Finite Group Databasebeta

← #14744110

Subgroups — #14744110

Order 2816.

660 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081301C211yesmaximal, characteristic, complemented
2#13080849C211yesmaximal, characteristic
3D4×#4325C211yesmaximal, characteristic
4#13068270C211yesmaximal, characteristic, complemented
5#13068160C211yesmaximal, characteristic, complemented
6#13068060C211yesmaximal, characteristic, complemented
7#13068041C211yesmaximal, characteristic, complemented
8#13067966C211yesmaximal, characteristic, complemented
9#13067871C211yesmaximal, characteristic, complemented
10#13067865C211yesmaximal, characteristic, complemented
11#13067793C211yesmaximal, characteristic
12#13067712C211yesmaximal, characteristic, complemented
13#13067459C211yesmaximal, characteristic, complemented
14SD16⋊(C11⋊C8)C211yesmaximal, characteristic, complemented
15C11×#3359C211yesmaximal, characteristic, complemented
16C11×#557C2211yescharacteristic, complemented
17D4×Q8×C11C2211yescharacteristic
18C22×#4325—21no—
19#10623115C2211yescharacteristic
20D4×D44C2211yescharacteristic
21C11×#487—21no—
22C11×#487C2211yescharacteristic, complemented
23C11×#475—21no—
24C11×#475C2211yescharacteristic, complemented
25C11×#461—21no—
26C11×#461C2211yescharacteristic
27C8×Q8×C11C2211yescharacteristic, complemented
28C4×C11×SD16—21no—
29C4×C11×SD16C2211yescharacteristic
30#10622840—21no—
31#10622782—21no—
32#10622706C2211yescharacteristic, complemented
33#10622701C2211yescharacteristic
34#10622700C2211yescharacteristic
35#10622698C2211yescharacteristic
36#10622696C2211yescharacteristic
37#10622691C2211yescharacteristic, complemented
38#10622681—21no—
39#10622676—21no—
40#10622661—21no—
41#10622659—21no—
42#10622644C2211yescharacteristic, complemented
43C4×#4326—21no—
44#10622641—21no—
45#10622640C2211yescharacteristic
46#10622640C2211yescharacteristic
47C4×#4325C2211yescharacteristic
48Q8×C11⋊C8C2211yescharacteristic, complemented
49D4×C11⋊C8C2211yescharacteristic
50#10622620C2211yescharacteristic
51#10622479—21no—
52#10622425—21no—
53#10622383—21no—
54#10622307C2211yescharacteristic
55#10622301C2211yescharacteristic
56#10622185C2211yescharacteristic, complemented
57#10622185C2211yescharacteristic, complemented
58Q8⋊(C11⋊C8)C2211yescharacteristic, complemented
59Q8⋊(C11⋊C8)C2211yescharacteristic, complemented
60D4⋊(C11⋊C8)C2211yescharacteristic
61#10622124C2211yescharacteristic, complemented
62#10622123C2211yescharacteristic
63#10622121C2211yescharacteristic
64#10622118C2211yescharacteristic, complemented
65#10622096C2211yescharacteristic, complemented
66#10622093C2211yescharacteristic, complemented
67C22×Q8×C11—21no—
68C2×D4×D11—21no—
69C22×D44—21no—
70C2×C11×SD16—21no—
71C2×C11×SD16D411yescharacteristic
72C11×C4⋊Q8—21no—
73C11×C4⋊Q8—21no—
74C11×C4⋊Q8C2311yescharacteristic
75C11×C4⋊Q8C2311yescharacteristic
76C11×#125—21no—
77C11×#125—41no—
78C11×C22⋊Q8—21no—
79C11×C22⋊Q8—41no—
80C4×Q8×C11—21no—
81C4×Q8×C11—21no—
82C4×Q8×C11C2311yescharacteristic
83C4×Q8×C11C2311yescharacteristic
84C4×D4×C11—21no—
85C4×D4×C11C2311yescharacteristic
86#66999—21no—
87C2×#4326—21no—
88C2×#4325—21no—
89C2×#4325—21no—
90C2×#4325—21no—
91C2×#4325—21no—
92C2×#4325—21no—
93C2×#4325—44no—
94C2×#4325D411yescharacteristic
95#66983—21no—
