Finite Group Databasebeta

← #26025409

Subgroups — #26025409

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×#15667989C211yesmaximal, characteristic, complemented
2C22×#13083551C211yesmaximal, characteristic
3#19151527C212yesmaximal, complemented
4#19151511C212yesmaximal, complemented
5#19151490C212yesmaximal, complemented
6#19151487C212yesmaximal, complemented
7#19151461C211yesmaximal, characteristic, complemented
8#19151453C211yesmaximal, characteristic
9#19151453C211yesmaximal, characteristic
10C22⋊C4×Dic89C211yesmaximal, characteristic, complemented
11#381×C89C211yesmaximal, characteristic, complemented
12C24×D89C2211yescharacteristic
13C22×Dic178C2211yescharacteristic, complemented
14C23×Dic89C2211yescharacteristic
15#15667989—24no—
16C2×C4⋊Dic89C2211yescharacteristic, complemented
17C2×#13083553C2211yescharacteristic, complemented
18C2×#13083553C2211yescharacteristic, complemented
19C2×C22⋊Dic89C2211yescharacteristic
20C2×C22⋊Dic89C2211yescharacteristic
21C2×#13083551—24no—
22C2×#13083551C2212yes—
23C2×#13083551C2212yes—
24C2×#13083551C2212yes—
25C2×#13083551C2212yes—
26C2×#13083551C2212yes—
27C2×#13083551C2212yes—
28C2×C4×Dic89C2212yescomplemented
29#15667919C2212yescomplemented
30#15667919C2212yescomplemented
31#15667919C2212yescomplemented
32C23×C4×C89C2211yescharacteristic
33C2×C22⋊C4×C89C2211yescharacteristic
34C2×C22⋊C4×C89C2211yescharacteristic
35#95×C89C2212yescomplemented
36#95×C89C2212yescomplemented
37C23×D89—22no—
38C23×D89—24no—
39C23×D89—22no—
40C23×D89—22no—
41C23×D89—42no—
42C23×D89C2312yes—
43C2×Dic178—22no—
44C2×Dic178—42no—
45C22×Dic89—42no—
46C22×Dic89D414yes—
47C22×Dic89C2311yescharacteristic
48C22×Dic89C2312yes—
49C22×Dic89C2311yescharacteristic
50C22×Dic89C2311yescharacteristic
51C22×Dic89C2311yescharacteristic
52C4⋊Dic89—22no—
53#13083553—22no—
54#13083553—22no—
55C22⋊Dic89—22no—
56C22⋊Dic89—22no—
57#13083551—24no—
58#13083551—24no—
59#13083551—24no—
60#13083551—24no—
61#13083551—42no—
62#13083551—42no—
63C4×Dic89—42no—
64C24×C89C2311yescharacteristic
65C22×C4×C89—22no—
66C22×C4×C89—22no—
67C22×C4×C89—22no—
68C22×C4×C89C2311yescharacteristic
69C22×C4×C89C2312yes—
70C22×C4×C89C2311yescharacteristic
71C22×C4×C89C2312yes—
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—22no—
104C2×Dic89—22no—
105C2×Dic89—21no—
106C2×Dic89—21no—
107C2×Dic89—22no—
108C2×Dic89—22no—
109C2×Dic89—22no—
110C2×Dic89—22no—
111C2×Dic89—22no—
112C2×Dic89—44no—
113C2×Dic89C2×D412yes—
114C2×Dic89C2×D412yes—
115Dic178—44no—
116C22×C89—22no—
117C22×C89—22no—
118C22×C89—24no—
119C22×C89—24no—
120C22×C89#12414yes—
121C22×C89C22×D411yescharacteristic
122C22×C89C2×#4112yes—
123C22×C89C2×#4111yescharacteristic
124C22×C89C2×#4111yescharacteristic
125C22×C89H(5,𝔽2)12yes—
126C2×D89—24no—
127C2×D89—24no—
128C2×D89—24no—
129C2×D89—416no—
130C2×D89—42no—
131C2×D89—42no—
132C2×D89—42no—
133C2×D89—42no—
134C4×C89—41no—
135C4×C89—42no—
136C4×C89—41no—
137C4×C89—42no—
138Dic89—22no—
139Dic89—22no—
140Dic89—41no—
141Dic89—41no—
142Dic89—42no—
143C2×C89—24no—
144C2×C89#52511yescharacteristic
145C2×C89C2×#12411yescharacteristic
146C2×C89#53411yescharacteristic
147C2×C89#55112yes—
148C2×C89#55112yes—
149D89—44no—
150#2561—891nomaximal, Sylow
151C89#256111yescharacteristic, complemented, Sylow
152C2×C22⋊Q8—891no—
153C22×C22⋊C4—891no—
154#397—892no—
155#393—892no—
156#388—892no—
157#388—892no—
158#381—891no—
