Finite Group Databasebeta

← #16796405

Subgroups — #16796405

Order 3328.

642 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13131673C211yesmaximal, characteristic
2#13131637C211yesmaximal, characteristic, complemented
3#13130481C211yesmaximal, characteristic, complemented
4#13130474C211yesmaximal, characteristic, complemented
5#13130462C211yesmaximal, characteristic, complemented
6#13130451C211yesmaximal, characteristic, complemented
7#13130450C211yesmaximal, characteristic, complemented
8#13130439C211yesmaximal, characteristic, complemented
9#13130427C211yesmaximal, characteristic, complemented
10#13130419C211yesmaximal, characteristic, complemented
11#13130400C211yesmaximal, characteristic, complemented
12#13130180C211yesmaximal, characteristic, complemented
13#13130171C211yesmaximal, characteristic
14#13130059C211yesmaximal, characteristic, complemented
15#13123660C211yesmaximal, characteristic
16#41×Dic13C2211yescharacteristic
17C2×#88205C411yescharacteristic
18C2×#88141C2211yescharacteristic
19#11719158C2211yescharacteristic
20#11719158C2211yescharacteristic
21#11719144—21no—
22#11719144—21no—
23D4×#1057C2211yescharacteristic
24D4×#1057C2211yescharacteristic
25#11719130C2211yescharacteristic
26#11719129—21no—
27#11719129C2211yescharacteristic
28#11719128—21no—
29C4×#6122—21no—
30C4×#6122C2211yescharacteristic
31C4×#6122C2211yescharacteristic
32C2×#88110—21no—
33#11719080C2211yescharacteristic
34#11719080C2211yescharacteristic
35#11719078—21no—
36#11719078—21no—
37#11719074C2211yescharacteristic
38#11719074C2211yescharacteristic
39C13×#417C411yescharacteristic
40#11718781C411yescharacteristic
41M16×Dic13C2211yescharacteristic
42#11718625C411yescharacteristic
43#11718451C2211yescharacteristic
44#11718451C2211yescharacteristic
45#11718450C411yescharacteristic
46#11718450C411yescharacteristic
47#11718419C2211yescharacteristic
48#11718419C2211yescharacteristic
49#11718418C411yescharacteristic
50#11718418C411yescharacteristic
51Q8⋊#1057C2211yescharacteristic
52Q8⋊#1057C2211yescharacteristic
53D4⋊#1057C2211yescharacteristic
54D4⋊#1057C2211yescharacteristic
55#11718256C2211yescharacteristic
56#11718255C2211yescharacteristic
57#11718254C2211yescharacteristic
58#11718253C2211yescharacteristic
59#1057⋊C8C2211yescharacteristic
60#1057⋊C8C2211yescharacteristic
61#11718251C2211yescharacteristic
62C8×#1057C2211yescharacteristic
63#11718244C2211yescharacteristic
64#11718244C2211yescharacteristic
65#11718244C2211yescharacteristic
66#11718244C2211yescharacteristic
67C2×C13×#41C2×C411yescharacteristic
68C22×Dic26C2×C411yescharacteristic
69C2×#6122—21no—
70C2×#6122—21no—
71C2×#6122D411yescharacteristic
72C2×#6122D411yescharacteristic
73C22×#1057—21no—
