Finite Group Databasebeta

← #14738920

Subgroups — #14738920

Order 2816.

606 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079978C211yesmaximal, characteristic
2#13079640C211yesmaximal, characteristic, complemented
3#13079010C211yesmaximal, characteristic, complemented
4#13068184C211yesmaximal, characteristic, complemented
5#13068177C211yesmaximal, characteristic, complemented
6#13068170C211yesmaximal, characteristic, complemented
7#13068163C211yesmaximal, characteristic, complemented
8#13068060C211yesmaximal, characteristic, complemented
9#13068053C211yesmaximal, characteristic, complemented
10#13068046C211yesmaximal, characteristic, complemented
11#13068039C211yesmaximal, characteristic, complemented
12#13067383C211yesmaximal, characteristic, complemented
13#13067319C211yesmaximal, characteristic, complemented
14#13067287C211yesmaximal, characteristic, complemented
15C11×#2969C211yesmaximal, characteristic, complemented
16C11×#529C2211yescharacteristic
17#10623008C2211yescharacteristic
18C2×#66922C2211yescharacteristic
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#10622746—21no—
30#10622746—21no—
31#10622682—21no—
32#10622679—21no—
33#10622673—21no—
34#10622670—21no—
35#10622663—21no—
36#10622662—21no—
37#10622653—21no—
38#10622652—21no—
39#10622644C2211yescharacteristic
40#10622644C2211yescharacteristic
41#10622640C2211yescharacteristic
42#10622633C2211yescharacteristic
43#10622632C2211yescharacteristic
44#10622632C2211yescharacteristic
45#10622628C2211yescharacteristic
46#10622620C2211yescharacteristic
47#10622539C2211yescharacteristic
48#10622537C2211yescharacteristic
49#10622327—21no—
50#10622327—21no—
51#10622307C2211yescharacteristic
52#10622307C2211yescharacteristic
53#10622294C2211yescharacteristic
54#10622294C2211yescharacteristic
55#10622124C2211yescharacteristic
56#10622124C2211yescharacteristic
57#10622124C2211yescharacteristic
58#10622124C2211yescharacteristic
59#10622123C2211yescharacteristic
60#10622123C2211yescharacteristic
61#10622120C2211yescharacteristic
62#10622120C2211yescharacteristic
63#10622096C2211yescharacteristic
64#10622096C2211yescharacteristic
65#10622095C2211yescharacteristic
66#10622095C2211yescharacteristic
67C2×#4339—21no—
68C22×Dic22—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×#4326—21no—
86C2×#4325—21no—
87C2×#4324—21no—
88C2×#4324—21no—
89C2×#4323—21no—
90#66983—21no—
91#66983—21no—
92C2×C4⋊Dic11—21no—
93C2×C4⋊Dic11—21no—
94C2×#4318—21no—
95#66928—21no—
96#66927C2311yescharacteristic
97C4×D44—21no—
98C4×D44—21no—
99#66922—21no—
100#66922—21no—
101#66922—21no—
102#66922C2311yescharacteristic
103#66922C2311yescharacteristic
104#66922C2311yescharacteristic
105C11×C4⋊C8—21no—
106C11×C4⋊C8—21no—
107C11×C4⋊C8C2311yescharacteristic
108C11×C4⋊C8C2311yescharacteristic
109C11×C22⋊C8—21no—
110C11×C22⋊C8—21no—
111C11×C22⋊C8—21no—
112C11×#97—21no—
113C11×#97D411yescharacteristic
114C11×#97D411yescharacteristic
115C4×C8×C11—21no—
116C4×C8×C11—21no—
117C4×C8×C11C2311yescharacteristic
118C4×C8×C11C2311yescharacteristic
119#66899—21no—
120#66896—21no—
121C22⋊(C11⋊C8)—21no—
122#66885—21no—
