Finite Group Databasebeta

← #14737680

Subgroups — #14737680

Order 2816.

716 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079042C211yesmaximal, characteristic, complemented
2#13078767C211yesmaximal, characteristic, complemented
3#41×C11⋊C8C211yesmaximal, characteristic, complemented
4#13067984C211yesmaximal, characteristic, complemented
5#13067979C211yesmaximal, characteristic, complemented
6#13067974C211yesmaximal, characteristic, complemented
7#13067969C211yesmaximal, characteristic, complemented
8#13067966C211yesmaximal, characteristic, complemented
9#13067962C211yesmaximal, characteristic, complemented
10#13067959C211yesmaximal, characteristic, complemented
11#13067955C211yesmaximal, characteristic, complemented
12#13067377C211yesmaximal, characteristic, complemented
13#13067322C211yesmaximal, characteristic, complemented
14#13067321C211yesmaximal, characteristic, complemented
15C11×#3115C211yesmaximal, characteristic, complemented
16C11×#532C2211yescharacteristic
17C4×C11×#41C2211yescharacteristic
18C2×#67003—21no—
19C2×#67003—21no—
20#10623008C2211yescharacteristic
21C11×#482—21no—
22C11×#475C2211yescharacteristic
23C11×#474C2211yescharacteristic
24C11×#460C2211yescharacteristic
25C11×#459C2211yescharacteristic
26C11×#449—21no—
27C11×#442—21no—
28C11×#440—21no—
29C11×#432C2211yescharacteristic
30#10622851—21no—
31#10622705C2211yescharacteristic
32#10622698C2211yescharacteristic
33#10622689C2211yescharacteristic
34#10622686C2211yescharacteristic
35#10622672—21no—
36#10622672—21no—
37#10622640C2211yescharacteristic
38#10622639—21no—
39Q8×C11⋊C8C2211yescharacteristic
40Q8×C11⋊C8C2211yescharacteristic
41#10622633C2211yescharacteristic
42#10622628C2211yescharacteristic
43#10622627—21no—
44D4×C11⋊C8—21no—
45D4×C11⋊C8—21no—
46D4×C11⋊C8C2211yescharacteristic
47D4×C11⋊C8C2211yescharacteristic
48#10622620C2211yescharacteristic
49#10622616—21no—
50#10622539C2211yescharacteristic
51#10622538—21no—
52#10622538C2211yescharacteristic
53C2×C4×C11⋊C8—21no—
54C2×C4×C11⋊C8C2211yescharacteristic
55#10622185C2211yescharacteristic
56#10622185C2211yescharacteristic
57#10622182C2211yescharacteristic
58#10622182C2211yescharacteristic
59#10622124C2211yescharacteristic
60#10622124C2211yescharacteristic
61#10622123C2211yescharacteristic
62#10622123C2211yescharacteristic
63#10622118C2211yescharacteristic
64#10622118C2211yescharacteristic
65#10622117C2211yescharacteristic
66#10622117C2211yescharacteristic
67C2×C11×#41—21no—
68C2×C11×#41D411yescharacteristic
69C2×#4339—21no—
70C2×C11×SD16—21no—
71C2×C11×D8—21no—
72C11×C4⋊Q8C2311yescharacteristic
73C11×#127C2311yescharacteristic
74C11×#124—21no—
75C11×#121—21no—
76C11×#121—21no—
77C4×Q8×C11D411yescharacteristic
78C4×Q8×C11C2311yescharacteristic
79C4×D4×C11—21no—
80C4×D4×C11—21no—
81C4×D4×C11—21no—
82C4×D4×C11—21no—
83C4×D4×C11D411yescharacteristic
84C4×D4×C11C2311yescharacteristic
