Finite Group Databasebeta

← #26026061

Subgroups — #26026061

Order 11392.

668 conjugacy classes of subgroups; only the 157 normal subgroups are shown.

normal subgroups only

This group has 668 conjugacy classes of subgroups — too many to draw. Only its 157 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×C22⋊Dic89C211yesmaximal, characteristic
3#19151534C212yesmaximal, complemented
4#19151521C212yesmaximal, complemented
5#19151521C212yesmaximal, complemented
6#19151510C212yesmaximal, complemented
7#19151473C211yesmaximal, characteristic, complemented
8#19151470C211yesmaximal, characteristic, complemented
9#19151456C211yesmaximal, characteristic, complemented
10#19151454C211yesmaximal, characteristic
11#379×C89C211yesmaximal, characteristic
12C22×Dic178C2211yescharacteristic, complemented
13C23×Dic89C2211yescharacteristic
14C23×Dic89C2211yescharacteristic
15#15667989—24no—
16C2×C4⋊Dic89C2211yescharacteristic, complemented
17C2×C4⋊Dic89C2212yescomplemented
18C2×#13083553C2211yescharacteristic, complemented
19C2×#13083553C2211yescharacteristic, complemented
20C2×#13083553C2212yescomplemented
21C2×#13083553C2212yescomplemented
22C2×C22⋊Dic89—24no—
23C2×C22⋊Dic89C2211yescharacteristic
24C2×C22⋊Dic89C2211yescharacteristic
25C2×C22⋊Dic89C2212yes—
26C2×C22⋊Dic89C2212yes—
27C2×C22⋊Dic89C2212yes—
28C2×C22⋊Dic89C2212yes—
29#15667919C2212yescomplemented
30#15667919C2212yescomplemented
31#15667919C2212yescomplemented
32C25×C89C2211yescharacteristic
33C2×C22⋊C4×C89C2211yescharacteristic
34C2×C22⋊C4×C89C2211yescharacteristic
35C2×C22⋊C4×C89C2212yes—
36C2×C22⋊C4×C89C2212yes—
37C2×Dic178—22no—
38C2×Dic178—42no—
39C22×Dic89—22no—
40C22×Dic89—42no—
41C22×Dic89—42no—
42C22×Dic89D414yes—
43C22×Dic89C2312yes—
44C22×Dic89C2311yescharacteristic
45C22×Dic89C2312yes—
46C22×Dic89C2311yescharacteristic
47C22×Dic89C2311yescharacteristic
48C22×Dic89C2311yescharacteristic
49C4⋊Dic89—22no—
50C4⋊Dic89—42no—
51#13083553—22no—
52#13083553—22no—
53#13083553—42no—
54#13083553—42no—
55C22⋊Dic89—22no—
56C22⋊Dic89—22no—
57C22⋊Dic89—24no—
58C22⋊Dic89—24no—
59C22⋊Dic89—42no—
60C22⋊Dic89—42no—
61C24×C89—22no—
62C24×C89—22no—
63C24×C89—42no—
64C24×C89—42no—
65C24×C89Q814yescomplemented
66C24×C89C2312yes—
67C24×C89C2311yescharacteristic
68C22×C4×C89C2311yescharacteristic
69C22×C4×C89C2312yes—
70C22×C4×C89C2311yescharacteristic
71C22⋊C4×C89—22no—
72C22⋊C4×C89—22no—
73C22⋊C4×C89—42no—
74C22⋊C4×C89—42no—
75C23×C89—22no—
76C23×C89—22no—
77C23×C89—28no—
78C23×C89—22no—
79C23×C89—22no—
80C23×C89—22no—
81C23×C89—22no—
82C23×C89—22no—
83C23×C89—22no—
84C23×C89—48no—
85C23×C89—44no—
86C23×C89—44no—
87C23×C89—48no—
88C23×C89C2×D412yes—
89C23×C89C2×Q814yes—
90C23×C89C2×Q812yes—
91C23×C89#4112yes—
92C23×C89C2411yescharacteristic
93C2×C4×C89—21no—
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×Dic89—22no—
101C2×Dic89—22no—
102C2×Dic89—22no—
103C2×Dic89—21no—
104C2×Dic89—21no—
105C2×Dic89—22no—
106C2×Dic89—22no—
107C2×Dic89—22no—
108C2×Dic89—22no—
109C2×Dic89—22no—
110C2×Dic89—22no—
111C2×Dic89—22no—
112C2×Dic89—44no—
113C2×Dic89—44no—
114C2×Dic89C2×D412yes—
115C2×Dic89C2×D412yes—
116Dic178—44no—
117C22×C89—22no—
118C22×C89—22no—
119C22×C89—24no—
120C22×C89—24no—
121C22×C89—24no—
122C22×C89—24no—
123C22×C89—24no—
124C22×C89—416no—
125C22×C89—42no—
126C22×C89—42no—
127C22×C89—42no—
128C22×C89—42no—
129C22×C89C22⋊Q814yes—
130C22×C89C22×D411yescharacteristic
131C22×C89C22×Q811yescharacteristic
132C22×C89C2×#4111yescharacteristic
133C22×C89H(5,𝔽2)12yes—
134C22×C89H(5,𝔽2)12yes—
135C4×C89—41no—
136C4×C89—41no—
137C4×C89—42no—
138Dic89—22no—
139Dic89—22no—
140Dic89—41no—
141Dic89—41no—
142Dic89—42no—
143Dic89—42no—
144C2×C89—24no—
145C2×C89—44no—
146C2×C89C2×C22⋊Q811yescharacteristic
147C2×C89#53411yescharacteristic
148C2×C89#53511yescharacteristic
149C2×C89#53812yes—
