Finite Group Databasebeta

← #15834277

Subgroups — #15834277

Order 3328.

606 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13124867C211yesmaximal, characteristic
2#13123925C211yesmaximal, characteristic, complemented
3#13123902C211yesmaximal, characteristic
4#13113741C211yesmaximal, characteristic, complemented
5#13113723C211yesmaximal, characteristic, complemented
6#13113711C211yesmaximal, characteristic, complemented
7#13113696C211yesmaximal, characteristic, complemented
8#13113676C211yesmaximal, characteristic, complemented
9#13113675C211yesmaximal, characteristic, complemented
10#13113651C211yesmaximal, characteristic, complemented
11#13113633C211yesmaximal, characteristic, complemented
12#13113614C211yesmaximal, characteristic, complemented
13#13113306C211yesmaximal, characteristic
14#13113136C211yesmaximal, characteristic, complemented
15C13×#1479C211yesmaximal, characteristic, complemented
16C2×C4×Q8×C13C2211yescharacteristic
17#11719182C2211yescharacteristic
18C13×#431C2211yescharacteristic
19C13×#431C2211yescharacteristic
20#11718888C411yescharacteristic
21#11718888C411yescharacteristic
22#11718688C411yescharacteristic
23#11718688C411yescharacteristic
24C4×#6106C2211yescharacteristic
25C4×#6106C2211yescharacteristic
26C4×#6106C2211yescharacteristic
27C4×#6106C2211yescharacteristic
28#11718685—21no—
29#11718685—21no—
30#11718685C2211yescharacteristic
31#11718685C2211yescharacteristic
32Q8×#1055C2211yescharacteristic
33Q8×#1055C2211yescharacteristic
34#11718681C411yescharacteristic
35#11718681C411yescharacteristic
36#11718629C411yescharacteristic
37#11718629C411yescharacteristic
38#11718587—21no—
39#11718587C2211yescharacteristic
40#11718586—21no—
41#11718586C2211yescharacteristic
42#11718586C2211yescharacteristic
43#11718499C2211yescharacteristic
44#11718499C2211yescharacteristic
45#11718495C2211yescharacteristic
46#11718495C2211yescharacteristic
47#11718388—21no—
48#11718388—21no—
49#11718349—21no—
50C8×D52—21no—
51C13×Q8⋊C8C2211yescharacteristic
52C13×Q8⋊C8C2211yescharacteristic
53C13×Q8⋊C8C2211yescharacteristic
54C13×Q8⋊C8C2211yescharacteristic
55#11718072C2211yescharacteristic
56#11718072C2211yescharacteristic
57#11718071C2211yescharacteristic
58#11718071C2211yescharacteristic
59#11718051C2211yescharacteristic
60#11718051C2211yescharacteristic
61#11718051C2211yescharacteristic
62#11718051C2211yescharacteristic
63#11718047C2211yescharacteristic
64#11718046C2211yescharacteristic
65#11718046C2211yescharacteristic
66C8×#1055C2211yescharacteristic
67C22×Q8×C13C2×C411yescharacteristic
68C2×#6127—21no—
69C4×Q8×C13—21no—
70C4×Q8×C13—21no—
71C4×Q8×C13C2×C411yescharacteristic
72C4×Q8×C13C2×C411yescharacteristic
73C4×Q8×C13C2311yescharacteristic
74C4×Q8×C13C2311yescharacteristic
75C2×C13×C4⋊C4—21no—
76C2×C13×C4⋊C4C2×C411yescharacteristic
77C2×C42×C13—21no—
78C2×C42×C13C2311yescharacteristic
79C2×#6106C2×C411yescharacteristic
80C2×#6106C2×C411yescharacteristic
81C2×#6106C2×C411yescharacteristic
82C2×#6106C2×C411yescharacteristic
83#88184—21no—
84#88184C2×C411yescharacteristic
85#88184C2×C411yescharacteristic
86C2×#6094—21no—
87C2×#6094—21no—
88C2×C8×D13—21no—
89C2×C8×D13—21no—
90#88129—21no—
91#88128C2×C411yescharacteristic
92C4×D52—21no—
93C4×D52C2311yescharacteristic
94C4×D52C2311yescharacteristic
95#88123C2×C411yescharacteristic
96C13×C4⋊C8—21no—
97C13×C4⋊C8C2311yescharacteristic
98C13×C4⋊C8C2311yescharacteristic
99C13×C22⋊C8—21no—
100C13×C22⋊C8—21no—
