Finite Group Databasebeta

← C131×#9041 #45694925

Subgroups — C131×#9041 #45694925

Order 33536.

1050 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#447×C131C211yesmaximal, characteristic
2#2325×C131C211yesmaximal, characteristic, complemented
3#1786×C131C211yesmaximal, characteristic, complemented
4C2×#327×C131C211yesmaximal, characteristic, complemented
5#1438×C131C211yesmaximal, characteristic, complemented
6#1294×C131C211yesmaximal, characteristic, complemented
7#1280×C131C211yesmaximal, characteristic, complemented
8C23×D4×C131C2211yescharacteristic
9C22×D8×C131—21no—
10C2×#121×C131C2211yescharacteristic
11C2×C4×D4×C131—21no—
12C22×C22⋊C4×C131—21no—
13C22×C22⋊C4×C131—21no—
14#447×C131—22no—
15#447×C131C414yescomplemented
16C2×#102×C131—21no—
17C2×#102×C131—21no—
18C2×#102×C131—21no—
19C2×C22⋊C8×C131C2211yescharacteristic
20C2×C22⋊C8×C131C2211yescharacteristic
21#388×C131—21no—
22#387×C131—21no—
23#386×C131—21no—
24#386×C131—21no—
25#385×C131—21no—
26#380×C131C2211yescharacteristic
27C2×#95×C131C2211yescharacteristic
28C2×#95×C131C2211yescharacteristic
29#327×C131—22no—
30C25×C131—21no—
31C22×D4×C131—21no—
32C22×D4×C131—21no—
33C22×D4×C131—21no—
34C22×D4×C131—21no—
35C22×D4×C131—21no—
36C22×D4×C131—21no—
37C22×D4×C131—42no—
38C22×D4×C131—42no—
39C22×D4×C131C2×C412yescomplemented
40C22×D4×C131D411yescharacteristic
41C23×C4×C131—21no—
42C23×C4×C131—21no—
43C23×C4×C131D411yescharacteristic
44C23×C4×C131D411yescharacteristic
45C23×C4×C131C2311yescharacteristic
46C2×D8×C131—24no—
47C2×D8×C131—42no—
48C2×D8×C131—42no—
49C22×C8×C131—21no—
50C22×C8×C131—21no—
51#121×C131—21no—
52#121×C131—21no—
53#121×C131C2×C412yes—
54#121×C131D412yes—
55C4×D4×C131—42no—
56C4×D4×C131—42no—
57C2×C4⋊C4×C131—21no—
58C2×C4⋊C4×C131D411yescharacteristic
59C2×C4⋊C4×C131D411yescharacteristic
60C2×C4⋊C4×C131D411yescharacteristic
61C2×C22⋊C4×C131—21no—
62C2×C22⋊C4×C131—21no—
63C2×C22⋊C4×C131—21no—
64C2×C22⋊C4×C131—21no—
65C2×C22⋊C4×C131—21no—
66C2×C22⋊C4×C131—42no—
67C2×C22⋊C4×C131—42no—
68C2×C22⋊C4×C131—42no—
69C2×C22⋊C4×C131—42no—
70C2×C22⋊C4×C131—42no—
71C2×C22⋊C4×C131—42no—
72C2×C42×C131—21no—
73#102×C131—24no—
74#102×C131—42no—
75#102×C131—42no—
76C22⋊C8×C131—21no—
77C22⋊C8×C131—21no—
78C22⋊C8×C131—21no—
79C22⋊C8×C131C2×C412yescomplemented
80#95×C131—21no—
81#95×C131—21no—
82#95×C131—21no—
83#95×C131—21no—
84#95×C131—21no—
85#95×C131—21no—
86#95×C131—21no—
87C24×C131—22no—
88C24×C131—22no—
89C24×C131—22no—
90C24×C131—21no—
91C24×C131—41no—
92C24×C131—41no—
93C24×C131—41no—
94C24×C131—41no—
95C24×C131—41no—
96C24×C131—41no—
97C24×C131—41no—
98C24×C131—41no—
99C24×C131—41no—
100C24×C131—41no—
101C24×C131—41no—
102C24×C131—41no—
