Finite Group Databasebeta

← C131×#24056 #45709940

Subgroups — C131×#24056 #45709940

Order 33536.

1820 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3484×C131C211yesmaximal, characteristic
2#2849×C131C212yesmaximal, complemented
3C2×#386×C131C211yesmaximal, characteristic, complemented
4#2044×C131C214yesmaximal, complemented
5#1898×C131C212yesmaximal, complemented
6#1867×C131C212yesmaximal, complemented
7#1790×C131C212yesmaximal, complemented
8#1781×C131C211yesmaximal, characteristic, complemented
9C2×H(5,𝔽2)×C131C2211yescharacteristic
10C23×D4×C131C2211yescharacteristic
11C24×C4×C131C2211yescharacteristic, complemented
12#546×C131—22no—
13#546×C131—22no—
14D42×C131—22no—
15D42×C131—22no—
16#535×C131—21no—
17#534×C131—21no—
18#534×C131C2212yes—
19#525×C131—21no—
20C2×#123×C131—22no—
21C2×#120×C131—21no—
22C2×#120×C131C2212yes—
23#518×C131C2211yescharacteristic
24C22×C22⋊C4×C131—21no—
25C22×C22⋊C4×C131C2211yescharacteristic, complemented
26C2×#99×C131C2212yes—
27C2×#99×C131C2212yescomplemented
28C2×#99×C131C2214yescomplemented
29#386×C131—21no—
30#386×C131—21no—
31#386×C131—22no—
32#386×C131C2212yes—
33#386×C131C2212yescomplemented
34#386×C131C2214yescomplemented
35#385×C131—22no—
36#385×C131C2214yescomplemented
37#381×C131—22no—
38#379×C131C2212yescomplemented
39C2×#95×C131—21no—
40#342×C131C2214yescomplemented
41C25×C131D411yescharacteristic
42C25×C131C2311yescharacteristic
43H(5,𝔽2)×C131—24no—
44H(5,𝔽2)×C131—42no—
45C2×#41×C131—21no—
46C2×#41×C131—22no—
47C22×D4×C131—21no—
48C22×D4×C131—22no—
49C22×D4×C131—22no—
50C22×D4×C131—22no—
51C22×D4×C131—21no—
52C22×D4×C131—21no—
53C22×D4×C131—24no—
54C22×D4×C131—42no—
55C22×D4×C131D411yescharacteristic
56C22×D4×C131D411yescharacteristic
57C22×D4×C131D412yes—
58C22×D4×C131D412yes—
59C22×D4×C131C2312yes—
60C22×D4×C131C2311yescharacteristic
61C22×D4×C131C2311yescharacteristic
62C23×C4×C131—21no—
63C23×C4×C131—22no—
64C23×C4×C131—21no—
65C23×C4×C131—22no—
66C23×C4×C131—21no—
67C23×C4×C131—44no—
68C23×C4×C131D411yescharacteristic
69C23×C4×C131C2312yes—
70#127×C131—22no—
71#124×C131—22no—
72#123×C131—22no—
73#123×C131—22no—
74#123×C131—22no—
75#123×C131—48no—
76C22⋊Q8×C131—21no—
77C22⋊Q8×C131—21no—
78#121×C131—21no—
79#121×C131—21no—
80#121×C131—22no—
81#121×C131—22no—
82#121×C131—22no—
83#121×C131—22no—
84#121×C131—22no—
85#121×C131—22no—
86#120×C131—22no—
87#120×C131—22no—
88#120×C131—22no—
89#120×C131—22no—
90#120×C131—22no—
91#120×C131—22no—
92#120×C131—22no—
93#120×C131—22no—
94#120×C131—22no—
95C4×D4×C131—22no—
96C4×D4×C131—22no—
97C4×D4×C131—22no—
98C4×D4×C131—22no—
99#117×C131—21no—
100C2×C4⋊C4×C131—24no—
101C2×C22⋊C4×C131—21no—
102C2×C22⋊C4×C131—21no—
103C2×C22⋊C4×C131—21no—
104C2×C22⋊C4×C131—22no—
105C2×C22⋊C4×C131—22no—
106C2×C22⋊C4×C131—21no—
107C2×C22⋊C4×C131—22no—
108C2×C22⋊C4×C131—24no—
109C2×C22⋊C4×C131—22no—
110C2×C22⋊C4×C131—42no—
111C2×C22⋊C4×C131—44no—
112C2×C22⋊C4×C131D412yes—
