Finite Group Databasebeta

← #15833060

Subgroups — #15833060

Order 3328.

638 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13124842C211yesmaximal, characteristic
2#13123932C211yesmaximal, characteristic, complemented
3#13123857C211yesmaximal, characteristic
4#13113693C211yesmaximal, characteristic, complemented
5#13113691C211yesmaximal, characteristic, complemented
6#13113674C211yesmaximal, characteristic, complemented
7#13113651C211yesmaximal, characteristic, complemented
8#13113645C211yesmaximal, characteristic, complemented
9SD16×#1055C211yesmaximal, characteristic, complemented
10#13113635C211yesmaximal, characteristic, complemented
11#13113613C211yesmaximal, characteristic, complemented
12#13113277C211yesmaximal, characteristic
13#13113255C211yesmaximal, characteristic, complemented
14#13113132C211yesmaximal, characteristic, complemented
15C13×#1582C211yesmaximal, characteristic, complemented
16#11719283C2211yescharacteristic
17C4×D4×D13C2211yescharacteristic
18C13×#446C2211yescharacteristic, complemented
19C4×C13×SD16C2211yescharacteristic
20C8×D4×C13C2211yescharacteristic
21#11718830C411yescharacteristic
22#11718823C411yescharacteristic
23C8×C22⋊D13—21no—
24C2×#88060—21no—
25C4×#6106C2211yescharacteristic
26Q8×#1055C2211yescharacteristic, complemented
27C4×#6105C2211yescharacteristic
28D4×#1055C2211yescharacteristic
29#11718531C411yescharacteristic
30#11718523C411yescharacteristic
31#11718501—21no—
32#11718496C2211yescharacteristic
33#11718495C2211yescharacteristic
34#11718494C2211yescharacteristic
35#11718492—21no—
36#11718491C2211yescharacteristic, complemented
37#11718479C411yescharacteristic
38#11718466C411yescharacteristic
39#11718437C411yescharacteristic
40#11718422C411yescharacteristic
41#11718386—21no—
42D13×C22⋊C8—21no—
43#11718370—21no—
44#11718362—21no—
45C4×#6095C2211yescharacteristic
46C4×#6094C2211yescharacteristic
47C8×D52C2211yescharacteristic
48#11718346C2211yescharacteristic
49#11718346C2211yescharacteristic
50#11718340C2211yescharacteristic, complemented
51C13×#334C2211yescharacteristic, complemented
52C13×Q8⋊C8C2211yescharacteristic, complemented
53C13×D4⋊C8C2211yescharacteristic
54C13×#322C2211yescharacteristic, complemented
55Q8⋊#1055C2211yescharacteristic, complemented
56D4⋊#1055C2211yescharacteristic
57#11718076C2211yescharacteristic, complemented
58#11718075C2211yescharacteristic
59#11718071C2211yescharacteristic, complemented
60#11718071C2211yescharacteristic, complemented
61#11718051C2211yescharacteristic
62#11718049C2211yescharacteristic, complemented
63#11718048C2211yescharacteristic, complemented
64#11718046C2211yescharacteristic, complemented
65#11718046C2211yescharacteristic, complemented
66C8×#1055C2211yescharacteristic, complemented
67C2×D4×D13C2×C411yescharacteristic
68C22×C4×D13—21no—
69C2×C13×SD16C2×C411yescharacteristic
70C22×C8×C13—21no—
71C4×Q8×C13C2311yescharacteristic
