Finite Group Databasebeta

← #26024521

Subgroups — #26024521

Order 11392.

672 conjugacy classes of subgroups; only the 139 normal subgroups are shown.

normal subgroups only

This group has 672 conjugacy classes of subgroups — too many to draw. Only its 139 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×#15667970C211yesmaximal, characteristic, complemented
2C2×C22⋊C4×D89C211yesmaximal, characteristic
3#19151535C211yesmaximal, characteristic, complemented
4#19151534C211yesmaximal, characteristic, complemented
5#19151524C211yesmaximal, characteristic, complemented
6#19151491C212yesmaximal, complemented
7#19151487C212yesmaximal, complemented
8#19151472C212yesmaximal, complemented
9#19151460C211yesmaximal, characteristic, complemented
10#19151453C212yesmaximal
11#397×C89C211yesmaximal, characteristic, complemented
12C24×D89C2211yescharacteristic
13C22×C4×D89C2211yescharacteristic
14C22×C4×D89C2211yescharacteristic
15#15667970—24no—
16C2×C4⋊Dic89C2211yescharacteristic, complemented
17C2×C4⋊Dic89C2212yescomplemented
18C2×#13083553C2212yescomplemented
19C2×C22⋊Dic89C2211yescharacteristic
20C2×C22⋊Dic89C2212yes—
21C2×#13083551C2212yes—
22C2×#13083551C2212yes—
23C2×#13083551C2212yes—
24C2×#13083551C2211yescharacteristic
25C2×#13083551C2211yescharacteristic
26C2×#13083551C2212yes—
27C22⋊C4×D89—24no—
28C2×C4×Dic89C2212yescomplemented
29#15667919C2212yescomplemented
30#15667919C2211yescharacteristic, complemented
31#15667919C2212yescomplemented
32C2×C4⋊C4×C89C2211yescharacteristic, complemented
33C2×C22⋊C4×C89C2212yes—
34C2×C22⋊C4×C89C2211yescharacteristic
35#95×C89C2211yescharacteristic, complemented
36#95×C89C2212yescomplemented
37C23×D89—22no—
38C23×D89—22no—
39C23×D89—22no—
40C23×D89—24no—
41C23×D89—42no—
42C23×D89C2311yescharacteristic
43C23×D89C2311yescharacteristic
44C22×Dic89C2311yescharacteristic
45C22×Dic89C2312yes—
46C22×Dic89C2312yes—
47C22×Dic89C2311yescharacteristic
48C2×C4×D89—24no—
49C2×C4×D89—22no—
50C2×C4×D89—42no—
51C2×C4×D89D414yes—
52C4⋊Dic89—22no—
53C4⋊Dic89—42no—
54#13083553—42no—
55C22⋊Dic89—22no—
56C22⋊Dic89—42no—
57#13083551—24no—
58#13083551—24no—
59#13083551—24no—
60#13083551—22no—
61#13083551—22no—
62#13083551—42no—
63C4×Dic89—24no—
64C24×C89C2311yescharacteristic
65C22×C4×C89C2311yescharacteristic
66C22×C4×C89C2312yes—
67C22×C4×C89C2312yes—
68C22×C4×C89C2311yescharacteristic
69C4⋊C4×C89—22no—
70C22⋊C4×C89—24no—
71C22⋊C4×C89—22no—
72C23×C89—21no—
73C23×C89—21no—
74C23×C89—22no—
75C23×C89—22no—
76C23×C89#4112yes—
77C23×C89C2411yescharacteristic
78C22×D89—21no—
79C22×D89—21no—
80C22×D89—22no—
81C22×D89—28no—
82C22×D89—21no—
83C22×D89—22no—
84C22×D89—21no—
