Finite Group Databasebeta

← #14743451

Subgroups — #14743451

Order 2816.

648 conjugacy classes of subgroups.

The subgroup lattice has 614 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13080841C211yesmaximal, characteristic, complemented
2#13080527C211yesmaximal, characteristic, complemented
3#13080431C211yesmaximal, characteristic
4#13068279C211yesmaximal, characteristic, complemented
5#13068165C211yesmaximal, characteristic, complemented
6#13068060C211yesmaximal, characteristic, complemented
7#13068055C211yesmaximal, characteristic, complemented
8#13067978C211yesmaximal, characteristic, complemented
9#13067898C211yesmaximal, characteristic, complemented
10#13067886C211yesmaximal, characteristic, complemented
11#13067793C211yesmaximal, characteristic, complemented
12#13067726C211yesmaximal, characteristic, complemented
13#13067446C211yesmaximal, characteristic, complemented
14#13067426C211yesmaximal, characteristic, complemented
15C11×#3393C211yesmaximal, characteristic, complemented
16C11×#556C2211yescharacteristic
17C11×#556C2211yescharacteristic, complemented
18#10623082C2211yescharacteristic
19D4×D44C2211yescharacteristic
20C11×#495—21no—
21C11×#494C2211yescharacteristic, complemented
22C11×#464—21no—
23C11×#464—21no—
24C11×#461C2211yescharacteristic
25C11×#461C2211yescharacteristic, complemented
26C8×Q8×C11C2211yescharacteristic, complemented
27C4×C11×Q16—21no—
28C4×C11×D8C2211yescharacteristic
29#10622769—21no—
30#10622706C2211yescharacteristic, complemented
31#10622701C2211yescharacteristic
32#10622701C2211yescharacteristic
33#10622700C2211yescharacteristic
34#10622700C2211yescharacteristic
35#10622692C2211yescharacteristic, complemented
36#10622664—21no—
37#10622662—21no—
38#10622660—21no—
39#10622659—21no—
40#10622644C2211yescharacteristic, complemented
41#10622640C2211yescharacteristic
42C4×#4325C2211yescharacteristic
43#10622628C2211yescharacteristic
44#10622625C2211yescharacteristic
45D4×C11⋊C8C2211yescharacteristic, complemented
46#10622620C2211yescharacteristic
47#10622616—21no—
48#10622615—21no—
49#10622614—21no—
50#10622609—21no—
51#10622495—21no—
52#10622388—21no—
53D11×#102—21no—
54#10622307C2211yescharacteristic
55C8×D44C2211yescharacteristic
56#10622185C2211yescharacteristic, complemented
57#10622185C2211yescharacteristic, complemented
58Q8⋊(C11⋊C8)C2211yescharacteristic, complemented
59D4⋊(C11⋊C8)C2211yescharacteristic
60D4⋊(C11⋊C8)C2211yescharacteristic, complemented
61#10622124C2211yescharacteristic, complemented
62#10622123C2211yescharacteristic
63#10622121C2211yescharacteristic
64#10622117C2211yescharacteristic, complemented
65#10622096C2211yescharacteristic, complemented
66#10622092C2211yescharacteristic, complemented
67C2×D4×D11—21no—
68C2×#4339—21no—
69C22×D44—21no—
70C2×C11×Q16—21no—
71C2×C11×Q16—21no—
72C2×C11×SD16—21no—
73C2×C11×SD16—21no—
74C2×C11×D8D411yescharacteristic
75C11×C4⋊Q8C2311yescharacteristic
76C11×C4⋊Q8C2311yescharacteristic
77C11×#126—41no—
78C11×#126—41no—
79C11×#124—21no—
80C11×#124—21no—
81C11×C22⋊Q8—21no—
82C11×C22⋊Q8—21no—
83C4×Q8×C11—21no—
84C4×Q8×C11—21no—
85C4×Q8×C11C2311yescharacteristic
86C4×D4×C11C2311yescharacteristic
87C4×D4×C11C2311yescharacteristic
88C11×#117—21no—
89C11×#117—21no—
90C2×#4326—21no—
