Finite Group Databasebeta

← #14745156

Subgroups — #14745156

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#13081287C211yesmaximal, characteristic, complemented
2#13080434C211yesmaximal, characteristic, complemented
3#13080237C211yesmaximal, characteristic
4#13068209C211yesmaximal, characteristic, complemented
5#13068136C211yesmaximal, characteristic, complemented
6#13068100C211yesmaximal, characteristic, complemented
7#13068034C211yesmaximal, characteristic, complemented
8#13068027C211yesmaximal, characteristic, complemented
9#13067741C211yesmaximal, characteristic, complemented
10#13067731C211yesmaximal, characteristic, complemented
11#13067694C211yesmaximal, characteristic, complemented
12#13067688C211yesmaximal, characteristic, complemented
13#13067506C211yesmaximal, characteristic, complemented
14SD16×C11⋊C8C211yesmaximal, characteristic, complemented
15C11×#3385C211yesmaximal, characteristic, complemented
16Q82×C11C2211yescharacteristic, complemented
17C11×#554C2211yescharacteristic
18C2×#66967—21no—
19#10623108C2211yescharacteristic
20D4×D44C2211yescharacteristic
21C11×#501—21no—
22C11×#500C2211yescharacteristic, complemented
23C11×#479—21no—
24C11×#477C2211yescharacteristic, complemented
25C11×#476C2211yescharacteristic
26C11×#474—21no—
27C11×#446C2211yescharacteristic, complemented
28C11×#440—21no—
29C4×C11×SD16C2211yescharacteristic
30#10622701—21no—
31#10622701C2211yescharacteristic
32#10622701C2211yescharacteristic, complemented
33#10622698C2211yescharacteristic
34#10622698C2211yescharacteristic, complemented
35#10622697—21no—
36#10622697C2211yescharacteristic
37#10622697C2211yescharacteristic
38#10622661—21no—
39#10622659—21no—
40#10622640—21no—
41#10622640C2211yescharacteristic
42#10622640C2211yescharacteristic
43#10622640C2211yescharacteristic, complemented
44C4×#4325—21no—
45C4×#4325C2211yescharacteristic
46Q8×C11⋊C8C2211yescharacteristic, complemented
47#10622628C2211yescharacteristic
48D4×C11⋊C8C2211yescharacteristic
49#10622581—21no—
50C2×#66873—21no—
51#10622478—21no—
52#10622424—21no—
53#10622386—21no—
54#10622308C2211yescharacteristic
55#10622301C2211yescharacteristic
56#10622184C2211yescharacteristic, complemented
57#10622184C2211yescharacteristic, complemented
58Q8⋊(C11⋊C8)C2211yescharacteristic, complemented
59Q8⋊(C11⋊C8)C2211yescharacteristic, complemented
60D4⋊(C11⋊C8)C2211yescharacteristic
61#10622123C2211yescharacteristic
62#10622123C2211yescharacteristic, complemented
63#10622121C2211yescharacteristic
64#10622118C2211yescharacteristic, complemented
65#10622095C2211yescharacteristic, complemented
66C8×C11⋊C8C2211yescharacteristic, complemented
67C2×#4343—21no—
68C2×D4×D11—21no—
69C22×D44—21no—
70C2×C11×SD16D411yescharacteristic
71C11×C4⋊Q8—21no—
72C11×C4⋊Q8—21no—
73C11×C4⋊Q8—41no—
74C11×C4⋊Q8C2311yescharacteristic
75C11×C4⋊Q8C2311yescharacteristic
76C11×#125—21no—
77C11×C22⋊Q8—21no—
78C11×C22⋊Q8—41no—
79C4×Q8×C11—21no—
80C4×Q8×C11—21no—
81C4×Q8×C11C2311yescharacteristic
82C4×Q8×C11C2311yescharacteristic
83C4×D4×C11—21no—
84C4×D4×C11C2311yescharacteristic
85C2×C11×C4⋊C4—21no—
86C2×#4325—21no—
87C2×#4325—21no—
88C2×#4325—21no—
89C2×#4325—41no—
90C2×#4325—41no—
91C2×#4325D411yescharacteristic
92C2×#4323—21no—
93#66983—21no—
94C22×C11⋊C8—21no—
95#66967—44no—
96C2×D88—21no—
97C2×D88—21no—
98C2×#4313—21no—
99#66948—21no—
100#66948—21no—
101#66948—41no—
102#66935—41no—
103#66927—21no—
104#66927C2311yescharacteristic
105#66927C2311yescharacteristic
106C4×D44—21no—
107C4×D44C2311yescharacteristic
108C11×#107—21no—
109C11×#107—21no—
110C11×#107—21no—
111C11×#106—21no—
112C11×#106D411yescharacteristic
113C11×C4⋊C8—21no—
114C11×C4⋊C8C2311yescharacteristic
