Finite Group Databasebeta

← #26025243

Subgroups — #26025243

Order 11392.

604 conjugacy classes of subgroups; only the 151 normal subgroups are shown.

normal subgroups only

This group has 604 conjugacy classes of subgroups — too many to draw. Only its 151 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×#15668011C211yesmaximal, characteristic, complemented
2C2×#15667998C212yesmaximal
3C2×#15667972C211yesmaximal, characteristic
4#19151525C211yesmaximal, characteristic, complemented
5#19151524C211yesmaximal, characteristic, complemented
6#19151523C211yesmaximal, characteristic, complemented
7#19151502C212yesmaximal, complemented
8#19151457C212yesmaximal, complemented
9#19151456C212yesmaximal, complemented
10#19151449C211yesmaximal, characteristic, complemented
11#397×C89C211yesmaximal, characteristic, complemented
12C22×Dic178C2212yes—
13C22×C22⋊D89C2211yescharacteristic
14C23×Dic89C2211yescharacteristic
15C22×C4×D89C2211yescharacteristic
16#15668011—24no—
17#15667998—28no—
18#15667972—24no—
19C2×C4⋊Dic89C2211yescharacteristic
20C2×#13083553C2212yes—
21C2×#13083553C2212yes—
22C2×#13083553C2211yescharacteristic
23C2×C22⋊Dic89C2212yes—
24C2×#13083551C2212yes—
25C2×#13083551C2212yes—
26C2×#13083551C2211yescharacteristic
27C2×C4×Dic89C2212yes—
28C2×C4×Dic89C2211yescharacteristic
29#15667919C2211yescharacteristic
30#15667919C2212yes—
31#15667919C2212yes—
32#15667919C2212yes—
33C2×C4⋊C4×C89C2211yescharacteristic
34C2×C22⋊C4×C89C2212yes—
35C2×C22⋊C4×C89C2211yescharacteristic
36#95×C89C2211yescharacteristic
37#95×C89C2212yes—
38C23×D89C2311yescharacteristic
39C2×Dic178—24no—
40C2×Dic178—24no—
41C2×Dic178—24no—
42C2×C22⋊D89—22no—
43C2×C22⋊D89—22no—
44C2×C22⋊D89D414yes—
45C22×Dic89—22no—
46C22×Dic89—24no—
47C22×Dic89C2311yescharacteristic
48C22×Dic89C2312yes—
49C22×Dic89C2312yes—
50C22×Dic89C2311yescharacteristic
51C22×Dic89C2311yescharacteristic
52C2×C4×D89—22no—
53C2×C4×D89—24no—
54C4⋊Dic89—22no—
55#13083553—22no—
56#13083553—24no—
57#13083553—24no—
58C22⋊Dic89—24no—
59#13083551—24no—
60#13083551—24no—
61#13083551—22no—
62C4×Dic89—24no—
63C4×Dic89D414yes—
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—22no—
74C23×C89—21no—
75C23×C89—22no—
76C23×C89C2×D412yes—
77C23×C89C2411yescharacteristic
78C22×D89—21no—
79C22×D89—22no—
80C22×D89—21no—
81C22×D89—22no—
82C22×D89C2×D412yes—
83C2×C4×C89—22no—
84C2×C4×C89—22no—
85C2×C4×C89—22no—
86C2×C4×C89—21no—
87C2×C4×C89—22no—
88C2×C4×C89—22no—
89C2×C4×C89—22no—
90C2×C4×C89—22no—
91C2×C4×C89—22no—
92C2×C4×C89C2×D412yes—
93C22⋊D89—28no—
94C2×Dic89—22no—
95C2×Dic89—22no—
96C2×Dic89—21no—
97C2×Dic89—22no—
98C2×Dic89—22no—
99C2×Dic89—22no—
100C2×Dic89—22no—
101C2×Dic89—22no—
102C2×Dic89—44no—
103C2×Dic89C2×D412yes—
104C2×Dic89C2×D412yes—
105C2×Dic89C2×D412yes—
106C2×Dic89#4112yes—
107C2×Dic89#4114yes—
108C4×D89—44no—
109Dic178—48no—
110C22×C89—22no—
111C22×C89—24no—
112C22×C89—41no—
113C22×C89—41no—
114C22×C89—42no—
115C22×C89C22×D411yescharacteristic
116C22×C89C22×D411yescharacteristic
117C22×C89C2×#4111yescharacteristic
118C22×C89C2×#4112yes—
119C22×C892−1+412yes—
120C2×D89—22no—
121C2×D89—24no—
122C2×D89—41no—
123C2×D89—41no—
124C2×D89—42no—
125C4×C89—22no—
126C4×C89—42no—
127C4×C89—41no—
128C4×C89—42no—
129Dic89—42no—
130Dic89—41no—
131Dic89—42no—
132Dic89#12114yes—
133Dic89#12414yescomplemented
134C2×C89—42no—
135C2×C89C2×#12111yescharacteristic
136C2×C89C2×#12411yescharacteristic
137C2×C89#53611yescharacteristic
138C2×C89#54712yes—
139C2×C89#55612yes—