72C4×D4×C13C2311yescharacteristic
73#88200C2×C411yescharacteristic
74#88198C2×C411yescharacteristic
75C2×#6106C2×C411yescharacteristic
76D4×Dic13C2×C411yescharacteristic
77C2×#6105C2×C411yescharacteristic
78C4×C22⋊D13—21no—
79C22×#1055—21no—
80C2×#6095C2×C411yescharacteristic
81C2×#6094—21no—
82C2×C8×D13—21no—
83C2×C8×D13—21no—
84#88151C2×C411yescharacteristic
85#88150—21no—
86#88147C2×C411yescharacteristic
87C4⋊C4×D13C2×C411yescharacteristic
88#88143—21no—
89#88142C2×C411yescharacteristic
90#88135—21no—
91C22⋊C4×D13—21no—
92C4×D52C2311yescharacteristic
93#88126—21no—
94C42×D13C2311yescharacteristic
95C4×Dic26—21no—
96C4×Dic26C2311yescharacteristic
97C13×#106C2×C411yescharacteristic
98C13×C4⋊C8—21no—
99C13×C4⋊C8C2311yescharacteristic
100C13×C4⋊C8C2311yescharacteristic
101C13×#103C2×C411yescharacteristic
102C13×#102C2×C411yescharacteristic
103C13×C22⋊C8—21no—
104C13×#97—21no—
105C4×C8×C13C2311yescharacteristic
106C4×C8×C13C2311yescharacteristic
107C4×C8×C13C2311yescharacteristic
108#88075C2×C411yescharacteristic
109#88072C2×C411yescharacteristic
110C22⋊#1055—21no—
111#88061C2×C411yescharacteristic
112#88060—21no—
113#88060—21no—
114#88060—21no—
115#88060—21no—
116#88060C2×C411yescharacteristic
117#88060C2×C411yescharacteristic
118#88060D411yescharacteristic
119#88060D411yescharacteristic
120#88057C2×C411yescharacteristic
121#88056C2×C411yescharacteristic
122#88055—21no—
123#88055—21no—
124#88055—21no—
125#88054—21no—
126#88054—21no—
127#88054C2×C411yescharacteristic
128#88054C2×C411yescharacteristic
129#88054D411yescharacteristic
130#88054D411yescharacteristic
131C8×Dic13—21no—
132C8×Dic13—21no—
133#88050C2×C411yescharacteristic
134#88049C2×C411yescharacteristic
135#88048C2×C411yescharacteristic
136#88048C2×C411yescharacteristic
137C4⋊#1055—21no—
138C4⋊#1055C2311yescharacteristic
139C4⋊#1055C2311yescharacteristic
140C4×#1055—21no—
141C4×#1055C2311yescharacteristic
142C4×#1055C2311yescharacteristic
143C4×#1055C2311yescharacteristic
144#17924—131nomaximal, Sylow
145C23×D13—21no—
146C2×Q8×C13C22×C411yescharacteristic
147C2×D4×C13C22×C411yescharacteristic
148C22×C4×C13—21no—
149C2×C22⋊D13—21no—
150C22×Dic13—21no—
151D4×D13—22no—
152D4×D13—22no—
153C2×D52C22×C411yescharacteristic
154C2×C4×D13—21no—
155C2×C4×D13—21no—
156C2×C4×D13—21no—
157C2×C4×D13—81no—
158C2×C4×D13—81no—
159C2×C4×D13C22×C411yescharacteristic
160C2×C4×D13C2×D411yescharacteristic
161C2×C4×D13#4111yescharacteristic
162C2×Dic26—21no—
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#6106—22no—
181#6105—22no—
182#6103—21no—
183#6103—21no—
184#6103—21no—
185#6103—21no—
186C4⋊Dic13—21no—
187C4⋊Dic13C22×C411yescharacteristic
188C4⋊Dic13C22×C411yescharacteristic
189#6101—21no—
190#6101—21no—
191#6101—21no—
192#6101—21no—
193#6101—21no—
194#6101—21no—
195C4×Dic13—21no—
196C4×Dic13C22×C411yescharacteristic
197C4×Dic13C2×D411yescharacteristic
198C4×Dic13#4111yescharacteristic
199C2×#1055—21no—
200C2×#1055—21no—
