Finite Group Databasebeta

← #16796273

Subgroups — #16796273

Order 3328.

616 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13131745C211yesmaximal, characteristic, complemented
2#13131697C211yesmaximal, characteristic
3#13130478C211yesmaximal, characteristic, complemented
4#13130470C211yesmaximal, characteristic, complemented
5#13130464C211yesmaximal, characteristic, complemented
6#13130454C211yesmaximal, characteristic, complemented
7#13130443C211yesmaximal, characteristic, complemented
8#13130440C211yesmaximal, characteristic, complemented
9#13130426C211yesmaximal, characteristic, complemented
10#13130421C211yesmaximal, characteristic, complemented
11#13130407C211yesmaximal, characteristic, complemented
12#13130198C211yesmaximal, characteristic, complemented
13#13130137C211yesmaximal, characteristic
14#13130057C211yesmaximal, characteristic, complemented
15#13124841C211yesmaximal, characteristic
16#11719327C2211yescharacteristic
17C2×#88147C2211yescharacteristic
18#11719158C2211yescharacteristic, complemented
19Q8×#1057C2211yescharacteristic, complemented
20#11719130C2211yescharacteristic
21#11719127—21no—
22#11719125C2211yescharacteristic
23D13⋊(C22⋊C8)—21no—
24#11719119C2211yescharacteristic
25#11719119C2211yescharacteristic
26#11719080C2211yescharacteristic, complemented
27#11719078—21no—
28#11719076C2211yescharacteristic
29#11719076C2211yescharacteristic
30#11719075—21no—
31#11719075—21no—
32#11719074—21no—
33#11719074C2211yescharacteristic, complemented
34#11719073C2211yescharacteristic
35#11719073C2211yescharacteristic
36#11719068—21no—
37#11719068—21no—
38C13×#483C411yescharacteristic
39#11718707C411yescharacteristic
40#11718632C411yescharacteristic
41#11718531C411yescharacteristic
42#11718531C411yescharacteristic
43#11718513C2211yescharacteristic
44#11718513C2211yescharacteristic
45#11718479C411yescharacteristic
46#11718479C411yescharacteristic
47#11718449C2211yescharacteristic
48#11718449C2211yescharacteristic
49#11718392C411yescharacteristic
50#11718379C2211yescharacteristic
51Q8⋊#1057C2211yescharacteristic, complemented
52Q8⋊#1057C2211yescharacteristic, complemented
53#11718256C2211yescharacteristic, complemented
54#11718255C2211yescharacteristic, complemented
55#11718254C2211yescharacteristic, complemented
56#11718253C2211yescharacteristic, complemented
57#1057⋊C8C2211yescharacteristic, complemented
58#1057⋊C8C2211yescharacteristic, complemented
59#11718251C2211yescharacteristic, complemented
60C8×#1057C2211yescharacteristic, complemented
61#11718244C2211yescharacteristic, complemented
62#11718244C2211yescharacteristic, complemented
63#11718243C2211yescharacteristic
64#11718243C2211yescharacteristic
65#11718243C2211yescharacteristic
66#11718243C2211yescharacteristic
67C22×D52C2×C411yescharacteristic
68C22×C4×D13—21no—
69C2×#6118—21no—
70C2×#6118—21no—
71C2×D13⋊C8—21no—
72C2×D13⋊C8—21no—
73C13×C22⋊Q8C2×C411yescharacteristic
74C2×C13×C4⋊C4C2×C411yescharacteristic
75Q8×Dic13C2311yescharacteristic
76#88198C2×C411yescharacteristic
77C2×#6106C2×C411yescharacteristic
78C2×#6106C2×C411yescharacteristic
79C2×#6103—21no—
80#88178C2×C411yescharacteristic
81C2×C4×Dic13C2311yescharacteristic
82C2×#6095C2×C411yescharacteristic
83C2×#6095C2×C411yescharacteristic
84#88147—21no—
85#88147—21no—
86#88147C2×C411yescharacteristic
87#88147C2×C411yescharacteristic
