Finite Group Databasebeta

← #14745394

Subgroups — #14745394

Order 2816.

666 conjugacy classes of subgroups.

The subgroup lattice has 626 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13080860C211yesmaximal, characteristic, complemented
2#13080566C211yesmaximal, characteristic, complemented
3#13080434C211yesmaximal, characteristic, complemented
4#13068220C211yesmaximal, characteristic, complemented
5#13068156C211yesmaximal, characteristic, complemented
6#13068146C211yesmaximal, characteristic, complemented
7#13068027C211yesmaximal, characteristic, complemented
8#13068023C211yesmaximal, characteristic, complemented
9#13067760C211yesmaximal, characteristic, complemented
10#13067750C211yesmaximal, characteristic, complemented
11#13067681C211yesmaximal, characteristic, complemented
12#13067669C211yesmaximal, characteristic, complemented
13#13067506C211yesmaximal, characteristic, complemented
14D8×C11⋊C8C211yesmaximal, characteristic, complemented
15C11×#3366C211yesmaximal, characteristic, complemented
16C11×#554C2211yescharacteristic
17C11×#550C2211yescharacteristic, complemented
18#10623094C2211yescharacteristic
19D4×D44C2211yescharacteristic
20C11×#490—21no—
21C11×#486C2211yescharacteristic, complemented
22C11×#478—21no—
23C11×#476C2211yescharacteristic, complemented
24C11×#459—21no—
25C11×#459C2211yescharacteristic
26C11×#446C2211yescharacteristic, complemented
27C11×#442—21no—
28C4×C11×D8C2211yescharacteristic
29#10622851—21no—
30#10622846—21no—
31#10622769—21no—
32#10622705C2211yescharacteristic, complemented
33#10622701C2211yescharacteristic
34#10622697C2211yescharacteristic
35#10622686C2211yescharacteristic
36#10622685C2211yescharacteristic
37#10622683C2211yescharacteristic, complemented
38#10622661—21no—
39#10622659—21no—
40#10622651—21no—
41#10622648—21no—
42#10622640C2211yescharacteristic
43C4×#4325C2211yescharacteristic
44#10622634C2211yescharacteristic, complemented
45#10622628C2211yescharacteristic
46D4×C11⋊C8C2211yescharacteristic
47D4×C11⋊C8C2211yescharacteristic, complemented
48#10622621C2211yescharacteristic
49#10622581—21no—
50C2×#66873—21no—
51#10622498—21no—
52#10622395—21no—
53#10622383—21no—
54#10622307C2211yescharacteristic
55#10622301C2211yescharacteristic
56#10622184C2211yescharacteristic, complemented
57#10622182C2211yescharacteristic, complemented
58Q8⋊(C11⋊C8)C2211yescharacteristic, complemented
59D4⋊(C11⋊C8)C2211yescharacteristic
60D4⋊(C11⋊C8)C2211yescharacteristic, complemented
61#10622123C2211yescharacteristic
62#10622121C2211yescharacteristic
63#10622119C2211yescharacteristic, complemented
64#10622118C2211yescharacteristic, complemented
65#10622096C2211yescharacteristic, complemented
66C8×C11⋊C8C2211yescharacteristic, complemented
67C2×C11×#41—21no—
68C2×D4×D11—21no—
69C22×D44—21no—
70C2×C11×D8—21no—
71C2×C11×D8D411yescharacteristic
72C11×C4⋊Q8C2311yescharacteristic
73C11×#127—21no—
74C11×#127C2311yescharacteristic
75C11×#125—21no—
76C11×C22⋊Q8—21no—
77C11×C22⋊Q8—41no—
78C11×#121—21no—
79C11×#121—41no—
80C4×Q8×C11C2311yescharacteristic
81C4×D4×C11—21no—
82C4×D4×C11—21no—
83C4×D4×C11C2311yescharacteristic
84C4×D4×C11C2311yescharacteristic
85C2×C11×C4⋊C4—21no—
86C2×#4326—41no—
87C2×#4325—21no—
88C2×#4325D411yescharacteristic
89#66991—21no—
90C2×#4323—21no—
91C2×#4323—21no—
