Finite Group Databasebeta

← C131×#29610 #45715494

Subgroups — C131×#29610 #45715494

Order 33536.

1594 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#535×C131C211yesmaximal, characteristic, complemented
2#3094×C131C211yesmaximal, characteristic, complemented
3#3006×C131C211yesmaximal, characteristic, complemented
4#2433×C131C211yesmaximal, characteristic, complemented
5#2037×C131C214yesmaximal, complemented
6#2002×C131C214yesmaximal, complemented
7#1826×C131C211yesmaximal, characteristic, complemented
8#1789×C131C211yesmaximal, characteristic, complemented
9#1783×C131C211yesmaximal, characteristic, complemented
10C22×#41×C131C2211yescharacteristic
11C23×D4×C131C2211yescharacteristic
12C2×AGL(1,ℤ/8)×C131C2212yescomplemented
13#535×C131—22no—
14#535×C131—22no—
15#535×C131—22no—
16#535×C131C2214yes—
17C2×#127×C131—21no—
18C2×#127×C131C2212yescomplemented
19C2×#124×C131—21no—
20C2×#121×C131—21no—
21C2×#121×C131—21no—
22C2×#121×C131C2211yescharacteristic
23C2×#120×C131—22no—
24C2×#120×C131—22no—
25C2×#117×C131C2211yescharacteristic
26#482×C131—22no—
27#481×C131—21no—
28#480×C131—21no—
29#449×C131—22no—
30#448×C131—21no—
31#447×C131—21no—
32#428×C131C2212yescomplemented
33C2×#104×C131C2214yescomplemented
34#418×C131C2212yescomplemented
35#417×C131C2212yescomplemented
36C2×#100×C131C2214yescomplemented
37#407×C131C2211yescharacteristic
38#407×C131C2211yescharacteristic
39#392×C131—22no—
40#390×C131C2212yescomplemented
41C4×C22⋊C4×C131C2211yescharacteristic
42#339×C131C2214yescomplemented
43C25×C131D412yes—
44C2×#41×C131—21no—
45C2×#41×C131—21no—
46C2×#41×C131—44no—
47C2×#41×C131D412yescomplemented
48C2×#41×C131C2312yes—
49C22×Q8×C131D411yescharacteristic, complemented
50C22×D4×C131—21no—
51C22×D4×C131—22no—
52C22×D4×C131—22no—
53C22×D4×C131—21no—
54C22×D4×C131—24no—
55C22×D4×C131—21no—
56C22×D4×C131—21no—
57C22×D4×C131—21no—
58C22×D4×C131—21no—
59C22×D4×C131—44no—
60C22×D4×C131D412yes—
61C22×D4×C131D411yescharacteristic, complemented
62C22×D4×C131C2311yescharacteristic
63C22×D4×C131C2312yes—
64C23×C4×C131—21no—
65C23×C4×C131C2311yescharacteristic
66AGL(1,ℤ/8)×C131—44no—
67C2×SD16×C131—22no—
68C2×D8×C131—22no—
69C2×M16×C131C2312yes—
70C2×M16×C131C2312yes—
71#127×C131—24no—
72#127×C131—24no—
73#127×C131—44no—
74#124×C131—24no—
75#124×C131—24no—
76#121×C131—24no—
77#121×C131—24no—
78#121×C131—24no—
79#121×C131—24no—
80#121×C131—21no—
81#121×C131—21no—
82#121×C131—21no—
83#121×C131—21no—
84#120×C131—28no—
85#120×C131—28no—
86#120×C131—48no—
87#117×C131—21no—
88#117×C131—21no—
89#117×C131D412yescomplemented
90#117×C131C2312yes—
91C2×C4⋊C4×C131D411yescharacteristic, complemented
92C2×C4⋊C4×C131D411yescharacteristic, complemented
93C2×C4⋊C4×C131C2311yescharacteristic
94C2×C22⋊C4×C131—22no—
95C2×C22⋊C4×C131—22no—
96C2×C22⋊C4×C131—21no—
97C2×C22⋊C4×C131—21no—
98C2×C22⋊C4×C131—24no—
99C2×C22⋊C4×C131—21no—
100C2×C42×C131—21no—
101C2×C42×C131C2312yes—
102#107×C131—22no—
103#106×C131—22no—
104#104×C131—44no—
105#103×C131—22no—
106#102×C131—22no—
107#102×C131—22no—
108#102×C131—22no—