96C22×C11⋊C8—21no—
97C2×#4313—21no—
98#66951—41no—
99#66948—21no—
100#66945—21no—
101#66935—41no—
102#66928—21no—
103#66927C2311yescharacteristic
104C4×D44C2311yescharacteristic
105#66922C2311yescharacteristic
106C4×Dic22—21no—
107C11×#106—21no—
108C11×#106D411yescharacteristic
109C11×C4⋊C8—21no—
110C11×C4⋊C8C2311yescharacteristic
111C11×#103—21no—
112C11×#103—21no—
113C11×#103—21no—
114C11×#103—21no—
115C11×#103D411yescharacteristic
116C11×#102D411yescharacteristic
117C4×C8×C11—21no—
118C4×C8×C11C2311yescharacteristic
119#66899—21no—
120#66899D411yescharacteristic
121#66896—21no—
122C22⋊(C11⋊C8)—21no—
123#66885—21no—
124#66885—21no—
125(C2×D11)⋊C8—21no—
126#66874—21no—
127#66874—21no—
128#66874—21no—
129#66873—21no—
130#66873—21no—
131#66873—21no—
132#66873—41no—
133#66873D411yescharacteristic
134#66872D411yescharacteristic
135#66871—21no—
136#66871—21no—
137#66871—41no—
138C4⋊(C11⋊C8)—21no—
139C4⋊(C11⋊C8)C2311yescharacteristic
140C4⋊(C11⋊C8)C2311yescharacteristic
141C4⋊(C11⋊C8)C2311yescharacteristic
142C4×C11⋊C8—21no—
143C4×C11⋊C8C2311yescharacteristic
144C4×C11⋊C8C2311yescharacteristic
145#19821—111nomaximal, Sylow
146C23×D11—41no—
147C2×Q8×C11—21no—
148C2×Q8×C11—21no—
149C2×Q8×C11—41no—
150C2×Q8×C11—42no—
151C2×Q8×C11—81no—
152C2×Q8×C11C2×D411yescharacteristic
153C2×Q8×C11C2×D411yescharacteristic
154C2×D4×C11C2×D411yescharacteristic
155C22×C4×C11—21no—
156C22×C4×C11—41no—
157C2×C22⋊D11—41no—
158D4×D11—42no—
159D4×D11—81no—
160C2×D44—21no—
161C2×D44—21no—
162C2×D44—21no—
163C2×D44—41no—
164C2×D44—42no—
165C2×D44—81no—
166C2×D44C2×D411yescharacteristic
167C2×C4×D11—21no—
168C2×Dic22—21no—
169C11×SD16—22no—
170C11×SD16—42no—
171C2×C8×C11—21no—
172C2×C8×C11C2×D411yescharacteristic
173C2×C8×C11C2×D411yescharacteristic
174C11×C4⋊C4—21no—
175C11×C4⋊C4—21no—
176C11×C4⋊C4—21no—
177C11×C4⋊C4—21no—
178C11×C4⋊C4—21no—
179C11×C4⋊C4—21no—
180C11×C4⋊C4—41no—
181C11×C4⋊C4—41no—
182C11×C4⋊C4—41no—
183C11×C4⋊C4—41no—
184C11×C4⋊C4C2×D411yescharacteristic
185C11×C4⋊C4C2×D411yescharacteristic
186C11×C4⋊C4C2×D411yescharacteristic
187C11×C22⋊C4—21no—
188C11×C22⋊C4—41no—
189C42×C11—21no—
190C42×C11—21no—
191C42×C11—41no—
192C42×C11C2411yescharacteristic
193#4326—42no—
194#4325—22no—
195#4325—42no—
196#4325—42no—
197#4325—42no—
198#4325—81no—
199#4325—81no—
200(C2×D11)⋊C4—21no—
201(C2×D11)⋊C4—41no—
202(C2×D11)⋊C4—41no—
203(C2×D11)⋊C4—41no—
204C4⋊Dic11—21no—
205C4⋊Dic11—21no—
206C4⋊Dic11C2×D411yescharacteristic
207Dic11⋊C4—41no—
208C4×Dic11—41no—
209C2×C11⋊C8—21no—
210C2×C11⋊C8—21no—
211C2×C11⋊C8—21no—
212C2×C11⋊C8—21no—
213C2×C11⋊C8—42no—
214C2×C11⋊C8C2×D411yescharacteristic
215C2×C11⋊C8C2×D411yescharacteristic
216#4313—81no—
217#3364—111no—
218#3359D1111yescharacteristic, complemented
219#3324—111no—
220D4×SD16—111no—
221#1719—111no—
222#1699—111no—
223#1682—111no—
224#1679—111no—
225#1666—111no—
226#1650—111no—
227#1649—111no—
228#1639—111no—
229#1626—111no—
230#1583—111no—
231SD16⋊C8—111no—
232C23×C11—21no—
233C22×D11—21no—
234C22×D11—41no—
235C22×D11—82no—
236C22×D11—82no—
237C22×D11—161no—
238Q8×C11—21no—
239Q8×C11—21no—
240Q8×C11—21no—
241Q8×C11—41no—
242Q8×C11—41no—
243Q8×C11—41no—
244Q8×C11—41no—
245Q8×C11—82no—
246Q8×C11AGL(1,ℤ/8)12yes—
247D4×C11—21no—
248D4×C11#13512yes—
249C2×C4×C11—21no—
250C2×C4×C11—21no—
