Finite Group Databasebeta

← #15832536

Subgroups — #15832536

Order 3328.

662 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
1C8×#6131C211yesmaximal, characteristic
2D13×#446C211yesmaximal, characteristic, complemented
3C4×#88172C211yesmaximal, characteristic
4#13113707C211yesmaximal, characteristic, complemented
5#13113695C211yesmaximal, characteristic, complemented
6#13113691C211yesmaximal, characteristic, complemented
7#13113687C211yesmaximal, characteristic, complemented
8#13113683C211yesmaximal, characteristic, complemented
9#13113675C211yesmaximal, characteristic, complemented
10#13113671C211yesmaximal, characteristic, complemented
11#13113585C211yesmaximal, characteristic, complemented
12#13113229C211yesmaximal, characteristic, complemented
13#13113222C211yesmaximal, characteristic
14#13113124C211yesmaximal, characteristic, complemented
15C13×#1587C211yesmaximal, characteristic, complemented
16C2×#88172C411yescharacteristic
17C4×#6131C2211yescharacteristic
18C4×Q8×D13C2211yescharacteristic
19C13×#446C2211yescharacteristic
20C8×Q8×C13C2211yescharacteristic
21C4×C13×Q16C2211yescharacteristic
22#11718845C411yescharacteristic
23C4×#6107C2211yescharacteristic
24C4×#6106C2211yescharacteristic
25#11718685C2211yescharacteristic
26Q8×#1055C2211yescharacteristic
27#11718550C411yescharacteristic
28#11718542C411yescharacteristic
29#11718495—21no—
30#11718495C2211yescharacteristic
31#11718494—21no—
32#11718494C2211yescharacteristic
33D13×C4⋊C8—21no—
34D13×C4⋊C8C2211yescharacteristic
35#11718492C2211yescharacteristic
36#11718489—21no—
37#11718478C411yescharacteristic
38#11718464C411yescharacteristic
39#11718463C411yescharacteristic
40#11718450C411yescharacteristic
41D13×#97—21no—
42#11718362—21no—
43C4×#6095C2211yescharacteristic
44C4×#6094C2211yescharacteristic
45C8×D52—21no—
46C8×D52C2211yescharacteristic
47#11718346C2211yescharacteristic
48C4×C8×D13—21no—
49C4×C8×D13C2211yescharacteristic
50#11718340C2211yescharacteristic
51C13×#334C2211yescharacteristic
52C13×Q8⋊C8C2211yescharacteristic
53C13×Q8⋊C8C2211yescharacteristic
54C13×#322C2211yescharacteristic
55Q8⋊#1055C2211yescharacteristic
56Q8⋊#1055C2211yescharacteristic
57#11718076C2211yescharacteristic
58#11718075C2211yescharacteristic
59#11718072C2211yescharacteristic
60#11718071C2211yescharacteristic
61#11718051C2211yescharacteristic
62#11718050C2211yescharacteristic
63#11718048C2211yescharacteristic
64#11718046C2211yescharacteristic
65#11718046C2211yescharacteristic
66#11718046C2211yescharacteristic
67C2×#6131C2×C411yescharacteristic
68C2×Q8×D13C2×C411yescharacteristic
69C2×C13×Q16C2×C411yescharacteristic
70C4×Q8×C13C2311yescharacteristic
71C4×Q8×C13C2311yescharacteristic
72Q8×Dic13C2×C411yescharacteristic
73Q8×Dic13C2×C411yescharacteristic
74C2×#6107C2×C411yescharacteristic
75C2×#6106C2×C411yescharacteristic
76#88172—24no—
77C2×#6095C2×C411yescharacteristic
78C2×#6094C2×C411yescharacteristic
79C2×#6094C2×C411yescharacteristic
80C2×C8×D13—21no—
81C2×C8×D13—21no—
82C2×C8×D13—21no—
83C2×C8×D13D411yescharacteristic
84C2×C8×D13D411yescharacteristic
85#88147—21no—
86#88147C2×C411yescharacteristic
87#88146—21no—
88#88146C2×C411yescharacteristic
89C4⋊C4×D13—21no—
90C4⋊C4×D13C2×C411yescharacteristic
91#88141—21no—
92#88141C2×C411yescharacteristic
93C4×D52—21no—
94C4×D52C2311yescharacteristic
