Finite Group Databasebeta

← #26033636

Subgroups — #26033636

Order 11392.

1040 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19152215C212yesmaximal, complemented
2#19152213C212yesmaximal, complemented
3#19152211C211yesmaximal, characteristic, complemented
4#19152210C211yesmaximal, characteristic, complemented
5#19152202C211yesmaximal, characteristic, complemented
6#19152191C214yesmaximal, complemented
7#19152180C214yesmaximal, complemented
8#19152154C211yesmaximal, characteristic, complemented
9#19152146C211yesmaximal, characteristic, complemented
10#19152129C214yesmaximal, complemented
11#19152125C214yesmaximal, complemented
12#19152108C212yesmaximal, complemented
13C4×#13083573C212yesmaximal, complemented
14#117×D89C211yesmaximal, characteristic, complemented
15#540×C89C211yesmaximal, characteristic, complemented
16C2×#13083573C2212yes—
17C22×C4×D89C2211yescharacteristic
18#15668012C2211yescharacteristic, complemented
19#15668011C2212yescomplemented
20#15668007C2214yes—
21#15668005C2214yes—
22#15668005C2214yescomplemented
23#15668005C2214yescomplemented
24#15668004C2211yescharacteristic, complemented
25#15668003C2214yescomplemented
26#15668002C2214yescomplemented
27#15667999C2214yes—
28#15667999C2212yescomplemented
29#15667998C2214yes—
30#15667995C2214yes—
31#15667994C2214yes—
32#15667993C2214yes—
33#15667993C2214yescomplemented
34#15667992C2212yes—
35#15667991C2212yes—
36#15667991C2214yescomplemented
37#15667990C2214yes—
38#15667989C2214yescomplemented
39#15667984C2214yes—
40#15667983C2214yes—
41#15667983C2212yes—
42#15667980C2214yes—
43C4×Dic178C2212yescomplemented
44#15667977C2214yescomplemented
45#15667977C2212yescomplemented
46D4×Dic89C2214yes—
47D4×Dic89C2214yescomplemented
48D4×Dic89C2212yescomplemented
49C4×C22⋊D89C2214yes—
50#15667972C2214yes—
51#15667972C2214yes—
52#15667971C2211yescharacteristic
53#15667970C2212yes—
54#15667970C2212yes—
55#15667969C2211yescharacteristic
56#15667969C2211yescharacteristic
57#15667968C2212yes—
58#15667968C2214yescomplemented
59C4⋊C4×D89C2212yes—
60C22⋊C4×D89C2212yes—
61C2×C4×Dic89C2214yescomplemented
62C42×D89C2211yescharacteristic
63C42×D89C2211yescharacteristic
64#127×C89C2211yescharacteristic, complemented
65#125×C89C2211yescharacteristic, complemented
66#123×C89C2214yescomplemented
67#121×C89C2214yes—
68#121×C89C2212yes—
69C4×D4×C89C2212yescomplemented
70#117×C89C2211yescharacteristic
71C23×D89C2311yescharacteristic
72#13083573—28no—
73C2×Dic178C2312yes—
74C2×Dic178C2314yes—
75C2×C22⋊D89C2314yes—
76C2×C22⋊D89C2314yes—
77C22×Dic89C2311yescharacteristic
78C22×Dic89C2314yes—
79C22×Dic89C2314yes—
80C2×C4×D89—24no—
81C2×C4×D89C2311yescharacteristic
82C2×C4×D89C2311yescharacteristic
83C2×C4×D89C2311yescharacteristic
84C2×C4×D89C2312yes—
85C2×C4×D89C2312yes—
86C2×C4×D89C2311yescharacteristic
87C4⋊Dic89C2312yes—
88C4⋊Dic89C2312yes—
89C4⋊Dic89C2314yes—
90C4⋊Dic89C2314yes—
91#13083553C2312yes—
92#13083553C2312yes—
93#13083553C2314yes—
94#13083553C2314yes—
95#13083553C2314yes—
96#13083553C2314yes—
97#13083553C2314yes—
98C22⋊Dic89C2312yes—
99C22⋊Dic89C2314yes—
100C22⋊Dic89C2314yes—
101C22⋊Dic89C2314yes—
102C22⋊Dic89C2314yes—
103C22⋊Dic89C2314yes—
104#13083551C2312yes—
105#13083551C2312yes—
106#13083551C2314yes—
107#13083551C2314yes—
108C4×Dic89C2312yes—
109C4×Dic89C2312yes—
110C4×Dic89C2314yes—
111C4×Dic89C2311yescharacteristic
112C4×Dic89C2311yescharacteristic
113C4×Dic89C2314yes—
114C4×Dic89C2314yes—
115C2×D4×C89C2312yes—
116C2×D4×C89C2314yes—
117C2×D4×C89C2314yes—
118C22×C4×C89C2311yescharacteristic
119C22×C4×C89C2314yes—
120C4⋊C4×C89C2312yes—
121C4⋊C4×C89C2312yes—
122C4⋊C4×C89C2314yes—
123C22⋊C4×C89C2312yes—
124C22⋊C4×C89C2314yes—
125C22⋊C4×C89C2314yes—
126C42×C89C2311yescharacteristic
127C42×C89C2311yescharacteristic
128C23×C89C2411yescharacteristic
129C23×C89C2414yes—
130C22×D89—22no—
131C22×D89—42no—
132C22×D89C2411yescharacteristic
133C22×D89C2411yescharacteristic
134D4×C89—24no—
135D4×C89—44no—
136D4×C89—44no—
137C2×C4×C89—22no—
138C2×C4×C89—44no—
139C2×C4×C89C2412yes—
140C2×C4×C89C2412yes—
141C2×C4×C89C2411yescharacteristic
142C2×C4×C89C2414yes—
143C2×C4×C89C2411yescharacteristic
144C22⋊D89—28no—
145C22⋊D89—44no—
146C2×Dic89—22no—
147C2×Dic89—28no—
148C2×Dic89—44no—
149C2×Dic89C2412yes—
150C2×Dic89C2412yes—
151C2×Dic89C2414yes—
152C2×Dic89C2414yes—
