Finite Group Databasebeta

← #15834363

Subgroups — #15834363

Order 3328.

654 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13123855C211yesmaximal, characteristic, complemented
2#13123844C211yesmaximal, characteristic, complemented
3C4×#88170C211yesmaximal, characteristic
4#13113728C211yesmaximal, characteristic, complemented
5#13113725C211yesmaximal, characteristic, complemented
6#13113686C211yesmaximal, characteristic, complemented
7#13113683C211yesmaximal, characteristic, complemented
8#13113665C211yesmaximal, characteristic, complemented
9#13113662C211yesmaximal, characteristic, complemented
10SD16×#1055C211yesmaximal, characteristic, complemented
11#13113596C211yesmaximal, characteristic, complemented
12#13113269C211yesmaximal, characteristic, complemented
13#13113267C211yesmaximal, characteristic, complemented
14C8×#6094C211yesmaximal, characteristic, complemented
15C8×C13×SD16C211yesmaximal, characteristic, complemented
16C2×#88170C411yescharacteristic
17C4×#6131C2211yescharacteristic
18C4×#6129C2211yescharacteristic
19C8×Q8×C13C2211yescharacteristic
20C4×C13×SD16C2211yescharacteristic
21C8×D4×C13C2211yescharacteristic
22SD16×Dic13C411yescharacteristic
23#11718772—21no—
24C2×#88055—21no—
25C4×#6107C2211yescharacteristic
26Q8×#1055C2211yescharacteristic
27C4×#6104C2211yescharacteristic
28D4×#1055C2211yescharacteristic
29#11718521C411yescharacteristic
30#11718513C411yescharacteristic
31#11718499—21no—
32#11718499C2211yescharacteristic
33#11718496—21no—
34#11718496C2211yescharacteristic
35#11718496C2211yescharacteristic
36#11718492C2211yescharacteristic
37#11718465C411yescharacteristic
38#11718451C411yescharacteristic
39#11718433C411yescharacteristic
40#11718417C411yescharacteristic
41#11718391—21no—
42#11718380—21no—
43C4×#6095C2211yescharacteristic
44#11718349—21no—
45#11718349C2211yescharacteristic
46C4×#6094—21no—
47C4×#6094C2211yescharacteristic
48#11718346C2211yescharacteristic
49C4×C8×D13C2211yescharacteristic
50#11718340C2211yescharacteristic
51C13×#334C2211yescharacteristic
52C13×Q8⋊C8C2211yescharacteristic
53C13×D4⋊C8C2211yescharacteristic
54C82×C13C2211yescharacteristic
55Q8⋊#1055C2211yescharacteristic
56D4⋊#1055C2211yescharacteristic
57#11718076C2211yescharacteristic
58#11718075C2211yescharacteristic
59#11718071C2211yescharacteristic
60#11718071C2211yescharacteristic
61#11718051C2211yescharacteristic
62#11718049C2211yescharacteristic
63#11718048C2211yescharacteristic
64#11718047C2211yescharacteristic
65#11718046C2211yescharacteristic
66C8×#1055C2211yescharacteristic
67C2×#6131C2×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×#6104C2×C411yescharacteristic
77C4×C22⋊D13—21no—
78C2×C4×Dic13—21no—
79C22×#1055—21no—
80#88170—24no—
81C2×#6095C2×C411yescharacteristic
82C2×#6094—21no—
83C2×#6094—21no—
84C2×#6094D411yescharacteristic
