Finite Group Databasebeta

← #14745268

Subgroups — #14745268

Order 2816.

648 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081265C211yesmaximal, characteristic, complemented
2#13080849C211yesmaximal, characteristic, complemented
3#13080423C211yesmaximal, characteristic
4#13068219C211yesmaximal, characteristic, complemented
5#13068188C211yesmaximal, characteristic, complemented
6#13068177C211yesmaximal, characteristic, complemented
7#13068069C211yesmaximal, characteristic, complemented
8#13068062C211yesmaximal, characteristic, complemented
9#13067900C211yesmaximal, characteristic, complemented
10#13067884C211yesmaximal, characteristic, complemented
11#13067731C211yesmaximal, characteristic, complemented
12#13067688C211yesmaximal, characteristic, complemented
13#13067499C211yesmaximal, characteristic, complemented
14SD16×C11⋊C8C211yesmaximal, characteristic, complemented
15C11×#3331C211yesmaximal, characteristic, complemented
16C11×#554C2211yescharacteristic, complemented
17C11×#547C2211yescharacteristic
18#10623115C2211yescharacteristic
19D4×D44C2211yescharacteristic
20C11×#487C2211yescharacteristic, complemented
21C11×#483—21no—
22C11×#476C2211yescharacteristic
23C11×#470—21no—
24C11×#462C2211yescharacteristic, complemented
25C11×#452—21no—
26C4×C11×SD16C2211yescharacteristic
27C11×#436C2211yescharacteristic, complemented
28C11×#417—21no—
29#10622782—21no—
30#10622706C2211yescharacteristic, complemented
31#10622701C2211yescharacteristic
32#10622700C2211yescharacteristic
33#10622698C2211yescharacteristic
34#10622697C2211yescharacteristic
35#10622692C2211yescharacteristic, complemented
36#10622681—21no—
37#10622676—21no—
38#10622651—21no—
39#10622649—21no—
40#10622640C2211yescharacteristic
41Q8×C11⋊C8C2211yescharacteristic, complemented
42#10622632C2211yescharacteristic, complemented
43C4×#4324—21no—
44#10622629—21no—
45#10622628C2211yescharacteristic
46C4×#4323C2211yescharacteristic
47D4×C11⋊C8C2211yescharacteristic
48#10622620C2211yescharacteristic
49#10622580—21no—
50C2×#66873—21no—
51#10622479—21no—
52#10622425—21no—
53#10622383—21no—
54#10622307C2211yescharacteristic
55#10622301C2211yescharacteristic
56#10622185C2211yescharacteristic, complemented
57#10622184C2211yescharacteristic, complemented
58Q8⋊(C11⋊C8)C2211yescharacteristic, complemented
59D4⋊(C11⋊C8)C2211yescharacteristic
60D4⋊(C11⋊C8)C2211yescharacteristic, complemented
61#10622124C2211yescharacteristic, complemented
62#10622123C2211yescharacteristic
63#10622121C2211yescharacteristic
64#10622117C2211yescharacteristic, complemented
65#10622095C2211yescharacteristic, complemented
66C8×C11⋊C8C2211yescharacteristic, complemented
67C2×C11×#41—21no—
68C2×D4×D11—21no—
69C22×D44—21no—
70C2×C11×Q16—21no—
71C2×C11×SD16D411yescharacteristic
72C2×C11×M16—21no—
73C11×C4⋊Q8C2311yescharacteristic
74C11×C4⋊Q8C2311yescharacteristic
75C11×#125—21no—
76C11×#123—41no—
77C11×C22⋊Q8—21no—
78C11×C22⋊Q8—21no—
79C11×C22⋊Q8—41no—
80C11×#121—21no—
81C4×Q8×C11C2311yescharacteristic
82C4×D4×C11—21no—
83C4×D4×C11C2311yescharacteristic
84C4×D4×C11C2311yescharacteristic
85C2×C11×C4⋊C4—21no—
86C2×C11×C4⋊C4—21no—
87#66999—21no—
