Finite Group Databasebeta

← #14745401

Subgroups — #14745401

Order 2816.

666 conjugacy classes of subgroups.

The subgroup lattice has 626 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081319C211yesmaximal, characteristic, complemented
2#13080852C211yesmaximal, characteristic, complemented
3#13080442C211yesmaximal, characteristic, complemented
4#13068220C211yesmaximal, characteristic, complemented
5#13068158C211yesmaximal, characteristic, complemented
6#13068147C211yesmaximal, characteristic, complemented
7#13068025C211yesmaximal, characteristic, complemented
8#13068022C211yesmaximal, characteristic, complemented
9#13067761C211yesmaximal, characteristic, complemented
10#13067749C211yesmaximal, characteristic, complemented
11#13067681C211yesmaximal, characteristic, complemented
12#13067669C211yesmaximal, characteristic, complemented
13#13067507C211yesmaximal, characteristic, complemented
14C8×#4323C211yesmaximal, characteristic, complemented
15C11×#3305C211yesmaximal, characteristic, complemented
16C11×#555C2211yescharacteristic
17C11×#550C2211yescharacteristic, complemented
18#10623110C2211yescharacteristic
19D4×D44C2211yescharacteristic
20C11×#486C2211yescharacteristic, complemented
21C11×#482—21no—
22C11×#477C2211yescharacteristic, complemented
23C11×#466—21no—
24C11×#459C2211yescharacteristic
25C11×#449—21no—
26C4×C11×SD16C2211yescharacteristic
27C8×D4×C11C2211yescharacteristic, complemented
28C11×#416—21no—
29#10622782—21no—
30#10622705C2211yescharacteristic, complemented
31#10622701C2211yescharacteristic
32#10622697C2211yescharacteristic
33#10622686C2211yescharacteristic
34#10622685—21no—
35#10622685C2211yescharacteristic
36#10622684—21no—
37#10622683C2211yescharacteristic, complemented
38#10622652—21no—
39#10622649—21no—
40#10622640C2211yescharacteristic
41#10622637C2211yescharacteristic, complemented
42#10622628C2211yescharacteristic
43#10622627—21no—
44C4×#4323C2211yescharacteristic
45#10622625C2211yescharacteristic
46#10622622—21no—
47#10622621C2211yescharacteristic
48#10622621C2211yescharacteristic, complemented
49#10622616—21no—
50#10622614—21no—
51#10622476—21no—
52#10622420—21no—
53D11×#102—21no—
54#10622307C2211yescharacteristic
55C8×D44C2211yescharacteristic
56#10622184C2211yescharacteristic, complemented
57#10622182C2211yescharacteristic, complemented
58Q8⋊(C11⋊C8)C2211yescharacteristic, complemented
59D4⋊(C11⋊C8)C2211yescharacteristic
60D4⋊(C11⋊C8)C2211yescharacteristic, complemented
61#10622123C2211yescharacteristic
62#10622121C2211yescharacteristic
63#10622119C2211yescharacteristic, complemented
64#10622117C2211yescharacteristic, complemented
65#10622095C2211yescharacteristic, complemented
66C8×C11⋊C8C2211yescharacteristic, complemented
67C2×C11×#41—21no—
68C2×D4×D11—21no—
69C22×D44—21no—
70C2×C11×SD16D411yescharacteristic
71C2×C11×D8—21no—
72C22×C8×C11—21no—
73C11×C4⋊Q8C2311yescharacteristic
74C11×#127—21no—
75C11×#127C2311yescharacteristic
76C11×#124—41no—
77C11×#121—21no—
78C11×#121—21no—
79C11×#121—21no—
80C11×#121—41no—
81C4×Q8×C11C2311yescharacteristic
82C4×D4×C11—21no—
83C4×D4×C11C2311yescharacteristic
84C4×D4×C11C2311yescharacteristic
85C11×#117—21no—
86C11×#117—21no—
87#66999—21no—
88C2×#4326—41no—
89C2×#4325—21no—
90C2×#4323—21no—
91C2×#4323—21no—
92C2×#4323—41no—
93C2×#4323D411yescharacteristic
94#66983—21no—
95C2×#4318—21no—
96C2×C8×D11—21no—