88#88147C2311yescharacteristic
89#88147C2311yescharacteristic
90#88143—21no—
91#88142C2×C411yescharacteristic
92#88141—21no—
93#88141C2311yescharacteristic
94#88132—21no—
95#88131—21no—
96C22⋊#1057—21no—
97C22⋊#1057—21no—
98C22⋊#1057—21no—
99C22⋊#1057D411yescharacteristic
100C22⋊#1057D411yescharacteristic
101#88112—21no—
102#88112—21no—
103#88112D411yescharacteristic
104#88112D411yescharacteristic
105#88111—21no—
106#88111—21no—
107#88111—21no—
108#88111—21no—
109#88110—21no—
110#88110—21no—
111#88110—21no—
112C4⋊#1057—21no—
113C4⋊#1057—21no—
114C4⋊#1057—21no—
115C4⋊#1057C2311yescharacteristic
116C4⋊#1057C2311yescharacteristic
117C4⋊#1057C2311yescharacteristic
118C4⋊#1057C2311yescharacteristic
119C4×#1057—21no—
120C4×#1057—21no—
121C4×#1057—21no—
122C4×#1057C2311yescharacteristic
123C4×#1057C2311yescharacteristic
124C4×#1057C2311yescharacteristic
125C4×#1057C2311yescharacteristic
126C13×#106C2×C411yescharacteristic
127C13×#106C2×C411yescharacteristic
128C13×#103C2×C411yescharacteristic
129C13×#103C2×C411yescharacteristic
130C13×C22⋊C8C2×C411yescharacteristic
131C22⋊#1055C2×C411yescharacteristic
132#88061C2×C411yescharacteristic
133#88061C2×C411yescharacteristic
134#88054C2×C411yescharacteristic
135#88054C2×C411yescharacteristic
136C8×Dic13C2311yescharacteristic
137C8×Dic13C2311yescharacteristic
138#88050C2×C411yescharacteristic
139#88050C2×C411yescharacteristic
140#88049C2×C411yescharacteristic
141#88049C2×C411yescharacteristic
142#88048C2×C411yescharacteristic
143#88048C2×C411yescharacteristic
144#18028—131nomaximal, Sylow
145C23×D13—21no—
146C2×Q8×C13C22×C411yescharacteristic
147C22×C4×C13—21no—
148C22×C4×C13C22×C411yescharacteristic
149C22×Dic13C2×D411yescharacteristic
150C22×Dic13#4111yescharacteristic
151C2×D52—22no—
152C2×D52—21no—
153C2×D52—41no—
154C2×D52C22×C411yescharacteristic
155C2×D52C22×C411yescharacteristic
156C2×C4×D13—21no—
157C2×C4×D13—21no—
158C2×C4×D13—21no—
159C2×C4×D13—21no—
160C2×C4×D13—81no—
161C2×C4×D13—81no—
162C2×Dic26—21no—
163C2×Dic26C22×C411yescharacteristic
164C2×#1057—21no—
165C2×#1057—21no—
166C2×#1057—21no—
167C2×#1057—21no—
168C2×#1057—21no—
169C2×#1057—21no—
170C2×#1057C2×D411yescharacteristic
171C2×#1057C2×D411yescharacteristic
172C2×#1057C2×D411yescharacteristic
173C2×#1057C2×D411yescharacteristic
174#6118—81no—
175#6118—81no—
176D13⋊C8—81no—
177D13⋊C8—81no—
178C2×C8×C13C22×C411yescharacteristic
179C2×C8×C13C22×C411yescharacteristic
180C13×C4⋊C4—21no—
181C13×C4⋊C4—21no—
182C13×C4⋊C4C22×C411yescharacteristic
183C13×C4⋊C4C22×C411yescharacteristic
184C13×C4⋊C4C22×C411yescharacteristic
185C13×C22⋊C4—21no—
186C22⋊Dic13—21no—
187#6106—22no—
188#6106—41no—
189#6103—21no—
190#6103—21no—
191#6103—21no—
192#6103—21no—
193C4⋊Dic13—21no—
194C4⋊Dic13C22×C411yescharacteristic
195#6101—21no—
196#6101—21no—
197#6101—21no—
198#6101—21no—
199#6101—21no—
200C4×Dic13—21no—
201C4×Dic13—21no—
202C4×Dic13C22×C411yescharacteristic
203C4×Dic13C2×D411yescharacteristic
204C4×Dic13#4111yescharacteristic
205C4×Dic13C2411yescharacteristic
206C2×#1055C22×C411yescharacteristic
207C2×#1055C22×C411yescharacteristic
208#6095—22no—
209#6095—41no—
210#3101—131no—
211#2986—131no—
212#2974—131no—
213#1592—131no—
214#1590—131no—
215#1588—131no—
216#1585—131no—
217#1583—131no—
218#1582—131no—
219SD16⋊C8—131no—
220C8×SD16—131no—
221#1572—131no—
222#1497—131no—
223#1478—131no—
224#1454—131no—