251C2×C4×C11—21no—
252C2×C4×C11—21no—
253C2×C4×C11—21no—
254C2×C4×C11—41no—
255C2×C4×C11—41no—
256C2×C4×C11—41no—
257C2×C4×C11—41no—
258C2×C4×C11—82no—
259C2×C4×C11C22×D411yescharacteristic
260C2×C4×C11C22×D411yescharacteristic
261C2×C4×C11H(5,𝔽2)11yescharacteristic
262C22⋊D11—82no—
263C2×Dic11—21no—
264C2×Dic11—41no—
265D44—21no—
266D44—21no—
267D44—41no—
268D44—41no—
269D44—41no—
270D44—41no—
271D44—81no—
272D44—82no—
273C4×D11—41no—
274C4×D11—41no—
275Dic22—41no—
276Dic22—41no—
277C8×C11—21no—
278C8×C11—21no—
279C8×C11—41no—
280C11⋊C8—21no—
281C11⋊C8—21no—
282C11⋊C8—41no—
283C11⋊C8—41no—
284C11⋊C8—41no—
285C11⋊C8—41no—
286C22×SD16—221no—
287#557C2×D1111yescharacteristic, complemented
288#556—111no—
289D4×Q8C2×D1111yescharacteristic
290D42—111no—
291#500—111no—
292#492—111no—
293#488—221no—
294#487—21no—
295#487—111no—
296#487C2×D1111yescharacteristic, complemented
297#486—111no—
298#486—111no—
299#482—221no—
300#479—221no—
301#475—21no—
302#475C2×D1111yescharacteristic, complemented
303#474—111no—
304#474—111no—
305#468—221no—
306#465—221no—
307#464—221no—
308#462—111no—
309#461—21no—
310#461—111no—
311#461C2×D1111yescharacteristic
312#460—111no—
313#460—111no—
314#450—221no—
315#450—221no—
316#448—221no—
317C8×Q8—111no—
318C8×Q8C2×D1111yescharacteristic, complemented
319C4×Q16—221no—
320C4×SD16—21no—
321C4×SD16—111no—
322C4×SD16C2×D1111yescharacteristic
323#436—111no—
324C8×D4—111no—
325#418—221no—
326#335—111no—
327#334—111no—
328#332—111no—
329#332—111no—
330#332—111no—
331#331—111no—
332Q8⋊C8—111no—
333Q8⋊C8—111no—
334D4⋊C8—111no—
335D4⋊C8—111no—
336#322—111no—
337C22×C11—22no—
338C22×C11—41no—
339C22×C11—41no—
340C22×C11D4211yescharacteristic
341C2×D11—41no—
342C2×D11—41no—
343C2×D11—41no—
344C2×D11—81no—
345C2×D11—81no—
346C2×D11—81no—
347C2×D11—164no—
348C4×C11—22no—
349C4×C11—21no—
350C4×C11—41no—
351C4×C11—41no—
352C4×C11—41no—
353C4×C11—41no—
354C4×C11—81no—
355C4×C11—81no—
356C4×C11C2×#13511yescharacteristic
357C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
358C4×C11#57711yescharacteristic
359C4×C11#57711yescharacteristic
360Dic11—41no—
361Dic11—81no—
362C22×Q8—21no—
363C22×D4—221no—
364C22×D4—221no—
365C2×Q16—221no—
366C2×SD16—21no—
367C2×SD16—111no—
368C2×SD16—221no—
369C2×SD16—221no—
370C2×SD16—221no—
371C2×SD16—221no—
372C2×SD16—221no—
373C2×SD16—444no—
374C2×SD16C22⋊D1111yescharacteristic
375C2×M16—221no—
376C22×C8—221no—
377C4⋊Q8—21no—
378C4⋊Q8—21no—
379C4⋊Q8—111no—
380C4⋊Q8C22×D1111yescharacteristic
381C4⋊Q8C22×D1111yescharacteristic
382#127—111no—
383#126—441no—
384#125—21no—
385#125—41no—
386#124—221no—
387C22⋊Q8—21no—
388C22⋊Q8—41no—
389C22⋊Q8—221no—
390#121—221no—
391#121—221no—
392#120—441no—
393C4×Q8—21no—
394C4×Q8—21no—
395C4×Q8—221no—
396C4×Q8C22×D1111yescharacteristic
397C4×Q8C22×D1111yescharacteristic
398C4×D4—21no—
399C4×D4—111no—
400C4×D4C22×D1111yescharacteristic
401#117—221no—
402#107—221no—
403#107—221no—
404#107—441no—
405#106—21no—
406#106—111no—
407#106C22⋊D1111yescharacteristic
408C4⋊C8—21no—
409C4⋊C8—111no—
410C4⋊C8—111no—
411C4⋊C8—111no—
412C4⋊C8—221no—
413C4⋊C8C22×D1111yescharacteristic
414#103—21no—
415#103—21no—
416#103—21no—
417#103—21no—
418#103—111no—
419#103—221no—
420#103—221no—
421#103—221no—
422#103—221no—
423#103C22⋊D1111yescharacteristic