109#100×C131—44no—
110C22⋊C8×C131—21no—
111C22⋊C8×C131—21no—
112C22⋊C8×C131—21no—
113C22⋊C8×C131—21no—
114#95×C131—21no—
115C24×C131—22no—
116C24×C131—21no—
117C24×C131—22no—
118C24×C131—21no—
119C24×C131—44no—
120C24×C131—44no—
121C24×C131—82no—
122C24×C131C2×D411yescharacteristic
123C24×C131C2×D414yes—
124#41×C131—24no—
125#41×C131—24no—
126#41×C131—42no—
127#41×C131—42no—
128#41×C131—44no—
129#41×C131—44no—
130C2×Q8×C131—21no—
131C2×Q8×C131—42no—
132C2×Q8×C131C2×D412yes—
133C2×D4×C131—22no—
134C2×D4×C131—22no—
135C2×D4×C131—28no—
136C2×D4×C131—28no—
137C2×D4×C131—22no—
138C2×D4×C131—22no—
139C2×D4×C131—21no—
140C2×D4×C131—22no—
141C2×D4×C131—22no—
142C2×D4×C131—21no—
143C2×D4×C131—21no—
144C2×D4×C131—24no—
145C2×D4×C131—24no—
146C2×D4×C131—24no—
147C2×D4×C131—42no—
148C2×D4×C131—44no—
149C2×D4×C131—44no—
150C2×D4×C131—44no—
151C2×D4×C131—44no—
152C2×D4×C131—44no—
153C2×D4×C131—48no—
154C2×D4×C131—44no—
155C2×D4×C131—44no—
156C2×D4×C131—48no—
157C2×D4×C131—41no—
158C2×D4×C131—41no—
159C2×D4×C131—84no—
160C2×D4×C131—84no—
161C2×D4×C131—84no—
162C2×D4×C131C2×D412yes—
163C22×C4×C131—24no—
164C22×C4×C131—21no—
165C22×C4×C131—21no—
166C22×C4×C131—21no—
167C22×C4×C131—22no—
168C22×C4×C131—22no—
169C22×C4×C131—22no—
170C22×C4×C131—21no—
171C22×C4×C131—44no—
172C22×C4×C131C2×D411yescharacteristic
173C22×C4×C131C2×D411yescharacteristic
174C22×C4×C131C2×D411yescharacteristic
175C22×C4×C131C2×D411yescharacteristic
176C22×C4×C131C2×D411yescharacteristic
177C22×C4×C131C2411yescharacteristic
178SD16×C131—44no—
179D8×C131—44no—
180M16×C131—24no—
181M16×C131—24no—
182C2×C8×C131—22no—
183C2×C8×C131—22no—
184C4⋊C4×C131—21no—
185C4⋊C4×C131—21no—
186C4⋊C4×C131—21no—
187C4⋊C4×C131—21no—
188C4⋊C4×C131C2×D412yes—
189C4⋊C4×C131C2×D412yes—
190C22⋊C4×C131—28no—
191C22⋊C4×C131—28no—
192C22⋊C4×C131—24no—
193C22⋊C4×C131—22no—
194C22⋊C4×C131—22no—
195C22⋊C4×C131—48no—
196C22⋊C4×C131—41no—
197C22⋊C4×C131—41no—
198C42×C131—22no—
199C42×C131—22no—
200C42×C131—24no—
201C23×C131—22no—
202C23×C131—22no—
203C23×C131—24no—
204C23×C131—22no—
205C23×C131—24no—
206C23×C131—24no—
207C23×C131—41no—
208C23×C131—44no—
209C23×C131—44no—
210C23×C131—42no—
211C23×C131—44no—
212C23×C131—44no—
213C23×C131—42no—
214C23×C131—44no—
215C23×C131—42no—
216C23×C131—42no—
217C23×C131—42no—
218C23×C131—44no—
219C23×C131—41no—
220C23×C131—42no—
221C23×C131—82no—
222C23×C131—82no—
223C23×C131—816no—
224C23×C131#12011yescharacteristic
225C23×C131#12011yescharacteristic
226C23×C131C22×D411yescharacteristic
227Q8×C131—22no—
228Q8×C131—22no—
229Q8×C131—42no—
230D4×C131—22no—
231D4×C131—22no—
232D4×C131—44no—
233D4×C131—44no—
234D4×C131—42no—
235D4×C131—44no—
236D4×C131—44no—
237D4×C131—44no—
238D4×C131—42no—
239D4×C131—44no—
240D4×C131—42no—
241D4×C131—88no—
242D4×C131—88no—
243D4×C131—816no—
244D4×C131—82no—
245D4×C131—82no—
246C2×C4×C131—22no—
247C2×C4×C131—22no—
248C2×C4×C131—22no—
249C2×C4×C131—22no—
250C2×C4×C131—22no—
251C2×C4×C131—24no—
252C2×C4×C131—22no—
253C2×C4×C131—22no—
254C2×C4×C131—22no—
255C2×C4×C131—44no—
