Finite Group Databasebeta

← #15832572

Subgroups — #15832572

Order 3328.

698 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#13123946C211yesmaximal, characteristic, complemented
2#13123874C211yesmaximal, characteristic, complemented
3C4×#88168C211yesmaximal, characteristic
4#13113715C211yesmaximal, characteristic, complemented
5#13113714C211yesmaximal, characteristic, complemented
6#13113699C211yesmaximal, characteristic, complemented
7#13113698C211yesmaximal, characteristic, complemented
8#13113676C211yesmaximal, characteristic, complemented
9#13113668C211yesmaximal, characteristic, complemented
10#13113667C211yesmaximal, characteristic, complemented
11#13113585C211yesmaximal, characteristic, complemented
12#13113217C211yesmaximal, characteristic, complemented
13D13×D4⋊C8C211yesmaximal, characteristic, complemented
14#13113124C211yesmaximal, characteristic, complemented
15C13×#1583C211yesmaximal, characteristic, complemented
16C2×#88168C411yescharacteristic
17C4×#6131C2211yescharacteristic
18C4×D4×D13C2211yescharacteristic
19C8×Q8×C13C2211yescharacteristic, complemented
20C4×C13×SD16C2211yescharacteristic
21C13×#436C2211yescharacteristic
22#11718825C411yescharacteristic
23#11718789—21no—
24#11718787—21no—
25C4×#6106C2211yescharacteristic
26Q8×#1055C2211yescharacteristic, complemented
27C4×#6104C2211yescharacteristic
28#11718673C2211yescharacteristic
29#11718530C411yescharacteristic
30#11718522C411yescharacteristic
31#11718499C2211yescharacteristic
32#11718495—21no—
33#11718495C2211yescharacteristic, complemented
34#11718494C2211yescharacteristic
35D13×C4⋊C8—21no—
36D13×C4⋊C8C2211yescharacteristic
37#11718478C411yescharacteristic
38#11718464C411yescharacteristic
39#11718446C411yescharacteristic
40#11718431C411yescharacteristic
41#11718390—21no—
42#11718387—21no—
43C4×D104C2211yescharacteristic
44#11718349C2211yescharacteristic
45C4×#6094C2211yescharacteristic
46C8×D52—21no—
47C8×D52C2211yescharacteristic, complemented
48#11718346—21no—
49#11718346C2211yescharacteristic
50C4×C8×D13C2211yescharacteristic
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#11718046C2211yescharacteristic, complemented
65#11718046C2211yescharacteristic, complemented
66#11718046C2211yescharacteristic, complemented
67C2×#6131C2×C411yescharacteristic
68C2×D4×D13C2×C411yescharacteristic
69C22×C4×D13—21no—
70C2×C13×SD16C2×C411yescharacteristic
71C2×C13×M16—21no—
72C4×Q8×C13C2311yescharacteristic
73C4×D4×C13C2311yescharacteristic
74Q8×Dic13C2×C411yescharacteristic
75C2×#6106C2×C411yescharacteristic
76D4×Dic13C2×C411yescharacteristic
77C2×#6104C2×C411yescharacteristic
78C4×C22⋊D13—21no—
79C2×#6099—21no—
80#88168—24no—
81C2×D104C2×C411yescharacteristic
82C2×#6094—21no—
83C2×#6094—21no—
84C2×#6094C2×C411yescharacteristic
85C2×#6094C2×C411yescharacteristic
86C2×C8×D13—21no—
87C2×C8×D13—21no—
88C2×C8×D13—21no—
89C2×C8×D13—21no—
90#88147—21no—
91#88147C2×C411yescharacteristic
92#88147C2×C411yescharacteristic
93#88146—21no—
94#88146C2×C411yescharacteristic
95C4⋊C4×D13C2×C411yescharacteristic
96#88135—21no—
97C22⋊C4×D13—21no—
98C4×D52—21no—
99C4×D52C2311yescharacteristic
100C4×D52C2311yescharacteristic
101C42×D13—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#88060D411yescharacteristic
125#88060D411yescharacteristic
126#88058C2×C411yescharacteristic
127#88055C2×C411yescharacteristic
