Finite Group Databasebeta

← #14745379

Subgroups — #14745379

Order 2816.

668 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#13081023C211yesmaximal, characteristic, complemented
2#13080860C211yesmaximal, characteristic
3D4×#4325C211yesmaximal, characteristic, complemented
4#13068219C211yesmaximal, characteristic, complemented
5#13068160C211yesmaximal, characteristic, complemented
6#13068156C211yesmaximal, characteristic, complemented
7#13067989C211yesmaximal, characteristic, complemented
8#13067959C211yesmaximal, characteristic, complemented
9#13067843C211yesmaximal, characteristic, complemented
10#13067793C211yesmaximal, characteristic, complemented
11#13067781C211yesmaximal, characteristic, complemented
12#13067726C211yesmaximal, characteristic, complemented
13#13067506C211yesmaximal, characteristic, complemented
14D8×C11⋊C8C211yesmaximal, characteristic, complemented
15C11×#3367C211yesmaximal, characteristic, complemented
16C11×#556C2211yescharacteristic, complemented
17D4×Q8×C11C2211yescharacteristic
18C22×#4325—21no—
19#10623094C2211yescharacteristic
20D4×D44C2211yescharacteristic
21C11×#489—21no—
22C11×#487C2211yescharacteristic, complemented
23C11×#477—21no—
24C11×#474C2211yescharacteristic, complemented
25C11×#463—21no—
26C11×#461C2211yescharacteristic
27C11×#446C2211yescharacteristic, complemented
28C11×#440—21no—
29C4×C11×D8C2211yescharacteristic
30#10622840—21no—
31#10622769—21no—
32#10622706C2211yescharacteristic, complemented
33#10622701C2211yescharacteristic
34#10622700C2211yescharacteristic
35#10622698C2211yescharacteristic
36#10622696C2211yescharacteristic
37#10622692C2211yescharacteristic, complemented
38#10622661—21no—
39#10622661—21no—
40#10622659—21no—
41#10622658—21no—
42#10622640C2211yescharacteristic
43C4×#4325C2211yescharacteristic
44#10622634C2211yescharacteristic, complemented
45#10622628C2211yescharacteristic
46D4×C11⋊C8C2211yescharacteristic
47D4×C11⋊C8C2211yescharacteristic, complemented
48#10622621C2211yescharacteristic
49#10622616—21no—
50#10622611—21no—
51#10622498—21no—
52#10622395—21no—
53#10622383—21no—
54#10622307C2211yescharacteristic
55#10622301C2211yescharacteristic
56#10622185C2211yescharacteristic, complemented
57#10622185C2211yescharacteristic, complemented
58Q8⋊(C11⋊C8)C2211yescharacteristic, complemented
59D4⋊(C11⋊C8)C2211yescharacteristic
60D4⋊(C11⋊C8)C2211yescharacteristic, complemented
61#10622123C2211yescharacteristic
62#10622121C2211yescharacteristic
63#10622119C2211yescharacteristic, complemented
64#10622118C2211yescharacteristic, complemented
65#10622096C2211yescharacteristic, complemented
66C8×C11⋊C8C2211yescharacteristic, complemented
67C22×Q8×C11—21no—
68C2×D4×D11—21no—
69C22×D44—21no—
70C2×C11×SD16—21no—
71C2×C11×D8D411yescharacteristic
72C11×C4⋊Q8—21no—
73C11×C4⋊Q8C2311yescharacteristic
74C11×C4⋊Q8C2311yescharacteristic
75C11×#126—41no—
76C11×#124—21no—
77C11×C22⋊Q8—21no—
78C11×C22⋊Q8—21no—
79C11×C22⋊Q8—41no—
80C4×Q8×C11—21no—
81C4×Q8×C11C2311yescharacteristic
82C4×D4×C11—21no—
83C4×D4×C11C2311yescharacteristic
84C4×D4×C11C2311yescharacteristic
85C11×#117—21no—
86C2×#4325—21no—
87C2×#4325—21no—
88C2×#4325—21no—
89C2×#4325—21no—
90C2×#4325—44no—
91C2×#4325D411yescharacteristic
92#66991—21no—
93C2×#4323—21no—
94#66983—21no—
95#66983—21no—
96#66979—21no—
97C22×C11⋊C8—21no—
98C22×C11⋊C8—21no—
99C2×#4313—21no—
100#66948—21no—
101#66945—21no—
102#66938—41no—
103#66935—41no—
104#66927C2311yescharacteristic
105C4×D44C2311yescharacteristic
106#66922C2311yescharacteristic
107C11×#107—21no—
108C11×#107D411yescharacteristic
109C11×C4⋊C8—21no—
110C11×C4⋊C8C2311yescharacteristic
111C11×#103—21no—
112C11×#103—21no—
113C11×#103—21no—
114C11×#102—21no—
115C11×#102D411yescharacteristic
116C11×#102D411yescharacteristic
117C11×#97—21no—
118C4×C8×C11C2311yescharacteristic
119#66899—21no—
120#66899—21no—
121#66899D411yescharacteristic
122#66896—21no—
123C22⋊(C11⋊C8)—21no—
124C22⋊(C11⋊C8)—21no—
125#66885—21no—
