Finite Group Databasebeta

← #14737463

Subgroups — #14737463

Order 2816.

624 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#13079942C211yesmaximal, characteristic, complemented
2#13079588C211yesmaximal, characteristic, complemented
3#13079354C211yesmaximal, characteristic, complemented
4#13068177C211yesmaximal, characteristic, complemented
5#13068149C211yesmaximal, characteristic, complemented
6#13068122C211yesmaximal, characteristic, complemented
7#13068100C211yesmaximal, characteristic, complemented
8#13068060C211yesmaximal, characteristic, complemented
9#13068032C211yesmaximal, characteristic, complemented
10#13067991C211yesmaximal, characteristic, complemented
11#13067971C211yesmaximal, characteristic, complemented
12#13067368C211yesmaximal, characteristic, complemented
13#13067276C211yesmaximal, characteristic, complemented
14#13067263C211yesmaximal, characteristic, complemented
15C11×#2969C211yesmaximal, characteristic, complemented
16C11×#529C2211yescharacteristic
17#10623008C2211yescharacteristic
18#10623008C2211yescharacteristic
19C11×#446C2211yescharacteristic
20C8×Q8×C11C2211yescharacteristic
21C11×#436—21no—
22C11×#436C2211yescharacteristic
23C11×#435—21no—
24C8×D4×C11C2211yescharacteristic
25C11×#433—21no—
26C11×#431C2211yescharacteristic
27C11×#405—21no—
28C4×C11×M16C2211yescharacteristic
29#10622748—21no—
30#10622748—21no—
31#10622681—21no—
32#10622679—21no—
33#10622672—21no—
34#10622670—21no—
35#10622661—21no—
36#10622660—21no—
37#10622651—21no—
38#10622650—21no—
39#10622644C2211yescharacteristic
40#10622640C2211yescharacteristic
41#10622640C2211yescharacteristic
42#10622634C2211yescharacteristic
43#10622632C2211yescharacteristic
44#10622628C2211yescharacteristic
45#10622628C2211yescharacteristic
46#10622621C2211yescharacteristic
47#10622538C2211yescharacteristic
48C2×C4⋊(C11⋊C8)C2211yescharacteristic
49#10622324—21no—
50#10622324—21no—
51#10622308C2211yescharacteristic
52#10622307C2211yescharacteristic
53#10622307C2211yescharacteristic
54#10622293C2211yescharacteristic
55#10622124C2211yescharacteristic
56#10622124C2211yescharacteristic
57#10622123C2211yescharacteristic
58#10622123C2211yescharacteristic
59#10622123C2211yescharacteristic
60#10622123C2211yescharacteristic
61#10622119C2211yescharacteristic
62#10622119C2211yescharacteristic
63#10622096C2211yescharacteristic
64#10622096C2211yescharacteristic
65#10622095C2211yescharacteristic
66#10622095C2211yescharacteristic
67C2×#4339—21no—
68C2×#4339—21no—
69C2×C11×M16—21no—
70C2×C11×M16D411yescharacteristic
71C2×C11×M16D411yescharacteristic
72C22×C8×C11—21no—
73C11×#126—21no—
74C11×#125D411yescharacteristic
75C11×#124D411yescharacteristic
76C11×#123—21no—
77C11×C22⋊Q8D411yescharacteristic
78C11×#121D411yescharacteristic
