Finite Group Databasebeta

← #16795794

Subgroups — #16795794

Order 3328.

606 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13131740C211yesmaximal, characteristic, complemented
2#13131701C211yesmaximal, characteristic
3#13130480C211yesmaximal, characteristic, complemented
4#13130478C211yesmaximal, characteristic, complemented
5#13130471C211yesmaximal, characteristic, complemented
6#13130470C211yesmaximal, characteristic, complemented
7#13130464C211yesmaximal, characteristic, complemented
8#13130463C211yesmaximal, characteristic, complemented
9#13130444C211yesmaximal, characteristic, complemented
10#13130443C211yesmaximal, characteristic, complemented
11#13130407C211yesmaximal, characteristic, complemented
12#13130177C211yesmaximal, characteristic
13#13130158C211yesmaximal, characteristic, complemented
14#13130053C211yesmaximal, characteristic, complemented
15#13124841C211yesmaximal, characteristic
16#11719327C2211yescharacteristic
17C2×#88147C2211yescharacteristic
18#11719158C2211yescharacteristic, complemented
19Q8×#1057C2211yescharacteristic, complemented
20#11719130C2211yescharacteristic
21#11719127—21no—
22#11719127—21no—
23C4×#6122C2211yescharacteristic
24#11719119C2211yescharacteristic
25#11719119C2211yescharacteristic
26#11719080—21no—
27#11719080C2211yescharacteristic, complemented
28#11719078—21no—
29#11719076—21no—
30#11719076—21no—
31#11719076C2211yescharacteristic
32#11719076C2211yescharacteristic
33#11719076C2211yescharacteristic
34#11719076C2211yescharacteristic
35#11719074C2211yescharacteristic, complemented
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×#6122—21no—
70C2×#6118—21no—
71C2×#6118—21no—
72C2×#6118—21no—
73C2×#6118—21no—
74C13×C22⋊Q8C2×C411yescharacteristic
75C2×C13×C4⋊C4C2×C411yescharacteristic
76Q8×Dic13C2311yescharacteristic
77#88198C2×C411yescharacteristic
78C2×#6106C2×C411yescharacteristic
79C2×#6106C2×C411yescharacteristic
80C2×#6103—21no—
81#88178C2×C411yescharacteristic
82C2×C4×Dic13C2311yescharacteristic
83C2×#6095C2×C411yescharacteristic
84C2×#6095C2×C411yescharacteristic
85#88147—21no—
86#88147—21no—
87#88147C2×C411yescharacteristic
88#88147C2×C411yescharacteristic
89#88147C2311yescharacteristic
90#88147C2311yescharacteristic
91#88143—21no—
92#88142C2×C411yescharacteristic
93#88141—21no—
94#88141C2311yescharacteristic
95#88132—21no—
96#88131—21no—
97C22⋊#1057—21no—
98C22⋊#1057—21no—
99C22⋊#1057D411yescharacteristic
100C22⋊#1057D411yescharacteristic
101#88112—21no—
102#88112—21no—
103#88111—21no—
104#88111—21no—
105#88111—21no—
106#88111—21no—
107#88110—21no—
108#88110—21no—
109#88110—21no—
110#88110—21no—
111C4⋊#1057—21no—
112C4⋊#1057—21no—
113C4⋊#1057D411yescharacteristic
114C4⋊#1057D411yescharacteristic
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#17952—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—21no—