85C11×#117—21no—
86C11×#117D411yescharacteristic
87C2×C42×C11—21no—
88C2×C42×C11C2311yescharacteristic
89#67003—44no—
90#67003—44no—
91C2×#4326—21no—
92C2×#4326—21no—
93C2×#4325—21no—
94C2×#4325—21no—
95C2×#4325—21no—
96C2×#4324—21no—
97C2×#4324—21no—
98C2×#4323—21no—
99C2×#4323—21no—
100C2×#4323—21no—
101#66983—21no—
102#66983—21no—
103C22×C11⋊C8—21no—
104C22×C11⋊C8—21no—
105C22×C11⋊C8D411yescharacteristic
106C22×C11⋊C8D411yescharacteristic
107#66928—21no—
108#66927C2311yescharacteristic
109C4×D44—21no—
110C4×D44—21no—
111#66922C2311yescharacteristic
112C11×#107—21no—
113C11×#106—21no—
114C11×C4⋊C8C2311yescharacteristic
115C11×C4⋊C8C2311yescharacteristic
116C11×#103—21no—
117C11×#102—21no—
118C11×#102—21no—
119C11×#102—21no—
120C11×C22⋊C8—21no—
121C11×#97—21no—
122#66899—21no—
123#66896—21no—
124C22⋊(C11⋊C8)—21no—
125C22⋊(C11⋊C8)—21no—
126C22⋊(C11⋊C8)—21no—
127C22⋊(C11⋊C8)—21no—
128#66873—21no—
129#66873—21no—
130#66872—21no—
131#66871—21no—
132C4⋊(C11⋊C8)—21no—
133C4⋊(C11⋊C8)—21no—
134C4⋊(C11⋊C8)C2311yescharacteristic
135C4⋊(C11⋊C8)C2311yescharacteristic
136C4⋊(C11⋊C8)C2311yescharacteristic
137C4⋊(C11⋊C8)C2311yescharacteristic
138#66867—21no—
139C4×C11⋊C8—21no—
140C4×C11⋊C8—21no—
141C4×C11⋊C8—21no—
142C4×C11⋊C8D411yescharacteristic
143C4×C11⋊C8D411yescharacteristic
144C4×C11⋊C8C2311yescharacteristic
145C4×C11⋊C8C2311yescharacteristic
146#19269—111nomaximal, Sylow
147C11×#41—22no—
148C11×#41—22no—
149C11×#41—42no—
150C11×#41—42no—
151C2×Q8×C11—21no—
152C2×Q8×C11C2×D411yescharacteristic
153C2×D4×C11—21no—
154C2×D4×C11—21no—
155C2×D4×C11—21no—
156C2×D4×C11—21no—
157C2×D4×C11—41no—
158C2×D4×C11C2×D411yescharacteristic
159C22×C4×C11—21no—
160C22×C4×C11—21no—
161C22×C4×C11—21no—
162C22×C4×C11—41no—
163C22×C4×C11C2×D411yescharacteristic
164C22×C4×C11C2×D411yescharacteristic
165C22×C4×C11#4111yescharacteristic
166C2×C22⋊D11—41no—
167#4339—42no—
168#4339—42no—
169C2×D44—21no—
170C2×D44—21no—
171C2×D44—21no—
172C2×C4×D11—41no—
173C2×Dic22—21no—
174C11×SD16—42no—
175C11×D8—42no—
176C2×C8×C11—21no—
177C2×C8×C11—21no—
178C11×C4⋊C4—21no—
179C11×C4⋊C4—21no—
180C11×C4⋊C4—21no—
181C11×C4⋊C4—21no—
182C11×C4⋊C4C2×D411yescharacteristic
183C11×C4⋊C4C2×D411yescharacteristic
184C11×C22⋊C4—21no—
185C11×C22⋊C4—21no—
186C11×C22⋊C4—21no—
187C11×C22⋊C4—41no—
188C11×C22⋊C4—41no—
189C42×C11—21no—
190C42×C11—21no—
191C42×C11—21no—
192C42×C11C2×D411yescharacteristic
193C42×C11C2×D411yescharacteristic
194C42×C11#4111yescharacteristic
195C42×C11C2411yescharacteristic
196#4326—42no—
197#4326—42no—
198#4325—42no—
199#4325—42no—
200#4325—42no—
201#4324—42no—
202#4324—42no—
203#4323—42no—
204#4323—42no—
205#4323—42no—
206(C2×D11)⋊C4—41no—
207(C2×D11)⋊C4—41no—
208C4⋊Dic11—21no—
209C4⋊Dic11—21no—
210C2×C11⋊C8—22no—
211C2×C11⋊C8—22no—
212C2×C11⋊C8—21no—
213C2×C11⋊C8—21no—
214C2×C11⋊C8—21no—
215C2×C11⋊C8—21no—
216C2×C11⋊C8—42no—
217C2×C11⋊C8—42no—
218C2×C11⋊C8C2×D411yescharacteristic