225C23×C13C4×D411yescharacteristic
226C22×D13—21no—
227C22×D13—21no—
228C22×D13—42no—
229C22×D13—42no—
230C22×D13—81no—
231Q8×C13—21no—
232Q8×C13—21no—
233C2×C4×C13—21no—
234C2×C4×C13—21no—
235C2×C4×C13—21no—
236C2×C4×C13—21no—
237C2×C4×C13—21no—
238C2×C4×C13—21no—
239C2×C4×C13—81no—
240C2×C4×C13C4×D411yescharacteristic
241C2×C4×C13C23×C411yescharacteristic
242C2×Dic13—21no—
243C2×Dic13—21no—
244C2×Dic13—21no—
245C2×Dic13—21no—
246C2×Dic13—41no—
247C2×Dic13C4×D411yescharacteristic
248C2×Dic13C4×D411yescharacteristic
249C2×Dic13C22×D411yescharacteristic
250C2×Dic13C2×#4111yescharacteristic
251D52—21no—
252D52—21no—
253D52—21no—
254D52—42no—
255D52#13112yes—
256C4×D13—41no—
257C4×D13—41no—
258C4×D13—41no—
259C4×D13—41no—
260C4×D13—81no—
261C4×D13—81no—
262Dic26—21no—
263Dic26—21no—
264Dic26—42no—
265#1057—21no—
266#1057—21no—
267#1057—21no—
268#1057—21no—
269#1057—41no—
270#1057—41no—
271#1057—41no—
272#1057—41no—
273#1057—41no—
274#1057—41no—
275C8×C13—21no—
276C8×C13—21no—
277#1055—21no—
278#1055—21no—
279#533—131no—
280C2×C4×D4—131no—
281#483—131no—
282#483#26111yescharacteristic
283#476—131no—
284#476—131no—
285#461—131no—
286#461—131no—
287#450—131no—
288#450—131no—
289#446—131no—
290#446—131no—
291#446—261no—
292C8×Q8—131no—
293C8×Q8—131no—
294C8×Q8—261no—
295C4×SD16—131no—
296C4×SD16—131no—
297C4×SD16—131no—
298C4×SD16—131no—
299#436—131no—
300#436—131no—
301#435—261no—
302#435—261no—
303C8×D4—131no—
304C8×D4—131no—
305#433—261no—
306#433—261no—
307#432—131no—
308#431—131no—
309#431—131no—
310#431—131no—
311#431—131no—
312#407—261no—
313C2×C22⋊C8—261no—
314#335—131no—
315#335—131no—
316#334—131no—
317#334—131no—
318Q8⋊C8—131no—
319Q8⋊C8—131no—
320Q8⋊C8—131no—
321Q8⋊C8—131no—
322D4⋊C8—131no—
323D4⋊C8—131no—
324D4⋊C8—131no—
325D4⋊C8—131no—
326#322—131no—
327#322—131no—
328#322—131no—
329C82—131no—
330C22×C13—21no—
331C22×C13—21no—
332C22×C13—21no—
333C22×C13C2×C4×D411yescharacteristic
334C2×D13—22no—
335C2×D13—41no—
336C2×D13—41no—
337C2×D13—41no—
338C2×D13—41no—
339C2×D13—41no—
340C2×D13—84no—
341C4×C13—21no—
342C4×C13—41no—
343C4×C13—41no—
344C4×C13—41no—
345C4×C13—41no—
346C4×C13C2×#13111yescharacteristic
347C4×C13#56811yescharacteristic
348Dic13—21no—
349Dic13—21no—
350Dic13—21no—
351Dic13—41no—
352Dic13—41no—
353Dic13#57711yescharacteristic
354Dic13#57711yescharacteristic
355C22×D4—131no—
356C23×C4—261no—
357C2×SD16—131no—
358C2×SD16—131no—
359C2×SD16—131no—
360C2×SD16—131no—
361C2×M16—261no—
362C2×M16—261no—
363C22×C8—261no—
364C22×C8—261no—
365C4⋊Q8—131no—
366C4⋊Q8—131no—
367#125—261no—
368C22⋊Q8—131no—
369C22⋊Q8—261no—
370C22⋊Q8C2×#26111yescharacteristic
371C4×Q8—131no—
372C4×Q8—131no—
373C4×Q8—261no—
374C4×D4—131no—
375C4×D4—131no—
376C4×D4—131no—
377C4×D4—131no—
378C4×D4—261no—
379C4×D4—261no—
380#117—261no—
381C2×C4⋊C4C2×#26111yescharacteristic
382C2×C22⋊C4—261no—
383C2×C42—131no—
384#106—131no—
385#106—131no—
386#106C2×#26111yescharacteristic
387#106C2×#26111yescharacteristic
388C4⋊C8—131no—
389C4⋊C8—131no—
390C4⋊C8—131no—
391C4⋊C8—131no—
392C4⋊C8—131no—
393C4⋊C8—131no—
394C4⋊C8—131no—
395C4⋊C8—131no—
396C4⋊C8—261no—
397C4⋊C8—261no—
398C4⋊C8—261no—
399C4⋊C8—261no—
400C4⋊C8—261no—
401#103—131no—
402#103—131no—
403#103C2×#26111yescharacteristic
404#103C2×#26111yescharacteristic
405#102—131no—
406#102—131no—
407#102—131no—
408#102—131no—
409C22⋊C8—131no—
