Finite Group Databasebeta

← #14743271

Subgroups — #14743271

Order 2816.

668 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081522C211yesmaximal, characteristic, complemented
2#13080442C211yesmaximal, characteristic
3D4×#4325C211yesmaximal, characteristic
4#13068241C211yesmaximal, characteristic, complemented
5#13068090C211yesmaximal, characteristic, complemented
6#13068032C211yesmaximal, characteristic, complemented
7#13068013C211yesmaximal, characteristic, complemented
8#13067988C211yesmaximal, characteristic, complemented
9#13067822C211yesmaximal, characteristic, complemented
10#13067781C211yesmaximal, characteristic, complemented
11#13067731C211yesmaximal, characteristic
12#13067694C211yesmaximal, characteristic, complemented
13#13067453C211yesmaximal, characteristic, complemented
14#13067426C211yesmaximal, characteristic, complemented
15Q8×C11×SD16C211yesmaximal, characteristic, complemented
16Q82×C11C2211yescharacteristic, complemented
17D4×Q8×C11C2211yescharacteristic
18C22×#4325—21no—
19#10623110C2211yescharacteristic
20D4×D44C2211yescharacteristic
21C11×#498—21no—
22C11×#498C2211yescharacteristic, complemented
23C11×#476—21no—
24C11×#476C2211yescharacteristic
25C11×#475—21no—
26C11×#475C2211yescharacteristic, complemented
27C8×Q8×C11C2211yescharacteristic, complemented
28C4×C11×SD16—21no—
29C4×C11×SD16C2211yescharacteristic
30#10622840—21no—
31#10622782—21no—
32#10622706C2211yescharacteristic, complemented
33#10622700—21no—
34#10622698C2211yescharacteristic
35#10622698C2211yescharacteristic
36#10622697C2211yescharacteristic
37#10622696C2211yescharacteristic
38#10622693—21no—
39#10622691C2211yescharacteristic, complemented
40#10622661—21no—
41#10622659—21no—
42#10622640C2211yescharacteristic
43#10622640C2211yescharacteristic
44#10622639—21no—
45C4×#4325C2211yescharacteristic
46#10622637C2211yescharacteristic, complemented
47#10622635—21no—
48#10622634C2211yescharacteristic, complemented
49D4×C11⋊C8C2211yescharacteristic
50#10622621C2211yescharacteristic
51#10622476—21no—
52#10622420—21no—
53D11×#102—21no—
54#10622307C2211yescharacteristic
55C8×D44C2211yescharacteristic
56#10622185C2211yescharacteristic, complemented
57#10622184C2211yescharacteristic, complemented
58Q8⋊(C11⋊C8)C2211yescharacteristic, complemented
59Q8⋊(C11⋊C8)C2211yescharacteristic, complemented
60D4⋊(C11⋊C8)C2211yescharacteristic
61#10622123C2211yescharacteristic
62#10622121C2211yescharacteristic
63#10622119C2211yescharacteristic, complemented
64#10622117C2211yescharacteristic, complemented
65#10622095C2211yescharacteristic, complemented
66#10622092C2211yescharacteristic, complemented
67C22×Q8×C11—21no—
68C2×D4×D11—21no—
69C22×D44—21no—
70C2×C11×SD16D411yescharacteristic
71C11×C4⋊Q8—21no—
72C11×C4⋊Q8—21no—
73C11×C4⋊Q8—21no—
74C11×C4⋊Q8—41no—
75C11×C4⋊Q8C2311yescharacteristic
76C11×C4⋊Q8C2311yescharacteristic
77C11×C22⋊Q8—21no—
78C11×C22⋊Q8—41no—
79C4×Q8×C11—21no—
80C4×Q8×C11—21no—
81C4×Q8×C11C2311yescharacteristic
82C4×Q8×C11C2311yescharacteristic
83C4×D4×C11—21no—
84C4×D4×C11C2311yescharacteristic
85#66999—21no—
86C2×#4325—21no—