101C4×C8×C13—21no—
102C4×C8×C13C2311yescharacteristic
103C4×C8×C13C2311yescharacteristic
104#88075C2×C411yescharacteristic
105#88075C2×C411yescharacteristic
106#88075C2×C411yescharacteristic
107#88075C2×C411yescharacteristic
108C22⋊#1055—21no—
109C22⋊#1055C2×C411yescharacteristic
110C22⋊#1055C2×C411yescharacteristic
111C22⋊#1055D411yescharacteristic
112C22⋊#1055D411yescharacteristic
113#88060—21no—
114#88060—21no—
115#88060—21no—
116#88060—21no—
117#88049C2×C411yescharacteristic
118#88049C2×C411yescharacteristic
119#88049C2×C411yescharacteristic
120#88049C2×C411yescharacteristic
121#88048C2×C411yescharacteristic
122#88048C2×C411yescharacteristic
123#88048C2×C411yescharacteristic
124#88048C2×C411yescharacteristic
125C4⋊#1055—21no—
126C4⋊#1055—21no—
127C4⋊#1055—21no—
128C4⋊#1055—21no—
129C4⋊#1055C2×C411yescharacteristic
130C4⋊#1055C2×C411yescharacteristic
131C4⋊#1055D411yescharacteristic
132C4⋊#1055D411yescharacteristic
133C4⋊#1055C2311yescharacteristic
134C4⋊#1055C2311yescharacteristic
135#88043—21no—
136#88043—21no—
137#88043—21no—
138C4×#1055—21no—
139C4×#1055—21no—
140C4×#1055C2311yescharacteristic
141C4×#1055C2311yescharacteristic
142C4×#1055C2311yescharacteristic
143C4×#1055C2311yescharacteristic
144#18030—131nomaximal, Sylow
145C2×Q8×C13—21no—
146C2×Q8×C13—22no—
147C2×Q8×C13—41no—
148C2×Q8×C13C22×C411yescharacteristic
149C2×Q8×C13C22×C411yescharacteristic
150C22×C4×C13—21no—
151C22×C4×C13—21no—
152C22×C4×C13C22×C411yescharacteristic
153C22×C4×C13C2×D411yescharacteristic
154C22×C4×C13#4111yescharacteristic
155C2×C22⋊D13—21no—
156C2×C22⋊D13—21no—
157#6127—81no—
158#6127—81no—
159C2×D52—21no—
160C2×D52—21no—
161C2×D52C22×C411yescharacteristic
162C2×D52C22×C411yescharacteristic
163C2×C4×D13—21no—
164C2×C4×D13—21no—
165C2×Dic26—21no—
166C2×C8×C13—21no—
167C2×C8×C13—21no—
168C2×C8×C13—21no—
169C2×C8×C13—21no—
170C13×C4⋊C4—21no—
171C13×C4⋊C4—21no—
172C13×C4⋊C4—21no—
173C13×C4⋊C4—21no—
174C13×C4⋊C4—21no—
175C13×C4⋊C4C22×C411yescharacteristic
176C13×C4⋊C4C22×C411yescharacteristic
177C42×C13—21no—
178C42×C13—21no—
179C42×C13—21no—
180C42×C13—21no—
181C42×C13C22×C411yescharacteristic
182C42×C13C2×D411yescharacteristic
183C42×C13#4111yescharacteristic
184C42×C13C2411yescharacteristic
185#6106—22no—
186#6106—22no—
187#6106—41no—
188#6106—41no—
189#6103—21no—
190#6103—21no—
191#6103—21no—
192#6103—21no—
193C4⋊Dic13—21no—
194C4⋊Dic13C22×C411yescharacteristic
195C4⋊Dic13C22×C411yescharacteristic
196C2×#1055—21no—
197C2×#1055—21no—
198C2×#1055C22×C411yescharacteristic
199C2×#1055C22×C411yescharacteristic
200C2×#1055C22×C411yescharacteristic
201C2×#1055C22×C411yescharacteristic
202C2×#1055C2×D411yescharacteristic
203C2×#1055C2×D411yescharacteristic
204C2×#1055C2×D411yescharacteristic
205C2×#1055C2×D411yescharacteristic
206#6094—81no—
207#6094—81no—
208C8×D13—81no—
209C8×D13—81no—
210#3103—131no—
211#2984—131no—
212#2979—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#1572—131no—
222#1496—131no—
223#1479D1311yescharacteristic, complemented
224#1454—131no—
225C23×C13C4×D411yescharacteristic
226C22×D13—21no—
227C22×D13—21no—
228Q8×C13—21no—
229Q8×C13—21no—
230Q8×C13—21no—
231Q8×C13—42no—
232Q8×C13#13112yes—
233C2×C4×C13—21no—
234C2×C4×C13—21no—
235C2×C4×C13—21no—
236C2×C4×C13—21no—
237C2×C4×C13—21no—
238C2×C4×C13—21no—
239C2×C4×C13—21no—
240C2×C4×C13—21no—
241C2×C4×C13—41no—
242C2×C4×C13—42no—
243C2×C4×C13—42no—
244C2×C4×C13C4×D411yescharacteristic
245C2×C4×C13C4×D411yescharacteristic
