Finite Group Databasebeta

← #16796071

Subgroups — #16796071

Order 3328.

672 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13131631C211yesmaximal, characteristic, complemented
2#13131576C211yesmaximal, characteristic
3#13130480C211yesmaximal, characteristic, complemented
4#13130478C211yesmaximal, characteristic, complemented
5#13130464C211yesmaximal, characteristic, complemented
6#13130463C211yesmaximal, characteristic, complemented
7#13130454C211yesmaximal, characteristic, complemented
8#13130452C211yesmaximal, characteristic, complemented
9#13130428C211yesmaximal, characteristic, complemented
10#13130426C211yesmaximal, characteristic, complemented
11#13130405C211yesmaximal, characteristic, complemented
12#13130184C211yesmaximal, characteristic, complemented
13C2×#11718243C211yesmaximal, characteristic
14#13130047C211yesmaximal, characteristic, complemented
15#13124841C211yesmaximal, characteristic
16C2×D13⋊M16—21no—
17#11719327C2211yescharacteristic
18C2×#88147C2211yescharacteristic
19#11719158C2211yescharacteristic, complemented
20Q8×#1057C2211yescharacteristic, complemented
21#11719129C2211yescharacteristic
22#11719126—21no—
23C4×#6122C2211yescharacteristic
24C2×C4⋊#1057C2211yescharacteristic
25C2×C4×#1057C2211yescharacteristic
26#11719080—21no—
27#11719080C2211yescharacteristic, complemented
28#11719078—21no—
29#11719076C2211yescharacteristic
30#11719076C2211yescharacteristic
31#11719075—21no—
32#11719075—21no—
33#11719074C2211yescharacteristic, complemented
34#11719073C2211yescharacteristic
35#11719073C2211yescharacteristic
36#11719067—21no—
37#11719062—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#11718256C2211yescharacteristic, complemented
55#11718254C2211yescharacteristic, complemented
56#11718254C2211yescharacteristic, complemented
57#1057⋊C8C2211yescharacteristic, complemented
58#1057⋊C8C2211yescharacteristic, complemented
59#11718251C2211yescharacteristic, complemented
60#11718251C2211yescharacteristic, 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×#6122D411yescharacteristic
71C2×#6122D411yescharacteristic
72C22×#1057—21no—
73C22×#1057—21no—
74D13⋊M16—44no—
75C2×#6118—21no—
76C2×#6118—21no—
77C2×D13⋊C8—21no—
78C2×D13⋊C8—21no—
79C13×C22⋊Q8C2×C411yescharacteristic
80C2×C13×C4⋊C4C2×C411yescharacteristic
81Q8×Dic13C2311yescharacteristic
82#88198C2×C411yescharacteristic
83C2×#6106C2×C411yescharacteristic
84C2×#6106C2×C411yescharacteristic
85C2×#6103—21no—
86#88178C2×C411yescharacteristic
87C2×C4×Dic13C2311yescharacteristic
88C2×#6095C2×C411yescharacteristic
89C2×#6095C2×C411yescharacteristic
90#88147—21no—
91#88147—21no—
92#88147C2×C411yescharacteristic
93#88147C2×C411yescharacteristic
94#88147C2311yescharacteristic
95#88147C2311yescharacteristic