123#66885—21no—
124#66885—21no—
125#66885—21no—
126#66880—21no—
127#66880—21no—
128#66880—21no—
129#66880—21no—
130#66874—21no—
131#66874—21no—
132#66874—21no—
133#66874—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
143#66867—21no—
144#19383—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—
153C22×Dic11—41no—
154#4339—42no—
155#4339—42no—
156C2×D44—21no—
157C2×D44—21no—
158C2×D44—21no—
159C2×C4×D11—41no—
160C2×Dic22—21no—
161C2×Dic22—21no—
162C2×Dic22—21no—
163C2×Dic22—41no—
164C2×Dic22—81no—
165C2×Dic22—81no—
166C11×M16—41no—
167C11×M16—41no—
168C11×M16—42no—
169C2×C8×C11—21no—
170C2×C8×C11—21no—
171C2×C8×C11—42no—
172C2×C8×C11C2×D411yescharacteristic
173C2×C8×C11C2×D411yescharacteristic
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⋊C4C2×D411yescharacteristic
181C11×C4⋊C4C2×D411yescharacteristic
182C11×C22⋊C4—21no—
183C11×C22⋊C4—21no—
184C11×C22⋊C4—21no—
185C11×C22⋊C4—21no—
186C11×C22⋊C4—21no—
187C42×C11—21no—
188C42×C11C2×D411yescharacteristic
189C42×C11C2×D411yescharacteristic
190C42×C11#4111yescharacteristic
191C42×C11C2411yescharacteristic
192#4326—81no—
193#4326—81no—
194#4325—81no—
195#4324—81no—
196#4324—81no—
197#4323—81no—
198(C2×D11)⋊C4—41no—
199(C2×D11)⋊C4—41no—
200C4⋊Dic11—21no—
201C4⋊Dic11—21no—
202C4⋊Dic11—21no—
203C4⋊Dic11—21no—
204C4⋊Dic11—21no—
205C4⋊Dic11—21no—
206C4⋊Dic11—41no—
207C4⋊Dic11—41no—
208#4318—81no—
209C2×C11⋊C8—21no—
210C2×C11⋊C8—21no—
211C2×C11⋊C8—21no—
212C2×C11⋊C8—21no—
213#3251—111no—
214#3218—111no—
215#3141—111no—
216#2969D1111yescharacteristic, complemented
217#1702—111no—
218#1701—111no—
219#1700—111no—
220#1699—111no—
221#1682—111no—
222#1681—111no—
223#1680—111no—
224#1679—111no—
225#1569—111no—
226#1553—111no—
227#1546—111no—
228C23×C11—21no—
229C23×C11#12111yescharacteristic
230C22×D11—41no—
231Q8×C11—21no—
232Q8×C11—21no—
233D4×C11—21no—
234D4×C11—21no—
235D4×C11—81no—
236C2×C4×C11—21no—
237C2×C4×C11—21no—
238C2×C4×C11—21no—
239C2×C4×C11—21no—
240C2×C4×C11—21no—
241C2×C4×C11—21no—
242C2×C4×C11—21no—
243C2×C4×C11—41no—
244C2×C4×C11—41no—
245C2×C4×C11—41no—
246C2×C4×C11#12111yescharacteristic
247C2×C4×C11#12111yescharacteristic
248C2×C4×C11#12111yescharacteristic
249C2×C4×C11C22×D411yescharacteristic
250C2×C4×C11C22×D411yescharacteristic
251C2×C4×C11C2×#4111yescharacteristic
252C22⋊D11—82no—
253C2×Dic11—41no—
254C2×Dic11—41no—
255C2×Dic11—41no—
256C2×Dic11—82no—
257D44—41no—
258D44—41no—
259D44—41no—
260D44—41no—
261D44—81no—
262C4×D11—82no—
263Dic22—41no—
264Dic22—41no—
265Dic22—41no—
266Dic22—41no—
267Dic22—41no—
268Dic22—41no—
269Dic22—82no—
270C8×C11—21no—
271C8×C11—21no—
272C8×C11—21no—
273C8×C11—21no—
274C8×C11—41no—
275C8×C11—41no—
276C11⋊C8—41no—
277C11⋊C8—41no—
278C11⋊C8—41no—
279C11⋊C8—41no—
280#532—111no—
281C2×C4⋊Q8—111no—
282#529C2×D1111yescharacteristic
283#497—221no—
284#491—221no—
285#489—221no—
286#489—221no—
287#487—111no—
288#487—111no—
289#486—111no—
290#486—111no—
291#478—221no—
292#475—111no—
293#474—111no—
294#469—221no—
295#468—221no—
296#463—221no—
297#462—111no—
298#462—111no—
299#461—111no—
300#461—111no—
301#460—111no—
302#459—111no—
303#451—221no—
304#448—221no—
