Finite Group Databasebeta

← #14744111

Subgroups — #14744111

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#13081254C211yesmaximal, characteristic, complemented
2#13080841C211yesmaximal, characteristic
3SD16×D44C211yesmaximal, characteristic
4#13068271C211yesmaximal, characteristic, complemented
5#13068161C211yesmaximal, characteristic, complemented
6#13068062C211yesmaximal, characteristic, complemented
7#13068036C211yesmaximal, characteristic, complemented
8#13067964C211yesmaximal, characteristic, complemented
9#13067872C211yesmaximal, characteristic, complemented
10#13067863C211yesmaximal, characteristic, complemented
11#13067794C211yesmaximal, characteristic
12#13067712C211yesmaximal, characteristic, complemented
13#13067460C211yesmaximal, characteristic, complemented
14#13067426C211yesmaximal, characteristic, complemented
15C11×#3364C211yesmaximal, characteristic, complemented
16C11×#557C2211yescharacteristic, complemented
17C11×#556C2211yescharacteristic
18C2×SD16×D11—21no—
19Q8×D44C2211yescharacteristic
20D4×D44C2211yescharacteristic
21C11×#488—21no—
22C11×#487C2211yescharacteristic, complemented
23C11×#479—21no—
24C11×#474C2211yescharacteristic
25C11×#464—21no—
26C11×#462C2211yescharacteristic, complemented
27C8×Q8×C11C2211yescharacteristic, complemented
28C4×C11×Q16—21no—
29C4×C11×SD16C2211yescharacteristic
30#10622701C2211yescharacteristic
31#10622701C2211yescharacteristic
32#10622700C2211yescharacteristic
33#10622696—21no—
34#10622696C2211yescharacteristic
35#10622694—21no—
36#10622694C2211yescharacteristic, complemented
37#10622691C2211yescharacteristic, complemented
38#10622662—21no—
39#10622659—21no—
40#10622640C2211yescharacteristic
41#10622640C2211yescharacteristic
42C4×#4325—21no—
43C4×#4325C2211yescharacteristic
44Q8×C11⋊C8C2211yescharacteristic, complemented
45#10622633—21no—
46#10622633C2211yescharacteristic, complemented
47#10622632C2211yescharacteristic
48#10622625C2211yescharacteristic
49#10622616—21no—
50#10622614—21no—
51#10622477—21no—
52#10622419—21no—
53#10622389—21no—
54#10622306C2211yescharacteristic
55C8×D44C2211yescharacteristic
56#10622185C2211yescharacteristic, complemented
57#10622185C2211yescharacteristic, complemented
58Q8⋊(C11⋊C8)C2211yescharacteristic, complemented
59Q8⋊(C11⋊C8)C2211yescharacteristic, complemented
60D4⋊(C11⋊C8)C2211yescharacteristic
61#10622123C2211yescharacteristic
62#10622121C2211yescharacteristic
63#10622120C2211yescharacteristic, complemented
64#10622117C2211yescharacteristic, complemented
65#10622095C2211yescharacteristic, complemented
66#10622092C2211yescharacteristic, complemented
67C2×Q8×D11—21no—
68C2×D4×D11—21no—
69C22×D44—21no—
70C2×C11×Q16—21no—
71C2×C11×SD16D411yescharacteristic
72C11×C4⋊Q8—21no—
73C11×C4⋊Q8C2311yescharacteristic
74C11×C4⋊Q8C2311yescharacteristic
75C11×#126—41no—
76C11×#125—21no—
77C11×#125—41no—
78C11×#124—21no—
79C11×C22⋊Q8—21no—
80C4×Q8×C11—21no—
81C4×Q8×C11—21no—
82C4×Q8×C11—21no—
83C4×Q8×C11C2311yescharacteristic
84C4×Q8×C11C2311yescharacteristic
85C4×D4×C11C2311yescharacteristic
86C11×#117—21no—
87C2×#4325—21no—
88C2×#4325—21no—
89C2×#4325—21no—
90C2×#4325D411yescharacteristic
91C2×#4324—21no—
92#66983—21no—
93C2×#4318—21no—
94SD16×D11—44no—
95C2×#4314—21no—
96C2×#4314—21no—
97C2×C8×D11—21no—
98#66950—21no—
99#66950—41no—
100#66948—21no—
101#66935—41no—
102#66927C2311yescharacteristic
103C4×D44—21no—
104C4×D44C2311yescharacteristic
105#66922—21no—
106#66922C2311yescharacteristic
107C11×#107—21no—
108C11×#106D411yescharacteristic
109C11×C4⋊C8—21no—
110C11×C4⋊C8C2311yescharacteristic
111C11×#103—21no—
112C11×#103—21no—
113C11×#103—21no—
114C11×#103D411yescharacteristic
115C11×#102—21no—
116C11×#102D411yescharacteristic
117C4×C8×C11—21no—
118C4×C8×C11C2311yescharacteristic
119#66899—21no—
120#66899—21no—
121#66899—21no—
122#66899—21no—
123#66899D411yescharacteristic
124C22⋊(C11⋊C8)—21no—
125(C2×D11)⋊C8—21no—
126#66874—21no—
127#66873—21no—
128#66873—21no—
129#66873—21no—
130#66873—21no—
131#66873—21no—
132#66873—41no—
133#66873D411yescharacteristic
134#66872—21no—
135#66872D411yescharacteristic
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×C11C2×D411yescharacteristic
150C2×Q8×C11C2×D411yescharacteristic
151C2×D4×C11C2×D411yescharacteristic
152C22×C4×C11—21no—
153C2×C22⋊D11—41no—
154Q8×D11—42no—
155Q8×D11—81no—
156D4×D11—42no—
157D4×D11—81no—
158C2×D44—21no—
159C2×D44—21no—
160C2×D44—21no—
161C2×D44—41no—
162C2×D44—42no—
163C2×D44—81no—
164C2×D44C2×D411yescharacteristic
165C2×C4×D11—21no—
166C2×C4×D11—41no—
167C2×Dic22—21no—
168C2×Dic22—41no—
169C11×Q16—42no—
170C11×SD16—22no—
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—
189C11×C22⋊C4—41no—