88C2×#4325—21no—
89C2×#4325—41no—
90C2×#4324—21no—
91C2×#4323—21no—
92C2×#4323D411yescharacteristic
93#66983—21no—
94C22×C11⋊C8—21no—
95C2×#4313—21no—
96#66951—41no—
97#66948—21no—
98#66945—21no—
99#66935—41no—
100#66928—21no—
101#66927C2311yescharacteristic
102C4×D44C2311yescharacteristic
103#66922C2311yescharacteristic
104C4×Dic22—21no—
105C11×#106—21no—
106C11×#106D411yescharacteristic
107C11×C4⋊C8C2311yescharacteristic
108C11×#103—21no—
109C11×#103—21no—
110C11×#103—21no—
111C11×#103D411yescharacteristic
112C11×#102—21no—
113C11×#102D411yescharacteristic
114C11×C22⋊C8—21no—
115C4×C8×C11C2311yescharacteristic
116#66896—21no—
117#66896D411yescharacteristic
118C22⋊(C11⋊C8)—21no—
119#66885—21no—
120#66885—21no—
121(C2×D11)⋊C8—21no—
122#66874—21no—
123#66874—21no—
124#66874—21no—
125#66873—21no—
126#66873—21no—
127#66873—21no—
128#66873—21no—
129#66873—21no—
130#66873—21no—
131#66873D411yescharacteristic
132#66872—21no—
133#66872—41no—
134#66871—21no—
135#66871—21no—
136#66871D411yescharacteristic
137C4⋊(C11⋊C8)—21no—
138C4⋊(C11⋊C8)C2311yescharacteristic
139C4⋊(C11⋊C8)C2311yescharacteristic
140C4⋊(C11⋊C8)C2311yescharacteristic
141C4×C11⋊C8—21no—
142C4×C11⋊C8C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144#19901—111nomaximal, Sylow
145C23×D11—41no—
146C11×#41—42no—
147C11×#41—81no—
148C2×Q8×C11—21no—
149C2×Q8×C11—21no—
150C2×Q8×C11C2×D411yescharacteristic
151C2×D4×C11—41no—
152C2×D4×C11C2×D411yescharacteristic
153C2×D4×C11C2×D411yescharacteristic
154C22×C4×C11—21no—
155C22×C4×C11—21no—
156C22×C4×C11—41no—
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×Dic22—21no—
170C11×Q16—81no—
171C11×SD16—22no—
172C11×M16—81no—
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⋊C4—41no—
184C11×C4⋊C4C2×D411yescharacteristic
185C11×C4⋊C4C2×D411yescharacteristic
186C11×C4⋊C4C2×D411yescharacteristic
187C11×C22⋊C4—21no—
188C11×C22⋊C4—21no—
189C11×C22⋊C4—41no—
190C11×C22⋊C4—41no—
191C42×C11—21no—
192C42×C11C2411yescharacteristic
193#4325—81no—
194#4325—82no—
195#4324—42no—
196#4323—41no—
197#4323—81no—
198(C2×D11)⋊C4—21no—
199(C2×D11)⋊C4—41no—
200(C2×D11)⋊C4—41no—
201(C2×D11)⋊C4—41no—
202C4⋊Dic11—21no—
203C4⋊Dic11—21no—
204C4⋊Dic11C2×D411yescharacteristic
205Dic11⋊C4—41no—
206C4×Dic11—41no—
207C2×C11⋊C8—21no—
208C2×C11⋊C8—21no—
209C2×C11⋊C8—21no—
210C2×C11⋊C8—21no—
211C2×C11⋊C8—81no—
212C2×C11⋊C8C2×D411yescharacteristic
213C2×C11⋊C8C2×D411yescharacteristic
214#4313—81no—
215#3360—111no—
216#3331D1111yescharacteristic, complemented
217#3324—111no—
218#3294—111no—
219#1708—111no—
220#1703—111no—
221#1701—111no—
222#1683—111no—
223#1682—111no—
224#1654—111no—
225#1652—111no—
226#1629—111no—
227#1622—111no—
228#1589—111no—
229C8×SD16—111no—
230C23×C11—21no—
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—41no—
240Q8×C11—41no—
241Q8×C11—81no—
242D4×C11—21no—
243D4×C11—21no—
244D4×C11—21no—
245D4×C11—82no—
246D4×C11#13512yes—
247C2×C4×C11—21no—
248C2×C4×C11—21no—
249C2×C4×C11—21no—
250C2×C4×C11—21no—
251C2×C4×C11—41no—
252C2×C4×C11—41no—
253C2×C4×C11—41no—
254C2×C4×C11—41no—
255C2×C4×C11—41no—
256C2×C4×C11—41no—
257C2×C4×C11—82no—
258C2×C4×C11—161no—
