Finite Group Databasebeta

← #15832574

Subgroups — #15832574

Order 3328.

650 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13123943C211yesmaximal, characteristic
2#13123918C211yesmaximal, characteristic, complemented
3C4×#88169C211yesmaximal, characteristic
4#13113706C211yesmaximal, characteristic, complemented
5#13113705C211yesmaximal, characteristic, complemented
6#13113694C211yesmaximal, characteristic, complemented
7#13113693C211yesmaximal, characteristic, complemented
8#13113689C211yesmaximal, characteristic, complemented
9#13113688C211yesmaximal, characteristic, complemented
10#13113669C211yesmaximal, characteristic, complemented
11#13113585C211yesmaximal, characteristic, complemented
12#13113215C211yesmaximal, characteristic
13D13×Q8⋊C8C211yesmaximal, characteristic, complemented
14#13113124C211yesmaximal, characteristic, complemented
15C13×#1582C211yesmaximal, characteristic, complemented
16C2×#88169C411yescharacteristic
17C4×Q8×D13C2211yescharacteristic
18C4×#6129C2211yescharacteristic
19C13×#446C2211yescharacteristic
20C4×C13×SD16C2211yescharacteristic
21C8×D4×C13C2211yescharacteristic
22#11718825C411yescharacteristic
23C8×C22⋊D13—21no—
24C2×#88054—21no—
25C4×#6107C2211yescharacteristic
26#11718685C2211yescharacteristic
27C4×#6105C2211yescharacteristic
28D4×#1055C2211yescharacteristic
29#11718522C411yescharacteristic
30#11718514C411yescharacteristic
31#11718496—21no—
32#11718494C2211yescharacteristic
33D13×C4⋊C8C2211yescharacteristic
34#11718492C2211yescharacteristic
35#11718491C2211yescharacteristic
36#11718489—21no—
37#11718463C411yescharacteristic
38#11718450C411yescharacteristic
39#11718432C411yescharacteristic
40#11718418C411yescharacteristic
41#11718386—21no—
42#11718379—21no—
43#11718366—21no—
44#11718362—21no—
45C4×Dic52C2211yescharacteristic
46C4×#6094C2211yescharacteristic
47#11718346C2211yescharacteristic
48C4×C8×D13C2211yescharacteristic
49#11718340C2211yescharacteristic
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#11718046C2211yescharacteristic
65#11718046C2211yescharacteristic
66#11718046C2211yescharacteristic
67C2×Q8×D13C2×C411yescharacteristic
68C2×#6129C2×C411yescharacteristic
69C2×C13×SD16C2×C411yescharacteristic
70C22×C8×C13—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—
79C22×#1055—21no—
80#88169—24no—
81C2×Dic52C2×C411yescharacteristic
82C2×#6094C2×C411yescharacteristic
83C2×#6094C2×C411yescharacteristic
84C2×C8×D13—21no—
85C2×C8×D13—21no—
86#88146C2×C411yescharacteristic
87C4⋊C4×D13—21no—
88C4⋊C4×D13C2×C411yescharacteristic
89#88141—21no—
90#88141C2×C411yescharacteristic
91#88141C2×C411yescharacteristic
92#88135—21no—
93#88131—21no—
94C42×D13—21no—
95C42×D13C2311yescharacteristic
96C4×Dic26—21no—
97C4×Dic26C2311yescharacteristic
98C4×Dic26C2311yescharacteristic
99C13×#106C2×C411yescharacteristic
100C13×C4⋊C8—21no—
101C13×C4⋊C8C2311yescharacteristic
102C13×C4⋊C8C2311yescharacteristic
103C13×#103C2×C411yescharacteristic
104C13×#102C2×C411yescharacteristic
105C13×C22⋊C8—21no—
