Finite Group Databasebeta

← C131×#19831 #45705715

Subgroups — C131×#19831 #45705715

Order 33536.

614 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3392×C131C211yesmaximal, characteristic, complemented
2#3364×C131C211yesmaximal, characteristic, complemented
3#3332×C131C211yesmaximal, characteristic
4#3302×C131C211yesmaximal, characteristic, complemented
5#1719×C131C211yesmaximal, characteristic, complemented
6#1699×C131C211yesmaximal, characteristic, complemented
7#1682×C131C211yesmaximal, characteristic, complemented
8#1680×C131C211yesmaximal, characteristic, complemented
9#1665×C131C211yesmaximal, characteristic, complemented
10#1648×C131C211yesmaximal, characteristic, complemented
11#1647×C131C211yesmaximal, characteristic, complemented
12#1641×C131C211yesmaximal, characteristic, complemented
13#1628×C131C211yesmaximal, characteristic, complemented
14#1583×C131C211yesmaximal, characteristic, complemented
15SD16⋊C8×C131C211yesmaximal, characteristic, complemented
16#557×C131C2211yescharacteristic
17#556×C131C2211yescharacteristic
18#550×C131C2211yescharacteristic
19#547×C131C2211yescharacteristic
20#500×C131C2211yescharacteristic
21#492×C131—21no—
22#492×C131C2211yescharacteristic
23#488×C131—21no—
24#487×C131C2211yescharacteristic
25#487×C131C2211yescharacteristic
26#486×C131C2211yescharacteristic
27#486×C131C2211yescharacteristic
28#485×C131—21no—
29#481×C131—21no—
30#479×C131—21no—
31#475×C131C2211yescharacteristic
32#474×C131C2211yescharacteristic
33#474×C131C2211yescharacteristic
34#469×C131—21no—
35#467×C131—21no—
36#464×C131—21no—
37#462×C131C2211yescharacteristic
38#462×C131C2211yescharacteristic
39#461×C131—21no—
40#461×C131C2211yescharacteristic
41#460×C131—21no—
42#460×C131C2211yescharacteristic
43#459×C131C2211yescharacteristic
44#452×C131—21no—
45#449×C131—21no—
46C8×Q8×C131C2211yescharacteristic
47C8×Q8×C131C2211yescharacteristic
48C4×Q16×C131—21no—
49C4×SD16×C131—21no—
50C4×SD16×C131C2211yescharacteristic
51C4×SD16×C131C2211yescharacteristic
52#436×C131C2211yescharacteristic
53C8×D4×C131C2211yescharacteristic
54#417×C131—21no—
55#416×C131—21no—
56#335×C131C2211yescharacteristic
57#334×C131C2211yescharacteristic
58#332×C131C2211yescharacteristic
59#332×C131C2211yescharacteristic
60#332×C131C2211yescharacteristic
61#331×C131C2211yescharacteristic
62Q8⋊C8×C131C2211yescharacteristic
63Q8⋊C8×C131C2211yescharacteristic
64D4⋊C8×C131C2211yescharacteristic
65D4⋊C8×C131C2211yescharacteristic
66#322×C131C2211yescharacteristic
67C2×#41×C131—21no—
68C2×#41×C131—21no—
69C2×Q16×C131—21no—
70C2×Q16×C131—21no—
71C2×SD16×C131—21no—
72C2×SD16×C131—21no—
73C2×SD16×C131—21no—
74C2×SD16×C131—21no—
75C2×SD16×C131D411yescharacteristic
76C2×SD16×C131D411yescharacteristic
77C2×D8×C131—21no—
78C2×M16×C131—21no—
79C22×C8×C131—21no—
80C4⋊Q8×C131—21no—
81C4⋊Q8×C131C2311yescharacteristic
82C4⋊Q8×C131C2311yescharacteristic
83C4⋊Q8×C131C2311yescharacteristic
84#127×C131—21no—
85#127×C131C2311yescharacteristic
86#126×C131—41no—
87#125×C131—21no—
88#125×C131—41no—
89#124×C131—21no—
90#123×C131—41no—
91C22⋊Q8×C131—21no—
92C22⋊Q8×C131—21no—
93#121×C131—21no—
94#121×C131—21no—
95#121×C131—41no—
96C4×Q8×C131—21no—
97C4×Q8×C131—21no—
98C4×Q8×C131—21no—
99C4×Q8×C131C2311yescharacteristic
100C4×Q8×C131C2311yescharacteristic
101C4×D4×C131—21no—
102C4×D4×C131C2311yescharacteristic
103C4×D4×C131C2311yescharacteristic
104#117×C131—21no—
105C2×C4⋊C4×C131—21no—
106#107×C131—21no—
107#107×C131—21no—
108#107×C131—41no—
109#106×C131—21no—
110#106×C131D411yescharacteristic
111#106×C131D411yescharacteristic