190C42×C11—21no—
191C42×C11—21no—
192C42×C11—41no—
193C42×C11—41no—
194C42×C11C2411yescharacteristic
195#4325—22no—
196#4325—42no—
197#4325—42no—
198#4325—81no—
199#4324—42no—
200(C2×D11)⋊C4—21no—
201(C2×D11)⋊C4—41no—
202(C2×D11)⋊C4—41no—
203C4⋊Dic11—21no—
204C4⋊Dic11—21no—
205C4⋊Dic11—41no—
206C4⋊Dic11C2×D411yescharacteristic
207#4318—81no—
208C2×C11⋊C8—21no—
209C2×C11⋊C8—21no—
210C2×C11⋊C8—21no—
211C2×C11⋊C8—21no—
212C2×C11⋊C8C2×D411yescharacteristic
213C2×C11⋊C8C2×D411yescharacteristic
214#4314—42no—
215#4314—81no—
216C8×D11—42no—
217#3364D1111yescharacteristic, complemented
218#3359—111no—
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×C11AGL(1,ℤ/8)12yes—
246D4×C11—21no—
247D4×C11—21no—
248C2×C4×C11—21no—
249C2×C4×C11—21no—
250C2×C4×C11—21no—
251C2×C4×C11—21no—
252C2×C4×C11—21no—
253C2×C4×C11—41no—
254C2×C4×C11—41no—
255C2×C4×C11—41no—
256C2×C4×C11—41no—
257C2×C4×C11C22×D411yescharacteristic
258C2×C4×C11C22×D411yescharacteristic
259C2×C4×C11H(5,𝔽2)11yescharacteristic
260C22⋊D11—82no—
261C2×Dic11—21no—
262C2×Dic11—41no—
263D44—21no—
264D44—41no—
265D44—41no—
266D44—41no—
267D44—41no—
268D44—81no—
269D44—82no—
270D44#13512yes—
271C4×D11—41no—
272C4×D11—41no—
273C4×D11—82no—
274Dic22—41no—
275Dic22—41no—
276Dic22—82no—
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#556C2×D1111yescharacteristic
289D4×Q8—111no—
290D42—111no—
291#500—111no—
292#492—111no—
293#488—21no—
294#487—111no—
295#487—221no—
296#487C2×D1111yescharacteristic, complemented
297#486—111no—
298#486—111no—
299#482—221no—
300#479—21no—
301#475—111no—
302#475—221no—
303#474—111no—
304#474C2×D1111yescharacteristic
305#468—221no—
306#465—221no—
307#464—21no—
308#462C2×D1111yescharacteristic, complemented
309#461—111no—
310#461—111no—
311#461—221no—
312#460—111no—
313#460—111no—
314#450—221no—
315#450—221no—
316#448—221no—
317C8×Q8—111no—
318C8×Q8C2×D1111yescharacteristic, complemented
319C4×Q16—21no—
320C4×SD16—111no—
321C4×SD16—221no—
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—41no—
338C22×C11—41no—
339C22×C11—41no—
340C22×C11D4211yescharacteristic
341C2×D11—22no—
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—221no—
363C22×D4—221no—
364C22×D4—221no—
365C2×Q16—21no—
366C2×SD16—111no—
367C2×SD16—221no—
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—111no—
379C4⋊Q8—221no—
380C4⋊Q8C22×D1111yescharacteristic
381C4⋊Q8C22×D1111yescharacteristic
382#127—111no—
383#126—41no—
384#125—21no—
385#125—41no—
386#124—21no—
387C22⋊Q8—21no—
388C22⋊Q8—221no—
389C22⋊Q8—441no—
390#121—221no—
391#121—221no—
392#120—441no—
393C4×Q8—21no—
394C4×Q8—21no—
395C4×Q8—21no—
396C4×Q8C22×D1111yescharacteristic
397C4×Q8C22×D1111yescharacteristic
398C4×D4—111no—
399C4×D4—221no—
400C4×D4C22×D1111yescharacteristic
401#117—21no—
402#107—21no—
403#107—221no—
404#107—441no—
405#106—111no—
406#106—221no—
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—111no—
418#103—221no—
419#103—221no—
420#103—221no—
421#103—221no—
422#103—221no—
423#103C22⋊D1111yescharacteristic
424#102—21no—
425#102—111no—
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—81no—
441C2×C11#326511yescharacteristic
442C2×C11#328211yescharacteristic
443C2×C11#328911yescharacteristic
444D11—42no—
445D11—161no—
446C24—441no—
447C2×Q8—21no—
448C2×Q8—21no—
449C2×Q8—221no—
450C2×Q8—441no—
451C2×Q8—442no—
452C2×Q8—881no—
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—221no—
468C22×C4—441no—
469Q16—42no—
470SD16—22no—
471SD16—222no—
472SD16—442no—
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—41no—
509C22⋊C4—221no—
510C22⋊C4—441no—
511C22⋊C4—441no—
512C42—21no—
513C42—21no—
514C42—41no—
515C42—41no—
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—441no—
532Q8—441no—
533Q8—882no—
534Q8#6700212yes—
535D4—21no—
536D4—21no—
537D4—112no—
538D4—221no—
539D4—441no—
540D4—441no—
541D4—441no—
542D4—441no—
543D4—881no—
544D4—882no—
545D4—882no—
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—221no—
556C2×C4—441no—
557C2×C4—441no—
558C2×C4—441no—
559C2×C4—882no—
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—41no—
573C22—41no—
574C22—41no—
575C22—222no—
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—
593C4D11×#13511yescharacteristic
594C4#1062330111yescharacteristic
595C4C2×#6700211yescharacteristic
596C4#1062336811yescharacteristic
597C2—81no—
598C2—442no—
599C2—1761no—
600C2#1308011211yescharacteristic
601C2#1308031711yescharacteristic
602C2#1308038711yescharacteristic
subgroupG/H
centerC22D4×C22⋊D11
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3364C2
socleC22×C11D42
prime radicalD4×D44C22
hypercenter#3364D11
hypocenterC11#19821
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #3364