97#66949—41no—
98#66948—21no—
99C4⋊C4×D11—21no—
100#66935—41no—
101#66927C2311yescharacteristic
102C4×D44—21no—
103C4×D44C2311yescharacteristic
104#66923—21no—
105#66922C2311yescharacteristic
106C11×#107—21no—
107C11×#106D411yescharacteristic
108C11×C4⋊C8C2311yescharacteristic
109C11×#103—21no—
110C11×#103D411yescharacteristic
111C11×#102—21no—
112C11×#102—21no—
113C11×#102—21no—
114C11×#102D411yescharacteristic
115C11×C22⋊C8—21no—
116C4×C8×C11C2311yescharacteristic
117#66896—21no—
118#66896—21no—
119#66896—21no—
120#66896—21no—
121#66896—21no—
122#66896D411yescharacteristic
123C22⋊(C11⋊C8)—21no—
124#66885—21no—
125#66885—21no—
126(C2×D11)⋊C8—21no—
127#66873—21no—
128#66873—21no—
129#66873—21no—
130#66873—21no—
131#66873—21no—
132#66873D411yescharacteristic
133#66872—21no—
134#66872—21no—
135#66872—21no—
136#66871D411yescharacteristic
137C4⋊(C11⋊C8)—21no—
138C4⋊(C11⋊C8)C2311yescharacteristic
139C4⋊(C11⋊C8)C2311yescharacteristic
140C4⋊(C11⋊C8)C2311yescharacteristic
141#66867—21no—
142C4×C11⋊C8C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144#19911—111nomaximal, Sylow
145C23×D11—41no—
146C11×#41—42no—
147C11×#41—81no—
148C2×Q8×C11—21no—
149C2×Q8×C11C2×D411yescharacteristic
150C2×D4×C11—21no—
151C2×D4×C11—21no—
152C2×D4×C11—21no—
153C2×D4×C11—41no—
154C2×D4×C11—41no—
155C2×D4×C11—41no—
156C2×D4×C11C2×D411yescharacteristic
157C2×D4×C11C2×D411yescharacteristic
158C22×C4×C11—21no—
159C22×C4×C11—21no—
160C22×C4×C11—41no—
161C2×C22⋊D11—41no—
162D4×D11—42no—
163D4×D11—81no—
164C2×D44—21no—
165C2×D44—21no—
166C2×D44—21no—
167C2×D44—41no—
168C2×D44—42no—
169C2×D44—81no—
170C2×D44C2×D411yescharacteristic
171C2×C4×D11—21no—
172C2×C4×D11—41no—
173C2×Dic22—21no—
174C11×SD16—41no—
175C11×D8—81no—
176C2×C8×C11—21no—
177C2×C8×C11—81no—
178C2×C8×C11C2×D411yescharacteristic
179C2×C8×C11C2×D411yescharacteristic
180C11×C4⋊C4—21no—
181C11×C4⋊C4—21no—
182C11×C4⋊C4—21no—
183C11×C4⋊C4C2×D411yescharacteristic
184C11×C4⋊C4C2×D411yescharacteristic
185C11×C4⋊C4C2×D411yescharacteristic
186C11×C22⋊C4—21no—
187C11×C22⋊C4—21no—
188C11×C22⋊C4—41no—
189C11×C22⋊C4—41no—
190C11×C22⋊C4—41no—
191C42×C11—21no—
192C42×C11—41no—
193C42×C11C2411yescharacteristic
194#4326—82no—
195#4325—81no—
196#4323—22no—
197#4323—42no—
198#4323—81no—
199#4323—82no—
200(C2×D11)⋊C4—21no—
201(C2×D11)⋊C4—41no—
202(C2×D11)⋊C4—41no—
203C4⋊Dic11—21no—
204C4⋊Dic11—21no—
205C4⋊Dic11C2×D411yescharacteristic
206Dic11⋊C4—41no—
207Dic11⋊C4—41no—
208#4318—81no—
209C2×C11⋊C8—21no—
210C2×C11⋊C8—21no—
211C2×C11⋊C8—21no—
212C2×C11⋊C8—21no—
213C2×C11⋊C8C2×D411yescharacteristic
214C2×C11⋊C8C2×D411yescharacteristic
215C8×D11—81no—
216#3366—111no—
217#3325—111no—
218#3305D1111yescharacteristic, complemented
219#3295—111no—
220#1709—111no—
221#1698—111no—
222#1697—111no—
223#1677—111no—
224#1677—111no—
225#1634—111no—
226#1632—111no—
227#1621—111no—
228#1619—111no—
229#1590—111no—
230C8×D8—111no—
231C23×C11—21no—
232C23×C11—21no—
233C23×C11—41no—
234C22×D11—21no—
235C22×D11—41no—
236C22×D11—82no—
237C22×D11—82no—
238C22×D11—161no—
239Q8×C11—21no—
240Q8×C11—21no—
241Q8×C11—81no—
242D4×C11—21no—
243D4×C11—21no—
244D4×C11—21no—
245D4×C11—21no—
246D4×C11—41no—
247D4×C11—41no—
248D4×C11—41no—
249D4×C11—41no—
250D4×C11—81no—
251D4×C11—82no—
252D4×C11—161no—
253D4×C11—161no—
254C2×C4×C11—21no—
255C2×C4×C11—21no—
256C2×C4×C11—21no—
257C2×C4×C11—21no—