92C2×#4323—41no—
93#66983—21no—
94#66983—21no—
95#66979—21no—
96C22×C11⋊C8—21no—
97C22×C11⋊C8—21no—
98C2×#4313—21no—
99#66948—21no—
100#66945—21no—
101#66938—41no—
102#66935—41no—
103#66927C2311yescharacteristic
104C4×D44C2311yescharacteristic
105#66922C2311yescharacteristic
106C11×#107D411yescharacteristic
107C11×#106—21no—
108C11×C4⋊C8—21no—
109C11×C4⋊C8C2311yescharacteristic
110C11×#102—21no—
111C11×#102—21no—
112C11×#102—21no—
113C11×#102—21no—
114C11×#102D411yescharacteristic
115C11×#102D411yescharacteristic
116C11×#97—21no—
117C4×C8×C11C2311yescharacteristic
118#66899—21no—
119#66899D411yescharacteristic
120#66896—21no—
121#66896—21no—
122#66896—21no—
123#66896—21no—
124C22⋊(C11⋊C8)—21no—
125C22⋊(C11⋊C8)—21no—
126#66885—21no—
127#66885—21no—
128(C2×D11)⋊C8—21no—
129#66873—21no—
130#66873—21no—
131#66873—21no—
132#66873—21no—
133#66873—21no—
134#66873D411yescharacteristic
135#66872—21no—
136#66872—21no—
137#66872D411yescharacteristic
138#66871—21no—
139C4⋊(C11⋊C8)C2311yescharacteristic
140C4⋊(C11⋊C8)C2311yescharacteristic
141C4⋊(C11⋊C8)C2311yescharacteristic
142C4×C11⋊C8C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144#19911—111nomaximal, Sylow
145C23×D11—41no—
146C11×#41—42no—
147C11×#41—81no—
148C2×Q8×C11—21no—
149C2×Q8×C11C2×D411yescharacteristic
150C2×D4×C11—21no—
151C2×D4×C11—21no—
152C2×D4×C11—21no—
153C2×D4×C11—41no—
154C2×D4×C11—41no—
155C2×D4×C11C2×D411yescharacteristic
156C2×D4×C11C2×D411yescharacteristic
157C22×C4×C11—21no—
158C22×C4×C11—21no—
159C22×C4×C11—41no—
160C22×C4×C11—41no—
161C2×C22⋊D11—41no—
162C2×C22⋊D11—41no—
163D4×D11—42no—
164D4×D11—81no—
165C2×D44—21no—
166C2×D44—21no—
167C2×D44—21no—
168C2×D44—41no—
169C2×D44—42no—
170C2×D44—81no—
171C2×D44C2×D411yescharacteristic
172C2×C4×D11—21no—
173C2×Dic22—21no—
174C11×D8—22no—
175C11×D8—42no—
176C2×C8×C11—21no—
177C2×C8×C11C2×D411yescharacteristic
178C2×C8×C11C2×D411yescharacteristic
179C11×C4⋊C4—21no—
180C11×C4⋊C4—21no—
181C11×C4⋊C4—21no—
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
193C22⋊Dic11—41no—
194#4326—82no—
195#4325—41no—
196#4325—81no—
197#4323—81no—
198#4323—81no—
199#4323—82no—
200(C2×D11)⋊C4—21no—
201(C2×D11)⋊C4—41no—
202(C2×D11)⋊C4—41no—
203C4⋊Dic11—21no—
204C4⋊Dic11—21no—
205C4⋊Dic11C2×D411yescharacteristic
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⋊C8—81no—
213C2×C11⋊C8C2×D411yescharacteristic
214C2×C11⋊C8C2×D411yescharacteristic
215#4313—81no—
216#3366D1111yescharacteristic, complemented
217#3325—111no—
218#3305—111no—
219#3295—111no—
220#1709—111no—
221#1698—111no—
222#1697—111no—
223#1677—111no—
224#1677—111no—
225#1634—111no—
226#1632—111no—
227#1621—111no—
228#1619—111no—
229#1590—111no—
230C8×D8—111no—
231C23×C11—21no—
232C23×C11—21no—
233C23×C11—41no—
234C22×D11—21no—
235C22×D11—41no—
236C22×D11—82no—
237C22×D11—82no—
238C22×D11—161no—
239Q8×C11—21no—
240Q8×C11—21no—
241Q8×C11—81no—
242D4×C11—21no—
243D4×C11—21no—
244D4×C11—21no—
245D4×C11—41no—
246D4×C11—41no—
247D4×C11—41no—
248D4×C11—41no—
249D4×C11—81no—
250D4×C11—82no—
251D4×C11—161no—
252D4×C11#13512yes—
253C2×C4×C11—21no—
254C2×C4×C11—21no—
255C2×C4×C11—21no—
256C2×C4×C11—21no—
257C2×C4×C11—41no—
258C2×C4×C11—41no—
259C2×C4×C11—41no—
260C2×C4×C11—41no—
261C2×C4×C11—41no—
262C2×C4×C11—82no—
263C2×C4×C11—161no—
264C2×C4×C11C22×D411yescharacteristic