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—21no—
267D44—41no—
268D44—41no—
269D44—41no—
270D44—41no—
271D44—81no—
272D44—82no—
273C4×D11—41no—
274C4×D11—41no—
275Dic22—41no—
276Dic22—41no—
277C8×C11—21no—
278C8×C11—21no—
279C8×C11—41no—
280C11⋊C8—22no—
281C11⋊C8—21no—
282C11⋊C8—21no—
283C11⋊C8—41no—
284C11⋊C8—41no—
285C11⋊C8—41no—
286#556—111no—
287#554C2×D1111yescharacteristic, complemented
288#547C2×D1111yescharacteristic
289D42—111no—
290#498—111no—
291#492—111no—
292#488—221no—
293#487—111no—
294#487C2×D1111yescharacteristic, complemented
295#486—111no—
296#486—111no—
297#483—21no—
298#482—221no—
299#480—221no—
300#479—221no—
301#476—111no—
302#476C2×D1111yescharacteristic
303#474—111no—
304#474—111no—
305#470—21no—
306#468—221no—
307#466—221no—
308#463—221no—
309#462C2×D1111yescharacteristic, complemented
310#461—111no—
311#460—111no—
312#459—111no—
313#452—21no—
314#450—221no—
315#447—221no—
316C8×Q8—111no—
317C4×SD16—221no—
318C4×SD16C2×D1111yescharacteristic
319C4×D8—111no—
320#436—111no—
321#436C2×D1111yescharacteristic, complemented
322C8×D4—111no—
323#418—221no—
324#417—21no—
325C2×#102—221no—
326#335—111no—
327#334—111no—
328#333—111no—
329#332—111no—
330#332—111no—
331#331—111no—
332Q8⋊C8—111no—
333D4⋊C8—111no—
334D4⋊C8—111no—
335D4⋊C8—111no—
336C82—111no—
337C22×C11—22no—
338C22×C11—41no—
339C22×C11—41no—
340C22×C11—41no—
341C22×C11—41no—
342C22×C11—41no—
343C22×C11D4211yescharacteristic
344C2×D11—41no—
345C2×D11—41no—
346C2×D11—41no—
347C2×D11—81no—
348C2×D11—81no—
349C2×D11—81no—
350C2×D11—164no—
351C4×C11—21no—
352C4×C11—41no—
353C4×C11—41no—
354C4×C11—41no—
355C4×C11—41no—
356C4×C11—81no—
357C4×C11—81no—
358C4×C11C2×#13511yescharacteristic
359C4×C11#57511yescharacteristic
360C4×C11#57611yescharacteristic
361C4×C11#57711yescharacteristic
362Dic11—41no—
363Dic11—81no—
364C2×#41—21no—
365C22×D4—221no—
366C22×D4—221no—
367C2×Q16—21no—
368C2×SD16—221no—
369C2×SD16—221no—
370C2×SD16—441no—
371C2×SD16C22⋊D1111yescharacteristic
372C2×D8—111no—
373C2×D8—221no—
374C2×M16—21no—
375C2×M16—221no—
376C22×C8—221no—
377C4⋊Q8—111no—
378C4⋊Q8C22×D1111yescharacteristic
379C4⋊Q8C22×D1111yescharacteristic
380#127—111no—
381#126—441no—
382#125—21no—
383#124—221no—
384#123—41no—
385C22⋊Q8—21no—
386C22⋊Q8—21no—
387C22⋊Q8—41no—
388C22⋊Q8—221no—
389#121—21no—
390#121—221no—
391#121—221no—
392#120—441no—
393C4×Q8—221no—
394C4×Q8C22×D1111yescharacteristic
395C4×D4—21no—
396C4×D4—111no—
397C4×D4C22×D1111yescharacteristic
398C4×D4C22×D1111yescharacteristic
399#117—221no—
400C2×C4⋊C4—21no—
401C2×C4⋊C4—21no—
402#107—111no—
403#107—221no—
404#107—221no—
405#106—21no—
406#106—221no—
407#106—441no—
408#106C22⋊D1111yescharacteristic
409C4⋊C8—111no—
410C4⋊C8—111no—
411C4⋊C8—111no—
412C4⋊C8—221no—
413C4⋊C8C22×D1111yescharacteristic
414#103—21no—
415#103—21no—
416#103—21no—
417#103—221no—
418#103—221no—
419#103—221no—
420#103C22⋊D1111yescharacteristic
421#102—21no—
422#102—111no—
423#102—111no—
424#102—221no—
425#102—221no—
426#102—221no—
427#102—221no—
428#102—221no—
429#102—221no—
430#102—221no—
431#102—221no—
432#102—221no—
433#102C22⋊D1111yescharacteristic
434C22⋊C8—21no—
435C22⋊C8—221no—
436C22⋊C8—221no—