74C22×#1057—21no—
75C2×C13×M16C2×C411yescharacteristic
76C2×C13×C4⋊C4C2×C411yescharacteristic
77#88205—24no—
78Q8×Dic13C2×C411yescharacteristic
79Q8×Dic13C2311yescharacteristic
80C2×#6107C2×C411yescharacteristic
81C2×#6107C2×C411yescharacteristic
82D4×Dic13—21no—
83D4×Dic13—21no—
84D4×Dic13C2×C411yescharacteristic
85D4×Dic13C2311yescharacteristic
86C2×#6105C2×C411yescharacteristic
87C2×#6105C2×C411yescharacteristic
88#88180—21no—
89#88180C2×C411yescharacteristic
90C2×#6101—21no—
91C2×C4×Dic13—21no—
92C2×C4×Dic13—21no—
93C2×C4×Dic13C2311yescharacteristic
94C2×#6099C2×C411yescharacteristic
95#88141—21no—
96#88141—21no—
97#88141C2×C411yescharacteristic
98#88141C2×C411yescharacteristic
99#88141C2311yescharacteristic
100#88141C2311yescharacteristic
101C22⋊#1057—21no—
102C22⋊#1057—21no—
103C22⋊#1057—21no—
104#88112—21no—
105#88112—21no—
106#88112—21no—
107#88112—21no—
108#88112—21no—
109#88110—21no—
110#88110—21no—
111#88110—21no—
112#88110—21no—
113#88110—21no—
114#88110—21no—
115#88110D411yescharacteristic
116#88110D411yescharacteristic
117C4⋊#1057—21no—
118C4⋊#1057—21no—
119C4⋊#1057C2311yescharacteristic
120C4⋊#1057C2311yescharacteristic
121C4⋊#1057C2311yescharacteristic
122C4⋊#1057C2311yescharacteristic
123C4×#1057—21no—
124C4×#1057—21no—
125C4×#1057C2311yescharacteristic
126C4×#1057C2311yescharacteristic
127C4×#1057C2311yescharacteristic
128C4×#1057C2311yescharacteristic
129C13×#103C2×C411yescharacteristic
130C13×#103C2×C411yescharacteristic
131C13×#102C2×C411yescharacteristic
132C13×#102C2×C411yescharacteristic
133#88056C2×C411yescharacteristic
134#88056C2×C411yescharacteristic
135#88056C2×C411yescharacteristic
136#88056C2×C411yescharacteristic
137#88055C2×C411yescharacteristic
138#88055C2×C411yescharacteristic
139C8×Dic13C2311yescharacteristic
140C8×Dic13C2311yescharacteristic
141#88048C2×C411yescharacteristic
142#88048C2×C411yescharacteristic
143#88047C2×C411yescharacteristic
144#88047C2×C411yescharacteristic
145#18047—131nomaximal, Sylow
146C13×#41—22no—
147C13×#41—41no—
148C2×Q8×C13C22×C411yescharacteristic
149C2×D4×C13—21no—
150C2×D4×C13C22×C411yescharacteristic
151C22×C4×C13—21no—
152C22×C4×C13—21no—
153C22×C4×C13C22×C411yescharacteristic
154C22×Dic13—21no—
155C22×Dic13—21no—
156C22×Dic13—21no—
157C22×Dic13C2×D411yescharacteristic
158C22×Dic13#4111yescharacteristic
159C2×Dic26—22no—
160C2×Dic26—21no—
161C2×Dic26—41no—
162C2×Dic26C22×C411yescharacteristic
163C2×Dic26C22×C411yescharacteristic
164#6122—22no—
165#6122—41no—
166#6122—42no—
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
180C13×M16—41no—
181C2×C8×C13C22×C411yescharacteristic
182C2×C8×C13C22×C411yescharacteristic
183C13×C4⋊C4—21no—
184C13×C4⋊C4C22×C411yescharacteristic
