Finite Group Databasebeta

← #15634939

Subgroups — #15634939

Order 2816.

1958 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082503C211yesmaximal, characteristic, complemented
2#13081669C214yesmaximal, complemented
3#13081632C214yesmaximal, complemented
4#13081608C214yesmaximal, complemented
5#13081597C214yesmaximal, complemented
6#13079088C212yesmaximal, complemented
7C2×#10622689C211yesmaximal, characteristic, complemented
8#13078133C212yesmaximal, complemented
9#13078128C212yesmaximal, complemented
10#13078103C211yesmaximal, characteristic, complemented
11#13078092C211yesmaximal, characteristic, complemented
12#13077551C211yesmaximal, characteristic, complemented
13#13077473C212yesmaximal, complemented
14C4×#67003C211yesmaximal, characteristic, complemented
15C11×#3508C211yesmaximal, characteristic, complemented
16C11×#559C2214yes—
17C11×#550C2214yes—
18C11×#546—24no—
19C11×#540—22no—
20C11×#535C2212yes—
21C11×#533C2211yescharacteristic
22C11×#532—22no—
23C2×C11×#127C2211yescharacteristic
24C11×#518C2212yes—
25C4×C11×#41C2211yescharacteristic
26C2×#67004C2212yes—
27C2×#67003C2211yescharacteristic
28C22×#4324C2212yes—
29C22×#4324C2212yes—
30C2×#66985C2212yes—
31#10623259—22no—
32#10623228—22no—
33#10623173—24no—
34#10623115C2214yescomplemented
35#10623101C2214yescomplemented
36#10623057C2212yes—
37#10623047C2212yes—
38C4×#4339C2211yescharacteristic
39C2×#66922C2211yescharacteristic
40#10622846C2211yescharacteristic
41#10622828C2212yes—
42#10622689C2214yes—
43#10622689C2214yes—
44#10622689C2214yescomplemented
45#10622688C2214yes—
46#10622688C2218yescomplemented
47#10622687C2214yescomplemented
48#10622685C2214yes—
49#10622673C2214yescomplemented
50#10622672C2214yescomplemented
51#10622667C2218yescomplemented
52#10622644C2214yescomplemented
53C4×#4326C2212yescomplemented
54C4×#4325C2212yescomplemented
55#10622637C2214yescomplemented
56Q8×C11⋊C8C2214yescomplemented
57#10622632C2214yescomplemented
58#10622632C2218yescomplemented
59#10622631C2218yescomplemented
60C4×#4324C2218yescomplemented
61C4×#4324C2212yescomplemented
62#10622629C2218yescomplemented
63C4×#4323C2212yescomplemented
64#10622617C2212yes—
65#10622615C2211yescharacteristic
66#10622612C2212yes—
67#10622611C2211yescharacteristic
68#10622610C2212yes—
69#10622537C2211yescharacteristic
70C2×C4×C11⋊C8C2211yescharacteristic
71C2×C11×#41—24no—
72C2×C11×#41C2311yescharacteristic
73C22×D4×C11—22no—
74C22×D4×C11C2312yes—
75C2×#4339C2311yescharacteristic
76C22×Dic22C2312yes—
77C11×C4⋊Q8D412yes—
78C11×#127—21no—
79C11×#127—21no—
80C11×#127C2314yes—
81C11×#127C2314yes—
82C11×#125D412yes—
83C11×#124—24no—
84C11×#124C2314yes—
85C11×#123—28no—
86C11×C22⋊Q8D414yes—
87C11×#121—24no—
88C11×#121—24no—
89C11×#121—28no—
90C11×#120—24no—
91C4×Q8×C11C2312yes—
92C4×Q8×C11C2314yes—
93C4×D4×C11—22no—
94C4×D4×C11—24no—
95C4×D4×C11—24no—
96C4×D4×C11C2312yes—
97C4×D4×C11C2318yes—
98C11×#117—21no—
99C11×#117C2311yescharacteristic
100C11×#117C2312yes—
101C2×C11×C22⋊C4—24no—
102C2×C42×C11—21no—
103C2×C42×C11C2311yescharacteristic
104#67004—44no—
105#67003—24no—
106#66999—24no—
107Q8×Dic11—24no—
108C2×#4326C2311yescharacteristic
109C2×#4326C2314yes—
110C2×#4325C2311yescharacteristic
111C2×#4324—28no—
112C2×#4324—44no—
113C2×#4324C2314yes—
114C2×#4324C2314yes—
