Finite Group Databasebeta

← C131×#23901 #45709785

Subgroups — C131×#23901 #45709785

Order 33536.

2056 conjugacy classes of subgroups.

The subgroup lattice has 664 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3484×C131C211yesmaximal, characteristic
2C22×#123×C131C211yesmaximal, characteristic, complemented
3C2×#458×C131C212yesmaximal, complemented
4#2849×C131C212yesmaximal, complemented
5#2022×C131C214yesmaximal, complemented
6#1898×C131C212yesmaximal, complemented
7#1890×C131C212yesmaximal, complemented
8#1781×C131C211yesmaximal, characteristic, complemented
9C2×H(5,𝔽2)×C131C2211yescharacteristic
10C23×D4×C131C2211yescharacteristic
11C24×C4×C131C2211yescharacteristic, complemented
12#546×C131—24no—
13D42×C131—24no—
14#535×C131—21no—
15#534×C131—21no—
16#534×C131C2212yes—
17#525×C131—21no—
18C2×#123×C131—21no—
19C2×#123×C131—21no—
20C2×#123×C131—28no—
21C2×#123×C131C2212yes—
22C2×#123×C131C2212yescomplemented
23C2×#123×C131C2214yescomplemented
24C2×#120×C131—21no—
25C2×#120×C131C2212yes—
26#518×C131C2211yescharacteristic
27C22×C4⋊C4×C131—21no—
28C22×C22⋊C4×C131—21no—
29C22×C22⋊C4×C131C2211yescharacteristic, complemented
30#458×C131—28no—
31C2×#99×C131C2212yes—
32C2×#99×C131C2214yescomplemented
33C2×#99×C131C2212yescomplemented
34#386×C131—24no—
35#385×C131—24no—
36#381×C131C2214yescomplemented
37#379×C131C2212yescomplemented
38#342×C131C2214yescomplemented
39C25×C131D411yescharacteristic
40C25×C131C2311yescharacteristic
41H(5,𝔽2)×C131—24no—
42H(5,𝔽2)×C131—42no—
43C2×#41×C131—21no—
44C2×#41×C131—22no—
45C22×D4×C131—21no—
46C22×D4×C131—22no—
47C22×D4×C131—24no—
48C22×D4×C131—22no—
49C22×D4×C131—24no—
50C22×D4×C131—42no—
51C22×D4×C131D411yescharacteristic
52C22×D4×C131D411yescharacteristic
53C22×D4×C131D414yes—
54C22×D4×C131C2312yes—
55C22×D4×C131C2311yescharacteristic
56C22×D4×C131C2311yescharacteristic
57C23×C4×C131—21no—
58C23×C4×C131—21no—
59C23×C4×C131—21no—
60C23×C4×C131—24no—
61C23×C4×C131—24no—
62C23×C4×C131—42no—
63C23×C4×C131D411yescharacteristic
64C23×C4×C131C2312yes—
65#127×C131—22no—
66#124×C131—22no—
67#123×C131—28no—
68#123×C131—28no—
69#123×C131—22no—
70#123×C131—24no—
71#123×C131—22no—
72#123×C131—22no—
73#123×C131—24no—
74#123×C131—24no—
75#123×C131—28no—
76#123×C131—44no—
77#123×C131D418yescomplemented
78C22⋊Q8×C131—22no—
79#121×C131—22no—
80#121×C131—24no—
81#121×C131—24no—
82#121×C131—24no—
83#120×C131—24no—
84#120×C131—22no—
85#120×C131—22no—
86#120×C131—22no—
87#120×C131—22no—
88#120×C131—24no—
89#120×C131—22no—
90C4×D4×C131—24no—
