Finite Group Databasebeta

← #16795225

Subgroups — #16795225

Order 3328.

754 conjugacy classes of subgroups.

The subgroup lattice has 622 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13131754C211yesmaximal, characteristic, complemented
2#13131684C211yesmaximal, characteristic, complemented
3#13130434C211yesmaximal, characteristic, complemented
4#13130433C211yesmaximal, characteristic, complemented
5#13130426C211yesmaximal, characteristic, complemented
6SD16⋊#1057C211yesmaximal, characteristic, complemented
7#13130420C211yesmaximal, characteristic, complemented
8SD16×#1057C211yesmaximal, characteristic, complemented
9#13130417C211yesmaximal, characteristic, complemented
10#13130416C211yesmaximal, characteristic, complemented
11#13130388C211yesmaximal, characteristic, complemented
12#13130130C211yesmaximal, characteristic, complemented
13D13⋊(D4⋊C8)C211yesmaximal, characteristic, complemented
14#13130034C211yesmaximal, characteristic, complemented
15#13123641C211yesmaximal, characteristic
16C2×#88168C411yescharacteristic
17C4×#6131C2211yescharacteristic
18C4×D4×D13C2211yescharacteristic
19Q8×#1057C2211yescharacteristic, complemented
20Q8×#1057C2211yescharacteristic, complemented
21D4×#1057C2211yescharacteristic
22D4×#1057C2211yescharacteristic
23D13⋊(C22⋊C8)—21no—
24C2×#88111—21no—
25#11719073—21no—
26#11719073—21no—
27#11719073C2211yescharacteristic
28#11719073C2211yescharacteristic
29#11719073C2211yescharacteristic, complemented
30#11719073C2211yescharacteristic, complemented
31#11719063—21no—
32#11719063—21no—
33#11719051C2211yescharacteristic
34D13⋊(C4⋊C8)—21no—
35D13⋊(C4⋊C8)C2211yescharacteristic
36#11719049—21no—
37#11719049C2211yescharacteristic
38C4×D13⋊C8C2211yescharacteristic
39C13×#440C411yescharacteristic
40SD16×Dic13C2211yescharacteristic
41#11718687C411yescharacteristic
42#11718675C411yescharacteristic
43#11718542C411yescharacteristic
44#11718533C2211yescharacteristic
45#11718464C411yescharacteristic
46#11718449C2211yescharacteristic
47#11718431C411yescharacteristic
48#11718417C2211yescharacteristic
49#11718372C411yescharacteristic
50#11718368C2211yescharacteristic
51Q8⋊#1057C2211yescharacteristic, complemented
52Q8⋊#1057C2211yescharacteristic, complemented
53D4⋊#1057C2211yescharacteristic
54D4⋊#1057C2211yescharacteristic
55#11718256C2211yescharacteristic, complemented
56#11718255C2211yescharacteristic, complemented
57#11718254C2211yescharacteristic, complemented
58#11718253C2211yescharacteristic, complemented
59#11718251C2211yescharacteristic, complemented
60#11718251C2211yescharacteristic, complemented
61C8×#1057C2211yescharacteristic, complemented
62C8×#1057C2211yescharacteristic, complemented
63#11718243C2211yescharacteristic
64#11718243C2211yescharacteristic
65#11718243C2211yescharacteristic, complemented
66#11718243C2211yescharacteristic, complemented
67C2×#6131C2×C411yescharacteristic
68C2×D4×D13C2×C411yescharacteristic
69C22×C4×D13—21no—
70C22×#1057—21no—
71C22×#1057—21no—
72C2×D13⋊C8—21no—
73C2×D13⋊C8—21no—
74C2×D13⋊C8—21no—
75C2×D13⋊C8—21no—
76C2×D13⋊C8—21no—
77C2×D13⋊C8—21no—
78C2×C13×SD16C2×C411yescharacteristic
79C4×Q8×C13C2×C411yescharacteristic
80C4×D4×C13C2×C411yescharacteristic
81Q8×Dic13C2311yescharacteristic
82C2×#6106C2×C411yescharacteristic
83D4×Dic13C2311yescharacteristic
84C2×#6104C2×C411yescharacteristic
85C4×C22⋊D13—21no—
86#88168C818yescomplemented
87C2×D104C2×C411yescharacteristic
88C2×#6094C2×C411yescharacteristic
89C2×#6094C2×C411yescharacteristic
90#88147—21no—
91#88147C2311yescharacteristic
92#88147C2311yescharacteristic
93#88146—21no—