126#66885—21no—
127(C2×D11)⋊C8—21no—
128#66874—41no—
129#66873—21no—
130#66873—21no—
131#66873—21no—
132#66873—41no—
133#66873D411yescharacteristic
134#66872—21no—
135#66872—21no—
136#66872—21no—
137#66872D411yescharacteristic
138#66871—21no—
139#66871—21no—
140C4⋊(C11⋊C8)C2311yescharacteristic
141C4⋊(C11⋊C8)C2311yescharacteristic
142C4⋊(C11⋊C8)C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144C4×C11⋊C8C2311yescharacteristic
145#19910—111nomaximal, Sylow
146C23×D11—41no—
147C2×Q8×C11—21no—
148C2×Q8×C11—21no—
149C2×Q8×C11—41no—
150C2×Q8×C11—42no—
151C2×Q8×C11—81no—
152C2×Q8×C11C2×D411yescharacteristic
153C2×D4×C11C2×D411yescharacteristic
154C2×D4×C11C2×D411yescharacteristic
155C22×C4×C11—21no—
156C22×C4×C11—21no—
157C22×C4×C11—41no—
158C2×C22⋊D11—41no—
159C2×C22⋊D11—41no—
160D4×D11—42no—
161D4×D11—81no—
162C2×D44—21no—
163C2×D44—21no—
164C2×D44—21no—
165C2×D44—41no—
166C2×D44—42no—
167C2×D44—81no—
168C2×D44C2×D411yescharacteristic
169C2×C4×D11—21no—
170C2×Dic22—21no—
171C11×SD16—42no—
172C11×D8—22no—
173C2×C8×C11—21no—
174C2×C8×C11C2×D411yescharacteristic
175C2×C8×C11C2×D411yescharacteristic
176C11×C4⋊C4—21no—
177C11×C4⋊C4—21no—
178C11×C4⋊C4—21no—
179C11×C4⋊C4—21no—
180C11×C4⋊C4—21no—
181C11×C4⋊C4—41no—
182C11×C4⋊C4—41no—
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
194C22⋊Dic11—41no—
195#4325—22no—
196#4325—42no—
197#4325—42no—
198#4325—42no—
199#4325—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—42no—
213C2×C11⋊C8—42no—
214C2×C11⋊C8C2×D411yescharacteristic
215C2×C11⋊C8C2×D411yescharacteristic
216#4313—81no—
217#3367D1111yescharacteristic, complemented
218#3340—111no—
219#3325—111no—
220D4×SD16—111no—
221#1708—111no—
222#1699—111no—
223#1698—111no—
224#1671—111no—
225#1665—111no—
226#1646—111no—
227#1639—111no—
228#1637—111no—
229#1628—111no—
230#1590—111no—
231C8×D8—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—
245Q8×C11—82no—
246D4×C11—21no—
247D4×C11—21no—
248D4×C11—21no—
249D4×C11#13512yes—
250C2×C4×C11—21no—
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—82no—
261C2×C4×C11C22×D411yescharacteristic
262C2×C4×C11C22×D411yescharacteristic
263C2×C4×C11H(5,𝔽2)11yescharacteristic
264C22⋊D11—82no—
265C22⋊D11—161no—
266C2×Dic11—21no—
267C2×Dic11—41no—
268D44—21no—
269D44—21no—
270D44—41no—
271D44—41no—
272D44—41no—
273D44—41no—
274D44—81no—
275D44—82no—
276C4×D11—41no—
277C4×D11—41no—
278Dic22—81no—
279C8×C11—21no—
280C8×C11—21no—
281C8×C11—41no—
282C11⋊C8—21no—
283C11⋊C8—41no—
284C11⋊C8—41no—
285C11⋊C8—41no—
286C11⋊C8—41no—
287C11⋊C8AGL(1,ℤ/8)12yes—
288C22×SD16—221no—
289#556C2×D1111yescharacteristic, complemented
290#555—111no—
291D4×Q8C2×D1111yescharacteristic
292D42—111no—
293#498—111no—
294#492—111no—
295#489—21no—
296#487—111no—
297#487C2×D1111yescharacteristic, complemented
298#486—111no—
299#486—111no—
300#485—221no—
301#482—221no—
302#482—221no—
303#477—21no—
304#477—111no—
305#476—111no—
306#474—111no—
307#474C2×D1111yescharacteristic, complemented
308#469—221no—
309#465—221no—
310#465—221no—
311#463—21no—
312#461—111no—
313#461C2×D1111yescharacteristic
314#460—111no—
315#459—111no—
316#450—221no—
317#448—221no—
318#447—221no—
319#446C2×D1111yescharacteristic, complemented
320#440—21no—
321C4×SD16—111no—
322C4×D8C2×D1111yescharacteristic
323#436—111no—
324C8×D4—111no—
325C8×D4—111no—
326#427—221no—
327#418—221no—
328#335—111no—
329#334—111no—
330#333—111no—
331#332—111no—
332#332—111no—
333#331—111no—
334Q8⋊C8—111no—
335D4⋊C8—111no—
336D4⋊C8—111no—
337D4⋊C8—111no—
338C82—111no—
339C22×C11—22no—
340C22×C11—41no—
341C22×C11—41no—
342C22×C11—41no—
343C22×C11—41no—
344C22×C11—41no—
345C22×C11D4211yescharacteristic
346C2×D11—41no—
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×C11C2×AGL(1,ℤ/8)11yescharacteristic
362C4×C11#57711yescharacteristic
363C4×C11#57711yescharacteristic
364Dic11—41no—
365Dic11—81no—
366C22×Q8—21no—
367C22×D4—221no—
368C22×D4—221no—
369C2×SD16—21no—
370C2×SD16—111no—