79C4×Q8×C11C2311yescharacteristic
80C4×D4×C11—21no—
81C4×D4×C11C2311yescharacteristic
82C11×#117—21no—
83C2×C42×C11C2311yescharacteristic
84C2×#4326—21no—
85C2×#4325—21no—
86C2×#4325—21no—
87C2×#4324—21no—
88C2×#4323—21no—
89C2×#4323—21no—
90#66983—21no—
91#66983—21no—
92#66983—21no—
93#66983—21no—
94C22×C11⋊C8—21no—
95C2×D88—21no—
96C2×D88—21no—
97#66928—21no—
98#66928—21no—
99#66927C2311yescharacteristic
100#66927C2311yescharacteristic
101C4×D44—21no—
102C4×D44—21no—
103C4×D44—21no—
104C4×D44—21no—
105#66922C2311yescharacteristic
106#66922C2311yescharacteristic
107C11×C4⋊C8—21no—
108C11×C4⋊C8—21no—
109C11×C4⋊C8C2311yescharacteristic
110C11×C4⋊C8C2311yescharacteristic
111C11×C22⋊C8—21no—
112C11×C22⋊C8—21no—
113C11×C22⋊C8—21no—
114C11×#97—21no—
115C11×#97D411yescharacteristic
116C11×#97D411yescharacteristic
117C4×C8×C11—21no—
118C4×C8×C11—21no—
119C4×C8×C11C2311yescharacteristic
120C4×C8×C11C2311yescharacteristic
121#66899—21no—
122#66896—21no—
123C22⋊(C11⋊C8)—21no—
124#66885—21no—
125#66885—21no—
126#66885—21no—
127#66885—21no—
128#66881—21no—
129#66881—21no—
130#66874—21no—
131#66874—21no—
132#66873—21no—
133#66873—21no—
134#66873—21no—
135#66873—21no—
136#66872—21no—
137#66871—21no—
138C4⋊(C11⋊C8)—21no—
139C4⋊(C11⋊C8)C2311yescharacteristic
140C4⋊(C11⋊C8)C2311yescharacteristic
141C4⋊(C11⋊C8)C2311yescharacteristic
142C4⋊(C11⋊C8)C2311yescharacteristic
143C4×C11⋊C8—21no—
144#19248—111nomaximal, Sylow
145C2×Q8×C11C2×D411yescharacteristic
146C2×D4×C11—21no—
147C2×D4×C11C2×D411yescharacteristic
148C22×C4×C11—21no—
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11#4111yescharacteristic
152C2×C22⋊D11—41no—
153C2×C22⋊D11—41no—
154#4339—81no—
155#4339—81no—
156#4339—82no—
157C2×D44—21no—
158C2×D44—21no—
159C2×D44—21no—
160C2×D44—21no—
161C2×D44—21no—
162C2×D44—21no—
163C2×C4×D11—41no—
164C2×C4×D11—41no—
165C2×Dic22—21no—
166C2×Dic22—21no—
167C11×M16—22no—
168C11×M16—41no—
169C11×M16—42no—
170C2×C8×C11—21no—
171C2×C8×C11—21no—
172C2×C8×C11—42no—
173C2×C8×C11C2×D411yescharacteristic
174C2×C8×C11C2×D411yescharacteristic
175C2×C8×C11C2×D411yescharacteristic
176C2×C8×C11C2×D411yescharacteristic
177C11×C4⋊C4—21no—
178C11×C4⋊C4—21no—
179C11×C4⋊C4—21no—
180C11×C4⋊C4—21no—
181C11×C4⋊C4C2×D411yescharacteristic
182C11×C4⋊C4C2×D411yescharacteristic
183C11×C22⋊C4—21no—
184C11×C22⋊C4—21no—
185C11×C22⋊C4—21no—
186C11×C22⋊C4—21no—
187C11×C22⋊C4—21no—
188C42×C11—21no—
189C42×C11C2×D411yescharacteristic
190C42×C11C2×D411yescharacteristic
191C42×C11#4111yescharacteristic
192C42×C11C2411yescharacteristic
193#4326—81no—
194#4325—81no—
195#4325—81no—
196#4324—81no—
197#4323—81no—
198#4323—81no—
199(C2×D11)⋊C4—41no—
200(C2×D11)⋊C4—41no—
201(C2×D11)⋊C4—41no—
202(C2×D11)⋊C4—41no—
203C4⋊Dic11—21no—
204C4⋊Dic11—21no—
205C4⋊Dic11—21no—