85C22×D89—22no—
86C22×D89—48no—
87C22×D89—48no—
88C22×D89—44no—
89C22×D89—44no—
90C22×D89C2×D412yes—
91C22×D89#4112yes—
92C22×D89#4114yes—
93C2×C4×C89—22no—
94C2×C4×C89—21no—
95C2×C4×C89—22no—
96C2×C4×C89—22no—
97C2×C4×C89—22no—
98C2×C4×C89—22no—
99C2×C4×C89—22no—
100C2×C4×C89—22no—
101C2×C4×C89—22no—
102C2×C4×C89C2×D412yes—
103C2×Dic89—22no—
104C2×Dic89—22no—
105C2×Dic89—21no—
106C2×Dic89—22no—
107C2×Dic89—22no—
108C2×Dic89—22no—
109C2×Dic89—22no—
110C2×Dic89—22no—
111C2×Dic89—22no—
112C2×Dic89C2×D412yes—
113C4×D89—28no—
114C4×D89—44no—
115C22×C89—22no—
116C22×C89—24no—
117C22×C89—41no—
118C22×C89—41no—
119C22×C89—42no—
120C22×C89C22×D411yescharacteristic
121C22×C89C2×#4112yes—
122C22×C89C2×#4111yescharacteristic
123C22×C89C2×#4111yescharacteristic
124C22×C89H(5,𝔽2)12yes—
125C2×D89—22no—
126C2×D89—22no—
127C2×D89—24no—
128C2×D89—24no—
129C2×D89—22no—
130C2×D89—24no—
131C2×D89—416no—
132C2×D89—41no—
133C2×D89—41no—
134C2×D89—42no—
135C2×D89#12314yes—
136C4×C89—22no—
137C4×C89—42no—
138C4×C89—41no—
139C4×C89—42no—
140Dic89—22no—
141Dic89—41no—
142Dic89—42no—
143Dic89—42no—
144C2×C89—42no—
145C2×C89C2×#12311yescharacteristic
146C2×C89#52511yescharacteristic
147C2×C89#53511yescharacteristic
148C2×C89#55112yes—
149C2×C89#55112yes—
150D89—24no—
151D89—42no—
152#2482—891nomaximal, Sylow
153C89#248211yescharacteristic, complemented, Sylow
154C2×#117—891no—
155C22×C22⋊C4—891no—
156#399—891no—
157#399—891no—
158#397—891no—
159#397D8911yescharacteristic, complemented
160#388—892no—
161#388—892no—
162#385—892no—
163#381—891no—
164#379—892no—
165C25—891no—
166C23×C4—891no—
167C23×C4—891no—
168#117—1784no—
169C2×C4⋊C4—892no—
170C2×C4⋊C4—892no—
171C2×C4⋊C4—891no—
172C2×C4⋊C4C2×D8911yescharacteristic, complemented
173C2×C22⋊C4—892no—
174C2×C22⋊C4—892no—
175C2×C22⋊C4—891no—
176C2×C22⋊C4—891no—
177C2×C22⋊C4—891no—
178C2×C22⋊C4—892no—
179C2×C22⋊C4—892no—
180C2×C22⋊C4—892no—
181C2×C22⋊C4—1784no—
182C2×C22⋊C4C2×D8911yescharacteristic
183C2×C22⋊C4C2×D8912yes—
184C2×C42—892no—
185#95—892no—
186#95—891no—
187#95—892no—
188#95C2×D8911yescharacteristic, complemented
189#95C2×D8912yescomplemented
190C24—891no—
191C24—891no—
192C24—3562no—
193C24—1784no—
194C24—1782no—
195C24—1782no—
196C24—1782no—
197C24C22×D8911yescharacteristic
198C22×C4—891no—
199C22×C4—894no—
200C22×C4—892no—
201C22×C4—891no—
202C22×C4—892no—
203C22×C4—3562no—
204C22×C4—1782no—
205C22×C4—1784no—
206C22×C4C22×D8912yes—
207C22×C4C22×D8912yes—
208C22×C4C22×D8911yescharacteristic
209C22×C4C22×D8911yescharacteristic
210C4⋊C4—22no—
211C4⋊C4—3562no—
212C4⋊C4—3562no—
213C4⋊C4—1782no—
214C22⋊C4—24no—
215C22⋊C4—22no—
216C22⋊C4—3562no—