112C4⋊C8×C131—21no—
113C4⋊C8×C131—21no—
114C4⋊C8×C131C2311yescharacteristic
115C4⋊C8×C131C2311yescharacteristic
116C4⋊C8×C131C2311yescharacteristic
117C4⋊C8×C131C2311yescharacteristic
118#103×C131—21no—
119#103×C131—21no—
120#103×C131—21no—
121#103×C131—21no—
122#103×C131—21no—
123#103×C131—21no—
124#103×C131—21no—
125#103×C131—21no—
126#103×C131D411yescharacteristic
127#103×C131D411yescharacteristic
128#102×C131—21no—
129#102×C131—21no—
130#102×C131—21no—
131#102×C131—21no—
132#102×C131—21no—
133#102×C131—21no—
134#102×C131—41no—
135#102×C131D411yescharacteristic
136#102×C131D411yescharacteristic
137C22⋊C8×C131—21no—
138C22⋊C8×C131—21no—
139C4×C8×C131—21no—
140C4×C8×C131—21no—
141C4×C8×C131C2311yescharacteristic
142C4×C8×C131C2311yescharacteristic
143C4×C8×C131C2311yescharacteristic
144#41×C131—42no—
145#41×C131—42no—
146#41×C131—81no—
147#41×C131—81no—
148C2×Q8×C131—21no—
149C2×Q8×C131—21no—
150C2×Q8×C131—21no—
151C2×Q8×C131C2×D411yescharacteristic
152C2×Q8×C131C2×D411yescharacteristic
153C2×D4×C131—21no—
154C2×D4×C131—21no—
155C2×D4×C131—21no—
156C2×D4×C131—41no—
157C2×D4×C131—41no—
158C2×D4×C131—41no—
159C2×D4×C131C2×D411yescharacteristic
160C2×D4×C131C2×D411yescharacteristic
161C22×C4×C131—21no—
162C22×C4×C131—21no—
163C22×C4×C131—41no—
164C22×C4×C131—41no—
165Q16×C131—42no—
166Q16×C131—81no—
167SD16×C131—22no—
168SD16×C131—41no—
169SD16×C131—42no—
170SD16×C131—81no—
171SD16×C131—81no—
172SD16×C131—81no—
173D8×C131—81no—
174M16×C131—81no—
175C2×C8×C131—21no—
176C2×C8×C131—21no—
177C2×C8×C131—21no—
178C2×C8×C131—21no—
179C2×C8×C131—21no—
180C2×C8×C131—81no—
181C2×C8×C131C2×D411yescharacteristic
182C2×C8×C131C2×D411yescharacteristic
183C2×C8×C131C2×D411yescharacteristic
184C2×C8×C131C2×D411yescharacteristic
185C4⋊C4×C131—21no—
186C4⋊C4×C131—21no—
187C4⋊C4×C131—21no—
188C4⋊C4×C131—21no—
189C4⋊C4×C131—21no—
190C4⋊C4×C131—21no—
191C4⋊C4×C131—21no—
192C4⋊C4×C131—21no—
193C4⋊C4×C131—41no—
194C4⋊C4×C131—41no—
195C4⋊C4×C131—41no—
196C4⋊C4×C131—41no—
197C4⋊C4×C131—41no—
198C4⋊C4×C131C2×D411yescharacteristic
199C4⋊C4×C131C2×D411yescharacteristic
200C4⋊C4×C131C2×D411yescharacteristic
201C4⋊C4×C131C2×D411yescharacteristic
202C22⋊C4×C131—21no—
203C22⋊C4×C131—21no—
204C22⋊C4×C131—41no—
205C22⋊C4×C131—41no—
206C22⋊C4×C131—41no—
207C22⋊C4×C131—41no—
208C42×C131—21no—
209C42×C131—21no—
210C42×C131—41no—
211C42×C131—41no—
212C42×C131C2411yescharacteristic
213C23×C131—21no—
214C23×C131—21no—
215C23×C131—41no—
216Q8×C131—21no—
217Q8×C131—21no—
218Q8×C131—21no—
219Q8×C131—41no—
220Q8×C131—41no—
221Q8×C131—41no—
222Q8×C131—41no—
223Q8×C131—41no—
224Q8×C131—41no—
225Q8×C131#13512yes—
226D4×C131—21no—
227D4×C131—21no—
228D4×C131—21no—
229D4×C131—21no—
230D4×C131—41no—
231D4×C131—41no—
232D4×C131—41no—
233D4×C131—41no—
234D4×C131—82no—
235D4×C131—81no—
236D4×C131—82no—
237D4×C131—161no—
238C2×C4×C131—21no—
239C2×C4×C131—21no—
240C2×C4×C131—21no—
241C2×C4×C131—21no—
242C2×C4×C131—21no—
243C2×C4×C131—21no—
244C2×C4×C131—41no—
245C2×C4×C131—41no—
246C2×C4×C131—41no—
247C2×C4×C131—41no—
248C2×C4×C131—41no—
249C2×C4×C131—41no—
250C2×C4×C131—41no—
251C2×C4×C131—82no—
252C2×C4×C131—82no—
253C2×C4×C131C22×D411yescharacteristic
254C2×C4×C131C22×D411yescharacteristic
255C2×C4×C131H(5,𝔽2)11yescharacteristic
256C8×C131—21no—
257C8×C131—21no—
258C8×C131—21no—
259C8×C131—21no—
260C8×C131—41no—
261C8×C131—41no—
262C8×C131—41no—
263C8×C131—41no—
264C8×C131—41no—
265C22×C131—41no—
266C22×C131—41no—
267C22×C131—41no—
268C22×C131—41no—
269C22×C131—41no—
270C22×C131—41no—
271C22×C131—81no—