128#88055C2×C411yescharacteristic
129#88054—21no—
130#88054D411yescharacteristic
131#88054D411yescharacteristic
132C8×Dic13—21no—
133C8×Dic13—21no—
134#88049C2×C411yescharacteristic
135#88049C2×C411yescharacteristic
136#88048C2×C411yescharacteristic
137#88047C2×C411yescharacteristic
138C4⋊#1055—21no—
139C4⋊#1055C2311yescharacteristic
140C4⋊#1055C2311yescharacteristic
141C4×#1055—21no—
142C4×#1055C2311yescharacteristic
143C4×#1055C2311yescharacteristic
144C4×#1055C2311yescharacteristic
145#17875—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#6131M1614yescomplemented
154D4×D13—22no—
155D4×D13—22no—
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
170C13×SD16—22no—
171C13×M16—81no—
172C2×C8×C13—21no—
173C2×C8×C13—21no—
174C2×C8×C13—21no—
175C2×C8×C13C22×C411yescharacteristic
176C2×C8×C13C22×C411yescharacteristic
177C2×C8×C13C2×D411yescharacteristic
178C2×C8×C13C2×D411yescharacteristic
179C13×C4⋊C4—21no—
180C13×C4⋊C4C22×C411yescharacteristic
181C13×C4⋊C4C22×C411yescharacteristic
182C13×C22⋊C4—21no—
183C42×C13—21no—
184C42×C13C2411yescharacteristic
185C22⋊Dic13—21no—
186#6106—22no—
187#6104—22no—
188#6103—21no—
189#6103—21no—
190#6103—21no—
191#6103—21no—
192#6103—21no—
193C4⋊Dic13—21no—
194C4⋊Dic13C22×C411yescharacteristic
195C4⋊Dic13C22×C411yescharacteristic
196#6101—21no—
197C4×Dic13—21no—
198C4×Dic13—21no—
199C4×Dic13C22×C411yescharacteristic
200C4×Dic13C2×D411yescharacteristic
201C4×Dic13#4111yescharacteristic
202#6099—81no—
203C2×#1055—21no—
204C2×#1055—21no—
205C2×#1055—21no—
206C2×#1055C22×C411yescharacteristic
207C2×#1055C22×C411yescharacteristic
208C2×#1055C2×D411yescharacteristic
209C2×#1055C2×D411yescharacteristic
210D104—22no—
211#6094—22no—
212#6094—22no—
213#6094—81no—
214#6094—81no—
215C8×D13—42no—
216C8×D13—81no—
217C8×D13—81no—
218C8×D13—81no—
219#2988—131no—
220#2975—131no—
221C4×AGL(1,ℤ/8)—131no—
222#1588—131no—
223#1588—131no—
224#1586—131no—
225#1586—131no—
226#1583—131no—
227#1583D1311yescharacteristic, complemented
228#1581—131no—
229#1581—131no—
230#1565—131no—
231#1476—131no—
232C2×D4⋊C8—131no—
233#1451—131no—
234C23×C13—21no—
235C22×D13—21no—
236C22×D13—21no—
237C22×D13—42no—
238C22×D13—81no—
239C22×D13—81no—
240C22×D13C4×D411yescharacteristic
241Q8×C13—21no—
242Q8×C13C2×M1612yes—
243D4×C13—21no—
244D4×C13—21no—
245C2×C4×C13—21no—
246C2×C4×C13—21no—
247C2×C4×C13—21no—
248C2×C4×C13—41no—
249C2×C4×C13—41no—
250C2×C4×C13C23×C411yescharacteristic
251C2×C4×C13C22×D411yescharacteristic
252C2×C4×C13C2×#4111yescharacteristic
253C22⋊D13—42no—
254C2×Dic13—21no—
255C2×Dic13—21no—
256C2×Dic13—81no—
257C2×Dic13C4×D411yescharacteristic
258C2×Dic13C4×D411yescharacteristic
259C2×Dic13C4×D411yescharacteristic
260D52—24no—
261D52—21no—
262D52—21no—
263D52—21no—
264D52C2×M1612yes—
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×D13C2×M1612yes—
277C4×D13#13112yes—
278C8×C13—21no—
279C8×C13—21no—
280C8×C13—21no—
281C8×C13—21no—
282C8×C13—41no—
283C8×C13—41no—
284C8×C13—41no—
285#1055—22no—
286#1055—21no—
287#1055—21no—
288#1055—21no—
289#1055—21no—
290#1055—41no—
291#1055—41no—
292C2×AGL(1,ℤ/8)—131no—
293C4×#41—131no—
294C2×C4×D4—131no—
295C8×Q8—131no—
296C8×Q8C2×D1311yescharacteristic, complemented
297#442—131no—
298#442—131no—
299#440—131no—
300#440—131no—
301C4×SD16—131no—
302C4×SD16C2×D1311yescharacteristic
303C4×D8—131no—
304C4×D8—131no—
305#436—131no—