206C4⋊Dic11—21no—
207C2×C11⋊C8—21no—
208C2×C11⋊C8—21no—
209C2×C11⋊C8—21no—
210C2×C11⋊C8—21no—
211C2×C11⋊C8—81no—
212D88—42no—
213D88—42no—
214#3247—111no—
215#3212—111no—
216#3184—111no—
217#2969D1111yescharacteristic, complemented
218#1701—111no—
219#1697—111no—
220#1692—111no—
221#1688—111no—
222#1682—111no—
223#1678—111no—
224#1671—111no—
225#1667—111no—
226#1565—111no—
227#1543—111no—
228#1540—111no—
229C23×C11—21no—
230C23×C11#12111yescharacteristic
231C22×D11—41no—
232C22×D11—41no—
233Q8×C11—21no—
234Q8×C11—21no—
235D4×C11—21no—
236D4×C11—21no—
237D4×C11—81no—
238C2×C4×C11—21no—
239C2×C4×C11—21no—
240C2×C4×C11—21no—
241C2×C4×C11—21no—
242C2×C4×C11—21no—
243C2×C4×C11—21no—
244C2×C4×C11—21no—
245C2×C4×C11—41no—
246C2×C4×C11—41no—
247C2×C4×C11—41no—
248C2×C4×C11#12111yescharacteristic
249C2×C4×C11#12111yescharacteristic
250C2×C4×C11#12111yescharacteristic
251C2×C4×C11C22×D411yescharacteristic
252C2×C4×C11C22×D411yescharacteristic
253C2×C4×C11C2×#4111yescharacteristic
254C22⋊D11—82no—
255C22⋊D11—82no—
256C2×Dic11—41no—
257C2×Dic11—41no—
258D44—41no—
259D44—41no—
260D44—41no—
261D44—41no—
262D44—41no—
263D44—41no—
264D44—41no—
265D44—41no—
266D44—81no—
267D44—81no—
268C4×D11—82no—
269C4×D11—82no—
270Dic22—41no—
271Dic22—41no—
272Dic22—81no—
273C8×C11—21no—
274C8×C11—21no—
275C8×C11—21no—
276C8×C11—41no—
277C8×C11—41no—
278C8×C11#13512yes—
279C11⋊C8—41no—
280C11⋊C8—41no—
281C11⋊C8—41no—
282C11⋊C8—41no—
283#532—111no—
284#532—111no—
285#529C2×D1111yescharacteristic
286#498—111no—
287#495—221no—
288#493—111no—
289#488—221no—
290#486—111no—
291#486—111no—
292#478—221no—
293#477—111no—
294#476—111no—
295#469—221no—
296#469—221no—
297#466—221no—
298#465—221no—
299#463—221no—
300#462—111no—
301#461—111no—
302#460—111no—
303#460—111no—
304#459—111no—
305#459—111no—
306#452—221no—
307#449—221no—
308#446C2×D1111yescharacteristic
309C8×Q8C2×D1111yescharacteristic
310#442—221no—
311#442—221no—
312#436—21no—
313#436C2×D1111yescharacteristic
314#435—21no—
315C8×D4C2×D1111yescharacteristic
316#433—21no—
317#431—111no—
318#431C2×D1111yescharacteristic
319C2×C4⋊C8—111no—
320#405—21no—
321C4×M16C2×D1111yescharacteristic
322#335—111no—
323#335—111no—
324#334—111no—
325#334—111no—
326#333—111no—
327#333—111no—
328#332—111no—
329#332—111no—
330#331—111no—
331#331—111no—
332#331—111no—
333#331—111no—
334C22×C11—21no—
335C22×C11—21no—
336C22×C11—21no—
337C22×C11—41no—
338C22×C11—41no—
339C22×C11—41no—
340C22×C11C2×#12111yescharacteristic
341C2×D11—81no—
342C2×D11—81no—
343C2×D11—81no—
344C2×D11—81no—
345C2×D11—81no—
346C2×D11—81no—
347C4×C11—21no—
348C4×C11—21no—
349C4×C11—21no—
350C4×C11—21no—
351C4×C11—41no—
352C4×C11—41no—
353C4×C11—41no—
354C4×C11C2×#13511yescharacteristic
355C4×C11#57511yescharacteristic