94#88146C2×C411yescharacteristic
95C4⋊C4×D13C2×C411yescharacteristic
96#88135—21no—
97C22⋊C4×D13—21no—
98C4×D52—21no—
99C4×D52C2×C411yescharacteristic
100C4×D52C2×C411yescharacteristic
101C42×D13—21no—
102C42×D13C2311yescharacteristic
103C22⋊#1057—21no—
104C22⋊#1057—21no—
105#88112—21no—
106#88112D411yescharacteristic
107#88112D411yescharacteristic
108#88111—21no—
109#88111—21no—
110#88111—21no—
111#88111—21no—
112#88111—21no—
113#88111D411yescharacteristic
114#88111D411yescharacteristic
115C4⋊#1057—21no—
116C4⋊#1057—21no—
117C4⋊#1057C2311yescharacteristic
118C4⋊#1057C2311yescharacteristic
119C4⋊#1057C2311yescharacteristic
120C4⋊#1057C2311yescharacteristic
121C4×#1057—21no—
122C4×#1057—21no—
123C4×#1057—21no—
124C4×#1057—21no—
125C4×#1057C2311yescharacteristic
126C4×#1057C2311yescharacteristic
127C4×#1057C2311yescharacteristic
128C4×#1057C2311yescharacteristic
129C13×#107C2×C411yescharacteristic
130C13×#103C2×C411yescharacteristic
131C13×#102C2×C411yescharacteristic
132C13×#97C2×C411yescharacteristic
133#88075C2×C411yescharacteristic
134#88072C2×C411yescharacteristic
135#88061C2×C411yescharacteristic
136#88061C2×C411yescharacteristic
137#88057C2×C411yescharacteristic
138C8×Dic13C2311yescharacteristic
139C8×Dic13C2311yescharacteristic
140#88049C2×C411yescharacteristic
141#88049C2×C411yescharacteristic
142#88048C2×C411yescharacteristic
143#88047C2×C411yescharacteristic
144#88043C2×C411yescharacteristic
145#17852—131nomaximal, Sylow
146C23×D13—21no—
147C2×Q8×C13C22×C411yescharacteristic
148C2×D4×C13C22×C411yescharacteristic
149C22×C4×C13—21no—
150C2×C22⋊D13—21no—
151C22×Dic13—21no—
152#6131—22no—
153#6131C2×C814yescomplemented
154D4×D13—22no—
155D4×D13C2×C814yescomplemented
156C2×D52—21no—
157C2×D52C22×C411yescharacteristic
158C2×D52C22×C411yescharacteristic
159C2×C4×D13—21no—
160C2×C4×D13—21no—
161C2×C4×D13—21no—
162C2×C4×D13—21no—
163C2×C4×D13—21no—
164C2×C4×D13—21no—
165C2×C4×D13—81no—
166C2×C4×D13—81no—
167C2×C4×D13C22×C411yescharacteristic
168C2×C4×D13C2×D411yescharacteristic
169C2×C4×D13#4111yescharacteristic
170C2×#1057—21no—
171C2×#1057—21no—
172C2×#1057—21no—
173C2×#1057—21no—
174C2×#1057—21no—
175C2×#1057—21no—
176C2×#1057—81no—
177C2×#1057—81no—
178C2×#1057C2×D411yescharacteristic
179C2×#1057C2×D411yescharacteristic
180C2×#1057C2×D411yescharacteristic
181C2×#1057C2×D411yescharacteristic
182D13⋊C8—42no—
183D13⋊C8—81no—
184D13⋊C8—81no—
185D13⋊C8—81no—
186D13⋊C8—81no—
187D13⋊C8—81no—
188C13×SD16C2×C814yescomplemented
189C2×C8×C13C22×C411yescharacteristic
190C2×C8×C13C22×C411yescharacteristic
191C13×C4⋊C4—21no—
192C13×C4⋊C4C22×C411yescharacteristic
193C13×C4⋊C4C22×C411yescharacteristic
194C13×C22⋊C4—21no—
195C42×C13—21no—
196C42×C13C22×C411yescharacteristic
197C22⋊Dic13—21no—
198#6106C2×C814yescomplemented
199#6104C2×C814yescomplemented
200#6103—21no—
201#6103—21no—
202#6103—21no—
203#6103—21no—
204#6103—21no—
205C4⋊Dic13—21no—
206C4⋊Dic13C22×C411yescharacteristic
207C4⋊Dic13C22×C411yescharacteristic
208#6101—21no—
209C4×Dic13—21no—
210C4×Dic13—21no—
211C4×Dic13C2×D411yescharacteristic
212C4×Dic13#4111yescharacteristic
213C4×Dic13C2411yescharacteristic
214C2×#1055C22×C411yescharacteristic
215C2×#1055C22×C411yescharacteristic
216D104C2×C814yescomplemented
217#6094—22no—
218#6094C2×C814yescomplemented
219#2988—131no—
220#2972—131no—
221C4×AGL(1,ℤ/8)—131no—
222#1580—131no—
223#1580—131no—
224SD16⋊C8—131no—
225SD16⋊C8—131no—
226C8×SD16—131no—
227C8×SD16—131no—
228C8×D8—131no—
229C8×D8—131no—
230#1565—131no—
231#1476—131no—
232C2×D4⋊C8—131no—
233C8×M16—131no—
234C23×C13—21no—
235C22×D13—21no—
236C22×D13—21no—
