Finite Group Databasebeta

← #15832928

Subgroups — #15832928

Order 3328.

712 conjugacy classes of subgroups.

The subgroup lattice has 614 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13124887C211yesmaximal, characteristic
2#13123813C211yesmaximal, characteristic, complemented
3C8×D4×D13C211yesmaximal, characteristic, complemented
4#13113675C211yesmaximal, characteristic, complemented
5#13113673C211yesmaximal, characteristic, complemented
6#13113664C211yesmaximal, characteristic, complemented
7#13113662C211yesmaximal, characteristic, complemented
8#13113661C211yesmaximal, characteristic, complemented
9#13113658C211yesmaximal, characteristic, complemented
10#13113646C211yesmaximal, characteristic, complemented
11#13113620C211yesmaximal, characteristic, complemented
12#13113277C211yesmaximal, characteristic, complemented
13#13113248C211yesmaximal, characteristic, complemented
14#13113124C211yesmaximal, characteristic, complemented
15C13×SD16⋊C8C211yesmaximal, characteristic, complemented
16C22×C8×D13—21no—
17#11719285C2211yescharacteristic
18C4×D4×D13C2211yescharacteristic
19C8×Q8×C13C2211yescharacteristic, complemented
20C4×C13×SD16C2211yescharacteristic
21C8×D4×C13C2211yescharacteristic
22#11718830C411yescharacteristic
23#11718826C411yescharacteristic
24C8×C22⋊D13—21no—
25C4×#6106C2211yescharacteristic
26#11718685C2211yescharacteristic, complemented
27C4×#6104C2211yescharacteristic
28D4×#1055C2211yescharacteristic
29#11718532C411yescharacteristic
30#11718524C411yescharacteristic
31#11718501—21no—
32#11718499C2211yescharacteristic, complemented
33#11718497—21no—
34#11718496C2211yescharacteristic
35#11718495C2211yescharacteristic
36D13×C4⋊C8C2211yescharacteristic
37#11718480C411yescharacteristic
38#11718470C411yescharacteristic
39#11718434C411yescharacteristic
40#11718427C411yescharacteristic
41#11718386—21no—
42D13×C22⋊C8—21no—
43C4×D104C2211yescharacteristic
44#11718350—21no—
45C4×#6094C2211yescharacteristic
46C8×D52—21no—
47C8×D52C2211yescharacteristic
48C8×D52C2211yescharacteristic, complemented
49#11718346C2211yescharacteristic
50C4×C8×D13C2211yescharacteristic
51C13×#335C2211yescharacteristic, 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#11718049C2211yescharacteristic, complemented
64#11718046C2211yescharacteristic, complemented
65#11718046C2211yescharacteristic, complemented
66#11718046C2211yescharacteristic, complemented
67C2×D4×D13C2×C411yescharacteristic
68C22×C4×D13—21no—
69C2×C13×SD16C2×C411yescharacteristic
70C22×C8×C13—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—
79C22×#1055—21no—
80C2×D104C2×C411yescharacteristic
81C2×#6094—21no—
82C2×#6094—21no—
83C2×C8×D13—21no—
84C2×C8×D13—21no—
85C2×C8×D13—21no—
86C2×C8×D13—21no—
87C2×C8×D13—44no—
88C2×C8×D13D411yescharacteristic
89C2×C8×D13D411yescharacteristic
90#88152—21no—
91#88149C2×C411yescharacteristic
92#88148—21no—
93#88147C2×C411yescharacteristic
94C4⋊C4×D13C2×C411yescharacteristic
95#88144C2×C411yescharacteristic
96#88135—21no—
97C22⋊C4×D13—21no—
98C4×D52—21no—
99C4×D52C2311yescharacteristic
100C4×D52C2311yescharacteristic
101#88126—21no—
102C42×D13C2311yescharacteristic
103C13×#106C2×C411yescharacteristic
104C13×C4⋊C8—21no—
105C13×C4⋊C8C2311yescharacteristic
106C13×C4⋊C8C2311yescharacteristic
107C13×#103C2×C411yescharacteristic
108C13×#102C2×C411yescharacteristic
109C13×C22⋊C8—21no—
110C4×C8×C13—21no—
111C4×C8×C13C2311yescharacteristic
112C4×C8×C13C2311yescharacteristic
113C4×C8×C13C2311yescharacteristic
114#88075C2×C411yescharacteristic
115#88072C2×C411yescharacteristic
116C22⋊#1055—21no—
117#88061C2×C411yescharacteristic
118#88061C2×C411yescharacteristic
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#88055—21no—
128#88055—21no—
129#88054—21no—
130#88054C2×C411yescharacteristic
131#88054C2×C411yescharacteristic
132C8×Dic13D411yescharacteristic
133C8×Dic13D411yescharacteristic
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#17914—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—22no—
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—22no—
167C2×C8×C13—21no—