113C2×C22⋊C4×C131D412yes—
114C2×C22⋊C4×C131C2314yes—
115C2×C22⋊C4×C131C2312yes—
116C2×C22⋊C4×C131C2312yes—
117#99×C131—24no—
118#99×C131—42no—
119#99×C131—44no—
120#95×C131—22no—
121#95×C131—22no—
122#95×C131—24no—
123#95×C131—24no—
124C24×C131—22no—
125C24×C131—22no—
126C24×C131—21no—
127C24×C131—22no—
128C24×C131—21no—
129C24×C131—21no—
130C24×C131—42no—
131C24×C131—42no—
132C24×C131—41no—
133C24×C131—42no—
134C24×C131—42no—
135C24×C131C2×D411yescharacteristic
136C24×C131C2×D412yes—
137C24×C131C2×D412yes—
138C24×C131C2×D411yescharacteristic
139C24×C131C2×D412yes—
140C24×C131C2×D411yescharacteristic
141C24×C131C2×D411yescharacteristic
142C24×C131C2411yescharacteristic
143#41×C131—48no—
144#41×C131—42no—
145#41×C131—42no—
146C2×Q8×C131—21no—
147C2×D4×C131—22no—
148C2×D4×C131—22no—
149C2×D4×C131—22no—
150C2×D4×C131—21no—
151C2×D4×C131—22no—
152C2×D4×C131—22no—
153C2×D4×C131—22no—
154C2×D4×C131—22no—
155C2×D4×C131—22no—
156C2×D4×C131—22no—
157C2×D4×C131—22no—
158C2×D4×C131—22no—
159C2×D4×C131—22no—
160C2×D4×C131—24no—
161C2×D4×C131—22no—
162C2×D4×C131—24no—
163C2×D4×C131—22no—
164C2×D4×C131—22no—
165C2×D4×C131—22no—
166C2×D4×C131—22no—
167C2×D4×C131—22no—
168C2×D4×C131—41no—
169C2×D4×C131—41no—
170C2×D4×C131—48no—
171C2×D4×C131—48no—
172C2×D4×C131—48no—
173C2×D4×C131—42no—
174C2×D4×C131—42no—
175C2×D4×C131—44no—
176C2×D4×C131—44no—
177C2×D4×C131—82no—
178C2×D4×C131—82no—
179C2×D4×C131#4114yes—
180C22×C4×C131—21no—
181C22×C4×C131—24no—
182C22×C4×C131—22no—
183C22×C4×C131—28no—
184C22×C4×C131—21no—
185C22×C4×C131—21no—
186C22×C4×C131—22no—
187C22×C4×C131—24no—
188C22×C4×C131—21no—
189C22×C4×C131—21no—
190C22×C4×C131—22no—
191C22×C4×C131—24no—
192C22×C4×C131—22no—
193C22×C4×C131—44no—
194C22×C4×C131—41no—
195C22×C4×C131—44no—
196C22×C4×C131—48no—
197C22×C4×C131—42no—
198C22×C4×C131—44no—
199C22×C4×C131—42no—
200C22×C4×C131—41no—
201C22×C4×C131—41no—
202C22×C4×C131—42no—
203C22×C4×C131—42no—
204C22×C4×C131—42no—
205C22×C4×C131C2×D412yes—
206C22×C4×C131C2×D411yescharacteristic
207C22×C4×C131C2×D411yescharacteristic
208C22×C4×C131C2×D412yes—
209C22×C4×C131C2×D412yes—
210C4⋊C4×C131—21no—
211C4⋊C4×C131—21no—
212C4⋊C4×C131—22no—
213C4⋊C4×C131—22no—
214C4⋊C4×C131—48no—
215C22⋊C4×C131—22no—
216C22⋊C4×C131—22no—
217C22⋊C4×C131—22no—
218C22⋊C4×C131—22no—
219C22⋊C4×C131—22no—
220C22⋊C4×C131—22no—
221C22⋊C4×C131—22no—
222C22⋊C4×C131—22no—
223C22⋊C4×C131—22no—
224C22⋊C4×C131—22no—
225C22⋊C4×C131—22no—
226C22⋊C4×C131—24no—
227C22⋊C4×C131—24no—
228C22⋊C4×C131—24no—
229C22⋊C4×C131—44no—
230C22⋊C4×C131—44no—
231C22⋊C4×C131—48no—
232C22⋊C4×C131—44no—
233C22⋊C4×C131—42no—
234C22⋊C4×C131—44no—
235C42×C131—22no—
236C23×C131—21no—
237C23×C131—21no—
238C23×C131—22no—
239C23×C131—22no—
240C23×C131—21no—
241C23×C131—21no—
242C23×C131—21no—
243C23×C131—24no—
244C23×C131—24no—
245C23×C131—24no—
246C23×C131—24no—
247C23×C131—21no—
248C23×C131—21no—
249C23×C131—22no—