265C2×C4×C11C22×D411yescharacteristic
266C2×C4×C11H(5,𝔽2)11yescharacteristic
267C22⋊D11—82no—
268C22⋊D11—161no—
269C2×Dic11—21no—
270C2×Dic11—41no—
271D44—21no—
272D44—21no—
273D44—41no—
274D44—41no—
275D44—41no—
276D44—41no—
277D44—81no—
278D44—82no—
279C4×D11—41no—
280C4×D11—41no—
281Dic22—81no—
282C8×C11—21no—
283C8×C11—21no—
284C8×C11—41no—
285C11⋊C8—22no—
286C11⋊C8—21no—
287C11⋊C8—21no—
288C11⋊C8—41no—
289C11⋊C8—41no—
290C11⋊C8—41no—
291#555—111no—
292#554C2×D1111yescharacteristic
293#550C2×D1111yescharacteristic, complemented
294D42—111no—
295#494—111no—
296#493—111no—
297#490—21no—
298#486—111no—
299#486—111no—
300#486—111no—
301#486C2×D1111yescharacteristic, complemented
302#482—221no—
303#482—221no—
304#481—221no—
305#478—21no—
306#477—111no—
307#476—111no—
308#476—111no—
309#476C2×D1111yescharacteristic, complemented
310#469—221no—
311#466—221no—
312#465—221no—
313#460—111no—
314#459—21no—
315#459—111no—
316#459—111no—
317#459C2×D1111yescharacteristic
318#450—221no—
319#449—221no—
320#447—221no—
321#446C2×D1111yescharacteristic, complemented
322#442—21no—
323C4×SD16—111no—
324C4×D8C2×D1111yescharacteristic
325#436—111no—
326C8×D4—111no—
327C8×D4—111no—
328#418—221no—
329#416—221no—
330C2×#102—221no—
331#335—111no—
332#334—111no—
333#333—111no—
334#333—111no—
335#331—111no—
336#331—111no—
337Q8⋊C8—111no—
338D4⋊C8—111no—
339D4⋊C8—111no—
340D4⋊C8—111no—
341C82—111no—
342C22×C11—22no—
343C22×C11—41no—
344C22×C11—41no—
345C22×C11—41no—
346C22×C11—41no—
347C22×C11—41no—
348C22×C11—81no—
349C22×C11—81no—
350C22×C11—81no—
351C22×C11D4211yescharacteristic
352C2×D11—41no—
353C2×D11—41no—
354C2×D11—41no—
355C2×D11—81no—
356C2×D11—81no—
357C2×D11—81no—
358C2×D11—164no—
359C4×C11—21no—
360C4×C11—41no—
361C4×C11—41no—
362C4×C11—41no—
363C4×C11—41no—
364C4×C11—81no—
365C4×C11C2×#13511yescharacteristic
366C4×C11#57511yescharacteristic
367C4×C11#57611yescharacteristic
368C4×C11#57711yescharacteristic
369Dic11—41no—
370Dic11—81no—
371C2×#41—21no—
372C22×D4—221no—
373C22×D4—221no—
374C2×Q16—441no—
375C2×SD16—111no—
376C2×SD16—221no—
377C2×D8—21no—
378C2×D8—221no—
379C2×D8—221no—
380C2×D8—441no—
381C2×D8C22⋊D1111yescharacteristic
382C2×M16—221no—
383C22×C8—221no—
384C22×C8—221no—
385C4⋊Q8—111no—
386C4⋊Q8C22×D1111yescharacteristic
387#127—21no—
388#127—111no—
389#127C22×D1111yescharacteristic
390#125—21no—
391#124—441no—
392C22⋊Q8—21no—
393C22⋊Q8—41no—
394#121—21no—
395#121—41no—
396#121—221no—
397#121—221no—
398#121—221no—
399#121—221no—
400#120—441no—
401C4×Q8C22×D1111yescharacteristic
402C4×D4—21no—
403C4×D4—21no—
404C4×D4—111no—
405C4×D4C22×D1111yescharacteristic
406C4×D4C22×D1111yescharacteristic
407#117—221no—
408#117—221no—
409C2×C4⋊C4—21no—
410#107—221no—
411#107C22⋊D1111yescharacteristic
412#106—21no—
413#106—111no—
414#106—221no—
415#106—221no—
416C4⋊C8—21no—
417C4⋊C8—111no—
418C4⋊C8—111no—
419C4⋊C8—111no—
420C4⋊C8C22×D1111yescharacteristic
421#103—111no—
422#103—221no—
423#102—21no—
424#102—21no—
425#102—21no—
426#102—21no—
427#102—111no—
428#102—221no—
429#102—221no—
430#102—221no—
431#102—221no—
432#102—221no—
433#102—221no—
434#102—221no—
435#102—221no—
436#102—221no—
437#102—221no—
438#102—221no—
439#102C22⋊D1111yescharacteristic
440#102C22⋊D1111yescharacteristic
441C22⋊C8—221no—
442C22⋊C8—221no—
443C22⋊C8—221no—
