Finite Group Databasebeta

← #15625318

Subgroups — #15625318

Order 2816.

2162 conjugacy classes of subgroups.

The subgroup lattice has 626 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623229C211yesmaximal, characteristic, complemented
2#13081943C211yesmaximal, characteristic, complemented
3#13079680C214yesmaximal, complemented
4#13079678C214yesmaximal, complemented
5#13079669C214yesmaximal, complemented
6#13079667C214yesmaximal, complemented
7#13079069C211yesmaximal, characteristic, complemented
8#13079068C211yesmaximal, characteristic, complemented
9#13079019C211yesmaximal, characteristic, complemented
10#13078079C214yesmaximal, complemented
11#13077869C214yesmaximal, complemented
12#13077252C211yesmaximal, characteristic, complemented
13C11×#3142C211yesmaximal, characteristic, complemented
14C2×#41×D11C2212yes—
15C11×#532C2211yescharacteristic
16C2×C11×#125C2211yescharacteristic, complemented
17#10623363C2212yes—
18C2×#67002C2214yescomplemented
19C2×#66961C2214yescomplemented
20#10623255C2212yescomplemented
21#10623246C2212yescomplemented
22#10623229—24no—
23#10623229C2214yescomplemented
24#10623229C2214yescomplemented
25#10623206C2212yescomplemented
26#10623205C2212yescomplemented
27#10623136—22no—
28#10623128—22no—
29#10623078—24no—
30C2×#66948—22no—
31C2×#66948C2212yes—
32C2×#66947—22no—
33C2×#66946C2212yescomplemented
34#10623008C2211yescharacteristic
35C2×#66927C2211yescharacteristic, complemented
36C2×#66925C2211yescharacteristic
37C11×#491C2212yescomplemented
38C11×#490C2212yescomplemented
39C11×#488C2214yescomplemented
40C11×#417C2214yescomplemented
41C4×C11×M16C2211yescharacteristic, complemented
42#10622739C2212yes—
43#10622731C2212yescomplemented
44#10622698C2212yescomplemented
45#10622686C2212yescomplemented
46#10622682C2212yescomplemented
47#10622681C2214yescomplemented
48#10622680C2212yescomplemented
49#10622671C2214yescomplemented
50#10622579C2214yescomplemented
51C4×#4318C2211yescharacteristic, complemented
52#10622432C2218yescomplemented
53#10622431C2218yescomplemented
54#10622424C2218yescomplemented
55#10622419C2218yescomplemented
56#10622400C2218yescomplemented
57#10622399C2218yescomplemented
58#10622394C2218yescomplemented
59#10622386C2218yescomplemented
60#10622325C2214yescomplemented
61#10622322C2214yescomplemented
62#10622308C2212yescomplemented
63#10622306C2212yescomplemented
64#10622303C2214yescomplemented
65C2×C11×#41C2312yes—
66#41×D11—48no—
67C2×#4343C2312yes—
68C2×Q8×D11C2312yes—
69C2×#4341—22no—
70C2×#4341C2312yes—
71C2×D4×D11—22no—
72C2×D4×D11C2312yes—
73C2×#4339—22no—
74C2×#4339C2312yes—
75C22×D44—22no—
76C22×D44—22no—
77C22×D44C2312yes—
78C22×C4×D11—22no—
79C22×C4×D11—22no—
80C22×C4×D11C2311yescharacteristic
81C2×C11×M16C2312yes—
82C11×C4⋊Q8C2311yescharacteristic
83C11×#127C2311yescharacteristic
84C11×#125—22no—
85C11×#125C2312yes—
86C11×#125C2312yes—
87C11×#124C2312yes—
88C11×#121—22no—
89C4×D4×C11—22no—
90C2×C11×C4⋊C4—22no—
91C2×C11×C4⋊C4C2312yes—
92C2×C42×C11C2311yescharacteristic
93#67002—48no—
94#67000C2312yes—
95#66997C2312yes—
96C2×#4325C2318yes—
97#66993C2312yes—
98#66992—24no—
99#66992—24no—
100#66990—24no—
101#66989C2312yes—
102C2×#4323C2318yes—
103#66983—22no—
104C4×C22⋊D11—24no—
