Finite Group Databasebeta

← #15634927

Subgroups — #15634927

Order 2816.

2078 conjugacy classes of subgroups.

The subgroup lattice has 652 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082492C211yesmaximal, characteristic, complemented
2#13082490C211yesmaximal, characteristic, complemented
3#13081662C214yesmaximal, complemented
4#13081657C214yesmaximal, complemented
5#13081627C214yesmaximal, complemented
6#13081587C214yesmaximal, complemented
7#13079101C212yesmaximal, complemented
8C2×#10622686C211yesmaximal, characteristic, complemented
9#13078121C212yesmaximal, complemented
10#13078118C212yesmaximal, complemented
11#13078097C211yesmaximal, characteristic, complemented
12#13077546C211yesmaximal, characteristic, complemented
13#13077464C212yesmaximal, complemented
14C4×#67003C211yesmaximal, characteristic, complemented
15C11×#3038C211yesmaximal, characteristic, complemented
16C2×C11×AGL(1,ℤ/8)C2212yes—
17C2×C11×#127C2211yescharacteristic
18C4×C11×#41C2211yescharacteristic
19#10623361C2212yes—
20C2×#67003C2211yescharacteristic
21#10623337—24no—
22#10623336C2212yes—
23#10623329C2212yes—
24C22×#4323C2212yes—
25C22×#4323C2212yes—
26C2×#66961C2212yes—
27#10623250—22no—
28#10623249C2214yescomplemented
29#10623247—22no—
30#10623244C2214yescomplemented
31#10623116C2214yescomplemented
32#10623084C2214yescomplemented
33#10623081—24no—
34#10623066—22no—
35#10623052C2212yes—
36#10623008—22no—
37C2×#66927C2211yescharacteristic
38C4×#4339C2211yescharacteristic
39#10623001C2211yescharacteristic
40C11×#460C2214yescomplemented
41C11×#459C2214yescomplemented
42C11×#423C2211yescharacteristic
43C11×#418C2212yes—
44#10622846C2211yescharacteristic
45#10622789C2214yescomplemented
46#10622781C2214yescomplemented
47#10622778C2218yescomplemented
48#10622767C2214yescomplemented
49#10622764C2214yescomplemented
50#10622763C2218yescomplemented
51#10622744C2212yes—
52#10622735C2212yes—
53#10622732C2212yes—
54#10622686C2214yes—
55#10622686C2214yes—
56C4×#4326C2212yescomplemented
57C4×#4325C2212yescomplemented
58C4×#4324C2212yescomplemented
59C4×#4323C2212yescomplemented
60#10622615C2211yescharacteristic
61#10622611C2211yescharacteristic
62C2×C4×C11⋊C8C2211yescharacteristic
63#10622461C2214yescomplemented
64#10622456C2214yescomplemented
65#10622444C2214yescomplemented
66#10622443C2214yescomplemented
67#10622400C2218yescomplemented
68#10622399C2218yescomplemented
69#10622398C2218yescomplemented
70#10622369C2218yescomplemented
71C2×C11×#41C2311yescharacteristic
72C22×D4×C11—22no—
73C22×D4×C11C2312yes—
74C2×#4341—24no—
75C2×#4339—24no—
76C2×#4339C2311yescharacteristic
77C22×D44—22no—
78C22×D44C2312yes—
79C11×AGL(1,ℤ/8)—44no—
80C2×C11×SD16C2314yes—
81C2×C11×D8C2314yes—
82C2×C11×M16C2312yes—
83C11×#127—21no—
84C11×#127—21no—
85C11×#127C2314yes—
86C4×Q8×C11C2312yes—
87C4×D4×C11—22no—
88C4×D4×C11C2312yes—
89C11×#117—21no—
90C11×#117C2311yescharacteristic
91C2×C42×C11—21no—
92C2×C42×C11C2311yescharacteristic
93#67006—24no—
94C2×C22⋊Dic11—24no—
95#67003—24no—
96#67000C2314yes—
97C2×#4326C2311yescharacteristic
98C2×#4325C2311yescharacteristic
99#66993C2314yes—
100#66993C2314yes—
101#66992—28no—
102#66991—24no—
103#66991—24no—
104#66990—24no—
105#66989—24no—
106#66989C2314yes—
107#66988—28no—
108D4×Dic11—24no—
109D4×Dic11—24no—
110D4×Dic11C2318yes—
111C2×#4324C2311yescharacteristic