96#88143—21no—
97#88142C2×C411yescharacteristic
98#88141—21no—
99#88141C2311yescharacteristic
100#88132—21no—
101#88131—21no—
102#88112—21no—
103#88112—21no—
104#88112—21no—
105#88111—21no—
106#88111—21no—
107#88111—21no—
108#88111—21no—
109#88110—21no—
110#88110—21no—
111#88110D411yescharacteristic
112#88110D411yescharacteristic
113C4⋊#1057—21no—
114C4⋊#1057—21no—
115C4⋊#1057—21no—
116C4⋊#1057C2311yescharacteristic
117C4⋊#1057C2311yescharacteristic
118C4⋊#1057C2311yescharacteristic
119C4⋊#1057C2311yescharacteristic
120C4×#1057—21no—
121C4×#1057—21no—
122C4×#1057—21no—
123C4×#1057C2311yescharacteristic
124C4×#1057C2311yescharacteristic
125C4×#1057C2311yescharacteristic
126C4×#1057C2311yescharacteristic
127C13×#106C2×C411yescharacteristic
128C13×#106C2×C411yescharacteristic
129C13×#103C2×C411yescharacteristic
130C13×#103C2×C411yescharacteristic
131C13×C22⋊C8C2×C411yescharacteristic
132C22⋊#1055C2×C411yescharacteristic
133#88061C2×C411yescharacteristic
134#88061C2×C411yescharacteristic
135#88054C2×C411yescharacteristic
136#88054C2×C411yescharacteristic
137C8×Dic13C2311yescharacteristic
138C8×Dic13C2311yescharacteristic
139#88050C2×C411yescharacteristic
140#88050C2×C411yescharacteristic
141#88049C2×C411yescharacteristic
142#88049C2×C411yescharacteristic
143#88048C2×C411yescharacteristic
144#88048C2×C411yescharacteristic
145#18000—131nomaximal, Sylow
146C23×D13—21no—
147C2×Q8×C13C22×C411yescharacteristic
148C22×C4×C13—21no—
149C22×C4×C13C22×C411yescharacteristic
150C22×Dic13C2×D411yescharacteristic
151C22×Dic13#4111yescharacteristic
152C2×D52—22no—
153C2×D52—21no—
154C2×D52—41no—
155C2×D52C22×C411yescharacteristic
156C2×D52C22×C411yescharacteristic
157C2×C4×D13—21no—
158C2×C4×D13—21no—
159C2×C4×D13—21no—
160C2×C4×D13—21no—
161C2×C4×D13—42no—
162C2×C4×D13—42no—
163C2×Dic26—21no—
164C2×Dic26C22×C411yescharacteristic
165#6122—22no—
166#6122—22no—
167#6122—42no—
168C2×#1057—21no—
169C2×#1057—21no—
170C2×#1057—21no—
171C2×#1057—21no—
172C2×#1057—21no—
173C2×#1057—21no—
174C2×#1057—42no—
175C2×#1057—42no—
176C2×#1057C2×D411yescharacteristic
177C2×#1057C2×D411yescharacteristic
178C2×#1057C2×D411yescharacteristic
179C2×#1057C2×D411yescharacteristic
180#6118—42no—
181#6118—42no—
182D13⋊C8—42no—
183D13⋊C8—42no—
184C2×C8×C13C22×C411yescharacteristic
185C2×C8×C13C22×C411yescharacteristic
186C13×C4⋊C4—21no—
187C13×C4⋊C4—21no—
188C13×C4⋊C4C22×C411yescharacteristic
189C13×C4⋊C4C22×C411yescharacteristic
190C13×C4⋊C4C22×C411yescharacteristic
191C13×C22⋊C4—21no—
192C22⋊Dic13—21no—
193#6106—22no—
194#6106—41no—
195#6103—21no—
196#6103—21no—
197#6103—21no—
198#6103—21no—
199C4⋊Dic13—21no—
200C4⋊Dic13C22×C411yescharacteristic
201#6101—21no—
202#6101—21no—
203#6101—21no—
204#6101—21no—
205#6101—21no—