105C2×(C2×D11)⋊C4—22no—
106C2×(C2×D11)⋊C4—22no—
107C2×(C2×D11)⋊C4D412yes—
108C2×Dic11⋊C4D412yes—
109C2×C4×Dic11C2311yescharacteristic
110C2×#4318C2312yes—
111#66961—48no—
112C2×D88C2318yes—
113C2×#4314C2318yes—
114#66949—24no—
115#66948—24no—
116#66948—28no—
117#66948—28no—
118#66948C2318yes—
119#66947—24no—
120#66947—28no—
121#66947—28no—
122#66946—24no—
123#66946C2318yes—
124#66937—24no—
125#66936—24no—
126#66935—24no—
127#66931—24no—
128#66928C2312yes—
129#66927—22no—
130#66927C2312yes—
131#66927C2312yes—
132#66927C2311yescharacteristic
133C4×D44—22no—
134#66925D414yes—
135#66925C2312yes—
136#66925C2312yes—
137#66922C2311yescharacteristic
138C11×#103C2318yes—
139C11×#102C2318yes—
140C11×#97C2312yes—
141C4×C8×C11C2312yes—
142(C2×D11)⋊C8C2318yes—
143Dic11⋊C8C2318yes—
144#66874C2318yes—
145#66873C2318yes—
146#66867C2312yes—
147C4×C11⋊C8C2312yes—
148#60808—111nomaximal, Sylow
149C23×D11—22no—
150C23×D11—22no—
151C23×D11C2×D411yescharacteristic
152C11×#41—28no—
153C2×Q8×C11C2412yes—
154C2×D4×C11—22no—
155C2×D4×C11—22no—
156C2×D4×C11C2412yes—
157C22×C4×C11—22no—
158C22×C4×C11—22no—
159C22×C4×C11C2×D412yes—
160C22×C4×C11C2411yescharacteristic
161C2×C22⋊D11—22no—
162C2×C22⋊D11—24no—
163C2×C22⋊D11—22no—
164C2×C22⋊D11—22no—
165C22×Dic11—22no—
166C22×Dic11C2×D411yescharacteristic
167C22×Dic11C2×D412yes—
168#4343—44no—
169Q8×D11—44no—
170#4341—44no—
171#4341—48no—
172D4×D11—44no—
173D4×D11—48no—
174#4339—28no—
175#4339—48no—
176C2×D44—22no—
177C2×D44—28no—
178C2×D44—22no—
179C2×D44—22no—
180C2×D44—24no—
181C2×D44—24no—
182C2×D44—28no—
183C2×D44—84no—
184C2×D44—84no—
185C2×D44C2412yes—
186C2×D44C2414yes—
187C2×C4×D11—22no—
188C2×C4×D11—28no—
189C2×C4×D11—22no—
190C2×C4×D11—22no—
191C2×C4×D11—24no—
192C2×C4×D11—48no—
193C2×C4×D11—84no—
194C2×C4×D11C2×D412yes—
195C2×C4×D11C2412yes—
196C2×Dic22—22no—
197C2×Dic22C2412yes—
198C11×M16—24no—
199C2×C8×C11C2414yes—
200C11×C4⋊C4—22no—
201C11×C4⋊C4—24no—
202C11×C4⋊C4—24no—
203C11×C4⋊C4—22no—
204C11×C4⋊C4C2414yes—
205C11×C22⋊C4—24no—
206C42×C11C2×D412yes—
207C42×C11C2411yescharacteristic
208C42×C11C2411yescharacteristic
209C22⋊Dic11—24no—
210#4325—48no—
211#4323—48no—
212(C2×D11)⋊C4—24no—
213(C2×D11)⋊C4—28no—
214(C2×D11)⋊C4—28no—
215(C2×D11)⋊C4—24no—
216(C2×D11)⋊C4C2×D414yes—
217(C2×D11)⋊C4C2×D414yes—
218C4⋊Dic11—22no—
219Dic11⋊C4—24no—
220Dic11⋊C4C2×D414yes—
221Dic11⋊C4C2×D414yes—
222C4×Dic11C2×D412yes—
223C4×Dic11C2412yes—
224#4318—24no—
225C2×C11⋊C8C2414yes—
226D88—48no—
227#4314—48no—
228C2×#540—111no—
229#3449—111no—
230#3221—114no—
231#3221—114no—
232#3220—114no—
233#3220—114no—
234#3151—111no—
235#3151—111no—
236#3142—111no—
237#3142D1111yescharacteristic, complemented
238#3036—114no—
239#3006—114no—
240#2921—111no—
241C23×C11—22no—
242C23×C11C22×D411yescharacteristic
243C22×D11—22no—
244C22×D11—24no—
245C22×D11—22no—
246C22×D11—42no—
247C22×D11—44no—
248C22×D11—44no—
249C22×D11—44no—
250C22×D11—44no—
251C22×D11—84no—
252C22×D11C22×D412yes—
253Q8×C11—24no—
254D4×C11—24no—
255D4×C11—44no—
256D4×C11—82no—
257C2×C4×C11—22no—
258C2×C4×C11—24no—
259C2×C4×C11—42no—
260C2×C4×C11—44no—
261C2×C4×C11—44no—
262C2×C4×C11C22×D412yes—
263C2×C4×C11C22×D412yes—
264C2×C4×C11C22×D411yescharacteristic
265C2×C4×C11H(5,𝔽2)14yes—
