Finite Group Databasebeta

← #14745133

Subgroups — #14745133

Order 2816.

686 conjugacy classes of subgroups.

The subgroup lattice has 622 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081511C211yesmaximal, characteristic, complemented
2#13080442C211yesmaximal, characteristic, complemented
3#13080216C211yesmaximal, characteristic
4#13068219C211yesmaximal, characteristic, complemented
5#13068113C211yesmaximal, characteristic, complemented
6#13068090C211yesmaximal, characteristic, complemented
7#13068036C211yesmaximal, characteristic, complemented
8#13068025C211yesmaximal, characteristic, complemented
9#13067822C211yesmaximal, characteristic, complemented
10#13067793C211yesmaximal, characteristic, complemented
11#13067767C211yesmaximal, characteristic, complemented
12#13067719C211yesmaximal, characteristic, complemented
13#13067507C211yesmaximal, characteristic, complemented
14C8×#4323C211yesmaximal, characteristic, complemented
15C11×#3298C211yesmaximal, characteristic, complemented
16D4×Q8×C11C2211yescharacteristic, complemented
17C11×#547C2211yescharacteristic
18C2×#67002—21no—
19#10623110C2211yescharacteristic
20D4×D44C2211yescharacteristic
21C11×#487C2211yescharacteristic, complemented
22C11×#483—21no—
23C11×#475C2211yescharacteristic, complemented
24C11×#465—21no—
25C11×#461C2211yescharacteristic
26C11×#448—21no—
27C4×C11×SD16C2211yescharacteristic
28C8×D4×C11C2211yescharacteristic, complemented
29C2×C11×#103—21no—
30#10622851—21no—
31#10622782—21no—
32#10622706C2211yescharacteristic, complemented
33#10622701C2211yescharacteristic
34#10622700C2211yescharacteristic
35#10622698C2211yescharacteristic
36#10622697—21no—
37#10622696C2211yescharacteristic
38#10622693—21no—
39#10622692C2211yescharacteristic, complemented
40#10622662—21no—
41#10622659—21no—
42#10622640C2211yescharacteristic
43#10622637C2211yescharacteristic, complemented
44#10622628C2211yescharacteristic
45#10622627—21no—
46C4×#4323C2211yescharacteristic
47#10622625C2211yescharacteristic
48#10622622—21no—
49#10622621C2211yescharacteristic
50#10622621C2211yescharacteristic, complemented
51#10622476—21no—
52#10622420—21no—
53D11×#102—21no—
54#10622307C2211yescharacteristic
55C8×D44C2211yescharacteristic
56#10622185C2211yescharacteristic, complemented
57#10622185C2211yescharacteristic, complemented
58Q8⋊(C11⋊C8)C2211yescharacteristic, complemented
59D4⋊(C11⋊C8)C2211yescharacteristic
60D4⋊(C11⋊C8)C2211yescharacteristic, complemented
61#10622123C2211yescharacteristic
62#10622121C2211yescharacteristic
63#10622119C2211yescharacteristic, complemented
64#10622117C2211yescharacteristic, complemented
65#10622095C2211yescharacteristic, complemented
66C8×C11⋊C8C2211yescharacteristic, complemented
67C2×C11×#41—21no—
68C22×Q8×C11—21no—
69C2×D4×D11—21no—
70C22×D44—21no—
71C2×C11×SD16—21no—
72C2×C11×SD16D411yescharacteristic
73C22×C8×C11—21no—
74C11×C4⋊Q8—21no—
75C11×C4⋊Q8C2311yescharacteristic
76C11×C4⋊Q8C2311yescharacteristic
77C11×#123—41no—
78C11×C22⋊Q8—21no—
79C11×C22⋊Q8—21no—
80C11×C22⋊Q8—41no—
81C11×#121—21no—
82C4×Q8×C11C2311yescharacteristic
83C4×D4×C11—21no—
84C4×D4×C11C2311yescharacteristic
85C4×D4×C11C2311yescharacteristic
86C2×C11×C4⋊C4—21no—
87#67002—44no—
88#66999—21no—
89C2×#4325—21no—
90C2×#4325—21no—
91C2×#4325—21no—
92C2×#4325—21no—
93C2×#4323—21no—