201C2×#1055—21no—
202C2×#1055—81no—
203C2×#1055C22×C411yescharacteristic
204C2×#1055C22×C411yescharacteristic
205C2×#1055C2×D411yescharacteristic
206C2×#1055C2×D411yescharacteristic
207#6095—22no—
208#6094—42no—
209C8×D13—81no—
210C8×D13—81no—
211#3101—131no—
212#2985—131no—
213#2972—131no—
214#1585—131no—
215#1585—131no—
216#1582—131no—
217#1582D1311yescharacteristic, complemented
218SD16⋊C8—131no—
219SD16⋊C8—131no—
220C8×SD16—131no—
221C8×SD16—131no—
222#1572—131no—
223#1490—131no—
224#1485—131no—
225#1453—131no—
226C23×C13—21no—
227C22×D13—21no—
228C22×D13—24no—
229C22×D13—81no—
230C22×D13—81no—
231C22×D13C4×D411yescharacteristic
232Q8×C13—21no—
233Q8×C13—21no—
234D4×C13—21no—
235D4×C13#13112yes—
236C2×C4×C13—21no—
237C2×C4×C13—21no—
238C2×C4×C13—21no—
239C2×C4×C13—41no—
240C2×C4×C13—41no—
241C2×C4×C13C23×C411yescharacteristic
242C2×C4×C13C22×D411yescharacteristic
243C2×C4×C13C2×#4111yescharacteristic
244C22⋊D13—24no—
245C2×Dic13—21no—
246C2×Dic13—21no—
247C2×Dic13—21no—
248C2×Dic13—81no—
249C2×Dic13C4×D411yescharacteristic
250C2×Dic13C4×D411yescharacteristic
251C2×Dic13C4×D411yescharacteristic
252D52—21no—
253D52#13112yes—
254C4×D13—21no—
255C4×D13—21no—
256C4×D13—21no—
257C4×D13—21no—
258C4×D13—41no—
259C4×D13—41no—
260C4×D13—41no—
261C4×D13—81no—
262C4×D13—81no—
263Dic26—21no—
264Dic26—21no—
265Dic26—81no—
266C8×C13—21no—
267C8×C13—21no—
268C8×C13—21no—
269C8×C13—21no—
270C8×C13—41no—
271C8×C13—41no—
272C8×C13—41no—
273#1055—22no—
274#1055—21no—
275#1055—21no—
276#1055—21no—
277#1055—21no—
278#1055—41no—
279#1055—41no—
280#533—131no—
281C2×C4×D4—131no—
282#483—131no—
283#483—131no—
284#476—131no—
285#476—131no—
286#461—131no—
287#461—131no—
288#450—131no—
289#450—131no—
290#446—131no—
291#446—261no—
292#446—261no—
293#446C2×D1311yescharacteristic, complemented
294C8×Q8—131no—
295C8×Q8—131no—
296C4×SD16—131no—
297C4×SD16—131no—
298C4×SD16—131no—
299C4×SD16C2×D1311yescharacteristic
300C8×D4—131no—
301C8×D4—131no—
302C8×D4—131no—
303C8×D4—261no—
304C8×D4—261no—
305C8×D4C2×D1311yescharacteristic
306#433—261no—
307#433—261no—
308#432—131no—
309#431—131no—
310#431—131no—
311#431—131no—
312C2×C22⋊C8—261no—
313C2×C22⋊C8—261no—
314C4×M16—131no—
315#335—131no—
316#335—131no—
317#334—131no—
318#334C2×D1311yescharacteristic, complemented
319Q8⋊C8—131no—
320Q8⋊C8—131no—
321Q8⋊C8—131no—
322Q8⋊C8C2×D1311yescharacteristic, complemented
323D4⋊C8—131no—
324D4⋊C8—131no—
325D4⋊C8—131no—
326D4⋊C8C2×D1311yescharacteristic
327#322—131no—
328#322—131no—
329#322C2×D1311yescharacteristic, complemented
330C82—131no—
331C22×C13—22no—
332C22×C13—41no—
333C22×C13—41no—
334C22×C13C2×C4×D411yescharacteristic
335C2×D13—21no—
336C2×D13—22no—
337C2×D13—21no—
338C2×D13—21no—
339C2×D13—41no—
340C2×D13—41no—
341C2×D13—84no—
342C4×C13—21no—
343C4×C13—41no—
344C4×C13—41no—
345C4×C13—41no—
346C4×C13C2×#13111yescharacteristic
347C4×C13C2×#13111yescharacteristic