103C24×C131C2×D411yescharacteristic
104C2×D4×C131—22no—
105C2×D4×C131—22no—
106C2×D4×C131—22no—
107C2×D4×C131—22no—
108C2×D4×C131—22no—
109C2×D4×C131—22no—
110C2×D4×C131—22no—
111C2×D4×C131—22no—
112C2×D4×C131—21no—
113C2×D4×C131—41no—
114C2×D4×C131—41no—
115C2×D4×C131—41no—
116C2×D4×C131—41no—
117C2×D4×C131—41no—
118C2×D4×C131—41no—
119C2×D4×C131—44no—
120C2×D4×C131—44no—
121C2×D4×C131—44no—
122C2×D4×C131—44no—
123C2×D4×C131—41no—
124C2×D4×C131—41no—
125C2×D4×C131—41no—
126C2×D4×C131—41no—
127C2×D4×C131—41no—
128C2×D4×C131—41no—
129C2×D4×C131C22⋊C412yescomplemented
130C22×C4×C131—21no—
131C22×C4×C131—21no—
132C22×C4×C131—21no—
133C22×C4×C131—22no—
134C22×C4×C131—21no—
135C22×C4×C131—21no—
136C22×C4×C131—21no—
137C22×C4×C131—21no—
138C22×C4×C131—21no—
139C22×C4×C131—41no—
140C22×C4×C131—41no—
141C22×C4×C131—42no—
142C22×C4×C131—41no—
143C22×C4×C131—41no—
144C22×C4×C131—41no—
145C22×C4×C131—41no—
146C22×C4×C131—41no—
147C22×C4×C131—41no—
148C22×C4×C131—41no—
149C22×C4×C131—41no—
150C22×C4×C131—41no—
151C22×C4×C131—41no—
152C22×C4×C131—81no—
153C22×C4×C131—81no—
154C22×C4×C131D812yescomplemented
155C22×C4×C131C22×C411yescharacteristic
156C22×C4×C131C2×D411yescharacteristic
157C22×C4×C131C2×D411yescharacteristic
158C22×C4×C131C2×D411yescharacteristic
159C22×C4×C131#4111yescharacteristic
160C22×C4×C131#4111yescharacteristic
161D8×C131—48no—
162C2×C8×C131—22no—
163C2×C8×C131—41no—
164C2×C8×C131—41no—
165C2×C8×C131—41no—
166C2×C8×C131—41no—
167C2×C8×C131—41no—
168C4⋊C4×C131—21no—
169C4⋊C4×C131—41no—
170C4⋊C4×C131—41no—
171C4⋊C4×C131—42no—
172C4⋊C4×C131C22⋊C412yescomplemented
173C22⋊C4×C131—22no—
174C22⋊C4×C131—22no—
175C22⋊C4×C131—42no—
176C22⋊C4×C131—48no—
177C22⋊C4×C131—48no—
178C22⋊C4×C131—41no—
179C22⋊C4×C131—41no—
180C22⋊C4×C131—81no—
181C22⋊C4×C131—81no—
182C42×C131—42no—
183C23×C131—21no—
184C23×C131—21no—
185C23×C131—21no—
186C23×C131—21no—
187C23×C131—24no—
188C23×C131—22no—
189C23×C131—42no—
190C23×C131—42no—
191C23×C131—42no—
192C23×C131—42no—
193C23×C131—42no—
194C23×C131—42no—
195C23×C131—42no—
196C23×C131—42no—
197C23×C131—42no—
198C23×C131—42no—
199C23×C131—42no—
200C23×C131—42no—
201C23×C131—42no—
202C23×C131—42no—
203C23×C131—42no—
204C23×C131—42no—
205C23×C131—41no—
206C23×C131—41no—
207C23×C131—41no—
208C23×C131—41no—
209C23×C131—41no—
210C23×C131—41no—
211C23×C131—42no—
212C23×C131—42no—
213C23×C131—81no—
214C23×C131—81no—
215C23×C131—81no—
216C23×C131—81no—
217C23×C131—81no—
218C23×C131—81no—
219C23×C131—81no—
220C23×C131—81no—
221C23×C131—81no—
222C23×C131—81no—
223C23×C131—81no—
224C23×C131—81no—
225C23×C131—81no—
226C23×C131—81no—
227C23×C131—81no—
228C23×C131—81no—
229C23×C131C4×D411yescharacteristic
230C23×C131#12011yescharacteristic
