Finite Group Databasebeta

← #16795213

Subgroups — #16795213

Order 3328.

802 conjugacy classes of subgroups.

The subgroup lattice has 626 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13131642C211yesmaximal, characteristic, complemented
2D4×D13⋊C8C211yesmaximal, 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#13130136C211yesmaximal, characteristic, complemented
13#13130134C211yesmaximal, characteristic, complemented
14#13130034C211yesmaximal, characteristic, complemented
15#13123641C211yesmaximal, characteristic
16C22×D13⋊C8—21no—
17C2×#88168C411yescharacteristic
18C4×#6131C2211yescharacteristic
19C4×D4×D13C2211yescharacteristic
20Q8×#1057C2211yescharacteristic, complemented
21Q8×#1057C2211yescharacteristic, complemented
22D4×#1057C2211yescharacteristic
23D4×#1057C2211yescharacteristic
24D13⋊(C22⋊C8)—21no—
25#11719073—21no—
26#11719073—21no—
27#11719073C2211yescharacteristic
28#11719073C2211yescharacteristic
29#11719073C2211yescharacteristic, complemented
30#11719073C2211yescharacteristic, complemented
31#11719063—21no—
32#11719063—21no—
33#11719051—21no—
34#11719051C2211yescharacteristic
35D13⋊(C4⋊C8)C2211yescharacteristic
36#11719049C2211yescharacteristic
37C4×D13⋊C8—21no—
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—44no—
78C2×D13⋊C8D411yescharacteristic
79C2×D13⋊C8D411yescharacteristic
80C2×C13×SD16C2×C411yescharacteristic
81C4×Q8×C13C2×C411yescharacteristic
82C4×D4×C13C2×C411yescharacteristic
83Q8×Dic13C2311yescharacteristic
84C2×#6106C2×C411yescharacteristic
85D4×Dic13C2311yescharacteristic
86C2×#6104C2×C411yescharacteristic
87C4×C22⋊D13—21no—
88#88168C818yescomplemented
89C2×D104C2×C411yescharacteristic
90C2×#6094C2×C411yescharacteristic
91C2×#6094C2×C411yescharacteristic
92#88147—21no—
93#88147C2311yescharacteristic
94#88147C2311yescharacteristic
95#88146—21no—
96#88146C2×C411yescharacteristic
97C4⋊C4×D13C2×C411yescharacteristic
98#88135—21no—
99C22⋊C4×D13—21no—
100C4×D52—21no—
101C4×D52C2×C411yescharacteristic
102C4×D52C2×C411yescharacteristic
103C42×D13—21no—
104C42×D13C2311yescharacteristic
105C22⋊#1057—21no—
106C22⋊#1057—21no—
107#88112—21no—
108#88112—21no—
109#88111—21no—
110#88111—21no—
111#88111—21no—
112#88111—21no—
113#88111—21no—
114#88111—21no—
115C4⋊#1057—21no—
116C4⋊#1057—21no—
117C4⋊#1057C2311yescharacteristic
118C4⋊#1057C2311yescharacteristic
119C4⋊#1057C2311yescharacteristic
120C4⋊#1057C2311yescharacteristic
121C4×#1057—21no—
122C4×#1057—21no—
123C4×#1057—21no—
124C4×#1057D411yescharacteristic
125C4×#1057D411yescharacteristic
126C4×#1057C2311yescharacteristic
127C4×#1057C2311yescharacteristic
128C4×#1057C2311yescharacteristic
129C4×#1057C2311yescharacteristic
130C13×#107C2×C411yescharacteristic
131C13×#103C2×C411yescharacteristic
