Finite Group Databasebeta

← #15634937

Subgroups — #15634937

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#13082502C211yesmaximal, characteristic, complemented
2#13082492C211yesmaximal, characteristic, complemented
3#13081667C214yesmaximal, complemented
4#13081634C214yesmaximal, complemented
5#13081610C214yesmaximal, complemented
6#13081595C214yesmaximal, complemented
7#13079093C212yesmaximal, complemented
8C2×#10622306C211yesmaximal, characteristic, complemented
9#13078140C212yesmaximal, complemented
10#13078131C212yesmaximal, complemented
11#13078103C211yesmaximal, characteristic, complemented
12#13078096C211yesmaximal, characteristic, complemented
13#13077550C211yesmaximal, characteristic, complemented
14#13077474C212yesmaximal, complemented
15C4×C11×#135C211yesmaximal, characteristic, complemented
16C2×C11×#135C2211yescharacteristic
17C4×C11×#41C2211yescharacteristic
18C4×C11×#41C2211yescharacteristic
19#10623361C2212yes—
20#10623356C2212yes—
21C2×#67004C2212yes—
22C2×#67002C2212yes—
23C22×#4314C2212yes—
24C22×#4314C2212yes—
25#10623116C2214yes—
26#10623098C2214yescomplemented
27#10623084C2214yes—
28#10623081—24no—
29#10623073C2214yescomplemented
30#10623072—24no—
31#10623066—22no—
32#10623052C2212yes—
33#10623049—22no—
34#10623047C2212yes—
35#10623008—22no—
36C2×#66927C2211yescharacteristic
37#10623001—22no—
38#10623001C2211yescharacteristic
39C2×#66922C2211yescharacteristic
40C4×C11×Q16C2212yescomplemented
41C4×C11×SD16C2212yescomplemented
42C4×C11×SD16C2212yescomplemented
43C4×C11×D8C2212yescomplemented
44C11×#427C2211yescharacteristic
45C11×#416C2211yescharacteristic
46C11×#416C2211yescharacteristic
47C2×C4×C8×C11C2211yescharacteristic
48#10622803C2214yescomplemented
49#10622788C2214yescomplemented
50#10622781C2214yescomplemented
51#10622767C2214yescomplemented
52#10622715C2212yes—
53#10622714C2212yes—
54#10622644C2214yescomplemented
55#10622640C2214yes—
56#10622632C2214yescomplemented
57#10622628C2214yes—
58#10622617C2212yes—
59#10622614C2212yes—
60#10622537C2211yescharacteristic
61#10622502C2218yescomplemented
62#10622465C2218yescomplemented
63#10622431C2218yescomplemented
64#10622411C2218yescomplemented
65#10622400C2218yescomplemented
66#10622375C2218yescomplemented
67#10622306C2214yes—
68#10622306C2214yes—
69#10622292C2214yescomplemented
70C8×Dic22C2214yescomplemented
71C2×C11×#41C2311yescharacteristic
72C2×C11×#41C2311yescharacteristic
73C2×#4339—24no—
74C22×D44—22no—
75C22×D44C2312yes—
76C22×Dic22C2312yes—
77C11×#135—24no—
78C2×C11×Q16C2311yescharacteristic
79C2×C11×SD16C2311yescharacteristic
80C2×C11×SD16C2311yescharacteristic
81C2×C11×D8C2311yescharacteristic
82C22×C8×C11C2311yescharacteristic
83C22×C8×C11C2311yescharacteristic
84C4×Q8×C11C2312yes—
85C4×Q8×C11C2312yes—
86C4×D4×C11—22no—
87C4×D4×C11—22no—
88C4×D4×C11C2312yes—
89C4×D4×C11C2312yes—
90C11×#117—21no—
91C11×#117—21no—
92C11×#117C2311yescharacteristic
93C11×#117C2311yescharacteristic
94C2×C42×C11—21no—
95C2×C42×C11—21no—
96C2×C42×C11C2311yescharacteristic
97#67004—44no—
98#67002—44no—
99#67000C2314yes—
100#66997C2314yes—
101C2×#4326C2314yes—
102C2×#4325C2314yes—
103#66993C2314yes—
104#66990—24no—
105#66989C2314yes—
106#66988—24no—
107C2×#4324C2314yes—
108C2×#4323C2314yes—
