Finite Group Databasebeta

← #16795231

Subgroups — #16795231

Order 3328.

702 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13131754C211yesmaximal, characteristic
2#13131730C211yesmaximal, characteristic, complemented
3#13130430C211yesmaximal, characteristic, complemented
4#13130429C211yesmaximal, characteristic, complemented
5#13130428C211yesmaximal, characteristic, complemented
6#13130426C211yesmaximal, characteristic, complemented
7#13130423C211yesmaximal, characteristic, complemented
8Q16×#1057C211yesmaximal, characteristic, complemented
9#13130421C211yesmaximal, characteristic, complemented
10#13130420C211yesmaximal, characteristic, complemented
11#13130388C211yesmaximal, characteristic, complemented
12#13130130C211yesmaximal, characteristic
13D13⋊(Q8⋊C8)C211yesmaximal, characteristic, complemented
14#13130034C211yesmaximal, characteristic, complemented
15#13123652C211yesmaximal, characteristic
16C2×#88172C411yescharacteristic
17C4×#6131C2211yescharacteristic
18C4×Q8×D13C2211yescharacteristic
19Q8×#1057C2211yescharacteristic
20Q8×#1057C2211yescharacteristic
21Q8×#1057C2211yescharacteristic
22Q8×#1057C2211yescharacteristic
23#11719074—21no—
24#11719074—21no—
25#11719074C2211yescharacteristic
26#11719074C2211yescharacteristic
27#11719073—21no—
28#11719073—21no—
29#11719073C2211yescharacteristic
30#11719073C2211yescharacteristic
31#11719051—21no—
32#11719051C2211yescharacteristic
33D13⋊(C4⋊C8)—21no—
34D13⋊(C4⋊C8)C2211yescharacteristic
35#11719049—21no—
36#11719049—21no—
37#11719049C2211yescharacteristic
38C4×D13⋊C8C2211yescharacteristic
39C13×#441C411yescharacteristic
40Q16×Dic13C2211yescharacteristic
41#11718691C411yescharacteristic
42#11718687C411yescharacteristic
43#11718522C411yescharacteristic
44#11718513C2211yescharacteristic
45#11718464C411yescharacteristic
46#11718463C411yescharacteristic
47#11718451C2211yescharacteristic
48#11718449C2211yescharacteristic
49#11718371C411yescharacteristic
50#11718368C2211yescharacteristic
51Q8⋊#1057C2211yescharacteristic
52Q8⋊#1057C2211yescharacteristic
53Q8⋊#1057C2211yescharacteristic
54Q8⋊#1057C2211yescharacteristic
55#11718256C2211yescharacteristic
56#11718255C2211yescharacteristic
57#11718254C2211yescharacteristic
58#11718253C2211yescharacteristic
59#11718251C2211yescharacteristic
60#11718251C2211yescharacteristic
61C8×#1057C2211yescharacteristic
62C8×#1057C2211yescharacteristic
63#11718244C2211yescharacteristic
64#11718244C2211yescharacteristic
65#11718243C2211yescharacteristic
66#11718243C2211yescharacteristic
67C2×#6131C2×C411yescharacteristic
68C2×Q8×D13C2×C411yescharacteristic
69C2×D13⋊C8—21no—
70C2×D13⋊C8—21no—
71C2×D13⋊C8—21no—
72C2×D13⋊C8—21no—
73C2×C13×Q16C2×C411yescharacteristic
74C4×Q8×C13C2×C411yescharacteristic
75C4×Q8×C13C2×C411yescharacteristic
76Q8×Dic13C2311yescharacteristic
77Q8×Dic13C2311yescharacteristic