168C2×C8×C13—21no—
169C2×C8×C13—21no—
170C2×C8×C13—42no—
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—22no—
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
200C2×#1055—21no—
201C2×#1055—21no—
202C2×#1055—21no—
203C2×#1055—42no—
204C2×#1055C22×C411yescharacteristic
205C2×#1055C22×C411yescharacteristic
206C2×#1055C2×D411yescharacteristic
207C2×#1055C2×D411yescharacteristic
208D104—22no—
209#6094—42no—
210#6094—42no—
211C8×D13—22no—
212C8×D13—41no—
213C8×D13—42no—
214C8×D13—42no—
215C8×D13—42no—
216C8×D13—42no—
217#3105—131no—
218#2966—131no—
219C2×C8×D4—131no—
220#1582—131no—
221#1582—131no—
222#1581—131no—
223#1581—131no—
224#1580—131no—
225#1580—131no—
226SD16⋊C8—131no—
227SD16⋊C8D1311yescharacteristic, complemented
228#1573—131no—
229#1490—131no—
230#1483—131no—
231#1451—131no—
232C23×C13—21no—
233C22×D13—24no—
234C22×D13—21no—
235C22×D13—21no—
236C22×D13—42no—
237C22×D13—42no—
238C22×D13C4×D411yescharacteristic
239Q8×C13—21no—
240Q8×C13—21no—
241D4×C13—21no—
242D4×C13#13112yes—
243C2×C4×C13—21no—
244C2×C4×C13—21no—
245C2×C4×C13—21no—
246C2×C4×C13—41no—
247C2×C4×C13—41no—
248C2×C4×C13C23×C411yescharacteristic
249C2×C4×C13C22×D411yescharacteristic
250C2×C4×C13C2×#4111yescharacteristic
251C22⋊D13—24no—
252C2×Dic13—21no—
253C2×Dic13—21no—
254C2×Dic13—42no—
255C2×Dic13C4×D411yescharacteristic
256C2×Dic13C4×D411yescharacteristic
257C2×Dic13C4×D411yescharacteristic
258D52—21no—
259D52—21no—
260D52—21no—
261D52—42no—
262D52#13112yes—
263C4×D13—22no—
264C4×D13—21no—
265C4×D13—21no—
266C4×D13—21no—
267C4×D13—21no—
268C4×D13—42no—
269C4×D13—42no—
270C4×D13—41no—
271C4×D13—41no—
272C4×D13—41no—
273C4×D13—41no—
274C8×C13—21no—
275C8×C13—21no—
276C8×C13—21no—
277C8×C13—21no—
278C8×C13—41no—
279C8×C13—41no—
280C8×C13—41no—
281#1055—21no—
282#1055—21no—
283#1055—21no—
284#1055—41no—
285#1055—41no—
286#1055—41no—
287#1055AGL(1,ℤ/8)12yes—
288C23×C8—261no—
289#529—131no—
290C2×C4×D4—131no—
291#484—131no—
292#481—131no—
293#478—131no—
294#478—131no—
295#463—131no—
296#463—131no—
297#450—131no—
298#447—131no—
299#446—131no—
300C8×Q8C2×D1311yescharacteristic, complemented
301C4×SD16—131no—
302C4×SD16C2×D1311yescharacteristic
303C4×D8—131no—
304C4×D8—131no—
305#436—131no—
306#435—261no—
307C8×D4—131no—
308C8×D4—131no—
309C8×D4—131no—
310C8×D4—131no—
311C8×D4—261no—
312C8×D4—261no—
313C8×D4—261no—
314C8×D4C2×D1311yescharacteristic
315#433—261no—
316#432—131no—
317#431—131no—
318C2×C4⋊C8—131no—
319C2×C22⋊C8—261no—
320#405—261no—
321C4×M16—131no—
322C2×C4×C8—131no—
323#335—131no—
324#335C2×D1311yescharacteristic, complemented
325#334—131no—
326#334—131no—
327Q8⋊C8—131no—
328Q8⋊C8C2×D1311yescharacteristic, complemented
329D4⋊C8—131no—
330D4⋊C8—131no—
331D4⋊C8—131no—
332D4⋊C8—131no—
333D4⋊C8—131no—
334D4⋊C8C2×D1311yescharacteristic
335#322—131no—
336#322—131no—
337#322—131no—
338#322C2×D1311yescharacteristic, complemented
339C22×C13—22no—
340C22×C13—41no—
341C22×C13—41no—
342C22×C13C2×C4×D411yescharacteristic
343C2×D13—21no—
344C2×D13—21no—
345C2×D13—22no—
346C2×D13—48no—
347C2×D13—41no—
348C2×D13—41no—
349C2×D13—41no—
350C2×D13—41no—
351C2×D13—41no—
352C2×D13#44412yes—
353C4×C13—21no—
354C4×C13—41no—
355C4×C13—41no—
356C4×C13—41no—
357C4×C13C2×#13111yescharacteristic
358C4×C13C2×#13111yescharacteristic
359C4×C13C2×AGL(1,ℤ/8)11yescharacteristic
360C4×C13#57511yescharacteristic
361Dic13—21no—
362Dic13—21no—
363Dic13—21no—
364Dic13—41no—
365Dic13—41no—
366C22×D4—131no—
367C23×C4—261no—
368C2×SD16—131no—
369C2×SD16C4×D1311yescharacteristic
370C2×D8—131no—
371C2×D8—131no—
372C2×M16—261no—
373C2×M16—261no—
374C22×C8—21no—
375C22×C8—131no—
376C22×C8—131no—
377C22×C8—261no—
378C22×C8—261no—
379C22×C8—261no—
380C22×C8—261no—
381C22×C8—261no—
382C22×C8—524no—
383#126—261no—
384#125—131no—
385#124—131no—
386#123—261no—
387C22⋊Q8—131no—
388#121—131no—
389C4×Q8C22×D1311yescharacteristic
390C4×D4—131no—
391C4×D4—131no—
392C4×D4—131no—
393C4×D4—131no—
394C4×D4—261no—
395C4×D4—261no—
396C4×D4—261no—
397C4×D4C22×D1311yescharacteristic
398#117—261no—
399C2×C4⋊C4—131no—
400C2×C22⋊C4—261no—