91C4×D4×C131—24no—
92#117×C131—21no—
93C2×C4⋊C4×C131—28no—
94C2×C4⋊C4×C131—22no—
95C2×C4⋊C4×C131—22no—
96C2×C4⋊C4×C131—24no—
97C2×C22⋊C4×C131—28no—
98C2×C22⋊C4×C131—22no—
99C2×C22⋊C4×C131—22no—
100C2×C22⋊C4×C131—22no—
101C2×C22⋊C4×C131—21no—
102C2×C22⋊C4×C131—21no—
103C2×C22⋊C4×C131—24no—
104C2×C22⋊C4×C131—24no—
105C2×C22⋊C4×C131—24no—
106C2×C22⋊C4×C131D414yes—
107C2×C22⋊C4×C131C2314yes—
108C2×C22⋊C4×C131C2312yes—
109C2×C22⋊C4×C131C2312yes—
110#99×C131—24no—
111#99×C131—28no—
112#99×C131—42no—
113#95×C131—28no—
114C24×C131—22no—
115C24×C131—22no—
116C24×C131—21no—
117C24×C131—22no—
118C24×C131—22no—
119C24×C131—44no—
120C24×C131—41no—
121C24×C131—44no—
122C24×C131C2×D411yescharacteristic
123C24×C131C2×D414yes—
124C24×C131C2×D411yescharacteristic
125C24×C131C2×D412yes—
126C24×C131C2×D411yescharacteristic
127C24×C131C2×D411yescharacteristic
128C24×C131C2411yescharacteristic
129#41×C131—48no—
130#41×C131—42no—
131#41×C131—42no—
132C2×Q8×C131—21no—
133C2×D4×C131—22no—
134C2×D4×C131—22no—
135C2×D4×C131—22no—
136C2×D4×C131—21no—
137C2×D4×C131—24no—
138C2×D4×C131—22no—
139C2×D4×C131—22no—
140C2×D4×C131—22no—
141C2×D4×C131—24no—
142C2×D4×C131—22no—
143C2×D4×C131—22no—
144C2×D4×C131—22no—
145C2×D4×C131—22no—
146C2×D4×C131—22no—
147C2×D4×C131—24no—
148C2×D4×C131—24no—
149C2×D4×C131—24no—
150C2×D4×C131—22no—
151C2×D4×C131—41no—
152C2×D4×C131—41no—
153C2×D4×C131—416no—
154C2×D4×C131—48no—
155C2×D4×C131—42no—
156C2×D4×C131—42no—
157C2×D4×C131—48no—
158C2×D4×C131—84no—
159C2×D4×C131C2×D414yes—
160C22×C4×C131—24no—
161C22×C4×C131—24no—
162C22×C4×C131—21no—
163C22×C4×C131—22no—
164C22×C4×C131—24no—
165C22×C4×C131—22no—
166C22×C4×C131—24no—
167C22×C4×C131—22no—
168C22×C4×C131—22no—
169C22×C4×C131—22no—
170C22×C4×C131—24no—
171C22×C4×C131—22no—
172C22×C4×C131—22no—
173C22×C4×C131—24no—
174C22×C4×C131—41no—
175C22×C4×C131—416no—
176C22×C4×C131—44no—
177C22×C4×C131—42no—
178C22×C4×C131—42no—
179C22×C4×C131—42no—
180C22×C4×C131—42no—
181C22×C4×C131C2×D412yes—
182C22×C4×C131C2×D411yescharacteristic
183C22×C4×C131C2×D411yescharacteristic
184C22×C4×C131C2×D414yes—
185C22×C4×C131C2×D414yescomplemented
186C4⋊C4×C131—28no—
187C4⋊C4×C131—22no—
188C4⋊C4×C131—24no—
189C4⋊C4×C131—28no—
190C4⋊C4×C131—48no—
191C22⋊C4×C131—24no—
192C22⋊C4×C131—28no—
193C22⋊C4×C131—22no—
194C22⋊C4×C131—24no—
195C22⋊C4×C131—24no—
196C22⋊C4×C131—28no—
197C22⋊C4×C131—24no—
198C22⋊C4×C131—24no—
199C22⋊C4×C131—22no—
200C22⋊C4×C131—22no—
201C22⋊C4×C131—22no—
202C22⋊C4×C131—24no—
203C22⋊C4×C131—24no—
204C22⋊C4×C131—48no—
205C22⋊C4×C131—48no—
