Finite Group Databasebeta

← #14745386

Subgroups — #14745386

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#13081330C211yesmaximal, characteristic, complemented
2#13080852C211yesmaximal, characteristic
3SD16×D44C211yesmaximal, characteristic, complemented
4#13068218C211yesmaximal, characteristic, complemented
5#13068161C211yesmaximal, characteristic, complemented
6#13068158C211yesmaximal, characteristic, complemented
7#13067988C211yesmaximal, characteristic, complemented
8#13067957C211yesmaximal, characteristic, complemented
9#13067844C211yesmaximal, characteristic, complemented
10#13067794C211yesmaximal, characteristic, complemented
11#13067779C211yesmaximal, characteristic, complemented
12#13067726C211yesmaximal, characteristic, complemented
13#13067507C211yesmaximal, characteristic, complemented
14C8×#4323C211yesmaximal, characteristic, complemented
15C11×#3340C211yesmaximal, characteristic, complemented
16C11×#556C2211yescharacteristic, complemented
17C11×#555C2211yescharacteristic
18C2×SD16×D11—21no—
19Q8×D44C2211yescharacteristic
20D4×D44C2211yescharacteristic
21C11×#498C2211yescharacteristic, complemented
22C11×#485—21no—
23C11×#482—21no—
24C11×#477C2211yescharacteristic, complemented
25C11×#474C2211yescharacteristic
26C11×#465—21no—
27C4×C11×SD16C2211yescharacteristic
28C8×D4×C11C2211yescharacteristic, complemented
29C11×#427—21no—
30#10622701C2211yescharacteristic
31#10622701C2211yescharacteristic
32#10622697C2211yescharacteristic
33#10622696C2211yescharacteristic
34#10622694C2211yescharacteristic, complemented
35#10622694C2211yescharacteristic, complemented
36#10622670—21no—
37#10622668—21no—
38#10622652—21no—
39#10622649—21no—
40#10622640C2211yescharacteristic
41#10622639—21no—
42#10622637C2211yescharacteristic, complemented
43#10622634—21no—
44#10622632C2211yescharacteristic
45#10622628C2211yescharacteristic
46C4×#4323C2211yescharacteristic
47#10622625C2211yescharacteristic
48#10622620C2211yescharacteristic, complemented
49#10622616—21no—
50#10622614—21no—
51#10622477—21no—
52#10622419—21no—
53#10622389—21no—
54#10622306C2211yescharacteristic
55C8×D44C2211yescharacteristic
56#10622185C2211yescharacteristic, complemented
57#10622184C2211yescharacteristic, complemented
58Q8⋊(C11⋊C8)C2211yescharacteristic, complemented
59D4⋊(C11⋊C8)C2211yescharacteristic
60D4⋊(C11⋊C8)C2211yescharacteristic, complemented
61#10622123C2211yescharacteristic
62#10622121C2211yescharacteristic
63#10622120C2211yescharacteristic, complemented
64#10622117C2211yescharacteristic, complemented
65#10622095C2211yescharacteristic, complemented
66C8×C11⋊C8C2211yescharacteristic, complemented
67C2×Q8×D11—21no—
68C2×D4×D11—21no—
69C22×D44—21no—
70C2×C11×SD16D411yescharacteristic
71C22×C8×C11—21no—
72C11×C4⋊Q8C2311yescharacteristic
73C11×C4⋊Q8C2311yescharacteristic
74C11×#126—41no—
75C11×#124—21no—
76C11×#124—41no—
77C11×C22⋊Q8—21no—
78C11×#121—21no—
79C11×#121—21no—
80C4×Q8×C11—21no—
81C4×Q8×C11C2311yescharacteristic
82C4×D4×C11C2311yescharacteristic
83C4×D4×C11C2311yescharacteristic
84C11×#117—21no—
85C11×#117—21no—
86C11×#117—21no—
87C2×#4325—21no—
88C2×#4325—21no—
89C2×#4324—21no—
90C2×#4323—21no—
91C2×#4323D411yescharacteristic
92#66983—21no—
93C2×#4318—21no—
94SD16×D11—44no—
95C2×#4314—21no—
96C2×#4314—21no—
97C2×C8×D11—21no—
98#66950—21no—
99#66950—41no—
100#66948—21no—
101#66935—41no—
102#66927C2311yescharacteristic
103C4×D44—21no—
104C4×D44C2311yescharacteristic
105#66922—21no—
106#66922C2311yescharacteristic
107C11×#107—21no—
108C11×#107—21no—
109C11×#106—21no—
110C11×#106—21no—