95C42×D13—21no—
96C42×D13—21no—
97C42×D13C2311yescharacteristic
98C4×Dic26—21no—
99C4×Dic26C2311yescharacteristic
100C13×#107C2×C411yescharacteristic
101C13×C4⋊C8—21no—
102C13×C4⋊C8—21no—
103C13×C4⋊C8C2311yescharacteristic
104C13×C4⋊C8C2311yescharacteristic
105C13×#103C2×C411yescharacteristic
106C13×#103C2×C411yescharacteristic
107C13×#97—21no—
108C4×C8×C13—21no—
109C4×C8×C13C2311yescharacteristic
110C4×C8×C13C2311yescharacteristic
111C4×C8×C13C2311yescharacteristic
112#88075C2×C411yescharacteristic
113#88075C2×C411yescharacteristic
114#88061C2×C411yescharacteristic
115#88060—21no—
116#88060—21no—
117#88060—21no—
118#88060—21no—
119#88057C2×C411yescharacteristic
120#88056C2×C411yescharacteristic
121#88055—21no—
122#88055—21no—
123#88055C2×C411yescharacteristic
124#88055C2×C411yescharacteristic
125#88054—21no—
126#88054—21no—
127#88054—21no—
128#88054—21no—
129C8×Dic13—21no—
130C8×Dic13D411yescharacteristic
131C8×Dic13D411yescharacteristic
132#88050C2×C411yescharacteristic
133#88049C2×C411yescharacteristic
134#88048C2×C411yescharacteristic
135#88047C2×C411yescharacteristic
136C4⋊#1055—21no—
137C4⋊#1055—21no—
138C4⋊#1055C2311yescharacteristic
139C4⋊#1055C2311yescharacteristic
140#88043—21no—
141C4×#1055—21no—
142C4×#1055C2311yescharacteristic
143C4×#1055C2311yescharacteristic
144C4×#1055C2311yescharacteristic
145#17872—131nomaximal, Sylow
146C2×Q8×C13C22×C411yescharacteristic
147C2×Q8×C13C22×C411yescharacteristic
148#6131—22no—
149#6131M1614yes—
150Q8×D13—22no—
151Q8×D13—22no—
152C2×D52—21no—
153C2×D52C22×C411yescharacteristic
154C2×C4×D13—21no—
155C2×C4×D13—21no—
156C2×C4×D13—21no—
157C2×C4×D13—21no—
158C2×C4×D13—21no—
159C2×C4×D13C22×C411yescharacteristic
160C2×C4×D13C2×D411yescharacteristic
161C2×C4×D13#4111yescharacteristic
162C2×Dic26—21no—
163C2×Dic26C22×C411yescharacteristic
164C13×Q16—22no—
165C2×C8×C13—21no—
166C2×C8×C13—21no—
167C2×C8×C13—21no—
168C2×C8×C13C22×C411yescharacteristic
169C2×C8×C13C22×C411yescharacteristic
170C2×C8×C13C2×D411yescharacteristic
171C2×C8×C13C2×D411yescharacteristic
172C13×C4⋊C4—21no—
173C13×C4⋊C4—21no—
174C13×C4⋊C4C22×C411yescharacteristic
175C13×C4⋊C4C22×C411yescharacteristic
176C42×C13—21no—
177C42×C13—21no—
178C42×C13C2411yescharacteristic
179#6107—22no—
180#6106—22no—
181#6103—21no—
182#6103—21no—
183#6103—21no—
184C4⋊Dic13—21no—
185C4⋊Dic13—21no—
186C4⋊Dic13C22×C411yescharacteristic
187C4⋊Dic13C22×C411yescharacteristic
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×Dic13C22×C411yescharacteristic
197C4×Dic13C2×D411yescharacteristic
198C4×Dic13#4111yescharacteristic
199C2×#1055—21no—
200C2×#1055—21no—
201C2×#1055—21no—
202C2×#1055C22×C411yescharacteristic
203C2×#1055C22×C411yescharacteristic
204C2×#1055C2×D411yescharacteristic
205C2×#1055C2×D411yescharacteristic
206#6095—22no—
207#6094—22no—
208#6094—22no—
209C8×D13—22no—
210C8×D13—41no—
211C8×D13—42no—
212C8×D13—42no—
213C8×D13—42no—
214C8×#41—131no—
215C2×#446—131no—
216C4×#137—131no—
217#1587—131no—
218#1587D1311yescharacteristic, complemented
219#1585—131no—
220#1585—131no—
221#1584—131no—
222#1584—131no—
223#1582—131no—
224#1582—131no—
225#1565—131no—
226#1479—131no—
227#1477—131no—
228#1451—131no—
229C22×D13—21no—
230C22×D13C4×D411yescharacteristic
231Q8×C13—21no—
232Q8×C13—21no—
233Q8×C13—21no—
234Q8×C13C2×M1612yes—
235C2×C4×C13—21no—
236C2×C4×C13—21no—