91C2×#4325—21no—
92C2×#4325D411yescharacteristic
93#66991—21no—
94C2×#4323—21no—
95#66983—21no—
96#66977—21no—
97C2×#4318—21no—
98C22×C11⋊C8—21no—
99C2×C8×D11—21no—
100#66948—21no—
101C4⋊C4×D11—21no—
102#66936—41no—
103#66935—41no—
104#66927C2311yescharacteristic
105C4×D44C2311yescharacteristic
106#66922C2311yescharacteristic
107C11×#107D411yescharacteristic
108C11×C4⋊C8—21no—
109C11×C4⋊C8C2311yescharacteristic
110C11×#103—21no—
111C11×#103—21no—
112C11×#102D411yescharacteristic
113C11×#102D411yescharacteristic
114C4×C8×C11—21no—
115C4×C8×C11C2311yescharacteristic
116#66899D411yescharacteristic
117#66896—21no—
118C22⋊(C11⋊C8)—21no—
119C22⋊(C11⋊C8)—21no—
120#66885—21no—
121#66885—21no—
122(C2×D11)⋊C8—21no—
123#66874—21no—
124#66874—21no—
125#66874—21no—
126#66873—21no—
127#66873—21no—
128#66873—21no—
129#66873—21no—
130#66873—21no—
131#66873—21no—
132#66873—41no—
133#66873D411yescharacteristic
134#66872—41no—
135#66872D411yescharacteristic
136#66871—21no—
137#66871—21no—
138#66871—21no—
139C4⋊(C11⋊C8)C2311yescharacteristic
140C4⋊(C11⋊C8)C2311yescharacteristic
141C4⋊(C11⋊C8)C2311yescharacteristic
142C4×C11⋊C8C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144#19777—111nomaximal, Sylow
145C23×D11—41no—
146C2×Q8×C11—21no—
147C2×Q8×C11—21no—
148C2×Q8×C11C2×D411yescharacteristic
149C2×D4×C11C2×D411yescharacteristic
150C2×D4×C11C2×D411yescharacteristic
151C22×C4×C11—21no—
152C22×C4×C11—21no—
153C2×C22⋊D11—41no—
154C2×C22⋊D11—41no—
155D4×D11—42no—
156D4×D11—81no—
157#4339—42no—
158#4339—81no—
159C2×D44—21no—
160C2×D44—21no—
161C2×D44—21no—
162C2×D44—41no—
163C2×D44—42no—
164C2×D44—81no—
165C2×D44C2×D411yescharacteristic
166C2×C4×D11—21no—
167C2×C4×D11—41no—
168C2×Dic22—21no—
169C11×Q16—42no—
170C11×Q16—81no—
171C11×SD16—81no—
172C11×SD16—81no—
173C11×D8—41no—
174C2×C8×C11—21no—
175C2×C8×C11C2×D411yescharacteristic
176C2×C8×C11C2×D411yescharacteristic
177C11×C4⋊C4—21no—
178C11×C4⋊C4—21no—
179C11×C4⋊C4—21no—
180C11×C4⋊C4—21no—
181C11×C4⋊C4—21no—
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—21no—
189C11×C22⋊C4—41no—
190C11×C22⋊C4—41no—
191C11×C22⋊C4—41no—
192C11×C22⋊C4—41no—
193C42×C11—21no—
194C42×C11—41no—
195C42×C11—41no—
196C42×C11C2411yescharacteristic
197C22⋊Dic11—41no—
198#4326—81no—
199#4325—22no—
200#4325—81no—
201#4323—81no—
202(C2×D11)⋊C4—21no—
203(C2×D11)⋊C4—41no—
204C4⋊Dic11—21no—
205C4⋊Dic11—21no—
206C4⋊Dic11C2×D411yescharacteristic
207Dic11⋊C4—41no—
208#4318—81no—
209C2×C11⋊C8—21no—
210C2×C11⋊C8—21no—
211C2×C11⋊C8—21no—
212C2×C11⋊C8—21no—
213C2×C11⋊C8—81no—
214C2×C11⋊C8C2×D411yescharacteristic
215C2×C11⋊C8C2×D411yescharacteristic
216C8×D11—81no—
217#3393D1111yescharacteristic, complemented
218#3324—111no—
219#3302—111no—
220#3294—111no—
221#1720—111no—
222#1699—111no—
223#1682—111no—
224#1681—111no—
225#1669—111no—
226#1654—111no—
227#1652—111no—
228#1639—111no—
229#1628—111no—
230#1581—111no—
231SD16⋊C8—111no—
232C23×C11—21no—
233C23×C11—21no—
234C22×D11—21no—
235C22×D11—41no—
236C22×D11—82no—
237C22×D11—82no—
238C22×D11—161no—
239Q8×C11—21no—
240Q8×C11—21no—
241Q8×C11—41no—
242Q8×C11—41no—
243Q8×C11—41no—
244Q8×C11—41no—
245D4×C11—21no—
246D4×C11—21no—
247D4×C11—21no—
248D4×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×C11—41no—
258C2×C4×C11—41no—