250C23×C131—21no—
251C23×C131—21no—
252C23×C131—24no—
253C23×C131—42no—
254C23×C131—41no—
255C23×C131—41no—
256C23×C131—42no—
257C23×C131—41no—
258C23×C131—41no—
259C23×C131—42no—
260C23×C131—42no—
261C23×C131—48no—
262C23×C131—48no—
263C23×C131—41no—
264C23×C131—41no—
265C23×C131—41no—
266C23×C131—41no—
267C23×C131—48no—
268C23×C131—42no—
269C23×C131—42no—
270C23×C131—42no—
271C23×C131—42no—
272C23×C131—42no—
273C23×C131—81no—
274C23×C131—81no—
275C23×C131—84no—
276C23×C131—81no—
277C23×C131—81no—
278C23×C131#12012yes—
279C23×C131#12011yescharacteristic
280C23×C131#12011yescharacteristic
281C23×C131#12312yescomplemented
282C23×C131C22×D411yescharacteristic
283C23×C131C22×D412yes—
284C23×C131C2×#4112yes—
285C23×C131H(5,𝔽2)12yes—
286Q8×C131—42no—
287D4×C131—28no—
288D4×C131—44no—
289D4×C131—42no—
290D4×C131—44no—
291D4×C131—44no—
292D4×C131—42no—
293D4×C131—42no—
294D4×C131—44no—
295D4×C131—44no—
296D4×C131—44no—
297D4×C131—44no—
298D4×C131—82no—
299D4×C131—82no—
300D4×C131—82no—
301D4×C131—82no—
302C2×C4×C131—21no—
303C2×C4×C131—21no—
304C2×C4×C131—24no—
305C2×C4×C131—28no—
306C2×C4×C131—22no—
307C2×C4×C131—22no—
308C2×C4×C131—22no—
309C2×C4×C131—21no—
310C2×C4×C131—21no—
311C2×C4×C131—21no—
312C2×C4×C131—24no—
313C2×C4×C131—42no—
314C2×C4×C131—42no—
315C2×C4×C131—44no—
316C2×C4×C131—44no—
317C2×C4×C131—42no—
318C2×C4×C131—44no—
319C2×C4×C131—48no—
320C2×C4×C131—42no—
321C2×C4×C131—42no—
322C2×C4×C131—44no—
323C2×C4×C131—42no—
324C2×C4×C131—42no—
325C2×C4×C131—44no—
326C2×C4×C131—42no—
327C2×C4×C131—44no—
328C2×C4×C131—42no—
329C2×C4×C131—42no—
330C2×C4×C131—44no—
331C2×C4×C131—81no—
332C2×C4×C131—81no—
333C2×C4×C131—84no—
334C2×C4×C131#12312yescomplemented
335C22×C131—24no—
336C22×C131—24no—
337C22×C131—21no—
338C22×C131—21no—
339C22×C131—22no—
340C22×C131—21no—
341C22×C131—21no—
342C22×C131—22no—
343C22×C131—21no—
344C22×C131—21no—
345C22×C131—22no—
346C22×C131—22no—
347C22×C131—22no—
348C22×C131—22no—
349C22×C131—42no—
350C22×C131—42no—
351C22×C131—48no—
352C22×C131—48no—
353C22×C131—42no—
354C22×C131—42no—
355C22×C131—42no—
356C22×C131—42no—
357C22×C131—41no—
358C22×C131—41no—
359C22×C131—42no—
360C22×C131—41no—
361C22×C131—42no—
362C22×C131—41no—
363C22×C131—42no—
364C22×C131—41no—
365C22×C131—81no—
366C22×C131—84no—
367C22×C131—84no—
368C22×C131—84no—
369C22×C131—81no—
370C22×C131—162no—
371C22×C131B(4,𝔽2)12yes—
372C22×C131#45812yes—
373C22×C131C2×#12011yescharacteristic
374C22×C131C2×#12311yescharacteristic
375C22×C131#53411yescharacteristic
376C22×C131#54614yes—
377C4×C131—22no—
378C4×C131—41no—
379C4×C131—42no—
380C4×C131—44no—
381C4×C131—42no—
382C4×C131—42no—
383C4×C131—84no—
384C4×C131—82no—
385C2×C131—21no—
386C2×C131—24no—
387C2×C131—21no—
388C2×C131—22no—
389C2×C131—22no—
390C2×C131—42no—
391C2×C131—42no—
392C2×C131—81no—
393C2×C131—82no—
394C2×C131#240511yescharacteristic
395C2×C131C2×B(4,𝔽2)11yescharacteristic