231C23×C131#12111yescharacteristic
232C23×C131C2×D811yescharacteristic
233C23×C131#13511yescharacteristic
234C23×C131AGL(1,ℤ/8)11yescharacteristic
235C23×C131AGL(1,ℤ/8)11yescharacteristic
236D4×C131—24no—
237D4×C131—24no—
238D4×C131—42no—
239D4×C131—42no—
240D4×C131—42no—
241D4×C131—42no—
242D4×C131—42no—
243D4×C131—42no—
244D4×C131—42no—
245D4×C131—42no—
246D4×C131—42no—
247D4×C131—42no—
248D4×C131—42no—
249D4×C131—81no—
250C2×C4×C131—21no—
251C2×C4×C131—21no—
252C2×C4×C131—21no—
253C2×C4×C131—21no—
254C2×C4×C131—22no—
255C2×C4×C131—22no—
256C2×C4×C131—41no—
257C2×C4×C131—41no—
258C2×C4×C131—41no—
259C2×C4×C131—41no—
260C2×C4×C131—41no—
261C2×C4×C131—41no—
262C2×C4×C131—41no—
263C2×C4×C131—41no—
264C2×C4×C131—42no—
265C2×C4×C131—42no—
266C2×C4×C131—42no—
267C2×C4×C131—42no—
268C2×C4×C131—42no—
269C2×C4×C131—41no—
270C2×C4×C131—41no—
271C2×C4×C131—41no—
272C2×C4×C131—41no—
273C2×C4×C131—41no—
274C2×C4×C131—41no—
275C2×C4×C131—41no—
276C2×C4×C131—41no—
277C2×C4×C131—41no—
278C2×C4×C131—81no—
279C2×C4×C131—84no—
280C2×C4×C131—81no—
281C2×C4×C131—81no—
282C2×C4×C131—81no—
283C2×C4×C131—81no—
284C2×C4×C131—81no—
285C2×C4×C131C2×C22⋊C411yescharacteristic
286C2×C4×C131C4×D411yescharacteristic
287C2×C4×C131#12111yescharacteristic
288C2×C4×C131#12311yescharacteristic
289C8×C131—42no—
290C8×C131—81no—
291C22×C131—21no—
292C22×C131—21no—
293C22×C131—21no—
294C22×C131—21no—
295C22×C131—21no—
296C22×C131—21no—
297C22×C131—21no—
298C22×C131—21no—
299C22×C131—21no—
300C22×C131—21no—
301C22×C131—21no—
302C22×C131—21no—
303C22×C131—44no—
304C22×C131—44no—
305C22×C131—42no—
306C22×C131—42no—
307C22×C131—44no—
308C22×C131—42no—
309C22×C131—82no—
310C22×C131—82no—
311C22×C131—82no—
312C22×C131—82no—
313C22×C131—82no—
314C22×C131—82no—
315C22×C131—81no—
316C22×C131—82no—
317C22×C131—81no—
318C22×C131—82no—
319C22×C131—81no—
320C22×C131—82no—
321C22×C131—81no—
322C22×C131—82no—
323C22×C131—82no—
324C22×C131—82no—
325C22×C131#38611yescharacteristic
326C22×C131C4×D811yescharacteristic
327C22×C131#44211yescharacteristic
328C22×C131#44711yescharacteristic
329C22×C131#44911yescharacteristic
330C22×C131#45311yescharacteristic
331C22×C131#45411yescharacteristic
332C22×C131B(4,𝔽2)11yescharacteristic
333C22×C131B(4,𝔽2)11yescharacteristic
334C22×C131#45911yescharacteristic
335C22×C131#46311yescharacteristic
336C4×C131—21no—
337C4×C131—21no—
338C4×C131—21no—
339C4×C131—21no—
340C4×C131—42no—
341C4×C131—42no—
342C4×C131—82no—
343C4×C131—81no—
344C4×C131—81no—
345C4×C131—81no—
346C2×C131—21no—
347C2×C131—21no—
348C2×C131—21no—
349C2×C131—21no—
350C2×C131—82no—
351C2×C131—84no—
352C2×C131#159511yescharacteristic
353C2×C131#159711yescharacteristic