109#66983—24no—
110#66983—24no—
111#66979—24no—
112#66979C2312yes—
113C2×C4⋊Dic11—22no—
114#66977—24no—
115#66977—24no—
116#66977D414yes—
117C2×#4318C2312yes—
118C2×#4314—28no—
119C2×#4314—44no—
120C2×#4314C2314yes—
121C2×#4314C2314yes—
122C2×#4314C2318yes—
123#66947—28no—
124#66946C2318yes—
125#66942—28no—
126#66940C2318yes—
127#66937—28no—
128C22⋊C4×D11—24no—
129#66932—28no—
130#66930—24no—
131#66928—24no—
132#66927—21no—
133#66927—21no—
134#66927C2314yes—
135C4×D44—24no—
136C4×D44—24no—
137#66923—24no—
138#66923D412yes—
139#66922—21no—
140#66922—21no—
141#66922D412yes—
142#66922C2314yes—
143C4×Dic22—24no—
144C4×Dic22—24no—
145C4×Dic22C2314yes—
146C11×#107C2312yes—
147C11×#106C2312yes—
148C11×#103C2312yes—
149C11×#103C2312yes—
150C11×#102C2312yes—
151C11×#102C2312yes—
152C4×C8×C11C2312yes—
153C4×C8×C11C2312yes—
154#66879C2314yes—
155Dic11⋊C8C2318yes—
156C8×Dic11C2314yes—
157#66874C2318yes—
158#66873C2318yes—
159C4⋊(C11⋊C8)C2314yes—
160#61410—111nomaximal, Sylow
161C23×D11—22no—
162C11×#41—22no—
163C11×#41—22no—
164C11×#41—22no—
165C11×#41—22no—
166C2×Q8×C11C2411yescharacteristic
167C2×Q8×C11C2411yescharacteristic
168C2×D4×C11—21no—
169C2×D4×C11—21no—
170C2×D4×C11C2411yescharacteristic
171C2×D4×C11C2411yescharacteristic
172C22×C4×C11—21no—
173C22×C4×C11—22no—
174C22×C4×C11—21no—
175C22×C4×C11—22no—
176C22×C4×C11C2×D412yes—
177C22×C4×C11C2411yescharacteristic
178C2×C22⋊D11—28no—
179C22×Dic11—22no—
180#4339—88no—
181C2×D44—22no—
182C2×D44—24no—
183C2×D44—24no—
184C2×D44—24no—
185C2×D44—24no—
186C2×D44—84no—
187C2×D44C2414yes—
188C2×C4×D11—28no—
189C2×Dic22—22no—
190C2×Dic22—24no—
191C2×Dic22—24no—
192C2×Dic22C2×D414yes—
193C2×Dic22C2414yes—
194C11×Q16—22no—
195C11×SD16—22no—
196C11×SD16—22no—
197C11×D8—22no—
198C2×C8×C11—22no—
199C2×C8×C11#4114yescomplemented
200C2×C8×C11C2412yes—
201C2×C8×C11C2411yescharacteristic
202C2×C8×C11C2411yescharacteristic
203C11×C4⋊C4—22no—
204C11×C4⋊C4—22no—
205C11×C4⋊C4C2412yes—
206C11×C4⋊C4C2412yes—
207C11×C22⋊C4—21no—
208C11×C22⋊C4—21no—
209C11×C22⋊C4—22no—
210C11×C22⋊C4—22no—
211C42×C11—21no—
212C42×C11—22no—
213C42×C11—21no—
214C42×C11—22no—
215C42×C11C2×D411yescharacteristic
216C42×C11C2×D411yescharacteristic
217C42×C11C2412yes—
218C22⋊Dic11—28no—
219C22⋊Dic11C2×D414yes—
220#4326—44no—
221#4325—44no—
222#4324—44no—
223#4323—44no—
224(C2×D11)⋊C4—28no—
225(C2×D11)⋊C4—28no—
226C4⋊Dic11—24no—
227C4⋊Dic11—24no—
228C4⋊Dic11C2×D414yes—
229C4⋊Dic11C2×D414yes—
230Dic11⋊C4—28no—
231Dic11⋊C4—28no—
232Dic11⋊C4C2×D418yes—
233C4×Dic11—28no—
234C4×Dic11C2414yes—
235#4318—24no—
236C2×C11⋊C8C2414yes—
237#4314—28no—
238#4314—28no—
239#4314—48no—
240#3509—111no—
241#3508—111no—
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×#135D1111yescharacteristic, complemented
255C23×C11—21no—
256C23×C11—21no—
257C23×C11C22×D411yescharacteristic
258C22×D11—24no—
259C22×D11—44no—
260C22×D11—84no—
261Q8×C11—21no—
262Q8×C11—21no—
263Q8×C11—21no—
264Q8×C11—21no—
265D4×C11—21no—
266D4×C11—21no—
267D4×C11—21no—
268D4×C11—21no—
269D4×C11—42no—
270D4×C11—42no—
271C2×C4×C11—24no—
272C2×C4×C11—22no—
273C2×C4×C11—21no—
274C2×C4×C11—21no—
275C2×C4×C11—22no—
276C2×C4×C11—42no—
277C2×C4×C11—42no—
278C2×C4×C11—44no—
279C2×C4×C11—44no—
