Finite Group Databasebeta

← #15833982

Subgroups — #15833982

Order 3328.

670 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13124887C211yesmaximal, characteristic
2#13123839C211yesmaximal, characteristic, complemented
3#13123572C211yesmaximal, characteristic, complemented
4#13113739C211yesmaximal, characteristic, complemented
5#13113719C211yesmaximal, characteristic, complemented
6#13113703C211yesmaximal, characteristic, complemented
7#13113696C211yesmaximal, characteristic, complemented
8#13113667C211yesmaximal, characteristic, complemented
9#13113659C211yesmaximal, characteristic, complemented
10C8×#6106C211yesmaximal, characteristic, complemented
11#13113623C211yesmaximal, characteristic, complemented
12#13113300C211yesmaximal, characteristic, complemented
13#13113225C211yesmaximal, characteristic, complemented
14#13113134C211yesmaximal, characteristic, complemented
15C13×#1583C211yesmaximal, characteristic, complemented
16C2×M16×D13—21no—
17#11719285C2211yescharacteristic
18C4×D4×D13C2211yescharacteristic
19C8×Q8×C13C2211yescharacteristic, complemented
20C4×C13×SD16C2211yescharacteristic
21C13×#436C2211yescharacteristic
22#11718830C411yescharacteristic
23#11718826C411yescharacteristic
24#11718788—21no—
25C4×#6106C2211yescharacteristic
26#11718685C2211yescharacteristic, complemented
27C4×#6104C2211yescharacteristic
28#11718673C2211yescharacteristic
29#11718532C411yescharacteristic
30#11718524C411yescharacteristic
31#11718501—21no—
32#11718498C2211yescharacteristic
33#11718497—21no—
34#11718495C2211yescharacteristic
35#11718495C2211yescharacteristic, complemented
36#11718494C2211yescharacteristic
37#11718480C411yescharacteristic
38#11718470C411yescharacteristic
39#11718434C411yescharacteristic
40#11718427C411yescharacteristic
41#11718389—21no—
42#11718387—21no—
43C4×D104C2211yescharacteristic
44#11718350—21no—
45#11718349—21no—
46#11718349C2211yescharacteristic, complemented
47C4×#6094C2211yescharacteristic
48C8×D52C2211yescharacteristic
49#11718346C2211yescharacteristic
50#11718346C2211yescharacteristic
51C13×#334C2211yescharacteristic, complemented
52C13×Q8⋊C8C2211yescharacteristic, complemented
53C13×D4⋊C8C2211yescharacteristic
54C13×#322C2211yescharacteristic, complemented
55Q8⋊#1055C2211yescharacteristic, complemented
56D4⋊#1055C2211yescharacteristic
57#11718075C2211yescharacteristic
58#11718075C2211yescharacteristic, complemented
59#11718072C2211yescharacteristic, complemented
60#11718071C2211yescharacteristic, complemented
61#11718051C2211yescharacteristic
62#11718051C2211yescharacteristic, complemented
63#11718050C2211yescharacteristic, complemented
64#11718047C2211yescharacteristic, complemented
65#11718047C2211yescharacteristic, complemented
66C8×#1055C2211yescharacteristic, complemented
67C2×D4×D13C2×C411yescharacteristic
68C22×C4×D13—21no—
69C2×C13×SD16C2×C411yescharacteristic
70C2×C13×M16—21no—
71C4×Q8×C13C2311yescharacteristic
72C4×D4×C13C2311yescharacteristic
73#88201C2×C411yescharacteristic
74#88200C2×C411yescharacteristic
75C2×#6106C2×C411yescharacteristic
76D4×Dic13C2×C411yescharacteristic
77C2×#6104C2×C411yescharacteristic
78C4×C22⋊D13—21no—
79C2×#6099—21no—
80M16×D13—44no—
81C2×D104C2×C411yescharacteristic
82C2×#6094—21no—
83C2×#6094—21no—
84C2×#6094D411yescharacteristic
85C2×#6094D411yescharacteristic
86C2×C8×D13—21no—
87C2×C8×D13—21no—
88C2×C8×D13—21no—
89#88152—21no—
90#88149C2×C411yescharacteristic
91#88148—21no—
92#88147C2×C411yescharacteristic
93C4⋊C4×D13C2×C411yescharacteristic
94#88144C2×C411yescharacteristic