185C13×C4⋊C4C22×C411yescharacteristic
186C22⋊Dic13—21no—
187C22⋊Dic13—21no—
188C22⋊Dic13—21no—
189#6107—22no—
190#6107—22no—
191#6105—22no—
192#6105M1614yescomplemented
193C4⋊Dic13—21no—
194C4⋊Dic13—21no—
195C4⋊Dic13C22×C411yescharacteristic
196C4⋊Dic13C22×C411yescharacteristic
197#6101—21no—
198#6101—21no—
199#6101—21no—
200#6101—21no—
201C4×Dic13—21no—
202C4×Dic13—21no—
203C4×Dic13—21no—
204C4×Dic13—21no—
205C4×Dic13—21no—
206C4×Dic13—21no—
207C4×Dic13—21no—
208C4×Dic13C22×C411yescharacteristic
209C4×Dic13C2×D411yescharacteristic
210C4×Dic13#4111yescharacteristic
211C4×Dic13C2411yescharacteristic
212#6099—22no—
213C2×#1055C22×C411yescharacteristic
214C2×#1055C22×C411yescharacteristic
215#2970—131no—
216Q8×M16—131no—
217C4×#137—131no—
218#1593—131no—
219#1591—131no—
220#1587—131no—
221#1585—131no—
222#1584—131no—
223#1582—131no—
224SD16⋊C8—131no—
225C8×SD16—131no—
226#1569—131no—
227#1491—131no—
228#1489—131no—
229#1455—131no—
230C23×C13—21no—
231C23×C13C4×D411yescharacteristic
232Q8×C13—21no—
233Q8×C13—21no—
234D4×C13—21no—
235D4×C13—42no—
236D4×C13C2×M1612yes—
237C2×C4×C13—21no—
238C2×C4×C13—21no—
239C2×C4×C13—21no—
240C2×C4×C13—21no—
241C2×C4×C13—21no—
242C2×C4×C13—42no—
243C2×C4×C13—81no—
244C2×C4×C13C4×D411yescharacteristic
245C2×C4×C13C23×C411yescharacteristic
246C2×Dic13—21no—
247C2×Dic13—21no—
248C2×Dic13—21no—
249C2×Dic13—21no—
250C2×Dic13—21no—
251C2×Dic13—21no—
252C2×Dic13—41no—
253C2×Dic13—42no—
254C2×Dic13—41no—
255C2×Dic13—41no—
256C2×Dic13—81no—
257C2×Dic13C4×D411yescharacteristic
258C2×Dic13C4×D411yescharacteristic
259C2×Dic13C22×D411yescharacteristic
260C2×Dic13C2×#4111yescharacteristic
261Dic26—21no—
262Dic26—21no—
263Dic26—21no—
264Dic26—42no—
265Dic26C2×M1612yes—
266#1057—22no—
267#1057—21no—
268#1057—21no—
269#1057—21no—
270#1057—41no—
271#1057—41no—
272#1057—41no—
273#1057—41no—
274#1057—41no—
275#1057#13712yescomplemented
276C8×C13—21no—
277C8×C13—21no—
278#1055—21no—
279#1055C2×M1612yes—
280C2×#137—131no—
281C4×#41—131no—
282C2×C4×Q8—131no—
283#446—131no—
284#446—131no—
285#446—131no—
286#446—131no—
287#446—261no—
288#446—261no—
289C8×Q8—131no—
290C8×Q8—131no—
291#441—131no—
292#441—131no—
293#440—131no—
294#440—131no—
295C4×Q16—131no—
296C4×Q16—131no—
297C4×SD16—131no—
298C4×SD16—131no—
299#435—261no—
300#435—261no—
301C8×D4—131no—
302C8×D4—131no—
303#432—131no—
304#432—261no—
305#428—131no—
306#423—131no—
307#423—261no—
308#419—131no—
309#417#26111yescharacteristic
310C4×M16—131no—
311C4×M16—131no—
312C4×M16—131no—
313C4×M16—261no—
314C2×#97—261no—
315#335—131no—
316#335—131no—
317#334—131no—
318#334—131no—
319Q8⋊C8—131no—
320Q8⋊C8—131no—
321Q8⋊C8—131no—
322Q8⋊C8—131no—
323Q8⋊C8—131no—
324Q8⋊C8—131no—
325D4⋊C8—131no—