246C2×C4×C13C4×D411yescharacteristic
247C2×C4×C13C23×C411yescharacteristic
248C2×C4×C13C22×D411yescharacteristic
249C2×C4×C13C2×#4111yescharacteristic
250C22⋊D13—81no—
251C22⋊D13—81no—
252C2×Dic13—21no—
253C2×Dic13—21no—
254D52—21no—
255D52—21no—
256D52—21no—
257D52—21no—
258D52—42no—
259D52—81no—
260C4×D13—41no—
261C4×D13—41no—
262C4×D13—41no—
263C4×D13—41no—
264Dic26—81no—
265C8×C13—41no—
266C8×C13—41no—
267C8×C13—41no—
268C8×C13—41no—
269#1055—21no—
270#1055—21no—
271#1055—21no—
272#1055—21no—
273#1055—21no—
274#1055—21no—
275#1055—21no—
276#1055—21no—
277#1055—41no—
278#1055—41no—
279#532—131no—
280C2×C4×Q8C2×D1311yescharacteristic
281#481—131no—
282#481—131no—
283#475—131no—
284#475—131no—
285#460—131no—
286#460—131no—
287#448—131no—
288#448—131no—
289#446—131no—
290#446—131no—
291#446—261no—
292#446—261no—
293C8×Q8—131no—
294C8×Q8—131no—
295C4×SD16—131no—
296C4×SD16—131no—
297C4×SD16—131no—
298C4×SD16—131no—
299#436—131no—
300#436—131no—
301#436—261no—
302C8×D4—131no—
303C8×D4—131no—
304C8×D4—261no—
305#432—131no—
306#432—261no—
307#431—131no—
308#431—131no—
309#431—261no—
310#431C2×D1311yescharacteristic
311#431C2×D1311yescharacteristic
312#408—261no—
313#408—261no—
314#335—131no—
315#335—131no—
316#334—131no—
317#334—131no—
318Q8⋊C8C2×D1311yescharacteristic
319Q8⋊C8C2×D1311yescharacteristic
320Q8⋊C8C2×D1311yescharacteristic
321Q8⋊C8C2×D1311yescharacteristic
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—41no—
335C2×D13—41no—
336C2×D13—41no—
337C2×D13—41no—
338C2×D13—41no—
339C2×D13—41no—
340C4×C13—21no—
341C4×C13—22no—
342C4×C13—21no—
343C4×C13—21no—
344C4×C13—21no—
345C4×C13—41no—
346C4×C13—41no—
347C4×C13—41no—
348C4×C13C2×#13111yescharacteristic
349C4×C13#56811yescharacteristic
350C4×C13#57711yescharacteristic
351C4×C13#57711yescharacteristic
352Dic13—41no—
353Dic13—41no—
354C2×#41—261no—
355C22×Q8C4×D1311yescharacteristic
356C2×SD16—131no—
357C2×SD16—131no—
358C2×SD16—131no—
359C2×SD16—131no—
360C2×M16—261no—
361C2×M16—261no—
362C22×C8—261no—
363C22×C8—261no—
364C4⋊Q8—131no—
365#127—131no—
366#124—261no—
367#121—131no—
368#121—131no—
369#121—261no—
370C4×Q8—21no—
371C4×Q8—21no—
372C4×Q8C4×D1311yescharacteristic
373C4×Q8C4×D1311yescharacteristic
374C4×Q8C22×D1311yescharacteristic
375C4×Q8C22×D1311yescharacteristic
376C4×D4—131no—
377C4×D4—131no—
378C4×D4—261no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4C4×D1311yescharacteristic
381C2×C42—21no—
382C2×C42C22×D1311yescharacteristic
383#106—131no—
384#106—131no—
385#106—131no—
386#106—131no—
387C4⋊C8—21no—
388C4⋊C8—131no—
389C4⋊C8—131no—
390C4⋊C8—131no—
391C4⋊C8—131no—
392C4⋊C8—131no—
393C4⋊C8—131no—
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#102—131no—
405#102—131no—
406#102—131no—
407#102—131no—
408C22⋊C8—21no—
409C22⋊C8—21no—
410C22⋊C8—131no—
411C22⋊C8—131no—
412C22⋊C8—131no—
413C22⋊C8—131no—
414C22⋊C8—261no—
415C22⋊C8—261no—
416C22⋊C8—261no—
417C22⋊C8—261no—
418C22⋊C8—261no—
419#97—261no—
420#97—261no—
421#97—261no—
422C4×C8—21no—
423C4×C8—131no—
424C4×C8—131no—
425C4×C8—131no—
426C4×C8—131no—
427C4×C8—261no—
428C4×C8—261no—
429C4×C8C22×D1311yescharacteristic
430C4×C8C22×D1311yescharacteristic
431C2×C13—41no—
432C2×C13#293311yescharacteristic
433C2×C13#294911yescharacteristic
434C2×C13#295511yescharacteristic
435D13—81no—
436D13—81no—
437#41—1041no—
438#41—1041no—
439C2×Q8—21no—
440C2×Q8—22no—
441C2×Q8—41no—
442C2×Q8—261no—
443C2×Q8C2×C4×D1311yescharacteristic