266C2×C4×C11C2511yescharacteristic
267C22⋊D11—44no—
268C22⋊D11—44no—
269C22⋊D11—44no—
270C22⋊D11—84no—
271C2×Dic11—22no—
272C2×Dic11—22no—
273C2×Dic11—42no—
274C2×Dic11—44no—
275C2×Dic11C22×D414yes—
276C2×Dic11C22×D412yes—
277D44—28no—
278D44—24no—
279D44—44no—
280D44—44no—
281D44—82no—
282D44—84no—
283D44—84no—
284D44—88no—
285C4×D11—24no—
286C4×D11—24no—
287C4×D11—44no—
288C4×D11—44no—
289C4×D11—44no—
290C4×D11—88no—
291Dic22—24no—
292Dic22—44no—
293C8×C11—24no—
294C11⋊C8—24no—
295C22×#41—112no—
296C2×AGL(1,ℤ/8)—114no—
297C2×AGL(1,ℤ/8)—114no—
298#540—114no—
299#540—114no—
300#540—224no—
301#537—222no—
302#536—112no—
303#536—112no—
304#535—112no—
305#535—112no—
306#534—222no—
307#532—112no—
308#532—111no—
309#532C2×D1111yescharacteristic
310C2×#127—111no—
311C2×#125C2×D1111yescharacteristic, complemented
312#525—224no—
313C2×#123—222no—
314C2×#121—112no—
315C2×#121—222no—
316C2×C4×D4—112no—
317C2×#117—111no—
318#496—114no—
319#496—114no—
320#493—112no—
321#493—112no—
322#492—112no—
323#492—112no—
324#491—112no—
325#491C2×D1112yescomplemented
326#490—112no—
327#490C2×D1112yescomplemented
328#488—114no—
329#488C2×D1114yescomplemented
330#463—118no—
331#463—118no—
332#461—118no—
333#459—118no—
334#449—118no—
335#449—118no—
336#448—118no—
337#447—118no—
338#433—114no—
339#433—114no—
340#423—112no—
341#417—114no—
342#417C2×D1114yescomplemented
343#407—112no—
344C4×M16—111no—
345C4×M16C2×D1111yescharacteristic, complemented
346C22×C11—22no—
347C22×C11—44no—
348C22×C11—42no—
349C22×C11#53512yes—
350C22×C11C23×D411yescharacteristic
351C2×D11—24no—
352C2×D11—22no—
353C2×D11—44no—
354C2×D11—44no—
355C2×D11—44no—
356C2×D11—42no—
357C2×D11—44no—
358C2×D11—82no—
359C2×D11—88no—
360C2×D11—88no—
361C4×C11—22no—
362C4×C11—22no—
363C4×C11—44no—
364C4×C11—42no—
365C4×C11#53512yes—
366C4×C11C2×H(5,𝔽2)12yes—
367Dic11—24no—
368Dic11—22no—
369Dic11—42no—
370C2×#41—112no—
371C2×#41—112no—
372C2×#41—112no—
373C2×#41—222no—
374C2×#41—222no—
375C2×#41—448no—
376C2×#41C22×D1112yes—
377C22×Q8—112no—
378C22×D4—112no—
379C22×D4—112no—
380C22×D4—222no—
381C22×D4—222no—
382C22×D4—222no—
383C23×C4—111no—
384C23×C4—222no—
385C23×C4—222no—
386AGL(1,ℤ/8)—448no—
387AGL(1,ℤ/8)—448no—
388C2×SD16—118no—
389C2×SD16—118no—
390C2×D8—118no—
391C2×D8—118no—
392C2×M16—112no—
393C2×M16C22×D1112yes—
394C4⋊Q8—112no—
395C4⋊Q8—111no—
396C4⋊Q8C22×D1111yescharacteristic
397#127—112no—
398#127—112no—
399#127—112no—
400#127—111no—
401#127—222no—
402#127C22×D1111yescharacteristic
403#125—22no—
404#125C22×D1112yes—
405#125C22×D1112yes—
406#124—112no—
407#124—112no—
408#124—112no—
409#124C22×D1112yes—
410#123—224no—
411#123—224no—
412#123—228no—
413#123—228no—
414C22⋊Q8—224no—
415C22⋊Q8—224no—
416#121—22no—
417#121—118no—
418#121—224no—
419#121—228no—
420#121—228no—
421#121—224no—
422#121—224no—
423#121—224no—
424#121—222no—
425#120—224no—
426#120—224no—
427C4×D4—22no—
428C4×D4—118no—
429C4×D4—224no—
430C4×D4—224no—
431C4×D4—222no—
432#117—114no—
433#117—112no—
434#117—112no—
435C2×C4⋊C4—22no—
436C2×C4⋊C4—112no—
437C2×C4⋊C4C22×D1112yes—
438C2×C22⋊C4—112no—
439C2×C22⋊C4—222no—
440C2×C22⋊C4—222no—
441C2×C42—111no—
442C2×C42C22×D1111yescharacteristic
443C4⋊C8—118no—
444#103—118no—
445#103C22×D1118yes—
