Finite Group Databasebeta

← #14745249

Subgroups — #14745249

Order 2816.

666 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13080915C211yesmaximal, characteristic, complemented
2#13080852C211yesmaximal, characteristic, complemented
3#13080431C211yesmaximal, characteristic, complemented
4#13068229C211yesmaximal, characteristic, complemented
5#13068165C211yesmaximal, characteristic, complemented
6#13068151C211yesmaximal, characteristic, complemented
7#13068064C211yesmaximal, characteristic, complemented
8#13068053C211yesmaximal, characteristic, complemented
9#13067844C211yesmaximal, characteristic, complemented
10#13067793C211yesmaximal, characteristic, complemented
11#13067766C211yesmaximal, characteristic, complemented
12#13067705C211yesmaximal, characteristic, complemented
13#13067501C211yesmaximal, characteristic, complemented
14C8×#4323C211yesmaximal, characteristic, complemented
15C11×#3303C211yesmaximal, characteristic, complemented
16C11×#555C2211yescharacteristic
17C11×#547C2211yescharacteristic, complemented
18#10623082C2211yescharacteristic
19D4×D44C2211yescharacteristic
20C11×#487C2211yescharacteristic, complemented
21C11×#485—21no—
22C11×#476C2211yescharacteristic, complemented
23C11×#465—21no—
24C11×#461C2211yescharacteristic
25C11×#449—21no—
26C4×C11×D8C2211yescharacteristic
27C8×D4×C11C2211yescharacteristic, complemented
28C11×#416—21no—
29#10622769—21no—
30#10622706C2211yescharacteristic, complemented
31#10622701C2211yescharacteristic
32#10622701C2211yescharacteristic
33#10622700C2211yescharacteristic
34#10622697C2211yescharacteristic
35#10622694C2211yescharacteristic, complemented
36#10622655—21no—
37#10622652—21no—
38#10622650—21no—
39#10622649—21no—
40#10622632C2211yescharacteristic, complemented
41#10622628C2211yescharacteristic
42#10622628C2211yescharacteristic
43C4×#4323C2211yescharacteristic
44#10622625C2211yescharacteristic
45#10622625C2211yescharacteristic, complemented
46#10622620C2211yescharacteristic
47#10622616—21no—
48#10622614—21no—
49#10622583—21no—
50#10622579—21no—
51#10622495—21no—
52#10622388—21no—
53D11×#102—21no—
54#10622307C2211yescharacteristic
55C8×D44C2211yescharacteristic
56#10622185C2211yescharacteristic, complemented
57#10622184C2211yescharacteristic, complemented
58D4⋊(C11⋊C8)C2211yescharacteristic
59D4⋊(C11⋊C8)C2211yescharacteristic, complemented
60D4⋊(C11⋊C8)C2211yescharacteristic, complemented
61#10622124C2211yescharacteristic, complemented
62#10622123C2211yescharacteristic
63#10622121C2211yescharacteristic
64#10622117C2211yescharacteristic, complemented
65#10622096C2211yescharacteristic, complemented
66C8×C11⋊C8C2211yescharacteristic, complemented
67C2×C11×#41—21no—
68C2×D4×D11—21no—
69C2×#4339—21no—
70C22×D44—21no—
71C2×C11×SD16—21no—
72C2×C11×D8D411yescharacteristic
73C22×C8×C11—21no—
74C11×C4⋊Q8C2311yescharacteristic
75C11×C4⋊Q8C2311yescharacteristic
76C11×#124—41no—
77C11×#123—41no—
78C11×C22⋊Q8—21no—
79C11×#121—21no—
80C11×#121—21no—
81C11×#121—21no—
82C4×D4×C11C2311yescharacteristic
83C4×D4×C11C2311yescharacteristic
84C4×D4×C11C2311yescharacteristic
85C11×#117—21no—
86C11×#117—21no—
87C2×C11×C4⋊C4—21no—
88#66991—21no—
89C2×#4324—21no—
90C2×#4323—21no—
91C2×#4323—21no—
92C2×#4323D411yescharacteristic