348C4×C13#57711yescharacteristic
349C4×C13#57711yescharacteristic
350Dic13—21no—
351Dic13—21no—
352Dic13—21no—
353Dic13—41no—
354Dic13—41no—
355Dic13—41no—
356C22×D4—131no—
357C23×C4—261no—
358C2×SD16—131no—
359C2×SD16—131no—
360C2×SD16—131no—
361C2×SD16C4×D1311yescharacteristic
362C2×M16—261no—
363C22×C8—21no—
364C22×C8—261no—
365C22×C8—261no—
366C22×C8—261no—
367C4⋊Q8—131no—
368C4⋊Q8—131no—
369#125—261no—
370C22⋊Q8—131no—
371C22⋊Q8—131no—
372C22⋊Q8—261no—
373C4×Q8—131no—
374C4×Q8—261no—
375C4×Q8C22×D1311yescharacteristic
376C4×D4—131no—
377C4×D4—131no—
378C4×D4—131no—
379C4×D4—261no—
380C4×D4—261no—
381C4×D4C22×D1311yescharacteristic
382#117—261no—
383C2×C4⋊C4—131no—
384C2×C22⋊C4—261no—
385C2×C42—131no—
386#106—131no—
387#106—131no—
388#106—131no—
389#106C4×D1311yescharacteristic
390C4⋊C8—21no—
391C4⋊C8—131no—
392C4⋊C8—131no—
393C4⋊C8—131no—
394C4⋊C8—131no—
395C4⋊C8—131no—
396C4⋊C8—131no—
397C4⋊C8—261no—
398C4⋊C8—261no—
399C4⋊C8—261no—
400C4⋊C8C22×D1311yescharacteristic
401C4⋊C8C22×D1311yescharacteristic
402#103—131no—
403#103—131no—
404#103—131no—
405#103C4×D1311yescharacteristic
406#102—131no—
407#102—131no—
408#102—131no—
409#102C4×D1311yescharacteristic
410C22⋊C8—21no—
411C22⋊C8—131no—
412C22⋊C8—131no—
413C22⋊C8—131no—
414C22⋊C8—131no—
415C22⋊C8—261no—
416C22⋊C8—261no—
417C22⋊C8—261no—
418C22⋊C8—261no—
419C22⋊C8—261no—
420#97—21no—
421#97—261no—
422#97—261no—
423#97—261no—
424C4×C8—131no—
425C4×C8—131no—
426C4×C8—131no—
427C4×C8—261no—
428C4×C8—261no—
429C4×C8—261no—
430C4×C8C22×D1311yescharacteristic
431C4×C8C22×D1311yescharacteristic
432C4×C8C22×D1311yescharacteristic
433C2×C13—42no—
434C2×C13#292911yescharacteristic
435C2×C13#294911yescharacteristic
436C2×C13#295611yescharacteristic
437D13—41no—
438D13—42no—
439C24—261no—
440C2×Q8—131no—
441C2×Q8—261no—
442C2×Q8C2×C4×D1311yescharacteristic
443C2×D4—131no—
444C2×D4—261no—
445C2×D4—262no—
446C2×D4—262no—
447C2×D4C2×C4×D1311yescharacteristic
448C22×C4—21no—
449C22×C4—131no—
450C22×C4—131no—
451C22×C4—131no—
452C22×C4—261no—
453C22×C4—261no—
454C22×C4—261no—
455C22×C4—261no—
456C22×C4—1041no—
457C22×C4—1041no—
458SD16—22no—
459SD16—262no—
460SD16—262no—
461SD16—262no—
462M16—522no—
463C2×C8—21no—
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—81no—
467C2×C8—131no—
468C2×C8—131no—
469C2×C8—131no—
470C2×C8—131no—
471C2×C8—261no—
472C2×C8—261no—
473C2×C8—261no—
474C2×C8—1041no—
475C2×C8—1041no—
476C2×C8—1041no—
477C2×C8C2×C4×D1311yescharacteristic
478C2×C8C2×C4×D1311yescharacteristic
479C2×C8D4×D1311yescharacteristic
480C2×C8D4×D1311yescharacteristic
481C4⋊C4—21no—
482C4⋊C4—131no—
483C4⋊C4—131no—
484C4⋊C4—261no—
485C4⋊C4—261no—
486C4⋊C4—261no—
487C4⋊C4—261no—
488C4⋊C4—261no—
489C4⋊C4—261no—
490C4⋊C4—261no—
491C4⋊C4C2×C4×D1311yescharacteristic
492C4⋊C4C2×C4×D1311yescharacteristic
493C22⋊C4—21no—
494C22⋊C4—261no—
495C22⋊C4—261no—
496C22⋊C4—261no—
497C22⋊C4—261no—
498C22⋊C4—261no—
499C42—21no—
