Finite Group Databasebeta

← #15834251

Subgroups — #15834251

Order 3328.

616 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13124845C211yesmaximal, characteristic
2#13123937C211yesmaximal, characteristic, complemented
3#13123873C211yesmaximal, characteristic
4#13113737C211yesmaximal, characteristic, complemented
5#13113725C211yesmaximal, characteristic, complemented
6#13113713C211yesmaximal, characteristic, complemented
7#13113692C211yesmaximal, characteristic, complemented
8#13113678C211yesmaximal, characteristic, complemented
9#13113671C211yesmaximal, characteristic, complemented
10#13113647C211yesmaximal, characteristic, complemented
11#13113635C211yesmaximal, characteristic, complemented
12#13113308C211yesmaximal, characteristic, complemented
13#13113226C211yesmaximal, characteristic
14#13113136C211yesmaximal, characteristic, complemented
15C13×#1572C211yesmaximal, characteristic, complemented
16C2×C4×D52C2211yescharacteristic
17#11719175C2211yescharacteristic
18C13×#432C2211yescharacteristic
19C13×#431C2211yescharacteristic
20C13×#431C2211yescharacteristic
21#11718586C2211yescharacteristic
22#11718586C2211yescharacteristic
23#11718503C411yescharacteristic
24#11718503C411yescharacteristic
25#11718502C411yescharacteristic
26#11718502C411yescharacteristic
27#11718499C2211yescharacteristic
28#11718499C2211yescharacteristic
29#11718495C2211yescharacteristic
30#11718495C2211yescharacteristic
31#11718492C2211yescharacteristic, complemented
32#11718492C2211yescharacteristic, complemented
33#11718491C2211yescharacteristic, complemented
34#11718491C2211yescharacteristic, complemented
35#11718392C411yescharacteristic
36#11718392C411yescharacteristic
37#11718387—21no—
38D13×C22⋊C8—21no—
39#11718382C411yescharacteristic
40#11718382C411yescharacteristic
41#11718381—21no—
42#11718381—21no—
43#11718367—21no—
44#11718367—21no—
45C4×#6095C2211yescharacteristic
46C4×#6095C2211yescharacteristic
47C4×#6095C2211yescharacteristic
48C4×#6095C2211yescharacteristic
49#11718340—21no—
50C8×Dic26—21no—
51C13×#335C2211yescharacteristic, complemented
52C13×#335C2211yescharacteristic, complemented
53C13×#334C2211yescharacteristic, complemented
54C13×#334C2211yescharacteristic, complemented
55#11718076C2211yescharacteristic, complemented
56#11718076C2211yescharacteristic, complemented
57#11718076C2211yescharacteristic, complemented
58#11718076C2211yescharacteristic, complemented
59#11718075C2211yescharacteristic
60#11718075C2211yescharacteristic
61#11718075C2211yescharacteristic
62#11718075C2211yescharacteristic
63#11718047C2211yescharacteristic, complemented
64#11718046C2211yescharacteristic, complemented
65#11718046C2211yescharacteristic, complemented
66C8×#1055C2211yescharacteristic, complemented
67C22×D52C2×C411yescharacteristic
68C22×C4×D13—21no—
69C2×C42×C13C2311yescharacteristic
70C2×#6103—21no—
71#88180—21no—
72C2×C4⋊Dic13C2×C411yescharacteristic
73#88178—21no—
74#88178C2×C411yescharacteristic
75#88178C2×C411yescharacteristic
76C2×#6095C2×C411yescharacteristic
77C2×#6095C2×C411yescharacteristic
78C2×#6095C2×C411yescharacteristic
79C2×#6095C2×C411yescharacteristic
80C2×#6094—21no—
81C2×#6094—21no—
82C2×C8×D13—21no—
83C2×C8×D13—21no—
84C4×D52—21no—
85C4×D52—21no—
86C4×D52C2×C411yescharacteristic
87C4×D52C2×C411yescharacteristic
88C4×D52C2311yescharacteristic
89C4×D52C2311yescharacteristic
90#88124—21no—
91#88123C2×C411yescharacteristic