115C2×#4324C2311yescharacteristic
116C2×#4324C2314yes—
117C2×#4324C2318yes—
118C2×#4324C2314yes—
119#66985—44no—
120C2×#4323C2311yescharacteristic
121C2×#4323C2314yes—
122C4×C22⋊D11—22no—
123#66979C2311yescharacteristic
124C2×C4⋊Dic11—22no—
125C2×#4318C2312yes—
126C22×C11⋊C8C2311yescharacteristic
127C22×C11⋊C8C2311yescharacteristic
128#66951—28no—
129#66950—24no—
130#66945—24no—
131#66943—24no—
132#66943—28no—
133#66940—24no—
134#66939—24no—
135#66930—24no—
136#66928C2314yes—
137C4×D44C2312yes—
138#66925—21no—
139C42×D11—21no—
140#66922—21no—
141#66922—21no—
142#66922C2314yes—
143#66922C2314yes—
144C4×Dic22C2312yes—
145C4×Dic22C2318yes—
146#66899C2312yes—
147#66896C2318yes—
148#66896C2312yes—
149#66874C2312yes—
150#66874C2318yes—
151#66873C2312yes—
152#66872C2312yes—
153#66871C2312yes—
154C4⋊(C11⋊C8)C2314yes—
155C4⋊(C11⋊C8)C2318yes—
156#66867C2314yes—
157C4×C11⋊C8C2312yes—
158C4×C11⋊C8C2312yes—
159C4×C11⋊C8C2314yes—
160#61410—111nomaximal, Sylow
161C24×C11—22no—
162C11×#41—22no—
163C11×#41—22no—
164C11×#41—88no—
165C2×Q8×C11C2×D414yes—
166C2×Q8×C11C2411yescharacteristic
167C2×D4×C11—21no—
168C2×D4×C11—22no—
169C2×D4×C11—24no—
170C2×D4×C11—28no—
171C2×D4×C11—24no—
172C2×D4×C11—24no—
173C2×D4×C11—24no—
174C2×D4×C11—84no—
175C2×D4×C11C2414yes—
176C2×D4×C11C2411yescharacteristic
177C22×C4×C11—21no—
178C22×C4×C11—22no—
179C22×C4×C11—28no—
180C22×C4×C11C2×D412yes—
181C22×C4×C11C2411yescharacteristic
182C2×C22⋊D11—21no—
183C22×Dic11—22no—
184#4339—22no—
185#4339—22no—
186C2×D44C2411yescharacteristic
187C2×C4×D11—21no—
188C2×C4×D11—22no—
189C2×Dic22—22no—
190C2×Dic22—24no—
191C2×Dic22—24no—
192C2×Dic22C2411yescharacteristic
193C2×Dic22C2414yes—
194C11×C4⋊C4—22no—
195C11×C4⋊C4C2×D414yes—
196C11×C4⋊C4C2×D414yes—
197C11×C4⋊C4C2×D418yes—
198C11×C4⋊C4C2412yes—
199C11×C22⋊C4—21no—
200C11×C22⋊C4—28no—
201C11×C22⋊C4—22no—
202C11×C22⋊C4—28no—
203C11×C22⋊C4C2×D414yes—
204C42×C11—21no—
205C42×C11—22no—
206C42×C11C2×D411yescharacteristic
207C42×C11C2×D411yescharacteristic
208C42×C11C2412yes—
209C42×C11C2414yes—
210C22⋊Dic11—21no—
211#4326—22no—
212#4326—44no—
213#4325—22no—
214#4324—28no—
215#4324—28no—
216#4324—22no—
217#4324—44no—
218#4324—48no—
219#4324—44no—
220#4323—22no—
221#4323—44no—
222(C2×D11)⋊C4—22no—
223(C2×D11)⋊C4—28no—
224C4⋊Dic11—24no—
225C4⋊Dic11—24no—
226C4⋊Dic11—28no—
227C4⋊Dic11C2412yes—
228Dic11⋊C4—22no—
229Dic11⋊C4—28no—
230C4×Dic11—22no—
231C4×Dic11—28no—
232C4×Dic11—21no—
233#4318—24no—
234C2×C11⋊C8—22no—
235C2×C11⋊C8#4114yescomplemented
236C2×C11⋊C8C2412yes—
237C2×C11⋊C8C2414yes—
238C2×C11⋊C8C2411yescharacteristic
239C2×C11⋊C8C2411yescharacteristic
240#3509—111no—
241#3508D1111yescharacteristic, complemented
242#3400—114no—
243#3397—114no—
244#3394—114no—
245#3392—114no—
246#3154—112no—
247C2×#492—111no—
248#3043—112no—
249#3042—112no—
250#3039—111no—
251#3038—111no—
252#2960—111no—
253#2949—112no—
254C4×#135—111no—
255C23×C11—24no—
256C23×C11—21no—
257C23×C11—44no—
258C23×C11—84no—
259C23×C11C22×D411yescharacteristic
260C22×D11—21no—
261Q8×C11—28no—
262Q8×C11—21no—
263Q8×C11—21no—
264D4×C11—21no—
265D4×C11—24no—
266D4×C11—24no—
267D4×C11—21no—
268D4×C11—42no—
269D4×C11—44no—
270D4×C11—48no—
271D4×C11—84no—
272D4×C11—88no—
273C2×C4×C11—24no—
274C2×C4×C11—21no—
275C2×C4×C11—22no—