219C2×C11⋊C8C2×D411yescharacteristic
220C2×C11⋊C8C2×D411yescharacteristic
221C2×C11⋊C8C2×D411yescharacteristic
222#3147—111no—
223#3115—111no—
224#3115D1111yescharacteristic, complemented
225C8×#41—111no—
226#1670—111no—
227#1669—111no—
228#1668—111no—
229#1667—111no—
230#1666—111no—
231#1666—111no—
232#1665—111no—
233#1665—111no—
234#1568—111no—
235#1553—111no—
236#1553—111no—
237C23×C11—21no—
238C23×C11—41no—
239C23×C11#12111yescharacteristic
240C22×D11—41no—
241Q8×C11—21no—
242Q8×C11—41no—
243Q8×C11—41no—
244Q8×C11#13512yescomplemented
245D4×C11—24no—
246D4×C11—21no—
247D4×C11—41no—
248D4×C11—41no—
249D4×C11—41no—
250D4×C11—41no—
251D4×C11—81no—
252D4×C11—82no—
253D4×C11#13512yescomplemented
254C2×C4×C11—24no—
255C2×C4×C11—21no—
256C2×C4×C11—21no—
257C2×C4×C11—21no—
258C2×C4×C11—21no—
259C2×C4×C11—21no—
260C2×C4×C11—21no—
261C2×C4×C11—21no—
262C2×C4×C11—41no—
263C2×C4×C11—42no—
264C2×C4×C11—41no—
265C2×C4×C11—41no—
266C2×C4×C11—41no—
267C2×C4×C11—82no—
268C2×C4×C11#12111yescharacteristic
269C2×C4×C11#12111yescharacteristic
270C2×C4×C11#12111yescharacteristic
271C2×C4×C11C22×D411yescharacteristic
272C2×C4×C11C22×D411yescharacteristic
273C2×C4×C11C2×#4111yescharacteristic
274C22⋊D11—82no—
275C2×Dic11—41no—
276D44—41no—
277D44—41no—
278D44—41no—
279D44—41no—
280D44—81no—
281C4×D11—82no—
282Dic22—41no—
283Dic22—41no—
284C8×C11—41no—
285C8×C11—41no—
286C11⋊C8—21no—
287C11⋊C8—21no—
288C11⋊C8—41no—
289C11⋊C8—41no—
290C11⋊C8—41no—
291C11⋊C8—41no—
292C11⋊C8AGL(1,ℤ/8)12yes—
293C11⋊C8AGL(1,ℤ/8)12yes—
294C2×#135—221no—
295C2×#135—221no—
296#532—111no—
297#532C2×D1111yescharacteristic
298C4×#41C2×D1111yescharacteristic
299#495—221no—
300#495—221no—
301#494—111no—
302#493—111no—
303#492—111no—
304#492—111no—
305#482—21no—
306#482—221no—
307#475—111no—
308#475C2×D1111yescharacteristic
309#474—111no—
310#474C2×D1111yescharacteristic
311#460—111no—
312#460C2×D1111yescharacteristic
313#459—111no—
314#459C2×D1111yescharacteristic
315#449—21no—
316#449—221no—
317C8×Q8—111no—
318C8×Q8—111no—
319#442—21no—
320#442—221no—
321#440—21no—
322#440—221no—
323C8×D4—111no—
324C8×D4—111no—
325C8×D4—221no—
326C8×D4—221no—
327#432—111no—
328#432C2×D1111yescharacteristic
329#431—111no—
330#431—221no—
331C2×C4×C8—111no—
332C2×C4×C8—221no—
333#335—111no—
334#335—111no—
335#334—111no—
336#334—111no—
337#332—111no—
338#332—111no—
339#332—111no—
340#332—111no—
341#331—111no—
342#331—111no—
343#331—111no—
344#331—111no—
345C22×C11—21no—
346C22×C11—21no—
347C22×C11—22no—
348C22×C11—21no—
349C22×C11—41no—
350C22×C11—41no—
351C22×C11—81no—
352C22×C11—81no—
353C22×C11—81no—
354C22×C11C2×#12111yescharacteristic
355C2×D11—81no—
356C2×D11—81no—
357C2×D11—81no—
358C4×C11—21no—
359C4×C11—21no—
360C4×C11—22no—
361C4×C11—21no—
362C4×C11—21no—
363C4×C11—41no—
364C4×C11—41no—
365C4×C11—81no—
366C4×C11C2×#13511yescharacteristic
367C4×C11C2×#13511yescharacteristic
