Finite Group Databasebeta

← #26024525

Subgroups — #26024525

Order 11392.

672 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 672 conjugacy classes of subgroups — too many to draw. Only its 145 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×#15667968C211yesmaximal, characteristic, complemented
2C22×#13083551C211yesmaximal, characteristic
3#19151533C212yesmaximal, complemented
4#19151527C212yesmaximal, complemented
5#19151488C212yesmaximal, complemented
6#19151487C212yesmaximal, complemented
7#19151471C211yesmaximal, characteristic, complemented
8#19151459C211yesmaximal, characteristic, complemented
9#19151453C211yesmaximal, characteristic
10#19151453C211yesmaximal, characteristic
11#385×C89C211yesmaximal, characteristic, complemented
12C24×D89C2211yescharacteristic
13C23×Dic89C2211yescharacteristic
14#15667968—24no—
15C2×#13083553C2211yescharacteristic, complemented
16C2×#13083553C2211yescharacteristic, complemented
17C2×#13083553C2212yescomplemented
18C2×C22⋊Dic89C2211yescharacteristic
19C2×C22⋊Dic89C2211yescharacteristic
20C2×#13083551—24no—
21C2×#13083551C2212yes—
22C2×#13083551C2212yes—
23C2×#13083551C2212yes—
24C2×#13083551C2212yes—
25C2×#13083551C2212yes—
26C2×#13083551C2212yes—
27C2×C4×Dic89C2211yescharacteristic, complemented
28C2×C4×Dic89C2211yescharacteristic, complemented
29#15667919C2212yescomplemented
30#15667919C2212yescomplemented
31#15667919C2212yescomplemented
32C23×C4×C89C2211yescharacteristic
33C2×C4⋊C4×C89C2212yescomplemented
34C2×C22⋊C4×C89C2211yescharacteristic
35C2×C22⋊C4×C89C2211yescharacteristic
36#95×C89C2212yescomplemented
37C23×D89—22no—
38C23×D89—24no—
39C23×D89—22no—
40C23×D89—22no—
41C23×D89—42no—
42C23×D89C2312yes—
43C22×Dic89—22no—
44C22×Dic89—22no—
45C22×Dic89D414yes—
46C22×Dic89C2312yes—
47C22×Dic89C2311yescharacteristic
48C22×Dic89C2311yescharacteristic
49C22×Dic89C2311yescharacteristic
50C22×Dic89C2311yescharacteristic
51#13083553—22no—
52#13083553—22no—
53#13083553—42no—
54C22⋊Dic89—22no—
55C22⋊Dic89—22no—
56#13083551—24no—
57#13083551—24no—
58#13083551—24no—
59#13083551—24no—
60#13083551—42no—
61#13083551—42no—
62C4×Dic89—22no—
63C4×Dic89—22no—
64C24×C89C2311yescharacteristic
65C22×C4×C89—22no—
66C22×C4×C89—42no—
67C22×C4×C89C2311yescharacteristic
68C22×C4×C89C2312yes—
69C22×C4×C89C2312yes—
70C22×C4×C89C2311yescharacteristic
71C4⋊C4×C89—42no—
72C22⋊C4×C89—22no—
73C22⋊C4×C89—22no—
74C23×C89—22no—
75C23×C89—22no—
76C23×C89C2×D412yes—
77C23×C89#4112yes—
78C23×C89#4112yes—
79C23×C89C2411yescharacteristic
80C22×D89—28no—
81C22×D89—22no—
82C22×D89—22no—
83C22×D89—22no—
84C22×D89—22no—
85C22×D89—22no—
86C22×D89—22no—
87C22×D89—48no—
88C22×D89—48no—
89C22×D89—44no—
90C22×D89—44no—
91C22×D89#4114yes—
92C2×C4×C89—21no—
93C2×C4×C89—21no—
94C2×C4×C89—22no—
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×C89—44no—
103C2×Dic89—28no—
104C2×Dic89—21no—
105C2×Dic89—21no—
106C2×Dic89—21no—
107C2×Dic89—21no—
108C2×Dic89—21no—
109C2×Dic89—21no—
110C2×Dic89—22no—
111C2×Dic89—22no—
112C2×Dic89—22no—
113C2×Dic89—22no—
114C2×Dic89—22no—
115C2×Dic89C2×D412yes—
116C2×Dic89C2×D412yes—
117C22×C89—22no—
118C22×C89—22no—
119C22×C89—24no—
120C22×C89—24no—
121C22×C89#12314yes—
122C22×C89C22×D411yescharacteristic
123C22×C89C2×#4111yescharacteristic
124C22×C89C2×#4111yescharacteristic
125C22×C89C2×#4112yes—
126C22×C89H(5,𝔽2)12yes—
127C2×D89—24no—
128C2×D89—24no—
129C2×D89—24no—
130C2×D89—416no—
131C2×D89—42no—
132C2×D89—42no—
133C2×D89—42no—
134C2×D89—42no—
135C4×C89—41no—
136C4×C89—41no—
137C4×C89—42no—
138C4×C89—42no—
139Dic89—22no—
140Dic89—22no—
141Dic89—41no—
142Dic89—41no—
143Dic89—42no—
144C2×C89—24no—
145C2×C89C2×#12311yescharacteristic
146C2×C89#52511yescharacteristic
147C2×C89#53511yescharacteristic
148C2×C89#55112yes—
149C2×C89#55112yes—
150D89—44no—
151#2482—891nomaximal, Sylow
152C89#248211yescharacteristic, complemented, Sylow
153C2×#117—891no—