93#66983—21no—
94#66977—21no—
95C2×#4318—21no—
96C2×#4318—21no—
97C2×C8×D11—21no—
98#66948—21no—
99C4⋊C4×D11—21no—
100#66936—41no—
101#66935—41no—
102#66927C2311yescharacteristic
103C4×D44C2311yescharacteristic
104#66922C2311yescharacteristic
105C11×#107D411yescharacteristic
106C11×#106—21no—
107C11×C4⋊C8C2311yescharacteristic
108C11×#103—21no—
109C11×#103—21no—
110C11×#103—21no—
111C11×#102—21no—
112C11×#102D411yescharacteristic
113C11×#102D411yescharacteristic
114C11×C22⋊C8—21no—
115C4×C8×C11C2311yescharacteristic
116#66899—41no—
117#66896—21no—
118#66896D411yescharacteristic
119C22⋊(C11⋊C8)—21no—
120C22⋊(C11⋊C8)—21no—
121#66885—21no—
122#66885—21no—
123(C2×D11)⋊C8—21no—
124#66874—21no—
125#66874—21no—
126#66874—21no—
127#66873—21no—
128#66873—21no—
129#66873—21no—
130#66873—21no—
131#66873—21no—
132#66873—21no—
133#66873—41no—
134#66873D411yescharacteristic
135#66872—21no—
136#66871—21no—
137#66871—21no—
138#66871D411yescharacteristic
139C4⋊(C11⋊C8)C2311yescharacteristic
140C4⋊(C11⋊C8)C2311yescharacteristic
141C4⋊(C11⋊C8)C2311yescharacteristic
142C4×C11⋊C8C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144#19899—111nomaximal, Sylow
145C23×D11—41no—
146C11×#41—42no—
147C11×#41—81no—
148C2×Q8×C11—21no—
149C2×Q8×C11—21no—
150C2×D4×C11—41no—
151C2×D4×C11—41no—
152C2×D4×C11C2×D411yescharacteristic
153C2×D4×C11C2×D411yescharacteristic
154C2×D4×C11C2×D411yescharacteristic
155C22×C4×C11—21no—
156C22×C4×C11—21no—
157C22×C4×C11—21no—
158C22×C4×C11—41no—
159C2×C22⋊D11—41no—
160C2×C22⋊D11—41no—
161D4×D11—42no—
162D4×D11—81no—
163#4339—42no—
164#4339—81no—
165C2×D44—21no—
166C2×D44—21no—
167C2×D44—21no—
168C2×D44—41no—
169C2×D44—42no—
170C2×D44—81no—
171C2×D44C2×D411yescharacteristic
172C2×C4×D11—21no—
173C2×C4×D11—41no—
174C2×Dic22—21no—
175C11×SD16—81no—
176C11×D8—41no—
177C2×C8×C11—21no—
178C2×C8×C11—81no—
179C2×C8×C11C2×D411yescharacteristic
180C2×C8×C11C2×D411yescharacteristic
181C11×C4⋊C4—21no—
182C11×C4⋊C4—21no—
183C11×C4⋊C4—21no—
184C11×C4⋊C4—21no—
185C11×C4⋊C4—41no—
186C11×C4⋊C4C2×D411yescharacteristic
187C11×C4⋊C4C2×D411yescharacteristic
188C11×C4⋊C4C2×D411yescharacteristic
189C11×C22⋊C4—21no—
190C11×C22⋊C4—21no—
191C11×C22⋊C4—21no—
192C11×C22⋊C4—41no—
193C11×C22⋊C4—41no—
194C11×C22⋊C4—41no—
195C42×C11—41no—
196C42×C11C2411yescharacteristic
197C22⋊Dic11—41no—
198#4324—81no—
199#4323—22no—
200#4323—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—
209#4318—81no—
210C2×C11⋊C8—21no—
211C2×C11⋊C8—21no—
212C2×C11⋊C8—21no—
213C2×C11⋊C8—21no—
214C2×C11⋊C8C2×D411yescharacteristic
215C2×C11⋊C8C2×D411yescharacteristic
216C8×D11—81no—
217#3330—111no—
218#3325—111no—
219#3303D1111yescharacteristic, complemented
220#3294—111no—
221#1711—111no—
222#1699—111no—
223#1697—111no—
224#1683—111no—
225#1681—111no—
226#1646—111no—
227#1639—111no—
228#1635—111no—
229#1625—111no—
230#1589—111no—
231C8×D8—111no—
232C23×C11—21no—
233C23×C11—21no—
234C23×C11—21no—
235C22×D11—21no—
236C22×D11—41no—
237C22×D11—82no—
238C22×D11—82no—
239C22×D11—161no—
240Q8×C11—41no—
241Q8×C11—41no—
242Q8×C11—81no—
243D4×C11—21no—
244D4×C11—21no—
245D4×C11—21no—
246D4×C11—21no—
247D4×C11—21no—
248D4×C11—21no—
249D4×C11—82no—
250D4×C11—161no—
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—41no—