140D89—42no—
141#2547—891nomaximal, Sylow
142C89#254711yescharacteristic, complemented, Sylow
143C2×C4⋊Q8—891no—
144C2×#124—892no—
145C2×C4×D4—891no—
146#397—891no—
147#397—891no—
148#397—891no—
149#397D8911yescharacteristic, complemented
150#391—892no—
151#380—892no—
152#380—892no—
153C4×C4⋊C4—891no—
154C22×Q8—892no—
155C22×D4—891no—
156C23×C4—891no—
157C23×C4—891no—
158C4⋊Q8—1784no—
159#124—1788no—
160C4×D4—1784no—
161C2×C4⋊C4—891no—
162C2×C4⋊C4—892no—
163C2×C4⋊C4—891no—
164C2×C4⋊C4—892no—
165C2×C4⋊C4C2×D8911yescharacteristic
166C2×C22⋊C4—892no—
167C2×C22⋊C4—891no—
168C2×C22⋊C4—892no—
169C2×C22⋊C4—892no—
170C2×C22⋊C4C2×D8911yescharacteristic
171C2×C22⋊C4C2×D8912yes—
172C2×C42—891no—
173C2×C42—892no—
174#95—891no—
175#95—892no—
176#95—892no—
177#95—892no—
178#95C2×D8911yescharacteristic
179#95C2×D8912yes—
180C24—891no—
181C24C22×D8911yescharacteristic
182C2×Q8—1784no—
183C2×Q8—1784no—
184C2×Q8—1784no—
185C2×D4—894no—
186C2×D4—1782no—
187C2×D4—1782no—
188C22×C4—891no—
189C22×C4—891no—
190C22×C4—891no—
191C22×C4—892no—
192C22×C4—892no—
193C22×C4—1782no—
194C22×C4—1784no—
195C22×C4—1782no—
196C22×C4—1784no—
197C22×C4C22×D8911yescharacteristic
198C22×C4C22×D8912yes—
199C22×C4C22×D8912yes—
200C22×C4C22×D8911yescharacteristic
201C4⋊C4—22no—
202C4⋊C4—1782no—
203C4⋊C4—1784no—
204C4⋊C4—1784no—
205C4⋊C4—1782no—
206C22⋊C4—24no—
207C22⋊C4—22no—
208C22⋊C4—1784no—
209C22⋊C4—1784no—
210C22⋊C4—1784no—
211C22⋊C4—1782no—
212C42—894no—
213C42—1784no—
214C23—21no—
215C23—22no—
216C23—21no—
217C23—22no—
218C23—892no—
219C23—1781no—
220C23—1782no—
221C23—1781no—
222C23—1782no—
223C23D4×D8912yes—
224C23C23×D8911yescharacteristic
225Q8—3568no—
226D4—1788no—
227C2×C4—22no—
228C2×C4—22no—
229C2×C4—22no—
230C2×C4—21no—
231C2×C4—22no—
232C2×C4—22no—
233C2×C4—22no—
234C2×C4—22no—
235C2×C4—22no—
236C2×C4—892no—
237C2×C4—892no—
238C2×C4—892no—
239C2×C4—894no—
240C2×C4—892no—
241C2×C4—3564no—
242C2×C4—3564no—
243C2×C4—1782no—
244C2×C4—1782no—
245C2×C4—1781no—
246C2×C4—1782no—
247C2×C4—1782no—
248C2×C4—1782no—
249C2×C4—1782no—
250C2×C4—1782no—
251C2×C4D4×D8912yes—
252C22—24no—
253C22—22no—
254C22—41no—
255C22—42no—
256C22—41no—
257C22—3561no—
258C22—3562no—
259C22—3561no—
260C22—1784no—
261C22—1782no—
262C22C2×D4×D8911yescharacteristic
263C22C2×D4×D8911yescharacteristic
264C22#41×D8912yes—
265C22#41×D8911yescharacteristic
266C22#1566805912yes—
267C4—22no—
268C4—42no—
269C4—42no—
270C4—41no—
271C4—894no—
272C4—894no—
273C4—3562no—
274C4—3562no—
275C4—3561no—
276C2—42no—
277C2—3562no—
278C2#121×D8911yescharacteristic
279C2#124×D8911yescharacteristic
280C2#1915217011yescharacteristic
281C2#1915224612yes—
282C2#1915231512yes—
subgroupG/H
center, FrattiniC23C23×D89
commutator, socle, cosocleC23×C89C24
Fitting#397×C89C2
prime radicalC22×C22⋊D89C22
hypercenter#397D89
hypocenterC89#2547
LCSG ▷ C23×C89 ▷ C89
UCSC1 ◁ C23 ◁ #397

Complements

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

NH ≅ G/Ntype
1. C2×#15668011C2semidirect
4. #19151525C2semidirect
5. #19151524C2semidirect
6. #19151523C2semidirect
7. #19151502C2semidirect
8. #19151457C2semidirect
9. #19151456C2semidirect
10. #19151449C2semidirect
11. #397×C89C2semidirect
133. Dic89#124semidirect
142. C89#2547semidirect
149. #397D89semidirect

Maximal subgroups

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

subgroupindex
C2×#156680112
C2×#156679982
C2×#156679722
#191515252
#191515242
#191515232
#191515022
#191514572
#191514562
#191514492
#397×C892
#254789