Finite Group Databasebeta

← #14745163

Subgroups — #14745163

Order 2816.

684 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081522C211yesmaximal, characteristic, complemented
2#13080442C211yesmaximal, characteristic, complemented
3#13080236C211yesmaximal, characteristic
4#13068207C211yesmaximal, characteristic, complemented
5#13068137C211yesmaximal, characteristic, complemented
6#13068098C211yesmaximal, characteristic, complemented
7#13068032C211yesmaximal, characteristic, complemented
8#13068022C211yesmaximal, characteristic, complemented
9#13067743C211yesmaximal, characteristic, complemented
10#13067731C211yesmaximal, characteristic, complemented
11#13067694C211yesmaximal, characteristic, complemented
12#13067687C211yesmaximal, characteristic, complemented
13#13067507C211yesmaximal, characteristic, complemented
14C8×#4325C211yesmaximal, characteristic, complemented
15C11×#3362C211yesmaximal, characteristic, complemented
16Q82×C11C2211yescharacteristic, complemented
17C11×#550C2211yescharacteristic
18C2×#67002—21no—
19#10623110C2211yescharacteristic
20D4×D44C2211yescharacteristic
21C11×#486—21no—
22C11×#486C2211yescharacteristic, complemented
23C11×#476—21no—
24C11×#476C2211yescharacteristic
25C11×#460—21no—
26C11×#460C2211yescharacteristic, complemented
27C8×Q8×C11C2211yescharacteristic, complemented
28C4×C11×SD16—21no—
29C4×C11×SD16C2211yescharacteristic
30#10622851—21no—
31#10622782—21no—
32#10622700—21no—
33#10622698C2211yescharacteristic
34#10622697C2211yescharacteristic
35#10622693—21no—
36#10622691C2211yescharacteristic, complemented
37#10622689C2211yescharacteristic, complemented
38#10622686C2211yescharacteristic
39#10622685C2211yescharacteristic
40#10622652—21no—
41#10622649—21no—
42#10622640C2211yescharacteristic
43#10622640C2211yescharacteristic
44#10622639—21no—
45C4×#4325C2211yescharacteristic
46#10622637C2211yescharacteristic, complemented
47#10622635—21no—
48#10622634C2211yescharacteristic, complemented
49#10622625C2211yescharacteristic
50#10622621C2211yescharacteristic
51#10622476—21no—
52#10622420—21no—
53D11×#102—21no—
54#10622307C2211yescharacteristic
55C8×D44C2211yescharacteristic
56#10622184C2211yescharacteristic, complemented
57#10622182C2211yescharacteristic, complemented
58Q8⋊(C11⋊C8)C2211yescharacteristic, complemented
59Q8⋊(C11⋊C8)C2211yescharacteristic, complemented
60D4⋊(C11⋊C8)C2211yescharacteristic
61#10622123C2211yescharacteristic
62#10622121C2211yescharacteristic
63#10622119C2211yescharacteristic, complemented
64#10622118C2211yescharacteristic, complemented
65#10622095C2211yescharacteristic, complemented
66C8×C11⋊C8C2211yescharacteristic, complemented
67C2×C11×#41—21no—
68C2×D4×D11—21no—
69C22×D44—21no—
70C2×C11×SD16—21no—
71C2×C11×SD16D411yescharacteristic
72C11×C4⋊Q8—21no—
73C11×C4⋊Q8—21no—
74C11×C4⋊Q8—41no—
75C11×C4⋊Q8C2311yescharacteristic
76C11×#127—21no—
77C11×#127C2311yescharacteristic
78C11×#121—21no—
79C11×#121—41no—
80C4×Q8×C11—21no—
81C4×Q8×C11—21no—
82C4×Q8×C11C2311yescharacteristic
83C4×Q8×C11C2311yescharacteristic
84C4×D4×C11—21no—
85C4×D4×C11C2311yescharacteristic
86#67002—44no—
87#66999—21no—
88C2×#4325—21no—
89C2×#4325—21no—
90C2×#4325—41no—
91C2×#4325D411yescharacteristic