237C22×D13—24no—
238C22×D13—81no—
239C22×D13—81no—
240C22×D13C4×D411yescharacteristic
241Q8×C13—21no—
242Q8×C13C22×C812yes—
243D4×C13—21no—
244D4×C13C22×C812yes—
245C2×C4×C13—21no—
246C2×C4×C13—21no—
247C2×C4×C13—21no—
248C2×C4×C13—81no—
249C2×C4×C13C4×D411yescharacteristic
250C2×C4×C13C4×D411yescharacteristic
251C2×C4×C13C23×C411yescharacteristic
252C22⋊D13—24no—
253C2×Dic13—21no—
254C2×Dic13—21no—
255C2×Dic13—41no—
256C2×Dic13—41no—
257C2×Dic13C4×D411yescharacteristic
258C2×Dic13C22×D411yescharacteristic
259C2×Dic13C2×#4111yescharacteristic
260D52—24no—
261D52—21no—
262D52—21no—
263D52C22×C812yes—
264D52C22×C812yes—
265C4×D13—21no—
266C4×D13—21no—
267C4×D13—24no—
268C4×D13—41no—
269C4×D13—41no—
270C4×D13—41no—
271C4×D13—41no—
272C4×D13—41no—
273C4×D13—81no—
274C4×D13—81no—
275C4×D13—81no—
276C4×D13C22×C812yes—
277C4×D13#13112yes—
278#1057—22no—
279#1057—21no—
280#1057—21no—
281#1057—21no—
282#1057—21no—
283#1057—41no—
284#1057—41no—
285#1057—41no—
286#1057—41no—
287#1057—41no—
288C8×C13—21no—
289C8×C13C22×C812yes—
290#1055—21no—
291#1055C22×C812yes—
292C2×AGL(1,ℤ/8)—131no—
293C4×#41—131no—
294C2×C4×D4—131no—
295C8×Q8—131no—
296C8×Q8—131no—
297#442—131no—
298#442—131no—
299#440—131no—
300#440#26111yescharacteristic
301C4×SD16—131no—
302C4×SD16—131no—
303C4×D8—131no—
304C4×D8—131no—
305C8×D4—131no—
306C8×D4—131no—
307C8×D4—131no—
308C8×D4—131no—
309C8×D4—131no—
310C8×D4—131no—
311C8×D4—261no—
312C8×D4—261no—
313C8×D4—261no—
314C8×D4—261no—
315#431—131no—
316#431—131no—
317#431—261no—
318#428—131no—
319C2×C4⋊C8—131no—
320C2×C4⋊C8—261no—
321#418—131no—
322#417—131no—
323C2×C22⋊C8—261no—
324C2×C22⋊C8—261no—
325C4×M16—131no—
326C2×C4×C8—131no—
327#335—131no—
328#335—131no—
329#334—131no—
330#334—131no—
331Q8⋊C8—131no—
332Q8⋊C8—131no—
333D4⋊C8—131no—
334D4⋊C8—131no—
335D4⋊C8—131no—
336D4⋊C8—131no—
337D4⋊C8—131no—
338D4⋊C8—131no—
339#322—131no—
340#322—131no—
341C82—131no—
342C82—131no—
343C22×C13—22no—
344C22×C13—41no—
345C22×C13—41no—
346C22×C13C2×C4×D411yescharacteristic
347C2×D13—21no—
348C2×D13—21no—
349C2×D13—22no—
350C2×D13—22no—
351C2×D13—41no—
352C2×D13—41no—
353C2×D13—41no—
354C2×D13—41no—
355C2×D13—84no—
356C2×D13C8×D412yes—
357C4×C13—22no—
358C4×C13—21no—
359C4×C13—21no—
360C4×C13—41no—
361C4×C13—41no—
362C4×C13C23×C811yescharacteristic
363C4×C13C2×#13111yescharacteristic
364Dic13—21no—
365Dic13—41no—
366Dic13—41no—
367Dic13C8×D412yes—
368Dic13#57611yescharacteristic
369Dic13#57711yescharacteristic
370C2×#41—131no—
371C22×D4—131no—
372C23×C4—261no—
373AGL(1,ℤ/8)—138no—
374C2×SD16—131no—
375C2×SD16C2×#26111yescharacteristic
376C2×D8—131no—
377C2×D8—131no—
378C2×M16—131no—
379C2×M16—131no—
380C22×C8—261no—
381C22×C8—261no—
382C22×C8—261no—
383C22×C8—261no—
384C22×C8—261no—
385C22×C8—261no—
386C22×C8—261no—
387C22×C8—261no—
388C4×Q8—131no—
389C4×Q8C2×#26111yescharacteristic
390C4×D4—131no—
391C4×D4—131no—
392C4×D4—131no—
393C4×D4—131no—
394C4×D4—131no—
395C4×D4—261no—
396C4×D4—261no—
397C4×D4—261no—
398C4×D4—261no—
399C4×D4C2×#26111yescharacteristic
400#117—131no—
401#117—261no—
402C2×C4⋊C4—131no—
403C2×C22⋊C4—261no—
404C2×C42—131no—
405C2×C42—261no—
406#107—131no—
407#107C2×#26111yescharacteristic
408#106—131no—
409#106—131no—
410C4⋊C8—131no—
411C4⋊C8—131no—
412C4⋊C8—131no—
413C4⋊C8—131no—
414C4⋊C8—131no—
415C4⋊C8—131no—
416C4⋊C8—261no—
417C4⋊C8—261no—
418C4⋊C8—261no—
419#103—131no—
420#103C2×#26111yescharacteristic
421#102—131no—
422#102—131no—
423#102—131no—
424#102—131no—
425#102—131no—
426#102C2×#26111yescharacteristic
427C22⋊C8—131no—
428C22⋊C8—131no—
429C22⋊C8—261no—
430C22⋊C8—261no—
431C22⋊C8—261no—