305#446C2×D1111yescharacteristic
306C8×Q8C2×D1111yescharacteristic
307#436—21no—
308#436C2×D1111yescharacteristic
309#435—21no—
310C8×D4C2×D1111yescharacteristic
311#433—21no—
312#432—111no—
313#431C2×D1111yescharacteristic
314#423—111no—
315#417—221no—
316#417—221no—
317#405—21no—
318C4×M16C2×D1111yescharacteristic
319#335—111no—
320#335—111no—
321#334—111no—
322#334—111no—
323#332—111no—
324#332—111no—
325#332—111no—
326#332—111no—
327#332—111no—
328#332—111no—
329#331—111no—
330#331—111no—
331C22×C11—21no—
332C22×C11—21no—
333C22×C11—21no—
334C22×C11—41no—
335C22×C11—41no—
336C22×C11—41no—
337C22×C11C2×#12111yescharacteristic
338C2×D11—81no—
339C2×D11—81no—
340C2×D11—81no—
341C4×C11—21no—
342C4×C11—21no—
343C4×C11—21no—
344C4×C11—21no—
345C4×C11—41no—
346C4×C11—41no—
347C4×C11—41no—
348C4×C11#57511yescharacteristic
349C4×C11#57511yescharacteristic
350C4×C11#57611yescharacteristic
351C4×C11#57711yescharacteristic
352Dic11—81no—
353Dic11—81no—
354Dic11—81no—
355C2×#41—221no—
356C22×Q8—221no—
357C2×Q16—221no—
358C2×Q16—221no—
359C2×SD16—221no—
360C2×SD16—221no—
361C2×SD16—221no—
362C2×D8—221no—
363C2×M16—21no—
364C2×M16—221no—
365C2×M16C22⋊D1111yescharacteristic
366C2×M16C22⋊D1111yescharacteristic
367C22×C8—21no—
368C4⋊Q8—111no—
369C4⋊Q8—111no—
370C4⋊Q8—111no—
371C4⋊Q8—221no—
372C4⋊Q8—221no—
373C4⋊Q8—221no—
374#127—111no—
375#126—21no—
376#125D4411yescharacteristic
377#124—221no—
378#124D4411yescharacteristic
379#123—21no—
380C22⋊Q8D4411yescharacteristic
381#121—221no—
382#121—221no—
383#121D4411yescharacteristic
384C4×Q8C22×D1111yescharacteristic
385C4×D4—21no—
386C4×D4—221no—
387C4×D4—221no—
388C4×D4C22×D1111yescharacteristic
389#117—21no—
390C2×C4⋊C4—221no—
391C2×C4⋊C4—221no—
392C2×C42C22×D1111yescharacteristic
393#107—221no—
394#106—221no—
395C4⋊C8—21no—
396C4⋊C8—21no—
397C4⋊C8—111no—
398C4⋊C8—111no—
399C4⋊C8—111no—
400C4⋊C8—111no—
401C4⋊C8—221no—
402C4⋊C8C22×D1111yescharacteristic
403C4⋊C8C22×D1111yescharacteristic
404#103—221no—
405#103—221no—
406#103—221no—
407#103—221no—
408#103—221no—
409#103—221no—
410#103—221no—
411#103—221no—
412#103—221no—
413#102—221no—
414#102—221no—
415#102—221no—
416#102—221no—
417#102—221no—
418#102—221no—
419#102—221no—
420C22⋊C8—21no—
421C22⋊C8—21no—
422C22⋊C8—21no—
423C22⋊C8—221no—
424#97—21no—
425#97—221no—
426#97C22⋊D1111yescharacteristic
427#97C22⋊D1111yescharacteristic
428C4×C8—21no—
429C4×C8—21no—
430C4×C8C22×D1111yescharacteristic
431C4×C8C22×D1111yescharacteristic
432C2×C11—41no—
433C2×C11—81no—
434C2×C11#304011yescharacteristic
435C2×C11#306211yescharacteristic
436C2×C11#306911yescharacteristic
437D11—161no—
438#41—442no—
439#41—442no—
440C2×Q8—221no—
441C2×Q8—221no—
442C2×Q8—221no—
443C2×Q8—441no—
444C2×Q8—881no—
445C2×Q8—881no—
446C2×Q8C2×D4411yescharacteristic
447C2×D4—21no—
448C2×D4—221no—
449C2×D4—221no—
450C2×D4—221no—
451C2×D4—441no—
452C2×D4C2×D4411yescharacteristic
453C22×C4—21no—
454C22×C4—441no—
455C22×C4—441no—
456C22×C4C2×D4411yescharacteristic
457C22×C4#433911yescharacteristic
458C22×C4C2×C22⋊D1111yescharacteristic
459Q16—881no—
460Q16—881no—
461SD16—881no—
462SD16—881no—
463SD16—881no—