401C2×C42—131no—
402#107—131no—
403#107—131no—
404#106—131no—
405#106C4×D1311yescharacteristic
406C4⋊C8—21no—
407C4⋊C8—131no—
408C4⋊C8—131no—
409C4⋊C8—131no—
410C4⋊C8—131no—
411C4⋊C8—261no—
412C4⋊C8—261no—
413C4⋊C8C22×D1311yescharacteristic
414C4⋊C8C22×D1311yescharacteristic
415#103—131no—
416#103C4×D1311yescharacteristic
417#102—131no—
418#102—131no—
419#102—131no—
420#102—131no—
421#102—131no—
422#102C4×D1311yescharacteristic
423C22⋊C8—21no—
424C22⋊C8—131no—
425C22⋊C8—131no—
426C22⋊C8—261no—
427C22⋊C8—261no—
428C22⋊C8—261no—
429C22⋊C8—261no—
430C22⋊C8—261no—
431C22⋊C8—261no—
432#97—261no—
433#97—261no—
434#97—261no—
435C4×C8—21no—
436C4×C8—131no—
437C4×C8—131no—
438C4×C8—131no—
439C4×C8—131no—
440C4×C8—131no—
441C4×C8C22×D1311yescharacteristic
442C4×C8C22×D1311yescharacteristic
443C4×C8C22×D1311yescharacteristic
444C2×C13—42no—
445C2×C13#292911yescharacteristic
446C2×C13C4×AGL(1,ℤ/8)11yescharacteristic
447C2×C13C2×#44411yescharacteristic
448D13—22no—
449D13—42no—
450D13—81no—
451C24—261no—
452C2×Q8C2×C4×D1311yescharacteristic
453C2×D4—131no—
454C2×D4—131no—
455C2×D4—261no—
456C2×D4—261no—
457C2×D4—262no—
458C2×D4—262no—
459C2×D4C2×C4×D1311yescharacteristic
460C22×C4—21no—
461C22×C4—131no—
462C22×C4—131no—
463C22×C4—131no—
464C22×C4—261no—
465C22×C4—261no—
466C22×C4—261no—
467C22×C4—261no—
468C22×C4—261no—
469C22×C4—522no—
470C22×C4—522no—
471SD16—22no—
472SD16—262no—
473D8—262no—
474D8—262no—
475M16—522no—
476M16—522no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—21no—
480C2×C8—42no—
481C2×C8—131no—
482C2×C8—131no—
483C2×C8—131no—
484C2×C8—131no—
485C2×C8—262no—
486C2×C8—261no—
487C2×C8—261no—
488C2×C8—261no—
489C2×C8—521no—
490C2×C8—522no—
491C2×C8—522no—
492C2×C8—522no—
493C2×C8—522no—
494C2×C8—522no—
495C2×C8C2×C4×D1311yescharacteristic
496C2×C8C2×C4×D1311yescharacteristic
497C2×C8D4×D1311yescharacteristic
498C2×C8D4×D1311yescharacteristic
499C4⋊C4—21no—
500C4⋊C4—131no—
501C4⋊C4—131no—
502C4⋊C4—261no—
503C4⋊C4—261no—
504C4⋊C4—261no—
505C4⋊C4—261no—
506C4⋊C4C2×C4×D1311yescharacteristic
507C4⋊C4C2×C4×D1311yescharacteristic
508C22⋊C4—21no—
509C22⋊C4—261no—
510C22⋊C4—261no—
511C22⋊C4—261no—
512C22⋊C4—261no—
513C22⋊C4—261no—
514C22⋊C4—261no—
515C22⋊C4—261no—
516C22⋊C4—261no—
517C42—21no—
518C42—131no—
519C42—131no—
520C42—131no—
521C42C23×D1311yescharacteristic
522C13#1791411yescharacteristic, complemented, Sylow
523C23—21no—
524C23—131no—
525C23—264no—
526C23—261no—
527C23—261no—
528C23—522no—
529C23—522no—
530Q8—21no—
531Q8—21no—
532D4—21no—
533D4—132no—
534D4—264no—
535D4—261no—
536D4—261no—
537D4—261no—
538D4—522no—
539D4#8815512yes—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—131no—
546C2×C4—131no—
547C2×C4—131no—
548C2×C4—262no—
549C2×C4—261no—
550C2×C4—261no—
551C2×C4—261no—
552C2×C4—261no—
553C2×C4—261no—
554C2×C4—261no—
555C2×C4—522no—
556C2×C4—522no—
557C2×C4—522no—
558C2×C4—521no—
559C2×C4—521no—
560C2×C4—521no—
561C2×C4—521no—
562C2×C4C22×C4×D1311yescharacteristic
563C2×C4C2×D4×D1311yescharacteristic
564C2×C4#41×D1311yescharacteristic
565C8—21no—
566C8—21no—
567C8—21no—
568C8—21no—
569C8—41no—
570C8—41no—
571C8—41no—
572C8—132no—
573C8—261no—
574C8—261no—
575C8—261no—
576C8—521no—
577C8—521no—
578C8—521no—
579C22—22no—
580C22—41no—
581C22—41no—
582C22—132no—
583C22—261no—
584C22—261no—
585C22—262no—
586C22—528no—
587C22—521no—
588C22—521no—
589C22—521no—
590C22—521no—
591C22—521no—
592C22C4×D4×D1311yescharacteristic
593C4—21no—
594C4—41no—
595C4—41no—
596C4—41no—
597C4—261no—
598C4—261no—
599C4—261no—
600C4—521no—
601C4—521no—
602C4C2×#8815511yescharacteristic
603C4D13×#13111yescharacteristic
604C4D13×AGL(1,ℤ/8)11yescharacteristic
605C4#1171948211yescharacteristic
606C2—42no—
607C2—262no—
608C2—522no—
609C2—1041no—
610C2#1312352511yescharacteristic
611C2#1312364111yescharacteristic
612C2D13×#44411yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC42C23×D13
FittingC13×SD16⋊C8C2
socleC22×C13C2×C4×D4
prime radical#11718434C4
cosocleC42×C13C24
hypercenterSD16⋊C8D13
hypocenterC13#17914
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ SD16⋊C8