115C11×#103—21no—
116C11×#103D411yescharacteristic
117C11×#102—21no—
118C11×#102D411yescharacteristic
119C11×#97—21no—
120C4×C8×C11C2311yescharacteristic
121#66899D411yescharacteristic
122C22⋊(C11⋊C8)—21no—
123(C2×D11)⋊C8—21no—
124#66873—21no—
125#66873—21no—
126#66873—21no—
127#66873—21no—
128#66873—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
138C4⋊(C11⋊C8)—21no—
139C4⋊(C11⋊C8)C2311yescharacteristic
140C4⋊(C11⋊C8)C2311yescharacteristic
141C4⋊(C11⋊C8)C2311yescharacteristic
142C4×C11⋊C8—21no—
143C4×C11⋊C8C2311yescharacteristic
144C4×C11⋊C8C2311yescharacteristic
145#19893—111nomaximal, Sylow
146C23×D11—41no—
147C2×Q8×C11—21no—
148C2×Q8×C11—21no—
149C2×Q8×C11—41no—
150C2×Q8×C11C2×D411yescharacteristic
151C2×Q8×C11C2×D411yescharacteristic
152C2×D4×C11C2×D411yescharacteristic
153C22×C4×C11—21no—
154C22×C4×C11—41no—
155C2×C22⋊D11—41no—
156#4343—42no—
157#4343—81no—
158D4×D11—42no—
159D4×D11—81no—
160C2×D44—21no—
161C2×D44—21no—
162C2×D44—21no—
163C2×D44—21no—
164C2×D44—21no—
165C2×D44—21no—
166C2×D44—41no—
167C2×D44—41no—
168C2×D44—41no—
169C2×D44—42no—
170C2×D44—81no—
171C2×D44C2×D411yescharacteristic
172C2×C4×D11—21no—
173C2×C4×D11—41no—
174C11×SD16SD1614yescomplemented
175C2×C8×C11—21no—
176C2×C8×C11C2×D411yescharacteristic
177C2×C8×C11C2×D411yescharacteristic
178C11×C4⋊C4—21no—
179C11×C4⋊C4—21no—
180C11×C4⋊C4—21no—
181C11×C4⋊C4—21no—
182C11×C4⋊C4—21no—
183C11×C4⋊C4—21no—
184C11×C4⋊C4—41no—
185C11×C4⋊C4—41no—
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—41no—
193C42×C11—21no—
194C42×C11—21no—
195C42×C11—41no—
196C42×C11C2411yescharacteristic
197#4325—41no—
198#4325—42no—
199#4325—42no—
200#4325—81no—
201#4325—82no—
202#4325—82no—
203#4323—42no—
204(C2×D11)⋊C4—21no—
205(C2×D11)⋊C4—41no—
206(C2×D11)⋊C4—41no—
207C4⋊Dic11C2×D411yescharacteristic
208C2×C11⋊C8—21no—
209C2×C11⋊C8—21no—
210C2×C11⋊C8—21no—
211C2×C11⋊C8—21no—
212C2×C11⋊C8—81no—
213C2×C11⋊C8C2×D411yescharacteristic
214C2×C11⋊C8C2×D411yescharacteristic
215D88—42no—
216D88—81no—
217#4313—42no—
218#3385D1111yescharacteristic, complemented
219#3362—111no—
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—
234C22×D11—21no—
235C22×D11—41no—
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—81no—
245Q8×C11—161no—
246Q8×C11C2×SD1612yes—
247D4×C11—21no—
248D4×C11C2×SD1612yes—
249C2×C4×C11—21no—
250C2×C4×C11—21no—
251C2×C4×C11—21no—
252C2×C4×C11—21no—
253C2×C4×C11—21no—
254C2×C4×C11—41no—
255C2×C4×C11—41no—
256C2×C4×C11—41no—
257C2×C4×C11—41no—
258C2×C4×C11—161no—
259C2×C4×C11C22×D411yescharacteristic
260C2×C4×C11C22×D411yescharacteristic
261C2×C4×C11H(5,𝔽2)11yescharacteristic
262C22⋊D11—82no—
263C2×Dic11—21no—
264D44—21no—
265D44—21no—
266D44—41no—
267D44—41no—
268D44—41no—
269D44—41no—
270D44—41no—
271D44—41no—
272D44—41no—
273D44—41no—
274D44—82no—
275D44—81no—
276D44—81no—
277D44—82no—
278D44—161no—
279C4×D11—41no—
280C4×D11—41no—
281C4×D11—82no—
282C8×C11—21no—
283C8×C11—41no—
284C8×C11C2×SD1612yes—
285C11⋊C8—22no—
286C11⋊C8—21no—
287C11⋊C8—21no—
288C11⋊C8—41no—
289C11⋊C8—41no—
290C11⋊C8—41no—
291C2×AGL(1,ℤ/8)—221no—
292Q82C2×D1111yescharacteristic, complemented
293#554C2×D1111yescharacteristic
294#550—111no—
295D42—111no—
296#501—21no—
297#500C2×D1111yescharacteristic, complemented
298#493—111no—
299#492—111no—
300#492—111no—
301#486—111no—
302#486—111no—
303#486—221no—
304#481—221no—
305#479—21no—
306#477C2×D1111yescharacteristic, complemented
307#476—111no—
308#476—111no—
309#476—221no—
310#476C2×D1111yescharacteristic
311#474—21no—
312#469—221no—
313#465—221no—
314#460—111no—
315#460—111no—
316#460—111no—
317#460—221no—
318#459—111no—
319#450—221no—
320#449—221no—
321#447—221no—
322#446C2×D1111yescharacteristic, complemented