272C22×C131—81no—
273C22×C131—81no—
274C22×C131D4211yescharacteristic
275C4×C131—22no—
276C4×C131—21no—
277C4×C131—41no—
278C4×C131—41no—
279C4×C131—41no—
280C4×C131—41no—
281C4×C131—41no—
282C4×C131—81no—
283C4×C131—81no—
284C4×C131—81no—
285C4×C131C2×#13511yescharacteristic
286C4×C131#57511yescharacteristic
287C4×C131#57611yescharacteristic
288C4×C131#57711yescharacteristic
289C2×C131—81no—
290C2×C131—81no—
291C2×C131—161no—
292C2×C131#326811yescharacteristic
293C2×C131#328211yescharacteristic
294C2×C131#328911yescharacteristic
295#19831C13111yesmaximal, characteristic, direct product factor, Sylow
296C131#1983111yescharacteristic, direct product factor, Sylow
297#3392C2×C13111yescharacteristic, complemented
298#3364C2×C13111yescharacteristic, complemented
299#3332C2×C13111yescharacteristic
300#3302C2×C13111yescharacteristic, complemented
301#1719C2×C13111yescharacteristic, complemented
302#1699C2×C13111yescharacteristic, complemented
303#1682C2×C13111yescharacteristic, complemented
304#1680C2×C13111yescharacteristic, complemented
305#1665C2×C13111yescharacteristic, complemented
306#1648C2×C13111yescharacteristic, complemented
307#1647C2×C13111yescharacteristic, complemented
308#1641C2×C13111yescharacteristic, complemented
309#1628C2×C13111yescharacteristic, complemented
310#1583C2×C13111yescharacteristic, complemented
311SD16⋊C8C2×C13111yescharacteristic, complemented
312#557C22×C13111yescharacteristic
313#556C22×C13111yescharacteristic
314#550C22×C13111yescharacteristic
315#547C22×C13111yescharacteristic
316#500C22×C13111yescharacteristic
317#492—21no—
318#492C22×C13111yescharacteristic
319#488—21no—
320#487C22×C13111yescharacteristic
321#487C22×C13111yescharacteristic
322#486C22×C13111yescharacteristic
323#486C22×C13111yescharacteristic
324#485—21no—
325#481—21no—
326#479—21no—
327#475C22×C13111yescharacteristic
328#474C22×C13111yescharacteristic
329#474C22×C13111yescharacteristic
330#469—21no—
331#467—21no—
332#464—21no—
333#462C22×C13111yescharacteristic
334#462C22×C13111yescharacteristic
335#461—21no—
336#461C22×C13111yescharacteristic
337#460—21no—
338#460C22×C13111yescharacteristic
339#459C22×C13111yescharacteristic
340#452—21no—
341#449—21no—
342C8×Q8C22×C13111yescharacteristic
343C8×Q8C22×C13111yescharacteristic
344C4×Q16—21no—
345C4×SD16—21no—
346C4×SD16C22×C13111yescharacteristic
347C4×SD16C22×C13111yescharacteristic
348#436C22×C13111yescharacteristic
349C8×D4C22×C13111yescharacteristic
350#417—21no—
351#416—21no—
352#335C22×C13111yescharacteristic
353#334C22×C13111yescharacteristic
354#332C22×C13111yescharacteristic
355#332C22×C13111yescharacteristic
356#332C22×C13111yescharacteristic
357#331C22×C13111yescharacteristic
358Q8⋊C8C22×C13111yescharacteristic
359Q8⋊C8C22×C13111yescharacteristic
360D4⋊C8C22×C13111yescharacteristic
361D4⋊C8C22×C13111yescharacteristic
362#322C22×C13111yescharacteristic
363C2×#41—21no—
364C2×#41—21no—
365C2×Q16—21no—
366C2×Q16—21no—
367C2×SD16—21no—
368C2×SD16—21no—
369C2×SD16—21no—
370C2×SD16—21no—
371C2×SD16D4×C13111yescharacteristic
372C2×SD16D4×C13111yescharacteristic
373C2×D8—21no—
374C2×M16—21no—
375C22×C8—21no—
376C4⋊Q8—21no—
377C4⋊Q8C23×C13111yescharacteristic
378C4⋊Q8C23×C13111yescharacteristic
379C4⋊Q8C23×C13111yescharacteristic
380#127—21no—
381#127C23×C13111yescharacteristic
382#126—41no—
383#125—21no—
384#125—41no—
385#124—21no—
386#123—41no—
387C22⋊Q8—21no—
388C22⋊Q8—21no—
389#121—21no—
390#121—21no—
391#121—41no—
392C4×Q8—21no—
393C4×Q8—21no—
394C4×Q8—21no—
395C4×Q8C23×C13111yescharacteristic
396C4×Q8C23×C13111yescharacteristic