259C2×C4×C11—41no—
260C2×C4×C11—41no—
261C2×C4×C11—41no—
262C2×C4×C11—82no—
263C2×C4×C11C22×D411yescharacteristic
264C2×C4×C11C22×D411yescharacteristic
265C2×C4×C11H(5,𝔽2)11yescharacteristic
266C22⋊D11—82no—
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—82no—
281Dic22—41no—
282Dic22—41no—
283C8×C11—21no—
284C8×C11—21no—
285C8×C11—41no—
286C11⋊C8—21no—
287C11⋊C8—21no—
288C11⋊C8—41no—
289C11⋊C8—41no—
290C11⋊C8—41no—
291C11⋊C8—41no—
292#555C2×D1111yescharacteristic
293#547—111no—
294#547C2×D1111yescharacteristic, complemented
295D42—111no—
296#487—111no—
297#487—111no—
298#487C2×D1111yescharacteristic, complemented
299#486—111no—
300#486—111no—
301#486—111no—
302#485—21no—
303#484—221no—
304#482—221no—
305#480—221no—
306#476—111no—
307#476C2×D1111yescharacteristic, complemented
308#474—111no—
309#474—111no—
310#469—221no—
311#468—221no—
312#466—221no—
313#465—21no—
314#461—111no—
315#461C2×D1111yescharacteristic
316#459—111no—
317#459—111no—
318#449—21no—
319#449—221no—
320#447—221no—
321#447—221no—
322C4×D8—111no—
323C4×D8C2×D1111yescharacteristic
324#436—111no—
325#436—111no—
326C8×D4—111no—
327C8×D4C2×D1111yescharacteristic, complemented
328#418—221no—
329#417—221no—
330#416—21no—
331C2×#102—221no—
332#335—111no—
333#335—111no—
334#333—111no—
335#332—111no—
336#332—111no—
337#331—111no—
338D4⋊C8—111no—
339D4⋊C8—111no—
340D4⋊C8—111no—
341D4⋊C8—111no—
342C82—111no—
343C22×C11—41no—
344C22×C11—41no—
345C22×C11—41no—
346C22×C11—41no—
347C22×C11—41no—
348C22×C11—41no—
349C22×C11—41no—
350C22×C11—41no—
351C22×C11—41no—
352C22×C11D4211yescharacteristic
353C2×D11—22no—
354C2×D11—41no—
355C2×D11—41no—
356C2×D11—81no—
357C2×D11—81no—
358C2×D11—81no—
359C2×D11—164no—
360C4×C11—21no—
361C4×C11—41no—
362C4×C11—41no—
363C4×C11—41no—
364C4×C11—81no—
365C4×C11—81no—
366C4×C11C2×#13511yescharacteristic
367C4×C11#57511yescharacteristic
368C4×C11#57611yescharacteristic
369C4×C11#57611yescharacteristic
370Dic11—41no—
371Dic11—81no—
372C2×#41—21no—
373C2×#41—221no—
374C22×D4—221no—
375C22×D4—221no—
376C2×SD16—21no—
377C2×SD16—221no—
378C2×D8—111no—
379C2×D8—221no—
380C2×D8—221no—
381C2×D8C22⋊D1111yescharacteristic
382C2×M16—221no—
383C2×M16—221no—
384C22×C8—21no—
385C22×C8—221no—
386C4⋊Q8—111no—
387C4⋊Q8C22×D1111yescharacteristic
388C4⋊Q8C22×D1111yescharacteristic
389#127—111no—
390#124—41no—
391#123—41no—
392#123—441no—
393C22⋊Q8—21no—
394C22⋊Q8—221no—
395#121—21no—
396#121—21no—
397#121—21no—
398#121—221no—
399#121—221no—
400#121—221no—
401#120—441no—
402C4×D4—111no—
403C4×D4C22×D1111yescharacteristic
404C4×D4C22×D1111yescharacteristic
405C4×D4C22×D1111yescharacteristic
406#117—21no—
407#117—21no—
408C2×C4⋊C4—21no—
409C2×C4⋊C4—221no—
410#107—111no—
411#107—221no—
412#107—221no—
413#107C22⋊D1111yescharacteristic
414#106—21no—
415#106—221no—
416C4⋊C8—111no—
417C4⋊C8—111no—
418C4⋊C8—111no—
419C4⋊C8C22×D1111yescharacteristic
420#103—21no—
421#103—21no—
422#103—21no—
423#103—221no—
424#103—221no—
425#103—221no—
426#103—441no—
427#102—21no—
428#102—111no—
429#102—111no—
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—441no—
440#102C22⋊D1111yescharacteristic
441#102C22⋊D1111yescharacteristic
442C22⋊C8—21no—
443C22⋊C8—221no—
444C22⋊C8—221no—