258C2×C4×C11—41no—
259C2×C4×C11—41no—
260C2×C4×C11—41no—
261C2×C4×C11—41no—
262C2×C4×C11—41no—
263C2×C4×C11—82no—
264C2×C4×C11C22×D411yescharacteristic
265C2×C4×C11C22×D411yescharacteristic
266C2×C4×C11H(5,𝔽2)11yescharacteristic
267C22⋊D11—82no—
268C2×Dic11—21no—
269C2×Dic11—41no—
270D44—21no—
271D44—41no—
272D44—41no—
273D44—41no—
274D44—41no—
275D44—81no—
276D44—82no—
277D44#13512yes—
278C4×D11—41no—
279C4×D11—41no—
280C4×D11—161no—
281Dic22—81no—
282C8×C11—21no—
283C8×C11—21no—
284C8×C11—41no—
285C11⋊C8—22no—
286C11⋊C8—21no—
287C11⋊C8—21no—
288C11⋊C8—41no—
289C11⋊C8—41no—
290C11⋊C8—41no—
291#555C2×D1111yescharacteristic
292#554—111no—
293#550C2×D1111yescharacteristic, complemented
294D42—111no—
295#494—111no—
296#493—111no—
297#490—221no—
298#486—111no—
299#486—111no—
300#486—111no—
301#486C2×D1111yescharacteristic, complemented
302#482—21no—
303#482—221no—
304#481—221no—
305#478—221no—
306#477C2×D1111yescharacteristic, complemented
307#476—111no—
308#476—111no—
309#476—111no—
310#469—221no—
311#466—21no—
312#465—221no—
313#460—111no—
314#459—111no—
315#459—111no—
316#459—221no—
317#459C2×D1111yescharacteristic
318#450—221no—
319#449—21no—
320#447—221no—
321#446—111no—
322#442—221no—
323C4×SD16C2×D1111yescharacteristic
324C4×D8—111no—
325#436—111no—
326C8×D4—111no—
327C8×D4C2×D1111yescharacteristic, complemented
328#418—221no—
329#416—21no—
330C2×#102—221no—
331#335—111no—
332#334—111no—
333#333—111no—
334#333—111no—
335#331—111no—
336#331—111no—
337Q8⋊C8—111no—
338D4⋊C8—111no—
339D4⋊C8—111no—
340D4⋊C8—111no—
341C82—111no—
342C22×C11—41no—
343C22×C11—41no—
344C22×C11—41no—
345C22×C11—41no—
346C22×C11—41no—
347C22×C11—41no—
348C22×C11—81no—
349C22×C11—81no—
350C22×C11—81no—
351C22×C11D4211yescharacteristic
352C2×D11—22no—
353C2×D11—41no—
354C2×D11—41no—
355C2×D11—81no—
356C2×D11—81no—
357C2×D11—81no—
358C2×D11—164no—
359C4×C11—21no—
360C4×C11—41no—
361C4×C11—41no—
362C4×C11—41no—
363C4×C11—41no—
364C4×C11—81no—
365C4×C11C2×#13511yescharacteristic
366C4×C11#57511yescharacteristic
367C4×C11#57611yescharacteristic
368C4×C11#57711yescharacteristic
369Dic11—41no—
370Dic11—81no—
371C2×#41—21no—
372C22×D4—221no—
373C22×D4—221no—
374C2×Q16—441no—
375C2×SD16—221no—
376C2×SD16C22⋊D1111yescharacteristic
377C2×D8—21no—
378C2×D8—111no—
379C2×D8—221no—
380C2×D8—221no—
381C2×D8—441no—
382C2×M16—221no—
383C22×C8—21no—
384C22×C8—221no—
385C4⋊Q8—111no—
386C4⋊Q8C22×D1111yescharacteristic
387#127—21no—
388#127—111no—
389#127C22×D1111yescharacteristic
390#125—221no—
391#124—41no—
392C22⋊Q8—221no—
393C22⋊Q8—441no—
394#121—21no—
395#121—21no—
396#121—21no—
397#121—41no—
398#121—221no—
399#121—221no—
400#120—441no—
401C4×Q8C22×D1111yescharacteristic
402C4×D4—21no—
403C4×D4—111no—
404C4×D4—221no—
405C4×D4C22×D1111yescharacteristic
406C4×D4C22×D1111yescharacteristic
407#117—21no—
408#117—21no—
409C2×C4⋊C4—221no—
410#107—21no—
411#107—111no—
412#106—221no—
413#106—221no—
414#106—221no—
415#106C22⋊D1111yescharacteristic
416C4⋊C8—111no—
417C4⋊C8—111no—
418C4⋊C8—111no—
419C4⋊C8—221no—
420C4⋊C8C22×D1111yescharacteristic
421#103—21no—
422#103C22⋊D1111yescharacteristic
423#102—21no—
424#102—21no—
425#102—21no—
426#102—111no—
427#102—111no—
428#102—221no—
429#102—221no—
430#102—221no—
431#102—221no—
432#102—221no—
433#102—221no—
434#102—221no—
435#102—221no—
436#102—221no—
437#102—221no—
438#102—221no—
439#102—221no—