446#102—118no—
447#102C22×D1118yes—
448C22⋊C8—118no—
449#97—112no—
450#97C22×D1112yes—
451C4×C8—112no—
452C4×C8C22×D1112yes—
453C2×C11—22no—
454C2×C11—82no—
455C2×C11C2×#53511yescharacteristic
456C2×C11#358512yes—
457D11—42no—
458D11—84no—
459D11—82no—
460C24—111no—
461C24—222no—
462C24—222no—
463#41—28no—
464#41—228no—
465#41—448no—
466#41—444no—
467#41—448no—
468#41—444no—
469C2×Q8—112no—
470C2×Q8—222no—
471C2×Q8—444no—
472C2×Q8C23×D1112yes—
473C2×D4—22no—
474C2×D4—22no—
475C2×D4—112no—
476C2×D4—114no—
477C2×D4—222no—
478C2×D4—228no—
479C2×D4—222no—
480C2×D4—224no—
481C2×D4—222no—
482C2×D4—222no—
483C2×D4—222no—
484C2×D4—222no—
485C2×D4—224no—
486C2×D4—224no—
487C2×D4—228no—
488C2×D4—444no—
489C2×D4—448no—
490C2×D4—884no—
491C2×D4—884no—
492C2×D4C23×D1112yes—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—111no—
496C22×C4—112no—
497C22×C4—112no—
498C22×C4—112no—
499C22×C4—222no—
500C22×C4—228no—
501C22×C4—222no—
502C22×C4—222no—
503C22×C4—224no—
504C22×C4—222no—
505C22×C4—448no—
506C22×C4—884no—
507C22×C4D4×D1112yes—
508C22×C4C23×D1111yescharacteristic
509SD16—448no—
510SD16—448no—
511D8—448no—
512D8—448no—
513M16—24no—
514M16—224no—
515C2×C8—114no—
516C2×C8C23×D1114yes—
517C4⋊C4—24no—
518C4⋊C4—24no—
519C4⋊C4—22no—
520C4⋊C4—22no—
521C4⋊C4—114no—
522C4⋊C4—114no—
523C4⋊C4—224no—
524C4⋊C4—222no—
525C4⋊C4C23×D1114yes—
526C22⋊C4—24no—
527C22⋊C4—114no—
528C22⋊C4—114no—
529C22⋊C4—228no—
530C22⋊C4—228no—
531C22⋊C4—224no—
532C22⋊C4—224no—
533C22⋊C4—224no—
534C42—112no—
535C42—112no—
536C42D4×D1112yes—
537C42C23×D1111yescharacteristic
538C42C23×D1111yescharacteristic
539C11#6080811yescharacteristic, complemented, Sylow
540C23—22no—
541C23—112no—
542C23—222no—
543C23—224no—
544C23—222no—
545C23—442no—
546C23—444no—
547C23—444no—
548C23—444no—
549C23—444no—
550C23—884no—
551C23C2×D4×D1111yescharacteristic
552Q8—24no—
553Q8—224no—
554Q8—444no—
555D4—24no—
556D4—44no—
557D4—82no—
558D4—228no—
559D4—224no—
560D4—444no—
561D4—444no—
562D4—444no—
563D4—444no—
564D4—444no—
565D4—884no—
566D4—884no—
567D4—882no—
568D4—888no—
569D4—884no—
570C2×C4—22no—
571C2×C4—24no—
572C2×C4—42no—
573C2×C4—44no—
574C2×C4—44no—
575C2×C4—114no—
576C2×C4—112no—
577C2×C4—222no—
578C2×C4—224no—
579C2×C4—224no—
580C2×C4—222no—
581C2×C4—444no—
582C2×C4—444no—
583C2×C4—442no—
584C2×C4—444no—
585C2×C4—444no—
586C2×C4—888no—
587C2×C4C2×D4×D1112yes—
588C2×C4C2×D4×D1112yes—
589C2×C4C2×D4×D1111yescharacteristic
590C2×C4#6704214yes—
591C2×C4C24×D1111yescharacteristic
592C8—24no—
593C8—224no—
594C22—22no—
595C22—44no—
596C22—42no—
597C22—224no—
598C22—222no—
599C22—444no—
600C22—444no—
601C22—444no—
602C22—442no—
603C22—444no—
604C22—882no—
605C22—888no—
606C22—888no—
607C22#1062320512yes—
608C22C22×D4×D1111yescharacteristic
609C4—22no—
610C4—22no—
611C4—44no—
612C4—42no—
613C4—224no—
614C4—222no—
615C4—442no—
616C4#1062320512yes—
617C4C2×#6704212yes—
618C2—22no—
619C2—82no—
620C2—442no—
621C2—884no—
622C2—882no—
623C2C2×#1062320511yescharacteristic
624C2#1308339312yes—
subgroupG/H
centerC22C22×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3142C2
socleC22×C11C23×D4
hypercenter#3142D11
hypocenterC11#60808
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3142