206C22⋊C4×C131C2×D414yescomplemented
207C42×C131—22no—
208C23×C131—21no—
209C23×C131—21no—
210C23×C131—24no—
211C23×C131—21no—
212C23×C131—21no—
213C23×C131—21no—
214C23×C131—28no—
215C23×C131—28no—
216C23×C131—21no—
217C23×C131—21no—
218C23×C131—21no—
219C23×C131—22no—
220C23×C131—21no—
221C23×C131—24no—
222C23×C131—44no—
223C23×C131—42no—
224C23×C131—42no—
225C23×C131—44no—
226C23×C131—48no—
227C23×C131—48no—
228C23×C131—42no—
229C23×C131—42no—
230C23×C131—48no—
231C23×C131—42no—
232C23×C131—44no—
233C23×C131—44no—
234C23×C131—82no—
235C23×C131—84no—
236C23×C131—82no—
237C23×C131#12012yes—
238C23×C131#12012yes—
239C23×C131#12012yes—
240C23×C131C22×D411yescharacteristic
241C23×C131C22×D412yes—
242C23×C131C22×D412yes—
243C23×C131H(5,𝔽2)12yes—
244Q8×C131—42no—
245D4×C131—28no—
246D4×C131—44no—
247D4×C131—42no—
248D4×C131—44no—
249D4×C131—44no—
250D4×C131—42no—
251D4×C131—42no—
252D4×C131—44no—
253D4×C131—44no—
254D4×C131—48no—
255D4×C131—84no—
256D4×C131—84no—
257C2×C4×C131—21no—
258C2×C4×C131—21no—
259C2×C4×C131—24no—
260C2×C4×C131—24no—
261C2×C4×C131—21no—
262C2×C4×C131—24no—
263C2×C4×C131—22no—
264C2×C4×C131—21no—
265C2×C4×C131—21no—
266C2×C4×C131—28no—
267C2×C4×C131—24no—
268C2×C4×C131—44no—
269C2×C4×C131—44no—
270C2×C4×C131—48no—
271C2×C4×C131—44no—
272C2×C4×C131—48no—
273C2×C4×C131—48no—
274C2×C4×C131—42no—
275C2×C4×C131—42no—
276C2×C4×C131—42no—
277C2×C4×C131—44no—
278C2×C4×C131—44no—
279C2×C4×C131—48no—
280C2×C4×C131—44no—
281C2×C4×C131—82no—
282C2×C4×C131#12012yes—
283C22×C131—24no—
284C22×C131—24no—
285C22×C131—22no—
286C22×C131—24no—
287C22×C131—22no—
288C22×C131—22no—
289C22×C131—22no—
290C22×C131—22no—
291C22×C131—24no—
292C22×C131—42no—
293C22×C131—42no—
294C22×C131—416no—
295C22×C131—42no—
296C22×C131—42no—
297C22×C131—42no—
298C22×C131—42no—
299C22×C131—42no—
300C22×C131—42no—
301C22×C131—41no—
302C22×C131—44no—
303C22×C131—42no—
304C22×C131—81no—
305C22×C131—88no—
306C22×C131—84no—
307C22×C131—81no—
308C22×C131—162no—
309C22×C131#45814yescomplemented
310C22×C131C2×#12011yescharacteristic
311C22×C131C2×#12011yescharacteristic
312C22×C131#53411yescharacteristic
313C22×C131D4214yes—
314C4×C131—22no—
315C4×C131—44no—
316C4×C131—44no—
317C4×C131—41no—
318C4×C131—42no—
319C4×C131—44no—
320C4×C131—84no—
321C2×C131—21no—
322C2×C131—24no—
323C2×C131—21no—
324C2×C131—24no—
325C2×C131—42no—
326C2×C131—42no—
327C2×C131—81no—
328C2×C131—82no—
329C2×C131#240311yescharacteristic
330C2×C131C2×#45812yes—
331#23901C13111yesmaximal, characteristic, direct product factor, Sylow