87C2×#4325—21no—
88C2×#4325—21no—
89C2×#4325—21no—
90C2×#4325—21no—
91C2×#4325—41no—
92C2×#4325—44no—
93C2×#4325D411yescharacteristic
94#66983—21no—
95C22×C11⋊C8—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×#106—21no—
107C11×#106—21no—
108C11×#106—21no—
109C11×#106—21no—
110C11×#106D411yescharacteristic
111C11×C4⋊C8—21no—
112C11×C4⋊C8C2311yescharacteristic
113C11×#103—21no—
114C11×#103D411yescharacteristic
115C11×#102—21no—
116C11×#102D411yescharacteristic
117C4×C8×C11—21no—
118C4×C8×C11C2311yescharacteristic
119#66899—21no—
120#66899—21no—
121#66899D411yescharacteristic
122#66896—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#66873D411yescharacteristic
132#66872—21no—
133#66872—21no—
134#66872D411yescharacteristic
135#66871—21no—
136#66871—21no—
137#66871—21no—
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#19765—111nomaximal, Sylow
146C23×D11—41no—
147C2×Q8×C11—21no—
148C2×Q8×C11—21no—
149C2×Q8×C11—41no—
150C2×Q8×C11—41no—
151C2×Q8×C11—42no—
152C2×Q8×C11—81no—
153C2×Q8×C11C2×D411yescharacteristic
154C2×Q8×C11C2×D411yescharacteristic
155C2×D4×C11C2×D411yescharacteristic
156C22×C4×C11—21no—
157C22×C4×C11—41no—
158C2×C22⋊D11—41no—
159D4×D11—42no—
160D4×D11—81no—
161C2×D44—21no—
162C2×D44—21no—
163C2×D44—21no—
164C2×D44—41no—
165C2×D44—42no—
166C2×D44—81no—
167C2×D44C2×D411yescharacteristic
168C2×C4×D11—21no—
169C2×C4×D11—41no—
170C2×Dic22—21no—
171C11×SD16—22no—
172C2×C8×C11—21no—
173C2×C8×C11C2×D411yescharacteristic
174C2×C8×C11C2×D411yescharacteristic
175C11×C4⋊C4—21no—
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⋊C4—41no—
184C11×C4⋊C4C2×D411yescharacteristic
185C11×C4⋊C4C2×D411yescharacteristic
186C11×C4⋊C4C2×D411yescharacteristic
187C11×C22⋊C4—21no—
188C11×C22⋊C4—41no—
189C42×C11—21no—
190C42×C11—21no—
191C42×C11—41no—
192C42×C11C2411yescharacteristic
193#4325—42no—
194#4325—42no—
195#4325—42no—
196#4325—81no—
197#4325—81no—
198#4325—82no—
199#4325SD1614yescomplemented
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—
208C2×C11⋊C8—21no—
209C2×C11⋊C8—21no—
210C2×C11⋊C8—21no—
211C2×C11⋊C8—21no—
212C2×C11⋊C8—42no—
213C2×C11⋊C8C2×D411yescharacteristic
214C2×C11⋊C8C2×D411yescharacteristic
215C8×D11—81no—
216#3385—111no—
217Q8×SD16D1111yescharacteristic, complemented
218#3295—111no—
219D4×SD16—111no—
220#1714—111no—
221#1686—111no—
222#1678—111no—
223#1675—111no—
224#1671—111no—
225#1643—111no—
226#1637—111no—
227#1629—111no—
228#1623—111no—
229#1582—111no—
230SD16⋊C8—111no—
231C23×C11—21no—
232C22×D11—21no—
233C22×D11—41no—
234C22×D11—82no—
235C22×D11—82no—
236C22×D11—161no—
237Q8×C11—21no—
238Q8×C11—21no—
239Q8×C11—21no—
240Q8×C11—41no—
241Q8×C11—41no—
242Q8×C11—82no—
243Q8×C11—81no—
244Q8×C11—161no—
245Q8×C11C2×SD1612yes—
246D4×C11—21no—
247D4×C11#13712yes—
248C2×C4×C11—21no—
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—82no—
258C2×C4×C11C22×D411yescharacteristic
259C2×C4×C11C22×D411yescharacteristic
260C2×C4×C11H(5,𝔽2)11yescharacteristic
261C22⋊D11—82no—
262C2×Dic11—21no—
263C2×Dic11—41no—
264D44—21no—
265D44—41no—
266D44—41no—
267D44—41no—
268D44—41no—