444C2×Q8C2×C4×D1311yescharacteristic
445C2×D4—131no—
446C2×D4—131no—
447C2×D4—261no—
448C2×D4—261no—
449C2×D4—261no—
450C2×D4—261no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—261no—
454C22×C4—261no—
455C22×C4C2×C4×D1311yescharacteristic
456C22×C4D4×D1311yescharacteristic
457C22×C4#612911yescharacteristic
458SD16—262no—
459SD16—262no—
460SD16—521no—
461SD16—521no—
462M16—1041no—
463M16—1041no—
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—131no—
469C2×C8—131no—
470C2×C8—131no—
471C2×C8—131no—
472C2×C8—131no—
473C2×C8—131no—
474C2×C8—131no—
475C2×C8—131no—
476C2×C8—261no—
477C2×C8—261no—
478C2×C8—1041no—
479C2×C8—1041no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—131no—
486C4⋊C4—131no—
487C4⋊C4—261no—
488C4⋊C4C2×C4×D1311yescharacteristic
489C4⋊C4C2×C4×D1311yescharacteristic
490C22⋊C4—261no—
491C22⋊C4—261no—
492C22⋊C4—261no—
493C22⋊C4—261no—
494C42—21no—
495C42—21no—
496C42—21no—
497C42—21no—
498C42C2×C4×D1311yescharacteristic
499C42D4×D1311yescharacteristic
500C42#612911yescharacteristic
501C42C23×D1311yescharacteristic
502C13#1803011yescharacteristic, complemented, Sylow
503C23—261no—
504C23—261no—
505C23#8813511yescharacteristic
506Q8—21no—
507Q8—21no—
508Q8—21no—
509Q8—42no—
510Q8—1041no—
511Q8#8815512yes—
512D4—261no—
513D4—261no—
514D4—261no—
515D4—261no—
516D4—522no—
517D4—1041no—
518D4—1041no—
519D4—1041no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—41no—
529C2×C4—42no—
530C2×C4—42no—
531C2×C4—261no—
532C2×C4—261no—
533C2×C4—521no—
534C2×C4—521no—
535C2×C4—521no—
536C2×C4—521no—
537C2×C4#8813511yescharacteristic
538C2×C4#8813511yescharacteristic
539C2×C4#8813511yescharacteristic
540C2×C4C22×C4×D1311yescharacteristic
541C2×C4C2×D4×D1311yescharacteristic
542C2×C4C2×#612911yescharacteristic
543C8—41no—
544C8—41no—
545C8—41no—
546C8—41no—
547C8—261no—
548C8—261no—
549C8—261no—
550C8—261no—
551C8—261no—
552C8—261no—
553C8—261no—
554C8—261no—
555C8—521no—
556C8—521no—
557C22—21no—
558C22—21no—
559C22—21no—
560C22—521no—
561C22—521no—
562C22—521no—
563C22—521no—
564C22—521no—
565C22—521no—
566C22C2×#8813511yescharacteristic
567C4—21no—
568C4—21no—
569C4—21no—
570C4—21no—
571C4—22no—
572C4—41no—
573C4—41no—
574C4—41no—
575C4—521no—
576C4—521no—
577C4C2×#8815511yescharacteristic
578C4#1171945011yescharacteristic
579C4#1171948311yescharacteristic
580C4#1171948311yescharacteristic
581C2—41no—
582C2—1041no—
583C2—1041no—
584C2#1312355711yescharacteristic
585C2#1312369111yescharacteristic
586C2#1312373511yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC42C23×D13
FittingC13×#1479C2
socleC22×C13C2×C4×D4
prime radical#11719182C22
cosocleC42×C13C24
hypercenter#1479D13
hypocenterC13#18030
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1479

Complements

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

NH ≅ G/Ntype
2. #13123925C2semidirect
4. #13113741C2semidirect
5. #13113723C2semidirect
6. #13113711C2semidirect
7. #13113696C2semidirect
8. #13113676C2semidirect
9. #13113675C2semidirect
10. #13113651C2semidirect
11. #13113633C2semidirect
12. #13113614C2semidirect
14. #13113136C2semidirect
15. C13×#1479C2semidirect
223. #1479D13semidirect
502. C13#18030semidirect

Maximal subgroups

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

subgroupindex
#131248672
#131239252
#131239022
#131137412
#131137232
#131137112
#131136962
#131136762
#131136752
#131136512
#131136332
#131136142
#131133062
#131131362
C13×#14792
#1803013