Finite Group Databasebeta

← #15832503

Subgroups — #15832503

Order 3328.

748 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#13123801C211yesmaximal, characteristic, complemented
2C4×#88168C211yesmaximal, characteristic
3C8×D4×D13C211yesmaximal, characteristic, complemented
4#13113699C211yesmaximal, characteristic, complemented
5#13113697C211yesmaximal, characteristic, complemented
6#13113696C211yesmaximal, characteristic, complemented
7#13113694C211yesmaximal, characteristic, complemented
8#13113670C211yesmaximal, characteristic, complemented
9#13113667C211yesmaximal, characteristic, complemented
10#13113665C211yesmaximal, characteristic, complemented
11#13113585C211yesmaximal, characteristic, complemented
12#13113225C211yesmaximal, characteristic, complemented
13#13113222C211yesmaximal, characteristic, complemented
14#13113122C211yesmaximal, characteristic, complemented
15C13×#1582C211yesmaximal, characteristic, complemented
16C2×#88168C411yescharacteristic
17C22×C8×D13—21no—
18C4×#6131C2211yescharacteristic
19C4×D4×D13C2211yescharacteristic
20C13×#446C2211yescharacteristic, complemented
21C4×C13×SD16C2211yescharacteristic
22C8×D4×C13C2211yescharacteristic
23#11718825C411yescharacteristic
24C8×C22⋊D13—21no—
25C4×#6106C2211yescharacteristic
26#11718685C2211yescharacteristic, complemented
27C4×#6104C2211yescharacteristic
28D4×#1055C2211yescharacteristic
29#11718530C411yescharacteristic
30#11718522C411yescharacteristic
31#11718499C2211yescharacteristic, complemented
32#11718497—21no—
33#11718495C2211yescharacteristic
34#11718494—21no—
35#11718494C2211yescharacteristic
36D13×C4⋊C8C2211yescharacteristic
37#11718478C411yescharacteristic
38#11718464C411yescharacteristic
39#11718446C411yescharacteristic
40#11718431C411yescharacteristic
41#11718386—21no—
42D13×C22⋊C8—21no—
43#11718368—21no—
44#11718367—21no—
45C4×D104C2211yescharacteristic
46#11718349C2211yescharacteristic, complemented
47C4×#6094C2211yescharacteristic
48C8×D52C2211yescharacteristic
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#11718047C2211yescharacteristic, complemented
65#11718047C2211yescharacteristic, complemented
66#11718046C2211yescharacteristic, complemented
67C2×#6131C2×C411yescharacteristic
68C2×D4×D13C2×C411yescharacteristic
69C22×C4×D13—21no—
70C2×C13×SD16C2×C411yescharacteristic
71C22×C8×C13—21no—
72C4×Q8×C13C2311yescharacteristic
73C4×D4×C13C2311yescharacteristic
74Q8×Dic13C2×C411yescharacteristic
75C2×#6106C2×C411yescharacteristic
76D4×Dic13C2×C411yescharacteristic
77C2×#6104C2×C411yescharacteristic
78C4×C22⋊D13—21no—
79C22×#1055—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—44no—
90C2×C8×D13D411yescharacteristic
91C2×C8×D13D411yescharacteristic
92#88147—21no—
93#88147C2×C411yescharacteristic
94#88147C2×C411yescharacteristic
95#88146—21no—
96#88146C2×C411yescharacteristic
97C4⋊C4×D13C2×C411yescharacteristic
98#88135—21no—
99C22⋊C4×D13—21no—
100C4×D52—21no—
101C4×D52C2311yescharacteristic
102C4×D52C2311yescharacteristic
103C42×D13—21no—
104C42×D13C2311yescharacteristic
105C13×#106C2×C411yescharacteristic
106C13×C4⋊C8—21no—
107C13×C4⋊C8C2311yescharacteristic
108C13×C4⋊C8C2311yescharacteristic
109C13×#103C2×C411yescharacteristic