323C8×Q8—111no—
324#440—21no—
325C4×SD16—111no—
326C4×SD16—221no—
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—22no—
343C22×C11—41no—
344C22×C11—41no—
345C22×C11D4211yescharacteristic
346C2×D11—41no—
347C2×D11—41no—
348C2×D11—41no—
349C2×D11—81no—
350C2×D11—81no—
351C2×D11—81no—
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×C11—81no—
364C4×C11C22×SD1611yescharacteristic
365C4×C11#57511yescharacteristic
366C4×C11#57711yescharacteristic
367C4×C11#57711yescharacteristic
368Dic11—41no—
369C2×#41—221no—
370C22×D4—221no—
371C22×D4—221no—
372AGL(1,ℤ/8)—444no—
373C2×SD16—111no—
374C2×SD16—221no—
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⋊Q8C22×D1111yescharacteristic
389C4⋊Q8C22×D1111yescharacteristic
390#127—111no—
391#127—111no—
392#127—221no—
393#125—21no—
394C22⋊Q8—21no—
395C22⋊Q8—41no—
396#121—221no—
397#121—221no—
398#121—221no—
399#121—441no—
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—21no—
410#107—21no—
411#107—21no—
412#107—21no—
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—21no—
425#103—111no—
426#103C22⋊D1111yescharacteristic
427#102—21no—
428#102—111no—
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
440C22⋊C8—221no—
441C22⋊C8—221no—
442#97—21no—
443C4×C8—111no—
444C4×C8—111no—
445C4×C8—221no—
446C4×C8C22×D1111yescharacteristic
447C2×C11—42no—
448C2×C11#327511yescharacteristic
449C2×C11D4×SD1611yescharacteristic
450C2×C11#329211yescharacteristic
451D11—81no—
452D11—161no—
453D11—161no—
454C24—441no—
455#41—442no—
456#41—881no—
457C2×Q8—21no—
458C2×Q8—21no—
459C2×Q8—41no—
460C2×Q8D4×D1111yescharacteristic
461C2×Q8C2×C22⋊D1111yescharacteristic
462C2×D4—111no—
463C2×D4—221no—
464C2×D4—221no—
465C2×D4—221no—
466C2×D4—221no—
467C2×D4—221no—
468C2×D4—221no—
469C2×D4—441no—
470C2×D4—441no—
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—441no—
483SD16—442no—
484SD16—442no—
485SD16—882no—
486SD16—882no—
487SD16—881no—
488SD16#432514yescomplemented
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—21no—
508C4⋊C4—21no—
509C4⋊C4—41no—
510C4⋊C4—41no—
511C4⋊C4—41no—
512C4⋊C4—41no—
513C4⋊C4—111no—
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—221no—
529C23—441no—
530C23—441no—
531C23—882no—
532C23—882no—
533C23—1761no—
534Q8—21no—
535Q8—21no—
536Q8—21no—
537Q8—81no—
538Q8—81no—
539Q8—161no—
540Q8C2×#432512yes—
541D4—21no—
542D4—221no—
543D4—221no—
544D4—441no—
545D4—441no—
546D4—441no—
547D4—441no—
548D4—441no—
549D4—441no—
550D4—441no—
551D4—441no—
552D4—882no—
553D4—881no—
554D4—881no—
555D4—882no—
556D4—882no—
557D4—1761no—
558D4C2×#432512yes—
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—41no—
568C2×C4—161no—
569C2×C4—221no—
570C2×C4—441no—
571C2×C4—441no—
572C2×C4—882no—
573C2×C4C2×D4×D1111yescharacteristic
574C2×C4#6703711yescharacteristic
575C2×C4C22×C22⋊D1111yescharacteristic
576C8—21no—
577C8—41no—
578C8—222no—
579C8—221no—
580C8—221no—
581C8—441no—
582C8—441no—
583C8—441no—
584C8C2×#432512yes—
585C22—22no—
586C22—41no—
587C22—41no—
588C22—441no—
589C22—441no—
590C22—441no—
591C22—881no—
592C22—881no—
593C22—881no—
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—81no—
607C4—441no—
608C4#1062330811yescharacteristic
609C4#1062330911yescharacteristic
610C4C22×#432511yescharacteristic
611C4#1062336811yescharacteristic
612C2—42no—
613C2—881no—
614C2—1761no—
615C2—1761no—
616C2#1308024111yescharacteristic
617C2D4×#432511yescharacteristic
618C2#1308041311yescharacteristic
subgroupG/H
centerC22D4×C22⋊D11
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3385C2
socleC22×C11D42
prime radical#13080237C2
hypercenter#3385D11
hypocenterC11#19893
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #3385