424#102—111no—
425#102—221no—
426#102—221no—
427#102—221no—
428#102—221no—
429#102—221no—
430#102—221no—
431#102—441no—
432#102C22⋊D1111yescharacteristic
433C22⋊C8—221no—
434C22⋊C8—221no—
435C4×C8—21no—
436C4×C8—111no—
437C4×C8—111no—
438C4×C8—221no—
439C4×C8C22×D1111yescharacteristic
440C2×C11—42no—
441C2×C11#326511yescharacteristic
442C2×C11#328211yescharacteristic
443C2×C11#328911yescharacteristic
444D11—81no—
445D11—161no—
446C24—441no—
447C2×Q8—21no—
448C2×Q8—21no—
449C2×Q8—41no—
450C2×Q8—42no—
451C2×Q8—81no—
452C2×Q8—221no—
453C2×Q8D4×D1111yescharacteristic
454C2×Q8C2×C22⋊D1111yescharacteristic
455C2×D4—111no—
456C2×D4—221no—
457C2×D4—221no—
458C2×D4—221no—
459C2×D4—441no—
460C2×D4—442no—
461C2×D4—441no—
462C2×D4—442no—
463C2×D4—881no—
464C2×D4—881no—
465C2×D4C2×C22⋊D1111yescharacteristic
466C22×C4—21no—
467C22×C4—41no—
468C22×C4—221no—
469Q16—442no—
470SD16—22no—
471SD16—42no—
472SD16—222no—
473SD16—442no—
474SD16—442no—
475SD16—442no—
476SD16—881no—
477SD16—881no—
478M16—881no—
479C2×C8—21no—
480C2×C8—111no—
481C2×C8—111no—
482C2×C8—221no—
483C2×C8—221no—
484C2×C8—221no—
485C2×C8—221no—
486C2×C8—442no—
487C2×C8C2×C22⋊D1111yescharacteristic
488C2×C8C2×C22⋊D1111yescharacteristic
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—41no—
496C4⋊C4—41no—
497C4⋊C4—41no—
498C4⋊C4—41no—
499C4⋊C4—111no—
500C4⋊C4—221no—
501C4⋊C4—221no—
502C4⋊C4—441no—
503C4⋊C4D4×D1111yescharacteristic
504C4⋊C4C2×C22⋊D1111yescharacteristic
505C4⋊C4C2×C22⋊D1111yescharacteristic
506C22⋊C4—21no—
507C22⋊C4—41no—
508C22⋊C4—221no—
509C22⋊C4—441no—
510C22⋊C4—441no—
511C22⋊C4—441no—
512C42—21no—
513C42—21no—
514C42—41no—
515C42—441no—
516C42C23×D1111yescharacteristic
517C11#1982111yescharacteristic, complemented, Sylow
518C23—21no—
519C23—221no—
520C23—441no—
521C23—882no—
522C23—882no—
523C23—1761no—
524Q8—21no—
525Q8—21no—
526Q8—21no—
527Q8—41no—
528Q8—41no—
529Q8—41no—
530Q8—41no—
531Q8—82no—
532Q8—441no—
533Q8—441no—
534Q8#6696712yes—
535D4—21no—
536D4—221no—
537D4—221no—
538D4—441no—
539D4—441no—
540D4—441no—
541D4—441no—
542D4—881no—
543D4—882no—
544D4—882no—
545D4#6700312yes—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—82no—
556C2×C4—221no—
557C2×C4—441no—
558C2×C4—441no—
559C2×C4—441no—
560C2×C4C2×D4×D1111yescharacteristic
561C2×C4#6703711yescharacteristic
562C2×C4C22×C22⋊D1111yescharacteristic
563C8—21no—
564C8—21no—
565C8—41no—
566C8—221no—
567C8—221no—
568C8—441no—
569C8—441no—
570C8—441no—
571C8—441no—
572C22—22no—
573C22—41no—
574C22—41no—
575C22—441no—
576C22—441no—
577C22—441no—
578C22—881no—
579C22—881no—
580C22—881no—
581C22—1764no—
582C22D4×C22⋊D1111yescharacteristic
583C4—22no—
584C4—21no—
585C4—41no—
586C4—41no—
587C4—41no—
588C4—41no—
589C4—81no—
590C4—81no—
591C4—441no—
592C4—881no—
593C4C2×#6696711yescharacteristic
594C4#1062329311yescharacteristic
595C4C2×#6700311yescharacteristic
596C4#1062336811yescharacteristic
597C2—42no—
598C2—881no—
599C2—1761no—
600C2#1308011111yescharacteristic
601C2#1308032411yescharacteristic
602C2#1308038711yescharacteristic
subgroupG/H
centerC22D4×C22⋊D11
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3359C2
socleC22×C11D42
prime radicalD4×D44C22
hypercenter#3359D11
hypocenterC11#19821
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #3359