444#97—21no—
445C4×C8—111no—
446C4×C8—111no—
447C4×C8C22×D1111yescharacteristic
448C2×C11—42no—
449C2×C11—81no—
450C2×C11—161no—
451C2×C11#327311yescharacteristic
452C2×C11#328211yescharacteristic
453C2×C11#329211yescharacteristic
454D11—81no—
455D11—161no—
456C24—441no—
457#41—42no—
458#41—81no—
459C2×Q8—21no—
460C2×Q8—221no—
461C2×Q8D4×D1111yescharacteristic
462C2×D4—21no—
463C2×D4—21no—
464C2×D4—21no—
465C2×D4—41no—
466C2×D4—41no—
467C2×D4—111no—
468C2×D4—221no—
469C2×D4—221no—
470C2×D4—221no—
471C2×D4—441no—
472C2×D4—442no—
473C2×D4—441no—
474C2×D4—442no—
475C2×D4—441no—
476C2×D4—881no—
477C2×D4—881no—
478C2×D4C2×C22⋊D1111yescharacteristic
479C2×D4C2×C22⋊D1111yescharacteristic
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—41no—
483C22×C4—41no—
484C22×C4—221no—
485Q16—882no—
486SD16—441no—
487SD16—881no—
488D8—22no—
489D8—42no—
490D8—882no—
491D8—881no—
492D8—881no—
493M16—881no—
494C2×C8—21no—
495C2×C8—111no—
496C2×C8—111no—
497C2×C8—221no—
498C2×C8—221no—
499C2×C8—221no—
500C2×C8—221no—
501C2×C8—881no—
502C2×C8—881no—
503C2×C8C2×C22⋊D1111yescharacteristic
504C2×C8C2×C22⋊D1111yescharacteristic
505C4⋊C4—21no—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—41no—
509C4⋊C4—41no—
510C4⋊C4—111no—
511C4⋊C4—221no—
512C4⋊C4—221no—
513C4⋊C4D4×D1111yescharacteristic
514C4⋊C4C2×C22⋊D1111yescharacteristic
515C4⋊C4C2×C22⋊D1111yescharacteristic
516C22⋊C4—21no—
517C22⋊C4—21no—
518C22⋊C4—41no—
519C22⋊C4—41no—
520C22⋊C4—221no—
521C22⋊C4—441no—
522C22⋊C4—441no—
523C22⋊C4—441no—
524C42—21no—
525C42—441no—
526C42C23×D1111yescharacteristic
527C11#1991111yescharacteristic, complemented, Sylow
528C23—21no—
529C23—21no—
530C23—41no—
531C23—221no—
532C23—441no—
533C23—882no—
534C23—882no—
535C23—1761no—
536Q8—21no—
537Q8—21no—
538Q8—81no—
539Q8—881no—
540D4—21no—
541D4—21no—
542D4—21no—
543D4—41no—
544D4—41no—
545D4—41no—
546D4—41no—
547D4—81no—
548D4—82no—
549D4—161no—
550D4—221no—
551D4—221no—
552D4—441no—
553D4—441no—
554D4—441no—
555D4—441no—
556D4—881no—
557D4—882no—
558D4—882no—
559D4—1761no—
560D4#6700312yes—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—82no—
571C2×C4—161no—
572C2×C4—221no—
573C2×C4—441no—
574C2×C4—441no—
575C2×C4—441no—
576C2×C4C2×D4×D1111yescharacteristic
577C2×C4#6703711yescharacteristic
578C2×C4C22×C22⋊D1111yescharacteristic
579C8—21no—
580C8—21no—
581C8—41no—
582C8—222no—
583C8—221no—
584C8—221no—
585C8—441no—
586C8—441no—
587C8—441no—
588C22—22no—
589C22—41no—
590C22—41no—
591C22—41no—
592C22—41no—
593C22—41no—
594C22—81no—
595C22—81no—
596C22—81no—
597C22—441no—
598C22—441no—
599C22—441no—
600C22—881no—
601C22—881no—
602C22—881no—
603C22—1764no—
604C22D4×C22⋊D1111yescharacteristic
605C4—21no—
606C4—41no—
607C4—41no—
608C4—41no—
609C4—41no—
610C4—81no—
611C4—441no—
612C4—881no—
613C4#1062330411yescharacteristic
614C4#1062330511yescharacteristic
615C4C2×#6700311yescharacteristic
616C4#1062336811yescharacteristic
617C2—42no—
618C2—81no—
619C2—161no—
620C2—881no—
621C2—1761no—
622C2#1308022111yescharacteristic
623C2#1308032411yescharacteristic
624C2#1308041311yescharacteristic
subgroupG/H
centerC22D4×C22⋊D11
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3366C2
socleC22×C11D42
hypercenter#3366D11
hypocenterC11#19911
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #3366