276C2×C4×C11—42no—
277C2×C4×C11—44no—
278C2×C4×C11—88no—
279C2×C4×C11C22×D418yes—
280C2×C4×C11C22×D412yes—
281C2×C4×C11C22×D411yescharacteristic
282C2×C4×C11C22×D412yes—
283C2×C4×C11C2×#4112yes—
284C2×C4×C11H(5,𝔽2)12yes—
285C2×C4×C11C2511yescharacteristic
286C22⋊D11—42no—
287C2×Dic11—22no—
288C2×Dic11—21no—
289C2×Dic11—24no—
290C2×Dic11—44no—
291D44—21no—
292D44—21no—
293C4×D11—42no—
294C4×D11—44no—
295Dic22—24no—
296Dic22—21no—
297Dic22—21no—
298Dic22—24no—
299Dic22—44no—
300C11⋊C8—22no—
301C11⋊C8—24no—
302C11⋊C8C2×#4112yes—
303C11⋊C8C2×#4112yes—
304C2×#137—112no—
305C2×AGL(1,ℤ/8)—112no—
306C2×#135—111no—
307C22×SD16—112no—
308C22×SD16—112no—
309#559C2×D1114yes—
310#557—114no—
311#556—114no—
312#552—224no—
313#550C2×D1114yes—
314#546—24no—
315#541—222no—
316#540—22no—
317#536—112no—
318#535C2×D1112yes—
319#533—222no—
320#533C2×D1111yescharacteristic
321#532—22no—
322C2×C4⋊Q8—111no—
323C2×#127C2×D1111yescharacteristic
324#519—112no—
325#518C2×D1112yes—
326C4×#41—111no—
327C4×#41C2×D1111yescharacteristic
328#497—114no—
329#496—114no—
330#495—114no—
331#492—114no—
332#492—114no—
333#492—114no—
334#464—118no—
335#463—118no—
336#462—114no—
337#461—114no—
338#461—118no—
339#460—118no—
340#460—114no—
341#459—114no—
342#446—114no—
343C8×Q8—114no—
344#440—118no—
345C4×Q16—112no—
346C4×SD16—112no—
347C4×SD16—112no—
348C4×SD16—118no—
349C4×D8—112no—
350#427—111no—
351#424—112no—
352#423—111no—
353#419—112no—
354#418—112no—
355#416—111no—
356#416—111no—
357#405—112no—
358C2×C4×C8—111no—
359C22×C11—22no—
360C22×C11—41no—
361C22×C11—44no—
362C22×C11—42no—
363C22×C11—48no—
364C22×C11—164no—
365C22×C11#55012yes—
366C22×C11C23×D411yescharacteristic
367C2×D11—41no—
368C2×D11—42no—
369C4×C11—22no—
370C4×C11—28no—
371C4×C11—41no—
372C4×C11—42no—
373C4×C11#55012yes—
374C4×C11#57714yes—
375C4×C11C22×#4111yescharacteristic
376C4×C11C2×H(5,𝔽2)11yescharacteristic
377Dic11—44no—
378Dic11—41no—
379Dic11—42no—
380C2×#41—24no—
381C2×#41—111no—
382C2×#41C22×D1111yescharacteristic
383C22×Q8—112no—
384C22×D4—22no—
385C22×D4C22×D1112yes—
386#137—444no—
387AGL(1,ℤ/8)—444no—
388#135—224no—
389C2×Q16—111no—
390C2×Q16—114no—
391C2×SD16—111no—
392C2×SD16—114no—
393C2×SD16—114no—
394C2×SD16—111no—
395C2×SD16—118no—
396C2×SD16—114no—
397C2×SD16—114no—
398C2×SD16—228no—
399C2×SD16—444no—
400C2×D8—111no—
401C2×D8—114no—
402C2×M16—112no—
403C22×C8—111no—
404C22×C8—111no—
405C4⋊Q8—114no—
406C4⋊Q8—114no—
407C4⋊Q8—221no—
408C4⋊Q8—221no—
409C4⋊Q8C22⋊D1112yes—
410#127—21no—
411#127—21no—
412#127C22×D1114yes—
413#127C22×D1114yes—
414#126—228no—
415#125—224no—
416#125—228no—
417#125C22⋊D1112yes—
418#124—24no—
419#124—114no—
420#124C22×D1114yes—
421#123—28no—
422#123—224no—
423C22⋊Q8—224no—
424C22⋊Q8—224no—
425C22⋊Q8C22⋊D1114yes—
426#121—24no—
427#121—24no—
428#121—28no—
429#120—24no—
430C4×Q8—112no—
431C4×Q8—118no—
432C4×Q8—224no—
433C4×Q8—224no—
434C4×Q8C22×D1112yes—
435C4×Q8C22×D1114yes—
436C4×D4—22no—
437C4×D4—24no—
438C4×D4—24no—
439C4×D4—112no—
440C4×D4—222no—
441C4×D4C22×D1112yes—
442C4×D4C22×D1118yes—
443#117—21no—
444#117—111no—
445#117—224no—
446#117—224no—
447#117—221no—
448#117C22×D1111yescharacteristic
449#117C22×D1112yes—
450C2×C4⋊C4—222no—
451C2×C22⋊C4—24no—
452C2×C42—21no—
453C2×C42—221no—
454C2×C42C22×D1111yescharacteristic