206C4×Dic13—21no—
207C4×Dic13—21no—
208C4×Dic13C22×C411yescharacteristic
209C4×Dic13C2×D411yescharacteristic
210C4×Dic13#4111yescharacteristic
211C4×Dic13C2411yescharacteristic
212C2×#1055C22×C411yescharacteristic
213C2×#1055C22×C411yescharacteristic
214#6095—22no—
215#6095—41no—
216#3101—131no—
217#2962—131no—
218D4×M16—131no—
219#1592—131no—
220#1592—131no—
221#1588—131no—
222#1588—131no—
223#1585—131no—
224#1585—131no—
225SD16⋊C8—131no—
226SD16⋊C8—131no—
227#1571—131no—
228#1493—131no—
229C2×D4⋊C8—131no—
230#1451—131no—
231C23×C13C4×D411yescharacteristic
232C22×D13—21no—
233C22×D13—21no—
234C22×D13—42no—
235C22×D13—42no—
236C22×D13—81no—
237Q8×C13—21no—
238Q8×C13—21no—
239C2×C4×C13—21no—
240C2×C4×C13—21no—
241C2×C4×C13—21no—
242C2×C4×C13—21no—
243C2×C4×C13—21no—
244C2×C4×C13—21no—
245C2×C4×C13—42no—
246C2×C4×C13C4×D411yescharacteristic
247C2×C4×C13C23×C411yescharacteristic
248C2×Dic13—21no—
249C2×Dic13—21no—
250C2×Dic13—41no—
251C2×Dic13C4×D411yescharacteristic
252C2×Dic13C4×D411yescharacteristic
253C2×Dic13AGL(1,ℤ/8)12yes—
254C2×Dic13#13712yes—
255C2×Dic13C22×D411yescharacteristic
256C2×Dic13C2×#4111yescharacteristic
257D52—21no—
258D52—21no—
259D52—21no—
260D52—42no—
261D52#13112yes—
262C4×D13—41no—
263C4×D13—41no—
264C4×D13—41no—
265C4×D13—41no—
266C4×D13—42no—
267C4×D13—42no—
268Dic26—21no—
269Dic26—21no—
270Dic26—81no—
271#1057—22no—
272#1057—21no—
273#1057—21no—
274#1057—21no—
275#1057—21no—
276#1057—41no—
277#1057—41no—
278#1057—41no—
279#1057—41no—
280#1057—41no—
281C8×C13—21no—
282C8×C13—21no—
283#1055—21no—
284#1055—21no—
285C22×M16—261no—
286#533—131no—
287C2×C4×D4—131no—
288#483—131no—
289#483#26111yescharacteristic
290#476—131no—
291#476—131no—
292#461—131no—
293#461—131no—
294#450—131no—
295#450—131no—
296#446—131no—
297#446—131no—
298#446—261no—
299#446—261no—
300C8×Q8—131no—
301C8×Q8—131no—
302C4×SD16—131no—
303C4×SD16—131no—
304C4×SD16—131no—
305C4×SD16—131no—
306#436—131no—
307#436—131no—
308#435—261no—
309#435—261no—
310C8×D4—131no—
311C8×D4—131no—
312#431—131no—
313#424—261no—
314#423—131no—
315C2×C4⋊C8—131no—
316#407—261no—
317#405—261no—
318C4×M16—131no—
319C2×C4×C8—131no—
320#335—131no—
321#335—131no—
322#335—131no—
323#335—131no—
324Q8⋊C8—131no—
325Q8⋊C8—131no—
326Q8⋊C8—131no—
327Q8⋊C8—131no—
328D4⋊C8—131no—
329D4⋊C8—131no—
330D4⋊C8—131no—
331D4⋊C8—131no—
332#322—131no—
333#322—131no—
334#322—131no—
335#322—131no—
336C22×C13—21no—
337C22×C13—21no—
338C22×C13#44012yes—
339C22×C13C2×C4×D411yescharacteristic
340C2×D13—22no—
341C2×D13—41no—
342C2×D13—41no—
343C2×D13—41no—
344C2×D13—41no—
345C2×D13—41no—
346C2×D13—84no—
347C4×C13—21no—
348C4×C13—41no—
349C4×C13—41no—
350C4×C13—41no—
351C4×C13—41no—
352C4×C13C2×#13111yescharacteristic
353C4×C13#56811yescharacteristic