95#88135—21no—
96C22⋊C4×D13—21no—
97C4×D52—21no—
98C4×D52C2311yescharacteristic
99C4×D52C2311yescharacteristic
100#88126—21no—
101C42×D13C2311yescharacteristic
102C13×#106C2×C411yescharacteristic
103C13×C4⋊C8—21no—
104C13×C4⋊C8C2311yescharacteristic
105C13×C4⋊C8C2311yescharacteristic
106C13×#103C2×C411yescharacteristic
107C13×#102C2×C411yescharacteristic
108C13×C22⋊C8—21no—
109C4×C8×C13—21no—
110C4×C8×C13C2311yescharacteristic
111C4×C8×C13C2311yescharacteristic
112C4×C8×C13C2311yescharacteristic
113#88075C2×C411yescharacteristic
114#88072C2×C411yescharacteristic
115C22⋊#1055—21no—
116#88061C2×C411yescharacteristic
117#88061C2×C411yescharacteristic
118#88060—21no—
119#88060—21no—
120#88060—21no—
121#88060—21no—
122#88060—21no—
123#88060—21no—
124#88060C2×C411yescharacteristic
125#88060C2×C411yescharacteristic
126#88058C2×C411yescharacteristic
127#88055D411yescharacteristic
128#88055D411yescharacteristic
129#88054—21no—
130#88054—21no—
131#88054C2×C411yescharacteristic
132#88054C2×C411yescharacteristic
133C8×Dic13—21no—
134#88049C2×C411yescharacteristic
135#88049C2×C411yescharacteristic
136#88048C2×C411yescharacteristic
137#88047C2×C411yescharacteristic
138C4⋊#1055—21no—
139C4⋊#1055C2311yescharacteristic
140C4⋊#1055C2311yescharacteristic
141#88043—21no—
142C4×#1055C2311yescharacteristic
143C4×#1055C2311yescharacteristic
144C4×#1055C2311yescharacteristic
145#18008—131nomaximal, Sylow
146C23×D13—21no—
147C2×Q8×C13C22×C411yescharacteristic
148C2×D4×C13C22×C411yescharacteristic
149C22×C4×C13—21no—
150C2×C22⋊D13—21no—
151C22×Dic13—21no—
152D4×D13—22no—
153D4×D13—41no—
154C2×D52—21no—
155C2×D52C22×C411yescharacteristic
156C2×D52C22×C411yescharacteristic
157C2×C4×D13—21no—
158C2×C4×D13—21no—
159C2×C4×D13—21no—
160C2×C4×D13—21no—
161C2×C4×D13—42no—
162C2×C4×D13—42no—
163C2×C4×D13C22×C411yescharacteristic
164C2×C4×D13C2×D411yescharacteristic
165C2×C4×D13#4111yescharacteristic
166C13×SD16—41no—
167C13×M16—42no—
168C2×C8×C13—21no—
169C2×C8×C13—21no—
170C2×C8×C13—21no—
171C2×C8×C13C22×C411yescharacteristic
172C2×C8×C13C22×C411yescharacteristic
173C2×C8×C13C2×D411yescharacteristic
174C2×C8×C13C2×D411yescharacteristic
175C13×C4⋊C4—21no—
176C13×C4⋊C4C22×C411yescharacteristic
177C13×C4⋊C4C22×C411yescharacteristic
178C13×C22⋊C4—21no—
179C42×C13—21no—
180C42×C13C2411yescharacteristic
181C22⋊Dic13—21no—
182#6106—22no—
183#6104—41no—
184#6103—21no—
185#6103—21no—
186#6103—21no—
187#6103—21no—
188#6103—21no—
189#6103—21no—
190#6103—21no—
191C4⋊Dic13—21no—
192C4⋊Dic13C22×C411yescharacteristic
193C4⋊Dic13C22×C411yescharacteristic
194#6101—21no—
195#6101—21no—
196#6101—21no—
197C4×Dic13C22×C411yescharacteristic
198C4×Dic13C2×D411yescharacteristic
199C4×Dic13#4111yescharacteristic
200#6099—42no—
201C2×#1055—21no—
202C2×#1055—21no—
203C2×#1055—21no—
204C2×#1055C22×C411yescharacteristic
205C2×#1055C22×C411yescharacteristic
206C2×#1055C2×D411yescharacteristic
207C2×#1055C2×D411yescharacteristic
208D104—22no—
209#6094—22no—
210#6094—41no—
211#6094—42no—
212#6094—42no—
213C8×D13—42no—
214C8×D13—42no—
215C8×D13—42no—
216#3105—131no—
217#2969—131no—
218D4×M16—131no—
219#1592—131no—
220#1589—131no—
221#1586—131no—
222#1585—131no—
223#1583D1311yescharacteristic, complemented
224#1581—131no—
225#1580—131no—
226C8×SD16—131no—
227#1574—131no—
228#1495—131no—
229#1478—131no—
230#1453—131no—
231C23×C13—21no—
232C22×D13—21no—
233C22×D13—21no—
234C22×D13—42no—
235C22×D13—42no—
236C22×D13—81no—
237C22×D13C4×D411yescharacteristic
238Q8×C13—21no—
239Q8×C13—21no—
240D4×C13—21no—
241D4×C13—21no—