410C22⋊C8—131no—
411C22⋊C8—131no—
412C22⋊C8—261no—
413C22⋊C8—261no—
414C22⋊C8—261no—
415C22⋊C8—261no—
416C22⋊C8—261no—
417C22⋊C8—261no—
418C22⋊C8—261no—
419C22⋊C8C2×#26111yescharacteristic
420#97—261no—
421#97—261no—
422#97—261no—
423C4×C8—131no—
424C4×C8—131no—
425C4×C8—131no—
426C4×C8—131no—
427C4×C8—131no—
428C4×C8—131no—
429C4×C8—261no—
430C4×C8—261no—
431C4×C8—261no—
432C2×C13—41no—
433C2×C13#293311yescharacteristic
434C2×C13#294911yescharacteristic
435C2×C13#295511yescharacteristic
436D13—42no—
437D13—81no—
438C24—261no—
439C2×Q8—131no—
440C2×Q8—261no—
441C2×Q8C22×#26111yescharacteristic
442C2×D4—131no—
443C2×D4—131no—
444C2×D4—262no—
445C2×D4—261no—
446C2×D4—521no—
447C22×C4—21no—
448C22×C4—131no—
449C22×C4—131no—
450C22×C4—261no—
451C22×C4—261no—
452C22×C4—261no—
453C22×C4—261no—
454C22×C4—1041no—
455C22×C4—1041no—
456C22×C4C22×#26111yescharacteristic
457SD16—262no—
458SD16—262no—
459SD16—521no—
460SD16—521no—
461M16—1041no—
462M16—1041no—
463C2×C8—131no—
464C2×C8—131no—
465C2×C8—131no—
466C2×C8—131no—
467C2×C8—131no—
468C2×C8—131no—
469C2×C8—261no—
470C2×C8—261no—
471C2×C8—261no—
472C2×C8—261no—
473C2×C8—261no—
474C2×C8—261no—
475C2×C8—1041no—
476C2×C8—1041no—
477C2×C8C22×#26111yescharacteristic
478C2×C8C22×#26111yescharacteristic
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—131no—
482C4⋊C4—261no—
483C4⋊C4—261no—
484C4⋊C4—261no—
485C4⋊C4—261no—
486C4⋊C4—261no—
487C4⋊C4—261no—
488C4⋊C4C22×#26111yescharacteristic
489C4⋊C4C22×#26111yescharacteristic
490C4⋊C4C22×#26111yescharacteristic
491C22⋊C4—21no—
492C22⋊C4—261no—
493C22⋊C4—261no—
494C22⋊C4—261no—
495C22⋊C4—261no—
496C22⋊C4—261no—
497C42—131no—
498C42—131no—
499C42—131no—
500C42—131no—
501C42—261no—
502C42—261no—
503C13#1802811yescharacteristic, complemented, Sylow
504C23—261no—
505C23—261no—
506C23—522no—
507C23—522no—
508C23—1041no—
509C23D4×#26111yescharacteristic
510Q8—21no—
511Q8—21no—
512Q8—261no—
513Q8—261no—
514Q8—522no—
515D4—132no—
516D4—261no—
517D4—261no—
518D4—261no—
519D4—522no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—81no—
527C2×C4—131no—
528C2×C4—131no—
529C2×C4—131no—
530C2×C4—131no—
531C2×C4—261no—
532C2×C4—261no—
533C2×C4—261no—
534C2×C4—261no—
535C2×C4—521no—
536C2×C4—521no—
537C2×C4—521no—
538C2×C4—521no—
539C2×C4—521no—
540C2×C4—1041no—
541C2×C4—1041no—
542C2×C4D4×#26111yescharacteristic
543C2×C4C23×#26111yescharacteristic
544C8—21no—
545C8—21no—
546C8—261no—
547C8—261no—
548C8—261no—
549C8—261no—
550C8—261no—
551C8—261no—
552C8—521no—
553C8—521no—
554C8—521no—
555C8—521no—
556C8—521no—
557C8—521no—
558C22—21no—
559C22—21no—
560C22—21no—
561C22—262no—
562C22—521no—
563C22—521no—
564C22—521no—
565C22—521no—
566C22—521no—
567C22—1044no—
568C22C2×D4×#26111yescharacteristic
569C4—21no—
570C4—41no—
571C4—41no—
572C4—41no—
573C4—41no—
574C4—131no—
575C4—131no—
576C4—261no—
577C4—261no—
578C4—261no—
579C4—521no—
580C4—521no—
581C4D13⋊#13111yescharacteristic
582C4#1171962911yescharacteristic
583C2—41no—
584C2—522no—
585C2—1041no—
586C2#1313157011yescharacteristic
587C2#1313159611yescharacteristic
588C2#1313160911yescharacteristic
subgroupG/H
centerC22C2×D4×#261
commutatorC2×C4×C13C23×C4
FrattiniC2×C4C23×#261
FittingC13×#483C4
socleC22×C13C2×C4×D4
prime radicalC22×D52C2×C4
cosocleC4×Dic13C24
hypercenter#483#261
hypocenterC13#18028
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #483