85C2×#6094D411yescharacteristic
86C2×C8×D13C2×C411yescharacteristic
87C2×C8×D13C2×C411yescharacteristic
88#88147—21no—
89#88147C2×C411yescharacteristic
90#88146—21no—
91#88146C2×C411yescharacteristic
92#88146C2×C411yescharacteristic
93#88141C2×C411yescharacteristic
94#88135—21no—
95#88131—21no—
96C4×D52—21no—
97C4×D52C2311yescharacteristic
98C42×D13—21no—
99C42×D13C2311yescharacteristic
100C4×Dic26C2311yescharacteristic
101C13×#106C2×C411yescharacteristic
102C13×C4⋊C8—21no—
103C13×C4⋊C8C2311yescharacteristic
104C13×C4⋊C8C2311yescharacteristic
105C13×#103C2×C411yescharacteristic
106C13×#102C2×C411yescharacteristic
107C13×C22⋊C8—21no—
108C4×C8×C13—21no—
109C4×C8×C13C2311yescharacteristic
110C4×C8×C13C2311yescharacteristic
111C4×C8×C13C2311yescharacteristic
112#88075C2×C411yescharacteristic
113#88072C2×C411yescharacteristic
114C22⋊#1055—21no—
115#88061C2×C411yescharacteristic
116#88060—21no—
117#88060—21no—
118#88060—21no—
119#88060—21no—
120#88060—21no—
121#88057C2×C411yescharacteristic
122#88056C2×C411yescharacteristic
123#88055—21no—
124#88055—21no—
125#88055—21no—
126#88055—21no—
127#88055D411yescharacteristic
128#88055D411yescharacteristic
129#88054—21no—
130#88054—21no—
131#88054—21no—
132C8×Dic13C2×C411yescharacteristic
133C8×Dic13C2×C411yescharacteristic
134#88050C2×C411yescharacteristic
135#88049C2×C411yescharacteristic
136#88047C2×C411yescharacteristic
137#88047C2×C411yescharacteristic
138C4⋊#1055—21no—
139C4⋊#1055C2311yescharacteristic
140C4⋊#1055C2311yescharacteristic
141C4×#1055—21no—
142C4×#1055C2311yescharacteristic
143C4×#1055C2311yescharacteristic
144C4×#1055C2311yescharacteristic
145#18037—131nomaximal, Sylow
146C2×Q8×C13C22×C411yescharacteristic
147C2×D4×C13C22×C411yescharacteristic
148C22×C4×C13—21no—
149C2×C22⋊D13—21no—
150C22×Dic13—21no—
151C22×Dic13—21no—
152#6131—22no—
153#6131—41no—
154#6129—22no—
155#6129—41no—
156C2×D52—21no—
157C2×D52C22×C411yescharacteristic
158C2×C4×D13—21no—
159C2×C4×D13—21no—
160C2×C4×D13—21no—
161C2×C4×D13C22×C411yescharacteristic
162C2×C4×D13C2×D411yescharacteristic
163C2×C4×D13#4111yescharacteristic
164C2×Dic26C22×C411yescharacteristic
165C13×SD16M1614yescomplemented
166C2×C8×C13—21no—
167C2×C8×C13—21no—
168C2×C8×C13—21no—
169C2×C8×C13—42no—
170C2×C8×C13C22×C411yescharacteristic
171C2×C8×C13C22×C411yescharacteristic
172C2×C8×C13C2×D411yescharacteristic
173C2×C8×C13C2×D411yescharacteristic
174C13×C4⋊C4—21no—
175C13×C4⋊C4C22×C411yescharacteristic
176C13×C4⋊C4C22×C411yescharacteristic
177C13×C22⋊C4—21no—
178C42×C13—21no—
179C42×C13C2411yescharacteristic
180C22⋊Dic13—21no—
181#6107—22no—
182#6104—22no—
183#6103—21no—
184#6103—21no—
185#6103—21no—
186#6103—21no—
187C4⋊Dic13—21no—
188C4⋊Dic13C22×C411yescharacteristic
189C4⋊Dic13C22×C411yescharacteristic
190#6101—21no—
191#6101—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—42no—