94C2×#4323D411yescharacteristic
95#66983—21no—
96C2×#4318—21no—
97C2×C8×D11—21no—
98#66949—41no—
99#66948—21no—
100C4⋊C4×D11—21no—
101#66935—41no—
102#66927C2311yescharacteristic
103C4×D44—21no—
104C4×D44C2311yescharacteristic
105#66923—21no—
106#66922C2311yescharacteristic
107C11×#106—21no—
108C11×#106D411yescharacteristic
109C11×C4⋊C8C2311yescharacteristic
110C11×#103—21no—
111C11×#103—21no—
112C11×#103—21no—
113C11×#103—21no—
114C11×#103D411yescharacteristic
115C11×#102D411yescharacteristic
116C11×C22⋊C8—21no—
117C4×C8×C11C2311yescharacteristic
118#66899—21no—
119#66896—21no—
120#66896—21no—
121#66896D411yescharacteristic
122C22⋊(C11⋊C8)—21no—
123#66885—21no—
124#66885—21no—
125(C2×D11)⋊C8—21no—
126#66874—41no—
127#66873—21no—
128#66873—21no—
129#66873—21no—
130#66873—41no—
131#66873D411yescharacteristic
132#66872—21no—
133#66872—21no—
134#66872—21no—
135#66872—21no—
136#66871—21no—
137#66871D411yescharacteristic
138C4⋊(C11⋊C8)—21no—
139C4⋊(C11⋊C8)C2311yescharacteristic
140C4⋊(C11⋊C8)C2311yescharacteristic
141C4⋊(C11⋊C8)C2311yescharacteristic
142#66867—21no—
143C4×C11⋊C8C2311yescharacteristic
144C4×C11⋊C8C2311yescharacteristic
145#19891—111nomaximal, Sylow
146C23×D11—41no—
147C11×#41—42no—
148C11×#41—81no—
149C2×Q8×C11—21no—
150C2×Q8×C11—21no—
151C2×Q8×C11—41no—
152C2×Q8×C11—42no—
153C2×Q8×C11—81no—
154C2×Q8×C11C2×D411yescharacteristic
155C2×D4×C11—41no—
156C2×D4×C11C2×D411yescharacteristic
157C2×D4×C11C2×D411yescharacteristic
158C22×C4×C11—21no—
159C22×C4×C11—21no—
160C22×C4×C11—41no—
161C22×C4×C11—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×C4×D11—41no—
174C2×Dic22—21no—
175C11×SD16—41no—
176C11×SD16—81no—
177C2×C8×C11—21no—
178C2×C8×C11—81no—
179C2×C8×C11C2×D411yescharacteristic
180C2×C8×C11C2×D411yescharacteristic
181C11×C4⋊C4—21no—
182C11×C4⋊C4—21no—
183C11×C4⋊C4—21no—
184C11×C4⋊C4—21no—
185C11×C4⋊C4—21no—
186C11×C4⋊C4—41no—
187C11×C4⋊C4—41no—
188C11×C4⋊C4C2×D411yescharacteristic
189C11×C4⋊C4C2×D411yescharacteristic
190C11×C4⋊C4C2×D411yescharacteristic
191C11×C22⋊C4—21no—
192C11×C22⋊C4—21no—
193C11×C22⋊C4—41no—
194C11×C22⋊C4—41no—
195C42×C11—21no—
196C42×C11C2411yescharacteristic
197#4325—42no—
198#4325—42no—
199#4325—81no—
200#4325—81no—
201#4323—42no—
202#4323SD1614yescomplemented
203(C2×D11)⋊C4—21no—
204(C2×D11)⋊C4—41no—
205(C2×D11)⋊C4—41no—
206C4⋊Dic11—21no—
207C4⋊Dic11—21no—
208C4⋊Dic11C2×D411yescharacteristic
209Dic11⋊C4—41no—
210Dic11⋊C4—41no—
211#4318—42no—
212C2×C11⋊C8—21no—
213C2×C11⋊C8—21no—
214C2×C11⋊C8—21no—
215C2×C11⋊C8—21no—
216C2×C11⋊C8C2×D411yescharacteristic
217C2×C11⋊C8C2×D411yescharacteristic
218C8×D11—81no—
219#3384—111no—
220#3298D1111yescharacteristic, complemented
221#3295—111no—
222#3272—111no—
223#1708—111no—
224#1691—111no—
225#1686—111no—
226#1679—111no—
227#1677—111no—
228#1643—111no—
229#1639—111no—
230#1635—111no—
231#1627—111no—
232#1590—111no—
233C8×D8—111no—
234C23×C11—21no—
235C23×C11—21no—
236C22×D11—21no—
237C22×D11—41no—
238C22×D11—82no—
239C22×D11—82no—
240C22×D11—161no—
241Q8×C11—21no—
242Q8×C11—21no—
243Q8×C11—41no—
244Q8×C11—41no—
245Q8×C11—41no—
246Q8×C11—41no—
247Q8×C11—82no—
248D4×C11—21no—
249D4×C11—21no—
250D4×C11—21no—
251D4×C11—82no—
252D4×C11C2×SD1612yes—
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—41no—
263C2×C4×C11—82no—
264C2×C4×C11—82no—