110C13×#102C2×C411yescharacteristic
111C13×C22⋊C8—21no—
112C13×#97—21no—
113C4×C8×C13C2311yescharacteristic
114C4×C8×C13C2311yescharacteristic
115C4×C8×C13C2311yescharacteristic
116#88075C2×C411yescharacteristic
117#88072C2×C411yescharacteristic
118C22⋊#1055—21no—
119#88061C2×C411yescharacteristic
120#88061C2×C411yescharacteristic
121#88060—21no—
122#88060—21no—
123#88060—21no—
124#88060—21no—
125#88060—21no—
126#88060—21no—
127#88058C2×C411yescharacteristic
128#88055C2×C411yescharacteristic
129#88055C2×C411yescharacteristic
130#88054—21no—
131#88054—21no—
132C8×Dic13—21no—
133C8×Dic13D411yescharacteristic
134C8×Dic13D411yescharacteristic
135#88049C2×C411yescharacteristic
136#88049C2×C411yescharacteristic
137#88048C2×C411yescharacteristic
138#88047C2×C411yescharacteristic
139C4⋊#1055—21no—
140C4⋊#1055C2311yescharacteristic
141C4⋊#1055C2311yescharacteristic
142#88043—21no—
143C4×#1055C2311yescharacteristic
144C4×#1055C2311yescharacteristic
145C4×#1055C2311yescharacteristic
146#17869—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#6131—22no—
155D4×D13—22no—
156D4×D13M1614yescomplemented
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
171C13×SD16—22no—
172C2×C8×C13—21no—
173C2×C8×C13—21no—
174C2×C8×C13—21no—
175C2×C8×C13—42no—
176C2×C8×C13C22×C411yescharacteristic
177C2×C8×C13C22×C411yescharacteristic
178C2×C8×C13C2×D411yescharacteristic
179C2×C8×C13C2×D411yescharacteristic
180C13×C4⋊C4—21no—
181C13×C4⋊C4C22×C411yescharacteristic
182C13×C4⋊C4C22×C411yescharacteristic
183C13×C22⋊C4—21no—
184C42×C13—21no—
185C42×C13C2411yescharacteristic
186C22⋊Dic13—21no—
187#6106—22no—
188#6104—22no—
189#6103—21no—
190#6103—21no—
191#6103—21no—
192#6103—21no—
193#6103—21no—
194C4⋊Dic13—21no—
195C4⋊Dic13C22×C411yescharacteristic
196C4⋊Dic13C22×C411yescharacteristic
197#6101—21no—
198C4×Dic13—21no—
199C4×Dic13—21no—
200C4×Dic13C22×C411yescharacteristic
201C4×Dic13C2×D411yescharacteristic
202C4×Dic13#4111yescharacteristic
203C2×#1055—21no—
204C2×#1055—21no—
205C2×#1055—21no—
206C2×#1055—42no—
207C2×#1055C22×C411yescharacteristic
208C2×#1055C22×C411yescharacteristic
209C2×#1055C2×D411yescharacteristic
210C2×#1055C2×D411yescharacteristic
211D104—22no—
212#6094—22no—
213#6094—22no—
214#6094—42no—
215#6094—42no—
216C8×D13—22no—
217C8×D13—41no—
218C8×D13—42no—
219C8×D13—42no—
220C8×D13—42no—
221#2965—131no—
222C4×AGL(1,ℤ/8)—131no—
223C2×C8×D4—131no—
224#1586—131no—
225#1586—131no—
226#1585—131no—
227#1585—131no—
228#1582—131no—
229#1582D1311yescharacteristic, complemented
230#1581—131no—
231#1581—131no—
232#1565—131no—
233#1478—131no—
234#1477—131no—
235#1451—131no—
236C23×C13—21no—
237C22×D13—21no—
238C22×D13—24no—
239C22×D13—21no—
240C22×D13—42no—
241C22×D13—42no—
242C22×D13C4×D411yescharacteristic
243Q8×C13—21no—
244Q8×C13—21no—
245D4×C13—21no—
246D4×C13C2×M1612yes—
247C2×C4×C13—21no—
248C2×C4×C13—21no—
249C2×C4×C13—21no—
250C2×C4×C13—41no—
251C2×C4×C13—41no—
252C2×C4×C13C23×C411yescharacteristic
253C2×C4×C13C22×D411yescharacteristic
254C2×C4×C13C2×#4111yescharacteristic
255C22⋊D13—24no—
256C2×Dic13—21no—
257C2×Dic13—21no—
258C2×Dic13—42no—
259C2×Dic13C4×D411yescharacteristic
260C2×Dic13C4×D411yescharacteristic