112C2×#4323—28no—
113C2×#4323—44no—
114C2×#4323C2311yescharacteristic
115C2×#4323C2314yes—
116C2×#4323C2314yes—
117C2×#4323C2318yes—
118#66983—24no—
119#66983—24no—
120C4×C22⋊D11—22no—
121#66979C2311yescharacteristic
122#66979C2312yes—
123#66977D414yes—
124C22×C11⋊C8C2311yescharacteristic
125C22×C11⋊C8C2311yescharacteristic
126#66961—44no—
127C2×D88C2314yes—
128C2×#4314C2314yes—
129#66947—28no—
130#66946C2318yes—
131#66937—28no—
132C22⋊C4×D11—24no—
133#66928—24no—
134#66927—21no—
135#66927—21no—
136#66927C2314yes—
137C4×D44—24no—
138C4×D44—24no—
139C4×D44C2312yes—
140#66925—21no—
141C42×D11—21no—
142#66923D412yes—
143#66922D412yes—
144C4×Dic22C2312yes—
145C4×Dic22C2314yes—
146C11×C4⋊C8C2314yes—
147C11×#102C2318yes—
148#66899C2312yes—
149#66896C2312yes—
150#66885C2318yes—
151#66879C2314yes—
152Dic11⋊C8C2318yes—
153C8×Dic11C2314yes—
154#66874C2312yes—
155#66873C2312yes—
156#66872C2312yes—
157#66871C2312yes—
158C4×C11⋊C8C2312yes—
159C4×C11⋊C8C2312yes—
160#61409—111nomaximal, Sylow
161C24×C11—22no—
162C23×D11—22no—
163C11×#41—22no—
164C11×#41—22no—
165C2×Q8×C11C2411yescharacteristic
166C2×D4×C11—21no—
167C2×D4×C11—22no—
168C2×D4×C11—24no—
169C2×D4×C11—24no—
170C2×D4×C11—24no—
171C2×D4×C11—24no—
172C2×D4×C11—84no—
173C2×D4×C11C2411yescharacteristic
174C2×D4×C11C2414yes—
175C22×C4×C11—21no—
176C22×C4×C11—22no—
177C22×C4×C11C2×D412yes—
178C22×C4×C11C2411yescharacteristic
179C2×C22⋊D11—28no—
180C2×C22⋊D11—28no—
181C2×C22⋊D11—21no—
182C22×Dic11—28no—
183#4341—88no—
184#4339—22no—
185#4339—22no—
186#4339—88no—
187C2×D44—22no—
188C2×D44—24no—
189C2×D44—24no—
190C2×D44—24no—
191C2×D44—24no—
192C2×D44—84no—
193C2×D44C2411yescharacteristic
194C2×D44C2414yes—
195C2×C4×D11—28no—
196C2×C4×D11—21no—
197C2×C4×D11—22no—
198C2×Dic22C2×D414yes—
199C2×Dic22C2411yescharacteristic
200C11×SD16—44no—
201C11×D8—44no—
202C11×M16—24no—
203C2×C8×C11C2414yes—
204C11×C4⋊C4—22no—
205C11×C4⋊C4C2412yes—
206C11×C22⋊C4—21no—
207C11×C22⋊C4—22no—
208C42×C11—21no—
209C42×C11—22no—
210C42×C11C2×D411yescharacteristic
211C42×C11C2×D411yescharacteristic
212C42×C11C2412yes—
213C22⋊Dic11—28no—
214C22⋊Dic11—28no—
215C22⋊Dic11—21no—
216C22⋊Dic11C2×D414yes—
217#4326—22no—
218#4325—22no—
219#4324—22no—
220#4323—28no—
221#4323—28no—
222#4323—22no—
223#4323—48no—
224(C2×D11)⋊C4—28no—
225(C2×D11)⋊C4—28no—
226(C2×D11)⋊C4—22no—
227C4⋊Dic11C2×D414yes—
228C4⋊Dic11C2×D414yes—
229C4⋊Dic11C2412yes—
230Dic11⋊C4—22no—
231Dic11⋊C4C2×D418yes—
232C4×Dic11—22no—
233C4×Dic11—21no—
234C4×Dic11C2414yes—
235C2×C11⋊C8—22no—
236C2×C11⋊C8#4114yescomplemented
237C2×C11⋊C8C2412yes—
238C2×C11⋊C8C2411yescharacteristic
239C2×C11⋊C8C2411yescharacteristic
240D88—44no—
241#4314—44no—
242#3508—111no—
243#3508—111no—
244#3399—114no—
245#3399—114no—
246#3396—114no—
247#3391—114no—
248#3155—112no—
249C2×#493—111no—
250#3041—112no—
251#3041—112no—
252#3038—111no—
253#3038D1111yescharacteristic, complemented
254#2960—111no—
255#2948—112no—
256C4×#135—111no—
257C23×C11—24no—
258C23×C11—21no—
259C23×C11—44no—
260C23×C11—84no—
261C23×C11C22×D411yescharacteristic
262C22×D11—24no—
263C22×D11—21no—
264C22×D11—44no—
265C22×D11—84no—
266Q8×C11—21no—
267Q8×C11—21no—
268D4×C11—24no—
269D4×C11—21no—
270D4×C11—24no—
271D4×C11—21no—
272D4×C11—42no—
273D4×C11—44no—
274D4×C11—48no—
275D4×C11—84no—
276C2×C4×C11—24no—
277C2×C4×C11—21no—
278C2×C4×C11—22no—
279C2×C4×C11—42no—