153C2×Dic89C2411yescharacteristic
154C2×Dic89C2411yescharacteristic
155C4×D89—22no—
156C4×D89—22no—
157C4×D89—22no—
158C4×D89—42no—
159C4×D89—42no—
160C4×D89#4114yes—
161Dic178—24no—
162Dic178—44no—
163C22×C89—24no—
164C22×C89—21no—
165C22×C89—24no—
166C22×C89—24no—
167C22×C89—22no—
168C22×C89C2511yescharacteristic
169C2×D89—22no—
170C2×D89—21no—
171C2×D89—22no—
172C2×D89—44no—
173C2×D89C2×#4112yes—
174C4×C89—21no—
175C4×C89—24no—
176C4×C89—22no—
177C4×C89—22no—
178C4×C89C2×#4112yes—
179Dic89—24no—
180Dic89—21no—
181Dic89—22no—
182Dic89—24no—
183Dic89—22no—
184Dic89C2×#4112yes—
185C2×C89—41no—
186C2×C89—44no—
187C2×C89C22×#4111yescharacteristic
188C2×C89#58512yes—
189D89—22no—
190D89—41no—
191#3455—891nomaximal, Sylow
192C89#345511yescharacteristic, complemented, Sylow
193#542—892no—
194#542—892no—
195#541—891no—
196#541—891no—
197#540—891no—
198#540D8911yescharacteristic, complemented
199#539—894no—
200#538—894no—
201#533—891no—
202#532—891no—
203#529—894no—
204#529—894no—
205#525—892no—
206C4×#41—892no—
207C2×#117—891no—
208C2×#41—892no—
209C23×C4—891no—
210C4⋊Q8—892no—
211C4⋊Q8—891no—
212#127C2×D8911yescharacteristic, complemented
213#126—894no—
214#126—894no—
215#126—894no—
216#126—894no—
217#125—894no—
218#125—894no—
219#125—891no—
220#125C2×D8911yescharacteristic, complemented
221#124—894no—
222#124—892no—
223#124—894no—
224#123—894no—
225#123—894no—
226#123—894no—
227#123—894no—
228#123C2×D8914yescomplemented
229C22⋊Q8—892no—
230C22⋊Q8—894no—
231C22⋊Q8—892no—
232C22⋊Q8—894no—
233C22⋊Q8—894no—
234#121—892no—
235#121—894no—
236#121—894no—
237#121C2×D8912yes—
238#121C2×D8914yes—
239#120—894no—
240C4×Q8—892no—
241C4×Q8—894no—
242C4×Q8—892no—
243C4×D4—892no—
244C4×D4—894no—
245C4×D4—894no—
246C4×D4—894no—
247C4×D4—894no—
248C4×D4—894no—
249C4×D4C2×D8912yescomplemented
250#117—891no—
251#117—892no—
252#117—892no—
253#117—892no—
254#117—894no—
255#117—891no—
256#117—891no—
257#117C2×D8911yescharacteristic
258C2×C4⋊C4—892no—
259C2×C22⋊C4—892no—
260C2×C42—894no—
261C2×C42—891no—
262C2×C42—891no—
263C24—891no—
264#41—1788no—
265C2×Q8—894no—
266C2×Q8—892no—
267C2×D4—894no—
268C2×D4—894no—
269C2×D4C22×D8912yes—
270C2×D4C22×D8914yes—
271C2×D4C22×D8914yes—
272C22×C4—891no—
273C22×C4—894no—
274C22×C4—894no—
275C22×C4—891no—
276C22×C4—892no—
277C22×C4—892no—
278C22×C4—891no—
279C22×C4—891no—
280C22×C4—891no—
281C22×C4—1784no—
282C22×C4C22×D8911yescharacteristic
283C22×C4C22×D8914yes—
284C4⋊C4—892no—
285C4⋊C4—892no—
286C4⋊C4—892no—
287C4⋊C4—892no—
288C4⋊C4—894no—
289C4⋊C4—894no—
290C4⋊C4—894no—
291C4⋊C4—894no—
292C4⋊C4—894no—
293C4⋊C4—894no—
294C4⋊C4—894no—
295C4⋊C4C22×D8912yes—
296C4⋊C4C22×D8912yes—
297C4⋊C4C22×D8914yes—
298C22⋊C4—892no—
299C22⋊C4—894no—
300C22⋊C4—894no—
301C22⋊C4—894no—
302C22⋊C4—894no—
303C22⋊C4—894no—
304C22⋊C4—892no—
305C22⋊C4—892no—
306C22⋊C4—894no—
307C22⋊C4—894no—
308C22⋊C4C22×D8912yes—
309C22⋊C4C22×D8914yes—
310C22⋊C4C22×D8914yes—
311C42—892no—
312C42—892no—
313C42—894no—
314C42—891no—
315C42—891no—
316C42—894no—
317C42—894no—
318C42C22×D8911yescharacteristic
319C42C22×D8911yescharacteristic
320C23—891no—
321C23—891no—
322C23—3562no—
323C23—1782no—
324C23C23×D8911yescharacteristic
325C23C23×D8914yes—
326Q8—3564no—
327Q8—1784no—
328D4—24no—
329D4—44no—
330D4—44no—
331D4—3564no—
332D4—1788no—
333C2×C4—22no—
334C2×C4—44no—
335C2×C4—891no—
336C2×C4—894no—
337C2×C4—892no—
338C2×C4—892no—
339C2×C4—894no—
340C2×C4—894no—
341C2×C4—891no—
342C2×C4—3562no—
343C2×C4—3562no—
344C2×C4—3564no—
345C2×C4—1782no—
346C2×C4—1782no—
347C2×C4—1782no—
348C2×C4—1788no—
349C2×C4—1782no—
350C2×C4C23×D8912yes—
351C2×C4C23×D8914yes—
352C2×C4C23×D8912yes—
353C2×C4C23×D8911yescharacteristic
354C2×C4C23×D8911yescharacteristic
355C22—21no—
356C22—24no—
357C22—24no—
358C22—24no—
359C22—22no—
360C22—892no—
361C22—3564no—
362C22—1781no—
363C22—1782no—
364C22—1782no—
365C22C24×D8911yescharacteristic
366C4—21no—
367C4—22no—
368C4—24no—
369C4—22no—
370C4—892no—
371C4—1781no—
372C4—1784no—
373C4—1782no—
374C4—1784no—
375C4—1782no—
376C4#41×D8912yes—
377C2—44no—
378C2—41no—
379C2—3561no—
380C2—1782no—
381C2C2×#41×D8911yescharacteristic
382C2#1915243312yes—
subgroupG/H
center, FrattiniC22C24×D89
commutator, socle, cosocleC22×C89C25
Fitting#540×C89C2
hypercenter#540D89
hypocenterC89#3455
LCSG ▷ C22×C89 ▷ C89
UCSC1 ◁ C22 ◁ #540