269D44—81no—
270D44—82no—
271D44C2×SD1612yes—
272C4×D11—41no—
273C4×D11—41no—
274C4×D11—161no—
275Dic22—81no—
276C8×C11—21no—
277C8×C11—21no—
278C8×C11—41no—
279C11⋊C8—21no—
280C11⋊C8—41no—
281C11⋊C8—41no—
282C11⋊C8—41no—
283C11⋊C8—41no—
284C11⋊C8C2×SD1612yes—
285C22×SD16—221no—
286Q82C2×D1111yescharacteristic, complemented
287#554—111no—
288D4×Q8C2×D1111yescharacteristic
289D42—111no—
290#501—221no—
291#500—111no—
292#498—21no—
293#498C2×D1111yescharacteristic, complemented
294#492—111no—
295#492—111no—
296#487—111no—
297#486—111no—
298#481—221no—
299#479—221no—
300#477—111no—
301#476—21no—
302#476—111no—
303#476—111no—
304#476C2×D1111yescharacteristic
305#475—21no—
306#475C2×D1111yescharacteristic, complemented
307#474—221no—
308#465—221no—
309#465—221no—
310#461—111no—
311#460—111no—
312#460—111no—
313#450—221no—
314#450—221no—
315#448—221no—
316#446—111no—
317C8×Q8C2×D1111yescharacteristic, complemented
318#440—221no—
319C4×SD16—21no—
320C4×SD16—111no—
321C4×SD16C2×D1111yescharacteristic
322C8×D4—111no—
323C8×D4—111no—
324C2×#102—221no—
325#335—111no—
326#334—111no—
327#333—111no—
328#333—111no—
329#332—111no—
330#331—111no—
331Q8⋊C8—111no—
332Q8⋊C8—111no—
333D4⋊C8—111no—
334D4⋊C8—111no—
335#322—111no—
336C22×C11—22no—
337C22×C11—41no—
338C22×C11—41no—
339C22×C11D4211yescharacteristic
340C2×D11—22no—
341C2×D11—41no—
342C2×D11—41no—
343C2×D11—81no—
344C2×D11—81no—
345C2×D11—81no—
346C2×D11—164no—
347C4×C11—22no—
348C4×C11—21no—
349C4×C11—41no—
350C4×C11—41no—
351C4×C11—41no—
352C4×C11—41no—
353C4×C11—81no—
354C4×C11—81no—
355C4×C11C22×SD1611yescharacteristic
356C4×C11C2×#13711yescharacteristic
357C4×C11#57711yescharacteristic
358C4×C11#57711yescharacteristic
359Dic11—41no—
360Dic11—81no—
361C22×Q8—21no—
362C22×D4—221no—
363C22×D4—221no—
364C2×SD16—111no—
365C2×SD16—221no—
366C2×SD16—221no—
367C2×SD16—221no—
368C2×SD16—221no—
369C2×SD16—221no—
370C2×SD16—441no—
371C2×SD16—444no—
372C2×SD16C22⋊D1111yescharacteristic
373C22×C8—221no—
374C22×C8—221no—
375C4⋊Q8—21no—
376C4⋊Q8—21no—
377C4⋊Q8—21no—
378C4⋊Q8—41no—
379C4⋊Q8—111no—
380C4⋊Q8C22×D1111yescharacteristic
381C4⋊Q8C22×D1111yescharacteristic
382#127—111no—
383#125—221no—
384C22⋊Q8—21no—
385C22⋊Q8—41no—
386C22⋊Q8—221no—
387C22⋊Q8—441no—
388#121—221no—
389#121—221no—
390#120—441no—
391C4×Q8—21no—
392C4×Q8—21no—
393C4×Q8C22×D1111yescharacteristic
394C4×Q8C22×D1111yescharacteristic
395C4×D4—21no—
396C4×D4—111no—
397C4×D4—221no—
398C4×D4C22×D1111yescharacteristic
399C2×C4⋊C4—221no—
400#107—221no—
401#107—221no—
402#107—221no—
403#106—21no—
404#106—21no—
405#106—21no—
406#106—21no—
407#106—111no—
408#106—221no—
409#106—221no—
410#106C22⋊D1111yescharacteristic
411C4⋊C8—21no—
412C4⋊C8—111no—
413C4⋊C8—111no—
414C4⋊C8—111no—
415C4⋊C8—221no—
416C4⋊C8C22×D1111yescharacteristic
417#103—21no—
418#103—111no—
419#103—221no—
420#103—221no—
421#103—441no—
422#103C22⋊D1111yescharacteristic
423#102—21no—
424#102—111no—
425#102—221no—
426#102—221no—
427#102—221no—
428#102—221no—
429#102—221no—
430#102—221no—
431#102C22⋊D1111yescharacteristic
432C22⋊C8—221no—
433C22⋊C8—221no—
434#97—221no—