92C2×#4324—41no—
93C2×#4323—21no—
94C2×#4323—21no—
95C2×#4323—21no—
96#66983—21no—
97C2×#4318—21no—
98C2×C8×D11—21no—
99#66949—41no—
100#66948—21no—
101C4⋊C4×D11—21no—
102#66935—41no—
103#66927C2311yescharacteristic
104C4×D44—21no—
105C4×D44C2311yescharacteristic
106#66923—21no—
107#66922C2311yescharacteristic
108C11×#106—21no—
109C11×#106D411yescharacteristic
110C11×C4⋊C8—21no—
111C11×C4⋊C8C2311yescharacteristic
112C11×#103D411yescharacteristic
113C11×#102—21no—
114C11×#102—21no—
115C11×#102—21no—
116C11×#102—21no—
117C11×#102D411yescharacteristic
118C4×C8×C11—21no—
119C4×C8×C11C2311yescharacteristic
120#66899—21no—
121#66899D411yescharacteristic
122#66896—21no—
123#66896—21no—
124C22⋊(C11⋊C8)—21no—
125#66885—21no—
126#66885—21no—
127(C2×D11)⋊C8—21no—
128#66873—21no—
129#66873—21no—
130#66873—21no—
131#66873D411yescharacteristic
132#66872—21no—
133#66872—21no—
134#66872D411yescharacteristic
135#66871—21no—
136#66871—21no—
137#66871—21no—
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#19893—111nomaximal, Sylow
146C23×D11—41no—
147C11×#41—42no—
148C11×#41—81no—
149C2×Q8×C11—21no—
150C2×Q8×C11—41no—
151C2×Q8×C11C2×D411yescharacteristic
152C2×Q8×C11C2×D411yescharacteristic
153C2×D4×C11—21no—
154C2×D4×C11—21no—
155C2×D4×C11—21no—
156C2×D4×C11—41no—
157C2×D4×C11—41no—
158C2×D4×C11C2×D411yescharacteristic
159C22×C4×C11—21no—
160C22×C4×C11—41no—
161C2×C22⋊D11—41no—
162D4×D11—42no—
163D4×D11—81no—
164C2×D44—21no—
165C2×D44—21no—
166C2×D44—21no—
167C2×D44—41no—
168C2×D44—42no—
169C2×D44—81no—
170C2×D44C2×D411yescharacteristic
171C2×C4×D11—21no—
172C2×C4×D11—41no—
173C2×Dic22—21no—
174C11×SD16—41no—
175C11×SD16—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—21no—
183C11×C4⋊C4—41no—
184C11×C4⋊C4—41no—
185C11×C4⋊C4C2×D411yescharacteristic
186C11×C4⋊C4C2×D411yescharacteristic
187C11×C4⋊C4C2×D411yescharacteristic
188C11×C22⋊C4—21no—
189C11×C22⋊C4—41no—
190C42×C11—21no—
191C42×C11—21no—
192C42×C11—41no—
193C42×C11C2411yescharacteristic
194#4325—42no—
195#4325—81no—
196#4325—82no—
197#4325SD1614yescomplemented
198#4324—82no—
199#4323—42no—
200#4323—42no—
201#4323—81no—
202(C2×D11)⋊C4—21no—
203(C2×D11)⋊C4—41no—
204(C2×D11)⋊C4—41no—
205C4⋊Dic11—21no—
206C4⋊Dic11—21no—
207C4⋊Dic11C2×D411yescharacteristic
208Dic11⋊C4—41no—
209Dic11⋊C4—41no—
210#4318—42no—
211C2×C11⋊C8—21no—
212C2×C11⋊C8—21no—
213C2×C11⋊C8—21no—
214C2×C11⋊C8—21no—
215C2×C11⋊C8C2×D411yescharacteristic
216C2×C11⋊C8C2×D411yescharacteristic
217C8×D11—81no—
218#3385—111no—
219#3362D1111yescharacteristic, complemented
220#3295—111no—
221#3274—111no—
222#1706—111no—
223#1695—111no—
224#1688—111no—
225#1678—111no—
226#1677—111no—
227#1631—111no—
228#1629—111no—
229#1623—111no—
230#1622—111no—
231#1590—111no—
232C8×SD16—111no—
233C23×C11—21no—
234C23×C11—41no—
235C22×D11—21no—
236C22×D11—41no—
237C22×D11—82no—
238C22×D11—82no—
239C22×D11—161no—
240Q8×C11—21no—
241Q8×C11—21no—
242Q8×C11—21no—
243Q8×C11—81no—
244Q8×C11—161no—
245Q8×C11C2×SD1612yes—
246D4×C11—21no—
247D4×C11—21no—
248D4×C11—41no—
249D4×C11—41no—
250D4×C11—41no—
251D4×C11—41no—
252D4×C11—82no—
253D4×C11—81no—
254D4×C11—161no—
255C2×C4×C11—21no—
256C2×C4×C11—21no—
257C2×C4×C11—21no—
258C2×C4×C11—21no—
259C2×C4×C11—21no—
260C2×C4×C11—41no—