259C2×C4×C11C22×D411yescharacteristic
260C2×C4×C11C22×D411yescharacteristic
261C2×C4×C11H(5,𝔽2)11yescharacteristic
262C22⋊D11—82no—
263C22⋊D11—82no—
264C2×Dic11—21no—
265C2×Dic11—41no—
266D44—21no—
267D44—41no—
268D44—41no—
269D44—41no—
270D44—41no—
271D44—81no—
272D44—82no—
273D44#13512yes—
274C4×D11—41no—
275C4×D11—41no—
276C4×D11—82no—
277Dic22—41no—
278Dic22—41no—
279C8×C11—21no—
280C8×C11—21no—
281C8×C11—41no—
282C11⋊C8—21no—
283C11⋊C8—21no—
284C11⋊C8—41no—
285C11⋊C8—41no—
286C11⋊C8—41no—
287C11⋊C8—41no—
288#556C2×D1111yescharacteristic
289#556C2×D1111yescharacteristic, complemented
290#547—111no—
291D42—111no—
292#498—111no—
293#495—21no—
294#494C2×D1111yescharacteristic, complemented
295#487—111no—
296#486—111no—
297#486—111no—
298#486—111no—
299#485—221no—
300#482—221no—
301#480—221no—
302#474—111no—
303#474—111no—
304#474—111no—
305#468—221no—
306#467—221no—
307#466—221no—
308#464—21no—
309#464—21no—
310#462—111no—
311#461C2×D1111yescharacteristic
312#461C2×D1111yescharacteristic, complemented
313#460—111no—
314#459—111no—
315#452—221no—
316#450—221no—
317#447—221no—
318C8×Q8C2×D1111yescharacteristic, complemented
319C4×Q16—21no—
320C4×SD16—111no—
321C4×D8C2×D1111yescharacteristic
322#436—111no—
323C8×D4—111no—
324C8×D4—111no—
325#418—221no—
326#416—221no—
327C2×#102—221no—
328#335—111no—
329#335—111no—
330#332—111no—
331#332—111no—
332#332—111no—
333#331—111no—
334Q8⋊C8—111no—
335D4⋊C8—111no—
336D4⋊C8—111no—
337D4⋊C8—111no—
338#322—111no—
339C22×C11—41no—
340C22×C11—41no—
341C22×C11—41no—
342C22×C11—41no—
343C22×C11—41no—
344C22×C11—41no—
345C22×C11D4211yescharacteristic
346C2×D11—22no—
347C2×D11—41no—
348C2×D11—41no—
349C2×D11—81no—
350C2×D11—81no—
351C2×D11—81no—
352C2×D11—164no—
353C4×C11—21no—
354C4×C11—41no—
355C4×C11—41no—
356C4×C11—41no—
357C4×C11—41no—
358C4×C11—81no—
359C4×C11—81no—
360C4×C11C2×#13511yescharacteristic
361C4×C11#57511yescharacteristic
362C4×C11#57611yescharacteristic
363C4×C11#57611yescharacteristic
364Dic11—41no—
365Dic11—81no—
366C2×#41—221no—
367C22×D4—221no—
368C22×D4—221no—
369C2×Q16—21no—
370C2×Q16—21no—
371C2×Q16—221no—
372C2×SD16—21no—
373C2×SD16—21no—
374C2×SD16—111no—
375C2×SD16—221no—
376C2×D8—221no—
377C2×D8C22⋊D1111yescharacteristic
378C2×M16—221no—
379C22×C8—221no—
380C22×C8—221no—
381C4⋊Q8—111no—
382C4⋊Q8C22×D1111yescharacteristic
383C4⋊Q8C22×D1111yescharacteristic
384#127—111no—
385#126—41no—
386#126—41no—
387#124—21no—
388#124—21no—
389#123—441no—
390C22⋊Q8—21no—
391C22⋊Q8—21no—
392C22⋊Q8—221no—
393#121—221no—
394#121—221no—
395#121—221no—
396#120—441no—
397C4×Q8—21no—
398C4×Q8—21no—
399C4×Q8C22×D1111yescharacteristic
400C4×D4—111no—
401C4×D4C22×D1111yescharacteristic
402C4×D4C22×D1111yescharacteristic
403#117—21no—
404#117—21no—
405C2×C4⋊C4—221no—
406#107—221no—
407#107—221no—
408#107—221no—
409#107C22⋊D1111yescharacteristic
410#106—111no—
411#106—441no—
412C4⋊C8—21no—
413C4⋊C8—111no—
414C4⋊C8—111no—
415C4⋊C8—111no—
416C4⋊C8C22×D1111yescharacteristic
417#103—21no—
418#103—21no—
419#103—111no—
420#103—221no—
421#103—221no—
422#103—221no—
423#102—111no—
424#102—221no—
425#102—221no—
426#102—221no—
427#102—221no—
428#102—221no—
429#102—221no—
430#102—221no—
431#102—221no—
432#102—221no—
433#102—441no—
434#102C22⋊D1111yescharacteristic