435C4×C8—21no—
436C4×C8—111no—
437C4×C8—111no—
438C4×C8C22×D1111yescharacteristic
439C2×C11—42no—
440C2×C11#326611yescharacteristic
441C2×C11D4×SD1611yescharacteristic
442C2×C11#328811yescharacteristic
443D11—42no—
444D11—161no—
445C24—441no—
446C2×Q8—21no—
447C2×Q8—21no—
448C2×Q8—41no—
449C2×Q8—41no—
450C2×Q8—42no—
451C2×Q8—81no—
452C2×Q8—221no—
453C2×Q8D4×D1111yescharacteristic
454C2×Q8C2×C22⋊D1111yescharacteristic
455C2×D4—111no—
456C2×D4—221no—
457C2×D4—221no—
458C2×D4—221no—
459C2×D4—441no—
460C2×D4—442no—
461C2×D4—441no—
462C2×D4—442no—
463C2×D4—881no—
464C2×D4—881no—
465C2×D4C2×C22⋊D1111yescharacteristic
466C22×C4—21no—
467C22×C4—41no—
468C22×C4—221no—
469C22×C4—441no—
470SD16—22no—
471SD16—114no—
472SD16—442no—
473SD16—442no—
474SD16—442no—
475SD16—881no—
476SD16—881no—
477SD16—882no—
478C2×C8—21no—
479C2×C8—111no—
480C2×C8—111no—
481C2×C8—221no—
482C2×C8—221no—
483C2×C8—221no—
484C2×C8—221no—
485C2×C8—442no—
486C2×C8—881no—
487C2×C8C2×C22⋊D1111yescharacteristic
488C2×C8C2×C22⋊D1111yescharacteristic
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—41no—
496C4⋊C4—41no—
497C4⋊C4—41no—
498C4⋊C4—111no—
499C4⋊C4—221no—
500C4⋊C4—221no—
501C4⋊C4—441no—
502C4⋊C4—441no—
503C4⋊C4D4×D1111yescharacteristic
504C4⋊C4C2×C22⋊D1111yescharacteristic
505C4⋊C4C2×C22⋊D1111yescharacteristic
506C22⋊C4—21no—
507C22⋊C4—41no—
508C22⋊C4—221no—
509C22⋊C4—441no—
510C22⋊C4—441no—
511C42—21no—
512C42—21no—
513C42—41no—
514C42C23×D1111yescharacteristic
515C11#1976511yescharacteristic, complemented, Sylow
516C23—21no—
517C23—221no—
518C23—441no—
519C23—882no—
520C23—882no—
521C23—1761no—
522Q8—21no—
523Q8—21no—
524Q8—21no—
525Q8—41no—
526Q8—41no—
527Q8—82no—
528Q8—81no—
529Q8—161no—
530Q8—881no—
531Q8SD16×D1112yes—
532D4—21no—
533D4—112no—
534D4—221no—
535D4—441no—
536D4—441no—
537D4—441no—
538D4—441no—
539D4—881no—
540D4—882no—
541D4—882no—
542D4#6699512yes—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—82no—
553C2×C4—221no—
554C2×C4—441no—
555C2×C4—441no—
556C2×C4—441no—
557C2×C4—1761no—
558C2×C4C2×D4×D1111yescharacteristic
559C2×C4#6703711yescharacteristic
560C2×C4C22×C22⋊D1111yescharacteristic
561C8—21no—
562C8—21no—
563C8—41no—
564C8—112no—
565C8—221no—
566C8—441no—
567C8—441no—
568C8—441no—
569C8—441no—
570C22—22no—
571C22—41no—
572C22—41no—
573C22—222no—
574C22—441no—
575C22—441no—
576C22—881no—
577C22—881no—
578C22—881no—
579C22—1764no—
580C22D4×C22⋊D1111yescharacteristic
581C4—21no—
582C4—22no—
583C4—41no—
584C4—41no—
585C4—41no—
586C4—41no—
587C4—81no—
588C4—81no—
589C4—441no—
590C4—881no—
591C4C2×SD16×D1111yescharacteristic
592C4#1062329311yescharacteristic
593C4C2×#6699511yescharacteristic
594C4#1062336811yescharacteristic
595C2—42no—
596C2—442no—
597C2—1761no—
598C2#1308012711yescharacteristic
599C2SD16×C22⋊D1111yescharacteristic
600C2#1308037811yescharacteristic
subgroupG/H
centerC22D4×C22⋊D11
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingQ8×C11×SD16C2
socleC22×C11D42
prime radicalD4×D44C22
hypercenterQ8×SD16D11
hypocenterC11#19765
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ Q8×SD16