150C2×C89#54312yes—
151#2626—891nomaximal, Sylow
152C89#262611yescharacteristic, complemented, Sylow
153C2×C22⋊Q8—891no—
154C22×C22⋊C4—891no—
155#399—892no—
156#396—892no—
157#396—892no—
158#393—892no—
159#385—891no—
160#385—891no—
161#380—891no—
162#379—891no—
163#379D8911yescharacteristic
164C25C2×D8911yescharacteristic
165C22×Q8—891no—
166C23×C4—891no—
167C23×C4—891no—
168C22⋊Q8—1784no—
169C2×C4⋊C4—892no—
170C2×C4⋊C4—892no—
171C2×C4⋊C4—892no—
172C2×C4⋊C4—891no—
173C2×C4⋊C4—891no—
174C2×C4⋊C4—891no—
175C2×C22⋊C4—892no—
176C2×C22⋊C4—892no—
177C2×C22⋊C4—892no—
178C2×C22⋊C4—892no—
179C2×C22⋊C4—891no—
180C2×C22⋊C4—891no—
181C2×C22⋊C4—1784no—
182C2×C22⋊C4C2×D8911yescharacteristic
183C2×C22⋊C4C2×D8911yescharacteristic
184C2×C22⋊C4C2×D8912yes—
185C2×C22⋊C4C2×D8912yes—
186#95—892no—
187#95—892no—
188#95—892no—
189C24—22no—
190C24—22no—
191C24—42no—
192C24—42no—
193C24Dic17814yescomplemented
194C24C22×D8912yes—
195C24C22×D8911yescharacteristic
196C2×Q8—3562no—
197C2×Q8—1782no—
198C22×C4—894no—
199C22×C4—891no—
200C22×C4—891no—
201C22×C4—892no—
202C22×C4—891no—
203C22×C4—892no—
204C22×C4—891no—
205C22×C4—3562no—
206C22×C4—3562no—
207C22×C4—1782no—
208C22×C4C22×D8912yes—
209C22×C4C22×D8911yescharacteristic
210C22×C4C22×D8911yescharacteristic
211C4⋊C4—3562no—
212C4⋊C4—3562no—
213C4⋊C4—3562no—
214C4⋊C4—1782no—
215C4⋊C4—1782no—
216C4⋊C4—1782no—
217C22⋊C4—22no—
218C22⋊C4—22no—
219C22⋊C4—42no—
220C22⋊C4—42no—
221C22⋊C4—3562no—
222C22⋊C4—3562no—
223C22⋊C4—1784no—
224C22⋊C4—1784no—
225C22⋊C4—1782no—
226C22⋊C4—1782no—
227C23—22no—
228C23—22no—
229C23—28no—
230C23—22no—
231C23—22no—
232C23—22no—
233C23—22no—
234C23—22no—
235C23—22no—
236C23—48no—
237C23—44no—
238C23—44no—
239C23—48no—
240C23D4×D8912yes—
241C23C2×Dic17814yes—
242C23C2×Dic17812yes—
243C23#1308357312yes—
244C23C23×D8911yescharacteristic
245Q8—3564no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—22no—
249C2×C4—22no—
250C2×C4—22no—
251C2×C4—22no—
252C2×C4—22no—
253C2×C4—892no—
254C2×C4—892no—
255C2×C4—3564no—
256C2×C4—3564no—
257C2×C4—1782no—
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—
267C2×C4—1782no—
268C2×C4—1782no—
269C22—22no—
270C22—22no—
271C22—24no—
272C22—24no—
273C22—24no—
274C22—24no—
275C22—24no—
276C22—416no—
277C22—42no—
278C22—42no—
279C22—42no—
280C22—42no—
281C22#1566798914yes—
282C22C2×D4×D8911yescharacteristic
283C22C22×Dic17811yescharacteristic
284C22C2×#1308357311yescharacteristic
285C22#1566805712yes—
286C22#1566805712yes—
287C4—41no—
288C4—41no—
289C4—42no—
290C4—3561no—
291C4—3562no—
292C4—3561no—
293C4—3562no—
294C4—1782no—
295C4—1782no—
296C2—24no—
297C2—44no—
298C2C2×#1566798911yescharacteristic
299C2#1915215811yescharacteristic
300C2#1915216311yescharacteristic
301C2#1915218312yes—
302C2#1915222412yes—
subgroupG/H
center, FrattiniC23C23×D89
commutator, socle, cosocleC23×C89C24
Fitting#379×C89C2
prime radicalC25×C89C22
hypercenter#379D89
hypocenterC89#2626
LCSG ▷ C23×C89 ▷ C89
UCSC1 ◁ C23 ◁ #379

Complements

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

NH ≅ G/Ntype
1. C2×#15667989C2semidirect
3. #19151534C2semidirect
4. #19151521C2semidirect
5. #19151521C2semidirect
6. #19151510C2semidirect
7. #19151473C2semidirect
8. #19151470C2semidirect
9. #19151456C2semidirect
12. C22×Dic178C22semidirect
16. C2×C4⋊Dic89C22semidirect
17. C2×C4⋊Dic89C22semidirect
18. C2×#13083553C22semidirect
19. C2×#13083553C22semidirect
20. C2×#13083553C22semidirect
21. C2×#13083553C22semidirect
29. #15667919C22semidirect
30. #15667919C22semidirect
31. #15667919C22semidirect
65. C24×C89Q8semidirect
152. C89#2626semidirect
193. C24Dic178semidirect

Maximal subgroups

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

subgroupindex
C2×#156679892
C22×C22⋊Dic892
#191515342
#191515212
#191515102
#191514732
#191514702
#191514562
#191514542
#379×C892
#262689