256C2×C4×C131—42no—
257C2×C4×C131—42no—
258C2×C4×C131—42no—
259C2×C4×C131—42no—
260C2×C4×C131—42no—
261C2×C4×C131—44no—
262C2×C4×C131—42no—
263C2×C4×C131—41no—
264C2×C4×C131#12011yescharacteristic
265C2×C4×C131#12011yescharacteristic
266C2×C4×C131C22×D411yescharacteristic
267C2×C4×C131C22×D411yescharacteristic
268C2×C4×C131H(5,𝔽2)14yes—
269C8×C131—42no—
270C8×C131—42no—
271C22×C131—21no—
272C22×C131—21no—
273C22×C131—21no—
274C22×C131—21no—
275C22×C131—21no—
276C22×C131—21no—
277C22×C131—21no—
278C22×C131—44no—
279C22×C131—48no—
280C22×C131—42no—
281C22×C131—44no—
282C22×C131—42no—
283C22×C131—44no—
284C22×C131—42no—
285C22×C131—44no—
286C22×C131—84no—
287C22×C131—84no—
288C22×C131—88no—
289C22×C131—84no—
290C22×C131—88no—
291C22×C131—81no—
292C22×C131—81no—
293C22×C131—81no—
294C22×C131#45312yes—
295C22×C131C2×#12011yescharacteristic
296C22×C131#53412yes—
297C4×C131—21no—
298C4×C131—21no—
299C4×C131—44no—
300C4×C131—42no—
301C4×C131—42no—
302C4×C131—42no—
303C4×C131—81no—
304C4×C131#53412yes—
305C4×C131#53512yes—
306C2×C131—22no—
307C2×C131—22no—
308C2×C131—41no—
309C2×C131—84no—
310C2×C131—82no—
311C2×C131—161no—
312C2×C131#261311yescharacteristic
313C2×C131C2×#45311yescharacteristic
314C2×C131#301911yescharacteristic
315#29610C13111yesmaximal, characteristic, direct product factor, Sylow
316C131#2961011yescharacteristic, direct product factor, Sylow
317C2×#535C2×C13111yescharacteristic, complemented
318#3094C2×C13111yescharacteristic, complemented
319#3006C2×C13111yescharacteristic, complemented
320#2433C2×C13111yescharacteristic, complemented
321#2037C2×C13114yescomplemented
322#2002C2×C13114yescomplemented
323#1826C2×C13111yescharacteristic, complemented
324#1789C2×C13111yescharacteristic, complemented
325#1783C2×C13111yescharacteristic, complemented
326C22×#41C22×C13111yescharacteristic
327C23×D4C22×C13111yescharacteristic
328C2×AGL(1,ℤ/8)C22×C13112yescomplemented
329#535—22no—
330#535—22no—
331#535—22no—
332#535C22×C13114yes—
333C2×#127—21no—
334C2×#127C22×C13112yescomplemented
335C2×#124—21no—
336C2×#121—21no—
337C2×#121—21no—
338C2×#121C22×C13111yescharacteristic
339C2×#120—22no—
340C2×#120—22no—
341C2×#117C22×C13111yescharacteristic
342#482—22no—
343#481—21no—
344#480—21no—
345#449—22no—
346#448—21no—
347#447—21no—
348#428C22×C13112yescomplemented
349C2×#104C22×C13114yescomplemented
350#418C22×C13112yescomplemented
351#417C22×C13112yescomplemented
352C2×#100C22×C13114yescomplemented
353#407C22×C13111yescharacteristic
354#407C22×C13111yescharacteristic
355#392—22no—
356#390C22×C13112yescomplemented
357C4×C22⋊C4C22×C13111yescharacteristic
358#339C22×C13114yescomplemented
359C25D4×C13112yes—
360C2×#41—21no—
361C2×#41—21no—
362C2×#41—44no—
363C2×#41D4×C13112yescomplemented
364C2×#41C23×C13112yes—
365C22×Q8D4×C13111yescharacteristic, complemented
366C22×D4—21no—
367C22×D4—22no—
368C22×D4—22no—
369C22×D4—21no—
370C22×D4—24no—
371C22×D4—21no—
372C22×D4—21no—
373C22×D4—21no—
374C22×D4—21no—
375C22×D4—44no—
376C22×D4D4×C13112yes—
377C22×D4D4×C13111yescharacteristic, complemented
