Finite Group Databasebeta

← #14745242

Subgroups — #14745242

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#13080860C211yesmaximal, characteristic, complemented
2#13080544C211yesmaximal, characteristic, complemented
3#13080423C211yesmaximal, characteristic, complemented
4#13068229C211yesmaximal, characteristic, complemented
5#13068160C211yesmaximal, characteristic, complemented
6#13068149C211yesmaximal, characteristic, complemented
7#13068065C211yesmaximal, characteristic, complemented
8#13068055C211yesmaximal, characteristic, complemented
9#13067842C211yesmaximal, characteristic, complemented
10#13067794C211yesmaximal, characteristic, complemented
11#13067767C211yesmaximal, characteristic, complemented
12#13067705C211yesmaximal, characteristic, complemented
13#13067499C211yesmaximal, characteristic, complemented
14D8×C11⋊C8C211yesmaximal, characteristic, complemented
15C11×#3330C211yesmaximal, characteristic, complemented
16C11×#547C2211yescharacteristic
17C11×#547C2211yescharacteristic, complemented
18#10623094C2211yescharacteristic
19D4×D44C2211yescharacteristic
20C11×#487C2211yescharacteristic, complemented
21C11×#484—21no—
22C11×#474C2211yescharacteristic
23C11×#468—21no—
24C11×#461C2211yescharacteristic, complemented
25C11×#449—21no—
26C4×C11×D8C2211yescharacteristic
27C11×#436C2211yescharacteristic, complemented
28C11×#417—21no—
29#10622851—21no—
30#10622846—21no—
31#10622769—21no—
32#10622706C2211yescharacteristic, complemented
33#10622701C2211yescharacteristic
34#10622701C2211yescharacteristic
35#10622700C2211yescharacteristic
36#10622696C2211yescharacteristic
37#10622694C2211yescharacteristic, complemented
38#10622661—21no—
39#10622658—21no—
40#10622651—21no—
41#10622649—21no—
42#10622628C2211yescharacteristic
43#10622628C2211yescharacteristic
44C4×#4323C2211yescharacteristic
45D4×C11⋊C8C2211yescharacteristic
46D4×C11⋊C8C2211yescharacteristic, complemented
47#10622621C2211yescharacteristic
48#10622621C2211yescharacteristic, complemented
49#10622580—21no—
50C2×#66873—21no—
51#10622498—21no—
52#10622395—21no—
53#10622383—21no—
54#10622307C2211yescharacteristic
55#10622301C2211yescharacteristic
56#10622185C2211yescharacteristic, complemented
57#10622185C2211yescharacteristic, complemented
58D4⋊(C11⋊C8)C2211yescharacteristic
59D4⋊(C11⋊C8)C2211yescharacteristic, complemented
60D4⋊(C11⋊C8)C2211yescharacteristic, complemented
61#10622123C2211yescharacteristic
62#10622121C2211yescharacteristic
63#10622119C2211yescharacteristic, complemented
64#10622117C2211yescharacteristic, complemented
65#10622096C2211yescharacteristic, complemented
66C8×C11⋊C8C2211yescharacteristic, complemented
67C2×C11×#41—21no—
68C2×C11×#41—21no—
69C2×D4×D11—21no—
70C22×D44—21no—
71C2×C11×SD16—21no—
72C2×C11×D8D411yescharacteristic
73C2×C11×M16—21no—
74C11×C4⋊Q8C2311yescharacteristic
75C11×C4⋊Q8C2311yescharacteristic
76C11×#123—41no—
77C11×#123—41no—
78C11×C22⋊Q8—21no—
79C11×C22⋊Q8—21no—
80C11×#121—21no—
81C11×#121—21no—
82C4×D4×C11C2311yescharacteristic
83C4×D4×C11C2311yescharacteristic
84C4×D4×C11C2311yescharacteristic
85C2×C11×C4⋊C4—21no—
86C2×C11×C4⋊C4—21no—
87C2×#4325—21no—
88#66991—21no—
89C2×#4323—21no—
90C2×#4323—21no—
91C2×#4323D411yescharacteristic
92#66983—21no—
93#66983—21no—
94#66979—21no—
95C22×C11⋊C8—21no—
96C22×C11⋊C8—21no—
97C2×#4313—21no—
98#66948—21no—
99#66945—21no—
100#66938—41no—
101#66935—41no—
102#66927C2311yescharacteristic
103C4×D44C2311yescharacteristic
104#66922C2311yescharacteristic
105C11×#107—21no—
106C11×#107D411yescharacteristic
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—21no—
117#66899—21no—
118#66899—21no—
119#66896—21no—
120#66896—21no—
121#66896D411yescharacteristic
122C22⋊(C11⋊C8)—21no—
123C22⋊(C11⋊C8)—21no—
124#66885—21no—
125#66885—21no—
126(C2×D11)⋊C8—21no—
127#66874—41no—
128#66873—21no—
129#66873—21no—
130#66873—21no—
131#66873—21no—
132#66873—21no—
133#66873—41no—
134#66873D411yescharacteristic
135#66872—21no—
136#66872—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—42no—
148C11×#41—81no—
149C11×#41—81no—
150C2×Q8×C11—21no—
151C2×Q8×C11—21no—
152C2×D4×C11—41no—
153C2×D4×C11—41no—
154C2×D4×C11C2×D411yescharacteristic
155C2×D4×C11C2×D411yescharacteristic
156C2×D4×C11C2×D411yescharacteristic
157C22×C4×C11—21no—
158C22×C4×C11—21no—
159C22×C4×C11—21no—
160C22×C4×C11—41no—
161C22×C4×C11—41no—
162C2×C22⋊D11—41no—
163C2×C22⋊D11—41no—
164D4×D11—42no—
165D4×D11—81no—
166C2×D44—21no—
167C2×D44—21no—
168C2×D44—21no—
169C2×D44—41no—
170C2×D44—42no—
171C2×D44—81no—
172C2×D44C2×D411yescharacteristic
173C2×C4×D11—21no—
174C2×Dic22—21no—
175C11×SD16—81no—
176C11×D8—22no—
177C11×M16—81no—
178C2×C8×C11—21no—
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⋊C4—41no—
187C11×C4⋊C4C2×D411yescharacteristic