332C131#2390111yescharacteristic, direct product factor, Sylow
333#3484C2×C13111yescharacteristic
334C22×#123C2×C13111yescharacteristic, complemented
335C2×#458C2×C13112yescomplemented
336#2849C2×C13112yescomplemented
337#2022C2×C13114yescomplemented
338#1898C2×C13112yescomplemented
339#1890C2×C13112yescomplemented
340#1781C2×C13111yescharacteristic, complemented
341C2×H(5,𝔽2)C22×C13111yescharacteristic
342C23×D4C22×C13111yescharacteristic
343C24×C4C22×C13111yescharacteristic, complemented
344#546—24no—
345D42—24no—
346#535—21no—
347#534—21no—
348#534C22×C13112yes—
349#525—21no—
350C2×#123—21no—
351C2×#123—21no—
352C2×#123—28no—
353C2×#123C22×C13112yes—
354C2×#123C22×C13112yescomplemented
355C2×#123C22×C13114yescomplemented
356C2×#120—21no—
357C2×#120C22×C13112yes—
358#518C22×C13111yescharacteristic
359C22×C4⋊C4—21no—
360C22×C22⋊C4—21no—
361C22×C22⋊C4C22×C13111yescharacteristic, complemented
362#458—28no—
363C2×#99C22×C13112yes—
364C2×#99C22×C13114yescomplemented
365C2×#99C22×C13112yescomplemented
366#386—24no—
367#385—24no—
368#381C22×C13114yescomplemented
369#379C22×C13112yescomplemented
370#342C22×C13114yescomplemented
371C25D4×C13111yescharacteristic
372C25C23×C13111yescharacteristic
373H(5,𝔽2)—24no—
374H(5,𝔽2)—42no—
375C2×#41—21no—
376C2×#41—22no—
377C22×D4—21no—
378C22×D4—22no—
379C22×D4—24no—
380C22×D4—22no—
381C22×D4—24no—
382C22×D4—42no—
383C22×D4D4×C13111yescharacteristic
384C22×D4D4×C13111yescharacteristic
385C22×D4D4×C13114yes—
386C22×D4C23×C13112yes—
387C22×D4C23×C13111yescharacteristic
388C22×D4C23×C13111yescharacteristic
389C23×C4—21no—
390C23×C4—21no—
391C23×C4—21no—
392C23×C4—24no—
393C23×C4—24no—
394C23×C4—42no—
395C23×C4D4×C13111yescharacteristic
396C23×C4C23×C13112yes—
397#127—22no—
398#124—22no—
399#123—28no—
400#123—28no—
401#123—22no—
402#123—24no—
403#123—22no—
404#123—22no—
405#123—24no—
406#123—24no—
407#123—28no—
408#123—44no—
409#123D4×C13118yescomplemented
410C22⋊Q8—22no—
411#121—22no—
412#121—24no—
413#121—24no—
414#121—24no—
415#120—24no—
416#120—22no—
417#120—22no—
418#120—22no—
419#120—22no—
420#120—24no—
421#120—22no—
422C4×D4—24no—
423C4×D4—24no—
424#117—21no—
425C2×C4⋊C4—28no—
426C2×C4⋊C4—22no—
427C2×C4⋊C4—22no—
428C2×C4⋊C4—24no—
429C2×C22⋊C4—28no—
430C2×C22⋊C4—22no—
431C2×C22⋊C4—22no—
432C2×C22⋊C4—22no—
433C2×C22⋊C4—21no—
434C2×C22⋊C4—21no—
435C2×C22⋊C4—24no—
436C2×C22⋊C4—24no—
437C2×C22⋊C4—24no—
438C2×C22⋊C4D4×C13114yes—
439C2×C22⋊C4C23×C13114yes—
440C2×C22⋊C4C23×C13112yes—
441C2×C22⋊C4C23×C13112yes—
442#99—24no—
443#99—28no—