445C22⋊C8—221no—
446C4×C8—111no—
447C4×C8—111no—
448C4×C8C22×D1111yescharacteristic
449C2×C11—81no—
450C2×C11—81no—
451C2×C11—81no—
452C2×C11#327311yescharacteristic
453C2×C11#328011yescharacteristic
454C2×C11#329011yescharacteristic
455D11—42no—
456D11—161no—
457C24—441no—
458#41—42no—
459#41—81no—
460#41—442no—
461#41—881no—
462C2×Q8—21no—
463C2×Q8—21no—
464C2×Q8—221no—
465C2×D4—41no—
466C2×D4—41no—
467C2×D4—111no—
468C2×D4—221no—
469C2×D4—221no—
470C2×D4—221no—
471C2×D4—441no—
472C2×D4—442no—
473C2×D4—441no—
474C2×D4—442no—
475C2×D4—441no—
476C2×D4—881no—
477C2×D4—881no—
478C2×D4D4×D1111yescharacteristic
479C2×D4C2×C22⋊D1111yescharacteristic
480C2×D4C2×C22⋊D1111yescharacteristic
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—41no—
485C22×C4—221no—
486C22×C4—441no—
487SD16—81no—
488SD16—881no—
489D8—41no—
490D8—222no—
491D8—881no—
492D8—881no—
493M16—881no—
494M16—881no—
495C2×C8—21no—
496C2×C8—81no—
497C2×C8—111no—
498C2×C8—111no—
499C2×C8—221no—
500C2×C8—221no—
501C2×C8—221no—
502C2×C8—221no—
503C2×C8—881no—
504C2×C8C2×C22⋊D1111yescharacteristic
505C2×C8C2×C22⋊D1111yescharacteristic
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—41no—
511C4⋊C4—111no—
512C4⋊C4—221no—
513C4⋊C4—221no—
514C4⋊C4—441no—
515C4⋊C4D4×D1111yescharacteristic
516C4⋊C4C2×C22⋊D1111yescharacteristic
517C4⋊C4C2×C22⋊D1111yescharacteristic
518C22⋊C4—21no—
519C22⋊C4—21no—
520C22⋊C4—21no—
521C22⋊C4—41no—
522C22⋊C4—41no—
523C22⋊C4—41no—
524C22⋊C4—221no—
525C22⋊C4—441no—
526C22⋊C4—441no—
527C42—41no—
528C42C23×D1111yescharacteristic
529C11#1989911yescharacteristic, complemented, Sylow
530C23—21no—
531C23—21no—
532C23—21no—
533C23—221no—
534C23—441no—
535C23—882no—
536C23—882no—
537C23—1761no—
538Q8—41no—
539Q8—41no—
540Q8—81no—
541Q8—441no—
542Q8—441no—
543D4—21no—
544D4—21no—
545D4—21no—
546D4—21no—
547D4—21no—
548D4—21no—
549D4—82no—
550D4—112no—
551D4—161no—
552D4—221no—
553D4—441no—
554D4—441no—
555D4—441no—
556D4—441no—
557D4—881no—
558D4—882no—
559D4—882no—
560D4—882no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—82no—
573C2×C4—221no—
574C2×C4—441no—
575C2×C4—441no—
576C2×C4—441no—
577C2×C4—882no—
578C2×C4C2×D4×D1111yescharacteristic
579C2×C4#6703711yescharacteristic
580C2×C4C22×C22⋊D1111yescharacteristic
581C8—21no—
582C8—21no—
583C8—41no—
584C8—221no—
585C8—221no—
586C8—441no—
587C8—441no—
588C8—441no—
589C8—441no—
590C22—41no—
591C22—41no—
592C22—41no—
593C22—41no—
594C22—41no—
595C22—41no—
596C22—41no—
597C22—41no—
598C22—41no—
599C22—222no—
600C22—441no—
601C22—441no—
602C22—881no—
603C22—881no—
604C22—881no—
605C22—1764no—
606C22D4×C22⋊D1111yescharacteristic
607C4—21no—
608C4—41no—
609C4—41no—
610C4—41no—
611C4—81no—
612C4—81no—
613C4—441no—
614C4—881no—
615C4D11×#13511yescharacteristic
616C4#1062330011yescharacteristic
617C4#1062335311yescharacteristic
618C4#1062336611yescharacteristic
619C2—81no—
620C2—81no—
621C2—81no—
622C2—442no—
623C2—1761no—
624C2#1308022311yescharacteristic
625C2#1308029511yescharacteristic
626C2#1308039611yescharacteristic
subgroupG/H
centerC22D4×C22⋊D11
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3303C2
socleC22×C11D42
hypercenter#3303D11
hypocenterC11#19899
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #3303