280C2×C4×C11—44no—
281C2×C4×C11C22×D412yes—
282C2×C4×C11C22×D411yescharacteristic
283C2×C4×C11C22×D412yes—
284C2×C4×C11C2×#4112yes—
285C2×C4×C11H(5,𝔽2)12yes—
286C2×C4×C11C2511yescharacteristic
287C22⋊D11—42no—
288C22⋊D11—88no—
289C22⋊D11—88no—
290C2×Dic11—21no—
291C2×Dic11—22no—
292C2×Dic11—88no—
293C2×Dic11C22×D418yes—
294D44—24no—
295D44—21no—
296D44—24no—
297D44—21no—
298D44—44no—
299D44—48no—
300D44—84no—
301C4×D11—42no—
302C4×D11—44no—
303C4×D11—88no—
304Dic22—28no—
305Dic22—21no—
306Dic22—21no—
307C8×C11—24no—
308C11⋊C8—22no—
309C11⋊C8C2×#4112yes—
310C11⋊C8C2×#4112yes—
311C2×AGL(1,ℤ/8)—112no—
312C2×AGL(1,ℤ/8)C2×D1112yes—
313C2×#135—111no—
314C22×D8—112no—
315C22×D8—112no—
316#559—114no—
317#559—114no—
318#550—114no—
319#550—114no—
320#546—224no—
321#546—224no—
322#540—222no—
323#540—222no—
324#535—112no—
325#535—112no—
326#533—111no—
327#532—222no—
328#532—222no—
329C2×#127—111no—
330C2×#127C2×D1111yescharacteristic
331#518—112no—
332#518—112no—
333C4×#41—111no—
334C4×#41C2×D1111yescharacteristic
335#496—114no—
336#496—114no—
337#495—114no—
338#493—114no—
339#493—114no—
340#493—114no—
341#463—118no—
342#463—118no—
343#460—114no—
344#460C2×D1114yescomplemented
345#459—118no—
346#459—114no—
347#459—118no—
348#459C2×D1114yescomplemented
349#446—114no—
350C8×Q8—114no—
351#442—118no—
352C4×Q16—112no—
353C4×SD16—112no—
354C4×SD16—112no—
355C4×D8—112no—
356C4×D8—118no—
357#427—111no—
358#424—112no—
359#423C2×D1111yescharacteristic
360#418—112no—
361#418C2×D1112yes—
362#416—111no—
363#416—111no—
364#405—112no—
365C2×C4×C8—111no—
366C22×C11—22no—
367C22×C11—41no—
368C22×C11—44no—
369C22×C11—42no—
370C22×C11—48no—
371C22×C11—164no—
372C22×C11#55012yes—
373C22×C11C23×D411yescharacteristic
374C2×D11—44no—
375C2×D11—41no—
376C2×D11—48no—
377C2×D11—42no—
378C2×D11—164no—
379C4×C11—22no—
380C4×C11—41no—
381C4×C11—42no—
382C4×C11#55012yes—
383C4×C11#57614yes—
384C4×C11C22×#4111yescharacteristic
385C4×C11C2×H(5,𝔽2)11yescharacteristic
386Dic11—28no—
387Dic11—41no—
388Dic11—42no—
389C2×#41—111no—
390C2×#41—224no—
391C2×#41—224no—
392C2×#41C22×D1111yescharacteristic
393C22×D4—22no—
394C22×D4—112no—
395C22×D4—222no—
396C22×D4C22×D1112yes—
397AGL(1,ℤ/8)—44no—
398AGL(1,ℤ/8)—444no—
399#135—224no—
400C2×Q16—111no—
401C2×SD16—111no—
402C2×SD16—111no—
403C2×SD16—114no—
404C2×SD16C22×D1114yes—
405C2×D8—114no—
406C2×D8—114no—
407C2×D8—111no—
408C2×D8—118no—
409C2×D8—114no—
410C2×D8—228no—
411C2×D8—444no—
412C2×D8C22×D1114yes—
413C2×M16C22×D1112yes—
414C22×C8—111no—
415C22×C8—111no—
416C4⋊Q8—112no—
417#127—21no—
418#127—21no—
419#127—114no—
420#127—114no—
421#127—114no—
422#127—221no—
423#127—221no—
424#127C22×D1114yes—
425#125—112no—
426#124—114no—
427#124—114no—
428#124—224no—
429#124—224no—
430#123—228no—
431#123—228no—
432C22⋊Q8—114no—
433#121—228no—
434#121—224no—
435#121—224no—
436#121—224no—
437#121—224no—
438#121—228no—
439#120—224no—
440#120—224no—
441C4×Q8—114no—
442C4×Q8—112no—
443C4×Q8C22×D1112yes—
444C4×D4—22no—
445C4×D4—118no—
446C4×D4—118no—
447C4×D4—112no—
448C4×D4—224no—
449C4×D4—224no—
450C4×D4—224no—
451C4×D4—224no—
452C4×D4—222no—
453C4×D4C22×D1112yes—
454#117—21no—
455#117—112no—
456#117—111no—
457#117—221no—
458#117C22×D1111yescharacteristic
459C2×C22⋊C4—224no—
460C2×C22⋊C4—224no—
461C2×C42—21no—
462C2×C42—221no—
463C2×C42C22×D1111yescharacteristic