261C2×C4×C11—41no—
262C2×C4×C11—41no—
263C2×C4×C11—82no—
264C2×C4×C11C22×D411yescharacteristic
265C2×C4×C11C22×D411yescharacteristic
266C2×C4×C11H(5,𝔽2)11yescharacteristic
267C22⋊D11—82no—
268C2×Dic11—21no—
269C2×Dic11—41no—
270D44—21no—
271D44—41no—
272D44—41no—
273D44—41no—
274D44—41no—
275D44—81no—
276D44—82no—
277D44C2×SD1612yes—
278C4×D11—41no—
279C4×D11—41no—
280C4×D11—161no—
281Dic22—81no—
282C8×C11—21no—
283C8×C11—21no—
284C8×C11—41no—
285C11⋊C8—22no—
286C11⋊C8—21no—
287C11⋊C8—41no—
288C11⋊C8—41no—
289C11⋊C8—41no—
290C11⋊C8C2×SD1612yes—
291C2×AGL(1,ℤ/8)—221no—
292Q82C2×D1111yescharacteristic, complemented
293#554—111no—
294#550C2×D1111yescharacteristic
295D42—111no—
296#501—221no—
297#500—111no—
298#493—111no—
299#492—111no—
300#492—111no—
301#486—21no—
302#486—111no—
303#486C2×D1111yescharacteristic, complemented
304#481—221no—
305#479—221no—
306#477—111no—
307#476—21no—
308#476—111no—
309#476—111no—
310#476C2×D1111yescharacteristic
311#474—221no—
312#469—221no—
313#465—221no—
314#460—21no—
315#460—111no—
316#460—111no—
317#460C2×D1111yescharacteristic, complemented
318#459—111no—
319#450—221no—
320#449—221no—
321#447—221no—
322#446—111no—
323C8×Q8C2×D1111yescharacteristic, complemented
324#440—221no—
325C4×SD16—21no—
326C4×SD16—111no—
327C4×SD16C2×D1111yescharacteristic
328#436—111no—
329C8×D4—111no—
330C2×#102—221no—
331#334—111no—
332#334—111no—
333#333—111no—
334#333—111no—
335#331—111no—
336#331—111no—
337Q8⋊C8—111no—
338Q8⋊C8—111no—
339D4⋊C8—111no—
340D4⋊C8—111no—
341C82—111no—
342C22×C11—41no—
343C22×C11—41no—
344C22×C11—41no—
345C22×C11—81no—
346C22×C11—81no—
347C22×C11—81no—
348C22×C11D4211yescharacteristic
349C2×D11—22no—
350C2×D11—41no—
351C2×D11—41no—
352C2×D11—81no—
353C2×D11—81no—
354C2×D11—81no—
355C2×D11—164no—
356C4×C11—22no—
357C4×C11—21no—
358C4×C11—41no—
359C4×C11—41no—
360C4×C11—41no—
361C4×C11—41no—
362C4×C11—81no—
363C4×C11C22×SD1611yescharacteristic
364C4×C11#57511yescharacteristic
365C4×C11#57711yescharacteristic
366C4×C11#57711yescharacteristic
367Dic11—41no—
368Dic11—81no—
369C2×#41—21no—
370C22×D4—221no—
371C22×D4—221no—
372AGL(1,ℤ/8)—444no—
373C2×SD16—21no—
374C2×SD16—111no—
375C2×SD16—221no—
376C2×SD16—221no—
377C2×SD16—441no—
378C2×SD16—441no—
379C2×SD16C22⋊D1111yescharacteristic
380C2×D8—221no—
381C2×D8—221no—
382C2×D8—221no—
383C2×M16—221no—
384C22×C8—221no—
385C4⋊Q8—21no—
386C4⋊Q8—21no—
387C4⋊Q8—41no—
388C4⋊Q8—111no—
389C4⋊Q8C22×D1111yescharacteristic
390#127—21no—
391#127—111no—
392#127C22×D1111yescharacteristic
393#125—221no—
394C22⋊Q8—221no—
395C22⋊Q8—441no—
396#121—21no—
397#121—41no—
398#121—221no—
399#121—221no—
400#120—441no—
401C4×Q8—21no—
402C4×Q8—21no—
403C4×Q8C22×D1111yescharacteristic
404C4×Q8C22×D1111yescharacteristic
405C4×D4—21no—
406C4×D4—111no—
407C4×D4—221no—
408C4×D4C22×D1111yescharacteristic
409C2×C4⋊C4—221no—
410#107—221no—
411#107—221no—
412#107—221no—
413#106—21no—
414#106—111no—
415#106—221no—
416#106—221no—
417#106C22⋊D1111yescharacteristic
418C4⋊C8—21no—
419C4⋊C8—111no—
420C4⋊C8—111no—
421C4⋊C8—111no—
422C4⋊C8—221no—
423C4⋊C8C22×D1111yescharacteristic
424#103—111no—
425#103—221no—
426#103C22⋊D1111yescharacteristic
427#102—21no—
428#102—21no—
429#102—21no—