204C2×#1055C22×C411yescharacteristic
205C2×#1055C22×C411yescharacteristic
206C2×#1055C2×D411yescharacteristic
207C2×#1055C2×D411yescharacteristic
208#6095—22no—
209#6094—22no—
210#6094—22no—
211#6094—42no—
212#6094—42no—
213C8×D13—22no—
214C8×D13—41no—
215#2971—131no—
216#2970—131no—
217C4×#135—131no—
218#1590—131no—
219#1590—131no—
220#1584—131no—
221#1584—131no—
222#1581—131no—
223#1581—131no—
224C8×SD16—131no—
225C8×SD16D1311yescharacteristic, complemented
226#1568—131no—
227#1488—131no—
228#1488—131no—
229C8×M16—131no—
230C23×C13—21no—
231C22×D13—21no—
232C22×D13C4×D411yescharacteristic
233Q8×C13—21no—
234Q8×C13C2×M1612yes—
235D4×C13—21no—
236D4×C13C2×M1612yes—
237C2×C4×C13—21no—
238C2×C4×C13—21no—
239C2×C4×C13—21no—
240C2×C4×C13—41no—
241C2×C4×C13—41no—
242C2×C4×C13C23×C411yescharacteristic
243C2×C4×C13C22×D411yescharacteristic
244C2×C4×C13C2×#4111yescharacteristic
245C22⋊D13—42no—
246C2×Dic13—21no—
247C2×Dic13—21no—
248C2×Dic13—21no—
249C2×Dic13—42no—
250C2×Dic13—81no—
251C2×Dic13C4×D411yescharacteristic
252C2×Dic13C4×D411yescharacteristic
253C2×Dic13C4×D411yescharacteristic
254D52—21no—
255D52—21no—
256D52—42no—
257C4×D13—21no—
258C4×D13—21no—
259C4×D13—21no—
260C4×D13—21no—
261C4×D13—41no—
262C4×D13—42no—
263C4×D13—41no—
264C4×D13—41no—
265C4×D13—81no—
266Dic26—21no—
267Dic26—21no—
268C8×C13—21no—
269C8×C13—21no—
270C8×C13—41no—
271C8×C13—41no—
272C8×C13—41no—
273C8×C13C2×M1612yes—
274C8×C13#13512yescomplemented
275#1055—21no—
276#1055—21no—
277#1055—21no—
278#1055—41no—
279#1055—41no—
280#1055—41no—
281#1055#13512yescomplemented
282C2×#135—131no—
283C4×#41—131no—
284C4×#41—131no—
285#446—131no—
286#446—131no—
287C8×Q8—131no—
288C8×Q8C2×D1311yescharacteristic
289C4×Q16—131no—
290C4×Q16—131no—
291C4×SD16—131no—
292C4×SD16—131no—
293C4×SD16—131no—
294C4×SD16C2×D1311yescharacteristic
295C4×D8—131no—
296C4×D8—131no—
297#436—131no—
298#436—131no—
299#436—261no—
300#436—261no—
301#435—261no—
302#435—261no—
303C8×D4—131no—
304C8×D4C2×D1311yescharacteristic
305#432—131no—
306#432—131no—
307#432—261no—
308#432—261no—
309#431—131no—
310#427—131no—
311#416—131no—
312#416—131no—
313C4×M16—131no—
314C4×M16—261no—
315C2×#97—261no—
316C2×C4×C8—131no—
317#335—131no—
318#335—131no—
319#334—131no—
320#334C2×D1311yescharacteristic
321Q8⋊C8—131no—
322Q8⋊C8—131no—
323Q8⋊C8—131no—
324Q8⋊C8C2×D1311yescharacteristic
325D4⋊C8—131no—
326D4⋊C8—131no—
327D4⋊C8—131no—
328D4⋊C8C2×D1311yescharacteristic
329#322—131no—
330#322—131no—
331C82—131no—
332C82C2×D1311yescharacteristic
333C22×C13—22no—
334C22×C13—41no—
335C22×C13—41no—
336C22×C13C2×C4×D411yescharacteristic
337C2×D13—21no—
338C2×D13—21no—
339C2×D13—21no—
340C2×D13—41no—
341C2×D13—41no—
342C2×D13—41no—
343C4×C13—22no—
344C4×C13—21no—
345C4×C13—41no—
346C4×C13—41no—
347C4×C13C22×M1611yescharacteristic