455#107—112no—
456#106—112no—
457C4⋊C8—114no—
458C4⋊C8—118no—
459#103—112no—
460#103—112no—
461#103—118no—
462#102—112no—
463#102—118no—
464#102—112no—
465#97—114no—
466C4×C8—112no—
467C4×C8—112no—
468C4×C8—114no—
469C2×C11—22no—
470C2×C11—81no—
471C2×C11—84no—
472C2×C11C2×#55011yescharacteristic
473C2×C11C2×#57712yes—
474D11—81no—
475C24—22no—
476#41—22no—
477#41—22no—
478#41—88no—
479#41—222no—
480#41—222no—
481C2×Q8—114no—
482C2×Q8—111no—
483C2×Q8—222no—
484C2×Q8—224no—
485C2×Q8—224no—
486C2×Q8C2×C22⋊D1114yes—
487C2×Q8C23×D1111yescharacteristic
488C2×D4—21no—
489C2×D4—24no—
490C2×D4—24no—
491C2×D4—22no—
492C2×D4—24no—
493C2×D4—28no—
494C2×D4—24no—
495C2×D4—84no—
496C2×D4—111no—
497C2×D4—221no—
498C2×D4C23×D1114yes—
499C2×D4C23×D1111yescharacteristic
500C22×C4—21no—
501C22×C4—22no—
502C22×C4—28no—
503C22×C4—222no—
504C22×C4—222no—
505C22×C4—221no—
506C22×C4C2×C22⋊D1112yes—
507C22×C4C23×D1111yescharacteristic
508Q16—222no—
509Q16—444no—
510SD16—228no—
511SD16—228no—
512SD16—222no—
513SD16—222no—
514SD16—448no—
515SD16—444no—
516SD16—444no—
517D8—222no—
518D8—444no—
519M16—224no—
520C2×C8—114no—
521C2×C8—111no—
522C2×C8—111no—
523C2×C8—112no—
524C2×C8—114no—
525C2×C8—222no—
526C4⋊C4—22no—
527C4⋊C4—112no—
528C4⋊C4—224no—
529C4⋊C4—224no—
530C4⋊C4—222no—
531C4⋊C4—228no—
532C4⋊C4—228no—
533C4⋊C4C2×C22⋊D1114yes—
534C4⋊C4C2×C22⋊D1114yes—
535C4⋊C4C2×C22⋊D1118yes—
536C4⋊C4C23×D1112yes—
537C22⋊C4—21no—
538C22⋊C4—28no—
539C22⋊C4—22no—
540C22⋊C4—28no—
541C22⋊C4—221no—
542C22⋊C4—222no—
543C22⋊C4—228no—
544C22⋊C4C2×C22⋊D1114yes—
545C42—21no—
546C42—22no—
547C42—221no—
548C42—222no—
549C42—228no—
550C42C2×C22⋊D1111yescharacteristic
551C42C2×C22⋊D1111yescharacteristic
552C42C23×D1112yes—
553C42C23×D1114yes—
554C11#6141011yescharacteristic, complemented, Sylow
555C23—24no—
556C23—21no—
557C23—44no—
558C23—84no—
559C23—221no—
560C23C22×C22⋊D1111yescharacteristic
561Q8—28no—
562Q8—21no—
563Q8—21no—
564Q8—224no—
565Q8—221no—
566Q8—221no—
567Q8—224no—
568Q8—444no—
569D4—21no—
570D4—24no—
571D4—24no—
572D4—21no—
573D4—42no—
574D4—44no—
575D4—48no—
576D4—84no—
577D4—88no—
578D4—221no—
579D4—221no—
580D4—442no—
581C2×C4—24no—
582C2×C4—21no—
583C2×C4—22no—
584C2×C4—42no—
585C2×C4—44no—
586C2×C4—88no—
587C2×C4—222no—
588C2×C4—224no—
589C2×C4—221no—
590C2×C4—444no—
591C2×C4—442no—
592C2×C4—444no—
593C2×C4#41×D1112yes—
594C2×C4#6704212yes—
595C2×C4C22×C22⋊D1118yes—
596C2×C4C22×C22⋊D1112yes—
597C2×C4C22×C22⋊D1111yescharacteristic
598C2×C4C22×C22⋊D1112yes—
599C2×C4C24×D1111yescharacteristic
600C8—112no—
601C8—112no—
602C8—222no—
603C8—224no—
604C22—22no—
605C22—41no—
606C22—44no—
607C22—42no—
608C22—48no—
609C22—164no—
610C22—441no—
611C22—442no—
612C22#1062336512yes—
613C22C23×C22⋊D1111yescharacteristic
614C4—22no—
615C4—28no—
616C4—41no—
617C4—42no—
618C4—441no—
619C4—444no—
620C4—442no—
621C4#1062336512yes—
622C4#1062336714yes—
623C4C2×#41×D1111yescharacteristic
624C4C2×#6704211yescharacteristic
625C2—22no—
626C2—84no—
627C2—81no—
628C2—881no—
629C2C2×#1062336511yescharacteristic
630C2C2×#1062336712yes—
subgroupG/H
centerC22C23×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3508C2
socleC22×C11C23×D4
hypercenter#3508D11
hypocenterC11#61410
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ #533 ◁ #3508