378C22×D4C23×C13111yescharacteristic
379C22×D4C23×C13112yes—
380C23×C4—21no—
381C23×C4C23×C13111yescharacteristic
382AGL(1,ℤ/8)—44no—
383C2×SD16—22no—
384C2×D8—22no—
385C2×M16C23×C13112yes—
386C2×M16C23×C13112yes—
387#127—24no—
388#127—24no—
389#127—44no—
390#124—24no—
391#124—24no—
392#121—24no—
393#121—24no—
394#121—24no—
395#121—24no—
396#121—21no—
397#121—21no—
398#121—21no—
399#121—21no—
400#120—28no—
401#120—28no—
402#120—48no—
403#117—21no—
404#117—21no—
405#117D4×C13112yescomplemented
406#117C23×C13112yes—
407C2×C4⋊C4D4×C13111yescharacteristic, complemented
408C2×C4⋊C4D4×C13111yescharacteristic, complemented
409C2×C4⋊C4C23×C13111yescharacteristic
410C2×C22⋊C4—22no—
411C2×C22⋊C4—22no—
412C2×C22⋊C4—21no—
413C2×C22⋊C4—21no—
414C2×C22⋊C4—24no—
415C2×C22⋊C4—21no—
416C2×C42—21no—
417C2×C42C23×C13112yes—
418#107—22no—
419#106—22no—
420#104—44no—
421#103—22no—
422#102—22no—
423#102—22no—
424#102—22no—
425#100—44no—
426C22⋊C8—21no—
427C22⋊C8—21no—
428C22⋊C8—21no—
429C22⋊C8—21no—
430#95—21no—
431C24—22no—
432C24—21no—
433C24—22no—
434C24—21no—
435C24—44no—
436C24—44no—
437C24—82no—
438C24C2×D4×C13111yescharacteristic
439C24C2×D4×C13114yes—
440#41—24no—
441#41—24no—
442#41—42no—
443#41—42no—
444#41—44no—
445#41—44no—
446C2×Q8—21no—
447C2×Q8—42no—
448C2×Q8C2×D4×C13112yes—
449C2×D4—22no—
450C2×D4—22no—
451C2×D4—28no—
452C2×D4—28no—
453C2×D4—22no—
454C2×D4—22no—
455C2×D4—21no—
456C2×D4—22no—
457C2×D4—22no—
458C2×D4—21no—
459C2×D4—21no—
460C2×D4—24no—
461C2×D4—24no—
462C2×D4—24no—
463C2×D4—42no—
464C2×D4—44no—
465C2×D4—44no—
466C2×D4—44no—
467C2×D4—44no—
468C2×D4—44no—
469C2×D4—48no—
470C2×D4—44no—
471C2×D4—44no—
472C2×D4—48no—
473C2×D4—41no—
474C2×D4—41no—
475C2×D4—84no—
476C2×D4—84no—
477C2×D4—84no—
478C2×D4C2×D4×C13112yes—
479C22×C4—24no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—21no—
487C22×C4—44no—
488C22×C4C2×D4×C13111yescharacteristic
489C22×C4C2×D4×C13111yescharacteristic
490C22×C4C2×D4×C13111yescharacteristic
491C22×C4C2×D4×C13111yescharacteristic
492C22×C4C2×D4×C13111yescharacteristic
493C22×C4C24×C13111yescharacteristic
494SD16—44no—
495D8—44no—
496M16—24no—
497M16—24no—
498C2×C8—22no—
499C2×C8—22no—
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4C2×D4×C13112yes—
505C4⋊C4C2×D4×C13112yes—
506C22⋊C4—28no—
507C22⋊C4—28no—
508C22⋊C4—24no—
509C22⋊C4—22no—
510C22⋊C4—22no—
511C22⋊C4—48no—
512C22⋊C4—41no—
513C22⋊C4—41no—
514C42—22no—
515C42—22no—
516C42—24no—
517C23—22no—
518C23—22no—
519C23—24no—
520C23—22no—
521C23—24no—
522C23—24no—
523C23—41no—
524C23—44no—
525C23—44no—
526C23—42no—
527C23—44no—
528C23—44no—
529C23—42no—
530C23—44no—
531C23—42no—
532C23—42no—
533C23—42no—
534C23—44no—
535C23—41no—
536C23—42no—
537C23—82no—
538C23—82no—
539C23—816no—
540C23#120×C13111yescharacteristic
541C23#120×C13111yescharacteristic
542C23C22×D4×C13111yescharacteristic
543Q8—22no—
544Q8—22no—
545Q8—42no—
546D4—22no—
547D4—22no—
548D4—44no—
549D4—44no—
550D4—42no—
551D4—44no—
552D4—44no—
553D4—44no—
554D4—42no—
555D4—44no—
556D4—42no—
557D4—88no—
558D4—88no—
559D4—816no—