152C2×D52—41no—
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
164#6122—42no—
165C2×#1057—21no—
166C2×#1057—21no—
167C2×#1057—21no—
168C2×#1057—21no—
169C2×#1057—21no—
170C2×#1057—21no—
171C2×#1057C2×D411yescharacteristic
172C2×#1057C2×D411yescharacteristic
173C2×#1057C2×D411yescharacteristic
174C2×#1057C2×D411yescharacteristic
175#6118—81no—
176#6118—81no—
177#6118—81no—
178#6118—81no—
179C2×C8×C13C22×C411yescharacteristic
180C2×C8×C13C22×C411yescharacteristic
181C13×C4⋊C4—21no—
182C13×C4⋊C4—21no—
183C13×C4⋊C4C22×C411yescharacteristic
184C13×C4⋊C4C22×C411yescharacteristic
185C13×C4⋊C4C22×C411yescharacteristic
186C13×C22⋊C4—21no—
187C22⋊Dic13—21no—
188#6106—41no—
189#6106—41no—
190#6103—21no—
191#6103—21no—
192#6103—21no—
193#6103—21no—
194C4⋊Dic13—21no—
195C4⋊Dic13C22×C411yescharacteristic
196#6101—21no—
197#6101—21no—
198#6101—21no—
199#6101—21no—
200#6101—21no—
201C4×Dic13—21no—
202C4×Dic13—21no—
203C4×Dic13C22×C411yescharacteristic
204C4×Dic13C2×D411yescharacteristic
205C4×Dic13#4111yescharacteristic
206C4×Dic13C2411yescharacteristic
207C2×#1055C22×C411yescharacteristic
208C2×#1055C22×C411yescharacteristic
209#6095—41no—
210#6095—41no—
211#3101—131no—
212#2985—131no—
213#2975—131no—
214#1592—131no—
215#1592—131no—
216#1590—131no—
217#1590—131no—
218#1588—131no—
219#1588—131no—
220#1583—131no—
221#1583—131no—
222#1572—131no—
223#1490—131no—
224#1485—131no—
225#1453—131no—
226C23×C13C4×D411yescharacteristic
227C22×D13—21no—
228C22×D13—21no—
229C22×D13—42no—
230C22×D13—81no—
231C22×D13—81no—
232Q8×C13—21no—
233Q8×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—21no—
240C2×C4×C13—81no—
241C2×C4×C13C4×D411yescharacteristic
242C2×C4×C13C23×C411yescharacteristic
243C2×Dic13—21no—
244C2×Dic13—21no—
245C2×Dic13—21no—
246C2×Dic13—21no—
247C2×Dic13—41no—
248C2×Dic13C4×D411yescharacteristic
249C2×Dic13C4×D411yescharacteristic
250C2×Dic13C22×D411yescharacteristic
251C2×Dic13C2×#4111yescharacteristic
252D52—21no—
253D52—21no—
254D52—21no—
255D52—21no—
256D52—42no—
257C4×D13—41no—
258C4×D13—41no—
259C4×D13—41no—
260C4×D13—41no—
261C4×D13—81no—
262C4×D13—81no—
263Dic26—21no—
264Dic26—21no—
265Dic26—81no—
266#1057—22no—
267#1057—21no—
268#1057—21no—
269#1057—21no—
270#1057—21no—
271#1057—41no—
272#1057—41no—
273#1057—41no—
274#1057—41no—
275#1057—41no—
276C8×C13—21no—
277C8×C13—21no—
278#1055—21no—
279#1055—21no—
280#533—131no—
281C2×C4×D4—131no—
282#483—131no—
283#483#26111yescharacteristic
284#476—131no—
285#476—131no—
286#461—131no—
287#461—131no—
288#450—131no—
289#450—131no—
290#446—131no—
291#446—131no—
292#446—261no—
293#446—261no—
294C8×Q8—131no—
295C8×Q8—131no—
296C4×SD16—131no—
297C4×SD16—131no—
298C4×SD16—131no—
299C4×SD16—131no—
300#436—131no—
301#436—131no—
302#436—131no—
303#436—131no—
304#436—261no—
305#436—261no—
306#433—261no—
307#433—261no—
308#432—131no—