132C13×#102C2×C411yescharacteristic
133C13×#97C2×C411yescharacteristic
134#88075C2×C411yescharacteristic
135#88072C2×C411yescharacteristic
136#88061C2×C411yescharacteristic
137#88061C2×C411yescharacteristic
138#88057C2×C411yescharacteristic
139C8×Dic13C2311yescharacteristic
140C8×Dic13C2311yescharacteristic
141#88049C2×C411yescharacteristic
142#88049C2×C411yescharacteristic
143#88048C2×C411yescharacteristic
144#88047C2×C411yescharacteristic
145#88043C2×C411yescharacteristic
146C8×AGL(1,ℤ/8)—131nomaximal, Sylow
147C23×D13—21no—
148C2×Q8×C13C22×C411yescharacteristic
149C2×D4×C13C22×C411yescharacteristic
150C22×C4×C13—21no—
151C2×C22⋊D13—21no—
152C22×Dic13—21no—
153#6131—22no—
154#6131C2×C814yescomplemented
155D4×D13—22no—
156D4×D13C2×C814yescomplemented
157C2×D52—21no—
158C2×D52C22×C411yescharacteristic
159C2×D52C22×C411yescharacteristic
160C2×C4×D13—21no—
161C2×C4×D13—21no—
162C2×C4×D13—21no—
163C2×C4×D13—21no—
164C2×C4×D13—21no—
165C2×C4×D13—21no—
166C2×C4×D13—42no—
167C2×C4×D13—42no—
168C2×C4×D13C22×C411yescharacteristic
169C2×C4×D13C2×D411yescharacteristic
170C2×C4×D13#4111yescharacteristic
171C2×#1057—21no—
172C2×#1057—21no—
173C2×#1057—21no—
174C2×#1057—21no—
175C2×#1057—21no—
176C2×#1057—21no—
177C2×#1057—42no—
178C2×#1057—42no—
179C2×#1057C2×D411yescharacteristic
180C2×#1057C2×D411yescharacteristic
181C2×#1057C2×D411yescharacteristic
182C2×#1057C2×D411yescharacteristic
183D13⋊C8—22no—
184D13⋊C8—41no—
185D13⋊C8—42no—
186D13⋊C8—42no—
187D13⋊C8—42no—
188D13⋊C8—42no—
189D13⋊C8—42no—
190C13×SD16C2×C814yescomplemented
191C2×C8×C13C22×C411yescharacteristic
192C2×C8×C13C22×C411yescharacteristic
193C13×C4⋊C4—21no—
194C13×C4⋊C4C22×C411yescharacteristic
195C13×C4⋊C4C22×C411yescharacteristic
196C13×C22⋊C4—21no—
197C42×C13—21no—
198C42×C13C22×C411yescharacteristic
199C22⋊Dic13—21no—
200#6106C2×C814yescomplemented
201#6104C2×C814yescomplemented
202#6103—21no—
203#6103—21no—
204#6103—21no—
205#6103—21no—
206#6103—21no—
207C4⋊Dic13—21no—
208C4⋊Dic13C22×C411yescharacteristic
209C4⋊Dic13C22×C411yescharacteristic
210#6101—21no—
211C4×Dic13—21no—
212C4×Dic13—21no—
213C4×Dic13C2×D411yescharacteristic
214C4×Dic13#4111yescharacteristic
215C4×Dic13C2411yescharacteristic
216C2×#1055C22×C411yescharacteristic
217C2×#1055C22×C411yescharacteristic
218D104C2×C814yescomplemented
219#6094—22no—
220#6094C2×C814yescomplemented
221C8×#41—131no—
222C4×AGL(1,ℤ/8)—131no—
223C2×C8×D4—131no—
224#1580—131no—
225#1580—131no—
226SD16⋊C8—131no—
227SD16⋊C8—131no—
228C8×SD16—131no—
229C8×SD16—131no—
230C8×D8—131no—
231C8×D8—131no—
232#1565—131no—
233#1478—131no—
234#1477—131no—
235C8×M16—131no—
236C23×C13—21no—
237C22×D13—21no—
238C22×D13—21no—
239C22×D13—24no—
240C22×D13—42no—
241C22×D13—42no—
242C22×D13C4×D411yescharacteristic
243Q8×C13—21no—