432C22⋊C8—261no—
433C22⋊C8—261no—
434C22⋊C8—261no—
435C22⋊C8—261no—
436#97—131no—
437#97C2×#26111yescharacteristic
438C4×C8—131no—
439C4×C8—131no—
440C4×C8—131no—
441C4×C8—131no—
442C4×C8—131no—
443C4×C8—131no—
444C4×C8—261no—
445C4×C8—261no—
446C4×C8—261no—
447C4×C8—261no—
448C2×C13—42no—
449C2×C13C2×C8×D411yescharacteristic
450C2×C13#294611yescharacteristic
451C2×C13#295611yescharacteristic
452D13—22no—
453D13—42no—
454D13—42no—
455C24—261no—
456#41—134no—
457#41—262no—
458C2×Q8C22×#26111yescharacteristic
459C2×D4—134no—
460C2×D4—131no—
461C2×D4—131no—
462C2×D4—261no—
463C2×D4—262no—
464C2×D4—261no—
465C2×D4C22×#26111yescharacteristic
466C22×C4—21no—
467C22×C4—131no—
468C22×C4—131no—
469C22×C4—131no—
470C22×C4—261no—
471C22×C4—261no—
472C22×C4—261no—
473C22×C4—261no—
474C22×C4—261no—
475C22×C4—261no—
476C22×C4—261no—
477C22×C4—1041no—
478C22×C4—1041no—
479SD16—134no—
480SD16D13⋊C814yescomplemented
481D8—134no—
482D8—134no—
483M16—134no—
484M16—262no—
485C2×C8—131no—
486C2×C8—131no—
487C2×C8—131no—
488C2×C8—131no—
489C2×C8—131no—
490C2×C8—131no—
491C2×C8—261no—
492C2×C8—261no—
493C2×C8—261no—
494C2×C8—261no—
495C2×C8—261no—
496C2×C8—261no—
497C2×C8—522no—
498C2×C8—1041no—
499C2×C8—1041no—
500C2×C8—1041no—
501C2×C8—1041no—
502C2×C8—1041no—
503C2×C8—1041no—
504C2×C8—1041no—
505C2×C8C22×#26111yescharacteristic
506C2×C8C22×#26111yescharacteristic
507C4⋊C4—21no—
508C4⋊C4—131no—
509C4⋊C4—131no—
510C4⋊C4—261no—
511C4⋊C4—261no—
512C4⋊C4C22×#26111yescharacteristic
513C4⋊C4C22×#26111yescharacteristic
514C22⋊C4—21no—
515C22⋊C4—261no—
516C22⋊C4—261no—
517C22⋊C4—261no—
518C22⋊C4—261no—
519C22⋊C4—261no—
520C22⋊C4—261no—
521C42—21no—
522C42—131no—
523C42—131no—
524C42—131no—
525C42—261no—
526C42—261no—
527C42C22×#26111yescharacteristic
528C13#1785211yescharacteristic, complemented, Sylow
529C23—21no—
530C23—131no—
531C23—264no—
532C23—261no—
533C23—261no—
534C23—1041no—
535C23—1041no—
536Q8—21no—
537Q8C2×D13⋊C812yes—
538D4—21no—
539D4—132no—
540D4—132no—
541D4—264no—
542D4—264no—
543D4—261no—
544D4—261no—
545D4C2×D13⋊C812yes—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—81no—
550C2×C4—131no—
551C2×C4—131no—
552C2×C4—132no—
553C2×C4—132no—
554C2×C4—131no—
555C2×C4—261no—
556C2×C4—261no—
557C2×C4—264no—
558C2×C4—261no—
559C2×C4—261no—
560C2×C4—521no—
561C2×C4—521no—
562C2×C4—521no—
563C2×C4—521no—
564C2×C4—521no—
565C2×C4—521no—
566C2×C4—521no—
567C2×C4—1041no—
568C2×C4—1041no—
569C2×C4—1041no—
570C2×C4D4×#26111yescharacteristic
571C2×C4D4×#26111yescharacteristic
572C2×C4C23×#26111yescharacteristic
573C8—21no—
574C8—132no—
575C8—261no—
576C8—261no—
577C8—261no—
578C8—261no—
579C8—262no—
580C8—261no—
581C8—521no—
582C8—521no—
583C8—521no—
584C8—521no—
585C8—521no—
586C8C2×D13⋊C812yes—
587C22—22no—
588C22—41no—
589C22—41no—
590C22—132no—
591C22—261no—
592C22—261no—
593C22—262no—
594C22—262no—
595C22—521no—
596C22—521no—
597C22—521no—
598C22—521no—
599C22—1044no—
600C22C2×D4×#26111yescharacteristic
601C4—22no—
602C4—21no—
603C4—21no—
604C4—41no—
605C4—41no—
606C4—132no—
607C4—131no—
608C4—131no—
609C4—261no—
610C4—521no—
611C4—521no—
612C4C22×D13⋊C811yescharacteristic
613C4D13⋊#13111yescharacteristic
614C2—42no—
615C2—262no—
616C2—522no—
617C2—522no—
618C2D4×D13⋊C811yescharacteristic
619C2#1313159311yescharacteristic
620C2#1313161111yescharacteristic
subgroupG/H
centerC22C2×D4×#261
commutatorC4×C13C23×C8
FrattiniC2×C4C23×#261
FittingC13×#440C4
socleC22×C13C2×C4×D4
prime radicalC2×#88168C4
cosocleC4×Dic13C24
hypercenter#440#261
hypocenterC13#17852
LCSG ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