371C2×SD16—221no—
372C2×SD16—221no—
373C2×SD16—221no—
374C2×SD16—221no—
375C2×SD16—444no—
376C2×D8—221no—
377C2×D8C22⋊D1111yescharacteristic
378C2×M16—221no—
379C22×C8—221no—
380C22×C8—221no—
381C4⋊Q8—21no—
382C4⋊Q8—111no—
383C4⋊Q8C22×D1111yescharacteristic
384C4⋊Q8C22×D1111yescharacteristic
385#127—111no—
386#126—41no—
387#124—21no—
388#124—441no—
389C22⋊Q8—21no—
390C22⋊Q8—21no—
391C22⋊Q8—41no—
392#121—221no—
393#121—221no—
394#121—221no—
395#121—221no—
396#120—441no—
397C4×Q8—21no—
398C4×Q8C22×D1111yescharacteristic
399C4×D4—21no—
400C4×D4—111no—
401C4×D4C22×D1111yescharacteristic
402C4×D4C22×D1111yescharacteristic
403#117—21no—
404#117—221no—
405#117—221no—
406#107—21no—
407#107—221no—
408#107—221no—
409#107C22⋊D1111yescharacteristic
410#106—111no—
411#106—221no—
412#106—221no—
413#106—221no—
414C4⋊C8—21no—
415C4⋊C8—111no—
416C4⋊C8—111no—
417C4⋊C8—111no—
418C4⋊C8C22×D1111yescharacteristic
419#103—21no—
420#103—21no—
421#103—21no—
422#103—111no—
423#103—221no—
424#103—221no—
425#103—441no—
426#102—21no—
427#102—111no—
428#102—221no—
429#102—221no—
430#102—221no—
431#102—221no—
432#102—221no—
433#102—221no—
434#102—441no—
435#102C22⋊D1111yescharacteristic
436#102C22⋊D1111yescharacteristic
437C22⋊C8—221no—
438C22⋊C8—221no—
439C22⋊C8—221no—
440#97—21no—
441C4×C8—111no—
442C4×C8—111no—
443C4×C8C22×D1111yescharacteristic
444C2×C11—42no—
445C2×C11—81no—
446C2×C11#327211yescharacteristic
447C2×C11#328211yescharacteristic
448C2×C11#329011yescharacteristic
449D11—81no—
450D11—161no—
451C24—441no—
452C2×Q8—21no—
453C2×Q8—21no—
454C2×Q8—41no—
455C2×Q8—42no—
456C2×Q8—81no—
457C2×Q8—221no—
458C2×Q8D4×D1111yescharacteristic
459C2×D4—111no—
460C2×D4—221no—
461C2×D4—221no—
462C2×D4—221no—
463C2×D4—441no—
464C2×D4—442no—
465C2×D4—441no—
466C2×D4—442no—
467C2×D4—441no—
468C2×D4—881no—
469C2×D4—881no—
470C2×D4C2×C22⋊D1111yescharacteristic
471C2×D4C2×C22⋊D1111yescharacteristic
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—41no—
475C22×C4—221no—
476SD16—42no—
477SD16—222no—
478SD16—442no—
479SD16—442no—
480SD16—442no—
481SD16—881no—
482D8—22no—
483D8—881no—
484M16—881no—
485C2×C8—21no—
486C2×C8—111no—
487C2×C8—111no—
488C2×C8—221no—
489C2×C8—221no—
490C2×C8—221no—
491C2×C8—221no—
492C2×C8—442no—
493C2×C8—442no—
494C2×C8C2×C22⋊D1111yescharacteristic
495C2×C8C2×C22⋊D1111yescharacteristic
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—41no—
502C4⋊C4—41no—
503C4⋊C4—111no—
504C4⋊C4—221no—
505C4⋊C4—221no—
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—221no—
515C22⋊C4—441no—
516C22⋊C4—441no—
517C22⋊C4—441no—
518C42—21no—
519C42—41no—
520C42—441no—
521C42C23×D1111yescharacteristic
522C11#1991011yescharacteristic, 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—82no—
537Q8—881no—
538D4—21no—
539D4—21no—
540D4—21no—
541D4—221no—
542D4—221no—
543D4—441no—
544D4—441no—
545D4—441no—
546D4—441no—
547D4—881no—
548D4—882no—
549D4—882no—
550D4—1761no—
551D4#6700312yes—
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—82no—
563C2×C4—221no—
564C2×C4—441no—
565C2×C4—441no—
566C2×C4—441no—
567C2×C4C2×D4×D1111yescharacteristic
568C2×C4#6703711yescharacteristic
569C2×C4C22×C22⋊D1111yescharacteristic
570C8—21no—
571C8—21no—
572C8—41no—
573C8—112no—
574C8—221no—
575C8—441no—
576C8—441no—
577C8—441no—
578C8—441no—
579C22—22no—
580C22—41no—
581C22—41no—
582C22—41no—
583C22—41no—
584C22—41no—
585C22—441no—
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×AGL(1,ℤ/8)11yescharacteristic
603C4#1062330611yescharacteristic
604C4C2×#6700311yescharacteristic
605C4#1062336811yescharacteristic
606C2—42no—
607C2—81no—
608C2—881no—
609C2—1761no—
610C2#1308021011yescharacteristic
611C2#1308032411yescharacteristic
612C2#1308040211yescharacteristic
subgroupG/H
centerC22D4×C22⋊D11
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3367C2
socleC22×C11D42
prime radical#13080860C2
hypercenter#3367D11
hypocenterC11#19910
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #3367