500C42—131no—
501C42—131no—
502C42—131no—
503C42—261no—
504C42C23×D1311yescharacteristic
505C13#1792411yescharacteristic, complemented, Sylow
506C23—21no—
507C23—131no—
508C23—264no—
509C23—261no—
510C23—1041no—
511C23—1041no—
512Q8—21no—
513Q8—21no—
514Q8—261no—
515Q8—261no—
516Q8—1041no—
517D4—21no—
518D4—132no—
519D4—264no—
520D4—261no—
521D4#8816112yes—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—131no—
528C2×C4—131no—
529C2×C4—131no—
530C2×C4—261no—
531C2×C4—261no—
532C2×C4—261no—
533C2×C4—261no—
534C2×C4—261no—
535C2×C4—261no—
536C2×C4—261no—
537C2×C4—521no—
538C2×C4—521no—
539C2×C4—521no—
540C2×C4—1041no—
541C2×C4—1041no—
542C2×C4—1041no—
543C2×C4C22×C4×D1311yescharacteristic
544C2×C4C2×D4×D1311yescharacteristic
545C2×C4#41×D1311yescharacteristic
546C8—21no—
547C8—21no—
548C8—21no—
549C8—21no—
550C8—41no—
551C8—41no—
552C8—41no—
553C8—262no—
554C8—261no—
555C8—261no—
556C8—261no—
557C8—261no—
558C8—521no—
559C8—521no—
560C22—22no—
561C22—41no—
562C22—41no—
563C22—261no—
564C22—261no—
565C22—261no—
566C22—262no—
567C22—521no—
568C22—521no—
569C22—1044no—
570C22C4×D4×D1311yescharacteristic
571C4—21no—
572C4—41no—
573C4—41no—
574C4—41no—
575C4—261no—
576C4—261no—
577C4—261no—
578C4—521no—
579C4—521no—
580C4—521no—
581C4C2×#8816111yescharacteristic
582C4D13×#13111yescharacteristic
583C4#1171946711yescharacteristic
584C4#1171947511yescharacteristic
585C2—42no—
586C2—521no—
587C2—522no—
588C2#1312352711yescharacteristic
589C2#1312369011yescharacteristic
590C2#1312374411yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC42C23×D13
FittingC13×#1582C2
socleC22×C13C2×C4×D4
prime radicalC2×D4×D13C2×C4
cosocleC42×C13C24
hypercenter#1582D13
hypocenterC13#17924
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. #13123932C2semidirect
4. #13113693C2semidirect
5. #13113691C2semidirect
6. #13113674C2semidirect
7. #13113651C2semidirect
8. #13113645C2semidirect
9. SD16×#1055C2semidirect
10. #13113635C2semidirect
11. #13113613C2semidirect
13. #13113255C2semidirect
14. #13113132C2semidirect
15. C13×#1582C2semidirect
18. C13×#446C22semidirect
26. Q8×#1055C22semidirect
36. #11718491C22semidirect
50. #11718340C22semidirect
51. C13×#334C22semidirect
52. C13×Q8⋊C8C22semidirect
54. C13×#322C22semidirect
55. Q8⋊#1055C22semidirect
57. #11718076C22semidirect
59. #11718071C22semidirect
60. #11718071C22semidirect
62. #11718049C22semidirect
63. #11718048C22semidirect
64. #11718046C22semidirect
65. #11718046C22semidirect
66. C8×#1055C22semidirect
217. #1582D13semidirect
293. #446C2×D13semidirect
318. #334C2×D13semidirect
322. Q8⋊C8C2×D13semidirect
329. #322C2×D13semidirect
505. C13#17924semidirect

Maximal subgroups

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

subgroupindex
#131248422
#131239322
#131238572
#131136932
#131136912
#131136742
#131136512
#131136452
SD16×#10552
#131136352
#131136132
#131132772
#131132552
#131131322
C13×#15822
#1792413