242C2×C4×C13—21no—
243C2×C4×C13—21no—
244C2×C4×C13—21no—
245C2×C4×C13—41no—
246C2×C4×C13—41no—
247C2×C4×C13C23×C411yescharacteristic
248C2×C4×C13C22×D411yescharacteristic
249C2×C4×C13C2×#4111yescharacteristic
250C22⋊D13—42no—
251C2×Dic13—21no—
252C2×Dic13—21no—
253C2×Dic13—42no—
254C2×Dic13C4×D411yescharacteristic
255C2×Dic13C4×D411yescharacteristic
256C2×Dic13C4×D411yescharacteristic
257D52—21no—
258D52—21no—
259D52—21no—
260D52—81no—
261D52#13112yes—
262C4×D13—21no—
263C4×D13—21no—
264C4×D13—21no—
265C4×D13—21no—
266C4×D13—41no—
267C4×D13—42no—
268C4×D13—42no—
269C4×D13—41no—
270C4×D13—41no—
271C4×D13—41no—
272C4×D13—41no—
273C8×C13—21no—
274C8×C13—21no—
275C8×C13—21no—
276C8×C13—41no—
277C8×C13—41no—
278C8×C13—41no—
279C8×C13AGL(1,ℤ/8)12yes—
280#1055—21no—
281#1055—21no—
282#1055—21no—
283#1055—21no—
284#1055—41no—
285#1055—41no—
286#1055—41no—
287C22×M16—261no—
288#529—131no—
289C2×C4×D4—131no—
290#484—131no—
291#481—131no—
292#478—131no—
293#478—131no—
294#463—131no—
295#463—131no—
296#450—131no—
297#447—131no—
298#446—131no—
299C8×Q8C2×D1311yescharacteristic, complemented
300C4×SD16—131no—
301C4×SD16C2×D1311yescharacteristic
302C4×D8—131no—
303C4×D8—131no—
304#436—131no—
305#436—131no—
306#436—261no—
307#436C2×D1311yescharacteristic
308#435—261no—
309#435—261no—
310#435—261no—
311C8×D4—131no—
312C8×D4—131no—
313C8×D4—131no—
314#433—261no—
315#431—131no—
316#431—131no—
317#431—131no—
318#423—131no—
319#407—261no—
320#405—261no—
321C4×M16—131no—
322#335—131no—
323#335—131no—
324#334—131no—
325#334C2×D1311yescharacteristic, complemented
326Q8⋊C8—131no—
327Q8⋊C8C2×D1311yescharacteristic, complemented
328D4⋊C8—131no—
329D4⋊C8—131no—
330D4⋊C8—131no—
331D4⋊C8—131no—
332D4⋊C8—131no—
333D4⋊C8C2×D1311yescharacteristic
334#322—131no—
335#322—131no—
336#322C2×D1311yescharacteristic, complemented
337C82—131no—
338C22×C13—41no—
339C22×C13—41no—
340C22×C13—41no—
341C22×C13C2×C4×D411yescharacteristic
342C2×D13—21no—
343C2×D13—22no—
344C2×D13—21no—
345C2×D13—21no—
346C2×D13—41no—
347C2×D13—41no—
348C2×D13—41no—
349C2×D13—41no—
350C2×D13—41no—
351C2×D13—84no—
352C4×C13—21no—
353C4×C13—41no—
354C4×C13—41no—
355C4×C13—41no—
356C4×C13C2×#13111yescharacteristic
357C4×C13#56811yescharacteristic
358C4×C13C2×AGL(1,ℤ/8)11yescharacteristic
359C4×C13#57511yescharacteristic
360Dic13—21no—
361Dic13—21no—
362Dic13—21no—
363Dic13—41no—
364Dic13—41no—
365C22×D4—131no—
366C23×C4—261no—
367C2×SD16—131no—
368C2×SD16C4×D1311yescharacteristic
369C2×D8—131no—
370C2×D8—131no—
371C2×M16—21no—
372C2×M16—131no—
373C2×M16—131no—
374C2×M16—261no—
375C2×M16—261no—
376C2×M16—261no—
377C2×M16—524no—
378C22×C8—261no—
379C22×C8—261no—
380C22×C8—261no—
381#126—261no—
382#125—131no—
383#124—131no—
384#123—261no—
385C22⋊Q8—131no—
386#121—131no—
387C4×Q8C22×D1311yescharacteristic
388C4×D4—131no—
389C4×D4—131no—
390C4×D4—131no—
391C4×D4—131no—
392C4×D4—261no—
393C4×D4—261no—
394C4×D4—261no—
395C4×D4C22×D1311yescharacteristic
396#117—261no—
397C2×C4⋊C4—131no—
398C2×C22⋊C4—261no—
399C2×C42—131no—
400#107—131no—
401#107—131no—
402#106—131no—
403#106C4×D1311yescharacteristic
404C4⋊C8—21no—
405C4⋊C8—131no—
406C4⋊C8—131no—
407C4⋊C8—131no—
408C4⋊C8—131no—
409C4⋊C8—261no—
410C4⋊C8—261no—
411C4⋊C8—261no—
412C4⋊C8C22×D1311yescharacteristic
413C4⋊C8C22×D1311yescharacteristic
414#103—131no—
415#103C4×D1311yescharacteristic
416#102—131no—
417#102—131no—
418#102—131no—
419#102—131no—
420#102—131no—
421#102C4×D1311yescharacteristic
422C22⋊C8—21no—
423C22⋊C8—131no—
424C22⋊C8—131no—
425C22⋊C8—261no—