92#88123C2×C411yescharacteristic
93C4×Dic26—21no—
94C4×Dic26C2311yescharacteristic
95C4×Dic26C2311yescharacteristic
96C13×C4⋊C8C2×C411yescharacteristic
97C13×C4⋊C8C2×C411yescharacteristic
98C13×C4⋊C8C2311yescharacteristic
99C13×C4⋊C8C2311yescharacteristic
100C13×C4⋊C8C2311yescharacteristic
101C13×C4⋊C8C2311yescharacteristic
102C13×C22⋊C8—21no—
103C13×C22⋊C8—21no—
104C13×C22⋊C8C2×C411yescharacteristic
105C13×C22⋊C8C2×C411yescharacteristic
106C13×#97—21no—
107C4×C8×C13—21no—
108C4×C8×C13C2311yescharacteristic
109C4×C8×C13C2311yescharacteristic
110C22⋊#1055—21no—
111C22⋊#1055D411yescharacteristic
112C22⋊#1055D411yescharacteristic
113#88061C2×C411yescharacteristic
114#88061C2×C411yescharacteristic
115#88061C2×C411yescharacteristic
116#88061C2×C411yescharacteristic
117#88060—21no—
118#88060—21no—
119#88060—21no—
120#88060—21no—
121#88057C2×C411yescharacteristic
122#88057C2×C411yescharacteristic
123#88057C2×C411yescharacteristic
124#88057C2×C411yescharacteristic
125#88056C2×C411yescharacteristic
126#88056C2×C411yescharacteristic
127#88056C2×C411yescharacteristic
128#88056C2×C411yescharacteristic
129#88055—21no—
130#88055—21no—
131#88054—21no—
132#88054—21no—
133#88054—21no—
134#88054—21no—
135C8×Dic13—21no—
136C8×Dic13—21no—
137C4⋊#1055—21no—
138C4⋊#1055D411yescharacteristic
139C4⋊#1055D411yescharacteristic
140C4×#1055C2311yescharacteristic
141C4×#1055C2311yescharacteristic
142C4×#1055C2311yescharacteristic
143C4×#1055C2311yescharacteristic
144#18028—131nomaximal, Sylow
145C23×D13—21no—
146C22×C4×C13C22×C411yescharacteristic
147C22×C4×C13C2×D411yescharacteristic
148C22×C4×C13#4111yescharacteristic
149C22×Dic13—21no—
150C2×D52—22no—
151C2×D52—21no—
152C2×D52—41no—
153C2×D52C22×C411yescharacteristic
154C2×D52C22×C411yescharacteristic
155C2×C4×D13—21no—
156C2×C4×D13—21no—
157C2×C4×D13—21no—
158C2×C4×D13—21no—
159C2×C4×D13—81no—
160C2×C4×D13—81no—
161C2×Dic26—21no—
162C2×Dic26C22×C411yescharacteristic
163C2×Dic26C22×C411yescharacteristic
164C2×C8×C13—21no—
165C2×C8×C13—21no—
166C2×C8×C13—21no—
167C2×C8×C13—21no—
168C2×C8×C13C22×C411yescharacteristic
169C2×C8×C13C22×C411yescharacteristic
170C2×C8×C13C22×C411yescharacteristic
171C2×C8×C13C22×C411yescharacteristic
172C42×C13C22×C411yescharacteristic
173C42×C13C2×D411yescharacteristic
174C42×C13#4111yescharacteristic
175C42×C13C2411yescharacteristic
176C22⋊Dic13—21no—
177C22⋊Dic13—21no—
178#6103—21no—
179#6103—21no—
180#6103—21no—
181#6103—21no—
182C4⋊Dic13—21no—
183C4⋊Dic13—21no—
184C4⋊Dic13—21no—
185C4⋊Dic13—21no—
186C4⋊Dic13C22×C411yescharacteristic
187C4⋊Dic13C22×C411yescharacteristic
188C4⋊Dic13C22×C411yescharacteristic
189C4⋊Dic13C22×C411yescharacteristic
190#6101—21no—
191#6101—21no—
192#6101—21no—
193#6101—21no—
194C4×Dic13—21no—
195C4×Dic13—21no—
196C2×#1055—21no—
197C2×#1055—21no—
198C2×#1055C2×D411yescharacteristic
199C2×#1055C2×D411yescharacteristic
200C2×#1055C2×D411yescharacteristic
201C2×#1055C2×D411yescharacteristic
202#6095—22no—
203#6095—22no—
204#6095—41no—
205#6095—41no—
206#6094—81no—
207#6094—81no—
208C8×D13—81no—
209C8×D13—81no—
210#3101—131no—
211#2986—131no—
212#2974—131no—
213#1592—131no—
214#1590—131no—
215#1588—131no—
216#1585—131no—
217#1583—131no—
218#1582—131no—
219SD16⋊C8—131no—
220C8×SD16—131no—
221#1572D1311yescharacteristic, complemented
222#1497—131no—
223#1478—131no—
224#1454—131no—
225C23×C13C4×D411yescharacteristic
226C22×D13—21no—
227C22×D13—21no—
228C22×D13—42no—
229C22×D13—42no—