Complements

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

NH ≅ G/Ntype
1. #13081023C2semidirect
3. D4×#4325C2semidirect
4. #13068219C2semidirect
5. #13068160C2semidirect
6. #13068156C2semidirect
7. #13067989C2semidirect
8. #13067959C2semidirect
9. #13067843C2semidirect
10. #13067793C2semidirect
11. #13067781C2semidirect
12. #13067726C2semidirect
13. #13067506C2semidirect
14. D8×C11⋊C8C2semidirect
15. C11×#3367C2semidirect
16. C11×#556C22semidirect
22. C11×#487C22semidirect
24. C11×#474C22semidirect
27. C11×#446C22semidirect
32. #10622706C22semidirect
37. #10622692C22semidirect
44. #10622634C22semidirect
47. D4×C11⋊C8C22semidirect
56. #10622185C22semidirect
57. #10622185C22semidirect
58. Q8⋊(C11⋊C8)C22semidirect
60. D4⋊(C11⋊C8)C22semidirect
63. #10622119C22semidirect
64. #10622118C22semidirect
65. #10622096C22semidirect
66. C8×C11⋊C8C22semidirect
217. #3367D11semidirect
289. #556C2×D11semidirect
297. #487C2×D11semidirect
307. #474C2×D11semidirect
319. #446C2×D11semidirect
522. C11#19910semidirect

Maximal subgroups

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

subgroupindex
#130810232
#130808602
D4×#43252
#130682192
#130681602
#130681562
#130679892
#130679592
#130678432
#130677932
#130677812
#130677262
#130675062
D8×C11⋊C82
C11×#33672
#1991011