354C2×C131#159811yescharacteristic
355C2×C131#160011yescharacteristic
356C2×C131#187911yescharacteristic
357C2×C131#188311yescharacteristic
358C2×C131#188911yescharacteristic
359#9041C13111yesmaximal, characteristic, direct product factor, Sylow
360C131#904111yescharacteristic, direct product factor, Sylow
361C2×#447C2×C13111yescharacteristic
362#2325C2×C13111yescharacteristic, complemented
363#1786C2×C13111yescharacteristic, complemented
364C2×#327C2×C13111yescharacteristic, complemented
365#1438C2×C13111yescharacteristic, complemented
366#1294C2×C13111yescharacteristic, complemented
367#1280C2×C13111yescharacteristic, complemented
368C23×D4C22×C13111yescharacteristic
369C22×D8—21no—
370C2×#121C22×C13111yescharacteristic
371C2×C4×D4—21no—
372C22×C22⋊C4—21no—
373C22×C22⋊C4—21no—
374#447—22no—
375#447C4×C13114yescomplemented
376C2×#102—21no—
377C2×#102—21no—
378C2×#102—21no—
379C2×C22⋊C8C22×C13111yescharacteristic
380C2×C22⋊C8C22×C13111yescharacteristic
381#388—21no—
382#387—21no—
383#386—21no—
384#386—21no—
385#385—21no—
386#380C22×C13111yescharacteristic
387C2×#95C22×C13111yescharacteristic
388C2×#95C22×C13111yescharacteristic
389#327—22no—
390C25—21no—
391C22×D4—21no—
392C22×D4—21no—
393C22×D4—21no—
394C22×D4—21no—
395C22×D4—21no—
396C22×D4—21no—
397C22×D4—42no—
398C22×D4—42no—
399C22×D4C2×C4×C13112yescomplemented
400C22×D4D4×C13111yescharacteristic
401C23×C4—21no—
402C23×C4—21no—
403C23×C4D4×C13111yescharacteristic
404C23×C4D4×C13111yescharacteristic
405C23×C4C23×C13111yescharacteristic
406C2×D8—24no—
407C2×D8—42no—
408C2×D8—42no—
409C22×C8—21no—
410C22×C8—21no—
411#121—21no—
412#121—21no—
413#121C2×C4×C13112yes—
414#121D4×C13112yes—
415C4×D4—42no—
416C4×D4—42no—
417C2×C4⋊C4—21no—
418C2×C4⋊C4D4×C13111yescharacteristic
419C2×C4⋊C4D4×C13111yescharacteristic
420C2×C4⋊C4D4×C13111yescharacteristic
421C2×C22⋊C4—21no—
422C2×C22⋊C4—21no—
423C2×C22⋊C4—21no—
424C2×C22⋊C4—21no—
425C2×C22⋊C4—21no—
426C2×C22⋊C4—42no—
427C2×C22⋊C4—42no—
428C2×C22⋊C4—42no—
429C2×C22⋊C4—42no—
430C2×C22⋊C4—42no—
431C2×C22⋊C4—42no—
432C2×C42—21no—
433#102—24no—
434#102—42no—
435#102—42no—
436C22⋊C8—21no—
437C22⋊C8—21no—
438C22⋊C8—21no—
439C22⋊C8C2×C4×C13112yescomplemented
440#95—21no—
441#95—21no—
442#95—21no—
443#95—21no—
444#95—21no—
445#95—21no—
446#95—21no—
447C24—22no—
448C24—22no—
449C24—22no—
450C24—21no—
451C24—41no—
452C24—41no—
453C24—41no—
454C24—41no—
455C24—41no—
456C24—41no—
457C24—41no—
458C24—41no—
459C24—41no—
460C24—41no—
461C24—41no—
462C24—41no—
463C24C2×D4×C13111yescharacteristic
464C2×D4—22no—
465C2×D4—22no—
466C2×D4—22no—
467C2×D4—22no—
468C2×D4—22no—
469C2×D4—22no—
470C2×D4—22no—
471C2×D4—22no—
472C2×D4—21no—
473C2×D4—41no—
474C2×D4—41no—