306#436—131no—
307#436—131no—
308#436—261no—
309#436—261no—
310#436C2×D1311yescharacteristic
311C8×D4—131no—
312C8×D4—131no—
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—
323#407—261no—
324#407—261no—
325C4×M16—131no—
326C2×C4×C8—131no—
327#335—131no—
328#335—131no—
329#334—131no—
330#334C2×D1311yescharacteristic, complemented
331Q8⋊C8—131no—
332Q8⋊C8C2×D1311yescharacteristic, complemented
333D4⋊C8—131no—
334D4⋊C8—131no—
335D4⋊C8—131no—
336D4⋊C8—131no—
337D4⋊C8—131no—
338D4⋊C8C2×D1311yescharacteristic
339#322—131no—
340#322—131no—
341#322—131no—
342#322C2×D1311yescharacteristic, complemented
343C22×C13—41no—
344C22×C13—41no—
345C22×C13—41no—
346C22×C13C2×C4×D411yescharacteristic
347C2×D13—21no—
348C2×D13—21no—
349C2×D13—22no—
350C2×D13—41no—
351C2×D13—41no—
352C2×D13—41no—
353C2×D13—41no—
354C2×D13—41no—
355C2×D13—84no—
356C2×D13#43512yes—
357C4×C13—22no—
358C4×C13—21no—
359C4×C13—41no—
360C4×C13—41no—
361C4×C13C22×M1611yescharacteristic
362C4×C13C2×#13111yescharacteristic
363C4×C13#57611yescharacteristic
364C4×C13#57711yescharacteristic
365Dic13—21no—
366Dic13—21no—
367Dic13—41no—
368Dic13—41no—
369Dic13#43512yes—
370C2×#41—131no—
371C22×D4—131no—
372C23×C4—261no—
373AGL(1,ℤ/8)—264no—
374C2×SD16—131no—
375C2×SD16C4×D1311yescharacteristic
376C2×D8—131no—
377C2×D8—131no—
378C2×M16—21no—
379C2×M16—131no—
380C2×M16—131no—
381C2×M16—261no—
382C2×M16—261no—
383C2×M16—261no—
384C22×C8—261no—
385C22×C8—261no—
386C22×C8—261no—
387C22×C8—261no—
388C4×Q8—131no—
389C4×Q8C22×D1311yescharacteristic
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×D4C22×D1311yescharacteristic
400#117—131no—
401#117—261no—
402C2×C4⋊C4—131no—
403C2×C22⋊C4—261no—
404C2×C42—131no—
405C2×C42—261no—
406#107—131no—
407#107—131no—
408#106—131no—
409#106C4×D1311yescharacteristic
410C4⋊C8—21no—
411C4⋊C8—131no—
412C4⋊C8—131no—
413C4⋊C8—131no—
414C4⋊C8—131no—
415C4⋊C8—261no—
416C4⋊C8—261no—
417C4⋊C8C22×D1311yescharacteristic
418C4⋊C8C22×D1311yescharacteristic
419#103—131no—
420#103C4×D1311yescharacteristic
421#102—131no—
422#102—131no—
423#102—131no—
424#102—131no—
425#102—131no—
426#102C4×D1311yescharacteristic
427C22⋊C8—21no—
428C22⋊C8—131no—
429C22⋊C8—131no—
430C22⋊C8—261no—
431C22⋊C8—261no—
432C22⋊C8—261no—
433C22⋊C8—261no—
434C22⋊C8—261no—
435C22⋊C8—261no—
436#97—131no—
437#97—131no—
438C4×C8—21no—
439C4×C8—131no—
440C4×C8—131no—
441C4×C8—131no—
442C4×C8—261no—
443C4×C8—261no—
444C4×C8—261no—
445C4×C8C22×D1311yescharacteristic
446C4×C8C22×D1311yescharacteristic
447C4×C8C22×D1311yescharacteristic
448C2×C13—81no—
449C2×C13C2×#43511yescharacteristic
450C2×C13#294611yescharacteristic
451C2×C13#295611yescharacteristic
452D13—22no—
453D13—42no—
454D13—81no—
455C24—261no—
456#41—134no—
457#41—262no—
458C2×Q8C2×C4×D1311yescharacteristic
459C2×D4—131no—
460C2×D4—131no—
461C2×D4—261no—
462C2×D4—262no—
463C2×D4—262no—
464C2×D4—261no—
465C2×D4C2×C4×D1311yescharacteristic
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—22no—
480SD16—262no—
481D8—262no—
482D8—262no—
483M16—81no—
484M16—262no—
485M16—262no—
486M16—1041no—
487M16—1041no—
488M16—1041no—
489C2×C8—21no—
490C2×C8—21no—
491C2×C8—21no—
492C2×C8—131no—
493C2×C8—131no—
494C2×C8—131no—
495C2×C8—131no—
496C2×C8—261no—
497C2×C8—261no—
498C2×C8—261no—
499C2×C8—522no—
500C2×C8—1041no—
501C2×C8—1041no—
502C2×C8—1041no—
503C2×C8C2×C4×D1311yescharacteristic