106C13×#97—21no—
107C4×C8×C13C2311yescharacteristic
108C4×C8×C13C2311yescharacteristic
109C4×C8×C13C2311yescharacteristic
110#88075C2×C411yescharacteristic
111#88072C2×C411yescharacteristic
112C22⋊#1055—21no—
113#88060—21no—
114#88060D411yescharacteristic
115#88060D411yescharacteristic
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#88054D411yescharacteristic
129#88054D411yescharacteristic
130C8×Dic13—21no—
131C8×Dic13—21no—
132C8×Dic13—21no—
133C8×Dic13—21no—
134#88050C2×C411yescharacteristic
135#88050C2×C411yescharacteristic
136#88048C2×C411yescharacteristic
137#88047C2×C411yescharacteristic
138C4⋊#1055—21no—
139C4⋊#1055C2311yescharacteristic
140C4⋊#1055C2311yescharacteristic
141#88043—21no—
142C4×#1055C2311yescharacteristic
143C4×#1055C2311yescharacteristic
144C4×#1055C2311yescharacteristic
145#17876—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×D13—22no—
154#6129—22no—
155#6129M1614yes—
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—
165C2×C8×C13—21no—
166C2×C8×C13—21no—
167C2×C8×C13—21no—
168C2×C8×C13—81no—
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
200C2×#1055—21no—
201C2×#1055—21no—
202C2×#1055—21no—
203C2×#1055—81no—
204C2×#1055C22×C411yescharacteristic
205C2×#1055C22×C411yescharacteristic
206C2×#1055C2×D411yescharacteristic
207C2×#1055C2×D411yescharacteristic
208Dic52—22no—
209#6094—22no—
210#6094—22no—
211C8×D13—42no—
212C8×D13—81no—
213#2988—131no—
214#2983—131no—
215C4×#137—131no—
216#1587—131no—
217#1587—131no—
218#1585—131no—
219#1585—131no—
220#1584—131no—
221#1584—131no—
222#1582—131no—
223#1582D1311yescharacteristic, complemented
224#1565—131no—
225#1476—131no—
226C2×Q8⋊C8—131no—
227#1451—131no—
228C23×C13—21no—
229C22×D13C4×D411yescharacteristic
230Q8×C13—21no—
231Q8×C13—21no—
232D4×C13—21no—
233D4×C13C2×M1612yes—
234C2×C4×C13—21no—
235C2×C4×C13—21no—
236C2×C4×C13—21no—
237C2×C4×C13—41no—
238C2×C4×C13—41no—
239C2×C4×C13C23×C411yescharacteristic
240C2×C4×C13C22×D411yescharacteristic
241C2×C4×C13C2×#4111yescharacteristic
242C22⋊D13—24no—
243C2×Dic13—21no—
244C2×Dic13—24no—
245C2×Dic13—21no—
246C2×Dic13—21no—
247C2×Dic13—21no—
248C2×Dic13—81no—
249C2×Dic13C4×D411yescharacteristic
250C2×Dic13C4×D411yescharacteristic
251C2×Dic13C4×D411yescharacteristic
252C4×D13—21no—
253C4×D13—21no—
254C4×D13—41no—
255C4×D13—42no—
256C4×D13—81no—
257C4×D13C2×M1612yes—
258C4×D13#13112yes—
259Dic26—21no—
260Dic26—21no—
261Dic26—21no—
262Dic26—42no—
263Dic26C2×M1612yes—
264C8×C13—21no—
265C8×C13—21no—
266C8×C13—21no—
267C8×C13—21no—
268C8×C13—41no—
269C8×C13—41no—
270C8×C13—41no—
271#1055—22no—
272#1055—21no—
273#1055—21no—
274#1055—21no—
275#1055—21no—
276#1055—41no—
277#1055—41no—
278C2×#137—131no—
279C4×#41—131no—
280C2×C4×Q8—131no—
281#446—131no—
282#446—131no—
283#446—131no—
284#446—261no—
285#446—261no—
286#446C2×D1311yescharacteristic
287C8×Q8—131no—
288C8×Q8—131no—
289#441—131no—
290#441—131no—
291#440—131no—
292#440—131no—
293C4×Q16—131no—
294C4×Q16—131no—
295C4×SD16—131no—