244Q8×C13C22×C812yescomplemented
245D4×C13—21no—
246D4×C13C22×C812yes—
247C2×C4×C13—21no—
248C2×C4×C13—21no—
249C2×C4×C13—21no—
250C2×C4×C13—42no—
251C2×C4×C13C4×D411yescharacteristic
252C2×C4×C13C4×D411yescharacteristic
253C2×C4×C13C23×C411yescharacteristic
254C22⋊D13—24no—
255C2×Dic13—21no—
256C2×Dic13—21no—
257C2×Dic13—41no—
258C2×Dic13—41no—
259C2×Dic13C4×D411yescharacteristic
260C2×Dic13C22×D411yescharacteristic
261C2×Dic13C2×#4111yescharacteristic
262D52—24no—
263D52—21no—
264D52—21no—
265D52C22×C812yes—
266D52C22×C812yescomplemented
267C4×D13—21no—
268C4×D13—21no—
269C4×D13—24no—
270C4×D13—41no—
271C4×D13—42no—
272C4×D13—42no—
273C4×D13—42no—
274C4×D13—41no—
275C4×D13—41no—
276C4×D13—41no—
277C4×D13—41no—
278C4×D13C22×C812yes—
279C4×D13#13112yes—
280#1057—21no—
281#1057—21no—
282#1057—21no—
283#1057—41no—
284#1057—41no—
285#1057—41no—
286#1057—41no—
287#1057—41no—
288#1057—41no—
289#1057AGL(1,ℤ/8)12yescomplemented
290C8×C13—21no—
291C8×C13C22×C812yescomplemented
292#1055—21no—
293#1055C22×C812yescomplemented
294C2×AGL(1,ℤ/8)—131no—
295C23×C8—261no—
296C4×#41—131no—
297C2×C4×D4—131no—
298C8×Q8—131no—
299C8×Q8—131no—
300#442—131no—
301#442—131no—
302#440—131no—
303#440#26111yescharacteristic
304C4×SD16—131no—
305C4×SD16—131no—
306C4×D8—131no—
307C4×D8—131no—
308C8×D4—131no—
309C8×D4—131no—
310C8×D4—131no—
311C8×D4—131no—
312C8×D4—131no—
313C8×D4—131no—
314C8×D4—261no—
315C8×D4—261no—
316C8×D4—261no—
317C8×D4—261no—
318#431—131no—
319#431—131no—
320#431—261no—
321#428—131no—
322C2×C4⋊C8—131no—
323#418—131no—
324#417—131no—
325C2×C22⋊C8—261no—
326C4×M16—131no—
327C2×C4×C8—131no—
328C2×C4×C8—261no—
329#335—131no—
330#335—131no—
331#334—131no—
332#334—131no—
333Q8⋊C8—131no—
334Q8⋊C8—131no—
335D4⋊C8—131no—
336D4⋊C8—131no—
337D4⋊C8—131no—
338D4⋊C8—131no—
339D4⋊C8—131no—
340D4⋊C8—131no—
341#322—131no—
342#322—131no—
343C82—131no—
344C82—131no—
345C22×C13—22no—
346C22×C13—41no—
347C22×C13—41no—
348C22×C13C2×C4×D411yescharacteristic
349C2×D13—21no—
350C2×D13—21no—
351C2×D13—22no—
352C2×D13—22no—
353C2×D13—48no—
354C2×D13—41no—
355C2×D13—41no—
356C2×D13—41no—
357C2×D13—41no—
358C2×D13C8×D412yes—
359C4×C13—22no—
360C4×C13—21no—
361C4×C13—21no—
362C4×C13—41no—
363C4×C13—41no—
364C4×C13C23×C811yescharacteristic
365C4×C13C2×#13111yescharacteristic
366Dic13—21no—
367Dic13—41no—
368Dic13—41no—
369Dic13C8×D412yes—
370Dic13C2×AGL(1,ℤ/8)11yescharacteristic
371Dic13#57511yescharacteristic
372C2×#41—131no—
373C22×D4—131no—
374C23×C4—261no—
375AGL(1,ℤ/8)—138no—
376C2×SD16—131no—
377C2×SD16C2×#26111yescharacteristic
378C2×D8—131no—
379C2×D8—131no—
380C2×M16—131no—
381C2×M16—131no—
382C22×C8—131no—
383C22×C8—131no—
384C22×C8—261no—
385C22×C8—261no—
386C22×C8—261no—
387C22×C8—261no—
388C22×C8—261no—