464#107—112no—
465#106—112no—
466C4⋊C8—118no—
467C4⋊C8C22×D1114yes—
468#103—112no—
469#103—112no—
470#102—112no—
471#102—118no—
472#102—112no—
473#102C22×D1118yes—
474#97—114no—
475C4×C8—114no—
476C4×C8—112no—
477C4×C8—112no—
478C2×C11—22no—
479C2×C11—81no—
480C2×C11—84no—
481C2×C11C2×#55011yescharacteristic
482C2×C11C2×#57612yes—
483D11—81no—
484D11—84no—
485C24—22no—
486C24—222no—
487#41—22no—
488#41—22no—
489#41—222no—
490#41—222no—
491#41—888no—
492#41—888no—
493C2×Q8—114no—
494C2×Q8—111no—
495C2×Q8C23×D1111yescharacteristic
496C2×D4—21no—
497C2×D4—22no—
498C2×D4—24no—
499C2×D4—24no—
500C2×D4—24no—
501C2×D4—24no—
502C2×D4—84no—
503C2×D4—114no—
504C2×D4—111no—
505C2×D4—228no—
506C2×D4—228no—
507C2×D4—221no—
508C2×D4—222no—
509C2×D4—224no—
510C2×D4—224no—
511C2×D4—224no—
512C2×D4—224no—
513C2×D4—884no—
514C2×D4C23×D1111yescharacteristic
515C2×D4C23×D1114yes—
516C22×C4—21no—
517C22×C4—22no—
518C22×C4—228no—
519C22×C4—228no—
520C22×C4—221no—
521C22×C4—222no—
522C22×C4D4×D1112yes—
523C22×C4C23×D1111yescharacteristic
524Q16—222no—
525SD16—44no—
526SD16—222no—
527SD16—222no—
528SD16—444no—
529D8—44no—
530D8—228no—
531D8—228no—
532D8—222no—
533D8—444no—
534D8—448no—
535M16—24no—
536C2×C8—114no—
537C2×C8—111no—
538C2×C8—111no—
539C2×C8—112no—
540C2×C8—222no—
541C2×C8C23×D1114yes—
542C4⋊C4—22no—
543C4⋊C4—114no—
544C4⋊C4—114no—
545C4⋊C4—118no—
546C4⋊C4—112no—
547C4⋊C4—222no—
548C4⋊C4C23×D1112yes—
549C22⋊C4—21no—
550C22⋊C4—22no—
551C22⋊C4—114no—
552C22⋊C4—228no—
553C22⋊C4—228no—
554C22⋊C4—228no—
555C22⋊C4—228no—
556C22⋊C4—221no—
557C22⋊C4—222no—
558C42—21no—
559C42—22no—
560C42—114no—
561C42—221no—
562C42—222no—
563C42D4×D1111yescharacteristic
564C42D4×D1111yescharacteristic
565C42C23×D1112yes—
566C11#6140911yescharacteristic, complemented, Sylow
567C23—21no—
568C23—24no—
569C23—44no—
570C23—84no—
571C23—224no—
572C23—221no—
573C23—444no—
574C23—884no—
575C23C2×D4×D1111yescharacteristic
576Q8—21no—
577Q8—21no—
578Q8—228no—
579Q8—221no—
580Q8—221no—
581D4—21no—
582D4—24no—
583D4—24no—
584D4—21no—
585D4—42no—
586D4—48no—
587D4—44no—
588D4—84no—
589D4—221no—
590D4—224no—
591D4—224no—
592D4—221no—
593D4—442no—
594D4—448no—
595D4—444no—
596D4—884no—
597D4—888no—
598D4—888no—
599C2×C4—24no—
600C2×C4—22no—
601C2×C4—21no—
602C2×C4—44no—
603C2×C4—42no—
604C2×C4—118no—
605C2×C4—221no—
606C2×C4—222no—
607C2×C4—444no—
608C2×C4—442no—
609C2×C4—888no—
610C2×C4—888no—
611C2×C4C2×D4×D1112yes—
612C2×C4C2×D4×D1112yes—
613C2×C4C2×D4×D1111yescharacteristic
614C2×C4#6703712yes—
615C2×C4#41×D1112yes—
616C2×C4C24×D1111yescharacteristic
617C8—24no—
618C8—112no—
619C8—112no—
620C8—222no—
621C22—22no—
622C22—42no—
623C22—48no—
624C22—41no—
625C22—44no—
626C22—164no—
627C22—442no—
628C22—448no—
629C22—441no—
630C22—444no—
631C22—1764no—
632C22#1062313012yes—
633C22C22×D4×D1111yescharacteristic
634C4—22no—
635C4—42no—
636C4—41no—
637C4—228no—
638C4—442no—
639C4—441no—
640C4#1062313012yes—
641C4#1062330514yes—
642C4C2×#6703711yescharacteristic
643C4C2×#41×D1111yescharacteristic
644C2—22no—
645C2—84no—
646C2—81no—
647C2—884no—
648C2—881no—
649C2C2×#1062313011yescharacteristic
650C2C2×#1062330512yes—
subgroupG/H
centerC22C22×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3038C2
socleC22×C11C23×D4
hypercenter#3038D11
hypocenterC11#61409
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3038

