Finite Group Databasebeta

← #15832508

Subgroups — #15832508

Order 3328.

660 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13123799C211yesmaximal, characteristic
2C8×Q8×D13C211yesmaximal, characteristic, complemented
3C4×#88169C211yesmaximal, characteristic
4#13113717C211yesmaximal, characteristic, complemented
5#13113715C211yesmaximal, characteristic, complemented
6#13113706C211yesmaximal, characteristic, complemented
7#13113704C211yesmaximal, characteristic, complemented
8#13113688C211yesmaximal, characteristic, complemented
9#13113686C211yesmaximal, characteristic, complemented
10#13113677C211yesmaximal, characteristic, complemented
11#13113585C211yesmaximal, characteristic, complemented
12#13113229C211yesmaximal, characteristic, complemented
13#13113220C211yesmaximal, characteristic
14#13113122C211yesmaximal, characteristic, complemented
15C13×#1583C211yesmaximal, characteristic, complemented
16C2×#88169C411yescharacteristic
17C4×Q8×D13C2211yescharacteristic
18C4×#6129C2211yescharacteristic
19C8×Q8×C13C2211yescharacteristic
20C4×C13×SD16C2211yescharacteristic
21C13×#436C2211yescharacteristic
22#11718825C411yescharacteristic
23#11718788—21no—
24M16×Dic13—21no—
25C4×#6107C2211yescharacteristic
26Q8×#1055C2211yescharacteristic
27C4×#6105C2211yescharacteristic
28#11718673C2211yescharacteristic
29#11718522C411yescharacteristic
30#11718514C411yescharacteristic
31#11718494C2211yescharacteristic
32D13×C4⋊C8—21no—
33D13×C4⋊C8C2211yescharacteristic
34#11718492C2211yescharacteristic
35#11718491—21no—
36#11718491C2211yescharacteristic
37#11718463C411yescharacteristic
38#11718450C411yescharacteristic
39#11718432C411yescharacteristic
40#11718418C411yescharacteristic
41#11718389—21no—
42#11718379—21no—
43C4×Dic52C2211yescharacteristic
44C4×#6094C2211yescharacteristic
45#11718346C2211yescharacteristic
46C4×C8×D13—21no—
47C4×C8×D13C2211yescharacteristic
48#11718340C2211yescharacteristic
49C8×Dic26—21no—
50C8×Dic26C2211yescharacteristic
51C13×#334C2211yescharacteristic
52C13×Q8⋊C8C2211yescharacteristic
53C13×D4⋊C8C2211yescharacteristic
54C13×#322C2211yescharacteristic
55Q8⋊#1055C2211yescharacteristic
56D4⋊#1055C2211yescharacteristic
57#11718076C2211yescharacteristic
58#11718076C2211yescharacteristic
59#11718072C2211yescharacteristic
60#11718071C2211yescharacteristic
61#11718050C2211yescharacteristic
62#11718048C2211yescharacteristic
63#11718048C2211yescharacteristic
64#11718047C2211yescharacteristic
65#11718047C2211yescharacteristic
66#11718046C2211yescharacteristic
67C2×Q8×D13C2×C411yescharacteristic
68C2×#6129C2×C411yescharacteristic
69C2×C13×SD16C2×C411yescharacteristic
70C2×C13×M16—21no—
71C4×Q8×C13C2311yescharacteristic
72C4×D4×C13C2311yescharacteristic
73Q8×Dic13C2×C411yescharacteristic
74C2×#6107C2×C411yescharacteristic
75D4×Dic13C2×C411yescharacteristic
76C2×#6105C2×C411yescharacteristic