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

NH ≅ G/Ntype
1. #13131754C2semidirect
2. #13131684C2semidirect
3. #13130434C2semidirect
4. #13130433C2semidirect
5. #13130426C2semidirect
6. SD16⋊#1057C2semidirect
7. #13130420C2semidirect
8. SD16×#1057C2semidirect
9. #13130417C2semidirect
10. #13130416C2semidirect
11. #13130388C2semidirect
12. #13130130C2semidirect
13. D13⋊(D4⋊C8)C2semidirect
14. #13130034C2semidirect
19. Q8×#1057C22semidirect
20. Q8×#1057C22semidirect
29. #11719073C22semidirect
30. #11719073C22semidirect
51. Q8⋊#1057C22semidirect
52. Q8⋊#1057C22semidirect
55. #11718256C22semidirect
56. #11718255C22semidirect
57. #11718254C22semidirect
58. #11718253C22semidirect
59. #11718251C22semidirect
60. #11718251C22semidirect
61. C8×#1057C22semidirect
62. C8×#1057C22semidirect
65. #11718243C22semidirect
66. #11718243C22semidirect
86. #88168C8semidirect
153. #6131C2×C8semidirect
155. D4×D13C2×C8semidirect
188. C13×SD16C2×C8semidirect
198. #6106C2×C8semidirect
199. #6104C2×C8semidirect
216. D104C2×C8semidirect
218. #6094C2×C8semidirect
480. SD16D13⋊C8semidirect
528. C13#17852semidirect

Maximal subgroups

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

subgroupindex
#131317542
#131316842
#131304342
#131304332
#131304262
SD16⋊#10572
#131304202
SD16×#10572
#131304172
#131304162
#131303882
#131301302
D13⋊(D4⋊C8)2
#131300342
#131236412
#1785213