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—88no—
287C2×Dic11—24no—
288C2×Dic11—44no—
289C2×Dic11C22×D418yes—
290D44—24no—
291D44—24no—
292D44—44no—
293D44—48no—
294D44—84no—
295C4×D11—88no—
296Dic22—28no—
297Dic22—24no—
298Dic22—24no—
299Dic22—44no—
300C8×C11—22no—
301C8×C11C2×#4112yes—
302C8×C11C2×#4112yes—
303C11⋊C8—24no—
304C2×#137—112no—
305C2×AGL(1,ℤ/8)—112no—
306C2×#135C2×D1111yescharacteristic
307C22×SD16—112no—
308C22×SD16—112no—
309#559—114no—
310#557—114no—
311#556—114no—
312#552—224no—
313#550—114no—
314#546—224no—
315#541—222no—
316#540—222no—
317#536—112no—
318#535—112no—
319#533—111no—
320#533—222no—
321#532—222no—
322C2×C4⋊Q8—111no—
323C2×#127—111no—
324#519—112no—
325#518—112no—
326C4×#41C2×D1111yescharacteristic
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—114no—
340#460—118no—
341#459—114no—
342#446—114no—
343C8×Q8—114no—
344#440—118no—
345C4×Q16C2×D1112yescomplemented
346C4×SD16—118no—
347C4×SD16C2×D1112yescomplemented
348C4×SD16C2×D1112yescomplemented
349C4×D8C2×D1112yescomplemented
350#427C2×D1111yescharacteristic
351#424—112no—
352#423—111no—
353#419—112no—
354#418—112no—
355#416C2×D1111yescharacteristic
356#416C2×D1111yescharacteristic
357#405—112no—
358C2×C4×C8C2×D1111yescharacteristic
359C22×C11—22no—
360C22×C11—41no—
361C22×C11—41no—
362C22×C11—42no—
363C22×C11—42no—
364C22×C11#55012yes—
365C22×C11C23×D411yescharacteristic
366C2×D11—44no—
367C2×D11—48no—
368C2×D11—164no—
369C4×C11—22no—
370C4×C11—41no—
371C4×C11—41no—
372C4×C11—42no—
373C4×C11—42no—
374C4×C11#55012yes—
375C4×C11#57714yes—
376C4×C11C22×#4111yescharacteristic
377C4×C11C2×H(5,𝔽2)11yescharacteristic
378Dic11—28no—
379Dic11—44no—
380C2×#41—224no—
381C2×#41C22×D1111yescharacteristic
382C2×#41C22×D1111yescharacteristic
383C22×Q8—112no—
384C22×D4—112no—
385C22×D4—222no—
386#137—444no—
387AGL(1,ℤ/8)—444no—
388#135—24no—
389C2×Q16—114no—
390C2×Q16C22×D1111yescharacteristic
391C2×SD16—114no—
392C2×SD16—114no—
393C2×SD16—114no—
394C2×SD16—114no—
395C2×SD16—118no—
396C2×SD16—228no—
397C2×SD16—444no—
398C2×SD16C22×D1111yescharacteristic
399C2×SD16C22×D1111yescharacteristic
400C2×D8—114no—
401C2×D8C22×D1111yescharacteristic
402C2×M16—112no—
403C22×C8C22×D1111yescharacteristic
404C22×C8C22×D1111yescharacteristic
405C4⋊Q8—114no—
406C4⋊Q8—112no—
407C4⋊Q8—114no—
408C4⋊Q8—221no—
409C4⋊Q8—221no—
410#127—114no—
411#127—114no—
412#127—221no—
413#127—221no—
414#126—228no—
415#125—112no—
416#125—224no—
417#125—228no—
418#124—114no—
419#124—114no—
420#124—224no—
421#123—224no—
422#123—228no—
423C22⋊Q8—114no—
424C22⋊Q8—224no—
425C22⋊Q8—224no—
426#121—228no—
427#121—224no—
428#121—224no—
429#120—224no—
430C4×Q8—114no—
431C4×Q8—118no—
432C4×Q8—224no—
433C4×Q8—224no—
434C4×Q8C22×D1112yes—
435C4×Q8C22×D1112yes—
436C4×D4—22no—
437C4×D4—22no—
438C4×D4—118no—
439C4×D4—224no—
440C4×D4—224no—
441C4×D4C22×D1112yes—
442C4×D4C22×D1112yes—
443#117—21no—
444#117—21no—
445#117—112no—
446#117—224no—
447#117—224no—
448#117C22×D1111yescharacteristic
449#117C22×D1111yescharacteristic
450C2×C4⋊C4—222no—
451C2×C22⋊C4—224no—
452C2×C42—21no—
453C2×C42—21no—
454C2×C42C22×D1111yescharacteristic
455#107C22×D1112yes—
456#106C22×D1112yes—
457C4⋊C8—118no—
458C4⋊C8—114no—
459#103—118no—
460#103C22×D1112yes—