368C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
369C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
370Dic11—81no—
371C2×#41—21no—
372C2×#41—221no—
373C2×#41C22⋊D1111yescharacteristic
374#135—444no—
375#135—444no—
376C2×Q16—221no—
377C2×Q16—221no—
378C2×SD16—21no—
379C2×SD16—221no—
380C2×SD16—221no—
381C2×SD16—221no—
382C2×SD16—221no—
383C2×SD16—221no—
384C2×D8—21no—
385C2×D8—221no—
386C2×D8—221no—
387C2×D8—221no—
388C22×C8—111no—
389C22×C8—111no—
390C22×C8—221no—
391C22×C8—221no—
392C4⋊Q8—111no—
393C4⋊Q8C22×D1111yescharacteristic
394#127—111no—
395#127C22×D1111yescharacteristic
396#124—21no—
397#124—221no—
398#121—21no—
399#121—21no—
400#121—221no—
401#121—221no—
402C4×Q8C22⋊D1111yescharacteristic
403C4×Q8C22×D1111yescharacteristic
404C4×D4—21no—
405C4×D4—21no—
406C4×D4—21no—
407C4×D4—21no—
408C4×D4—221no—
409C4×D4—221no—
410C4×D4C22⋊D1111yescharacteristic
411C4×D4C22×D1111yescharacteristic
412#117—21no—
413#117C22⋊D1111yescharacteristic
414C2×C42—21no—
415C2×C42C22×D1111yescharacteristic
416#107—21no—
417#107—221no—
418#106—21no—
419#106—221no—
420C4⋊C8—111no—
421C4⋊C8—111no—
422C4⋊C8—111no—
423C4⋊C8—111no—
424C4⋊C8—221no—
425C4⋊C8—221no—
426C4⋊C8C22×D1111yescharacteristic
427C4⋊C8C22×D1111yescharacteristic
428#103—21no—
429#103—221no—
430#102—21no—
431#102—21no—
432#102—21no—
433#102—221no—
434#102—221no—
435#102—221no—
436C22⋊C8—21no—
437C22⋊C8—221no—
438C22⋊C8—221no—
439C22⋊C8—221no—
440C22⋊C8—221no—
441#97—21no—
442#97—221no—
443C4×C8—111no—
444C4×C8—111no—
445C4×C8—111no—
446C4×C8—111no—
447C4×C8—221no—
448C4×C8—221no—
449C4×C8—221no—
450C2×C11—41no—
451C2×C11—42no—
452C2×C11—161no—
453C2×C11#303811yescharacteristic
454C2×C11#305011yescharacteristic
455C2×C11#306711yescharacteristic
456D11—161no—
457#41—22no—
458#41—22no—
459#41—42no—
460#41—42no—
461#41—442no—
462#41—442no—
463C2×Q8—21no—
464C2×Q8—221no—
465C2×Q8C2×C22⋊D1111yescharacteristic
466C2×D4—21no—
467C2×D4—21no—
468C2×D4—21no—
469C2×D4—21no—
470C2×D4—41no—
471C2×D4—221no—
472C2×D4—221no—
473C2×D4—221no—
474C2×D4—441no—
475C2×D4C2×C22⋊D1111yescharacteristic
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—41no—
480C22×C4—441no—
481C22×C4D4×D1111yescharacteristic
482C22×C4#434111yescharacteristic
483C22×C4C2×C22⋊D1111yescharacteristic
484Q16—442no—
485Q16—442no—
486SD16—42no—
487SD16—442no—
488SD16—442no—
489SD16—442no—
490SD16—442no—
491SD16—442no—
492D8—42no—
493D8—442no—
494D8—442no—
495D8—442no—
496C2×C8—21no—
497C2×C8—21no—
498C2×C8—111no—
499C2×C8—111no—
500C2×C8—111no—
501C2×C8—111no—
502C2×C8—222no—
503C2×C8—222no—
504C2×C8—221no—
505C2×C8—221no—
506C2×C8—221no—
507C2×C8—221no—
508C2×C8—442no—
509C2×C8—442no—
510C4⋊C4—21no—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—21no—
514C4⋊C4—221no—
515C4⋊C4—221no—
516C4⋊C4C2×C22⋊D1111yescharacteristic
517C4⋊C4C2×C22⋊D1111yescharacteristic
518C22⋊C4—21no—
519C22⋊C4—21no—