430#102—21no—
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#102C22⋊D1111yescharacteristic
440C22⋊C8—221no—
441C22⋊C8—221no—
442#97—221no—
443C4×C8—21no—
444C4×C8—111no—
445C4×C8—111no—
446C4×C8C22×D1111yescharacteristic
447C2×C11—81no—
448C2×C11—161no—
449C2×C11#327511yescharacteristic
450C2×C11D4×SD1611yescharacteristic
451C2×C11#329211yescharacteristic
452D11—42no—
453D11—161no—
454C24—441no—
455#41—42no—
456#41—81no—
457C2×Q8—21no—
458C2×Q8—41no—
459C2×Q8—221no—
460C2×Q8D4×D1111yescharacteristic
461C2×Q8C2×C22⋊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—881no—
476C2×D4—881no—
477C2×D4C2×C22⋊D1111yescharacteristic
478C22×C4—21no—
479C22×C4—41no—
480C22×C4—221no—
481C22×C4—441no—
482SD16—41no—
483SD16—42no—
484SD16—114no—
485SD16—442no—
486SD16—882no—
487SD16—882no—
488SD16—881no—
489D8—442no—
490D8—442no—
491D8—881no—
492M16—442no—
493C2×C8—21no—
494C2×C8—111no—
495C2×C8—111no—
496C2×C8—221no—
497C2×C8—221no—
498C2×C8—221no—
499C2×C8—221no—
500C2×C8—881no—
501C2×C8C2×C22⋊D1111yescharacteristic
502C2×C8C2×C22⋊D1111yescharacteristic
503C4⋊C4—21no—
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—21no—
507C4⋊C4—41no—
508C4⋊C4—41no—
509C4⋊C4—111no—
510C4⋊C4—221no—
511C4⋊C4—221no—
512C4⋊C4—441no—
513C4⋊C4—441no—
514C4⋊C4D4×D1111yescharacteristic
515C4⋊C4C2×C22⋊D1111yescharacteristic
516C4⋊C4C2×C22⋊D1111yescharacteristic
517C22⋊C4—21no—
518C22⋊C4—41no—
519C22⋊C4—221no—
520C22⋊C4—441no—
521C22⋊C4—441no—
522C42—21no—
523C42—21no—
524C42—41no—
525C42C23×D1111yescharacteristic
526C11#1989311yescharacteristic, complemented, Sylow
527C23—21no—
528C23—41no—
529C23—221no—
530C23—441no—
531C23—882no—
532C23—882no—
533C23—1761no—
534Q8—21no—
535Q8—21no—
536Q8—21no—
537Q8—81no—
538Q8—161no—
539Q8—881no—
540Q8SD16×D1112yes—
541D4—21no—
542D4—21no—
543D4—41no—
544D4—41no—
545D4—41no—
546D4—41no—
547D4—82no—
548D4—81no—
549D4—112no—
550D4—161no—
551D4—221no—
552D4—441no—
553D4—441no—
554D4—441no—
555D4—441no—
556D4—881no—
557D4—882no—
558D4—882no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—82no—
568C2×C4—221no—
569C2×C4—441no—
570C2×C4—441no—
571C2×C4—441no—
572C2×C4—1761no—
573C2×C4C2×D4×D1111yescharacteristic
574C2×C4#6703711yescharacteristic
575C2×C4C22×C22⋊D1111yescharacteristic
576C8—21no—
577C8—21no—
578C8—41no—
579C8—112no—
580C8—222no—
581C8—221no—
582C8—441no—
583C8—441no—
584C8—441no—
585C22—41no—
586C22—41no—
587C22—41no—
588C22—81no—
589C22—81no—
590C22—81no—
591C22—222no—
592C22—441no—
593C22—441no—
594C22—881no—
595C22—881no—
596C22—881no—
597C22—1764no—
598C22D4×C22⋊D1111yescharacteristic
599C4—21no—
600C4—22no—
601C4—41no—
602C4—41no—
603C4—41no—
604C4—41no—
605C4—81no—
606C4—441no—
607C4—881no—
608C4C2×SD16×D1111yescharacteristic
609C4#1062329311yescharacteristic
610C4#1062335311yescharacteristic
611C4#1062336811yescharacteristic
612C2—81no—
613C2—161no—
614C2—442no—
615C2—1761no—
616C2#1308024811yescharacteristic
617C2SD16×C22⋊D1111yescharacteristic
618C2#1308041311yescharacteristic
subgroupG/H
centerC22D4×C22⋊D11
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3362C2
socleC22×C11D42
prime radical#13080236C2
hypercenter#3362D11
hypocenterC11#19893
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #3362