435#102C22⋊D1111yescharacteristic
436C22⋊C8—221no—
437C22⋊C8—221no—
438C22⋊C8—221no—
439C4×C8—21no—
440C4×C8—111no—
441C4×C8—111no—
442C4×C8C22×D1111yescharacteristic
443C2×C11—81no—
444C2×C11—81no—
445C2×C11#326811yescharacteristic
446C2×C11#328011yescharacteristic
447C2×C11#328911yescharacteristic
448D11—42no—
449D11—161no—
450C24—441no—
451#41—442no—
452#41—881no—
453C2×Q8—21no—
454C2×Q8—21no—
455C2×Q8—221no—
456C2×Q8D4×D1111yescharacteristic
457C2×D4—111no—
458C2×D4—221no—
459C2×D4—221no—
460C2×D4—221no—
461C2×D4—441no—
462C2×D4—442no—
463C2×D4—441no—
464C2×D4—442no—
465C2×D4—441no—
466C2×D4—881no—
467C2×D4—881no—
468C2×D4C2×C22⋊D1111yescharacteristic
469C2×D4C2×C22⋊D1111yescharacteristic
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—221no—
473C22×C4—441no—
474Q16—42no—
475Q16—81no—
476Q16—881no—
477SD16—81no—
478SD16—81no—
479SD16—222no—
480SD16—881no—
481D8—41no—
482D8—881no—
483M16—881no—
484C2×C8—21no—
485C2×C8—111no—
486C2×C8—111no—
487C2×C8—221no—
488C2×C8—221no—
489C2×C8—221no—
490C2×C8—221no—
491C2×C8—881no—
492C2×C8—881no—
493C2×C8C2×C22⋊D1111yescharacteristic
494C2×C8C2×C22⋊D1111yescharacteristic
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—41no—
501C4⋊C4—41no—
502C4⋊C4—111no—
503C4⋊C4—221no—
504C4⋊C4—221no—
505C4⋊C4—441no—
506C4⋊C4D4×D1111yescharacteristic
507C4⋊C4C2×C22⋊D1111yescharacteristic
508C4⋊C4C2×C22⋊D1111yescharacteristic
509C22⋊C4—21no—
510C22⋊C4—21no—
511C22⋊C4—41no—
512C22⋊C4—41no—
513C22⋊C4—41no—
514C22⋊C4—41no—
515C22⋊C4—221no—
516C22⋊C4—441no—
517C22⋊C4—441no—
518C42—21no—
519C42—41no—
520C42—41no—
521C42C23×D1111yescharacteristic
522C11#1977711yescharacteristic, complemented, Sylow
523C23—21no—
524C23—21no—
525C23—221no—
526C23—441no—
527C23—882no—
528C23—882no—
529C23—1761no—
530Q8—21no—
531Q8—21no—
532Q8—41no—
533Q8—41no—
534Q8—41no—
535Q8—41no—
536Q8—441no—
537Q8—441no—
538D4—21no—
539D4—21no—
540D4—21no—
541D4—21no—
542D4—112no—
543D4—221no—
544D4—441no—
545D4—441no—
546D4—441no—
547D4—441no—
548D4—881no—
549D4—882no—
550D4—882no—
551D4—882no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—221no—
563C2×C4—441no—
564C2×C4—441no—
565C2×C4—441no—
566C2×C4—882no—
567C2×C4C2×D4×D1111yescharacteristic
568C2×C4#6703711yescharacteristic
569C2×C4C22×C22⋊D1111yescharacteristic
570C8—21no—
571C8—21no—
572C8—41no—
573C8—221no—
574C8—221no—
575C8—441no—
576C8—441no—
577C8—441no—
578C8—441no—
579C22—41no—
580C22—41no—
581C22—41no—
582C22—41no—
583C22—41no—
584C22—41no—
585C22—222no—
586C22—441no—
587C22—441no—
588C22—881no—
589C22—881no—
590C22—881no—
591C22—1764no—
592C22D4×C22⋊D1111yescharacteristic
593C4—21no—
594C4—41no—
595C4—41no—
596C4—41no—
597C4—41no—
598C4—81no—
599C4—81no—
600C4—441no—
601C4—881no—
602C4D11×#13511yescharacteristic
603C4#1062330011yescharacteristic
604C4#1062335311yescharacteristic
605C4#1062336611yescharacteristic
606C2—81no—
607C2—81no—
608C2—442no—
609C2—1761no—
610C2#1308015711yescharacteristic
611C2#1308029511yescharacteristic
612C2#1308038711yescharacteristic
subgroupG/H
centerC22D4×C22⋊D11
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3393C2
socleC22×C11D42
prime radical#13080431C2
hypercenter#3393D11
hypocenterC11#19777
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #3393