326D4⋊C8—131no—
327#322—131no—
328#322—131no—
329#322—131no—
330C82—131no—
331C22×C13—21no—
332C22×C13—22no—
333C22×C13—21no—
334C22×C13—21no—
335C22×C13—41no—
336C22×C13—41no—
337C22×C13C2×C4×D411yescharacteristic
338C4×C13—21no—
339C4×C13—41no—
340C4×C13—41no—
341C4×C13—41no—
342C4×C13C22×M1611yescharacteristic
343C4×C13#56811yescharacteristic
344Dic13—22no—
345Dic13—21no—
346Dic13—21no—
347Dic13—21no—
348Dic13—41no—
349Dic13—41no—
350Dic13—41no—
351Dic13C2×#13711yescharacteristic
352Dic13#57511yescharacteristic
353C2×#41C2×#26111yescharacteristic
354C22×Q8—131no—
355#137—264no—
356C2×Q16—131no—
357C2×Q16—131no—
358C2×SD16—131no—
359C2×SD16—131no—
360C2×M16—131no—
361C2×M16—131no—
362C2×M16—131no—
363C2×M16—261no—
364C2×M16—261no—
365C2×M16C2×#26111yescharacteristic
366C22×C8—261no—
367C22×C8—261no—
368C4×Q8—131no—
369C4×Q8—131no—
370C4×Q8—131no—
371C4×Q8—131no—
372C4×Q8—131no—
373C4×Q8—131no—
374C4×Q8—261no—
375C4×Q8—261no—
376C4×D4—131no—
377C4×D4—131no—
378C4×D4—261no—
379C4×D4—261no—
380#117—131no—
381#117—261no—
382C2×C4⋊C4—261no—
383C2×C4⋊C4C2×#26111yescharacteristic
384C2×C42—131no—
385C2×C42—261no—
386C2×C42—261no—
387#107—131no—
388#107—131no—
389#106—131no—
390#106—131no—
391C4⋊C8—131no—
392C4⋊C8—131no—
393C4⋊C8—131no—
394C4⋊C8—131no—
395C4⋊C8—261no—
396C4⋊C8—261no—
397C4⋊C8—261no—
398C4⋊C8—261no—
399C4⋊C8—261no—
400C4⋊C8—261no—
401C4⋊C8—261no—
402#103—131no—
403#103—131no—
404#103—131no—
405#103—131no—
406#103C2×#26111yescharacteristic
407#103C2×#26111yescharacteristic
408#102C2×#26111yescharacteristic
409#102C2×#26111yescharacteristic
410C22⋊C8—261no—
411C22⋊C8—261no—
412C22⋊C8—261no—
413#97—131no—
414#97—131no—
415#97—131no—
416#97—131no—
417#97—261no—
418#97—261no—
419#97—261no—
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—
431C2×C13—41no—
432C2×C13—42no—
433C2×C13D4×M1611yescharacteristic
434C2×C13C4×#13711yescharacteristic
435C2×C13#295611yescharacteristic
436#41—22no—
437#41—41no—
438C2×Q8—131no—
439C2×Q8—131no—
440C2×Q8—262no—
441C2×Q8—261no—
442C2×Q8—521no—
443C2×Q8C22×#26111yescharacteristic
444C2×D4—21no—
445C2×D4C22×#26111yescharacteristic
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—131no—
449C22×C4—131no—
450C22×C4—261no—
451C22×C4—261no—
452C22×C4—261no—
453C22×C4C22×#26111yescharacteristic
454Q16—262no—
455Q16—262no—
456SD16—134no—
457SD16—262no—
458M16—41no—
459M16—262no—
460M16—262no—
461M16—521no—
462M16—522no—
463M16—522no—
464C2×C8—131no—
465C2×C8—131no—
466C2×C8—131no—
467C2×C8—131no—
468C2×C8—131no—
469C2×C8—131no—
470C2×C8—261no—
471C2×C8—261no—
472C2×C8—261no—
473C2×C8—261no—
474C2×C8—261no—
475C2×C8—261no—
476C2×C8—522no—
477C2×C8—522no—
478C2×C8C22×#26111yescharacteristic
479C2×C8C22×#26111yescharacteristic