217C22⋊C4—3562no—
218C22⋊C4—1782no—
219C22⋊C4—1784no—
220C22⋊C4—1784no—
221C22⋊C4—1784no—
222C22⋊C4—1782no—
223C22⋊C4—1782no—
224C42—1784no—
225C23—21no—
226C23—22no—
227C23—21no—
228C23—22no—
229C23—892no—
230C23—894no—
231C23—892no—
232C23—3568no—
233C23—3564no—
234C23—3564no—
235C23—3568no—
236C23—1788no—
237C23—1781no—
238C23—1782no—
239C23—1781no—
240C23—1782no—
241C23—1781no—
242C23—1781no—
243C23—1782no—
244C23#1308357312yes—
245C23C23×D8911yescharacteristic
246C2×C4—22no—
247C2×C4—22no—
248C2×C4—21no—
249C2×C4—22no—
250C2×C4—22no—
251C2×C4—22no—
252C2×C4—22no—
253C2×C4—22no—
254C2×C4—22no—
255C2×C4—892no—
256C2×C4—3564no—
257C2×C4—1788no—
258C2×C4—1782no—
259C2×C4—1781no—
260C2×C4—1782no—
261C2×C4—1782no—
262C2×C4—1782no—
263C2×C4—1782no—
264C2×C4—1782no—
265C2×C4—1782no—
266C2×C4—1782no—
267C2×C4D4×D8912yes—
268C22—24no—
269C22—22no—
270C22—41no—
271C22—42no—
272C22—41no—
273C22—894no—
274C22—35616no—
275C22—3561no—
276C22—3562no—
277C22—3561no—
278C22—1784no—
279C22—1782no—
280C22—1782no—
281C22—1784no—
282C22—1784no—
283C22—1782no—
284C22C2×D4×D8911yescharacteristic
285C22#41×D8912yes—
286C22#41×D8911yescharacteristic
287C22C2×#1308357311yescharacteristic
288C22#1566805812yes—
289C4—22no—
290C4—41no—
291C4—42no—
292C4—42no—
293C4—3561no—
294C4—3562no—
295C4—3562no—
296C4—1782no—
297C2—42no—
298C2—3562no—
299C2—1784no—
300C2#123×D8911yescharacteristic
301C2#1915210811yescharacteristic
302C2#1915216611yescharacteristic
303C2#1915227112yes—
304C2#1915227312yes—
subgroupG/H
center, FrattiniC23C23×D89
commutator, socle, cosocleC23×C89C24
Fitting#397×C89C2
prime radicalC24×D89C22
hypercenter#397D89
hypocenterC89#2482
LCSG ▷ C23×C89 ▷ C89
UCSC1 ◁ C23 ◁ #397

Complements

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

NH ≅ G/Ntype
1. C2×#15667970C2semidirect
3. #19151535C2semidirect
4. #19151534C2semidirect
5. #19151524C2semidirect
6. #19151491C2semidirect
7. #19151487C2semidirect
8. #19151472C2semidirect
9. #19151460C2semidirect
11. #397×C89C2semidirect
16. C2×C4⋊Dic89C22semidirect
17. C2×C4⋊Dic89C22semidirect
18. C2×#13083553C22semidirect
28. C2×C4×Dic89C22semidirect
29. #15667919C22semidirect
30. #15667919C22semidirect
31. #15667919C22semidirect
32. C2×C4⋊C4×C89C22semidirect
35. #95×C89C22semidirect
36. #95×C89C22semidirect
153. C89#2482semidirect
159. #397D89semidirect
172. C2×C4⋊C4C2×D89semidirect
188. #95C2×D89semidirect
189. #95C2×D89semidirect

Maximal subgroups

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

subgroupindex
C2×#156679702
C2×C22⋊C4×D892
#191515352
#191515342
#191515242
#191514912
#191514872
#191514722
#191514602
#191514532
#397×C892
#248289