230C22×D13—81no—
231C2×C4×C13—21no—
232C2×C4×C13—21no—
233C2×C4×C13—21no—
234C2×C4×C13—21no—
235C2×C4×C13—41no—
236C2×C4×C13C4×D411yescharacteristic
237C2×C4×C13C4×D411yescharacteristic
238C2×C4×C13C4×D411yescharacteristic
239C2×C4×C13C23×C411yescharacteristic
240C2×C4×C13C22×D411yescharacteristic
241C2×C4×C13C2×#4111yescharacteristic
242C2×Dic13—21no—
243C2×Dic13—21no—
244C2×Dic13—21no—
245C2×Dic13—21no—
246C2×Dic13—21no—
247C2×Dic13—21no—
248C2×Dic13—81no—
249D52—21no—
250D52—21no—
251D52—21no—
252D52—42no—
253D52#13112yes—
254C4×D13—41no—
255C4×D13—41no—
256C4×D13—41no—
257C4×D13—41no—
258C4×D13—81no—
259C4×D13—81no—
260Dic26—21no—
261Dic26—21no—
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—
272C8×C13—41no—
273#1055—21no—
274#1055—21no—
275#1055—21no—
276#1055—21no—
277#1055—41no—
278#1055—41no—
279#533—131no—
280C2×C4×D4—131no—
281#483—131no—
282#483—131no—
283#476—131no—
284#476—131no—
285#461—131no—
286#461—131no—
287#450—131no—
288#450—131no—
289#446—131no—
290#446—131no—
291#446—261no—
292C8×Q8—131no—
293C8×Q8—131no—
294C8×Q8—261no—
295C4×SD16—131no—
296C4×SD16—131no—
297C4×SD16—131no—
298C4×SD16—131no—
299#436—131no—
300#436—131no—
301#435—261no—
302#435—261no—
303C8×D4—131no—
304C8×D4—131no—
305#433—261no—
306#433—261no—
307#432C2×D1311yescharacteristic
308#431—131no—
309#431—131no—
310#431C2×D1311yescharacteristic
311#431C2×D1311yescharacteristic
312#407—261no—
313C2×C22⋊C8—261no—
314#335C2×D1311yescharacteristic, complemented
315#335C2×D1311yescharacteristic, complemented
316#334C2×D1311yescharacteristic, complemented
317#334C2×D1311yescharacteristic, complemented
318Q8⋊C8—131no—
319Q8⋊C8—131no—
320Q8⋊C8—131no—
321Q8⋊C8—131no—
322D4⋊C8—131no—
323D4⋊C8—131no—
324D4⋊C8—131no—
325D4⋊C8—131no—
326#322—131no—
327#322—131no—
328#322—131no—
329C82—131no—
330C22×C13—21no—
331C22×C13—21no—
332C22×C13—21no—
333C22×C13C2×C4×D411yescharacteristic
334C2×D13—22no—
335C2×D13—41no—
336C2×D13—41no—
337C2×D13—41no—
338C2×D13—41no—
339C2×D13—41no—
340C2×D13—84no—
341C4×C13—21no—
342C4×C13—21no—
343C4×C13—21no—
344C4×C13—21no—
345C4×C13C2×#13111yescharacteristic
346C4×C13#56811yescharacteristic
347C4×C13#57711yescharacteristic
348C4×C13#57711yescharacteristic
349Dic13—41no—
350Dic13—41no—
351Dic13—41no—
352Dic13—41no—
353Dic13—41no—
354Dic13—41no—
355C22×D4—131no—
356C23×C4—261no—
357C2×SD16—131no—
358C2×SD16—131no—
359C2×SD16—131no—
360C2×SD16—131no—
361C2×M16—261no—
362C2×M16—261no—
363C22×C8—261no—
364C22×C8—261no—
365C4⋊Q8—131no—
366C4⋊Q8—131no—
367#125—261no—
368C22⋊Q8—131no—
369C22⋊Q8—131no—
370C22⋊Q8—261no—
371C4×Q8—131no—
372C4×Q8—131no—
373C4×Q8—261no—
374C4×D4—131no—
375C4×D4—131no—
376C4×D4—131no—
377C4×D4—131no—
378C4×D4—261no—
379C4×D4—261no—
380#117—261no—
381C2×C4⋊C4—131no—
382C2×C22⋊C4—261no—
383C2×C42C22×D1311yescharacteristic
384#106—131no—
385#106—131no—
386#106—131no—
387#106—131no—
388C4⋊C8—131no—
389C4⋊C8—131no—
390C4⋊C8—261no—
391C4⋊C8—261no—
392C4⋊C8—261no—
393C4⋊C8—261no—
394C4⋊C8—261no—
395C4⋊C8C4×D1311yescharacteristic
396C4⋊C8C4×D1311yescharacteristic
397C4⋊C8C22×D1311yescharacteristic
398C4⋊C8C22×D1311yescharacteristic
399C4⋊C8C22×D1311yescharacteristic
400C4⋊C8C22×D1311yescharacteristic
401#103—131no—
402#103—131no—
403#103—131no—
404#103—131no—
405#102—131no—
406#102—131no—
407#102—131no—
408#102—131no—
409C22⋊C8—21no—
410C22⋊C8—21no—
411C22⋊C8—131no—
412C22⋊C8—131no—
413C22⋊C8—261no—
414C22⋊C8—261no—
