Finite Group Databasebeta

← #26023891

Subgroups — #26023891

Order 11392.

800 conjugacy classes of subgroups; only the 181 normal subgroups are shown.

normal subgroups only

This group has 800 conjugacy classes of subgroups — too many to draw. Only its 181 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
1C22×Q8×D89C211yesmaximal, characteristic
2C2×#15668011C212yesmaximal, complemented
3C2×#15667990C211yesmaximal, characteristic
4#19151519C211yesmaximal, characteristic, complemented
5#19151518C211yesmaximal, characteristic, complemented
6#19151517C211yesmaximal, characteristic, complemented
7#19151502C212yesmaximal, complemented
8#19151472C212yesmaximal
9#19151469C212yesmaximal
10#19151445C211yesmaximal, characteristic
11#395×C89C211yesmaximal, characteristic, complemented
12C22×Dic178C2211yescharacteristic
13C22×Dic178C2211yescharacteristic
14C22×Dic178C2212yes—
15C2×Q8×D89—28no—
16C2×Q8×D89—24no—
17C22×C4×D89C2212yes—
18C22×C4×D89C2211yescharacteristic
19#15668011—28no—
20#15667990—24no—
21C2×C4⋊Dic89C2212yes—
22C2×#13083553C2212yes—
23C2×#13083553C2212yes—
24C2×#13083553C2211yescharacteristic
25C2×#13083553C2211yescharacteristic
26C2×#13083551C2211yescharacteristic
27C2×#13083551C2211yescharacteristic
28C2×#13083551C2212yes—
29C2×C4×Dic89C2212yes—
30#15667919C2211yescharacteristic
31#15667919C2212yes—
32#15667919C2212yes—
33#15667919C2212yes—
34C22×Q8×C89C2211yescharacteristic
35C2×C4⋊C4×C89C2212yes—
36C2×C4⋊C4×C89C2211yescharacteristic
37#95×C89C2211yescharacteristic
38#95×C89C2212yes—
39C23×D89C2311yescharacteristic
40C2×Dic178—22no—
41C2×Dic178—24no—
42C2×Dic178—24no—
43C2×Dic178—24no—
44C2×Dic178—22no—
45C2×Dic178—24no—
46C2×Dic178D418yes—
47Q8×D89—232no—
48C22×Dic89C2311yescharacteristic
49C22×Dic89C2311yescharacteristic
50C22×Dic89C2312yes—
51C22×Dic89C2312yes—
52C22×Dic89C2311yescharacteristic
53C2×C4×D89—24no—
54C2×C4×D89—24no—
55C2×C4×D89—24no—
56C2×C4×D89—24no—
57C2×C4×D89D414yes—
58C4⋊Dic89—24no—
59#13083553—22no—
60#13083553—24no—
61#13083553—22no—
62#13083553—24no—
63#13083551—22no—
64#13083551—22no—
65#13083551Q818yescomplemented
66C4×Dic89—24no—
67C2×Q8×C89—24no—
68C2×Q8×C89—22no—
69C22×C4×C89C2311yescharacteristic
70C22×C4×C89C2311yescharacteristic
71C22×C4×C89C2312yes—
72C22×C4×C89C2311yescharacteristic
73C22×C4×C89C2312yes—
74C4⋊C4×C89—22no—
75C4⋊C4×C89—24no—
76C23×C89C2411yescharacteristic
77C22×D89—22no—
78C22×D89—21no—
79C22×D89—21no—
80C22×D89C2×D412yes—
81C22×D89C2×Q814yes—
82Q8×C89—28no—
83C2×C4×C89—22no—
84C2×C4×C89—22no—
85C2×C4×C89—22no—
86C2×C4×C89—22no—
87C2×C4×C89—22no—
88C2×C4×C89—21no—
89C2×C4×C89—21no—
90C2×C4×C89—22no—
91C2×C4×C89—21no—
92C2×C4×C89—21no—
93C2×C4×C89C2×D414yes—
94C2×C4×C89C2×D412yes—
95C2×C4×C89C2×Q814yescomplemented
96C2×Dic89—22no—
97C2×Dic89—22no—
98C2×Dic89—22no—
99C2×Dic89—22no—
100C2×Dic89—21no—
101C2×Dic89—21no—
102C2×Dic89—22no—
103C2×Dic89—21no—
104C2×Dic89—21no—
105C2×Dic89C2×D414yes—
106C2×Dic89C2×D414yes—
107C2×Dic89C2×D412yes—
108C2×Dic89C2×Q814yescomplemented
109C4×D89—216no—
110C4×D89—28no—
111Dic178—28no—
112Dic178—216no—
113Dic178—44no—
114C22×C89C22×D411yescharacteristic
115C22×C89C22×D412yes—
116C22×C89C22×Q812yes—
117C22×C892−1+411yescharacteristic
118C22×C892−1+411yescharacteristic
119C2×D89—22no—
120C2×D89—22no—
121C2×D89—24no—
122C2×D89—24no—
123C2×D89C4⋊Q814yescomplemented
124C4×C89—22no—
125C4×C89—24no—
126C4×C89—24no—
127C4×C89—41no—
128C4×C89—41no—
129Dic89—24no—
130Dic89—24no—
131Dic89—41no—
132Dic89—41no—
133Dic89#12014yes—
134C2×C89C2×#12011yescharacteristic
135C2×C89C2×C4⋊Q811yescharacteristic
136C2×C89#53611yescharacteristic