188C11×C4⋊C4C2×D411yescharacteristic
189C11×C4⋊C4C2×D411yescharacteristic
190C11×C22⋊C4—21no—
191C11×C22⋊C4—21no—
192C11×C22⋊C4—21no—
193C11×C22⋊C4—41no—
194C11×C22⋊C4—41no—
195C42×C11C2411yescharacteristic
196C22⋊Dic11—41no—
197#4325—81no—
198#4323—41no—
199#4323—81no—
200#4323—81no—
201(C2×D11)⋊C4—21no—
202(C2×D11)⋊C4—41no—
203(C2×D11)⋊C4—41no—
204C4⋊Dic11—21no—
205C4⋊Dic11—21no—
206C4⋊Dic11C2×D411yescharacteristic
207C4×Dic11—41no—
208C2×C11⋊C8—21no—
209C2×C11⋊C8—21no—
210C2×C11⋊C8—21no—
211C2×C11⋊C8—21no—
212C2×C11⋊C8—81no—
213C2×C11⋊C8—81no—
214C2×C11⋊C8C2×D411yescharacteristic
215C2×C11⋊C8C2×D411yescharacteristic
216#4313—81no—
217#3330D1111yescharacteristic, complemented
218#3325—111no—
219#3303—111no—
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—41no—
243Q8×C11—41no—
244D4×C11—21no—
245D4×C11—21no—
246D4×C11—21no—
247D4×C11—21no—
248D4×C11—21no—
249D4×C11—82no—
250D4×C11—82no—
251D4×C11#13512yes—
252C2×C4×C11—21no—
253C2×C4×C11—21no—
254C2×C4×C11—21no—
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—41no—
263C2×C4×C11—82no—
264C2×C4×C11—82no—
265C2×C4×C11C22×D411yescharacteristic
266C2×C4×C11C22×D411yescharacteristic
267C2×C4×C11H(5,𝔽2)11yescharacteristic
268C22⋊D11—82no—
269C22⋊D11—161no—
270C2×Dic11—21no—
271C2×Dic11—41no—
272D44—21no—
273D44—21no—
274D44—41no—
275D44—41no—
276D44—41no—
277D44—41no—
278D44—81no—
279D44—82no—
280C4×D11—41no—
281C4×D11—41no—
282Dic22—81no—
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#555—111no—
293#547C2×D1111yescharacteristic
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—221no—
303#484—21no—
304#482—221no—
305#480—221no—
306#476—111no—
307#476—111no—
308#474—111no—
309#474C2×D1111yescharacteristic
310#469—221no—
311#468—21no—
312#466—221no—
313#465—221no—
314#461—111no—
315#461C2×D1111yescharacteristic, complemented
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#436C2×D1111yescharacteristic, complemented
326C8×D4—111no—
327C8×D4—111no—
328#418—221no—
329#417—21no—
330#416—221no—
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—22no—
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—41no—
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—21no—
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—21no—
383C2×M16—221no—
384C22×C8—221no—
385C22×C8—221no—
386C4⋊Q8—111no—
387C4⋊Q8C22×D1111yescharacteristic
388C4⋊Q8C22×D1111yescharacteristic
389#127—111no—
390#124—441no—
391#123—41no—
392#123—41no—
393C22⋊Q8—21no—
394C22⋊Q8—21no—
395#121—21no—
396#121—21no—
397#121—221no—
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—221no—
407#117—221no—
408C2×C4⋊C4—21no—
409C2×C4⋊C4—21no—
410#107—21no—
411#107—111no—
412#107—221no—
413#107C22⋊D1111yescharacteristic
414#106—221no—
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—42no—
450C2×C11—81no—
451C2×C11—81no—
452C2×C11#327311yescharacteristic
453C2×C11#328011yescharacteristic
454C2×C11#329011yescharacteristic
455D11—81no—
456D11—161no—
457C24—441no—
458#41—42no—
459#41—42no—
460#41—81no—
461#41—81no—
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—41no—
486C22×C4—221no—
487SD16—81no—
488SD16—881no—
489D8—22no—
490D8—441no—
491D8—881no—
492D8—881no—
493M16—81no—
494M16—881no—
495C2×C8—21no—
496C2×C8—111no—
497C2×C8—111no—
498C2×C8—221no—
499C2×C8—221no—
500C2×C8—221no—
501C2×C8—221no—
502C2×C8—881no—
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—41no—
512C4⋊C4—111no—
513C4⋊C4—221no—
514C4⋊C4—221no—
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—221no—
524C22⋊C4—441no—
525C22⋊C4—441no—
526C22⋊C4—441no—
527C42—441no—
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—41no—
541Q8—41no—
542Q8—881no—
543D4—21no—
544D4—21no—
545D4—21no—
546D4—21no—
547D4—21no—
548D4—82no—
549D4—82no—
550D4—221no—
551D4—221no—
552D4—441no—
553D4—441no—
554D4—441no—
555D4—441no—
556D4—881no—
557D4—882no—
558D4—882no—
559D4—1761no—
560D4#6700312yes—
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—82no—
574C2×C4—221no—
575C2×C4—441no—
576C2×C4—441no—
577C2×C4—441no—
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—22no—
591C22—41no—
592C22—41no—
593C22—41no—
594C22—41no—
595C22—41no—
596C22—41no—
597C22—41no—
598C22—41no—
599C22—441no—
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—
615C4#1062330411yescharacteristic
616C4#1062330511yescharacteristic
617C4C2×#6700311yescharacteristic
618C4#1062336611yescharacteristic
619C2—42no—
620C2—81no—
621C2—81no—
622C2—881no—
623C2—1761no—
624C2#1308022111yescharacteristic
625C2#1308029711yescharacteristic
626C2#1308040211yescharacteristic
subgroupG/H
centerC22D4×C22⋊D11
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3330C2
socleC22×C11D42
hypercenter#3330D11
hypocenterC11#19899
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #3330