475C2×D4—41no—
476C2×D4—41no—
477C2×D4—41no—
478C2×D4—41no—
479C2×D4—44no—
480C2×D4—44no—
481C2×D4—44no—
482C2×D4—44no—
483C2×D4—41no—
484C2×D4—41no—
485C2×D4—41no—
486C2×D4—41no—
487C2×D4—41no—
488C2×D4—41no—
489C2×D4C22⋊C4×C13112yescomplemented
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—22no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—41no—
500C22×C4—41no—
501C22×C4—42no—
502C22×C4—41no—
503C22×C4—41no—
504C22×C4—41no—
505C22×C4—41no—
506C22×C4—41no—
507C22×C4—41no—
508C22×C4—41no—
509C22×C4—41no—
510C22×C4—41no—
511C22×C4—41no—
512C22×C4—81no—
513C22×C4—81no—
514C22×C4D8×C13112yescomplemented
515C22×C4C22×C4×C13111yescharacteristic
516C22×C4C2×D4×C13111yescharacteristic
517C22×C4C2×D4×C13111yescharacteristic
518C22×C4C2×D4×C13111yescharacteristic
519C22×C4#41×C13111yescharacteristic
520C22×C4#41×C13111yescharacteristic
521D8—48no—
522C2×C8—22no—
523C2×C8—41no—
524C2×C8—41no—
525C2×C8—41no—
526C2×C8—41no—
527C2×C8—41no—
528C4⋊C4—21no—
529C4⋊C4—41no—
530C4⋊C4—41no—
531C4⋊C4—42no—
532C4⋊C4C22⋊C4×C13112yescomplemented
533C22⋊C4—22no—
534C22⋊C4—22no—
535C22⋊C4—42no—
536C22⋊C4—48no—
537C22⋊C4—48no—
538C22⋊C4—41no—
539C22⋊C4—41no—
540C22⋊C4—81no—
541C22⋊C4—81no—
542C42—42no—
543C23—21no—
544C23—21no—
545C23—21no—
546C23—21no—
547C23—24no—
548C23—22no—
549C23—42no—
550C23—42no—
551C23—42no—
552C23—42no—
553C23—42no—
554C23—42no—
555C23—42no—
556C23—42no—
557C23—42no—
558C23—42no—
559C23—42no—
560C23—42no—
561C23—42no—
562C23—42no—
563C23—42no—
564C23—41no—
565C23—41no—
566C23—41no—
567C23—41no—
568C23—41no—
569C23—41no—
570C23—42no—
571C23—42no—
572C23—42no—
573C23—81no—
574C23—81no—
575C23—81no—
576C23—81no—
577C23—81no—
578C23—81no—
579C23—81no—
580C23—81no—
581C23—81no—
582C23—81no—
583C23—81no—
584C23—81no—
585C23—81no—
586C23—81no—
587C23—81no—
588C23—81no—
589C23C4×D4×C13111yescharacteristic
590C23#120×C13111yescharacteristic
591C23#121×C13111yescharacteristic
592C23C2×D8×C13111yescharacteristic
593C23#135×C13111yescharacteristic
594C23AGL(1,ℤ/8)×C13111yescharacteristic
595C23AGL(1,ℤ/8)×C13111yescharacteristic
596D4—24no—
597D4—24no—
598D4—42no—
599D4—42no—
600D4—42no—
601D4—42no—
602D4—42no—
603D4—42no—
604D4—42no—
605D4—42no—
606D4—42no—
607D4—42no—
608D4—42no—
609D4—81no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—22no—
615C2×C4—22no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—41no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—41no—
622C2×C4—41no—
623C2×C4—41no—
624C2×C4—42no—
625C2×C4—42no—
626C2×C4—42no—
627C2×C4—42no—
628C2×C4—42no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—81no—
639C2×C4—84no—
640C2×C4—81no—
641C2×C4—81no—
642C2×C4—81no—
643C2×C4—81no—
644C2×C4—81no—