78C2×#6107C2×C411yescharacteristic
79C2×#6106C2×C411yescharacteristic
80#88172C818yescomplemented
81C2×#6095C2×C411yescharacteristic
82C2×#6094C2×C411yescharacteristic
83C2×#6094C2×C411yescharacteristic
84#88147—21no—
85#88147C2311yescharacteristic
86#88146—21no—
87#88146C2×C411yescharacteristic
88C4⋊C4×D13—21no—
89C4⋊C4×D13C2×C411yescharacteristic
90#88141—21no—
91#88141C2311yescharacteristic
92C4×D52—21no—
93C4×D52C2×C411yescharacteristic
94C42×D13—21no—
95C42×D13—21no—
96C42×D13C2311yescharacteristic
97C4×Dic26—21no—
98C4×Dic26C2×C411yescharacteristic
99#88112—21no—
100#88112—21no—
101#88112—21no—
102#88112D411yescharacteristic
103#88112D411yescharacteristic
104#88111—21no—
105#88111—21no—
106#88111—21no—
107#88111D411yescharacteristic
108#88111D411yescharacteristic
109C4⋊#1057—21no—
110C4⋊#1057—21no—
111C4⋊#1057—21no—
112C4⋊#1057—21no—
113C4⋊#1057C2311yescharacteristic
114C4⋊#1057C2311yescharacteristic
115C4⋊#1057C2311yescharacteristic
116C4⋊#1057C2311yescharacteristic
117C4×#1057—21no—
118C4×#1057—21no—
119C4×#1057—21no—
120C4×#1057—21no—
121C4×#1057—21no—
122C4×#1057—21no—
123C4×#1057—21no—
124C4×#1057—21no—
125C4×#1057C2311yescharacteristic
126C4×#1057C2311yescharacteristic
127C4×#1057C2311yescharacteristic
128C4×#1057C2311yescharacteristic
129C13×#106C2×C411yescharacteristic
130C13×#103C2×C411yescharacteristic
131C13×#103C2×C411yescharacteristic
132C13×#97C2×C411yescharacteristic
133#88075C2×C411yescharacteristic
134#88075C2×C411yescharacteristic
135#88061C2×C411yescharacteristic
136#88058C2×C411yescharacteristic
137#88056C2×C411yescharacteristic
138C8×Dic13C2311yescharacteristic
139C8×Dic13C2311yescharacteristic
140#88050C2×C411yescharacteristic
141#88049C2×C411yescharacteristic
142#88048C2×C411yescharacteristic
143#88047C2×C411yescharacteristic
144#88043C2×C411yescharacteristic
145#17853—131nomaximal, Sylow
146C2×Q8×C13C22×C411yescharacteristic
147C2×Q8×C13C22×C411yescharacteristic
148#6131—22no—
149#6131C2×C814yes—
150Q8×D13—22no—
151Q8×D13C2×C814yescomplemented
152C2×D52—21no—
153C2×D52C22×C411yescharacteristic
154C2×C4×D13—21no—
155C2×C4×D13—21no—
156C2×C4×D13—21no—
157C2×C4×D13—21no—
158C2×C4×D13—21no—
159C2×C4×D13C22×C411yescharacteristic
160C2×C4×D13C2×D411yescharacteristic
161C2×C4×D13#4111yescharacteristic
162C2×Dic26—21no—
163C2×Dic26C22×C411yescharacteristic
164C2×#1057—21no—
165C2×#1057—21no—
166C2×#1057—21no—
167C2×#1057—21no—
168C2×#1057—21no—
169C2×#1057—21no—
170C2×#1057C2×D411yescharacteristic
171C2×#1057C2×D411yescharacteristic
172C2×#1057C2×D411yescharacteristic
173C2×#1057C2×D411yescharacteristic
174D13⋊C8—42no—
175D13⋊C8—81no—
176D13⋊C8—81no—
177D13⋊C8—81no—
178C13×Q16C2×C814yescomplemented
179C2×C8×C13C22×C411yescharacteristic
180C2×C8×C13C22×C411yescharacteristic
181C13×C4⋊C4—21no—
182C13×C4⋊C4—21no—
183C13×C4⋊C4C22×C411yescharacteristic