77C4×C22⋊D13—21no—
78C2×C4×Dic13—21no—
79C2×#6099—21no—
80#88169—24no—
81C2×Dic52C2×C411yescharacteristic
82C2×#6094C2×C411yescharacteristic
83C2×#6094C2×C411yescharacteristic
84C2×C8×D13—21no—
85C2×C8×D13D411yescharacteristic
86C2×C8×D13D411yescharacteristic
87#88146C2×C411yescharacteristic
88C4⋊C4×D13—21no—
89C4⋊C4×D13C2×C411yescharacteristic
90#88141—21no—
91#88141C2×C411yescharacteristic
92#88141C2×C411yescharacteristic
93#88135—21no—
94#88131—21no—
95C42×D13—21no—
96C42×D13C2311yescharacteristic
97C4×Dic26—21no—
98C4×Dic26C2311yescharacteristic
99C4×Dic26C2311yescharacteristic
100C13×#106C2×C411yescharacteristic
101C13×C4⋊C8—21no—
102C13×C4⋊C8C2311yescharacteristic
103C13×C4⋊C8C2311yescharacteristic
104C13×#103C2×C411yescharacteristic
105C13×#102C2×C411yescharacteristic
106C13×C22⋊C8—21no—
107C4×C8×C13—21no—
108C4×C8×C13C2311yescharacteristic
109C4×C8×C13C2311yescharacteristic
110C4×C8×C13C2311yescharacteristic
111#88075C2×C411yescharacteristic
112#88072C2×C411yescharacteristic
113C22⋊#1055—21no—
114#88060—21no—
115#88060—21no—
116#88058C2×C411yescharacteristic
117#88056C2×C411yescharacteristic
118#88056C2×C411yescharacteristic
119#88055—21no—
120#88055—21no—
121#88055C2×C411yescharacteristic
122#88055C2×C411yescharacteristic
123#88054—21no—
124#88054—21no—
125#88054—21no—
126#88054—21no—
127#88054—21no—
128#88054—21no—
129C8×Dic13—21no—
130C8×Dic13—21no—
131C8×Dic13—21no—
132C8×Dic13D411yescharacteristic
133C8×Dic13D411yescharacteristic
134#88050C2×C411yescharacteristic
135#88050C2×C411yescharacteristic
136#88048C2×C411yescharacteristic
137#88047C2×C411yescharacteristic
138C4⋊#1055—21no—
139C4⋊#1055C2311yescharacteristic
140C4⋊#1055C2311yescharacteristic
141C4×#1055—21no—
142C4×#1055C2311yescharacteristic
143C4×#1055C2311yescharacteristic
144C4×#1055C2311yescharacteristic
145#17870—131nomaximal, Sylow
146C2×Q8×C13C22×C411yescharacteristic
147C2×D4×C13C22×C411yescharacteristic
148C22×C4×C13—21no—
149C2×C22⋊D13—21no—
150C22×Dic13—21no—
151C22×Dic13—21no—
152Q8×D13—22no—
153Q8×D13M1614yescomplemented
154#6129—22no—
155#6129—22no—
156C2×C4×D13—21no—
157C2×C4×D13—21no—
158C2×C4×D13C22×C411yescharacteristic
159C2×C4×D13C2×D411yescharacteristic
160C2×C4×D13#4111yescharacteristic
161C2×Dic26—21no—
162C2×Dic26C22×C411yescharacteristic
163C2×Dic26C22×C411yescharacteristic
164C13×SD16—22no—
165C13×M16—42no—
166C2×C8×C13—21no—
167C2×C8×C13—21no—
168C2×C8×C13—21no—
169C2×C8×C13C22×C411yescharacteristic
170C2×C8×C13C22×C411yescharacteristic
171C2×C8×C13C2×D411yescharacteristic
172C2×C8×C13C2×D411yescharacteristic
173C13×C4⋊C4—21no—
174C13×C4⋊C4C22×C411yescharacteristic
175C13×C4⋊C4C22×C411yescharacteristic
176C13×C22⋊C4—21no—
177C42×C13—21no—
178C42×C13C2411yescharacteristic
179C22⋊Dic13—21no—
180#6107—22no—
181#6105—22no—
182#6103—21no—
183C4⋊Dic13—21no—
184C4⋊Dic13C22×C411yescharacteristic