440#102C22⋊D1111yescharacteristic
441C22⋊C8—21no—
442C22⋊C8—221no—
443C22⋊C8—221no—
444#97—221no—
445C4×C8—111no—
446C4×C8—111no—
447C4×C8C22×D1111yescharacteristic
448C2×C11—81no—
449C2×C11—81no—
450C2×C11—161no—
451C2×C11#327311yescharacteristic
452C2×C11#328211yescharacteristic
453C2×C11#329211yescharacteristic
454D11—42no—
455D11—161no—
456C24—441no—
457#41—42no—
458#41—81no—
459C2×Q8—21no—
460C2×Q8—221no—
461C2×Q8C2×C22⋊D1111yescharacteristic
462C2×D4—21no—
463C2×D4—21no—
464C2×D4—21no—
465C2×D4—41no—
466C2×D4—41no—
467C2×D4—41no—
468C2×D4—111no—
469C2×D4—221no—
470C2×D4—221no—
471C2×D4—221no—
472C2×D4—441no—
473C2×D4—442no—
474C2×D4—441no—
475C2×D4—442no—
476C2×D4—881no—
477C2×D4—881no—
478C2×D4D4×D1111yescharacteristic
479C2×D4C2×C22⋊D1111yescharacteristic
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—41no—
483C22×C4—221no—
484C22×C4—441no—
485Q16—882no—
486SD16—41no—
487SD16—881no—
488D8—81no—
489D8—222no—
490D8—442no—
491D8—882no—
492D8—881no—
493M16—881no—
494C2×C8—21no—
495C2×C8—81no—
496C2×C8—111no—
497C2×C8—111no—
498C2×C8—221no—
499C2×C8—221no—
500C2×C8—221no—
501C2×C8—221no—
502C2×C8—881no—
503C2×C8C2×C22⋊D1111yescharacteristic
504C2×C8C2×C22⋊D1111yescharacteristic
505C4⋊C4—21no—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—111no—
509C4⋊C4—221no—
510C4⋊C4—221no—
511C4⋊C4—441no—
512C4⋊C4—441no—
513C4⋊C4D4×D1111yescharacteristic
514C4⋊C4C2×C22⋊D1111yescharacteristic
515C4⋊C4C2×C22⋊D1111yescharacteristic
516C22⋊C4—21no—
517C22⋊C4—21no—
518C22⋊C4—41no—
519C22⋊C4—41no—
520C22⋊C4—41no—
521C22⋊C4—221no—
522C22⋊C4—441no—
523C22⋊C4—441no—
524C42—21no—
525C42—41no—
526C42C23×D1111yescharacteristic
527C11#1991111yescharacteristic, complemented, Sylow
528C23—21no—
529C23—21no—
530C23—41no—
531C23—221no—
532C23—441no—
533C23—882no—
534C23—882no—
535C23—1761no—
536Q8—21no—
537Q8—21no—
538Q8—81no—
539Q8—881no—
540D4—21no—
541D4—21no—
542D4—21no—
543D4—21no—
544D4—41no—
545D4—41no—
546D4—41no—
547D4—41no—
548D4—81no—
549D4—82no—
550D4—112no—
551D4—161no—
552D4—161no—
553D4—221no—
554D4—441no—
555D4—441no—
556D4—441no—
557D4—441no—
558D4—881no—
559D4—882no—
560D4—882no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—82no—
571C2×C4—221no—
572C2×C4—441no—
573C2×C4—441no—
574C2×C4—441no—
575C2×C4—1761no—
576C2×C4C2×D4×D1111yescharacteristic
577C2×C4#6703711yescharacteristic
578C2×C4C22×C22⋊D1111yescharacteristic
579C8—21no—
580C8—21no—
581C8—41no—
582C8—222no—
583C8—221no—
584C8—221no—
585C8—441no—
586C8—441no—
587C8—441no—
588C22—41no—
589C22—41no—
590C22—41no—
591C22—41no—
592C22—41no—
593C22—41no—
594C22—81no—
595C22—81no—
596C22—81no—
597C22—222no—
598C22—441no—
599C22—441no—
600C22—881no—
601C22—881no—
602C22—881no—
603C22—1764no—
604C22D4×C22⋊D1111yescharacteristic
605C4—21no—
606C4—41no—
607C4—41no—
608C4—41no—
609C4—41no—
610C4—81no—
611C4—441no—
612C4—881no—
613C4D11×#13511yescharacteristic
614C4#1062330111yescharacteristic
615C4#1062335311yescharacteristic
616C4#1062336611yescharacteristic
617C2—81no—
618C2—81no—
619C2—161no—
620C2—442no—
621C2—1761no—
622C2#1308022311yescharacteristic
623C2#1308031711yescharacteristic
624C2#1308041311yescharacteristic
subgroupG/H
centerC22D4×C22⋊D11
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3305C2
socleC22×C11D42
hypercenter#3305D11
hypocenterC11#19911
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #3305