296C4×SD16C2×D1311yescharacteristic
297C8×D4—131no—
298C8×D4—261no—
299C8×D4—261no—
300C8×D4C2×D1311yescharacteristic
301#432—261no—
302#432—261no—
303#431—131no—
304#431—131no—
305#431—261no—
306#428—131no—
307C2×C4⋊C8—131no—
308C2×C4⋊C8—261no—
309#419—131no—
310#417—131no—
311C4×M16—131no—
312C2×C4×C8—131no—
313#335—131no—
314#335—131no—
315#334—131no—
316#334C2×D1311yescharacteristic
317Q8⋊C8—131no—
318Q8⋊C8—131no—
319Q8⋊C8—131no—
320Q8⋊C8—131no—
321Q8⋊C8—131no—
322Q8⋊C8C2×D1311yescharacteristic
323D4⋊C8—131no—
324D4⋊C8C2×D1311yescharacteristic
325#322—131no—
326#322—131no—
327#322—131no—
328#322C2×D1311yescharacteristic
329C22×C13—22no—
330C22×C13—41no—
331C22×C13—41no—
332C22×C13C2×C4×D411yescharacteristic
333C2×D13—21no—
334C2×D13—21no—
335C2×D13#43512yes—
336C4×C13—21no—
337C4×C13—41no—
338C4×C13—41no—
339C4×C13—41no—
340C4×C13C22×M1611yescharacteristic
341C4×C13C2×#13111yescharacteristic
342C4×C13#57711yescharacteristic
343C4×C13#57811yescharacteristic
344Dic13—22no—
345Dic13—21no—
346Dic13—21no—
347Dic13—41no—
348Dic13—41no—
349Dic13—41no—
350Dic13#43512yes—
351C2×#41—131no—
352C22×Q8—131no—
353#137—264no—
354C2×Q16—131no—
355C2×Q16—131no—
356C2×SD16—131no—
357C2×SD16C4×D1311yescharacteristic
358C2×M16—131no—
359C2×M16—131no—
360C22×C8—21no—
361C22×C8—261no—
362C22×C8—261no—
363C22×C8—261no—
364C4×Q8—131no—
365C4×Q8—131no—
366C4×Q8—131no—
367C4×Q8—131no—
368C4×Q8—131no—
369C4×Q8—261no—
370C4×Q8—261no—
371C4×Q8C22×D1311yescharacteristic
372C4×D4—131no—
373C4×D4—261no—
374C4×D4—261no—
375C4×D4C22×D1311yescharacteristic
376#117—131no—
377#117—261no—
378C2×C4⋊C4—131no—
379C2×C4⋊C4—261no—
380C2×C42—131no—
381C2×C42—261no—
382C2×C42—261no—
383#107—131no—
384#107—131no—
385#106—131no—
386#106C4×D1311yescharacteristic
387C4⋊C8—21no—
388C4⋊C8—131no—
389C4⋊C8—131no—
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⋊C8C22×D1311yescharacteristic
399C4⋊C8C22×D1311yescharacteristic
400#103—131no—
401#103—131no—
402#103—131no—
403#103—131no—
404#103—131no—
405#103C4×D1311yescharacteristic
406#102—131no—
407#102C4×D1311yescharacteristic
408C22⋊C8—21no—
409C22⋊C8—131no—
410C22⋊C8—131no—
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—131no—
420C4×C8—131no—
421C4×C8—131no—
422C4×C8—261no—
423C4×C8—261no—
424C4×C8—261no—
425C4×C8—261no—
426C4×C8C22×D1311yescharacteristic
427C4×C8C22×D1311yescharacteristic
428C4×C8C22×D1311yescharacteristic
429C2×C13—42no—
430C2×C13C2×#43511yescharacteristic
431C2×C13#294711yescharacteristic
432C2×C13#295611yescharacteristic
433D13—22no—
434#41—134no—
435#41—262no—
436C2×Q8—131no—
437C2×Q8—131no—
438C2×Q8—261no—
439C2×Q8—262no—
440C2×Q8—262no—
441C2×Q8C2×C4×D1311yescharacteristic
442C2×D4—261no—
443C2×D4C2×C4×D1311yescharacteristic
444C22×C4—21no—
445C22×C4—131no—
446C22×C4—131no—
447C22×C4—131no—
448C22×C4—261no—
449C22×C4—261no—
450C22×C4—261no—
451C22×C4—261no—
452Q16—262no—
453Q16—262no—
454SD16—22no—
455SD16—262no—
456M16—262no—
457M16—262no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—81no—
