊C4×C89—22no—
69C23×C89—21no—
70C23×C89—22no—
71C23×C89—22no—
72C23×C89—21no—
73C23×C89#4112yes—
74C23×C89C2411yescharacteristic
75C22×D89—22no—
76C22×D89—22no—
77C22×D89—21no—
78C22×D89—21no—
79C22×D89C2×D412yes—
80C2×C4×C89—22no—
81C2×C4×C89—21no—
82C2×C4×C89—22no—
83C2×C4×C89—22no—
84C2×C4×C89—22no—
85C2×C4×C89—22no—
86C2×C4×C89—22no—
87C2×C4×C89—22no—
88C2×C4×C89—22no—
89C2×C4×C89C2×D412yes—
90C22⋊D89—28no—
91C2×Dic89—21no—
92C2×Dic89—22no—
93C2×Dic89—22no—
94C2×Dic89—21no—
95C2×Dic89—22no—
96C2×Dic89—21no—
97C2×Dic89—22no—
98C2×Dic89—22no—
99C2×Dic89—22no—
100C2×Dic89—44no—
101C2×Dic89C2×D412yes—
102C2×Dic89#4114yes—
103C2×Dic89#4112yes—
104C2×Dic89#4114yes—
105C4×D89—28no—
106C22×C89—22no—
107C22×C89—24no—
108C22×C89—41no—
109C22×C89—42no—
110C22×C89—41no—
111C22×C89C22×D411yescharacteristic
112C22×C89C2×#4112yes—
113C22×C89C2×#4111yescharacteristic
114C22×C89C2×#4111yescharacteristic
115C22×C89C2×#4112yes—
116C2×D89—22no—
117C2×D89—22no—
118C2×D89—22no—
119C2×D89—42no—
120C2×D89—42no—
121C4×C89—22no—
122C4×C89—42no—
123C4×C89—42no—
124C4×C89—41no—
125Dic89—22no—
126Dic89—24no—
127Dic89—41no—
128Dic89—42no—
129Dic89#12314yes—
130C2×C89—42no—
131C2×C89C2×#12311yescharacteristic
132C2×C89#52511yescharacteristic
133C2×C89#52912yes—
134C2×C89#52912yes—
135C2×C89#53211yescharacteristic
136D89—42no—
137#2395—891nomaximal, Sylow
138C89#239511yescharacteristic, complemented, Sylow
139C2×C4×D4—891no—
140C2×#117—891no—
141#400—891no—
142#399—891no—
143#398—891no—
144#397—892no—
145#397D8911yescharacteristic, complemented
146#394—892no—
147C4×C4⋊C4—892no—
148C4×C22⋊C4—892no—
149C4×C22⋊C4—891no—
150C22×D4—891no—
151C23×C4—891no—
152C23×C4—891no—
153C4×D4—1784no—
154#117—1784no—
155C2×C4⋊C4—891no—
156C2×C4⋊C4—891no—
157C2×C4⋊C4—892no—
158C2×C4⋊C4—892no—
159C2×C4⋊C4C2×D8911yescharacteristic
160C2×C22⋊C4—892no—
161C2×C22⋊C4—892no—
162C2×C22⋊C4—891no—
163C2×C22⋊C4—892no—
164C2×C22⋊C4C2×D8911yescharacteristic
165C2×C22⋊C4C2×D8912yes—
166C2×C42—892no—
167C2×C42—891no—
168C2×C42—892no—
169#95—892no—
170#95—892no—
171#95—891no—
172#95—892no—
173#95C2×D8911yescharacteristic
174#95C2×D8912yes—
175C24—891no—
176C24C22×D8911yescharacteristic
177C2×D4—1782no—
178C2×D4—1782no—
179C2×D4—1782no—
180C22×C4—891no—
181C22×C4—892no—
182C22×C4—891no—
183C22×C4—894no—
184C22×C4—891no—
185C22×C4—892no—
186C22×C4—1784no—
187C22×C4—1782no—
188C22×C4—1784no—
189C22×C4C22×D8912yes—
190C22×C4C22×D8912yes—
191C22×C4C22×D8911yescharacteristic
192C22×C4C22×D8911yescharacteristic
193C4⋊C4—22no—
194C4⋊C4—1784no—
195C4⋊C4—1784no—
196C4⋊C4—1782no—
197C4⋊C4—1782no—
198C22⋊C4—24no—
199C22⋊C4—22no—
200C22⋊C4—1784no—
201C22⋊C4—1784no—
202C22⋊C4—1782no—
203C22⋊C4—1784no—
204C42—1784no—
205C42—1782no—
206C42—1784no—
207C23—21no—
208C23—22no—
209C23—22no—
210C23—21no—
211C23—892no—
212C23—1782no—
213C23—1782no—
214C23—1781no—
215C23—1781no—
216C23#1308357312yes—
217C23C23×D8911yescharacteristic
218D4—1788no—
219C2×C4—22no—
220C2×C4—21no—
221C2×C4—22no—
222C2×C4—22no—
223C2×C4—22no—
224C2×C4—22no—
225C2×C4—22no—
226C2×C4—22no—
227C2×C4—22no—
228C2×C4—892no—
229C2×C4—894no—
230C2×C4—894no—
231C2×C4—892no—
232C2×C4—3564no—
233C2×C4—1788no—
234C2×C4—1782no—
235C2×C4—1781no—
236C2×C4—1782no—
237C2×C4—1782no—
238C2×C4—1782no—
239C2×C4—1781no—
240C2×C4—1782no—
241C2×C4—1782no—
242C2×C4—1781no—
243C2×C4D4×D8912yes—
244C22—22no—
245C22—24no—
246C22—42no—
247C22—41no—
248C22—41no—
249C22—3562no—
250C22—3562no—
251C22—1782no—
252C22—1782no—
253C22—1782no—
254C22C2×D4×D8911yescharacteristic
255C22#41×D8911yescharacteristic
256C22#41×D8912yes—
257C22#41×D8912yes—
258C22C2×#1308357311yescharacteristic
259C4—22no—
260C4—41no—
261C4—42no—
262C4—42no—
263C4—894no—
264C4—3562no—
265C4—3561no—
266C4—1784no—
267C4—1782no—
268C2—42no—
269C2—3562no—
270C2#123×D8911yescharacteristic
271C2#1915210811yescharacteristic
272C2#1915212512yes—
273C2#1915213112yes—
274C2#1915214711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D89
commutator, socle, cosocleC23×C89C24
Fitting#397×C89C2
prime radicalC22×C22⋊D89C22
hypercenter#397D89
hypocenterC89#2395
LCSG ▷ C23×C89 ▷ C89
UCSC1 ◁ C23 ◁ #397

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×#15667970C2semidirect
3. #19151538C2semidirect
4. #19151534C2semidirect
5. #19151529C2semidirect
6. #19151527C2semidirect
8. #19151449C2semidirect
9. C22⋊C4×Dic89C2semidirect
10. #19151445C2semidirect
11. #397×C89C2semidirect
138. C89#2395semidirect
145. #397D89semidirect

Maximal subgroups

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

subgroupindex
C2×#156679722
C2×#156679702
#191515382
#191515342
#191515292
#191515272
#191515132
#191514492
C22⋊C4×Dic892
#191514452
#397×C892
#239589