480C4⋊C4—21no—
481C4⋊C4—131no—
482C4⋊C4—131no—
483C4⋊C4—261no—
484C4⋊C4—261no—
485C4⋊C4—261no—
486C4⋊C4—261no—
487C4⋊C4—261no—
488C4⋊C4—261no—
489C4⋊C4C22×#26111yescharacteristic
490C4⋊C4C22×#26111yescharacteristic
491C22⋊C4—261no—
492C22⋊C4—261no—
493C22⋊C4—261no—
494C42—131no—
495C42—131no—
496C42—131no—
497C42—131no—
498C42—261no—
499C42—261no—
500C42—261no—
501C42—261no—
502C42—261no—
503C42—261no—
504C42—261no—
505C13#1804711yescharacteristic, complemented, Sylow
506C23—21no—
507C23D4×#26111yescharacteristic
508Q8—21no—
509Q8—21no—
510Q8—132no—
511Q8—261no—
512Q8—261no—
513Q8—261no—
514Q8—522no—
515D4—21no—
516D4—42no—
517D4D13⋊M1612yes—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—42no—
524C2×C4—81no—
525C2×C4—131no—
526C2×C4—131no—
527C2×C4—131no—
528C2×C4—131no—
529C2×C4—261no—
530C2×C4—261no—
531C2×C4—261no—
532C2×C4—261no—
533C2×C4—261no—
534C2×C4—261no—
535C2×C4—521no—
536C2×C4—521no—
537C2×C4—521no—
538C2×C4—522no—
539C2×C4—1041no—
540C2×C4D4×#26111yescharacteristic
541C2×C4C23×#26111yescharacteristic
542C8—21no—
543C8—21no—
544C8—132no—
545C8—132no—
546C8—261no—
547C8—261no—
548C8—261no—
549C8—262no—
550C8—261no—
551C8—521no—
552C8—521no—
553C8—521no—
554C8—521no—
555C8—521no—
556C22—21no—
557C22—22no—
558C22—21no—
559C22—21no—
560C22—41no—
561C22—41no—
562C22C2×D4×#26111yescharacteristic
563C4—21no—
564C4—41no—
565C4—41no—
566C4—41no—
567C4—131no—
568C4—131no—
569C4—262no—
570C4—261no—
571C4—261no—
572C4—261no—
573C4—521no—
574C4—521no—
575C4—521no—
576C4C2×D13⋊M1611yescharacteristic
577C4#1171962111yescharacteristic
578C2—41no—
579C2—42no—
580C2#1313157411yescharacteristic
581C2#137×#26111yescharacteristic
582C2#1313161011yescharacteristic
subgroupG/H
centerC22C2×D4×#261
commutatorC2×C4×C13C23×C4
FrattiniC2×C4C23×#261
FittingC13×#417C4
socleC22×C13C2×C4×D4
prime radicalC2×C13×#41C2×C4
cosocleC4×Dic13C24
hypercenter#417#261
hypocenterC13#18047
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #417

Complements

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

NH ≅ G/Ntype
2. #13131637C2semidirect
3. #13130481C2semidirect
4. #13130474C2semidirect
5. #13130462C2semidirect
6. #13130451C2semidirect
7. #13130450C2semidirect
8. #13130439C2semidirect
9. #13130427C2semidirect
10. #13130419C2semidirect
11. #13130400C2semidirect
12. #13130180C2semidirect
14. #13130059C2semidirect
192. #6105M16semidirect
275. #1057#137semidirect
505. C13#18047semidirect

Maximal subgroups

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

subgroupindex
#131316732
#131316372
#131304812
#131304742
#131304622
#131304512
#131304502
#131304392
#131304272
#131304192
#131304002
#131301802
#131301712
#131300592
#131236602
#1804713