265C2×C4×C11C22×D411yescharacteristic
266C2×C4×C11C22×D411yescharacteristic
267C2×C4×C11H(5,𝔽2)11yescharacteristic
268C22⋊D11—82no—
269C2×Dic11—21no—
270C2×Dic11—41no—
271D44—21no—
272D44—41no—
273D44—41no—
274D44—41no—
275D44—41no—
276D44—81no—
277D44—82no—
278D44C2×SD1612yes—
279C4×D11—41no—
280C4×D11—41no—
281C4×D11—161no—
282Dic22—81no—
283C8×C11—21no—
284C8×C11—21no—
285C8×C11—41no—
286C11⋊C8—21no—
287C11⋊C8—41no—
288C11⋊C8—41no—
289C11⋊C8—41no—
290C11⋊C8—41no—
291C11⋊C8C2×SD1612yes—
292C2×AGL(1,ℤ/8)—221no—
293#554—111no—
294D4×Q8C2×D1111yescharacteristic, complemented
295#547C2×D1111yescharacteristic
296D42—111no—
297#501—221no—
298#498—111no—
299#492—111no—
300#487—111no—
301#487C2×D1111yescharacteristic, complemented
302#486—111no—
303#486—111no—
304#483—21no—
305#481—221no—
306#478—221no—
307#476—111no—
308#476—111no—
309#476—221no—
310#475C2×D1111yescharacteristic, complemented
311#474—111no—
312#468—221no—
313#465—21no—
314#465—221no—
315#461—111no—
316#461C2×D1111yescharacteristic
317#460—111no—
318#459—111no—
319#450—221no—
320#450—221no—
321#449—221no—
322#448—21no—
323#446—111no—
324#442—221no—
325C4×SD16C2×D1111yescharacteristic
326C4×D8—111no—
327#436—111no—
328C8×D4—111no—
329C8×D4C2×D1111yescharacteristic, complemented
330C2×#103—21no—
331C2×#102—221no—
332#335—111no—
333#334—111no—
334#333—111no—
335#332—111no—
336#332—111no—
337#331—111no—
338Q8⋊C8—111no—
339D4⋊C8—111no—
340D4⋊C8—111no—
341D4⋊C8—111no—
342C82—111no—
343C22×C11—22no—
344C22×C11—41no—
345C22×C11—41no—
346C22×C11—41no—
347C22×C11—41no—
348C22×C11—41no—
349C22×C11D4211yescharacteristic
350C2×D11—22no—
351C2×D11—41no—
352C2×D11—41no—
353C2×D11—81no—
354C2×D11—81no—
355C2×D11—81no—
356C2×D11—164no—
357C4×C11—21no—
358C4×C11—41no—
359C4×C11—41no—
360C4×C11—41no—
361C4×C11—41no—
362C4×C11—81no—
363C4×C11—81no—
364C4×C11C22×SD1611yescharacteristic
365C4×C11#57511yescharacteristic
366C4×C11#57611yescharacteristic
367C4×C11#57711yescharacteristic
368Dic11—41no—
369Dic11—81no—
370C2×#41—21no—
371C22×Q8—21no—
372C22×D4—221no—
373C22×D4—221no—
374AGL(1,ℤ/8)—444no—
375C2×SD16—21no—
376C2×SD16—221no—
377C2×SD16—221no—
378C2×SD16—221no—
379C2×SD16—221no—
380C2×SD16C22⋊D1111yescharacteristic
381C2×D8—111no—
382C2×D8—221no—
383C2×M16—221no—
384C22×C8—21no—
385C22×C8—221no—
386C4⋊Q8—21no—
387C4⋊Q8—111no—
388C4⋊Q8C22×D1111yescharacteristic
389C4⋊Q8C22×D1111yescharacteristic
390#127—111no—
391#125—221no—
392#123—41no—
393C22⋊Q8—21no—
394C22⋊Q8—21no—
395C22⋊Q8—41no—
396C22⋊Q8—221no—
397C22⋊Q8—441no—
398#121—21no—
399#121—221no—
400#121—221no—
401#120—441no—
402C4×Q8C22×D1111yescharacteristic
403C4×D4—21no—
404C4×D4—111no—
405C4×D4—221no—
406C4×D4C22×D1111yescharacteristic
407C4×D4C22×D1111yescharacteristic
408C2×C4⋊C4—21no—
409C2×C4⋊C4—221no—
410#107—111no—
411#107—221no—
412#106—21no—
413#106—221no—
414#106—221no—
415#106—221no—
416#106—221no—
417#106C22⋊D1111yescharacteristic
418C4⋊C8—111no—
419C4⋊C8—111no—
420C4⋊C8—111no—
421C4⋊C8—221no—
422C4⋊C8C22×D1111yescharacteristic
423#103—21no—
424#103—21no—
425#103—21no—
426#103—21no—
427#103—221no—
428#103—441no—
429#103C22⋊D1111yescharacteristic
430#102—111no—
431#102—111no—
432#102—221no—
433#102—221no—
434#102—221no—
435#102—221no—
436#102—221no—
437#102—221no—
438#102—221no—
439#102—441no—