309#431—131no—
310#431—131no—
311#431—131no—
312#407—261no—
313#407—261no—
314C4×M16—131no—
315#335—131no—
316#335—131no—
317#334—131no—
318#334—131no—
319Q8⋊C8—131no—
320Q8⋊C8—131no—
321Q8⋊C8—131no—
322Q8⋊C8—131no—
323D4⋊C8—131no—
324D4⋊C8—131no—
325D4⋊C8—131no—
326D4⋊C8—131no—
327#322—131no—
328#322—131no—
329#322—131no—
330C82—131no—
331C22×C13—21no—
332C22×C13—21no—
333C22×C13—21no—
334C22×C13C2×C4×D411yescharacteristic
335C2×D13—41no—
336C2×D13—41no—
337C2×D13—41no—
338C2×D13—41no—
339C2×D13—41no—
340C2×D13—41no—
341C2×D13—84no—
342C4×C13—21no—
343C4×C13—41no—
344C4×C13—41no—
345C4×C13—41no—
346C4×C13—41no—
347C4×C13#56811yescharacteristic
348C4×C13#56811yescharacteristic
349Dic13—21no—
350Dic13—21no—
351Dic13—21no—
352Dic13—41no—
353Dic13—41no—
354Dic13#57711yescharacteristic
355Dic13#57711yescharacteristic
356C22×D4—131no—
357C23×C4—261no—
358C2×SD16—131no—
359C2×SD16—131no—
360C2×SD16—131no—
361C2×SD16—131no—
362C2×M16—261no—
363C2×M16—261no—
364C2×M16—261no—
365C2×M16—261no—
366C2×M16—261no—
367C4⋊Q8—131no—
368C4⋊Q8—131no—
369#125—261no—
370C22⋊Q8—131no—
371C22⋊Q8—261no—
372C22⋊Q8C2×#26111yescharacteristic
373C4×Q8—131no—
374C4×Q8—131no—
375C4×Q8—261no—
376C4×D4—131no—
377C4×D4—131no—
378C4×D4—131no—
379C4×D4—131no—
380C4×D4—261no—
381C4×D4—261no—
382#117—261no—
383C2×C4⋊C4C2×#26111yescharacteristic
384C2×C22⋊C4—261no—
385C2×C42—131no—
386#106—131no—
387#106—131no—
388#106C2×#26111yescharacteristic
389#106C2×#26111yescharacteristic
390C4⋊C8—131no—
391C4⋊C8—131no—
392C4⋊C8—131no—
393C4⋊C8—131no—
394C4⋊C8—131no—
395C4⋊C8—131no—
396C4⋊C8—131no—
397C4⋊C8—131no—
398C4⋊C8—261no—
399C4⋊C8—261no—
400C4⋊C8—261no—
401C4⋊C8—261no—
402#103—131no—
403#103—131no—
404#103C2×#26111yescharacteristic
405#103C2×#26111yescharacteristic
406#102—131no—
407#102—131no—
408#102—131no—
409#102—131no—
410C22⋊C8—131no—
411C22⋊C8—131no—
412C22⋊C8—131no—
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—
423#97—261no—
424C4×C8—131no—
425C4×C8—131no—
426C4×C8—131no—
427C4×C8—131no—
428C4×C8—131no—
429C4×C8—131no—
430C4×C8—261no—
431C4×C8—261no—
432C4×C8—261no—
433C2×C13—41no—
434C2×C13#293011yescharacteristic
435C2×C13#294911yescharacteristic
436C2×C13#295611yescharacteristic
437D13—81no—
438D13—81no—
439C24—261no—
440C2×Q8—131no—
441C2×Q8—261no—
442C2×Q8C22×#26111yescharacteristic
443C2×D4—131no—
444C2×D4—131no—
445C2×D4—261no—
446C2×D4—521no—
447C2×D4—521no—
448C22×C4—21no—
449C22×C4—131no—
450C22×C4—131no—
451C22×C4—261no—
452C22×C4—261no—
453C22×C4—261no—
454C22×C4—261no—
455C22×C4—1041no—
456C22×C4—1041no—
457C22×C4C22×#26111yescharacteristic
458SD16—521no—
459SD16—521no—
460SD16—521no—
461SD16—521no—
462M16—522no—
463M16—1041no—
464M16—1041no—
465M16—1041no—
466M16—1041no—
467C2×C8—131no—
468C2×C8—131no—
469C2×C8—131no—
470C2×C8—131no—
471C2×C8—131no—
472C2×C8—131no—
473C2×C8—261no—