Complements

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

NH ≅ G/Ntype
1. #19152215C2semidirect
2. #19152213C2semidirect
3. #19152211C2semidirect
4. #19152210C2semidirect
5. #19152202C2semidirect
6. #19152191C2semidirect
7. #19152180C2semidirect
8. #19152154C2semidirect
9. #19152146C2semidirect
10. #19152129C2semidirect
11. #19152125C2semidirect
12. #19152108C2semidirect
13. C4×#13083573C2semidirect
14. #117×D89C2semidirect
15. #540×C89C2semidirect
18. #15668012C22semidirect
19. #15668011C22semidirect
22. #15668005C22semidirect
23. #15668005C22semidirect
24. #15668004C22semidirect
25. #15668003C22semidirect
26. #15668002C22semidirect
28. #15667999C22semidirect
33. #15667993C22semidirect
36. #15667991C22semidirect
38. #15667989C22semidirect
43. C4×Dic178C22semidirect
44. #15667977C22semidirect
45. #15667977C22semidirect
47. D4×Dic89C22semidirect
48. D4×Dic89C22semidirect
58. #15667968C22semidirect
61. C2×C4×Dic89C22semidirect
64. #127×C89C22semidirect
65. #125×C89C22semidirect
66. #123×C89C22semidirect
69. C4×D4×C89C22semidirect
192. C89#3455semidirect
198. #540D89semidirect
212. #127C2×D89semidirect
220. #125C2×D89semidirect
228. #123C2×D89semidirect
249. C4×D4C2×D89semidirect

Maximal subgroups

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

subgroupindex
#191522152
#191522132
#191522112
#191522102
#191522022
#191521912
#191521802
#191521542
#191521462
#191521292
#191521252
#191521082
C4×#130835732
#117×D892
#540×C892
#345589