111C11×#106D411yescharacteristic
112C11×C4⋊C8C2311yescharacteristic
113C11×#103—21no—
114C11×#103D411yescharacteristic
115C11×#102—21no—
116C11×#102D411yescharacteristic
117C11×C22⋊C8—21no—
118C4×C8×C11C2311yescharacteristic
119#66899—21no—
120#66899—21no—
121#66899—21no—
122#66899—41no—
123#66896—21no—
124#66896D411yescharacteristic
125C22⋊(C11⋊C8)—21no—
126(C2×D11)⋊C8—21no—
127#66874—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#66871D411yescharacteristic
138C4⋊(C11⋊C8)—21no—
139C4⋊(C11⋊C8)C2311yescharacteristic
140C4⋊(C11⋊C8)C2311yescharacteristic
141C4⋊(C11⋊C8)C2311yescharacteristic
142#66867—21no—
143C4×C11⋊C8C2311yescharacteristic
144C4×C11⋊C8C2311yescharacteristic
145#19910—111nomaximal, Sylow
146C23×D11—41no—
147C2×Q8×C11—21no—
148C2×Q8×C11—21no—
149C2×Q8×C11C2×D411yescharacteristic
150C2×D4×C11—41no—
151C2×D4×C11C2×D411yescharacteristic
152C2×D4×C11C2×D411yescharacteristic
153C22×C4×C11—21no—
154C22×C4×C11—21no—
155C2×C22⋊D11—41no—
156Q8×D11—42no—
157Q8×D11—81no—
158D4×D11—42no—
159D4×D11—81no—
160C2×D44—21no—
161C2×D44—21no—
162C2×D44—21no—
163C2×D44—41no—
164C2×D44—42no—
165C2×D44—81no—
166C2×D44C2×D411yescharacteristic
167C2×C4×D11—21no—
168C2×C4×D11—41no—
169C2×Dic22—21no—
170C2×Dic22—41no—
171C11×SD16—22no—
172C2×C8×C11—21no—
173C2×C8×C11—42no—
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⋊C4C2×D411yescharacteristic
183C11×C4⋊C4C2×D411yescharacteristic
184C11×C4⋊C4C2×D411yescharacteristic
185C11×C22⋊C4—21no—
186C11×C22⋊C4—21no—
187C11×C22⋊C4—41no—
188C11×C22⋊C4—41no—
189C11×C22⋊C4—41no—
190C11×C22⋊C4—41no—
191C42×C11—21no—
192C42×C11—41no—
193C42×C11—41no—
194C42×C11C2411yescharacteristic
195#4325—42no—
196#4325—42no—
197#4324—42no—
198#4323—22no—
199#4323—81no—
200(C2×D11)⋊C4—21no—
201(C2×D11)⋊C4—41no—
202(C2×D11)⋊C4—41no—
203C4⋊Dic11—21no—
204C4⋊Dic11—21no—
205C4⋊Dic11—41no—
206C4⋊Dic11C2×D411yescharacteristic
207#4318—81no—
208C2×C11⋊C8—21no—
209C2×C11⋊C8—21no—
210C2×C11⋊C8—21no—
211C2×C11⋊C8—21no—
212C2×C11⋊C8C2×D411yescharacteristic
213C2×C11⋊C8C2×D411yescharacteristic
214#4314—42no—
215#4314—81no—
216C8×D11—42no—
217#3367—111no—
218#3340D1111yescharacteristic, complemented
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—81no—
244D4×C11—21no—
245D4×C11—21no—
246D4×C11—21no—
247D4×C11—21no—
248D4×C11—161no—
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—
263C2×Dic11—21no—
264C2×Dic11—41no—
265D44—21no—
266D44—41no—
267D44—41no—
268D44—41no—
269D44—41no—
270D44—81no—
271D44—82no—
272D44#13512yes—
273C4×D11—41no—
274C4×D11—41no—
275C4×D11—82no—
276Dic22—41no—
277Dic22—41no—
278Dic22—82no—
279C8×C11—21no—
280C8×C11—41no—
281C8×C11AGL(1,ℤ/8)12yes—
282C11⋊C8—21no—
283C11⋊C8—21no—
284C11⋊C8—41no—
285C11⋊C8—41no—
286C11⋊C8—41no—
287C11⋊C8—41no—
288C22×SD16—221no—
289#556C2×D1111yescharacteristic, complemented
290#555C2×D1111yescharacteristic
291D4×Q8—111no—
292D42—111no—
293#498C2×D1111yescharacteristic, complemented
294#492—111no—
295#489—221no—
296#487—111no—
297#487—111no—
298#486—111no—
299#486—111no—
300#485—21no—
301#482—21no—
302#482—221no—
303#477—221no—
304#477C2×D1111yescharacteristic, complemented
305#476—111no—
306#474—111no—
307#474C2×D1111yescharacteristic
308#469—221no—
309#465—21no—
310#465—221no—
311#463—221no—
312#461—111no—
313#461—111no—
314#460—111no—
315#459—111no—
316#450—221no—
317#448—221no—
318#447—221no—
319#446—111no—
320#440—221no—
321C4×SD16C2×D1111yescharacteristic
322C4×D8—111no—
323#436—111no—
324C8×D4—111no—
325C8×D4C2×D1111yescharacteristic, complemented
326#427—21no—