Complements

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

NH ≅ G/Ntype
1. #13080915C2semidirect
2. #13080852C2semidirect
3. #13080431C2semidirect
4. #13068229C2semidirect
5. #13068165C2semidirect
6. #13068151C2semidirect
7. #13068064C2semidirect
8. #13068053C2semidirect
9. #13067844C2semidirect
10. #13067793C2semidirect
11. #13067766C2semidirect
12. #13067705C2semidirect
13. #13067501C2semidirect
14. C8×#4323C2semidirect
15. C11×#3303C2semidirect
17. C11×#547C22semidirect
20. C11×#487C22semidirect
22. C11×#476C22semidirect
27. C8×D4×C11C22semidirect
30. #10622706C22semidirect
35. #10622694C22semidirect
40. #10622632C22semidirect
45. #10622625C22semidirect
56. #10622185C22semidirect
57. #10622184C22semidirect
59. D4⋊(C11⋊C8)C22semidirect
60. D4⋊(C11⋊C8)C22semidirect
61. #10622124C22semidirect
64. #10622117C22semidirect
65. #10622096C22semidirect
66. C8×C11⋊C8C22semidirect
219. #3303D11semidirect
294. #547C2×D11semidirect
298. #487C2×D11semidirect
307. #476C2×D11semidirect
327. C8×D4C2×D11semidirect
529. C11#19899semidirect

Maximal subgroups

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

subgroupindex
#130809152
#130808522
#130804312
#130682292
#130681652
#130681512
#130680642
#130680532
#130678442
#130677932
#130677662
#130677052
#130675012
C8×#43232
C11×#33032
#1989911