397C4×D4—21no—
398C4×D4C23×C13111yescharacteristic
399C4×D4C23×C13111yescharacteristic
400#117—21no—
401C2×C4⋊C4—21no—
402#107—21no—
403#107—21no—
404#107—41no—
405#106—21no—
406#106D4×C13111yescharacteristic
407#106D4×C13111yescharacteristic
408C4⋊C8—21no—
409C4⋊C8—21no—
410C4⋊C8C23×C13111yescharacteristic
411C4⋊C8C23×C13111yescharacteristic
412C4⋊C8C23×C13111yescharacteristic
413C4⋊C8C23×C13111yescharacteristic
414#103—21no—
415#103—21no—
416#103—21no—
417#103—21no—
418#103—21no—
419#103—21no—
420#103—21no—
421#103—21no—
422#103D4×C13111yescharacteristic
423#103D4×C13111yescharacteristic
424#102—21no—
425#102—21no—
426#102—21no—
427#102—21no—
428#102—21no—
429#102—21no—
430#102—41no—
431#102D4×C13111yescharacteristic
432#102D4×C13111yescharacteristic
433C22⋊C8—21no—
434C22⋊C8—21no—
435C4×C8—21no—
436C4×C8—21no—
437C4×C8C23×C13111yescharacteristic
438C4×C8C23×C13111yescharacteristic
439C4×C8C23×C13111yescharacteristic
440#41—42no—
441#41—42no—
442#41—81no—
443#41—81no—
444C2×Q8—21no—
445C2×Q8—21no—
446C2×Q8—21no—
447C2×Q8C2×D4×C13111yescharacteristic
448C2×Q8C2×D4×C13111yescharacteristic
449C2×D4—21no—
450C2×D4—21no—
451C2×D4—21no—
452C2×D4—41no—
453C2×D4—41no—
454C2×D4—41no—
455C2×D4C2×D4×C13111yescharacteristic
456C2×D4C2×D4×C13111yescharacteristic
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—41no—
460C22×C4—41no—
461Q16—42no—
462Q16—81no—
463SD16—22no—
464SD16—41no—
465SD16—42no—
466SD16—81no—
467SD16—81no—
468SD16—81no—
469D8—81no—
470M16—81no—
471C2×C8—21no—
472C2×C8—21no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—81no—
477C2×C8C2×D4×C13111yescharacteristic
478C2×C8C2×D4×C13111yescharacteristic
479C2×C8C2×D4×C13111yescharacteristic
480C2×C8C2×D4×C13111yescharacteristic
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—41no—
490C4⋊C4—41no—
491C4⋊C4—41no—
492C4⋊C4—41no—
493C4⋊C4—41no—
494C4⋊C4C2×D4×C13111yescharacteristic
495C4⋊C4C2×D4×C13111yescharacteristic
496C4⋊C4C2×D4×C13111yescharacteristic
497C4⋊C4C2×D4×C13111yescharacteristic
498C22⋊C4—21no—
499C22⋊C4—21no—
500C22⋊C4—41no—
501C22⋊C4—41no—
502C22⋊C4—41no—
503C22⋊C4—41no—
504C42—21no—
505C42—21no—
506C42—41no—
507C42—41no—
508C42C24×C13111yescharacteristic
509C23—21no—
510C23—21no—
511C23—41no—
512Q8—21no—
513Q8—21no—
514Q8—21no—
515Q8—41no—
516Q8—41no—
517Q8—41no—
518Q8—41no—
519Q8—41no—
520Q8—41no—
521Q8#135×C13112yes—
522D4—21no—
523D4—21no—
524D4—21no—
525D4—21no—
526D4—41no—
527D4—41no—
528D4—41no—
529D4—41no—
530D4—82no—
531D4—81no—
532D4—82no—
533D4—161no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—82no—
548C2×C4—82no—
549C2×C4C22×D4×C13111yescharacteristic
550C2×C4C22×D4×C13111yescharacteristic
551C2×C4H(5,𝔽2)×C13111yescharacteristic
552C8—21no—
553C8—21no—
554C8—21no—
555C8—21no—
556C8—41no—
557C8—41no—
558C8—41no—
559C8—41no—
560C8—41no—
561C22—41no—
562C22—41no—
563C22—41no—
564C22—41no—
565C22—41no—
566C22—41no—
567C22—81no—
568C22—81no—
569C22—81no—
570C22D42×C13111yescharacteristic
571C4—22no—
572C4—21no—
573C4—41no—
574C4—41no—
575C4—41no—
576C4—41no—
577C4—41no—
578C4—81no—
579C4—81no—
580C4—81no—
581C4C2×#135×C13111yescharacteristic
582C4#575×C13111yescharacteristic
583C4#576×C13111yescharacteristic
584C4#577×C13111yescharacteristic
585C2—81no—
586C2—81no—
587C2—161no—
588C2#3268×C13111yescharacteristic
589C2#3282×C13111yescharacteristic
590C2#3289×C13111yescharacteristic
subgroupG/H
center, socleC22×C131D42
commutator, Frattini, cosocleC42C24×C131
prime radical#3332×C131C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C131 ◁ C42×C131 ◁ G