415C22⋊C8—261no—
416C22⋊C8—261no—
417C22⋊C8—261no—
418C22⋊C8C4×D1311yescharacteristic
419C22⋊C8C4×D1311yescharacteristic
420#97—21no—
421#97—261no—
422#97—261no—
423C4×C8—21no—
424C4×C8—131no—
425C4×C8—131no—
426C4×C8—131no—
427C4×C8—131no—
428C4×C8—261no—
429C4×C8—261no—
430C4×C8C22×D1311yescharacteristic
431C4×C8C22×D1311yescharacteristic
432C2×C13—41no—
433C2×C13#293311yescharacteristic
434C2×C13#294911yescharacteristic
435C2×C13#295511yescharacteristic
436D13—42no—
437D13—81no—
438C24—261no—
439C2×Q8—131no—
440C2×Q8—131no—
441C2×Q8—261no—
442C2×D4—131no—
443C2×D4—131no—
444C2×D4—262no—
445C2×D4—261no—
446C2×D4—521no—
447C22×C4—261no—
448C22×C4—261no—
449C22×C4—261no—
450C22×C4—261no—
451C22×C4—261no—
452C22×C4—1041no—
453C22×C4—1041no—
454C22×C4C2×C4×D1311yescharacteristic
455C22×C4D4×D1311yescharacteristic
456C22×C4#613111yescharacteristic
457SD16—262no—
458SD16—262no—
459SD16—521no—
460SD16—521no—
461M16—1041no—
462M16—1041no—
463C2×C8—21no—
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—131no—
468C2×C8—131no—
469C2×C8—131no—
470C2×C8—131no—
471C2×C8—261no—
472C2×C8—261no—
473C2×C8—1041no—
474C2×C8—1041no—
475C2×C8C2×C4×D1311yescharacteristic
476C2×C8C2×C4×D1311yescharacteristic
477C2×C8C2×C4×D1311yescharacteristic
478C2×C8C2×C4×D1311yescharacteristic
479C4⋊C4—131no—
480C4⋊C4—131no—
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⋊C4—261no—
490C4⋊C4—261no—
491C22⋊C4—261no—
492C22⋊C4—261no—
493C22⋊C4—261no—
494C22⋊C4—261no—
495C22⋊C4—261no—
496C22⋊C4—261no—
497C42—261no—
498C42—261no—
499C42C2×C4×D1311yescharacteristic
500C42D4×D1311yescharacteristic
501C42#613111yescharacteristic
502C42C23×D1311yescharacteristic
503C13#1802811yescharacteristic, complemented, Sylow
504C23—261no—
505C23—261no—
506C23—522no—
507C23—522no—
508C23—1041no—
509C23#8814711yescharacteristic
510Q8—261no—
511Q8—261no—
512Q8—261no—
513Q8—261no—
514Q8—522no—
515D4—132no—
516D4—261no—
517D4—261no—
518D4—261no—
519D4—522no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—41no—
525C2×C4—261no—
526C2×C4—261no—
527C2×C4—261no—
528C2×C4—261no—
529C2×C4—261no—
530C2×C4—261no—
531C2×C4—521no—
532C2×C4—521no—
533C2×C4—521no—
534C2×C4—521no—
535C2×C4—1041no—
536C2×C4—1041no—
537C2×C4—1041no—
538C2×C4#8814711yescharacteristic
539C2×C4#8814711yescharacteristic
540C2×C4#8814711yescharacteristic
541C2×C4C22×C4×D1311yescharacteristic
542C2×C4C2×D4×D1311yescharacteristic
543C2×C4C2×#613111yescharacteristic
544C8—21no—
545C8—21no—
546C8—21no—
547C8—21no—
548C8—41no—
549C8—41no—
550C8—41no—
551C8—41no—
552C8—261no—
553C8—261no—
554C8—261no—
555C8—261no—
556C8—521no—
557C8—521no—
558C22—21no—
559C22—21no—
560C22—21no—
561C22—262no—
562C22—521no—
563C22—521no—
564C22—521no—
565C22—521no—
566C22—521no—
567C22—1044no—
568C22C2×#8814711yescharacteristic
569C4—21no—
570C4—21no—
571C4—21no—
572C4—21no—
573C4—521no—
574C4—521no—
575C4—521no—
576C4—521no—
577C4—521no—
578C4—521no—
579C4D13×#13111yescharacteristic
580C4#1171945511yescharacteristic
581C4#1171947511yescharacteristic
582C4#1171947511yescharacteristic
583C2—41no—
584C2—522no—
585C2—1041no—
586C2#1312356011yescharacteristic
587C2#1312369411yescharacteristic
588C2#1312373811yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC42C23×D13
FittingC13×#1572C2
socleC22×C13C2×C4×D4
prime radicalC22×D52C2×C4
cosocleC42×C13C24
hypercenter#1572D13
hypocenterC13#18028
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1572