348C4×C13#56811yescharacteristic
349C4×C13C2×#13511yescharacteristic
350C4×C13C2×#13511yescharacteristic
351Dic13—21no—
352Dic13—21no—
353Dic13—21no—
354Dic13—41no—
355Dic13—41no—
356Dic13—41no—
357C2×#41—131no—
358C2×#41—131no—
359#135—264no—
360C2×Q16—131no—
361C2×SD16—131no—
362C2×SD16C4×D1311yescharacteristic
363C2×D8—131no—
364C2×M16—131no—
365C2×M16—131no—
366C2×M16—261no—
367C2×M16—261no—
368C22×C8—21no—
369C22×C8—131no—
370C22×C8—131no—
371C22×C8—261no—
372C4×Q8—131no—
373C4×Q8—131no—
374C4×Q8—131no—
375C4×Q8C22×D1311yescharacteristic
376C4×D4—131no—
377C4×D4—131no—
378C4×D4—131no—
379C4×D4—261no—
380C4×D4—261no—
381C4×D4—261no—
382C4×D4—261no—
383C4×D4C22×D1311yescharacteristic
384#117—131no—
385#117—131no—
386#117—261no—
387#117—261no—
388C2×C42—131no—
389C2×C42—261no—
390C2×C42—261no—
391#107—131no—
392#107—131no—
393#106—131no—
394#106C4×D1311yescharacteristic
395C4⋊C8—21no—
396C4⋊C8—131no—
397C4⋊C8—131no—
398C4⋊C8—261no—
399C4⋊C8—261no—
400C4⋊C8—261no—
401C4⋊C8—261no—
402C4⋊C8C22×D1311yescharacteristic
403C4⋊C8C22×D1311yescharacteristic
404#103—131no—
405#103—131no—
406#103—131no—
407#103C4×D1311yescharacteristic
408#102—131no—
409#102—131no—
410#102—131no—
411#102C4×D1311yescharacteristic
412C22⋊C8—21no—
413C22⋊C8—261no—
414C22⋊C8—261no—
415C22⋊C8—261no—
416C22⋊C8—261no—
417C22⋊C8—261no—
418C22⋊C8—261no—
419#97—131no—
420#97—131no—
421#97—261no—
422#97—261no—
423#97—261no—
424#97—261no—
425C4×C8—21no—
426C4×C8—131no—
427C4×C8—131no—
428C4×C8—131no—
429C4×C8—131no—
430C4×C8—131no—
431C4×C8—261no—
432C4×C8C22×D1311yescharacteristic
433C4×C8C22×D1311yescharacteristic
434C4×C8C22×D1311yescharacteristic
435C2×C13—42no—
436C2×C13D4×M1611yescharacteristic
437C2×C13C4×#13511yescharacteristic
438C2×C13#295711yescharacteristic
439D13—41no—
440D13—81no—
441#41—262no—
442#41—262no—
443#41—521no—
444#41—521no—
445C2×Q8—131no—
446C2×Q8C2×C4×D1311yescharacteristic
447C2×D4—131no—
448C2×D4—261no—
449C2×D4—261no—
450C2×D4C2×C4×D1311yescharacteristic
451C22×C4—21no—
452C22×C4—131no—
453C22×C4—131no—
454C22×C4—131no—
455C22×C4—261no—
456C22×C4—261no—
457C22×C4—261no—
458C22×C4—261no—
459C22×C4—261no—
460Q16—262no—
461SD16—262no—
462SD16#609414yescomplemented
463D8—262no—
464M16—262no—
465M16—262no—
466M16—522no—
467M16—522no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—42no—
472C2×C8—131no—
473C2×C8—131no—
474C2×C8—131no—
475C2×C8—131no—
476C2×C8—262no—
477C2×C8—261no—
478C2×C8—261no—
479C2×C8—261no—
480C2×C8—521no—
481C2×C8—522no—
482C2×C8C2×C4×D1311yescharacteristic
483C2×C8C2×C4×D1311yescharacteristic
484C2×C8D4×D1311yescharacteristic
485C2×C8D4×D1311yescharacteristic
486C4⋊C4—21no—
487C4⋊C4—131no—
488C4⋊C4—131no—
489C4⋊C4—261no—
490C4⋊C4—261no—
491C4⋊C4—261no—
492C4⋊C4C2×C4×D1311yescharacteristic
493C4⋊C4C2×C4×D1311yescharacteristic