444#99—42no—
445#95—28no—
446C24—22no—
447C24—22no—
448C24—21no—
449C24—22no—
450C24—22no—
451C24—44no—
452C24—41no—
453C24—44no—
454C24C2×D4×C13111yescharacteristic
455C24C2×D4×C13114yes—
456C24C2×D4×C13111yescharacteristic
457C24C2×D4×C13112yes—
458C24C2×D4×C13111yescharacteristic
459C24C2×D4×C13111yescharacteristic
460C24C24×C13111yescharacteristic
461#41—48no—
462#41—42no—
463#41—42no—
464C2×Q8—21no—
465C2×D4—22no—
466C2×D4—22no—
467C2×D4—22no—
468C2×D4—21no—
469C2×D4—24no—
470C2×D4—22no—
471C2×D4—22no—
472C2×D4—22no—
473C2×D4—24no—
474C2×D4—22no—
475C2×D4—22no—
476C2×D4—22no—
477C2×D4—22no—
478C2×D4—22no—
479C2×D4—24no—
480C2×D4—24no—
481C2×D4—24no—
482C2×D4—22no—
483C2×D4—41no—
484C2×D4—41no—
485C2×D4—416no—
486C2×D4—48no—
487C2×D4—42no—
488C2×D4—42no—
489C2×D4—48no—
490C2×D4—84no—
491C2×D4C2×D4×C13114yes—
492C22×C4—24no—
493C22×C4—24no—
494C22×C4—21no—
495C22×C4—22no—
496C22×C4—24no—
497C22×C4—22no—
498C22×C4—24no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—24no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—24no—
506C22×C4—41no—
507C22×C4—416no—
508C22×C4—44no—
509C22×C4—42no—
510C22×C4—42no—
511C22×C4—42no—
512C22×C4—42no—
513C22×C4C2×D4×C13112yes—
514C22×C4C2×D4×C13111yescharacteristic
515C22×C4C2×D4×C13111yescharacteristic
516C22×C4C2×D4×C13114yes—
517C22×C4C2×D4×C13114yescomplemented
518C4⋊C4—28no—
519C4⋊C4—22no—
520C4⋊C4—24no—
521C4⋊C4—28no—
522C4⋊C4—48no—
523C22⋊C4—24no—
524C22⋊C4—28no—
525C22⋊C4—22no—
526C22⋊C4—24no—
527C22⋊C4—24no—
528C22⋊C4—28no—
529C22⋊C4—24no—
530C22⋊C4—24no—
531C22⋊C4—22no—
532C22⋊C4—22no—
533C22⋊C4—22no—
534C22⋊C4—24no—
535C22⋊C4—24no—
536C22⋊C4—48no—
537C22⋊C4—48no—
538C22⋊C4C2×D4×C13114yescomplemented
539C42—22no—
540C23—24no—
541C23—21no—
542C23—21no—
543C23—28no—
544C23—21no—
545C23—21no—
546C23—21no—
547C23—28no—
548C23—21no—
549C23—21no—
550C23—21no—
551C23—22no—
552C23—21no—
553C23—24no—
554C23—44no—
555C23—42no—
556C23—42no—
557C23—44no—
558C23—48no—
559C23—48no—
560C23—42no—
561C23—42no—
562C23—48no—
563C23—42no—
564C23—44no—
565C23—44no—
566C23—82no—
567C23—84no—
568C23—82no—
569C23#120×C13112yes—
570C23#120×C13112yes—
571C23#120×C13112yes—
572C23C22×D4×C13111yescharacteristic
573C23C22×D4×C13112yes—
574C23C22×D4×C13112yes—
575C23H(5,𝔽2)×C13112yes—
576Q8—42no—
577D4—28no—
578D4—44no—
579D4—42no—
580D4—44no—
581D4—44no—
582D4—48no—
583D4—42no—
584D4—42no—
585D4—44no—
586D4—44no—
587D4—84no—
588D4—84no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—24no—
592C2×C4—24no—
593C2×C4—22no—