504C2×C8C2×C4×D1311yescharacteristic
505C2×C8D4×D1311yescharacteristic
506C2×C8D4×D1311yescharacteristic
507C4⋊C4—21no—
508C4⋊C4—131no—
509C4⋊C4—131no—
510C4⋊C4—261no—
511C4⋊C4—261no—
512C4⋊C4C2×C4×D1311yescharacteristic
513C4⋊C4C2×C4×D1311yescharacteristic
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—
527C42C23×D1311yescharacteristic
528C13#1787511yescharacteristic, complemented, Sylow
529C23—21no—
530C23—131no—
531C23—261no—
532C23—261no—
533C23—522no—
534C23—1041no—
535C23—1041no—
536Q8—21no—
537Q8M16×D1312yes—
538D4—21no—
539D4—21no—
540D4—132no—
541D4—264no—
542D4—261no—
543D4—261no—
544D4—261no—
545D4—522no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—131no—
552C2×C4—132no—
553C2×C4—132no—
554C2×C4—131no—
555C2×C4—131no—
556C2×C4—264no—
557C2×C4—261no—
558C2×C4—261no—
559C2×C4—261no—
560C2×C4—261no—
561C2×C4—521no—
562C2×C4—521no—
563C2×C4—521no—
564C2×C4—521no—
565C2×C4—521no—
566C2×C4—1041no—
567C2×C4—1041no—
568C2×C4—1041no—
569C2×C4—1041no—
570C2×C4C22×C4×D1311yescharacteristic
571C2×C4C2×D4×D1311yescharacteristic
572C2×C4#41×D1311yescharacteristic
573C8—21no—
574C8—21no—
575C8—21no—
576C8—21no—
577C8—41no—
578C8—41no—
579C8—41no—
580C8—262no—
581C8—261no—
582C8—261no—
583C8—261no—
584C8—261no—
585C8—521no—
586C8—521no—
587C22—41no—
588C22—41no—
589C22—41no—
590C22—132no—
591C22—261no—
592C22—261no—
593C22—262no—
594C22—521no—
595C22—521no—
596C22—521no—
597C22—521no—
598C22—521no—
599C22—1044no—
600C22C4×D4×D1311yescharacteristic
601C4—21no—
602C4—22no—
603C4—41no—
604C4—41no—
605C4—132no—
606C4—261no—
607C4—261no—
608C4—521no—
609C4—521no—
610C4C2×M16×D1311yescharacteristic
611C4D13×#13111yescharacteristic
612C4#1171946711yescharacteristic
613C4#1171947411yescharacteristic
614C2—81no—
615C2—262no—
616C2—522no—
617C2—1041no—
618C2D13×#43511yescharacteristic
619C2#1312366311yescharacteristic
620C2#1312374411yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC42C23×D13
FittingC13×#1583C2
socleC22×C13C2×C4×D4
prime radicalC2×#88168C4
cosocleC42×C13C24
hypercenter#1583D13
hypocenterC13#17875
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
1. #13123946C2semidirect
2. #13123874C2semidirect
4. #13113715C2semidirect
5. #13113714C2semidirect
6. #13113699C2semidirect
7. #13113698C2semidirect
8. #13113676C2semidirect
9. #13113668C2semidirect
10. #13113667C2semidirect
11. #13113585C2semidirect
12. #13113217C2semidirect
13. D13×D4⋊C8C2semidirect
14. #13113124C2semidirect
15. C13×#1583C2semidirect
19. C8×Q8×C13C22semidirect
26. Q8×#1055C22semidirect
33. #11718495C22semidirect
47. C8×D52C22semidirect
51. C13×#334C22semidirect
52. C13×Q8⋊C8C22semidirect
54. C13×#322C22semidirect
55. Q8⋊#1055C22semidirect
58. #11718075C22semidirect
59. #11718072C22semidirect
60. #11718071C22semidirect
62. #11718051C22semidirect
63. #11718050C22semidirect
64. #11718046C22semidirect
65. #11718046C22semidirect
66. #11718046C22semidirect
153. #6131M16semidirect
227. #1583D13semidirect
296. C8×Q8C2×D13semidirect
330. #334C2×D13semidirect
332. Q8⋊C8C2×D13semidirect
342. #322C2×D13semidirect
528. C13#17875semidirect

Maximal subgroups

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

subgroupindex
#131239462
#131238742
C4×#881682
#131137152
#131137142
#131136992
#131136982
#131136762
#131136682
#131136672
#131135852
#131132172
D13×D4⋊C82
#131131242
C13×#15832
#1787513