185C4⋊Dic13C22×C411yescharacteristic
186#6101—21no—
187#6101—21no—
188#6101—21no—
189#6101—21no—
190#6101—21no—
191C4×Dic13—21no—
192C4×Dic13—21no—
193C4×Dic13—21no—
194C4×Dic13—21no—
195C4×Dic13—21no—
196C4×Dic13—21no—
197C4×Dic13C22×C411yescharacteristic
198C4×Dic13C2×D411yescharacteristic
199C4×Dic13#4111yescharacteristic
200#6099—42no—
201C2×#1055—21no—
202C2×#1055—21no—
203C2×#1055—21no—
204C2×#1055C22×C411yescharacteristic
205C2×#1055C22×C411yescharacteristic
206C2×#1055C2×D411yescharacteristic
207C2×#1055C2×D411yescharacteristic
208Dic52—22no—
209#6094—22no—
210#6094—22no—
211C8×D13—22no—
212C8×D13—41no—
213C8×D13—42no—
214#2965—131no—
215C2×C8×Q8—131no—
216C4×#137—131no—
217#1588—131no—
218#1588—131no—
219#1587—131no—
220#1587—131no—
221#1584—131no—
222#1584—131no—
223#1583—131no—
224#1583D1311yescharacteristic, complemented
225#1565—131no—
226#1479—131no—
227#1477—131no—
228#1451—131no—
229C23×C13—21no—
230C22×D13C4×D411yescharacteristic
231Q8×C13—21no—
232Q8×C13C2×M1612yes—
233D4×C13—21no—
234D4×C13—21no—
235C2×C4×C13—21no—
236C2×C4×C13—21no—
237C2×C4×C13—21no—
238C2×C4×C13—41no—
239C2×C4×C13—41no—
240C2×C4×C13C23×C411yescharacteristic
241C2×C4×C13C22×D411yescharacteristic
242C2×C4×C13C2×#4111yescharacteristic
243C22⋊D13—42no—
244C2×Dic13—21no—
245C2×Dic13—21no—
246C2×Dic13—21no—
247C2×Dic13—21no—
248C2×Dic13—42no—
249C2×Dic13—42no—
250C2×Dic13C4×D411yescharacteristic
251C2×Dic13C4×D411yescharacteristic
252C2×Dic13C4×D411yescharacteristic
253C4×D13—24no—
254C4×D13—21no—
255C4×D13—21no—
256C4×D13—41no—
257C4×D13—42no—
258C4×D13C2×M1612yes—
259C4×D13#13112yes—
260Dic26—21no—
261Dic26—24no—
262Dic26—21no—
263Dic26—21no—
264Dic26C2×M1612yes—
265C8×C13—21no—
266C8×C13—21no—
267C8×C13—21no—
268C8×C13—41no—
269C8×C13—41no—
270C8×C13—41no—
271C8×C13#13712yescomplemented
272#1055—21no—
273#1055—21no—
274#1055—21no—
275#1055—21no—
276#1055—41no—
277#1055—41no—
278#1055—41no—
279C2×#137—131no—
280C4×#41—131no—
281C2×C4×Q8—131no—
282#446—131no—
283#446—131no—
284C8×Q8—131no—
285C8×Q8—131no—
286C8×Q8—131no—
287C8×Q8—261no—
288C8×Q8—261no—
289C8×Q8C2×D1311yescharacteristic
290#441—131no—
291#441—131no—
292#440—131no—
293#440—131no—
294C4×Q16—131no—
295C4×Q16—131no—
296C4×SD16—131no—
297C4×SD16C2×D1311yescharacteristic
298#436—131no—
299#436C2×D1311yescharacteristic
300#435—261no—
301#435—261no—
302#431—131no—
303#431—131no—
304#431—261no—
305#428—131no—
306C2×C4⋊C8—131no—
307C2×C4⋊C8—261no—
308#419—131no—
309#417—131no—
310C4×M16—131no—
311C4×M16—261no—
312C2×C4×C8—131no—
313C2×C4×C8—261no—
314#335—131no—
315#335—131no—
316#334—131no—
317#334C2×D1311yescharacteristic
318Q8⋊C8—131no—
319Q8⋊C8—131no—
320Q8⋊C8—131no—
321Q8⋊C8—131no—
322Q8⋊C8—131no—
323Q8⋊C8C2×D1311yescharacteristic
324D4⋊C8—131no—
325D4⋊C8C2×D1311yescharacteristic
326#322—131no—
327#322—131no—
328#322—131no—