396C2×C131C2×#45811yescharacteristic
397#24056C13111yesmaximal, characteristic, direct product factor, Sylow
398C131#2405611yescharacteristic, direct product factor, Sylow
399#3484C2×C13111yescharacteristic
400#2849C2×C13112yescomplemented
401C2×#386C2×C13111yescharacteristic, complemented
402#2044C2×C13114yescomplemented
403#1898C2×C13112yescomplemented
404#1867C2×C13112yescomplemented
405#1790C2×C13112yescomplemented
406#1781C2×C13111yescharacteristic, complemented
407C2×H(5,𝔽2)C22×C13111yescharacteristic
408C23×D4C22×C13111yescharacteristic
409C24×C4C22×C13111yescharacteristic, complemented
410#546—22no—
411#546—22no—
412D42—22no—
413D42—22no—
414#535—21no—
415#534—21no—
416#534C22×C13112yes—
417#525—21no—
418C2×#123—22no—
419C2×#120—21no—
420C2×#120C22×C13112yes—
421#518C22×C13111yescharacteristic
422C22×C22⋊C4—21no—
423C22×C22⋊C4C22×C13111yescharacteristic, complemented
424C2×#99C22×C13112yes—
425C2×#99C22×C13114yescomplemented
426C2×#99C22×C13112yescomplemented
427#386—22no—
428#386—21no—
429#386—21no—
430#386C22×C13112yes—
431#386C22×C13114yescomplemented
432#386C22×C13112yescomplemented
433#385—22no—
434#385C22×C13114yescomplemented
435#381—22no—
436#379C22×C13112yescomplemented
437C2×#95—21no—
438#342C22×C13114yescomplemented
439C25D4×C13111yescharacteristic
440C25C23×C13111yescharacteristic
441H(5,𝔽2)—24no—
442H(5,𝔽2)—42no—
443C2×#41—21no—
444C2×#41—22no—
445C22×D4—21no—
446C22×D4—22no—
447C22×D4—22no—
448C22×D4—22no—
449C22×D4—21no—
450C22×D4—21no—
451C22×D4—24no—
452C22×D4—42no—
453C22×D4D4×C13111yescharacteristic
454C22×D4D4×C13111yescharacteristic
455C22×D4D4×C13112yes—
456C22×D4D4×C13112yes—
457C22×D4C23×C13112yes—
458C22×D4C23×C13111yescharacteristic
459C22×D4C23×C13111yescharacteristic
460C23×C4—21no—
461C23×C4—22no—
462C23×C4—21no—
463C23×C4—22no—
464C23×C4—21no—
465C23×C4—44no—
466C23×C4D4×C13111yescharacteristic
467C23×C4C23×C13112yes—
468#127—22no—
469#124—22no—
470#123—22no—
471#123—22no—
472#123—22no—
473#123—48no—
474C22⋊Q8—21no—
475C22⋊Q8—21no—
476#121—21no—
477#121—21no—
478#121—22no—
479#121—22no—
480#121—22no—
481#121—22no—
482#121—22no—
483#121—22no—
484#120—22no—
485#120—22no—
486#120—22no—
487#120—22no—
488#120—22no—
489#120—22no—
490#120—22no—
491#120—22no—
492#120—22no—
493C4×D4—22no—
494C4×D4—22no—
495C4×D4—22no—
496C4×D4—22no—
497#117—21no—
498C2×C4⋊C4—24no—
499C2×C22⋊C4—21no—
500C2×C22⋊C4—21no—
501C2×C22⋊C4—21no—
502C2×C22⋊C4—22no—
503C2×C22⋊C4—22no—
504C2×C22⋊C4—21no—
505C2×C22⋊C4—22no—
506C2×C22⋊C4—24no—
507C2×C22⋊C4—22no—
508C2×C22⋊C4—42no—
509C2×C22⋊C4—44no—
510C2×C22⋊C4D4×C13112yes—
511C2×C22⋊C4D4×C13112yes—
512C2×C22⋊C4C23×C13112yes—
513C2×C22⋊C4C23×C13114yes—
514C2×C22⋊C4C23×C13112yes—
515#99—24no—
516#99—42no—
517#99—44no—
518#95—22no—
519#95—22no—
520#95—24no—
521#95—24no—
522C24—22no—
523C24—22no—
524C24—21no—
525C24—22no—
526C24—21no—
527C24—21no—
528C24—42no—
529C24—42no—
530C24—41no—
531C24—42no—