184C13×C4⋊C4C22×C411yescharacteristic
185C42×C13—21no—
186C42×C13—21no—
187C42×C13C22×C411yescharacteristic
188#6107C2×C814yescomplemented
189#6106C2×C814yescomplemented
190#6103—21no—
191#6103—21no—
192#6103—21no—
193C4⋊Dic13—21no—
194C4⋊Dic13—21no—
195C4⋊Dic13C22×C411yescharacteristic
196C4⋊Dic13C22×C411yescharacteristic
197#6101—21no—
198#6101—21no—
199#6101—21no—
200C4×Dic13—21no—
201C4×Dic13—21no—
202C4×Dic13—21no—
203C4×Dic13—21no—
204C4×Dic13—21no—
205C4×Dic13C2×D411yescharacteristic
206C4×Dic13#4111yescharacteristic
207C4×Dic13C2411yescharacteristic
208C2×#1055C22×C411yescharacteristic
209C2×#1055C22×C411yescharacteristic
210#6095C2×C814yescomplemented
211#6094—22no—
212#6094C2×C814yescomplemented
213#2988—131no—
214#2982—131no—
215C4×#137—131no—
216#1579—131no—
217#1579—131no—
218SD16⋊C8—131no—
219SD16⋊C8—131no—
220C8×Q16—131no—
221C8×Q16—131no—
222C8×SD16—131no—
223C8×SD16—131no—
224#1565—131no—
225#1476—131no—
226C2×Q8⋊C8—131no—
227C8×M16—131no—
228C22×D13—21no—
229C22×D13C4×D411yescharacteristic
230Q8×C13—21no—
231Q8×C13—21no—
232Q8×C13C22×C812yes—
233Q8×C13C22×C812yes—
234C2×C4×C13—21no—
235C2×C4×C13—21no—
236C2×C4×C13—21no—
237C2×C4×C13—21no—
238C2×C4×C13C4×D411yescharacteristic
239C2×C4×C13C4×D411yescharacteristic
240C2×C4×C13C23×C411yescharacteristic
241C2×Dic13—21no—
242C2×Dic13—21no—
243C2×Dic13—21no—
244C2×Dic13C4×D411yescharacteristic
245C2×Dic13C22×D411yescharacteristic
246C2×Dic13C2×#4111yescharacteristic
247D52—24no—
248D52—21no—
249D52C22×C812yes—
250C4×D13—24no—
251C4×D13—21no—
252C4×D13—21no—
253C4×D13—24no—
254C4×D13—41no—
255C4×D13—41no—
256C4×D13—41no—
257C4×D13—81no—
258C4×D13—81no—
259C4×D13C22×C812yes—
260C4×D13#13112yes—
261Dic26—21no—
262Dic26—24no—
263Dic26C22×C812yes—
264#1057—22no—
265#1057—21no—
266#1057—21no—
267#1057—21no—
268#1057—21no—
269#1057—41no—
270#1057—41no—
271#1057—41no—
272#1057—41no—
273#1057—41no—
274C8×C13—21no—
275C8×C13C22×C812yes—
276#1055—21no—
277#1055C22×C812yes—
278C2×#137—131no—
279C4×#41—131no—
280C2×C4×Q8—131no—
281C8×Q8—131no—
282C8×Q8—131no—
283C8×Q8—131no—
284C8×Q8—131no—
285C8×Q8—131no—
286C8×Q8—131no—
287C8×Q8—261no—
288C8×Q8—261no—
289#441—131no—
290#441#26111yescharacteristic
291#440—131no—
292#440—131no—
293C4×Q16—131no—
294C4×Q16—131no—
295C4×SD16—131no—
296C4×SD16—131no—
297C8×D4—131no—
298C8×D4—131no—
299C8×D4—261no—
300C8×D4—261no—
301#431—131no—
302#431—131no—
303#431—261no—
304#431—261no—
305#431—261no—
306#428—131no—
307C2×C4⋊C8—131no—
308C2×C4⋊C8—261no—
309#419—131no—
310#417—131no—
311C4×M16—131no—
312C2×C4×C8—131no—
313#335—131no—
314#335—131no—
315#334—131no—
316#334—131no—
317Q8⋊C8—131no—
318Q8⋊C8—131no—
319Q8⋊C8—131no—
320Q8⋊C8—131no—
321Q8⋊C8—131no—
322Q8⋊C8—131no—
323D4⋊C8—131no—
324D4⋊C8—131no—
325#322—131no—
326#322—131no—
327C82—131no—
328C82—131no—