Complements

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

NH ≅ G/Ntype
2. #13123937C2semidirect
4. #13113737C2semidirect
5. #13113725C2semidirect
6. #13113713C2semidirect
7. #13113692C2semidirect
8. #13113678C2semidirect
9. #13113671C2semidirect
10. #13113647C2semidirect
11. #13113635C2semidirect
12. #13113308C2semidirect
14. #13113136C2semidirect
15. C13×#1572C2semidirect
31. #11718492C22semidirect
32. #11718492C22semidirect
33. #11718491C22semidirect
34. #11718491C22semidirect
51. C13×#335C22semidirect
52. C13×#335C22semidirect
53. C13×#334C22semidirect
54. C13×#334C22semidirect
55. #11718076C22semidirect
56. #11718076C22semidirect
57. #11718076C22semidirect
58. #11718076C22semidirect
63. #11718047C22semidirect
64. #11718046C22semidirect
65. #11718046C22semidirect
66. C8×#1055C22semidirect
221. #1572D13semidirect
314. #335C2×D13semidirect
315. #335C2×D13semidirect
316. #334C2×D13semidirect
317. #334C2×D13semidirect
503. C13#18028semidirect

Maximal subgroups

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

subgroupindex
#131248452
#131239372
#131238732
#131137372
#131137252
#131137132
#131136922
#131136782
#131136712
#131136472
#131136352
#131133082
#131132262
#131131362
C13×#15722
#1802813