154C22×C22⋊C4—891no—
155#399—892no—
156#397—892no—
157#388—892no—
158#388—892no—
159#385—891no—
160#385D8911yescharacteristic, complemented
161#381—891no—
162#379—891no—
163#379—891no—
164C25—891no—
165C23×C4—891no—
166C23×C4C2×D8911yescharacteristic
167#117—1784no—
168C2×C4⋊C4—892no—
169C2×C4⋊C4—891no—
170C2×C4⋊C4—891no—
171C2×C4⋊C4C2×D8912yescomplemented
172C2×C22⋊C4—892no—
173C2×C22⋊C4—892no—
174C2×C22⋊C4—891no—
175C2×C22⋊C4—891no—
176C2×C22⋊C4—892no—
177C2×C22⋊C4—892no—
178C2×C22⋊C4—892no—
179C2×C22⋊C4—892no—
180C2×C22⋊C4—1784no—
181C2×C22⋊C4C2×D8911yescharacteristic
182C2×C22⋊C4C2×D8911yescharacteristic
183C2×C42—891no—
184C2×C42—891no—
185#95—892no—
186#95—892no—
187#95—892no—
188#95C2×D8912yescomplemented
189C24—892no—
190C24—3562no—
191C24—1784no—
192C24—1782no—
193C24—1782no—
194C24—1782no—
195C24C22×D8911yescharacteristic
196C22×C4—22no—
197C22×C4—42no—
198C22×C4—894no—
199C22×C4—891no—
200C22×C4—891no—
201C22×C4—892no—
202C22×C4—891no—
203C22×C4—891no—
204C22×C4—1782no—
205C22×C4—1782no—
206C22×C4C22×D8912yes—
207C22×C4C22×D8912yes—
208C22×C4C22×D8911yescharacteristic
209C22×C4C22×D8911yescharacteristic
210C4⋊C4—42no—
211C4⋊C4—3562no—
212C4⋊C4—1782no—
213C4⋊C4—1782no—
214C22⋊C4—22no—
215C22⋊C4—22no—
216C22⋊C4—3562no—
217C22⋊C4—3562no—
218C22⋊C4—1784no—
219C22⋊C4—1784no—
220C22⋊C4—1784no—
221C22⋊C4—1784no—
222C22⋊C4—1782no—
223C22⋊C4—1782no—
224C42—1782no—
225C42—1782no—
226C23—22no—
227C23—22no—
228C23—894no—
229C23—3564no—
230C23—3568no—
231C23—3568no—
232C23—3564no—
233C23—1788no—
234C23—1782no—
235C23—1782no—
236C23—1782no—
237C23—1782no—
238C23—1782no—
239C23—1782no—
240C23D4×D8912yes—
241C23#1308357412yes—
242C23#1308357512yes—
243C23C23×D8911yescharacteristic
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—22no—
247C2×C4—22no—
248C2×C4—22no—
249C2×C4—22no—
250C2×C4—22no—
251C2×C4—22no—
252C2×C4—22no—
253C2×C4—22no—
254C2×C4—44no—
255C2×C4—892no—
256C2×C4—892no—
257C2×C4—1781no—
258C2×C4—1781no—
259C2×C4—1782no—
260C2×C4—1782no—
261C2×C4—1782no—
262C2×C4—1782no—
263C2×C4—1782no—
264C2×C4—1788no—
265C2×C4—1781no—
266C2×C4—1781no—
267C2×C4—1781no—
268C2×C4—1781no—
269C22—22no—
270C22—24no—
271C22—24no—
272C22—22no—
273C22—35616no—
274C22—3562no—
275C22—3562no—
276C22—3562no—
277C22—3562no—
278C22—1784no—
279C22—1784no—
280C22—1784no—
281C22#1566799714yes—
282C22C2×D4×D8911yescharacteristic
283C22#41×D8912yes—
284C22C2×#1308357411yescharacteristic
285C22C2×#1308357511yescharacteristic
286C22#1566805712yes—
287C4—42no—
288C4—41no—
289C4—42no—
290C4—41no—
291C4—3561no—
292C4—3562no—
293C4—3561no—
294C4—1782no—
295C4—1782no—
296C2—24no—
297C2—3564no—
298C2C2×#1566799711yescharacteristic
299C2#1915210611yescharacteristic
300C2#1915216311yescharacteristic
301C2#1915227512yes—
302C2#1915227712yes—
subgroupG/H
center, FrattiniC23C23×D89
commutator, socle, cosocleC23×C89C24
Fitting#385×C89C2
prime radicalC24×D89C22
hypercenter#385D89
hypocenterC89#2482
LCSG ▷ C23×C89 ▷ C89
UCSC1 ◁ C23 ◁ #385

Complements

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

NH ≅ G/Ntype
1. C2×#15667968C2semidirect
3. #19151533C2semidirect
4. #19151527C2semidirect
5. #19151488C2semidirect
6. #19151487C2semidirect
7. #19151471C2semidirect
8. #19151459C2semidirect
11. #385×C89C2semidirect
15. C2×#13083553C22semidirect
16. C2×#13083553C22semidirect
17. C2×#13083553C22semidirect
27. C2×C4×Dic89C22semidirect
28. C2×C4×Dic89C22semidirect
29. #15667919C22semidirect
30. #15667919C22semidirect
31. #15667919C22semidirect
33. C2×C4⋊C4×C89C22semidirect
36. #95×C89C22semidirect
152. C89#2482semidirect
160. #385D89semidirect
171. C2×C4⋊C4C2×D89semidirect
188. #95C2×D89semidirect

Maximal subgroups

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

subgroupindex
C2×#156679682
C22×#130835512
#191515332
#191515272
#191514882
#191514872
#191514712
#191514592
#191514532
#385×C892
#248289