329#322C2×D1311yescharacteristic
330C22×C13—41no—
331C22×C13—41no—
332C22×C13—41no—
333C22×C13C2×C4×D411yescharacteristic
334C2×D13—21no—
335C2×D13—21no—
336C2×D13#43512yes—
337C4×C13—22no—
338C4×C13—21no—
339C4×C13—41no—
340C4×C13—41no—
341C4×C13C22×M1611yescharacteristic
342C4×C13C2×#13111yescharacteristic
343C4×C13C2×#13711yescharacteristic
344C4×C13#57511yescharacteristic
345Dic13—22no—
346Dic13—21no—
347Dic13—21no—
348Dic13—41no—
349Dic13—41no—
350Dic13—41no—
351Dic13#43512yes—
352C2×#41—131no—
353C22×Q8—131no—
354#137—264no—
355C2×Q16—131no—
356C2×Q16—131no—
357C2×SD16—131no—
358C2×SD16C4×D1311yescharacteristic
359C2×M16—21no—
360C2×M16—131no—
361C2×M16—131no—
362C2×M16—261no—
363C22×C8—131no—
364C22×C8—131no—
365C22×C8—261no—
366C4×Q8—131no—
367C4×Q8—131no—
368C4×Q8—131no—
369C4×Q8—131no—
370C4×Q8—131no—
371C4×Q8—261no—
372C4×Q8—261no—
373C4×Q8C22×D1311yescharacteristic
374C4×D4—131no—
375C4×D4—261no—
376C4×D4—261no—
377C4×D4C22×D1311yescharacteristic
378#117—131no—
379#117—261no—
380C2×C4⋊C4—131no—
381C2×C4⋊C4—261no—
382C2×C42—131no—
383C2×C42—261no—
384C2×C42—261no—
385#107—131no—
386#107—131no—
387#106—131no—
388#106C4×D1311yescharacteristic
389C4⋊C8—21no—
390C4⋊C8—131no—
391C4⋊C8—131no—
392C4⋊C8—261no—
393C4⋊C8—261no—
394C4⋊C8—261no—
395C4⋊C8—261no—
396C4⋊C8—261no—
397C4⋊C8—261no—
398C4⋊C8—261no—
399C4⋊C8C22×D1311yescharacteristic
400C4⋊C8C22×D1311yescharacteristic
401#103—131no—
402#103—131no—
403#103—131no—
404#103—131no—
405#103—131no—
406#103C4×D1311yescharacteristic
407#102—131no—
408#102C4×D1311yescharacteristic
409C22⋊C8—21no—
410C22⋊C8—261no—
411C22⋊C8—261no—
412C22⋊C8—261no—
413#97—131no—
414#97—131no—
415#97—261no—
416#97—261no—
417C4×C8—21no—
418C4×C8—131no—
419C4×C8—131no—
420C4×C8—131no—
421C4×C8—131no—
422C4×C8—131no—
423C4×C8—261no—
424C4×C8—261no—
425C4×C8—261no—
426C4×C8—261no—
427C4×C8C22×D1311yescharacteristic
428C4×C8C22×D1311yescharacteristic
429C4×C8C22×D1311yescharacteristic
430C2×C13—81no—
431C2×C13C2×#43511yescharacteristic
432C2×C13C4×#13711yescharacteristic
433C2×C13#295511yescharacteristic
434D13—22no—
435#41—262no—
436#41—262no—
437C2×Q8—134no—
438C2×Q8—131no—
439C2×Q8—131no—
440C2×Q8—261no—
441C2×Q8—262no—
442C2×Q8C2×C4×D1311yescharacteristic
443C2×D4—261no—
444C2×D4C2×C4×D1311yescharacteristic
445C22×C4—21no—
446C22×C4—131no—
447C22×C4—131no—
448C22×C4—131no—
449C22×C4—261no—
450C22×C4—261no—
451C22×C4—261no—
452C22×C4—261no—
453Q16—262no—
454Q16—262no—
455SD16—22no—
456SD16—262no—
457M16—42no—
458M16—262no—
459M16—262no—
460M16—522no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—21no—
464C2×C8—131no—
465C2×C8—131no—
466C2×C8—131no—
467C2×C8—131no—
468C2×C8—262no—
469C2×C8—261no—
470C2×C8—261no—
471C2×C8—261no—
472C2×C8—521no—
473C2×C8—522no—
474C2×C8C2×C4×D1311yescharacteristic
475C2×C8C2×C4×D1311yescharacteristic