329C22×C13C2×C4×D411yescharacteristic
330C2×D13—21no—
331C2×D13—21no—
332C2×D13—22no—
333C2×D13—41no—
334C2×D13—41no—
335C2×D13C8×D412yes—
336C4×C13—22no—
337C4×C13—22no—
338C4×C13—21no—
339C4×C13—21no—
340C4×C13—41no—
341C4×C13—41no—
342C4×C13C23×C811yescharacteristic
343C4×C13C2×#13111yescharacteristic
344Dic13—22no—
345Dic13—21no—
346Dic13—41no—
347Dic13—41no—
348Dic13C8×D412yes—
349Dic13#57711yescharacteristic
350Dic13#57811yescharacteristic
351C2×#41—131no—
352C22×Q8—131no—
353#137—138no—
354C2×Q16—131no—
355C2×Q16C2×#26111yescharacteristic
356C2×SD16—131no—
357C2×SD16—131no—
358C2×M16—131no—
359C2×M16—131no—
360C22×C8—261no—
361C22×C8—261no—
362C22×C8—261no—
363C22×C8—261no—
364C4×Q8—131no—
365C4×Q8—131no—
366C4×Q8—131no—
367C4×Q8—131no—
368C4×Q8—261no—
369C4×Q8—261no—
370C4×Q8C2×#26111yescharacteristic
371C4×Q8C2×#26111yescharacteristic
372C4×D4—131no—
373C4×D4—131no—
374C4×D4—261no—
375C4×D4—261no—
376#117—131no—
377#117—261no—
378C2×C4⋊C4—131no—
379C2×C4⋊C4—261no—
380C2×C42—131no—
381C2×C42—261no—
382C2×C42—261no—
383#107—131no—
384#107—131no—
385#106—131no—
386#106C2×#26111yescharacteristic
387C4⋊C8—131no—
388C4⋊C8—131no—
389C4⋊C8—131no—
390C4⋊C8—131no—
391C4⋊C8—131no—
392C4⋊C8—131no—
393C4⋊C8—261no—
394C4⋊C8—261no—
395C4⋊C8—261no—
396C4⋊C8—261no—
397C4⋊C8—261no—
398C4⋊C8—261no—
399C4⋊C8—261no—
400#103—131no—
401#103—131no—
402#103—131no—
403#103—131no—
404#103C2×#26111yescharacteristic
405#103C2×#26111yescharacteristic
406#102—131no—
407#102—131no—
408C22⋊C8—131no—
409C22⋊C8—131no—
410C22⋊C8—261no—
411C22⋊C8—261no—
412C22⋊C8—261no—
413#97—131no—
414#97C2×#26111yescharacteristic
415C4×C8—131no—
416C4×C8—131no—
417C4×C8—131no—
418C4×C8—131no—
419C4×C8—131no—
420C4×C8—131no—
421C4×C8—261no—
422C4×C8—261no—
423C4×C8—261no—
424C4×C8—261no—
425C4×C8—261no—
426C4×C8—261no—
427C4×C8—261no—
428C4×C8—261no—
429C2×C13C2×C8×D411yescharacteristic
430C2×C13#294711yescharacteristic
431C2×C13#295611yescharacteristic
432D13—22no—
433D13—42no—
434#41—134no—
435#41—262no—
436C2×Q8—134no—
437C2×Q8—131no—
438C2×Q8—261no—
439C2×Q8—262no—
440C2×Q8C22×#26111yescharacteristic
441C2×Q8C22×#26111yescharacteristic
442C2×D4—131no—
443C2×D4—261no—
444C22×C4—131no—
445C22×C4—131no—
446C22×C4—131no—
447C22×C4—261no—
448C22×C4—261no—
449C22×C4—261no—
450C22×C4—261no—
451C22×C4—261no—
452Q16—134no—
453Q16D13⋊C814yescomplemented
454SD16—134no—
455SD16—134no—
456M16—134no—
457M16—262no—
458C2×C8—131no—
459C2×C8—131no—
460C2×C8—131no—
461C2×C8—131no—
462C2×C8—131no—
463C2×C8—131no—
464C2×C8—261no—
465C2×C8—261no—
466C2×C8—261no—
467C2×C8—261no—
468C2×C8—261no—
469C2×C8—261no—
470C2×C8—522no—
471C2×C8—1041no—
472C2×C8—1041no—
473C2×C8—1041no—
474C2×C8C22×#26111yescharacteristic
475C2×C8C22×#26111yescharacteristic
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—131no—
479C4⋊C4—131no—
480C4⋊C4—261no—