426C22⋊C8—261no—
427C22⋊C8—261no—
428C22⋊C8—261no—
429C22⋊C8—261no—
430C22⋊C8—261no—
431C22⋊C8—261no—
432#97—131no—
433#97—131no—
434#97—261no—
435C4×C8—21no—
436C4×C8—131no—
437C4×C8—131no—
438C4×C8—131no—
439C4×C8—261no—
440C4×C8C22×D1311yescharacteristic
441C4×C8C22×D1311yescharacteristic
442C4×C8C22×D1311yescharacteristic
443C2×C13—81no—
444C2×C13#293311yescharacteristic
445C2×C13C4×AGL(1,ℤ/8)11yescharacteristic
446C2×C13#295711yescharacteristic
447D13—41no—
448D13—42no—
449D13—81no—
450C24—261no—
451C2×Q8C2×C4×D1311yescharacteristic
452C2×D4—131no—
453C2×D4—131no—
454C2×D4—261no—
455C2×D4—261no—
456C2×D4—262no—
457C2×D4—521no—
458C2×D4C2×C4×D1311yescharacteristic
459C22×C4—21no—
460C22×C4—131no—
461C22×C4—131no—
462C22×C4—131no—
463C22×C4—261no—
464C22×C4—261no—
465C22×C4—261no—
466C22×C4—261no—
467C22×C4—261no—
468C22×C4—522no—
469C22×C4—522no—
470SD16—41no—
471SD16—262no—
472D8—262no—
473D8—521no—
474M16—42no—
475M16—262no—
476M16—521no—
477M16—522no—
478M16—522no—
479M16—522no—
480C2×C8—21no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—131no—
484C2×C8—131no—
485C2×C8—131no—
486C2×C8—131no—
487C2×C8—261no—
488C2×C8—261no—
489C2×C8—261no—
490C2×C8—522no—
491C2×C8—522no—
492C2×C8—522no—
493C2×C8C2×C4×D1311yescharacteristic
494C2×C8C2×C4×D1311yescharacteristic
495C2×C8D4×D1311yescharacteristic
496C2×C8D4×D1311yescharacteristic
497C4⋊C4—21no—
498C4⋊C4—131no—
499C4⋊C4—131no—
500C4⋊C4—261no—
501C4⋊C4—261no—
502C4⋊C4—261no—
503C4⋊C4—261no—
504C4⋊C4C2×C4×D1311yescharacteristic
505C4⋊C4C2×C4×D1311yescharacteristic
506C22⋊C4—21no—
507C22⋊C4—261no—
508C22⋊C4—261no—
509C22⋊C4—261no—
510C22⋊C4—261no—
511C22⋊C4—261no—
512C22⋊C4—261no—
513C22⋊C4—261no—
514C22⋊C4—261no—
515C42—21no—
516C42—131no—
517C42—131no—
518C42—131no—
519C42C23×D1311yescharacteristic
520C13#1800811yescharacteristic, complemented, Sylow
521C23—21no—
522C23—131no—
523C23—261no—
524C23—261no—
525C23—522no—
526C23—522no—
527C23—1041no—
528Q8—21no—
529Q8—21no—
530D4—21no—
531D4—21no—
532D4—132no—
533D4—261no—
534D4—261no—
535D4—261no—
536D4—522no—
537D4—1041no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—131no—
544C2×C4—131no—
545C2×C4—131no—
546C2×C4—261no—
547C2×C4—261no—
548C2×C4—261no—
549C2×C4—261no—
550C2×C4—261no—
551C2×C4—261no—
552C2×C4—521no—
553C2×C4—522no—
554C2×C4—522no—
555C2×C4—522no—
556C2×C4—521no—
557C2×C4—521no—
558C2×C4—521no—
559C2×C4—521no—
560C2×C4C22×C4×D1311yescharacteristic
561C2×C4C2×D4×D1311yescharacteristic
562C2×C4#41×D1311yescharacteristic
563C8—21no—
564C8—21no—
565C8—21no—
566C8—41no—
567C8—41no—
568C8—41no—
569C8—261no—
570C8—261no—
571C8—261no—
572C8—261no—
573C8—521no—
574C8—521no—
575C8—521no—
576C8#8816812yes—
577C22—41no—
578C22—41no—
579C22—41no—
580C22—261no—
581C22—261no—
582C22—261no—
583C22—262no—
584C22—521no—
585C22—521no—
586C22—521no—
587C22—521no—
588C22—521no—
589C22—1044no—
590C22C4×D4×D1311yescharacteristic
591C4—21no—
592C4—41no—
593C4—41no—
594C4—41no—
595C4—261no—
596C4—261no—
597C4—261no—
598C4—521no—
599C4—521no—
600C4#1171945011yescharacteristic
601C4D13×#13111yescharacteristic
602C4C2×#8816811yescharacteristic
603C4#1171947311yescharacteristic
604C2—81no—
605C2—521no—
606C2—522no—
607C2—1041no—
608C2#1312355911yescharacteristic
609C2C4×#8816811yescharacteristic
610C2#1312375011yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC42C23×D13
FittingC13×#1583C2
socleC22×C13C2×C4×D4
prime radical#11718434C4
cosocleC42×C13C24
hypercenter#1583D13
hypocenterC13#18008
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1583