159#381D8911yescharacteristic, complemented
160#379—891no—
161#379—891no—
162C4×C22⋊C4—891no—
163C25—891no—
164C22×Q8—891no—
165C23×C4—891no—
166C23×C4C2×D8911yescharacteristic
167C22⋊Q8—1784no—
168C2×C4⋊C4—891no—
169C2×C4⋊C4—891no—
170C2×C4⋊C4—891no—
171C2×C22⋊C4—892no—
172C2×C22⋊C4—892no—
173C2×C22⋊C4—891no—
174C2×C22⋊C4—891no—
175C2×C22⋊C4—892no—
176C2×C22⋊C4—892no—
177C2×C22⋊C4—892no—
178C2×C22⋊C4—892no—
179C2×C22⋊C4—1784no—
180C2×C22⋊C4C2×D8911yescharacteristic
181C2×C22⋊C4C2×D8911yescharacteristic
182C2×C42—892no—
183#95—892no—
184#95—892no—
185#95—892no—
186#95C2×D8912yescomplemented
187#95C2×D8912yescomplemented
188C24—892no—
189C24—3562no—
190C24—1784no—
191C24—1782no—
192C24—1782no—
193C24—1782no—
194C24C22×D8911yescharacteristic
195C2×Q8—3562no—
196C2×Q8—1782no—
197C22×C4—22no—
198C22×C4—22no—
199C22×C4—22no—
200C22×C4—894no—
201C22×C4—891no—
202C22×C4—891no—
203C22×C4—892no—
204C22×C4—891no—
205C22×C4—891no—
206C22×C4—3562no—
207C22×C4C22×D8912yes—
208C22×C4C22×D8912yes—
209C22×C4C22×D8911yescharacteristic
210C22×C4C22×D8911yescharacteristic
211C4⋊C4—1782no—
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—3562no—
225C23—22no—
226C23—22no—
227C23—894no—
228C23—3564no—
229C23—3568no—
230C23—3568no—
231C23—3564no—
232C23—1788no—
233C23—1782no—
234C23—1782no—
235C23—1782no—
236C23—1782no—
237C23—1782no—
238C23—1782no—
239C23D4×D8912yes—
240C23#1308357312yes—
241C23#1308357412yes—
242C23C23×D8911yescharacteristic
243Q8—3564no—
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—3564no—
258C2×C4—1781no—
259C2×C4—1781no—
260C2×C4—1782no—
261C2×C4—1782no—
262C2×C4—1782no—
263C2×C4—1782no—
264C2×C4—1782no—
265C2×C4—1782no—
266C2×C4—1782no—
267C22—22no—
268C22—24no—
269C22—24no—
270C22—22no—
271C22—35616no—
272C22—3562no—
273C22—3562no—
274C22—3562no—
275C22—3562no—
276C22—1784no—
277C22—1784no—
278C22—1784no—
279C22#1566799814yes—
280C22C2×D4×D8911yescharacteristic
281C22#41×D8912yes—
282C22C2×#1308357311yescharacteristic
283C22C2×#1308357411yescharacteristic
284C22#1566805812yes—
285C4—41no—
286C4—42no—
287C4—41no—
288C4—42no—
289C4—3561no—
290C4—3562no—
291C4—3561no—
292C4—1782no—
293C4—1782no—
294C2—24no—
295C2—3564no—
296C2#1915210611yescharacteristic
297C2C2×#1566799811yescharacteristic
298C2#1915215911yescharacteristic
299C2#1915227112yes—
300C2#1915227212yes—
subgroupG/H
center, FrattiniC23C23×D89
commutator, socle, cosocleC23×C89C24
Fitting#381×C89C2
prime radicalC24×D89C22
hypercenter#381D89
hypocenterC89#2561
LCSG ▷ C23×C89 ▷ C89
UCSC1 ◁ C23 ◁ #381

Complements

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

NH ≅ G/Ntype
1. C2×#15667989C2semidirect
3. #19151527C2semidirect
4. #19151511C2semidirect
5. #19151490C2semidirect
6. #19151487C2semidirect
7. #19151461C2semidirect
10. C22⋊C4×Dic89C2semidirect
11. #381×C89C2semidirect
13. C22×Dic178C22semidirect
16. C2×C4⋊Dic89C22semidirect
17. C2×#13083553C22semidirect
18. C2×#13083553C22semidirect
28. C2×C4×Dic89C22semidirect
29. #15667919C22semidirect
30. #15667919C22semidirect
31. #15667919C22semidirect
35. #95×C89C22semidirect
36. #95×C89C22semidirect
151. C89#2561semidirect
159. #381D89semidirect
186. #95C2×D89semidirect
187. #95C2×D89semidirect

Maximal subgroups

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

subgroupindex
C2×#156679892
C22×#130835512
#191515272
#191515112
#191514902
#191514872
#191514612
#191514532
C22⋊C4×Dic892
#381×C892
#256189