137C2×C89D4×Q812yes—
138C2×C89D4×Q812yes—
139D89—24no—
140#2434—891nomaximal, Sylow
141C89#243411yescharacteristic, complemented, Sylow
142C23×Q8—891no—
143C2×C4⋊Q8—892no—
144C2×C22⋊Q8—891no—
145#395—891no—
146#395—891no—
147#395—891no—
148#395D8911yescharacteristic, complemented
149#391—892no—
150#385—892no—
151#385—892no—
152C4×C22⋊C4—891no—
153C22×Q8—892no—
154C22×Q8—891no—
155C22×Q8—891no—
156C22×Q8—1784no—
157C22×Q8—1788no—
158C22×Q8C2×D8911yescharacteristic
159C23×C4—891no—
160C23×C4—892no—
161C4⋊Q8—1788no—
162C22⋊Q8—1784no—
163C2×C4⋊C4—891no—
164C2×C4⋊C4—891no—
165C2×C4⋊C4—892no—
166C2×C4⋊C4—892no—
167C2×C4⋊C4—892no—
168C2×C4⋊C4C2×D8911yescharacteristic
169C2×C4⋊C4C2×D8912yes—
170C2×C22⋊C4—892no—
171C2×C22⋊C4—891no—
172C2×C22⋊C4—891no—
173C2×C42—892no—
174#95—891no—
175#95—892no—
176#95—892no—
177#95—892no—
178#95C2×D8911yescharacteristic
179#95C2×D8912yes—
180C24—891no—
181C2×Q8—22no—
182C2×Q8—24no—
183C2×Q8—898no—
184C2×Q8—1782no—
185C2×Q8—1784no—
186C2×Q8—1784no—
187C2×Q8—1784no—
188C2×Q8—1784no—
189C2×Q8—17832no—
190C2×Q8—1782no—
191C22×C4—891no—
192C22×C4—892no—
193C22×C4—892no—
194C22×C4—894no—
195C22×C4—891no—
196C22×C4—891no—
197C22×C4—1784no—
198C22×C4—1784no—
199C22×C4—1784no—
200C22×C4—1784no—
201C22×C4C22×D8911yescharacteristic
202C22×C4C22×D8911yescharacteristic
203C22×C4C22×D8911yescharacteristic
204C22×C4C22×D8912yes—
205C22×C4C22×D8912yes—
206C4⋊C4—22no—
207C4⋊C4—24no—
208C4⋊C4—1782no—
209C4⋊C4—1784no—
210C4⋊C4—1784no—
211C4⋊C4—1782no—
212C4⋊C4—1784no—
213C22⋊C4—898no—
214C22⋊C4—1782no—
215C22⋊C4—1782no—
216C42—1784no—
217C23—892no—
218C23—894no—
219C23—1782no—
220C23—1781no—
221C23—1781no—
222C23C23×D8911yescharacteristic
223Q8—28no—
224Q8—3564no—
225Q8—17816no—
226Q8—1788no—
227C2×C4—22no—
228C2×C4—22no—
229C2×C4—22no—
230C2×C4—22no—
231C2×C4—22no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—22no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—894no—
238C2×C4—892no—
239C2×C4—894no—
240C2×C4—894no—
241C2×C4—1788no—
242C2×C4—17816no—
243C2×C4—1781no—
244C2×C4—1781no—
245C2×C4—1782no—
246C2×C4—1781no—
247C2×C4—1781no—
248C2×C4—1782no—
249C2×C4—1782no—
250C2×C4—1782no—
251C2×C4—1782no—
252C2×C4D4×D8912yes—
253C2×C4D4×D8914yes—
254C2×C4Q8×D8914yescomplemented
255C22—894no—
256C22—1782no—
257C22—1784no—
258C22—1784no—
259C22—1782no—
260C22C2×D4×D8911yescharacteristic
261C22C2×D4×D8912yes—
262C22C2×Q8×D8912yes—
263C22#1566805911yescharacteristic
264C22#1566806011yescharacteristic
265C4—24no—
266C4—22no—
267C4—24no—
268C4—41no—
269C4—41no—
270C4—894no—
271C4—3561no—
272C4—3561no—
273C4—1784no—
274C4—1784no—
275C2—1784no—
276C2#120×D8911yescharacteristic
277C2C4⋊Q8×D8911yescharacteristic
278C2#1915217111yescharacteristic
279C2#1915226112yes—
280C2#1915226312yes—
subgroupG/H
center, FrattiniC23C23×D89
commutator, socle, cosocleC23×C89C24
Fitting#395×C89C2
prime radicalC23×D89C23
hypercenter#395D89
hypocenterC89#2434
LCSG ▷ C23×C89 ▷ C89
UCSC1 ◁ C23 ◁ #395

Complements

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

NH ≅ G/Ntype
2. C2×#15668011C2semidirect
4. #19151519C2semidirect
5. #19151518C2semidirect
6. #19151517C2semidirect
7. #19151502C2semidirect
11. #395×C89C2semidirect
65. #13083551Q8semidirect
95. C2×C4×C89C2×Q8semidirect
108. C2×Dic89C2×Q8semidirect
123. C2×D89C4⋊Q8semidirect
141. C89#2434semidirect
148. #395D89semidirect
254. C2×C4Q8×D89semidirect

Maximal subgroups

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

subgroupindex
C22×Q8×D892
C2×#156680112
C2×#156679902
#191515192
#191515182
#191515172
#191515022
#191514722
#191514692
#191514452
#395×C892
#243489