440#102C22⋊D1111yescharacteristic
441C22⋊C8—21no—
442C22⋊C8—221no—
443C22⋊C8—221no—
444#97—221no—
445C4×C8—111no—
446C4×C8—111no—
447C4×C8C22×D1111yescharacteristic
448C2×C11—42no—
449C2×C11—81no—
450C2×C11#327311yescharacteristic
451C2×C11D4×SD1611yescharacteristic
452C2×C11#329011yescharacteristic
453D11—42no—
454D11—161no—
455C24—441no—
456#41—42no—
457#41—81no—
458C2×Q8—21no—
459C2×Q8—21no—
460C2×Q8—41no—
461C2×Q8—42no—
462C2×Q8—81no—
463C2×Q8—221no—
464C2×Q8C2×C22⋊D1111yescharacteristic
465C2×D4—41no—
466C2×D4—111no—
467C2×D4—221no—
468C2×D4—221no—
469C2×D4—221no—
470C2×D4—441no—
471C2×D4—442no—
472C2×D4—441no—
473C2×D4—442no—
474C2×D4—881no—
475C2×D4—881no—
476C2×D4D4×D1111yescharacteristic
477C2×D4C2×C22⋊D1111yescharacteristic
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—41no—
481C22×C4—41no—
482C22×C4—221no—
483C22×C4—441no—
484SD16—41no—
485SD16—81no—
486SD16—442no—
487SD16—442no—
488SD16—881no—
489SD16—881no—
490D8—114no—
491D8—442no—
492M16—442no—
493C2×C8—21no—
494C2×C8—81no—
495C2×C8—111no—
496C2×C8—111no—
497C2×C8—221no—
498C2×C8—221no—
499C2×C8—221no—
500C2×C8—221no—
501C2×C8—881no—
502C2×C8C2×C22⋊D1111yescharacteristic
503C2×C8C2×C22⋊D1111yescharacteristic
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—41no—
510C4⋊C4—41no—
511C4⋊C4—111no—
512C4⋊C4—221no—
513C4⋊C4—221no—
514C4⋊C4—441no—
515C4⋊C4—441no—
516C4⋊C4D4×D1111yescharacteristic
517C4⋊C4C2×C22⋊D1111yescharacteristic
518C4⋊C4C2×C22⋊D1111yescharacteristic
519C22⋊C4—21no—
520C22⋊C4—21no—
521C22⋊C4—41no—
522C22⋊C4—41no—
523C22⋊C4—221no—
524C22⋊C4—441no—
525C22⋊C4—441no—
526C42—21no—
527C42C23×D1111yescharacteristic
528C11#1989111yescharacteristic, complemented, Sylow
529C23—21no—
530C23—21no—
531C23—221no—
532C23—441no—
533C23—882no—
534C23—882no—
535C23—1761no—
536Q8—21no—
537Q8—21no—
538Q8—41no—
539Q8—41no—
540Q8—41no—
541Q8—41no—
542Q8—82no—
543Q8—881no—
544D4—21no—
545D4—21no—
546D4—21no—
547D4—82no—
548D4—112no—
549D4—221no—
550D4—441no—
551D4—441no—
552D4—441no—
553D4—441no—
554D4—881no—
555D4—882no—
556D4—882no—
557D4SD16×D1112yes—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—82no—
569C2×C4—82no—
570C2×C4—221no—
571C2×C4—441no—
572C2×C4—441no—
573C2×C4—441no—
574C2×C4—1761no—
575C2×C4C2×D4×D1111yescharacteristic
576C2×C4#6703711yescharacteristic
577C2×C4C22×C22⋊D1111yescharacteristic
578C8—21no—
579C8—21no—
580C8—41no—
581C8—112no—
582C8—221no—
583C8—441no—
584C8—441no—
585C8—441no—
586C8—441no—
587C22—22no—
588C22—41no—
589C22—41no—
590C22—41no—
591C22—41no—
592C22—41no—
593C22—222no—
594C22—441no—
595C22—441no—
596C22—881no—
597C22—881no—
598C22—881no—
599C22—1764no—
600C22D4×C22⋊D1111yescharacteristic
601C4—21no—
602C4—41no—
603C4—41no—
604C4—41no—
605C4—41no—
606C4—81no—
607C4—81no—
608C4—441no—
609C4—881no—
610C4C2×SD16×D1111yescharacteristic
611C4#1062329311yescharacteristic
612C4#1062335311yescharacteristic
613C4#1062336611yescharacteristic
614C2—42no—
615C2—81no—
616C2—442no—
617C2—1761no—
618C2#1308022311yescharacteristic
619C2SD16×C22⋊D1111yescharacteristic
620C2#1308040211yescharacteristic
subgroupG/H
centerC22D4×C22⋊D11
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3298C2
socleC22×C11D42
prime radical#13080216C2
hypercenter#3298D11
hypocenterC11#19891
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #3298