Complements

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

NH ≅ G/Ntype
1. #3392×C131C2semidirect
2. #3364×C131C2semidirect
4. #3302×C131C2semidirect
5. #1719×C131C2semidirect
6. #1699×C131C2semidirect
7. #1682×C131C2semidirect
8. #1680×C131C2semidirect
9. #1665×C131C2semidirect
10. #1648×C131C2semidirect
11. #1647×C131C2semidirect
12. #1641×C131C2semidirect
13. #1628×C131C2semidirect
14. #1583×C131C2semidirect
15. SD16⋊C8×C131C2semidirect
295. #19831C131direct (N × H)
296. C131#19831direct (N × H)
297. #3392C2×C131semidirect
298. #3364C2×C131semidirect
300. #3302C2×C131semidirect
301. #1719C2×C131semidirect
302. #1699C2×C131semidirect
303. #1682C2×C131semidirect
304. #1680C2×C131semidirect
305. #1665C2×C131semidirect
306. #1648C2×C131semidirect
307. #1647C2×C131semidirect
308. #1641C2×C131semidirect
309. #1628C2×C131semidirect
310. #1583C2×C131semidirect
311. SD16⋊C8C2×C131semidirect

Maximal subgroups

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

subgroupindex
#3392×C1312
#3364×C1312
#3332×C1312
#3302×C1312
#1719×C1312
#1699×C1312
#1682×C1312
#1680×C1312
#1665×C1312
#1648×C1312
#1647×C1312
#1641×C1312
#1628×C1312
#1583×C1312
SD16⋊C8×C1312
#19831131