Complements

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

NH ≅ G/Ntype
1. #13080860C2semidirect
2. #13080566C2semidirect
3. #13080434C2semidirect
4. #13068220C2semidirect
5. #13068156C2semidirect
6. #13068146C2semidirect
7. #13068027C2semidirect
8. #13068023C2semidirect
9. #13067760C2semidirect
10. #13067750C2semidirect
11. #13067681C2semidirect
12. #13067669C2semidirect
13. #13067506C2semidirect
14. D8×C11⋊C8C2semidirect
15. C11×#3366C2semidirect
17. C11×#550C22semidirect
21. C11×#486C22semidirect
23. C11×#476C22semidirect
26. C11×#446C22semidirect
32. #10622705C22semidirect
37. #10622683C22semidirect
44. #10622634C22semidirect
47. D4×C11⋊C8C22semidirect
56. #10622184C22semidirect
57. #10622182C22semidirect
58. Q8⋊(C11⋊C8)C22semidirect
60. D4⋊(C11⋊C8)C22semidirect
63. #10622119C22semidirect
64. #10622118C22semidirect
65. #10622096C22semidirect
66. C8×C11⋊C8C22semidirect
216. #3366D11semidirect
293. #550C2×D11semidirect
301. #486C2×D11semidirect
309. #476C2×D11semidirect
321. #446C2×D11semidirect
527. C11#19911semidirect

Maximal subgroups

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

subgroupindex
#130808602
#130805662
#130804342
#130682202
#130681562
#130681462
#130680272
#130680232
#130677602
#130677502
#130676812
#130676692
#130675062
D8×C11⋊C82
C11×#33662
#1991111