474C2×C8—261no—
475C2×C8—261no—
476C2×C8—261no—
477C2×C8—261no—
478C2×C8—261no—
479C2×C8C22×#26111yescharacteristic
480C2×C8C22×#26111yescharacteristic
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—131no—
484C4⋊C4—261no—
485C4⋊C4—261no—
486C4⋊C4—261no—
487C4⋊C4—261no—
488C4⋊C4—261no—
489C4⋊C4—261no—
490C4⋊C4C22×#26111yescharacteristic
491C4⋊C4C22×#26111yescharacteristic
492C4⋊C4C22×#26111yescharacteristic
493C22⋊C4—21no—
494C22⋊C4—261no—
495C22⋊C4—261no—
496C22⋊C4—261no—
497C22⋊C4—261no—
498C22⋊C4—261no—
499C42—131no—
500C42—131no—
501C42—131no—
502C42—131no—
503C42—261no—
504C42—261no—
505C13#1795211yescharacteristic, complemented, Sylow
506C23—261no—
507C23—261no—
508C23—522no—
509C23—1041no—
510C23—1041no—
511C23D4×#26111yescharacteristic
512Q8—21no—
513Q8—21no—
514Q8—261no—
515Q8—261no—
516Q8—1041no—
517D4—261no—
518D4—261no—
519D4—261no—
520D4—261no—
521D4—522no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—81no—
529C2×C4—131no—
530C2×C4—131no—
531C2×C4—131no—
532C2×C4—131no—
533C2×C4—261no—
534C2×C4—261no—
535C2×C4—261no—
536C2×C4—261no—
537C2×C4—521no—
538C2×C4—521no—
539C2×C4—521no—
540C2×C4—521no—
541C2×C4—521no—
542C2×C4—1041no—
543C2×C4—1041no—
544C2×C4D4×#26111yescharacteristic
545C2×C4C23×#26111yescharacteristic
546C8—21no—
547C8—21no—
548C8—261no—
549C8—261no—
550C8—261no—
551C8—261no—
552C8—262no—
553C8—261no—
554C8—261no—
555C8—521no—
556C8—521no—
557C8—521no—
558C8—521no—
559C8—521no—
560C22—21no—
561C22—21no—
562C22—21no—
563C22—521no—
564C22—521no—
565C22—521no—
566C22—521no—
567C22—521no—
568C22—521no—
569C22—1044no—
570C22C2×D4×#26111yescharacteristic
571C4—21no—
572C4—41no—
573C4—41no—
574C4—41no—
575C4—41no—
576C4—131no—
577C4—131no—
578C4—261no—
579C4—261no—
580C4—261no—
581C4—521no—
582C4—521no—
583C4#1171962911yescharacteristic
584C4#1171962911yescharacteristic
585C2—41no—
586C2—1041no—
587C2—1041no—
588C2#1313155711yescharacteristic
589C2#1313159611yescharacteristic
590C2#1313161111yescharacteristic
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#17952
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. #13131740C2semidirect
3. #13130480C2semidirect
4. #13130478C2semidirect
5. #13130471C2semidirect
6. #13130470C2semidirect
7. #13130464C2semidirect
8. #13130463C2semidirect
9. #13130444C2semidirect
10. #13130443C2semidirect
11. #13130407C2semidirect
13. #13130158C2semidirect
14. #13130053C2semidirect
18. #11719158C22semidirect
19. Q8×#1057C22semidirect
27. #11719080C22semidirect
35. #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
505. C13#17952semidirect

Maximal subgroups

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

subgroupindex
#131317402
#131317012
#131304802
#131304782
#131304712
#131304702
#131304642
#131304632
#131304442
#131304432
#131304072
#131301772
#131301582
#131300532
#131248412
#1795213