Complements

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

NH ≅ G/Ntype
1. #13081287C2semidirect
2. #13080434C2semidirect
4. #13068209C2semidirect
5. #13068136C2semidirect
6. #13068100C2semidirect
7. #13068034C2semidirect
8. #13068027C2semidirect
9. #13067741C2semidirect
10. #13067731C2semidirect
11. #13067694C2semidirect
12. #13067688C2semidirect
13. #13067506C2semidirect
14. SD16×C11⋊C8C2semidirect
15. C11×#3385C2semidirect
16. Q82×C11C22semidirect
22. C11×#500C22semidirect
24. C11×#477C22semidirect
27. C11×#446C22semidirect
32. #10622701C22semidirect
34. #10622698C22semidirect
43. #10622640C22semidirect
46. Q8×C11⋊C8C22semidirect
56. #10622184C22semidirect
57. #10622184C22semidirect
58. Q8⋊(C11⋊C8)C22semidirect
59. Q8⋊(C11⋊C8)C22semidirect
62. #10622123C22semidirect
64. #10622118C22semidirect
65. #10622095C22semidirect
66. C8×C11⋊C8C22semidirect
174. C11×SD16SD16semidirect
218. #3385D11semidirect
292. Q82C2×D11semidirect
297. #500C2×D11semidirect
306. #477C2×D11semidirect
322. #446C2×D11semidirect
488. SD16#4325semidirect
526. C11#19893semidirect

Maximal subgroups

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

subgroupindex
#130812872
#130804342
#130802372
#130682092
#130681362
#130681002
#130680342
#130680272
#130677412
#130677312
#130676942
#130676882
#130675062
SD16×C11⋊C82
C11×#33852
#1989311