261C2×Dic13C4×D411yescharacteristic
262D52—21no—
263D52—21no—
264D52—21no—
265D52—42no—
266D52C2×M1612yes—
267C4×D13—21no—
268C4×D13—21no—
269C4×D13—41no—
270C4×D13—42no—
271C4×D13—42no—
272C4×D13—42no—
273C4×D13—41no—
274C4×D13—41no—
275C4×D13—41no—
276C4×D13—41no—
277C4×D13—42no—
278C4×D13C2×M1612yes—
279C4×D13#13112yes—
280C8×C13—21no—
281C8×C13—21no—
282C8×C13—21no—
283C8×C13—41no—
284C8×C13—41no—
285C8×C13—41no—
286C8×C13AGL(1,ℤ/8)12yescomplemented
287#1055—21no—
288#1055—21no—
289#1055—21no—
290#1055—21no—
291#1055—41no—
292#1055—41no—
293#1055—41no—
294C2×AGL(1,ℤ/8)—131no—
295C23×C8—261no—
296C4×#41—131no—
297C2×C4×D4—131no—
298#446—131no—
299#446C2×D1311yescharacteristic, complemented
300#442—131no—
301#442—131no—
302#440—131no—
303#440—131no—
304C4×SD16—131no—
305C4×SD16C2×D1311yescharacteristic
306C4×D8—131no—
307C4×D8—131no—
308#436—131no—
309#436—131no—
310#435—261no—
311#435—261no—
312C8×D4—131no—
313C8×D4—131no—
314C8×D4—131no—
315C8×D4—261no—
316C8×D4—261no—
317C8×D4C2×D1311yescharacteristic
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—
327C4×M16—261no—
328C2×C4×C8—131no—
329#335—131no—
330#335—131no—
331#334—131no—
332#334C2×D1311yescharacteristic, complemented
333Q8⋊C8—131no—
334Q8⋊C8C2×D1311yescharacteristic, complemented
335D4⋊C8—131no—
336D4⋊C8—131no—
337D4⋊C8—131no—
338D4⋊C8—131no—
339D4⋊C8—131no—
340D4⋊C8C2×D1311yescharacteristic
341#322—131no—
342#322—131no—
343#322—131no—
344#322C2×D1311yescharacteristic, complemented
345C22×C13—22no—
346C22×C13—41no—
347C22×C13—41no—
348C22×C13C2×C4×D411yescharacteristic
349C2×D13—21no—
350C2×D13—21no—
351C2×D13—22no—
352C2×D13—48no—
353C2×D13—41no—
354C2×D13—41no—
355C2×D13—41no—
356C2×D13—41no—
357C2×D13—41no—
358C2×D13#43512yes—
359C4×C13—21no—
360C4×C13—41no—
361C4×C13—41no—
362C4×C13—41no—
363C4×C13C22×M1611yescharacteristic
364C4×C13C2×#13111yescharacteristic
365C4×C13C2×AGL(1,ℤ/8)11yescharacteristic
366C4×C13#57511yescharacteristic
367Dic13—21no—
368Dic13—21no—
369Dic13—41no—
370Dic13—41no—
371Dic13#43512yes—
372C2×#41—131no—
373C22×D4—131no—
374C23×C4—261no—
375AGL(1,ℤ/8)—264no—
376C2×SD16—131no—
377C2×SD16C4×D1311yescharacteristic
378C2×D8—131no—
379C2×D8—131no—
380C2×M16—131no—
381C2×M16—131no—
382C2×M16—261no—
383C2×M16—261no—
384C22×C8—21no—
385C22×C8—131no—
386C22×C8—131no—
387C22×C8—261no—
388C22×C8—261no—
389C22×C8—261no—
390C22×C8—261no—
391C22×C8—524no—
392C4×Q8—131no—
393C4×Q8C22×D1311yescharacteristic
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×D4C22×D1311yescharacteristic
404#117—131no—
405#117—261no—
406C2×C4⋊C4—131no—
407C2×C22⋊C4—261no—
408C2×C42—131no—
409C2×C42—261no—
410#107—131no—
411#107—131no—
412#106—131no—
413#106C4×D1311yescharacteristic
414C4⋊C8—21no—
415C4⋊C8—131no—
416C4⋊C8—131no—
417C4⋊C8—261no—
418C4⋊C8—261no—
419C4⋊C8—261no—
420C4⋊C8C22×D1311yescharacteristic
421C4⋊C8C22×D1311yescharacteristic
422#103—131no—
423#103C4×D1311yescharacteristic
424#102—131no—
425#102—131no—
426#102—131no—
427#102—131no—
428#102—131no—
429#102C4×D1311yescharacteristic
430C22⋊C8—21no—
431C22⋊C8—261no—
432C22⋊C8—261no—
433C22⋊C8—261no—
434C22⋊C8—261no—
435C22⋊C8—261no—
436C22⋊C8—261no—
437C22⋊C8—261no—
438#97—21no—
439#97—131no—
440#97—131no—