461#103C22×D1112yes—
462#102—118no—
463#102C22×D1112yes—
464#102C22×D1112yes—
465#97—114no—
466C4×C8—114no—
467C4×C8C22×D1112yes—
468C4×C8C22×D1112yes—
469C2×C11—22no—
470C2×C11—81no—
471C2×C11—81no—
472C2×C11C2×#55011yescharacteristic
473C2×C11C2×#57712yes—
474D11—84no—
475C24—222no—
476#41—22no—
477#41—22no—
478#41—22no—
479#41—22no—
480#41—888no—
481C2×Q8—114no—
482C2×Q8—114no—
483C2×Q8—222no—
484C2×Q8—224no—
485C2×Q8—224no—
486C2×Q8C23×D1111yescharacteristic
487C2×Q8C23×D1111yescharacteristic
488C2×D4—21no—
489C2×D4—21no—
490C2×D4—114no—
491C2×D4—228no—
492C2×D4—224no—
493C2×D4—222no—
494C2×D4—224no—
495C2×D4—224no—
496C2×D4—224no—
497C2×D4—884no—
498C2×D4C23×D1111yescharacteristic
499C2×D4C23×D1111yescharacteristic
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—228no—
505C22×C4—222no—
506C22×C4D4×D1112yes—
507C22×C4C23×D1111yescharacteristic
508Q16—22no—
509Q16—444no—
510SD16—22no—
511SD16—22no—
512SD16—228no—
513SD16—228no—
514SD16—448no—
515SD16—444no—
516SD16—444no—
517D8—22no—
518D8—444no—
519M16—224no—
520C2×C8—22no—
521C2×C8—114no—
522C2×C8#433914yescomplemented
523C2×C8C23×D1112yes—
524C2×C8C23×D1111yescharacteristic
525C2×C8C23×D1111yescharacteristic
526C4⋊C4—22no—
527C4⋊C4—22no—
528C4⋊C4—114no—
529C4⋊C4—114no—
530C4⋊C4—118no—
531C4⋊C4—228no—
532C4⋊C4—228no—
533C4⋊C4—224no—
534C4⋊C4—224no—
535C4⋊C4C23×D1112yes—
536C4⋊C4C23×D1112yes—
537C22⋊C4—21no—
538C22⋊C4—21no—
539C22⋊C4—22no—
540C22⋊C4—22no—
541C22⋊C4—114no—
542C22⋊C4—228no—
543C22⋊C4—228no—
544C22⋊C4—228no—
545C42—21no—
546C42—21no—
547C42—22no—
548C42—22no—
549C42—114no—
550C42—228no—
551C42D4×D1111yescharacteristic
552C42D4×D1111yescharacteristic
553C42C23×D1112yes—
554C11#6141011yescharacteristic, complemented, Sylow
555C23—21no—
556C23—21no—
557C23—224no—
558C23—444no—
559C23—884no—
560C23C2×D4×D1111yescharacteristic
561Q8—21no—
562Q8—21no—
563Q8—21no—
564Q8—21no—
565Q8—228no—
566Q8—224no—
567Q8—224no—
568Q8—444no—
569D4—21no—
570D4—21no—
571D4—21no—
572D4—21no—
573D4—42no—
574D4—42no—
575D4—224no—
576D4—224no—
577D4—448no—
578D4—444no—
579D4—884no—
580D4—888no—
581C2×C4—24no—
582C2×C4—22no—
583C2×C4—22no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—44no—
587C2×C4—44no—
588C2×C4—42no—
589C2×C4—42no—
590C2×C4—118no—
591C2×C4—224no—
592C2×C4—444no—
593C2×C4—888no—
594C2×C4C2×#433912yes—
595C2×C4C2×D4×D1112yes—
596C2×C4C2×D4×D1112yes—
597C2×C4C2×D4×D1111yescharacteristic
598C2×C4#6704212yes—
599C2×C4C24×D1111yescharacteristic
600C8—22no—
601C8—224no—
602C8C2×#433912yes—
603C8C2×#433912yes—
604C22—22no—
605C22—42no—
606C22—42no—
607C22—41no—
608C22—41no—
609C22—448no—
610C22—444no—
611C22—1764no—
612C22#1062308412yes—
613C22C22×D4×D1111yescharacteristic
614C4—22no—
615C4—42no—
616C4—42no—
617C4—41no—
618C4—41no—
619C4—228no—
620C4—444no—
621C4#1062308412yes—
622C4#1062330114yes—
623C4C22×#433911yescharacteristic
624C4C2×#6704211yescharacteristic
625C2—22no—
626C2—81no—
627C2—81no—
628C2—884no—
629C2C2×#1062308411yescharacteristic
630C2C2×#1062330112yes—
subgroupG/H
centerC22C22×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC4×C11×#135C2
socleC22×C11C23×D4
hypercenterC4×#135D11
hypocenterC11#61410
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C4×#135