Complements

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

NH ≅ G/Ntype
1. #13080841C2semidirect
2. #13080527C2semidirect
4. #13068279C2semidirect
5. #13068165C2semidirect
6. #13068060C2semidirect
7. #13068055C2semidirect
8. #13067978C2semidirect
9. #13067898C2semidirect
10. #13067886C2semidirect
11. #13067793C2semidirect
12. #13067726C2semidirect
13. #13067446C2semidirect
14. #13067426C2semidirect
15. C11×#3393C2semidirect
17. C11×#556C22semidirect
21. C11×#494C22semidirect
25. C11×#461C22semidirect
26. C8×Q8×C11C22semidirect
30. #10622706C22semidirect
35. #10622692C22semidirect
40. #10622644C22semidirect
45. D4×C11⋊C8C22semidirect
56. #10622185C22semidirect
57. #10622185C22semidirect
58. Q8⋊(C11⋊C8)C22semidirect
60. D4⋊(C11⋊C8)C22semidirect
61. #10622124C22semidirect
64. #10622117C22semidirect
65. #10622096C22semidirect
66. #10622092C22semidirect
217. #3393D11semidirect
289. #556C2×D11semidirect
294. #494C2×D11semidirect
312. #461C2×D11semidirect
318. C8×Q8C2×D11semidirect
522. C11#19777semidirect

Maximal subgroups

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

subgroupindex
#130808412
#130805272
#130804312
#130682792
#130681652
#130680602
#130680552
#130679782
#130678982
#130678862
#130677932
#130677262
#130674462
#130674262
C11×#33932
#1977711