441#97—261no—
442C4×C8—131no—
443C4×C8—131no—
444C4×C8—131no—
445C4×C8—131no—
446C4×C8—131no—
447C4×C8—261no—
448C4×C8C22×D1311yescharacteristic
449C4×C8C22×D1311yescharacteristic
450C4×C8C22×D1311yescharacteristic
451C2×C13—42no—
452C2×C13C2×#43511yescharacteristic
453C2×C13C4×AGL(1,ℤ/8)11yescharacteristic
454C2×C13#295511yescharacteristic
455D13—22no—
456D13—42no—
457D13—81no—
458C24—261no—
459#41—262no—
460#41—262no—
461C2×Q8C2×C4×D1311yescharacteristic
462C2×D4—134no—
463C2×D4—131no—
464C2×D4—131no—
465C2×D4—261no—
466C2×D4—262no—
467C2×D4—261no—
468C2×D4C2×C4×D1311yescharacteristic
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—22no—
483SD16—262no—
484D8—262no—
485D8—262no—
486M16—262no—
487M16—262no—
488M16—522no—
489M16—522no—
490C2×C8—21no—
491C2×C8—21no—
492C2×C8—21no—
493C2×C8—42no—
494C2×C8—131no—
495C2×C8—131no—
496C2×C8—131no—
497C2×C8—131no—
498C2×C8—262no—
499C2×C8—261no—
500C2×C8—261no—
501C2×C8—261no—
502C2×C8—521no—
503C2×C8—522no—
504C2×C8—522no—
505C2×C8—522no—
506C2×C8—522no—
507C2×C8C2×C4×D1311yescharacteristic
508C2×C8C2×C4×D1311yescharacteristic
509C2×C8D4×D1311yescharacteristic
510C2×C8D4×D1311yescharacteristic
511C4⋊C4—21no—
512C4⋊C4—131no—
513C4⋊C4—131no—
514C4⋊C4—261no—
515C4⋊C4—261no—
516C4⋊C4C2×C4×D1311yescharacteristic
517C4⋊C4C2×C4×D1311yescharacteristic
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—
531C42C23×D1311yescharacteristic
532C13#1786911yescharacteristic, complemented, Sylow
533C23—21no—
534C23—131no—
535C23—264no—
536C23—261no—
537C23—261no—
538C23—522no—
539C23—522no—
540Q8—21no—
541Q8—21no—
542D4—21no—
543D4—132no—
544D4—264no—
545D4—261no—
546D4—261no—
547D4—261no—
548D4—522no—
549D4M16×D1312yes—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—131no—
556C2×C4—132no—
557C2×C4—132no—
558C2×C4—131no—
559C2×C4—131no—
560C2×C4—261no—
561C2×C4—261no—
562C2×C4—261no—
563C2×C4—261no—
564C2×C4—521no—
565C2×C4—522no—
566C2×C4—522no—
567C2×C4—522no—
568C2×C4—522no—
569C2×C4—522no—
570C2×C4—521no—
571C2×C4—521no—
572C2×C4—521no—
573C2×C4—521no—
574C2×C4C22×C4×D1311yescharacteristic
575C2×C4C2×D4×D1311yescharacteristic
576C2×C4#41×D1311yescharacteristic
577C8—21no—
578C8—21no—
579C8—21no—
580C8—41no—
581C8—41no—
582C8—41no—
583C8—261no—
584C8—261no—
585C8—261no—
586C8—261no—
587C8—521no—
588C8—521no—
589C8—521no—
590C8#8816812yescomplemented
591C22—22no—
592C22—41no—
593C22—41no—
594C22—132no—
595C22—261no—
596C22—261no—
597C22—262no—
598C22—528no—
599C22—521no—
600C22—521no—
601C22—521no—
602C22—521no—
603C22—521no—
604C22C4×D4×D1311yescharacteristic
605C4—21no—
606C4—41no—
607C4—41no—
608C4—41no—
609C4—132no—
610C4—261no—
611C4—261no—
612C4—521no—
613C4—521no—
614C4C2×M16×D1311yescharacteristic
615C4D13×#13111yescharacteristic
616C4C2×#8816811yescharacteristic
617C4#1171947311yescharacteristic
618C2—42no—
619C2—262no—
620C2—522no—
621C2—1041no—
622C2D13×#43511yescharacteristic
623C2C4×#8816811yescharacteristic
624C2#1312373611yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC42C23×D13
FittingC13×#1582C2
socleC22×C13C2×C4×D4
prime radicalC2×#88168C4
cosocleC42×C13C24
hypercenter#1582D13
hypocenterC13#17869
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1582