389C22×C8—261no—
390C22×C8—261no—
391C22×C8—524no—
392C4×Q8—131no—
393C4×Q8C2×#26111yescharacteristic
394C4×D4—131no—
395C4×D4—131no—
396C4×D4—131no—
397C4×D4—131no—
398C4×D4—131no—
399C4×D4—261no—
400C4×D4—261no—
401C4×D4—261no—
402C4×D4—261no—
403C4×D4C2×#26111yescharacteristic
404#117—131no—
405#117—261no—
406C2×C4⋊C4—131no—
407C2×C22⋊C4—261no—
408C2×C42—131no—
409C2×C42—261no—
410#107—131no—
411#107C2×#26111yescharacteristic
412#106—131no—
413#106—131no—
414C4⋊C8—131no—
415C4⋊C8—131no—
416C4⋊C8—131no—
417C4⋊C8—131no—
418C4⋊C8—261no—
419C4⋊C8—261no—
420C4⋊C8—261no—
421C4⋊C8—261no—
422#103—131no—
423#103C2×#26111yescharacteristic
424#102—131no—
425#102—131no—
426#102—131no—
427#102—131no—
428#102—131no—
429#102C2×#26111yescharacteristic
430C22⋊C8—261no—
431C22⋊C8—261no—
432C22⋊C8—261no—
433C22⋊C8—261no—
434C22⋊C8—261no—
435C22⋊C8—261no—
436C22⋊C8—261no—
437C22⋊C8—261no—
438#97—131no—
439#97C2×#26111yescharacteristic
440C4×C8—131no—
441C4×C8—131no—
442C4×C8—131no—
443C4×C8—131no—
444C4×C8—131no—
445C4×C8—131no—
446C4×C8—131no—
447C4×C8—131no—
448C4×C8—261no—
449C4×C8—261no—
450C4×C8—261no—
451C2×C13—42no—
452C2×C13C2×C8×D411yescharacteristic
453C2×C13C4×AGL(1,ℤ/8)11yescharacteristic
454C2×C13#295511yescharacteristic
455D13—22no—
456D13—42no—
457D13—42no—
458C24—261no—
459#41—134no—
460#41—262no—
461C2×Q8C22×#26111yescharacteristic
462C2×D4—134no—
463C2×D4—131no—
464C2×D4—131no—
465C2×D4—261no—
466C2×D4—262no—
467C2×D4—261no—
468C2×D4C22×#26111yescharacteristic
469C22×C4—21no—
470C22×C4—131no—
471C22×C4—131no—
472C22×C4—131no—
473C22×C4—261no—
474C22×C4—261no—
475C22×C4—261no—
476C22×C4—261no—
477C22×C4—261no—
478C22×C4—261no—
479C22×C4—261no—
480C22×C4—522no—
481C22×C4—522no—
482SD16—134no—
483SD16D13⋊C814yescomplemented
484D8—134no—
485D8—134no—
486M16—134no—
487M16—262no—
488C2×C8—131no—
489C2×C8—131no—
490C2×C8—131no—
491C2×C8—131no—
492C2×C8—131no—
493C2×C8—131no—
494C2×C8—262no—
495C2×C8—261no—
496C2×C8—261no—
497C2×C8—261no—
498C2×C8—261no—
499C2×C8—261no—
500C2×C8—261no—
501C2×C8—522no—
502C2×C8—522no—
503C2×C8—522no—
504C2×C8—521no—
505C2×C8—522no—
506C2×C8—522no—
507C2×C8—522no—
508C2×C8—522no—
509C2×C8C22×#26111yescharacteristic
510C2×C8C22×#26111yescharacteristic
511C4⋊C4—21no—
512C4⋊C4—131no—
513C4⋊C4—131no—
514C4⋊C4—261no—
515C4⋊C4—261no—
516C4⋊C4C22×#26111yescharacteristic
517C4⋊C4C22×#26111yescharacteristic
518C22⋊C4—21no—
519C22⋊C4—261no—
520C22⋊C4—261no—
521C22⋊C4—261no—
522C22⋊C4—261no—
523C22⋊C4—261no—
524C22⋊C4—261no—
525C42—21no—
526C42—131no—
527C42—131no—
528C42—131no—
529C42—261no—
530C42—261no—
531C42C22×#26111yescharacteristic
532C13C8×AGL(1,ℤ/8)11yescharacteristic, complemented, Sylow
533C23—21no—
534C23—131no—
535C23—264no—
536C23—261no—
537C23—261no—
538C23—522no—