354Dic13—21no—
355Dic13—21no—
356Dic13—41no—
357Dic13—41no—
358Dic13#44012yes—
359Dic13C2×AGL(1,ℤ/8)11yescharacteristic
360Dic13C2×#13711yescharacteristic
361C22×D4—131no—
362C23×C4—261no—
363C2×SD16—131no—
364C2×SD16—131no—
365C2×SD16—131no—
366C2×SD16—131no—
367C2×M16—131no—
368C2×M16—131no—
369C2×M16—261no—
370C2×M16—261no—
371C2×M16—261no—
372C2×M16—524no—
373C22×C8—261no—
374C22×C8—261no—
375C22×C8—261no—
376C22×C8—261no—
377C4⋊Q8—131no—
378C4⋊Q8—131no—
379#125—261no—
380C22⋊Q8—131no—
381C22⋊Q8—261no—
382C22⋊Q8C2×#26111yescharacteristic
383C4×Q8—131no—
384C4×Q8—131no—
385C4×Q8—261no—
386C4×D4—131no—
387C4×D4—131no—
388C4×D4—131no—
389C4×D4—131no—
390C4×D4—261no—
391C4×D4—261no—
392#117—261no—
393C2×C4⋊C4C2×#26111yescharacteristic
394C2×C22⋊C4—261no—
395C2×C42—131no—
396#106—131no—
397#106—131no—
398#106C2×#26111yescharacteristic
399#106C2×#26111yescharacteristic
400C4⋊C8—131no—
401C4⋊C8—131no—
402C4⋊C8—131no—
403C4⋊C8—131no—
404C4⋊C8—131no—
405C4⋊C8—131no—
406C4⋊C8—261no—
407C4⋊C8—261no—
408C4⋊C8—261no—
409C4⋊C8—261no—
410C4⋊C8—261no—
411C4⋊C8—261no—
412#103—131no—
413#103—131no—
414#103C2×#26111yescharacteristic
415#103C2×#26111yescharacteristic
416#102—131no—
417#102—131no—
418#102—131no—
419#102—131no—
420C22⋊C8—131no—
421C22⋊C8—261no—
422C22⋊C8—261no—
423C22⋊C8—261no—
424C22⋊C8—261no—
425C22⋊C8C2×#26111yescharacteristic
426#97—131no—
427#97—131no—
428#97—261no—
429#97—261no—
430C4×C8—131no—
431C4×C8—131no—
432C4×C8—131no—
433C4×C8—131no—
434C4×C8—131no—
435C4×C8—131no—
436C4×C8—261no—
437C4×C8—261no—
438C4×C8—261no—
439C2×C13—22no—
440C2×C13#293311yescharacteristic
441C2×C13C2×#44011yescharacteristic
442C2×C13#295611yescharacteristic
443D13—42no—
444D13—81no—
445C24—261no—
446C2×Q8—131no—
447C2×Q8—261no—
448C2×Q8C22×#26111yescharacteristic
449C2×D4—131no—
450C2×D4—131no—
451C2×D4—262no—
452C2×D4—261no—
453C2×D4—521no—
454C22×C4—21no—
455C22×C4—131no—
456C22×C4—131no—
457C22×C4—261no—
458C22×C4—261no—
459C22×C4—261no—
460C22×C4—261no—
461C22×C4—522no—
462C22×C4—522no—
463C22×C4C22×#26111yescharacteristic
464SD16—262no—
465SD16—262no—
466SD16—521no—
467SD16—521no—
468M16—262no—
469M16—262no—
470M16—522no—
471M16—522no—
472M16—522no—
473C2×C8—131no—
474C2×C8—131no—
475C2×C8—131no—
476C2×C8—131no—
477C2×C8—131no—
478C2×C8—131no—
479C2×C8—261no—
480C2×C8—261no—
481C2×C8—261no—
482C2×C8—261no—
483C2×C8—261no—
484C2×C8—261no—
485C2×C8—522no—
486C2×C8—522no—
487C2×C8—522no—
488C2×C8—522no—
489C2×C8C22×#26111yescharacteristic
490C2×C8C22×#26111yescharacteristic
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—131no—
494C4⋊C4—261no—
495C4⋊C4—261no—
496C4⋊C4—261no—
497C4⋊C4—261no—
498C4⋊C4—261no—
499C4⋊C4—261no—
500C4⋊C4C22×#26111yescharacteristic