437C4×C8—111no—
438C4×C8—111no—
439C4×C8—221no—
440C4×C8C22×D1111yescharacteristic
441C2×C11—42no—
442C2×C11—81no—
443C2×C11#327511yescharacteristic
444C2×C11#328011yescharacteristic
445C2×C11#329111yescharacteristic
446D11—81no—
447D11—161no—
448C24—441no—
449#41—42no—
450#41—81no—
451C2×Q8—21no—
452C2×Q8—21no—
453C2×Q8—221no—
454C2×Q8C2×C22⋊D1111yescharacteristic
455C2×D4—41no—
456C2×D4—111no—
457C2×D4—221no—
458C2×D4—221no—
459C2×D4—221no—
460C2×D4—441no—
461C2×D4—442no—
462C2×D4—441no—
463C2×D4—442no—
464C2×D4—881no—
465C2×D4—881no—
466C2×D4D4×D1111yescharacteristic
467C2×D4C2×C22⋊D1111yescharacteristic
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—41no—
471C22×C4—41no—
472C22×C4—221no—
473Q16—81no—
474SD16—22no—
475SD16—442no—
476SD16—882no—
477SD16—881no—
478D8—441no—
479D8—881no—
480M16—81no—
481M16—881no—
482C2×C8—21no—
483C2×C8—111no—
484C2×C8—111no—
485C2×C8—221no—
486C2×C8—221no—
487C2×C8—221no—
488C2×C8—221no—
489C2×C8—881no—
490C2×C8C2×C22⋊D1111yescharacteristic
491C2×C8C2×C22⋊D1111yescharacteristic
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—41no—
498C4⋊C4—41no—
499C4⋊C4—41no—
500C4⋊C4—111no—
501C4⋊C4—221no—
502C4⋊C4—221no—
503C4⋊C4—441no—
504C4⋊C4D4×D1111yescharacteristic
505C4⋊C4C2×C22⋊D1111yescharacteristic
506C4⋊C4C2×C22⋊D1111yescharacteristic
507C22⋊C4—21no—
508C22⋊C4—21no—
509C22⋊C4—41no—
510C22⋊C4—41no—
511C22⋊C4—221no—
512C22⋊C4—441no—
513C22⋊C4—441no—
514C22⋊C4—441no—
515C42—21no—
516C42—441no—
517C42C23×D1111yescharacteristic
518C11#1990111yescharacteristic, complemented, Sylow
519C23—21no—
520C23—21no—
521C23—221no—
522C23—441no—
523C23—882no—
524C23—882no—
525C23—1761no—
526Q8—21no—
527Q8—21no—
528Q8—41no—
529Q8—41no—
530Q8—81no—
531Q8—441no—
532Q8—441no—
533D4—21no—
534D4—21no—
535D4—21no—
536D4—82no—
537D4—221no—
538D4—221no—
539D4—441no—
540D4—441no—
541D4—441no—
542D4—441no—
543D4—881no—
544D4—882no—
545D4—882no—
546D4#6700312yes—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—82no—
558C2×C4—161no—
559C2×C4—221no—
560C2×C4—441no—
561C2×C4—441no—
562C2×C4—441no—
563C2×C4C2×D4×D1111yescharacteristic
564C2×C4#6703711yescharacteristic
565C2×C4C22×C22⋊D1111yescharacteristic
566C8—21no—
567C8—21no—
568C8—41no—
569C8—222no—
570C8—221no—
571C8—221no—
572C8—441no—
573C8—441no—
574C8—441no—
575C22—22no—
576C22—41no—
577C22—41no—
578C22—41no—
579C22—41no—
580C22—41no—
581C22—441no—
582C22—441no—
583C22—441no—
584C22—881no—
585C22—881no—
586C22—881no—
587C22—1764no—
588C22D4×C22⋊D1111yescharacteristic
589C4—21no—
590C4—41no—
591C4—41no—
592C4—41no—
593C4—41no—
594C4—81no—
595C4—81no—
596C4—441no—
597C4—881no—
598C4#1062330811yescharacteristic
599C4#1062330911yescharacteristic
600C4C2×#6700311yescharacteristic
601C4#1062336611yescharacteristic
602C2—42no—
603C2—81no—
604C2—881no—
605C2—1761no—
606C2#1308024111yescharacteristic
607C2#1308029711yescharacteristic
608C2#1308040711yescharacteristic
subgroupG/H
centerC22D4×C22⋊D11
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3331C2
socleC22×C11D42
prime radical#13080423C2
hypercenter#3331D11
hypocenterC11#19901
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #3331