594C2×C4—24no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—28no—
599C2×C4—24no—
600C2×C4—44no—
601C2×C4—44no—
602C2×C4—48no—
603C2×C4—48no—
604C2×C4—48no—
605C2×C4—44no—
606C2×C4—42no—
607C2×C4—42no—
608C2×C4—42no—
609C2×C4—44no—
610C2×C4—44no—
611C2×C4—48no—
612C2×C4—44no—
613C2×C4—82no—
614C2×C4#120×C13112yes—
615C22—24no—
616C22—24no—
617C22—24no—
618C22—22no—
619C22—22no—
620C22—22no—
621C22—24no—
622C22—22no—
623C22—22no—
624C22—42no—
625C22—42no—
626C22—416no—
627C22—42no—
628C22—42no—
629C22—42no—
630C22—42no—
631C22—42no—
632C22—44no—
633C22—42no—
634C22—42no—
635C22—41no—
636C22—81no—
637C22—88no—
638C22—81no—
639C22—84no—
640C22—162no—
641C22#458×C13114yescomplemented
642C22C2×#120×C13111yescharacteristic
643C22C2×#120×C13111yescharacteristic
644C22#534×C13111yescharacteristic
645C22D42×C13114yes—
646C4—22no—
647C4—44no—
648C4—44no—
649C4—44no—
650C4—41no—
651C4—42no—
652C4—84no—
653C2—21no—
654C2—24no—
655C2—24no—
656C2—21no—
657C2—42no—
658C2—42no—
659C2—81no—
660C2—82no—
661C2#2403×C13111yescharacteristic
662C2C2×#458×C13112yes—
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. C22×#123×C131C2semidirect
3. C2×#458×C131C2semidirect
4. #2849×C131C2semidirect
5. #2022×C131C2semidirect
6. #1898×C131C2semidirect
7. #1890×C131C2semidirect
8. #1781×C131C2semidirect
11. C24×C4×C131C22semidirect
22. C2×#123×C131C22semidirect
23. C2×#123×C131C22semidirect
29. C22×C22⋊C4×C131C22semidirect
32. C2×#99×C131C22semidirect
33. C2×#99×C131C22semidirect
36. #381×C131C22semidirect
37. #379×C131C22semidirect
38. #342×C131C22semidirect
77. #123×C131D4semidirect
185. C22×C4×C131C2×D4semidirect
206. C22⋊C4×C131C2×D4semidirect
309. C22×C131#458semidirect
331. #23901C131direct (N × H)
332. C131#23901direct (N × H)
334. C22×#123C2×C131semidirect
335. C2×#458C2×C131semidirect
336. #2849C2×C131semidirect
337. #2022C2×C131semidirect
338. #1898C2×C131semidirect
339. #1890C2×C131semidirect
340. #1781C2×C131semidirect
343. C24×C4C22×C131semidirect
354. C2×#123C22×C131semidirect
355. C2×#123C22×C131semidirect
361. C22×C22⋊C4C22×C131semidirect
364. C2×#99C22×C131semidirect
365. C2×#99C22×C131semidirect
368. #381C22×C131semidirect
369. #379C22×C131semidirect
370. #342C22×C131semidirect
409. #123D4×C131semidirect
517. C22×C4C2×D4×C131semidirect
538. C22⋊C4C2×D4×C131semidirect
641. C22#458×C131semidirect

Maximal subgroups

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

subgroupindex
#3484×C1312
C22×#123×C1312
C2×#458×C1312
#2849×C1312
#2022×C1312
#1898×C1312
#1890×C1312
#1781×C1312
#23901131