Complements

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

NH ≅ G/Ntype
1. #13131745C2semidirect
3. #13130478C2semidirect
4. #13130470C2semidirect
5. #13130464C2semidirect
6. #13130454C2semidirect
7. #13130443C2semidirect
8. #13130440C2semidirect
9. #13130426C2semidirect
10. #13130421C2semidirect
11. #13130407C2semidirect
12. #13130198C2semidirect
14. #13130057C2semidirect
18. #11719158C22semidirect
19. Q8×#1057C22semidirect
26. #11719080C22semidirect
33. #11719074C22semidirect
51. Q8⋊#1057C22semidirect
52. Q8⋊#1057C22semidirect
53. #11718256C22semidirect
54. #11718255C22semidirect
55. #11718254C22semidirect
56. #11718253C22semidirect
57. #1057⋊C8C22semidirect
58. #1057⋊C8C22semidirect
59. #11718251C22semidirect
60. C8×#1057C22semidirect
61. #11718244C22semidirect
62. #11718244C22semidirect
503. C13#18028semidirect

Maximal subgroups

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

subgroupindex
#131317452
#131316972
#131304782
#131304702
#131304642
#131304542
#131304432
#131304402
#131304262
#131304212
#131304072
#131301982
#131301372
#131300572
#131248412
#1802813