501C4⋊C4C22×#26111yescharacteristic
502C4⋊C4C22×#26111yescharacteristic
503C22⋊C4—21no—
504C22⋊C4—261no—
505C22⋊C4—261no—
506C22⋊C4—261no—
507C22⋊C4—261no—
508C22⋊C4—261no—
509C42—131no—
510C42—131no—
511C42—131no—
512C42—131no—
513C42—261no—
514C42—261no—
515C13#1800011yescharacteristic, complemented, Sylow
516C23—261no—
517C23—261no—
518C23—522no—
519C23—522no—
520C23—1041no—
521C23D4×#26111yescharacteristic
522Q8—21no—
523Q8—21no—
524Q8—261no—
525Q8—261no—
526Q8—1041no—
527D4—132no—
528D4—261no—
529D4—261no—
530D4—261no—
531D4—522no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—42no—
539C2×C4—132no—
540C2×C4—132no—
541C2×C4—131no—
542C2×C4—131no—
543C2×C4—131no—
544C2×C4—131no—
545C2×C4—261no—
546C2×C4—261no—
547C2×C4—521no—
548C2×C4—521no—
549C2×C4—521no—
550C2×C4—521no—
551C2×C4—522no—
552C2×C4—522no—
553C2×C4—521no—
554C2×C4D4×#26111yescharacteristic
555C2×C4C23×#26111yescharacteristic
556C8—21no—
557C8—21no—
558C8—261no—
559C8—261no—
560C8—261no—
561C8—261no—
562C8—262no—
563C8—261no—
564C8—261no—
565C8—521no—
566C8—521no—
567C8—521no—
568C8—521no—
569C8—521no—
570C22—21no—
571C22—21no—
572C22—262no—
573C22—521no—
574C22—521no—
575C22—521no—
576C22—521no—
577C22—521no—
578C22—1044no—
579C22#1171910612yes—
580C22C2×D4×#26111yescharacteristic
581C4—21no—
582C4—41no—
583C4—41no—
584C4—41no—
585C4—41no—
586C4—131no—
587C4—131no—
588C4—132no—
589C4—261no—
590C4—261no—
591C4—521no—
592C4—521no—
593C4D13⋊#13111yescharacteristic
594C4#1171962911yescharacteristic
595C2—22no—
596C2—522no—
597C2—1041no—
598C2#1313157011yescharacteristic
599C2C2×#1171910611yescharacteristic
600C2#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#18000
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. #13131631C2semidirect
3. #13130480C2semidirect
4. #13130478C2semidirect
5. #13130464C2semidirect
6. #13130463C2semidirect
7. #13130454C2semidirect
8. #13130452C2semidirect
9. #13130428C2semidirect
10. #13130426C2semidirect
11. #13130405C2semidirect
12. #13130184C2semidirect
14. #13130047C2semidirect
19. #11719158C22semidirect
20. Q8×#1057C22semidirect
27. #11719080C22semidirect
33. #11719074C22semidirect
51. Q8⋊#1057C22semidirect
52. Q8⋊#1057C22semidirect
53. #11718256C22semidirect
54. #11718256C22semidirect
55. #11718254C22semidirect
56. #11718254C22semidirect
57. #1057⋊C8C22semidirect
58. #1057⋊C8C22semidirect
59. #11718251C22semidirect
60. #11718251C22semidirect
61. #11718244C22semidirect
62. #11718244C22semidirect
515. C13#18000semidirect

Maximal subgroups

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

subgroupindex
#131316312
#131315762
#131304802
#131304782
#131304642
#131304632
#131304542
#131304522
#131304282
#131304262
#131304052
#131301842
C2×#117182432
#131300472
#131248412
#1800013