Complements

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

NH ≅ G/Ntype
1. C2×#10623229C2semidirect
2. #13081943C2semidirect
3. #13079680C2semidirect
4. #13079678C2semidirect
5. #13079669C2semidirect
6. #13079667C2semidirect
7. #13079069C2semidirect
8. #13079068C2semidirect
9. #13079019C2semidirect
10. #13078079C2semidirect
11. #13077869C2semidirect
12. #13077252C2semidirect
13. C11×#3142C2semidirect
16. C2×C11×#125C22semidirect
18. C2×#67002C22semidirect
19. C2×#66961C22semidirect
20. #10623255C22semidirect
21. #10623246C22semidirect
23. #10623229C22semidirect
24. #10623229C22semidirect
25. #10623206C22semidirect
26. #10623205C22semidirect
33. C2×#66946C22semidirect
35. C2×#66927C22semidirect
37. C11×#491C22semidirect
38. C11×#490C22semidirect
39. C11×#488C22semidirect
40. C11×#417C22semidirect
41. C4×C11×M16C22semidirect
43. #10622731C22semidirect
44. #10622698C22semidirect
45. #10622686C22semidirect
46. #10622682C22semidirect
47. #10622681C22semidirect
48. #10622680C22semidirect
49. #10622671C22semidirect
50. #10622579C22semidirect
51. C4×#4318C22semidirect
52. #10622432C22semidirect
53. #10622431C22semidirect
54. #10622424C22semidirect
55. #10622419C22semidirect
56. #10622400C22semidirect
57. #10622399C22semidirect
58. #10622394C22semidirect
59. #10622386C22semidirect
60. #10622325C22semidirect
61. #10622322C22semidirect
62. #10622308C22semidirect
63. #10622306C22semidirect
64. #10622303C22semidirect
237. #3142D11semidirect
311. C2×#125C2×D11semidirect
325. #491C2×D11semidirect
327. #490C2×D11semidirect
329. #488C2×D11semidirect
342. #417C2×D11semidirect
345. C4×M16C2×D11semidirect
539. C11#60808semidirect

Maximal subgroups

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

subgroupindex
C2×#106232292
#130819432
#130796802
#130796782
#130796692
#130796672
#130790692
#130790682
#130790192
#130780792
#130778692
#130772522
C11×#31422
#6080811