Complements

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

NH ≅ G/Ntype
1. #13081319C2semidirect
2. #13080852C2semidirect
3. #13080442C2semidirect
4. #13068220C2semidirect
5. #13068158C2semidirect
6. #13068147C2semidirect
7. #13068025C2semidirect
8. #13068022C2semidirect
9. #13067761C2semidirect
10. #13067749C2semidirect
11. #13067681C2semidirect
12. #13067669C2semidirect
13. #13067507C2semidirect
14. C8×#4323C2semidirect
15. C11×#3305C2semidirect
17. C11×#550C22semidirect
20. C11×#486C22semidirect
22. C11×#477C22semidirect
27. C8×D4×C11C22semidirect
30. #10622705C22semidirect
37. #10622683C22semidirect
41. #10622637C22semidirect
48. #10622621C22semidirect
56. #10622184C22semidirect
57. #10622182C22semidirect
58. Q8⋊(C11⋊C8)C22semidirect
60. D4⋊(C11⋊C8)C22semidirect
63. #10622119C22semidirect
64. #10622117C22semidirect
65. #10622095C22semidirect
66. C8×C11⋊C8C22semidirect
218. #3305D11semidirect
293. #550C2×D11semidirect
301. #486C2×D11semidirect
306. #477C2×D11semidirect
327. C8×D4C2×D11semidirect
527. C11#19911semidirect

Maximal subgroups

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

subgroupindex
#130813192
#130808522
#130804422
#130682202
#130681582
#130681472
#130680252
#130680222
#130677612
#130677492
#130676812
#130676692
#130675072
C8×#43232
C11×#33052
#1991111