237C2×C4×C13—21no—
238C2×C4×C13—21no—
239C2×C4×C13C23×C411yescharacteristic
240C2×C4×C13C22×D411yescharacteristic
241C2×C4×C13C2×#4111yescharacteristic
242C2×Dic13—21no—
243C2×Dic13—21no—
244C2×Dic13—21no—
245C2×Dic13C4×D411yescharacteristic
246C2×Dic13C4×D411yescharacteristic
247C2×Dic13C4×D411yescharacteristic
248D52—24no—
249D52—21no—
250D52C2×M1612yes—
251C4×D13—21no—
252C4×D13—21no—
253C4×D13—24no—
254C4×D13—41no—
255C4×D13—42no—
256C4×D13—42no—
257C4×D13—42no—
258C4×D13—41no—
259C4×D13—41no—
260C4×D13C2×M1612yes—
261C4×D13#13112yes—
262Dic26—21no—
263Dic26—21no—
264Dic26—42no—
265C8×C13—21no—
266C8×C13—21no—
267C8×C13—21no—
268C8×C13—21no—
269C8×C13—41no—
270C8×C13—41no—
271C8×C13—41no—
272#1055—21no—
273#1055—21no—
274#1055—21no—
275#1055—41no—
276#1055—41no—
277#1055—41no—
278#1055#13712yescomplemented
279C2×#137—131no—
280C4×#41—131no—
281C2×C4×Q8—131no—
282#446—131no—
283#446—131no—
284#446—131no—
285#446—261no—
286#446—261no—
287#446C2×D1311yescharacteristic
288C8×Q8—131no—
289C8×Q8C2×D1311yescharacteristic
290#441—131no—
291#441—131no—
292#440—131no—
293#440—131no—
294C4×Q16—131no—
295C4×Q16C2×D1311yescharacteristic
296C4×SD16—131no—
297C4×SD16—131no—
298C8×D4—131no—
299C8×D4—131no—
300C8×D4—261no—
301C8×D4—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—
311C2×#97—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⋊C8C2×D1311yescharacteristic
323Q8⋊C8C2×D1311yescharacteristic
324D4⋊C8—131no—
325D4⋊C8—131no—
326#322—131no—
327#322—131no—
328#322—131no—
329#322C2×D1311yescharacteristic
330C22×C13C2×C4×D411yescharacteristic
331C2×D13—21no—
332C2×D13—21no—
333C2×D13—22no—
334C2×D13—41no—
335C2×D13—41no—
336C2×D13#43512yes—
337C4×C13—22no—
338C4×C13—21no—
339C4×C13—41no—
340C4×C13—41no—
341C4×C13—41no—
342C4×C13C22×M1611yescharacteristic
343C4×C13C2×#13111yescharacteristic
344C4×C13C2×#13711yescharacteristic
345C4×C13#57511yescharacteristic
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×Q16C4×D1311yescharacteristic
357C2×SD16—131no—
358C2×SD16—131no—
359C2×M16—131no—
360C2×M16—131no—
361C22×C8—131no—
362C22×C8—131no—
363C22×C8—261no—
364C22×C8—261no—
365C22×C8—261no—
366C4×Q8—131no—
367C4×Q8—131no—
368C4×Q8—131no—
369C4×Q8—131no—
370C4×Q8—261no—
371C4×Q8—261no—
372C4×Q8C22×D1311yescharacteristic
373C4×Q8C22×D1311yescharacteristic
374C4×D4—131no—
375C4×D4—131no—
376C4×D4—261no—
377C4×D4—261no—
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#107C4×D1311yescharacteristic
387#106—131no—
388#106—131no—
389C4⋊C8—21no—
390C4⋊C8—21no—
391C4⋊C8—131no—
392C4⋊C8—131no—
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#103C4×D1311yescharacteristic
406#103C4×D1311yescharacteristic
407#102—131no—
408#102—131no—
409C22⋊C8—261no—
410C22⋊C8—261no—
411C22⋊C8—261no—
412C22⋊C8—261no—
413#97—21no—
414#97—131no—
415#97—131no—
416#97—261no—
417#97—261no—
418#97—261no—
419C4×C8—21no—
420C4×C8—131no—
421C4×C8—131no—
422C4×C8—131no—
423C4×C8—131no—
424C4×C8—131no—
425C4×C8—261no—
426C4×C8—261no—
427C4×C8C22×D1311yescharacteristic
428C4×C8C22×D1311yescharacteristic
429C4×C8C22×D1311yescharacteristic
430C2×C13C2×#43511yescharacteristic
431C2×C13C4×#13711yescharacteristic
432C2×C13#295511yescharacteristic
433D13—22no—
434D13—42no—
435#41—134no—
436#41—262no—
437C2×Q8—131no—
438C2×Q8—261no—
439C2×Q8—262no—
440C2×Q8—262no—
441C2×Q8C2×C4×D1311yescharacteristic