Complements

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

NH ≅ G/Ntype
1. #13081301C2semidirect
4. #13068270C2semidirect
5. #13068160C2semidirect
6. #13068060C2semidirect
7. #13068041C2semidirect
8. #13067966C2semidirect
9. #13067871C2semidirect
10. #13067865C2semidirect
12. #13067712C2semidirect
13. #13067459C2semidirect
14. SD16⋊(C11⋊C8)C2semidirect
15. C11×#3359C2semidirect
16. C11×#557C22semidirect
22. C11×#487C22semidirect
24. C11×#475C22semidirect
27. C8×Q8×C11C22semidirect
32. #10622706C22semidirect
37. #10622691C22semidirect
42. #10622644C22semidirect
48. Q8×C11⋊C8C22semidirect
56. #10622185C22semidirect
57. #10622185C22semidirect
58. Q8⋊(C11⋊C8)C22semidirect
59. Q8⋊(C11⋊C8)C22semidirect
61. #10622124C22semidirect
64. #10622118C22semidirect
65. #10622096C22semidirect
66. #10622093C22semidirect
218. #3359D11semidirect
287. #557C2×D11semidirect
296. #487C2×D11semidirect
302. #475C2×D11semidirect
318. C8×Q8C2×D11semidirect
517. C11#19821semidirect

Maximal subgroups

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

subgroupindex
#130813012
#130808492
D4×#43252
#130682702
#130681602
#130680602
#130680412
#130679662
#130678712
#130678652
#130677932
#130677122
#130674592
SD16⋊(C11⋊C8)2
C11×#33592
#1982111