Complements

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

NH ≅ G/Ntype
1. #13081265C2semidirect
2. #13080849C2semidirect
4. #13068219C2semidirect
5. #13068188C2semidirect
6. #13068177C2semidirect
7. #13068069C2semidirect
8. #13068062C2semidirect
9. #13067900C2semidirect
10. #13067884C2semidirect
11. #13067731C2semidirect
12. #13067688C2semidirect
13. #13067499C2semidirect
14. SD16×C11⋊C8C2semidirect
15. C11×#3331C2semidirect
16. C11×#554C22semidirect
20. C11×#487C22semidirect
24. C11×#462C22semidirect
27. C11×#436C22semidirect
30. #10622706C22semidirect
35. #10622692C22semidirect
41. Q8×C11⋊C8C22semidirect
42. #10622632C22semidirect
56. #10622185C22semidirect
57. #10622184C22semidirect
58. Q8⋊(C11⋊C8)C22semidirect
60. D4⋊(C11⋊C8)C22semidirect
61. #10622124C22semidirect
64. #10622117C22semidirect
65. #10622095C22semidirect
66. C8×C11⋊C8C22semidirect
216. #3331D11semidirect
287. #554C2×D11semidirect
294. #487C2×D11semidirect
309. #462C2×D11semidirect
321. #436C2×D11semidirect
518. C11#19901semidirect

Maximal subgroups

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

subgroupindex
#130812652
#130808492
#130804232
#130682192
#130681882
#130681772
#130680692
#130680622
#130679002
#130678842
#130677312
#130676882
#130674992
SD16×C11⋊C82
C11×#33312
#1990111