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—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×C11C2×AGL(1,ℤ/8)11yescharacteristic
362C4×C11#57711yescharacteristic
363C4×C11#57711yescharacteristic
364Dic11—41no—
365Dic11—81no—
366C22×Q8—221no—
367C22×D4—221no—
368C22×D4—221no—
369C2×SD16—221no—
370C2×SD16—221no—
371C2×SD16—221no—
372C2×SD16—221no—
373C2×SD16—221no—
374C2×SD16—444no—
375C2×SD16C22⋊D1111yescharacteristic
376C2×D8—111no—
377C2×D8—221no—
378C2×M16—221no—
379C22×C8—21no—
380C22×C8—221no—
381C4⋊Q8—111no—
382C4⋊Q8—221no—
383C4⋊Q8C22×D1111yescharacteristic
384C4⋊Q8C22×D1111yescharacteristic
385#127—111no—
386#126—41no—
387#124—21no—
388#124—41no—
389C22⋊Q8—21no—
390C22⋊Q8—221no—
391C22⋊Q8—441no—
392#121—21no—
393#121—21no—
394#121—221no—
395#121—221no—
396#120—441no—
397C4×Q8—21no—
398C4×Q8C22×D1111yescharacteristic
399C4×D4—111no—
400C4×D4—221no—
401C4×D4C22×D1111yescharacteristic
402C4×D4C22×D1111yescharacteristic
403#117—21no—
404#117—21no—
405#117—21no—
406#107—21no—
407#107—21no—
408#107—111no—
409#107—221no—
410#106—21no—
411#106—21no—
412#106—221no—
413#106C22⋊D1111yescharacteristic
414C4⋊C8—111no—
415C4⋊C8—111no—
416C4⋊C8—111no—
417C4⋊C8—221no—
418C4⋊C8C22×D1111yescharacteristic
419#103—21no—
420#103—221no—
421#103—221no—
422#103—221no—
423#103—221no—
424#103—441no—
425#103C22⋊D1111yescharacteristic
426#102—21no—
427#102—111no—
428#102—111no—
429#102—221no—
430#102—221no—
431#102—221no—
432#102—221no—
433#102—221no—
434#102—221no—
435#102—441no—
436#102C22⋊D1111yescharacteristic
437C22⋊C8—21no—
438C22⋊C8—221no—
439C22⋊C8—221no—
440#97—221no—
441C4×C8—111no—
442C4×C8—111no—
443C4×C8C22×D1111yescharacteristic
444C2×C11—81no—
445C2×C11—81no—
446C2×C11#327211yescharacteristic
447C2×C11#328211yescharacteristic
448C2×C11#329011yescharacteristic
449D11—42no—
450D11—161no—
451C24—441no—
452C2×Q8—21no—
453C2×Q8—21no—
454C2×Q8—221no—
455C2×Q8—441no—
456C2×Q8—442no—
457C2×Q8—881no—
458C2×Q8C2×C22⋊D1111yescharacteristic
459C2×D4—41no—
460C2×D4—111no—
461C2×D4—221no—
462C2×D4—221no—
463C2×D4—221no—
464C2×D4—441no—
465C2×D4—442no—
466C2×D4—441no—
467C2×D4—442no—
468C2×D4—881no—
469C2×D4—881no—
470C2×D4D4×D1111yescharacteristic
471C2×D4C2×C22⋊D1111yescharacteristic
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—221no—
475C22×C4—441no—
476SD16—22no—
477SD16—442no—
478SD16—442no—
479SD16—442no—
480SD16—442no—
481SD16—881no—
482D8—222no—
483D8—881no—
484M16—881no—
485C2×C8—21no—
486C2×C8—42no—
487C2×C8—111no—
488C2×C8—111no—
489C2×C8—221no—
490C2×C8—221no—
491C2×C8—221no—
492C2×C8—221no—
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—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#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—81no—
535Q8—441no—
536Q8—441no—
537Q8—882no—
538D4—21no—
539D4—21no—
540D4—21no—
541D4—21no—
542D4—112no—
543D4—161no—
544D4—221no—
545D4—441no—
546D4—441no—
547D4—441no—
548D4—441no—
549D4—881no—
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—41no—
572C8—221no—
573C8—221no—
574C8—441no—
575C8—441no—
576C8—441no—
577C8—441no—
578C8#6700212yes—
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#1062330111yescharacteristic
604C4C2×#6700211yescharacteristic
605C4#1062336811yescharacteristic
606C2—81no—
607C2—81no—
608C2—442no—
609C2—1761no—
610C2#1308021611yescharacteristic
611C2#1308031711yescharacteristic
612C2#1308039611yescharacteristic
subgroupG/H
centerC22D4×C22⋊D11
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3340C2
socleC22×C11D42
prime radical#13080852C2
hypercenter#3340D11
hypocenterC11#19910
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #3340