481C4⋊C4—261no—
482C4⋊C4—261no—
483C4⋊C4—261no—
484C4⋊C4—261no—
485C4⋊C4C22×#26111yescharacteristic
486C4⋊C4C22×#26111yescharacteristic
487C22⋊C4—261no—
488C22⋊C4—261no—
489C22⋊C4—261no—
490C42—21no—
491C42—21no—
492C42—131no—
493C42—131no—
494C42—131no—
495C42—261no—
496C42—261no—
497C42—261no—
498C42—261no—
499C42—261no—
500C42C22×#26111yescharacteristic
501C13#1785311yescharacteristic, complemented, Sylow
502C23—131no—
503C23—261no—
504Q8—21no—
505Q8—21no—
506Q8—132no—
507Q8—264no—
508Q8—261no—
509Q8C2×D13⋊C812yes—
510Q8C2×D13⋊C812yes—
511D4—132no—
512D4—264no—
513D4—261no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—131no—
519C2×C4—131no—
520C2×C4—132no—
521C2×C4—132no—
522C2×C4—131no—
523C2×C4—261no—
524C2×C4—261no—
525C2×C4—264no—
526C2×C4—264no—
527C2×C4—261no—
528C2×C4—261no—
529C2×C4—261no—
530C2×C4—521no—
531C2×C4—521no—
532C2×C4—521no—
533C2×C4—1041no—
534C2×C4—1041no—
535C2×C4D4×#26111yescharacteristic
536C2×C4D4×#26111yescharacteristic
537C2×C4C23×#26111yescharacteristic
538C8—21no—
539C8—132no—
540C8—261no—
541C8—261no—
542C8—261no—
543C8—261no—
544C8—262no—
545C8—261no—
546C8—521no—
547C8—521no—
548C8—521no—
549C8—521no—
550C8—521no—
551C8C2×D13⋊C812yes—
552C22—132no—
553C22—261no—
554C22—261no—
555C22—262no—
556C22—521no—
557C22—521no—
558C22C2×D4×#26111yescharacteristic
559C4—22no—
560C4—22no—
561C4—21no—
562C4—21no—
563C4—41no—
564C4—41no—
565C4—132no—
566C4—131no—
567C4—131no—
568C4—262no—
569C4—261no—
570C4—521no—
571C4—521no—
572C4C22×D13⋊C811yescharacteristic
573C4D13⋊#13111yescharacteristic
574C2—262no—
575C2—522no—
576C2D4×D13⋊C811yescharacteristic
577C2#1313159411yescharacteristic
578C2#1313161111yescharacteristic
subgroupG/H
centerC22C2×D4×#261
commutatorC4×C13C23×C8
FrattiniC2×C4C23×#261
FittingC13×#441C4
socleC22×C13C2×C4×D4
prime radicalC2×#6131C2×C4
cosocleC4×Dic13C24
hypercenter#441#261
hypocenterC13#17853
LCSG ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #441

Complements

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

NH ≅ G/Ntype
2. #13131730C2semidirect
3. #13130430C2semidirect
4. #13130429C2semidirect
5. #13130428C2semidirect
6. #13130426C2semidirect
7. #13130423C2semidirect
8. Q16×#1057C2semidirect
9. #13130421C2semidirect
10. #13130420C2semidirect
11. #13130388C2semidirect
13. D13⋊(Q8⋊C8)C2semidirect
14. #13130034C2semidirect
80. #88172C8semidirect
151. Q8×D13C2×C8semidirect
178. C13×Q16C2×C8semidirect
188. #6107C2×C8semidirect
189. #6106C2×C8semidirect
210. #6095C2×C8semidirect
212. #6094C2×C8semidirect
453. Q16D13⋊C8semidirect
501. C13#17853semidirect

Maximal subgroups

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

subgroupindex
#131317542
#131317302
#131304302
#131304292
#131304282
#131304262
#131304232
Q16×#10572
#131304212
#131304202
#131303882
#131301302
D13⋊(Q8⋊C8)2
#131300342
#131236522
#1785313