356C4×C11#57611yescharacteristic
357C4×C11#57711yescharacteristic
358Dic11—81no—
359Dic11—81no—
360C2×#41—221no—
361C2×#41—221no—
362C2×Q16—221no—
363C2×SD16—221no—
364C2×SD16—221no—
365C2×SD16—221no—
366C2×D8—221no—
367C2×D8—221no—
368C2×D8—221no—
369C2×D8—221no—
370C2×M16—21no—
371C2×M16C22⋊D1111yescharacteristic
372C2×M16C22⋊D1111yescharacteristic
373C22×C8—21no—
374C22×C8—221no—
375C4⋊Q8—111no—
376C4⋊Q8—111no—
377#127—111no—
378#127—111no—
379#126—21no—
380#125D4411yescharacteristic
381#124—221no—
382#124—221no—
383#124D4411yescharacteristic
384#123—21no—
385C22⋊Q8D4411yescharacteristic
386#121—221no—
387#121—221no—
388#121—221no—
389#121—221no—
390#121D4411yescharacteristic
391C4×Q8C22×D1111yescharacteristic
392C4×D4—21no—
393C4×D4—221no—
394C4×D4—221no—
395C4×D4—221no—
396C4×D4—221no—
397C4×D4C22×D1111yescharacteristic
398#117—21no—
399C2×C42C22×D1111yescharacteristic
400#107—221no—
401#106—221no—
402#106—221no—
403#106—221no—
404C4⋊C8—21no—
405C4⋊C8—21no—
406C4⋊C8—111no—
407C4⋊C8—111no—
408C4⋊C8—111no—
409C4⋊C8—111no—
410C4⋊C8—221no—
411C4⋊C8C22×D1111yescharacteristic
412C4⋊C8C22×D1111yescharacteristic
413#103—221no—
414#103—221no—
415#103—221no—
416#102—221no—
417#102—221no—
418#102—221no—
419#102—221no—
420#102—221no—
421#102—221no—
422#102—221no—
423#102—221no—
424#102—221no—
425C22⋊C8—21no—
426C22⋊C8—21no—
427C22⋊C8—21no—
428C22⋊C8—221no—
429#97—21no—
430#97C22⋊D1111yescharacteristic
431#97C22⋊D1111yescharacteristic
432C4×C8—21no—
433C4×C8—21no—
434C4×C8—221no—
435C4×C8C22×D1111yescharacteristic
436C4×C8C22×D1111yescharacteristic
437C2×C11—41no—
438C2×C11—81no—
439C2×C11#303511yescharacteristic
440C2×C11#306211yescharacteristic
441C2×C11#306811yescharacteristic
442D11—161no—
443D11—161no—
444#41—881no—
445#41—881no—
446#41—882no—
447C2×Q8—221no—
448C2×Q8—221no—
449C2×Q8C2×D4411yescharacteristic
450C2×D4—21no—
451C2×D4—221no—
452C2×D4—221no—
453C2×D4—221no—
454C2×D4—221no—
455C2×D4—221no—
456C2×D4—221no—
457C2×D4—441no—
458C2×D4—441no—
459C2×D4C2×D4411yescharacteristic
460C22×C4—21no—
461C22×C4—441no—
462C22×C4—441no—
463C22×C4C2×D4411yescharacteristic
464C22×C4#433911yescharacteristic
465C22×C4C2×C22⋊D1111yescharacteristic
466Q16—881no—
467SD16—881no—
468SD16—881no—
469SD16—881no—
470D8—442no—
471D8—442no—
472D8—881no—
473D8—881no—
474M16—22no—
475M16—41no—
476M16—42no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—42no—
480C2×C8—221no—
481C2×C8—221no—
482C2×C8—221no—
483C2×C8—221no—
484C2×C8—881no—
485C2×C8C2×C22⋊D1111yescharacteristic
486C2×C8C2×C22⋊D1111yescharacteristic
487C2×C8C2×C22⋊D1111yescharacteristic
488C2×C8C2×C22⋊D1111yescharacteristic
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—221no—
494C4⋊C4—221no—
495C4⋊C4—221no—
496C4⋊C4—221no—
497C4⋊C4C2×D4411yescharacteristic