Complements

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

NH ≅ G/Ntype
1. #13123801C2semidirect
3. C8×D4×D13C2semidirect
4. #13113699C2semidirect
5. #13113697C2semidirect
6. #13113696C2semidirect
7. #13113694C2semidirect
8. #13113670C2semidirect
9. #13113667C2semidirect
10. #13113665C2semidirect
11. #13113585C2semidirect
12. #13113225C2semidirect
13. #13113222C2semidirect
14. #13113122C2semidirect
15. C13×#1582C2semidirect
20. C13×#446C22semidirect
26. #11718685C22semidirect
31. #11718499C22semidirect
46. #11718349C22semidirect
51. C13×#334C22semidirect
52. C13×Q8⋊C8C22semidirect
54. C13×#322C22semidirect
55. Q8⋊#1055C22semidirect
58. #11718075C22semidirect
59. #11718072C22semidirect
60. #11718071C22semidirect
62. #11718051C22semidirect
63. #11718050C22semidirect
64. #11718047C22semidirect
65. #11718047C22semidirect
66. #11718046C22semidirect
156. D4×D13M16semidirect
229. #1582D13semidirect
286. C8×C13AGL(1,ℤ/8)semidirect
299. #446C2×D13semidirect
332. #334C2×D13semidirect
334. Q8⋊C8C2×D13semidirect
344. #322C2×D13semidirect
532. C13#17869semidirect
590. C8#88168semidirect

Maximal subgroups

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

subgroupindex
#131238012
C4×#881682
C8×D4×D132
#131136992
#131136972
#131136962
#131136942
#131136702
#131136672
#131136652
#131135852
#131132252
#131132222
#131131222
C13×#15822
#1786913