476C2×C8D4×D1311yescharacteristic
477C2×C8D4×D1311yescharacteristic
478C4⋊C4—21no—
479C4⋊C4—131no—
480C4⋊C4—131no—
481C4⋊C4—261no—
482C4⋊C4—261no—
483C4⋊C4—261no—
484C4⋊C4—261no—
485C4⋊C4—261no—
486C4⋊C4—261no—
487C4⋊C4C2×C4×D1311yescharacteristic
488C4⋊C4C2×C4×D1311yescharacteristic
489C22⋊C4—21no—
490C22⋊C4—261no—
491C22⋊C4—261no—
492C42—21no—
493C42—131no—
494C42—131no—
495C42—131no—
496C42—261no—
497C42—261no—
498C42—261no—
499C42—261no—
500C42—261no—
501C42—261no—
502C42C23×D1311yescharacteristic
503C13#1787011yescharacteristic, complemented, Sylow
504C23—21no—
505C23—131no—
506Q8—21no—
507Q8—132no—
508Q8—264no—
509Q8—261no—
510Q8—261no—
511Q8—261no—
512Q8M16×D1312yes—
513D4—21no—
514D4—21no—
515D4—522no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—131no—
522C2×C4—132no—
523C2×C4—132no—
524C2×C4—131no—
525C2×C4—131no—
526C2×C4—264no—
527C2×C4—261no—
528C2×C4—261no—
529C2×C4—261no—
530C2×C4—261no—
531C2×C4—261no—
532C2×C4—261no—
533C2×C4—521no—
534C2×C4—522no—
535C2×C4—522no—
536C2×C4—522no—
537C2×C4C22×C4×D1311yescharacteristic
538C2×C4C2×D4×D1311yescharacteristic
539C2×C4#41×D1311yescharacteristic
540C8—21no—
541C8—21no—
542C8—21no—
543C8—41no—
544C8—41no—
545C8—41no—
546C8—261no—
547C8—261no—
548C8—261no—
549C8—261no—
550C8—521no—
551C8—521no—
552C8—521no—
553C8#8816912yescomplemented
554C22—41no—
555C22—41no—
556C22—41no—
557C22—132no—
558C22—261no—
559C22—261no—
560C22C4×D4×D1311yescharacteristic
561C4—21no—
562C4—22no—
563C4—41no—
564C4—41no—
565C4—132no—
566C4—261no—
567C4—261no—
568C4—262no—
569C4—521no—
570C4—521no—
571C4—521no—
572C4C2×M16×D1311yescharacteristic
573C4D13×#13111yescharacteristic
574C4C2×#8816911yescharacteristic
575C4#1171947311yescharacteristic
576C2—81no—
577C2—262no—
578C2D13×#43511yescharacteristic
579C2C4×#8816911yescharacteristic
580C2#1312373611yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC42C23×D13
FittingC13×#1583C2
socleC22×C13C2×C4×D4
prime radicalC2×#6129C2×C4
cosocleC42×C13C24
hypercenter#1583D13
hypocenterC13#17870
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1583

Complements

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

NH ≅ G/Ntype
2. C8×Q8×D13C2semidirect
4. #13113717C2semidirect
5. #13113715C2semidirect
6. #13113706C2semidirect
7. #13113704C2semidirect
8. #13113688C2semidirect
9. #13113686C2semidirect
10. #13113677C2semidirect
11. #13113585C2semidirect
12. #13113229C2semidirect
14. #13113122C2semidirect
15. C13×#1583C2semidirect
153. Q8×D13M16semidirect
224. #1583D13semidirect
271. C8×C13#137semidirect
503. C13#17870semidirect
553. C8#88169semidirect

Maximal subgroups

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

subgroupindex
#131237992
C8×Q8×D132
C4×#881692
#131137172
#131137152
#131137062
#131137042
#131136882
#131136862
#131136772
#131135852
#131132292
#131132202
#131131222
C13×#15832
#1787013