Complements

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

NH ≅ G/Ntype
2. #13123813C2semidirect
3. C8×D4×D13C2semidirect
4. #13113675C2semidirect
5. #13113673C2semidirect
6. #13113664C2semidirect
7. #13113662C2semidirect
8. #13113661C2semidirect
9. #13113658C2semidirect
10. #13113646C2semidirect
11. #13113620C2semidirect
12. #13113277C2semidirect
13. #13113248C2semidirect
14. #13113124C2semidirect
15. C13×SD16⋊C8C2semidirect
19. C8×Q8×C13C22semidirect
26. #11718685C22semidirect
32. #11718499C22semidirect
48. C8×D52C22semidirect
51. C13×#335C22semidirect
52. C13×Q8⋊C8C22semidirect
54. C13×#322C22semidirect
55. Q8⋊#1055C22semidirect
58. #11718075C22semidirect
59. #11718072C22semidirect
60. #11718071C22semidirect
62. #11718051C22semidirect
63. #11718049C22semidirect
64. #11718046C22semidirect
65. #11718046C22semidirect
66. #11718046C22semidirect
227. SD16⋊C8D13semidirect
300. C8×Q8C2×D13semidirect
324. #335C2×D13semidirect
328. Q8⋊C8C2×D13semidirect
338. #322C2×D13semidirect
522. C13#17914semidirect

Maximal subgroups

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

subgroupindex
#131248872
#131238132
C8×D4×D132
#131136752
#131136732
#131136642
#131136622
#131136612
#131136582
#131136462
#131136202
#131132772
#131132482
#131131242
C13×SD16⋊C82
#1791413