Complements

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

NH ≅ G/Ntype
2. #13123839C2semidirect
3. #13123572C2semidirect
4. #13113739C2semidirect
5. #13113719C2semidirect
6. #13113703C2semidirect
7. #13113696C2semidirect
8. #13113667C2semidirect
9. #13113659C2semidirect
10. C8×#6106C2semidirect
11. #13113623C2semidirect
12. #13113300C2semidirect
13. #13113225C2semidirect
14. #13113134C2semidirect
15. C13×#1583C2semidirect
19. C8×Q8×C13C22semidirect
26. #11718685C22semidirect
35. #11718495C22semidirect
46. #11718349C22semidirect
51. C13×#334C22semidirect
52. C13×Q8⋊C8C22semidirect
54. C13×#322C22semidirect
55. Q8⋊#1055C22semidirect
58. #11718075C22semidirect
59. #11718072C22semidirect
60. #11718071C22semidirect
62. #11718051C22semidirect
63. #11718050C22semidirect
64. #11718047C22semidirect
65. #11718047C22semidirect
66. C8×#1055C22semidirect
223. #1583D13semidirect
299. C8×Q8C2×D13semidirect
325. #334C2×D13semidirect
327. Q8⋊C8C2×D13semidirect
336. #322C2×D13semidirect
520. C13#18008semidirect

Maximal subgroups

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

subgroupindex
#131248872
#131238392
#131235722
#131137392
#131137192
#131137032
#131136962
#131136672
#131136592
C8×#61062
#131136232
#131133002
#131132252
#131131342
C13×#15832
#1800813