520C22⋊C4—21no—
521C22⋊C4—41no—
522C22⋊C4—41no—
523C22⋊C4—441no—
524C22⋊C4—441no—
525C42—21no—
526C42—21no—
527C42—21no—
528C42D4×D1111yescharacteristic
529C42#434111yescharacteristic
530C42C2×C22⋊D1111yescharacteristic
531C42C23×D1111yescharacteristic
532C11#1926911yescharacteristic, complemented, Sylow
533C23—21no—
534C23—41no—
535C23—441no—
536C23#6699211yescharacteristic
537Q8—21no—
538Q8—41no—
539Q8—41no—
540Q8—441no—
541Q8—441no—
542Q8#6700312yescomplemented
543D4—24no—
544D4—21no—
545D4—41no—
546D4—41no—
547D4—41no—
548D4—41no—
549D4—81no—
550D4—82no—
551D4—441no—
552D4—441no—
553D4—441no—
554D4—441no—
555D4—881no—
556D4—882no—
557D4#6700312yescomplemented
558C2×C4—24no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—41no—
567C2×C4—42no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—82no—
572C2×C4—441no—
573C2×C4—882no—
574C2×C4#6699211yescharacteristic
575C2×C4#6699211yescharacteristic
576C2×C4#6699211yescharacteristic
577C2×C4C2×D4×D1111yescharacteristic
578C2×C4C2×#434111yescharacteristic
579C2×C4C22×C22⋊D1111yescharacteristic
580C8—41no—
581C8—41no—
582C8—112no—
583C8—112no—
584C8—221no—
585C8—221no—
586C8—441no—
587C8—441no—
588C8—441no—
589C8—441no—
590C22—21no—
591C22—21no—
592C22—21no—
593C22—22no—
594C22—41no—
595C22—41no—
596C22—81no—
597C22—81no—
598C22—81no—
599C22—881no—
600C22—881no—
601C22—881no—
602C22C2×#6699211yescharacteristic
603C4—21no—
604C4—21no—
605C4—21no—
606C4—21no—
607C4—22no—
608C4—41no—
609C4—41no—
610C4—81no—
611C4—881no—
612C4D11×AGL(1,ℤ/8)11yescharacteristic
613C4D11×AGL(1,ℤ/8)11yescharacteristic
614C4C2×#6700311yescharacteristic
615C4C2×#6700311yescharacteristic
616C2—41no—
617C2—42no—
618C2—161no—
619C2—1761no—
620C2#1307809411yescharacteristic
621C2#1307819411yescharacteristic
622C2#1307833311yescharacteristic
subgroupG/H
centerC22C2×#66992
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3115C2
socleC22×C11C2×#121
hypercenter#3115D11
hypocenterC11#19269
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3115

Complements

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

NH ≅ G/Ntype
1. #13079042C2semidirect
2. #13078767C2semidirect
3. #41×C11⋊C8C2semidirect
4. #13067984C2semidirect
5. #13067979C2semidirect
6. #13067974C2semidirect
7. #13067969C2semidirect
8. #13067966C2semidirect
9. #13067962C2semidirect
10. #13067959C2semidirect
11. #13067955C2semidirect
12. #13067377C2semidirect
13. #13067322C2semidirect
14. #13067321C2semidirect
15. C11×#3115C2semidirect
224. #3115D11semidirect
244. Q8×C11#135semidirect
253. D4×C11#135semidirect
532. C11#19269semidirect
542. Q8#67003semidirect
557. D4#67003semidirect

Maximal subgroups

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

subgroupindex
#130790422
#130787672
#41×C11⋊C82
#130679842
#130679792
#130679742
#130679692
#130679662
#130679622
#130679592
#130679552
#130673772
#130673222
#130673212
C11×#31152
#1926911