Complements

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

NH ≅ G/Ntype
1. #13081254C2semidirect
4. #13068271C2semidirect
5. #13068161C2semidirect
6. #13068062C2semidirect
7. #13068036C2semidirect
8. #13067964C2semidirect
9. #13067872C2semidirect
10. #13067863C2semidirect
12. #13067712C2semidirect
13. #13067460C2semidirect
14. #13067426C2semidirect
15. C11×#3364C2semidirect
16. C11×#557C22semidirect
22. C11×#487C22semidirect
26. C11×#462C22semidirect
27. C8×Q8×C11C22semidirect
36. #10622694C22semidirect
37. #10622691C22semidirect
44. Q8×C11⋊C8C22semidirect
46. #10622633C22semidirect
56. #10622185C22semidirect
57. #10622185C22semidirect
58. Q8⋊(C11⋊C8)C22semidirect
59. Q8⋊(C11⋊C8)C22semidirect
63. #10622120C22semidirect
64. #10622117C22semidirect
65. #10622095C22semidirect
66. #10622092C22semidirect
217. #3364D11semidirect
287. #557C2×D11semidirect
296. #487C2×D11semidirect
308. #462C2×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
#130812542
#130808412
SD16×D442
#130682712
#130681612
#130680622
#130680362
#130679642
#130678722
#130678632
#130677942
#130677122
#130674602
#130674262
C11×#33642
#1982111