Complements

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

NH ≅ G/Ntype
1. #13081522C2semidirect
2. #13080442C2semidirect
4. #13068207C2semidirect
5. #13068137C2semidirect
6. #13068098C2semidirect
7. #13068032C2semidirect
8. #13068022C2semidirect
9. #13067743C2semidirect
10. #13067731C2semidirect
11. #13067694C2semidirect
12. #13067687C2semidirect
13. #13067507C2semidirect
14. C8×#4325C2semidirect
15. C11×#3362C2semidirect
16. Q82×C11C22semidirect
22. C11×#486C22semidirect
26. C11×#460C22semidirect
27. C8×Q8×C11C22semidirect
36. #10622691C22semidirect
37. #10622689C22semidirect
46. #10622637C22semidirect
48. #10622634C22semidirect
56. #10622184C22semidirect
57. #10622182C22semidirect
58. Q8⋊(C11⋊C8)C22semidirect
59. Q8⋊(C11⋊C8)C22semidirect
63. #10622119C22semidirect
64. #10622118C22semidirect
65. #10622095C22semidirect
66. C8×C11⋊C8C22semidirect
197. #4325SD16semidirect
219. #3362D11semidirect
292. Q82C2×D11semidirect
303. #486C2×D11semidirect
317. #460C2×D11semidirect
323. C8×Q8C2×D11semidirect
526. C11#19893semidirect

Maximal subgroups

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

subgroupindex
#130815222
#130804422
#130802362
#130682072
#130681372
#130680982
#130680322
#130680222
#130677432
#130677312
#130676942
#130676872
#130675072
C8×#43252
C11×#33622
#1989311