494C22⋊C4—21no—
495C22⋊C4—261no—
496C22⋊C4—261no—
497C22⋊C4—261no—
498C22⋊C4—261no—
499C22⋊C4—261no—
500C42—21no—
501C42—131no—
502C42—131no—
503C42—131no—
504C42—261no—
505C42—261no—
506C42—261no—
507C42—261no—
508C42—261no—
509C42C23×D1311yescharacteristic
510C13#1803711yescharacteristic, complemented, Sylow
511C23—21no—
512C23—131no—
513C23—261no—
514Q8—21no—
515Q8—261no—
516Q8—261no—
517Q8C2×#609412yes—
518D4—21no—
519D4—261no—
520D4—261no—
521D4—522no—
522D4—522no—
523D4C2×#609412yes—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—131no—
530C2×C4—131no—
531C2×C4—131no—
532C2×C4—261no—
533C2×C4—261no—
534C2×C4—261no—
535C2×C4—261no—
536C2×C4—261no—
537C2×C4—261no—
538C2×C4—261no—
539C2×C4—521no—
540C2×C4—522no—
541C2×C4—522no—
542C2×C4—521no—
543C2×C4—521no—
544C2×C4—1041no—
545C2×C4—1041no—
546C2×C4C22×C4×D1311yescharacteristic
547C2×C4C2×D4×D1311yescharacteristic
548C2×C4#41×D1311yescharacteristic
549C8—21no—
550C8—21no—
551C8—41no—
552C8—41no—
553C8—41no—
554C8—132no—
555C8—261no—
556C8—261no—
557C8—261no—
558C8—521no—
559C8—521no—
560C8—521no—
561C8C2×#609412yes—
562C8#8817012yescomplemented
563C22—22no—
564C22—41no—
565C22—41no—
566C22—261no—
567C22—261no—
568C22—261no—
569C22—521no—
570C22—521no—
571C22—521no—
572C22C4×D4×D1311yescharacteristic
573C4—21no—
574C4—22no—
575C4—41no—
576C4—41no—
577C4—261no—
578C4—261no—
579C4—261no—
580C4—521no—
581C4—521no—
582C4—521no—
583C4C22×#609411yescharacteristic
584C4#1171945511yescharacteristic
585C4C2×#8817011yescharacteristic
586C4D13×#13511yescharacteristic
587C2—42no—
588C2—521no—
589C2—1041no—
590C2D4×#609411yescharacteristic
591C2C4×#8817011yescharacteristic
592C2#1312374811yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC42C23×D13
FittingC8×C13×SD16C2
socleC22×C13C2×C4×D4
prime radicalC2×#88170C4
cosocleC42×C13C24
hypercenterC8×SD16D13
hypocenterC13#18037
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ C8×SD16

Complements

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

NH ≅ G/Ntype
1. #13123855C2semidirect
2. #13123844C2semidirect
4. #13113728C2semidirect
5. #13113725C2semidirect
6. #13113686C2semidirect
7. #13113683C2semidirect
8. #13113665C2semidirect
9. #13113662C2semidirect
10. SD16×#1055C2semidirect
11. #13113596C2semidirect
12. #13113269C2semidirect
13. #13113267C2semidirect
14. C8×#6094C2semidirect
15. C8×C13×SD16C2semidirect
165. C13×SD16M16semidirect
225. C8×SD16D13semidirect
274. C8×C13#135semidirect
281. #1055#135semidirect
462. SD16#6094semidirect
510. C13#18037semidirect
562. C8#88170semidirect

Maximal subgroups

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

subgroupindex
#131238552
#131238442
C4×#881702
#131137282
#131137252
#131136862
#131136832
#131136652
#131136622
SD16×#10552
#131135962
#131132692
#131132672
C8×#60942
C8×C13×SD162
#1803713