Complements

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

NH ≅ G/Ntype
1. #13081522C2semidirect
4. #13068241C2semidirect
5. #13068090C2semidirect
6. #13068032C2semidirect
7. #13068013C2semidirect
8. #13067988C2semidirect
9. #13067822C2semidirect
10. #13067781C2semidirect
12. #13067694C2semidirect
13. #13067453C2semidirect
14. #13067426C2semidirect
15. Q8×C11×SD16C2semidirect
16. Q82×C11C22semidirect
22. C11×#498C22semidirect
26. C11×#475C22semidirect
27. C8×Q8×C11C22semidirect
32. #10622706C22semidirect
39. #10622691C22semidirect
46. #10622637C22semidirect
48. #10622634C22semidirect
56. #10622185C22semidirect
57. #10622184C22semidirect
58. Q8⋊(C11⋊C8)C22semidirect
59. Q8⋊(C11⋊C8)C22semidirect
63. #10622119C22semidirect
64. #10622117C22semidirect
65. #10622095C22semidirect
66. #10622092C22semidirect
199. #4325SD16semidirect
217. Q8×SD16D11semidirect
286. Q82C2×D11semidirect
293. #498C2×D11semidirect
306. #475C2×D11semidirect
317. C8×Q8C2×D11semidirect
515. C11#19765semidirect

Maximal subgroups

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

subgroupindex
#130815222
#130804422
D4×#43252
#130682412
#130680902
#130680322
#130680132
#130679882
#130678222
#130677812
#130677312
#130676942
#130674532
#130674262
Q8×C11×SD162
#1976511