464D8—881no—
465M16—41no—
466M16—41no—
467M16—42no—
468M16—881no—
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—42no—
472C2×C8—221no—
473C2×C8—221no—
474C2×C8—221no—
475C2×C8—221no—
476C2×C8C2×C22⋊D1111yescharacteristic
477C2×C8C2×C22⋊D1111yescharacteristic
478C2×C8C2×C22⋊D1111yescharacteristic
479C2×C8C2×C22⋊D1111yescharacteristic
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—221no—
485C4⋊C4—221no—
486C4⋊C4—221no—
487C4⋊C4—221no—
488C4⋊C4—221no—
489C4⋊C4—221no—
490C4⋊C4—441no—
491C4⋊C4—441no—
492C4⋊C4C2×D4411yescharacteristic
493C4⋊C4C2×D4411yescharacteristic
494C22⋊C4—21no—
495C22⋊C4—21no—
496C22⋊C4—21no—
497C22⋊C4—21no—
498C22⋊C4—21no—
499C22⋊C4—441no—
500C22⋊C4—441no—
501C42—21no—
502C42C2×D4411yescharacteristic
503C42#433911yescharacteristic
504C42C2×C22⋊D1111yescharacteristic
505C42C23×D1111yescharacteristic
506C11#1938311yescharacteristic, complemented, Sylow
507C23—21no—
508C23—441no—
509C23#6698311yescharacteristic
510Q8—21no—
511Q8—21no—
512Q8—441no—
513Q8—441no—
514Q8—441no—
515Q8—441no—
516Q8—441no—
517Q8—441no—
518Q8—882no—
519D4—21no—
520D4—21no—
521D4—81no—
522D4—441no—
523D4—441no—
524D4—441no—
525D4—441no—
526D4—881no—
527D4—882no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—441no—
539C2×C4—441no—
540C2×C4—441no—
541C2×C4—882no—
542C2×C4—882no—
543C2×C4#6698311yescharacteristic
544C2×C4#6698311yescharacteristic
545C2×C4#6698311yescharacteristic
546C2×C4C22×D4411yescharacteristic
547C2×C4C2×#433911yescharacteristic
548C2×C4C22×C22⋊D1111yescharacteristic
549C8—21no—
550C8—21no—
551C8—21no—
552C8—21no—
553C8—41no—
554C8—41no—
555C8—441no—
556C8—441no—
557C8—441no—
558C8—441no—
559C22—21no—
560C22—21no—
561C22—21no—
562C22—41no—
563C22—41no—
564C22—41no—
565C22—881no—
566C22—881no—
567C22—881no—
568C22C2×#6698311yescharacteristic
569C4—21no—
570C4—21no—
571C4—21no—
572C4—21no—
573C4—41no—
574C4—41no—
575C4—41no—
576C4—881no—
577C4—881no—
578C4—881no—
579C4#1062328211yescharacteristic
580C4#1062328311yescharacteristic
581C4#1062335311yescharacteristic
582C4#1062335311yescharacteristic
583C2—41no—
584C2—81no—
585C2—1761no—
586C2#1307811011yescharacteristic
587C2#1307829611yescharacteristic
588C2#1307835311yescharacteristic
subgroupG/H
centerC22C2×#66983
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#2969C2
socleC22×C11C2×#121
prime radical#13079978C2
hypercenter#2969D11
hypocenterC11#19383
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
2. #13079640C2semidirect
3. #13079010C2semidirect
4. #13068184C2semidirect
5. #13068177C2semidirect
6. #13068170C2semidirect
7. #13068163C2semidirect
8. #13068060C2semidirect
9. #13068053C2semidirect
10. #13068046C2semidirect
11. #13068039C2semidirect
12. #13067383C2semidirect
13. #13067319C2semidirect
14. #13067287C2semidirect
15. C11×#2969C2semidirect
216. #2969D11semidirect
506. C11#19383semidirect

Maximal subgroups

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

subgroupindex
#130799782
#130796402
#130790102
#130681842
#130681772
#130681702
#130681632
#130680602
#130680532
#130680462
#130680392
#130673832
#130673192
#130672872
C11×#29692
#1938311