645C2×C4C2×C22⋊C4×C13111yescharacteristic
646C2×C4C4×D4×C13111yescharacteristic
647C2×C4#121×C13111yescharacteristic
648C2×C4#123×C13111yescharacteristic
649C8—42no—
650C8—81no—
651C22—21no—
652C22—21no—
653C22—21no—
654C22—21no—
655C22—21no—
656C22—21no—
657C22—21no—
658C22—21no—
659C22—21no—
660C22—21no—
661C22—21no—
662C22—21no—
663C22—44no—
664C22—44no—
665C22—42no—
666C22—42no—
667C22—44no—
668C22—42no—
669C22—82no—
670C22—82no—
671C22—82no—
672C22—82no—
673C22—82no—
674C22—82no—
675C22—81no—
676C22—82no—
677C22—82no—
678C22—81no—
679C22—82no—
680C22—81no—
681C22—82no—
682C22—81no—
683C22—82no—
684C22—82no—
685C22#386×C13111yescharacteristic
686C22C4×D8×C13111yescharacteristic
687C22#442×C13111yescharacteristic
688C22#447×C13111yescharacteristic
689C22#449×C13111yescharacteristic
690C22#453×C13111yescharacteristic
691C22#454×C13111yescharacteristic
692C22B(4,𝔽2)×C13111yescharacteristic
693C22B(4,𝔽2)×C13111yescharacteristic
694C22#459×C13111yescharacteristic
695C22#463×C13111yescharacteristic
696C4—21no—
697C4—21no—
698C4—21no—
699C4—21no—
700C4—42no—
701C4—42no—
702C4—82no—
703C4—81no—
704C4—81no—
705C4—81no—
706C2—21no—
707C2—21no—
708C2—21no—
709C2—21no—
710C2—84no—
711C2—82no—
712C2#1595×C13111yescharacteristic
713C2#1597×C13111yescharacteristic
714C2#1598×C13111yescharacteristic
715C2#1600×C13111yescharacteristic
716C2#1879×C13111yescharacteristic
717C2#1883×C13111yescharacteristic
718C2#1889×C13111yescharacteristic
subgroupG/H
center, socleC23×C131#120
commutatorC22×C4C22×C4×C131
Frattini, cosocleC23×C4C23×C131
prime radicalC2×#447×C131C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C131 ◁ C23×C4×C131 ◁ G

Complements

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

NH ≅ G/Ntype
2. #2325×C131C2semidirect
3. #1786×C131C2semidirect
4. C2×#327×C131C2semidirect
5. #1438×C131C2semidirect
6. #1294×C131C2semidirect
7. #1280×C131C2semidirect
15. #447×C131C4semidirect
39. C22×D4×C131C2×C4semidirect
79. C22⋊C8×C131C2×C4semidirect
129. C2×D4×C131C22⋊C4semidirect
154. C22×C4×C131D8semidirect
172. C4⋊C4×C131C22⋊C4semidirect
359. #9041C131direct (N × H)
360. C131#9041direct (N × H)
362. #2325C2×C131semidirect
363. #1786C2×C131semidirect
364. C2×#327C2×C131semidirect
365. #1438C2×C131semidirect
366. #1294C2×C131semidirect
367. #1280C2×C131semidirect
375. #447C4×C131semidirect
399. C22×D4C2×C4×C131semidirect
439. C22⋊C8C2×C4×C131semidirect
489. C2×D4C22⋊C4×C131semidirect
514. C22×C4D8×C131semidirect
532. C4⋊C4C22⋊C4×C131semidirect

Maximal subgroups

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

subgroupindex
C2×#447×C1312
#2325×C1312
#1786×C1312
C2×#327×C1312
#1438×C1312
#1294×C1312
#1280×C1312
#9041131