Complements

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

NH ≅ G/Ntype
1. #13081511C2semidirect
2. #13080442C2semidirect
4. #13068219C2semidirect
5. #13068113C2semidirect
6. #13068090C2semidirect
7. #13068036C2semidirect
8. #13068025C2semidirect
9. #13067822C2semidirect
10. #13067793C2semidirect
11. #13067767C2semidirect
12. #13067719C2semidirect
13. #13067507C2semidirect
14. C8×#4323C2semidirect
15. C11×#3298C2semidirect
16. D4×Q8×C11C22semidirect
21. C11×#487C22semidirect
23. C11×#475C22semidirect
28. C8×D4×C11C22semidirect
32. #10622706C22semidirect
39. #10622692C22semidirect
43. #10622637C22semidirect
50. #10622621C22semidirect
56. #10622185C22semidirect
57. #10622185C22semidirect
58. Q8⋊(C11⋊C8)C22semidirect
60. D4⋊(C11⋊C8)C22semidirect
63. #10622119C22semidirect
64. #10622117C22semidirect
65. #10622095C22semidirect
66. C8×C11⋊C8C22semidirect
202. #4323SD16semidirect
220. #3298D11semidirect
294. D4×Q8C2×D11semidirect
301. #487C2×D11semidirect
310. #475C2×D11semidirect
329. C8×D4C2×D11semidirect
528. C11#19891semidirect

Maximal subgroups

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

subgroupindex
#130815112
#130804422
#130802162
#130682192
#130681132
#130680902
#130680362
#130680252
#130678222
#130677932
#130677672
#130677192
#130675072
C8×#43232
C11×#32982
#1989111