498C4⋊C4C2×D4411yescharacteristic
499C22⋊C4—21no—
500C22⋊C4—21no—
501C22⋊C4—21no—
502C22⋊C4—21no—
503C22⋊C4—21no—
504C22⋊C4—441no—
505C22⋊C4—441no—
506C22⋊C4—441no—
507C22⋊C4—441no—
508C42—21no—
509C42C2×D4411yescharacteristic
510C42#433911yescharacteristic
511C42C2×C22⋊D1111yescharacteristic
512C42C23×D1111yescharacteristic
513C11#1924811yescharacteristic, complemented, Sylow
514C23—21no—
515C23—441no—
516C23—441no—
517C23#6698311yescharacteristic
518Q8—21no—
519Q8—21no—
520Q8—441no—
521Q8—441no—
522Q8—881no—
523D4—21no—
524D4—21no—
525D4—81no—
526D4—441no—
527D4—441no—
528D4—441no—
529D4—441no—
530D4—441no—
531D4—441no—
532D4—441no—
533D4—441no—
534D4—881no—
535D4—881no—
536D4—882no—
537D4—882no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—441no—
549C2×C4—441no—
550C2×C4—882no—
551C2×C4—882no—
552C2×C4#6698311yescharacteristic
553C2×C4#6698311yescharacteristic
554C2×C4#6698311yescharacteristic
555C2×C4C22×D4411yescharacteristic
556C2×C4C2×#433911yescharacteristic
557C2×C4C22×C22⋊D1111yescharacteristic
558C8—21no—
559C8—21no—
560C8—21no—
561C8—41no—
562C8—41no—
563C8—441no—
564C8—441no—
565C8—441no—
566C8—441no—
567C8#6700312yes—
568C22—21no—
569C22—21no—
570C22—21no—
571C22—41no—
572C22—41no—
573C22—41no—
574C22—881no—
575C22—881no—
576C22—881no—
577C22—881no—
578C22—881no—
579C22—881no—
580C22C2×#6698311yescharacteristic
581C4—21no—
582C4—21no—
583C4—21no—
584C4—21no—
585C4—41no—
586C4—41no—
587C4—41no—
588C4—881no—
589C4—881no—
590C4#1062328211yescharacteristic
591C4#1062328311yescharacteristic
592C4C2×#6700311yescharacteristic
593C4#1062335311yescharacteristic
594C2—41no—
595C2—81no—
596C2—1761no—
597C2—1761no—
598C2#1307807111yescharacteristic
599C2#1307829611yescharacteristic
600C2#1307834411yescharacteristic
subgroupG/H
centerC22C2×#66983
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#2969C2
socleC22×C11C2×#121
hypercenter#2969D11
hypocenterC11#19248
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2969

Complements

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

NH ≅ G/Ntype
1. #13079942C2semidirect
2. #13079588C2semidirect
3. #13079354C2semidirect
4. #13068177C2semidirect
5. #13068149C2semidirect
6. #13068122C2semidirect
7. #13068100C2semidirect
8. #13068060C2semidirect
9. #13068032C2semidirect
10. #13067991C2semidirect
11. #13067971C2semidirect
12. #13067368C2semidirect
13. #13067276C2semidirect
14. #13067263C2semidirect
15. C11×#2969C2semidirect
217. #2969D11semidirect
513. C11#19248semidirect

Maximal subgroups

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

subgroupindex
#130799422
#130795882
#130793542
#130681772
#130681492
#130681222
#130681002
#130680602
#130680322
#130679912
#130679712
#130673682
#130672762
#130672632
C11×#29692
#1924811