Finite Group Databasebeta

← #14745275

Subgroups — #14745275

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#13080926C211yesmaximal, characteristic, complemented
2#13080841C211yesmaximal, characteristic, complemented
3#13080431C211yesmaximal, characteristic
4#13068219C211yesmaximal, characteristic, complemented
5#13068193C211yesmaximal, characteristic, complemented
6#13068179C211yesmaximal, characteristic, complemented
7#13068064C211yesmaximal, characteristic, complemented
8#13068060C211yesmaximal, characteristic, complemented
9#13067898C211yesmaximal, characteristic, complemented
10#13067886C211yesmaximal, characteristic, complemented
11#13067731C211yesmaximal, characteristic, complemented
12#13067688C211yesmaximal, characteristic, complemented
13#13067501C211yesmaximal, characteristic, complemented
14C8×#4325C211yesmaximal, characteristic, complemented
15C11×#3360C211yesmaximal, characteristic, complemented
16C11×#556C2211yescharacteristic
17C11×#554C2211yescharacteristic, complemented
18#10623082C2211yescharacteristic
19D4×D44C2211yescharacteristic
20C11×#488—21no—
21C11×#487C2211yescharacteristic, complemented
22C11×#479—21no—
23C11×#476C2211yescharacteristic
24C11×#463—21no—
25C11×#461C2211yescharacteristic, complemented
26C8×Q8×C11C2211yescharacteristic, complemented
27C4×C11×SD16—21no—
28C4×C11×D8C2211yescharacteristic
29#10622769—21no—
30#10622706C2211yescharacteristic, complemented
31#10622701C2211yescharacteristic
32#10622700C2211yescharacteristic
33#10622698C2211yescharacteristic
34#10622697C2211yescharacteristic
35#10622692C2211yescharacteristic, complemented
36#10622665—21no—
37#10622662—21no—
38#10622660—21no—
39#10622659—21no—
40#10622644C2211yescharacteristic, complemented
41#10622640C2211yescharacteristic
42C4×#4325C2211yescharacteristic
43#10622628C2211yescharacteristic
44#10622625C2211yescharacteristic
45#10622625C2211yescharacteristic, complemented
46#10622620C2211yescharacteristic
47#10622616—21no—
48#10622614—21no—
49#10622584—21no—
50#10622579—21no—
51#10622495—21no—
52#10622388—21no—
53D11×#102—21no—
54#10622307C2211yescharacteristic
55C8×D44C2211yescharacteristic
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#10622118C2211yescharacteristic, complemented
65#10622096C2211yescharacteristic, complemented
66C8×C11⋊C8C2211yescharacteristic, complemented
67C2×D4×D11—21no—
68C2×#4339—21no—
69C22×D44—21no—
70C2×C11×SD16—21no—
71C2×C11×D8D411yescharacteristic
72C11×C4⋊Q8C2311yescharacteristic
73C11×C4⋊Q8C2311yescharacteristic
74C11×#126—41no—
75C11×#125—21no—
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×C11×C4⋊C4—21no—
87C2×#4326—21no—
88C2×#4325—21no—
89C2×#4325—41no—
90C2×#4325D411yescharacteristic
91#66991—21no—
92C2×#4323—21no—
93#66983—21no—
94#66977—21no—
95C2×#4318—21no—
96C2×#4318—21no—
97C2×C8×D11—21no—
98#66948—21no—
99C4⋊C4×D11—21no—
100#66936—41no—
101#66935—41no—
102#66927C2311yescharacteristic
103C4×D44C2311yescharacteristic
104#66922C2311yescharacteristic
105C11×#107D411yescharacteristic
106C11×#106—21no—
107C11×C4⋊C8—21no—
108C11×C4⋊C8C2311yescharacteristic
109C11×#103—21no—
110C11×#103—21no—
111C11×#103—21no—
112C11×#102—21no—
113C11×#102D411yescharacteristic
114C11×#102D411yescharacteristic
115C4×C8×C11—21no—
116C4×C8×C11C2311yescharacteristic
117#66899D411yescharacteristic
118#66896—21no—
119C22⋊(C11⋊C8)—21no—
120C22⋊(C11⋊C8)—21no—
121#66885—21no—
122#66885—21no—
123(C2×D11)⋊C8—21no—
124#66874—21no—
125#66874—21no—
126#66874—21no—
127#66873—21no—
128#66873—21no—
129#66873—21no—
130#66873—21no—
131#66873—21no—
132#66873—21no—
133#66873D411yescharacteristic
134#66872—21no—
135#66872—41no—
136#66872D411yescharacteristic
137#66871—21no—
138#66871—21no—
139C4⋊(C11⋊C8)C2311yescharacteristic
140C4⋊(C11⋊C8)C2311yescharacteristic
141C4⋊(C11⋊C8)C2311yescharacteristic
142C4×C11⋊C8C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144#19901—111nomaximal, Sylow
145C23×D11—41no—
146C2×Q8×C11—21no—
147C2×Q8×C11—21no—
148C2×Q8×C11C2×D411yescharacteristic
149C2×D4×C11C2×D411yescharacteristic
150C2×D4×C11C2×D411yescharacteristic
151C22×C4×C11—21no—
152C22×C4×C11—21no—
153C22×C4×C11—41no—
154C2×C22⋊D11—41no—
155C2×C22⋊D11—41no—
156D4×D11—42no—
157D4×D11—81no—
158#4339—42no—
159#4339—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—
170C11×SD16—42no—
171C11×D8—41no—
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—41no—
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#4326—81no—
196#4325—22no—
197#4325—81no—
198#4325—82no—
199#4323—81no—
200(C2×D11)⋊C4—21no—
201(C2×D11)⋊C4—41no—
202C4⋊Dic11—21no—
203C4⋊Dic11—21no—
204C4⋊Dic11C2×D411yescharacteristic
205Dic11⋊C4—41no—
206#4318—81no—
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
214C8×D11—81no—
215#3360D1111yescharacteristic, complemented
216#3331—111no—
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—21no—