560D4—82no—
561D4—82no—
562C2×C4—22no—
563C2×C4—22no—
564C2×C4—22no—
565C2×C4—22no—
566C2×C4—22no—
567C2×C4—24no—
568C2×C4—22no—
569C2×C4—22no—
570C2×C4—22no—
571C2×C4—44no—
572C2×C4—42no—
573C2×C4—42no—
574C2×C4—42no—
575C2×C4—42no—
576C2×C4—42no—
577C2×C4—44no—
578C2×C4—42no—
579C2×C4—41no—
580C2×C4#120×C13111yescharacteristic
581C2×C4#120×C13111yescharacteristic
582C2×C4C22×D4×C13111yescharacteristic
583C2×C4C22×D4×C13111yescharacteristic
584C2×C4H(5,𝔽2)×C13114yes—
585C8—42no—
586C8—42no—
587C22—21no—
588C22—21no—
589C22—21no—
590C22—21no—
591C22—21no—
592C22—21no—
593C22—21no—
594C22—44no—
595C22—48no—
596C22—42no—
597C22—44no—
598C22—42no—
599C22—44no—
600C22—42no—
601C22—44no—
602C22—84no—
603C22—88no—
604C22—84no—
605C22—84no—
606C22—88no—
607C22—81no—
608C22—81no—
609C22—81no—
610C22#453×C13112yes—
611C22C2×#120×C13111yescharacteristic
612C22#534×C13112yes—
613C4—21no—
614C4—21no—
615C4—44no—
616C4—42no—
617C4—42no—
618C4—42no—
619C4—81no—
620C4#534×C13112yes—
621C4#535×C13112yes—
622C2—22no—
623C2—22no—
624C2—41no—
625C2—84no—
626C2—82no—
627C2—161no—
628C2#2613×C13111yescharacteristic
629C2C2×#453×C13111yescharacteristic
630C2#3019×C13111yescharacteristic
subgroupG/H
center, socleC22×C131C2×#120
commutator, Frattini, cosocleC22×C4C24×C131
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C131 ◁ C23×C4×C131 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#535×C131C2semidirect
2. #3094×C131C2semidirect
3. #3006×C131C2semidirect
4. #2433×C131C2semidirect
5. #2037×C131C2semidirect
6. #2002×C131C2semidirect
7. #1826×C131C2semidirect
8. #1789×C131C2semidirect
9. #1783×C131C2semidirect
12. C2×AGL(1,ℤ/8)×C131C22semidirect
18. C2×#127×C131C22semidirect
32. #428×C131C22semidirect
33. C2×#104×C131C22semidirect
34. #418×C131C22semidirect
35. #417×C131C22semidirect
36. C2×#100×C131C22semidirect
40. #390×C131C22semidirect
42. #339×C131C22semidirect
47. C2×#41×C131D4semidirect
49. C22×Q8×C131D4semidirect
61. C22×D4×C131D4semidirect
89. #117×C131D4semidirect
91. C2×C4⋊C4×C131D4semidirect
92. C2×C4⋊C4×C131D4semidirect
315. #29610C131direct (N × H)
316. C131#29610direct (N × H)
317. C2×#535C2×C131semidirect
318. #3094C2×C131semidirect
319. #3006C2×C131semidirect
320. #2433C2×C131semidirect
321. #2037C2×C131semidirect
322. #2002C2×C131semidirect
323. #1826C2×C131semidirect
324. #1789C2×C131semidirect
325. #1783C2×C131semidirect
328. C2×AGL(1,ℤ/8)C22×C131semidirect
334. C2×#127C22×C131semidirect
348. #428C22×C131semidirect
349. C2×#104C22×C131semidirect
350. #418C22×C131semidirect
351. #417C22×C131semidirect
352. C2×#100C22×C131semidirect
356. #390C22×C131semidirect
358. #339C22×C131semidirect
363. C2×#41D4×C131semidirect
365. C22×Q8D4×C131semidirect
377. C22×D4D4×C131semidirect
405. #117D4×C131semidirect
407. C2×C4⋊C4D4×C131semidirect
408. C2×C4⋊C4D4×C131semidirect

Maximal subgroups

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

subgroupindex
C2×#535×C1312
#3094×C1312
#3006×C1312
#2433×C1312
#2037×C1312
#2002×C1312
#1826×C1312
#1789×C1312
#1783×C1312
#29610131