442C2×Q8C2×C4×D1311yescharacteristic
443C2×D4—131no—
444C2×D4—261no—
445C22×C4—131no—
446C22×C4—131no—
447C22×C4—131no—
448C22×C4—261no—
449C22×C4—261no—
450C22×C4—261no—
451C22×C4—261no—
452C22×C4—261no—
453Q16—22no—
454Q16—262no—
455SD16—262no—
456SD16—262no—
457M16—262no—
458M16—262no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—131no—
463C2×C8—131no—
464C2×C8—131no—
465C2×C8—131no—
466C2×C8—262no—
467C2×C8—261no—
468C2×C8—261no—
469C2×C8—261no—
470C2×C8—521no—
471C2×C8—522no—
472C2×C8—522no—
473C2×C8—522no—
474C2×C8C2×C4×D1311yescharacteristic
475C2×C8C2×C4×D1311yescharacteristic
476C2×C8D4×D1311yescharacteristic
477C2×C8D4×D1311yescharacteristic
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—131no—
481C4⋊C4—131no—
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—261no—
490C22⋊C4—261no—
491C22⋊C4—261no—
492C42—21no—
493C42—21no—
494C42—131no—
495C42—131no—
496C42—131no—
497C42—261no—
498C42—261no—
499C42—261no—
500C42—261no—
501C42—261no—
502C42C23×D1311yescharacteristic
503C13#1787211yescharacteristic, complemented, Sylow
504C23—131no—
505C23—261no—
506Q8—21no—
507Q8—21no—
508Q8—21no—
509Q8—261no—
510Q8—261no—
511Q8—522no—
512Q8M16×D1312yes—
513D4—132no—
514D4—264no—
515D4—261no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—131no—
521C2×C4—132no—
522C2×C4—132no—
523C2×C4—131no—
524C2×C4—131no—
525C2×C4—264no—
526C2×C4—261no—
527C2×C4—261no—
528C2×C4—261no—
529C2×C4—261no—
530C2×C4—261no—
531C2×C4—521no—
532C2×C4—522no—
533C2×C4—522no—
534C2×C4—522no—
535C2×C4—521no—
536C2×C4—521no—
537C2×C4C22×C4×D1311yescharacteristic
538C2×C4C2×D4×D1311yescharacteristic
539C2×C4#41×D1311yescharacteristic
540C8—21no—
541C8—21no—
542C8—21no—
543C8—21no—
544C8—41no—
545C8—41no—
546C8—41no—
547C8—132no—
548C8—261no—
549C8—261no—
550C8—261no—
551C8—521no—
552C8—521no—
553C8—521no—
554C22—132no—
555C22—261no—
556C22—261no—
557C22—262no—
558C22—521no—
559C22—521no—
560C22C4×D4×D1311yescharacteristic
561C4—21no—
562C4—22no—
563C4—41no—
564C4—41no—
565C4—41no—
566C4—132no—
567C4—261no—
568C4—261no—
569C4—521no—
570C4—521no—
571C4—521no—
572C4C2×M16×D1311yescharacteristic
573C4D13×#13111yescharacteristic
574C4D13×#13711yescharacteristic
575C4#1171948211yescharacteristic
576C2—262no—
577C2—522no—
578C2D13×#43511yescharacteristic
579C2#1312365211yescharacteristic
580C2#1312373411yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC42C23×D13
FittingC13×#1587C2
socleC22×C13C2×C4×D4
prime radicalC2×#6131C2×C4
cosocleC42×C13C24
hypercenter#1587D13
hypocenterC13#17872
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1587

Complements

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

NH ≅ G/Ntype
2. D13×#446C2semidirect
4. #13113707C2semidirect
5. #13113695C2semidirect
6. #13113691C2semidirect
7. #13113687C2semidirect
8. #13113683C2semidirect
9. #13113675C2semidirect
10. #13113671C2semidirect
11. #13113585C2semidirect
12. #13113229C2semidirect
14. #13113124C2semidirect
15. C13×#1587C2semidirect
218. #1587D13semidirect
278. #1055#137semidirect
503. C13#17872semidirect

Maximal subgroups

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

subgroupindex
C8×#61312
D13×#4462
C4×#881722
#131137072
#131136952
#131136912
#131136872
#131136832
#131136752
#131136712
#131135852
#131132292
#131132222
#131131242
C13×#15872
#1787213