246C2×C4×C11—21no—
247C2×C4×C11—21no—
248C2×C4×C11—21no—
249C2×C4×C11—21no—
250C2×C4×C11—41no—
251C2×C4×C11—41no—
252C2×C4×C11—41no—
253C2×C4×C11—41no—
254C2×C4×C11—41no—
255C2×C4×C11—41no—
256C2×C4×C11—161no—
257C2×C4×C11C22×D411yescharacteristic
258C2×C4×C11C22×D411yescharacteristic
259C2×C4×C11H(5,𝔽2)11yescharacteristic
260C22⋊D11—82no—
261C22⋊D11—82no—
262C2×Dic11—21no—
263C2×Dic11—41no—
264D44—21no—
265D44—41no—
266D44—41no—
267D44—41no—
268D44—41no—
269D44—81no—
270D44—82no—
271D44#13512yes—
272C4×D11—41no—
273C4×D11—41no—
274C4×D11—82no—
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#556C2×D1111yescharacteristic
287#554C2×D1111yescharacteristic, complemented
288#547—111no—
289D42—111no—
290#498—111no—
291#492—111no—
292#488—21no—
293#487—111no—
294#487C2×D1111yescharacteristic, complemented
295#486—111no—
296#486—111no—
297#483—221no—
298#482—221no—
299#480—221no—
300#479—21no—
301#476—111no—
302#476C2×D1111yescharacteristic
303#474—111no—
304#474—111no—
305#470—221no—
306#468—221no—
307#466—221no—
308#463—21no—
309#462—111no—
310#461C2×D1111yescharacteristic, complemented
311#460—111no—
312#459—111no—
313#452—221no—
314#450—221no—
315#447—221no—
316C8×Q8C2×D1111yescharacteristic, complemented
317C4×SD16—21no—
318C4×SD16—111no—
319C4×D8C2×D1111yescharacteristic
320#436—111no—
321#436—111no—
322C8×D4—111no—
323#418—221no—
324#417—221no—
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—41no—
338C22×C11—41no—
339C22×C11—41no—
340C22×C11—41no—
341C22×C11—41no—
342C22×C11—41no—
343C22×C11D4211yescharacteristic
344C2×D11—22no—
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—221no—
365C22×D4—221no—
366C22×D4—221no—
367C2×Q16—221no—
368C2×SD16—21no—
369C2×SD16—111no—
370C2×SD16—221no—
371C2×SD16—441no—
372C2×D8—221no—
373C2×D8C22⋊D1111yescharacteristic
374C2×M16—221no—
375C2×M16—221no—
376C22×C8—221no—
377C4⋊Q8—111no—
378C4⋊Q8C22×D1111yescharacteristic
379C4⋊Q8C22×D1111yescharacteristic
380#127—111no—
381#126—41no—
382#125—21no—
383#124—21no—
384#123—441no—
385C22⋊Q8—21no—
386C22⋊Q8—21no—
387C22⋊Q8—41no—
388C22⋊Q8—221no—
389#121—221no—
390#121—221no—
391#121—221no—
392#120—441no—
393C4×Q8—21no—
394C4×Q8C22×D1111yescharacteristic
395C4×D4—21no—
396C4×D4—111no—
397C4×D4C22×D1111yescharacteristic
398C4×D4C22×D1111yescharacteristic
399#117—21no—
400C2×C4⋊C4—21no—
401C2×C4⋊C4—221no—
402#107—221no—
403#107—221no—
404#107C22⋊D1111yescharacteristic
405#106—21no—
406#106—111no—
407#106—221no—
408#106—441no—
409C4⋊C8—21no—
410C4⋊C8—111no—
411C4⋊C8—111no—
412C4⋊C8—111no—
413C4⋊C8C22×D1111yescharacteristic
414#103—21no—
415#103—21no—
416#103—21no—
417#103—111no—
418#103—221no—
419#103—221no—
420#103—221no—
421#102—21no—
422#102—111no—
423#102—221no—
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#102C22⋊D1111yescharacteristic
433#102C22⋊D1111yescharacteristic
434C22⋊C8—221no—
435C22⋊C8—221no—
436C22⋊C8—221no—
437C4×C8—21no—
438C4×C8—111no—
439C4×C8—111no—
440C4×C8C22×D1111yescharacteristic
441C2×C11—81no—
442C2×C11—81no—
443C2×C11#327511yescharacteristic
444C2×C11#328011yescharacteristic
445C2×C11#329111yescharacteristic
446D11—42no—
447D11—161no—
448C24—441no—
449#41—442no—
450#41—881no—
451C2×Q8—21no—
452C2×Q8—21no—
453C2×Q8—221no—
454C2×Q8D4×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—441no—
464C2×D4—881no—
465C2×D4—881no—
466C2×D4C2×C22⋊D1111yescharacteristic
467C2×D4C2×C22⋊D1111yescharacteristic
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—41no—
471C22×C4—221no—
472C22×C4—441no—
473Q16—881no—
474SD16—42no—
475SD16—222no—
476SD16—882no—
477SD16—881no—
478D8—41no—
479D8—881no—
480M16—881no—
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—41no—
512C22⋊C4—221no—
513C22⋊C4—441no—
514C22⋊C4—441no—
515C42—21no—
516C42—41no—
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—21no—
537D4—112no—
538D4—221no—
539D4—441no—
540D4—441no—
541D4—441no—
542D4—441no—
543D4—881no—
544D4—882no—
545D4—882no—
546D4—882no—
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—161no—
558C2×C4—221no—
559C2×C4—441no—
560C2×C4—441no—
561C2×C4—441no—
562C2×C4—882no—
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—41no—
576C22—41no—
577C22—41no—
578C22—41no—
579C22—41no—
580C22—41no—
581C22—222no—
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—
598C4D11×#13511yescharacteristic
599C4#1062330011yescharacteristic
600C4#1062335311yescharacteristic
601C4#1062336811yescharacteristic
602C2—81no—
603C2—81no—
604C2—442no—
605C2—1761no—
606C2#1308024811yescharacteristic
607C2#1308029511yescharacteristic
608C2#1308040711yescharacteristic
subgroupG/H
centerC22D4×C22⋊D11
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3360C2
socleC22×C11D42
prime radical#13080431C2
hypercenter#3360D11
hypocenterC11#19901
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #3360