532C24—42no—
533C24C2×D4×C13111yescharacteristic
534C24C2×D4×C13112yes—
535C24C2×D4×C13112yes—
536C24C2×D4×C13111yescharacteristic
537C24C2×D4×C13112yes—
538C24C2×D4×C13111yescharacteristic
539C24C2×D4×C13111yescharacteristic
540C24C24×C13111yescharacteristic
541#41—48no—
542#41—42no—
543#41—42no—
544C2×Q8—21no—
545C2×D4—22no—
546C2×D4—22no—
547C2×D4—22no—
548C2×D4—21no—
549C2×D4—22no—
550C2×D4—22no—
551C2×D4—22no—
552C2×D4—22no—
553C2×D4—22no—
554C2×D4—22no—
555C2×D4—22no—
556C2×D4—22no—
557C2×D4—22no—
558C2×D4—24no—
559C2×D4—22no—
560C2×D4—24no—
561C2×D4—22no—
562C2×D4—22no—
563C2×D4—22no—
564C2×D4—22no—
565C2×D4—22no—
566C2×D4—41no—
567C2×D4—41no—
568C2×D4—48no—
569C2×D4—48no—
570C2×D4—48no—
571C2×D4—42no—
572C2×D4—42no—
573C2×D4—44no—
574C2×D4—44no—
575C2×D4—82no—
576C2×D4—82no—
577C2×D4#41×C13114yes—
578C22×C4—21no—
579C22×C4—24no—
580C22×C4—22no—
581C22×C4—28no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—22no—
585C22×C4—24no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—22no—
589C22×C4—24no—
590C22×C4—22no—
591C22×C4—44no—
592C22×C4—41no—
593C22×C4—44no—
594C22×C4—48no—
595C22×C4—42no—
596C22×C4—44no—
597C22×C4—42no—
598C22×C4—41no—
599C22×C4—41no—
600C22×C4—42no—
601C22×C4—42no—
602C22×C4—42no—
603C22×C4C2×D4×C13112yes—
604C22×C4C2×D4×C13111yescharacteristic
605C22×C4C2×D4×C13111yescharacteristic
606C22×C4C2×D4×C13112yes—
607C22×C4C2×D4×C13112yes—
608C4⋊C4—21no—
609C4⋊C4—21no—
610C4⋊C4—22no—
611C4⋊C4—22no—
612C4⋊C4—48no—
613C22⋊C4—22no—
614C22⋊C4—22no—
615C22⋊C4—22no—
616C22⋊C4—22no—
617C22⋊C4—22no—
618C22⋊C4—22no—
619C22⋊C4—22no—
620C22⋊C4—22no—
621C22⋊C4—22no—
622C22⋊C4—22no—
623C22⋊C4—22no—
624C22⋊C4—24no—
625C22⋊C4—24no—
626C22⋊C4—24no—
627C22⋊C4—44no—
628C22⋊C4—44no—
629C22⋊C4—48no—
630C22⋊C4—44no—
631C22⋊C4—42no—
632C22⋊C4—44no—
633C42—22no—
634C23—22no—
635C23—22no—
636C23—21no—
637C23—21no—
638C23—24no—
639C23—24no—
640C23—21no—
641C23—21no—
642C23—21no—
643C23—24no—
644C23—24no—
645C23—21no—
646C23—21no—
647C23—22no—
648C23—21no—
649C23—21no—
650C23—24no—
651C23—42no—
652C23—41no—
653C23—41no—
654C23—42no—
655C23—41no—
656C23—41no—
657C23—42no—
658C23—42no—
659C23—48no—
660C23—48no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23—48no—
666C23—42no—
667C23—42no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—81no—
672C23—81no—
673C23—84no—
674C23—81no—
675C23—81no—
676C23#120×C13112yes—
677C23#120×C13111yescharacteristic
678C23#120×C13111yescharacteristic
679C23#123×C13112yescomplemented
680C23C22×D4×C13111yescharacteristic
681C23C22×D4×C13112yes—
682C23C2×#41×C13112yes—
683C23H(5,𝔽2)×C13112yes—
684Q8—42no—
685D4—28no—
686D4—44no—
687D4—42no—
688D4—44no—
689D4—44no—
690D4—44no—
691D4—44no—
692D4—42no—
693D4—42no—
694D4—44no—
695D4—44no—
696D4—82no—
697D4—82no—
698D4—82no—
699D4—82no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—24no—