539C23—522no—
540Q8—21no—
541Q8C2×D13⋊C812yescomplemented
542D4—21no—
543D4—132no—
544D4—132no—
545D4—264no—
546D4—264no—
547D4—261no—
548D4—261no—
549D4C2×D13⋊C812yes—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—42no—
554C2×C4—131no—
555C2×C4—131no—
556C2×C4—132no—
557C2×C4—132no—
558C2×C4—131no—
559C2×C4—261no—
560C2×C4—261no—
561C2×C4—264no—
562C2×C4—261no—
563C2×C4—261no—
564C2×C4—521no—
565C2×C4—522no—
566C2×C4—522no—
567C2×C4—521no—
568C2×C4—521no—
569C2×C4—521no—
570C2×C4—521no—
571C2×C4—522no—
572C2×C4—521no—
573C2×C4—521no—
574C2×C4D4×#26111yescharacteristic
575C2×C4D4×#26111yescharacteristic
576C2×C4C23×#26111yescharacteristic
577C8—21no—
578C8—132no—
579C8—132no—
580C8—261no—
581C8—261no—
582C8—261no—
583C8—261no—
584C8—521no—
585C8—521no—
586C8—521no—
587C8—521no—
588C8—521no—
589C8—521no—
590C8C2×D13⋊C812yescomplemented
591C22—22no—
592C22—41no—
593C22—41no—
594C22—132no—
595C22—261no—
596C22—261no—
597C22—262no—
598C22—262no—
599C22—528no—
600C22—521no—
601C22—521no—
602C22—521no—
603C22—521no—
604C22C2×D4×#26111yescharacteristic
605C4—22no—
606C4—21no—
607C4—21no—
608C4—41no—
609C4—41no—
610C4—132no—
611C4—131no—
612C4—131no—
613C4—261no—
614C4—521no—
615C4—521no—
616C4C22×D13⋊C811yescharacteristic
617C4D13⋊#13111yescharacteristic
618C2—42no—
619C2—262no—
620C2—522no—
621C2—522no—
622C2D4×D13⋊C811yescharacteristic
623C2AGL(1,ℤ/8)×#26111yescharacteristic
624C2#1313160911yescharacteristic
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
hypocenterC13C8×AGL(1,ℤ/8)
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. #13131642C2semidirect
2. D4×D13⋊C8C2semidirect
3. #13130434C2semidirect
4. #13130433C2semidirect
5. #13130426C2semidirect
6. SD16⋊#1057C2semidirect
7. #13130420C2semidirect
8. SD16×#1057C2semidirect
9. #13130417C2semidirect
10. #13130416C2semidirect
11. #13130388C2semidirect
12. #13130136C2semidirect
13. #13130134C2semidirect
14. #13130034C2semidirect
20. Q8×#1057C22semidirect
21. 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
88. #88168C8semidirect
154. #6131C2×C8semidirect
156. D4×D13C2×C8semidirect
190. C13×SD16C2×C8semidirect
200. #6106C2×C8semidirect
201. #6104C2×C8semidirect
218. D104C2×C8semidirect
220. #6094C2×C8semidirect
244. Q8×C13C22×C8semidirect
266. D52C22×C8semidirect
289. #1057AGL(1,ℤ/8)semidirect
291. C8×C13C22×C8semidirect
293. #1055C22×C8semidirect
483. SD16D13⋊C8semidirect
532. C13C8×AGL(1,ℤ/8)semidirect
541. Q8C2×D13⋊C8semidirect
590. C8C2×D13⋊C8semidirect

Maximal subgroups

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

subgroupindex
#131316422
D4×D13⋊C82
#131304342
#131304332
#131304262
SD16⋊#10572
#131304202
SD16×#10572
#131304172
#131304162
#131303882
#131301362
#131301342
#131300342
#131236412
C8×AGL(1,ℤ/8)13