Complements

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

NH ≅ G/Ntype
1. #13082503C2semidirect
2. #13081669C2semidirect
3. #13081632C2semidirect
4. #13081608C2semidirect
5. #13081597C2semidirect
6. #13079088C2semidirect
7. C2×#10622689C2semidirect
8. #13078133C2semidirect
9. #13078128C2semidirect
10. #13078103C2semidirect
11. #13078092C2semidirect
12. #13077551C2semidirect
13. #13077473C2semidirect
14. C4×#67003C2semidirect
15. C11×#3508C2semidirect
34. #10623115C22semidirect
35. #10623101C22semidirect
44. #10622689C22semidirect
46. #10622688C22semidirect
47. #10622687C22semidirect
49. #10622673C22semidirect
50. #10622672C22semidirect
51. #10622667C22semidirect
52. #10622644C22semidirect
53. C4×#4326C22semidirect
54. C4×#4325C22semidirect
55. #10622637C22semidirect
56. Q8×C11⋊C8C22semidirect
57. #10622632C22semidirect
58. #10622632C22semidirect
59. #10622631C22semidirect
60. C4×#4324C22semidirect
61. C4×#4324C22semidirect
62. #10622629C22semidirect
63. C4×#4323C22semidirect
235. C2×C11⋊C8#41semidirect
241. #3508D11semidirect
554. C11#61410semidirect

Maximal subgroups

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

subgroupindex
#130825032
#130816692
#130816322
#130816082
#130815972
#130790882
C2×#106226892
#130781332
#130781282
#130781032
#130780922
#130775512
#130774732
C4×#670032
C11×#35082
#6141011