703C2×C4—28no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—24no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—44no—
714C2×C4—44no—
715C2×C4—42no—
716C2×C4—44no—
717C2×C4—48no—
718C2×C4—42no—
719C2×C4—44no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—44no—
724C2×C4—42no—
725C2×C4—44no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—44no—
729C2×C4—81no—
730C2×C4—81no—
731C2×C4—84no—
732C2×C4#123×C13112yescomplemented
733C22—24no—
734C22—24no—
735C22—22no—
736C22—21no—
737C22—21no—
738C22—22no—
739C22—21no—
740C22—21no—
741C22—21no—
742C22—21no—
743C22—22no—
744C22—22no—
745C22—22no—
746C22—22no—
747C22—42no—
748C22—42no—
749C22—48no—
750C22—48no—
751C22—42no—
752C22—42no—
753C22—42no—
754C22—42no—
755C22—41no—
756C22—41no—
757C22—42no—
758C22—41no—
759C22—42no—
760C22—41no—
761C22—42no—
762C22—41no—
763C22—81no—
764C22—84no—
765C22—84no—
766C22—81no—
767C22—84no—
768C22—162no—
769C22B(4,𝔽2)×C13112yes—
770C22#458×C13112yes—
771C22C2×#120×C13111yescharacteristic
772C22C2×#123×C13111yescharacteristic
773C22#534×C13111yescharacteristic
774C22#546×C13114yes—
775C4—22no—
776C4—44no—
777C4—42no—
778C4—42no—
779C4—41no—
780C4—42no—
781C4—82no—
782C4—84no—
783C2—21no—
784C2—24no—
785C2—21no—
786C2—22no—
787C2—22no—
788C2—42no—
789C2—42no—
790C2—81no—
791C2—82no—
792C2#2405×C13111yescharacteristic
793C2C2×B(4,𝔽2)×C13111yescharacteristic
794C2C2×#458×C13111yescharacteristic
subgroupG/H
center, socleC22×C131C2×#120
commutator, Frattini, cosocleC24C24×C131
prime radical#3484×C131C2
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C131 ◁ C25×C131 ◁ G

Complements

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

NH ≅ G/Ntype
2. #2849×C131C2semidirect
3. C2×#386×C131C2semidirect
4. #2044×C131C2semidirect
5. #1898×C131C2semidirect
6. #1867×C131C2semidirect
7. #1790×C131C2semidirect
8. #1781×C131C2semidirect
11. C24×C4×C131C22semidirect
25. C22×C22⋊C4×C131C22semidirect
27. C2×#99×C131C22semidirect
28. C2×#99×C131C22semidirect
33. #386×C131C22semidirect
34. #386×C131C22semidirect
36. #385×C131C22semidirect
38. #379×C131C22semidirect
40. #342×C131C22semidirect
281. C23×C131#123semidirect
334. C2×C4×C131#123semidirect
397. #24056C131direct (N × H)
398. C131#24056direct (N × H)
400. #2849C2×C131semidirect
401. C2×#386C2×C131semidirect
402. #2044C2×C131semidirect
403. #1898C2×C131semidirect
404. #1867C2×C131semidirect
405. #1790C2×C131semidirect
406. #1781C2×C131semidirect
409. C24×C4C22×C131semidirect
423. C22×C22⋊C4C22×C131semidirect
425. C2×#99C22×C131semidirect
426. C2×#99C22×C131semidirect
431. #386C22×C131semidirect
432. #386C22×C131semidirect
434. #385C22×C131semidirect
436. #379C22×C131semidirect
438. #342C22×C131semidirect
679. C23#123×C131semidirect
732. C2×C4#123×C131semidirect

Maximal subgroups

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

subgroupindex
#3484×C1312
#2849×C1312
C2×#386×C1312
#2044×C1312
#1898×C1312
#1867×C1312
#1790×C1312
#1781×C1312
#24056131