Complements

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

NH ≅ G/Ntype
1. #13080860C2semidirect
2. #13080544C2semidirect
3. #13080423C2semidirect
4. #13068229C2semidirect
5. #13068160C2semidirect
6. #13068149C2semidirect
7. #13068065C2semidirect
8. #13068055C2semidirect
9. #13067842C2semidirect
10. #13067794C2semidirect
11. #13067767C2semidirect
12. #13067705C2semidirect
13. #13067499C2semidirect
14. D8×C11⋊C8C2semidirect
15. C11×#3330C2semidirect
17. C11×#547C22semidirect
20. C11×#487C22semidirect
24. C11×#461C22semidirect
27. C11×#436C22semidirect
32. #10622706C22semidirect
37. #10622694C22semidirect
46. D4×C11⋊C8C22semidirect
48. #10622621C22semidirect
56. #10622185C22semidirect
57. #10622185C22semidirect
59. D4⋊(C11⋊C8)C22semidirect
60. D4⋊(C11⋊C8)C22semidirect
63. #10622119C22semidirect
64. #10622117C22semidirect
65. #10622096C22semidirect
66. C8×C11⋊C8C22semidirect
217. #3330D11semidirect
294. #547C2×D11semidirect
298. #487C2×D11semidirect
315. #461C2×D11semidirect
325. #436C2×D11semidirect
529. C11#19899semidirect

Maximal subgroups

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

subgroupindex
#130808602
#130805442
#130804232
#130682292
#130681602
#130681492
#130680652
#130680552
#130678422
#130677942
#130677672
#130677052
#130674992
D8×C11⋊C82
C11×#33302
#1989911