Complements

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

NH ≅ G/Ntype
1. #13081330C2semidirect
3. SD16×D44C2semidirect
4. #13068218C2semidirect
5. #13068161C2semidirect
6. #13068158C2semidirect
7. #13067988C2semidirect
8. #13067957C2semidirect
9. #13067844C2semidirect
10. #13067794C2semidirect
11. #13067779C2semidirect
12. #13067726C2semidirect
13. #13067507C2semidirect
14. C8×#4323C2semidirect
15. C11×#3340C2semidirect
16. C11×#556C22semidirect
21. C11×#498C22semidirect
24. C11×#477C22semidirect
28. C8×D4×C11C22semidirect
34. #10622694C22semidirect
35. #10622694C22semidirect
42. #10622637C22semidirect
48. #10622620C22semidirect
56. #10622185C22semidirect
57. #10622184C22semidirect
58. Q8⋊(C11⋊C8)C22semidirect
60. D4⋊(C11⋊C8)C22semidirect
63. #10622120C22semidirect
64. #10622117C22semidirect
65. #10622095C22semidirect
66. C8×C11⋊C8C22semidirect
218. #3340D11semidirect
289. #556C2×D11semidirect
293. #498C2×D11semidirect
304. #477C2×D11semidirect
325. C8×D4C2×D11semidirect
522. C11#19910semidirect

Maximal subgroups

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

subgroupindex
#130813302
#130808522
SD16×D442
#130682182
#130681612
#130681582
#130679882
#130679572
#130678442
#130677942
#130677792
#130677262
#130675072
C8×#43232
C11×#33402
#1991011