Complements

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

NH ≅ G/Ntype
1. #13082502C2semidirect
2. #13082492C2semidirect
3. #13081667C2semidirect
4. #13081634C2semidirect
5. #13081610C2semidirect
6. #13081595C2semidirect
7. #13079093C2semidirect
8. C2×#10622306C2semidirect
9. #13078140C2semidirect
10. #13078131C2semidirect
11. #13078103C2semidirect
12. #13078096C2semidirect
13. #13077550C2semidirect
14. #13077474C2semidirect
15. C4×C11×#135C2semidirect
26. #10623098C22semidirect
29. #10623073C22semidirect
40. C4×C11×Q16C22semidirect
41. C4×C11×SD16C22semidirect
42. C4×C11×SD16C22semidirect
43. C4×C11×D8C22semidirect
48. #10622803C22semidirect
49. #10622788C22semidirect
50. #10622781C22semidirect
51. #10622767C22semidirect
54. #10622644C22semidirect
56. #10622632C22semidirect
61. #10622502C22semidirect
62. #10622465C22semidirect
63. #10622431C22semidirect
64. #10622411C22semidirect
65. #10622400C22semidirect
66. #10622375C22semidirect
69. #10622292C22semidirect
70. C8×Dic22C22semidirect
199. C2×C8×C11#41semidirect
254. C4×#135D11semidirect
345. C4×Q16C2×D11semidirect
347. C4×SD16C2×D11semidirect
348. C4×SD16C2×D11semidirect
349. C4×D8C2×D11semidirect
522. C2×C8#4339semidirect
554. C11#61410semidirect

Maximal subgroups

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

subgroupindex
#130825022
#130824922
#130816672
#130816342
#130816102
#130815952
#130790932
C2×#106223062
#130781402
#130781312
#130781032
#130780962
#130775502
#130774742
C4×C11×#1352
#6141011