462C2×C8—131no—
463C2×C8—131no—
464C2×C8—131no—
465C2×C8—131no—
466C2×C8—261no—
467C2×C8—261no—
468C2×C8—261no—
469C2×C8—522no—
470C2×C8—1041no—
471C2×C8—1041no—
472C2×C8C2×C4×D1311yescharacteristic
473C2×C8C2×C4×D1311yescharacteristic
474C2×C8D4×D1311yescharacteristic
475C2×C8D4×D1311yescharacteristic
476C4⋊C4—21no—
477C4⋊C4—131no—
478C4⋊C4—131no—
479C4⋊C4—261no—
480C4⋊C4—261no—
481C4⋊C4—261no—
482C4⋊C4—261no—
483C4⋊C4—261no—
484C4⋊C4—261no—
485C4⋊C4C2×C4×D1311yescharacteristic
486C4⋊C4C2×C4×D1311yescharacteristic
487C22⋊C4—21no—
488C22⋊C4—261no—
489C22⋊C4—261no—
490C42—21no—
491C42—131no—
492C42—131no—
493C42—131no—
494C42—261no—
495C42—261no—
496C42—261no—
497C42—261no—
498C42—261no—
499C42—261no—
500C42C23×D1311yescharacteristic
501C13#1787611yescharacteristic, complemented, Sylow
502C23—21no—
503C23—131no—
504Q8—21no—
505Q8—21no—
506Q8—132no—
507Q8—261no—
508Q8—261no—
509Q8—261no—
510Q8—522no—
511D4—21no—
512D4—264no—
513D4M16×D1312yes—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—131no—
520C2×C4—132no—
521C2×C4—132no—
522C2×C4—131no—
523C2×C4—131no—
524C2×C4—264no—
525C2×C4—261no—
526C2×C4—261no—
527C2×C4—261no—
528C2×C4—261no—
529C2×C4—261no—
530C2×C4—261no—
531C2×C4—521no—
532C2×C4—522no—
533C2×C4—1041no—
534C2×C4—1041no—
535C2×C4C22×C4×D1311yescharacteristic
536C2×C4C2×D4×D1311yescharacteristic
537C2×C4#41×D1311yescharacteristic
538C8—21no—
539C8—21no—
540C8—21no—
541C8—21no—
542C8—41no—
543C8—41no—
544C8—41no—
545C8—262no—
546C8—261no—
547C8—261no—
548C8—261no—
549C8—261no—
550C8—521no—
551C8—521no—
552C22—22no—
553C22—41no—
554C22—41no—
555C22—132no—
556C22—261no—
557C22—261no—
558C22C4×D4×D1311yescharacteristic
559C4—21no—
560C4—41no—
561C4—41no—
562C4—41no—
563C4—132no—
564C4—261no—
565C4—261no—
566C4—262no—
567C4—521no—
568C4—521no—
569C4—521no—
570C4C2×M16×D1311yescharacteristic
571C4D13×#13111yescharacteristic
572C4#1171946711yescharacteristic
573C4#1171947611yescharacteristic
574C2—42no—
575C2—262no—
576C2D13×#43511yescharacteristic
577C2#1312367211yescharacteristic
578C2#1312374411yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC42C23×D13
FittingC13×#1582C2
socleC22×C13C2×C4×D4
prime radicalC2×#6129C2×C4
cosocleC42×C13C24
hypercenter#1582D13
hypocenterC13#17876
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1582

Complements

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

NH ≅ G/Ntype
2. #13123918C2semidirect
4. #13113706C2semidirect
5. #13113705C2semidirect
6. #13113694C2semidirect
7. #13113693C2semidirect
8. #13113689C2semidirect
9. #13113688C2semidirect
10. #13113669C2semidirect
11. #13113585C2semidirect
13. D13×Q8⋊C8C2semidirect
14. #13113124C2semidirect
15. C13×#1582C2semidirect
223. #1582D13semidirect
501. C13#17876semidirect

Maximal subgroups

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

subgroupindex
#131239432
#131239182
C4×#881692
#131137062
#131137052
#131136942
#131136932
#131136892
#131136882
#131136692
#131135852
#131132152
D13×Q8⋊C82
#131131242
C13×#15822
#1787613