Complements

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

NH ≅ G/Ntype
1. #13080926C2semidirect
2. #13080841C2semidirect
4. #13068219C2semidirect
5. #13068193C2semidirect
6. #13068179C2semidirect
7. #13068064C2semidirect
8. #13068060C2semidirect
9. #13067898C2semidirect
10. #13067886C2semidirect
11. #13067731C2semidirect
12. #13067688C2semidirect
13. #13067501C2semidirect
14. C8×#4325C2semidirect
15. C11×#3360C2semidirect
17. C11×#554C22semidirect
21. C11×#487C22semidirect
25. C11×#461C22semidirect
26. C8×Q8×C11C22semidirect
30. #10622706C22semidirect
35. #10622692C22semidirect
40. #10622644C22semidirect
45. #10622625C22semidirect
56. #10622185C22semidirect
57. #10622184C22semidirect
58. Q8⋊(C11⋊C8)C22semidirect
60. D4⋊(C11⋊C8)C22semidirect
61. #10622124C22semidirect
64. #10622118C22semidirect
65. #10622096C22semidirect
66. C8×C11⋊C8C22semidirect
215. #3360D11semidirect
287. #554C2×D11semidirect
294. #487C2×D11semidirect
310. #461C2×D11semidirect
316. C8×Q8C2×D11semidirect
518. C11#19901semidirect

Maximal subgroups

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

subgroupindex
#130809262
#130808412
#130804312
#130682192
#130681932
#130681792
#130680642
#130680602
#130678982
#130678862
#130677312
#130676882
#130675012
C8×#43252
C11×#33602
#1990111