Complements

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

NH ≅ G/Ntype
1. #13082492C2semidirect
2. #13082490C2semidirect
3. #13081662C2semidirect
4. #13081657C2semidirect
5. #13081627C2semidirect
6. #13081587C2semidirect
7. #13079101C2semidirect
8. C2×#10622686C2semidirect
9. #13078121C2semidirect
10. #13078118C2semidirect
11. #13078097C2semidirect
12. #13077546C2semidirect
13. #13077464C2semidirect
14. C4×#67003C2semidirect
15. C11×#3038C2semidirect
28. #10623249C22semidirect
30. #10623244C22semidirect
31. #10623116C22semidirect
32. #10623084C22semidirect
40. C11×#460C22semidirect
41. C11×#459C22semidirect
45. #10622789C22semidirect
46. #10622781C22semidirect
47. #10622778C22semidirect
48. #10622767C22semidirect
49. #10622764C22semidirect
50. #10622763C22semidirect
56. C4×#4326C22semidirect
57. C4×#4325C22semidirect
58. C4×#4324C22semidirect
59. C4×#4323C22semidirect
63. #10622461C22semidirect
64. #10622456C22semidirect
65. #10622444C22semidirect
66. #10622443C22semidirect
67. #10622400C22semidirect
68. #10622399C22semidirect
69. #10622398C22semidirect
70. #10622369C22semidirect
236. C2×C11⋊C8#41semidirect
253. #3038D11semidirect
344. #460C2×D11semidirect
348. #459C2×D11semidirect
566. C11#61409semidirect

Maximal subgroups

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

subgroupindex
#130824922
#130824902
#130816622
#130816572
#130816272
#130815872
#130791012
C2×#106226862
#130781212
#130781182
#130780972
#130775462
#130774642
C4×#670032
C11×#30382
#6140911