Finite Group Databasebeta

← C131×#24586 #45710470

Subgroups — C131×#24586 #45710470

Order 33536.

762 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#485×C131C211yesmaximal, characteristic
2C2×#427×C131C211yesmaximal, characteristic
3#2499×C131C211yesmaximal, characteristic
4#2346×C131C211yesmaximal, characteristic
5#2085×C131C211yesmaximal, characteristic, complemented
6#2084×C131C211yesmaximal, characteristic, complemented
7#2068×C131C211yesmaximal, characteristic, complemented
8#2066×C131C211yesmaximal, characteristic, complemented
9#1949×C131C211yesmaximal, characteristic, complemented
10#1947×C131C211yesmaximal, characteristic, complemented
11#1928×C131C211yesmaximal, characteristic, complemented
12#1927×C131C211yesmaximal, characteristic, complemented
13#1892×C131C211yesmaximal, characteristic
14#1850×C131C211yesmaximal, characteristic
15#1825×C131C211yesmaximal, characteristic
16C23×C8×C131C2211yescharacteristic
17C2×C22⋊Q8×C131C2211yescharacteristic
18C2×#117×C131C2211yescharacteristic
19C2×#117×C131C2211yescharacteristic
20#485×C131—24no—
21#427×C131—24no—
22C2×#107×C131C2211yescharacteristic
23C2×#107×C131C2211yescharacteristic
24C2×#107×C131C2211yescharacteristic
25C2×#106×C131C2211yescharacteristic
26C2×#106×C131C2211yescharacteristic
27C2×#106×C131C2211yescharacteristic
28C2×C4⋊C8×C131C2211yescharacteristic
29C2×C4⋊C8×C131C2211yescharacteristic
30C2×#103×C131C2211yescharacteristic
31C2×#103×C131C2211yescharacteristic
32C2×#103×C131C2211yescharacteristic
33C2×#103×C131C2211yescharacteristic
34C2×C22⋊C8×C131C2211yescharacteristic
35#397×C131—21no—
36#397×C131—21no—
37#391×C131C2211yescharacteristic
38#391×C131C2211yescharacteristic
39#389×C131C2211yescharacteristic
40#389×C131C2211yescharacteristic
41#388×C131—21no—
42#388×C131—21no—
43#387×C131—21no—
44#387×C131—21no—
45#384×C131C2211yescharacteristic
46#382×C131—21no—
47#382×C131C2211yescharacteristic
48#380×C131C2211yescharacteristic
49C4×C4⋊C4×C131C2211yescharacteristic
50C4×C4⋊C4×C131C2211yescharacteristic
51C4×C22⋊C4×C131C2211yescharacteristic
52#376×C131—21no—
53#340×C131C2211yescharacteristic
54#340×C131C2211yescharacteristic
55#340×C131C2211yescharacteristic
56#340×C131C2211yescharacteristic
57#340×C131C2211yescharacteristic
58#340×C131C2211yescharacteristic
59#336×C131C2211yescharacteristic
60#336×C131C2211yescharacteristic
61C22×Q8×C131C2311yescharacteristic
62C23×C4×C131C2311yescharacteristic
63C22×C8×C131—22no—
64C22×C8×C131—22no—
65C22×C8×C131—22no—
66C22×C8×C131C2311yescharacteristic
67C22×C8×C131C2311yescharacteristic
68C22×C8×C131C2311yescharacteristic
69C22×C8×C131C2311yescharacteristic
70C22⋊Q8×C131—22no—
71C22⋊Q8×C131—22no—
72#117×C131—22no—
73#117×C131—22no—
74#117×C131—22no—
75#117×C131D414yes—
76C2×C4⋊C4×C131—21no—
77C2×C4⋊C4×C131—21no—
78C2×C4⋊C4×C131—21no—
79C2×C4⋊C4×C131—21no—
80C2×C4⋊C4×C131—21no—
81C2×C4⋊C4×C131C2311yescharacteristic
82C2×C4⋊C4×C131C2311yescharacteristic
83C2×C4⋊C4×C131C2311yescharacteristic
84C2×C4⋊C4×C131C2311yescharacteristic
85C2×C4⋊C4×C131C2311yescharacteristic
86C2×C4⋊C4×C131C2311yescharacteristic
87C2×C4⋊C4×C131C2311yescharacteristic
88C2×C22⋊C4×C131—21no—
89C2×C22⋊C4×C131—21no—
90C2×C22⋊C4×C131—21no—
91C2×C22⋊C4×C131—21no—
92C2×C22⋊C4×C131D411yescharacteristic
93C2×C22⋊C4×C131D411yescharacteristic
94C2×C42×C131—21no—
95C2×C42×C131—21no—
96C2×C42×C131—21no—
97C2×C42×C131—21no—
98C2×C42×C131C2311yescharacteristic
99C2×C42×C131C2311yescharacteristic
100#107×C131—22no—
101#107×C131—22no—
102#107×C131—22no—
103#106×C131—22no—
104#106×C131—22no—
105#106×C131—22no—
106C4⋊C8×C131—22no—
107C4⋊C8×C131—22no—
108#103×C131—22no—
109#103×C131—22no—
110#103×C131—22no—
111#103×C131—22no—
112C22⋊C8×C131—22no—
113#95×C131—21no—
114#95×C131—21no—
115#95×C131—21no—
116#95×C131—21no—
117#95×C131—21no—
118#95×C131—21no—
119#95×C131—21no—
120#95×C131—21no—
121#95×C131—21no—
122#95×C131—21no—
123#95×C131—21no—
124#95×C131D411yescharacteristic
125#95×C131D411yescharacteristic
126C24×C131C2×D411yescharacteristic
127C2×Q8×C131—21no—
128C2×Q8×C131—21no—
129C2×Q8×C131—21no—
130C2×Q8×C131—21no—
131C2×Q8×C131—21no—
132C2×Q8×C131—21no—
133C22×C4×C131—21no—
134C22×C4×C131—21no—
135C22×C4×C131—21no—
136C22×C4×C131—21no—
137C22×C4×C131—21no—
138C22×C4×C131—21no—
139C22×C4×C131—21no—
140C22×C4×C131—21no—
141C22×C4×C131—21no—
142C22×C4×C131—21no—
143C22×C4×C131—21no—
144C22×C4×C131—21no—
145C22×C4×C131C2×D411yescharacteristic
146C22×C4×C131C2×D411yescharacteristic
147C22×C4×C131C2×D411yescharacteristic
148C22×C4×C131C2×D411yescharacteristic
149C22×C4×C131C2×D412yes—
150C22×C4×C131C2×D411yescharacteristic
151C22×C4×C131#4112yes—
152C22×C4×C131C2411yescharacteristic
153C2×C8×C131—28no—
154C2×C8×C131—21no—
155C2×C8×C131—21no—
156C2×C8×C131—21no—
157C2×C8×C131—21no—
158C2×C8×C131—21no—
159C2×C8×C131—21no—
160C2×C8×C131—21no—
161C2×C8×C131—21no—
162C2×C8×C131—21no—
163C2×C8×C131—21no—
164C2×C8×C131#4112yes—
165C2×C8×C131#4112yes—
166C4⋊C4×C131—21no—
167C4⋊C4×C131—21no—
168C4⋊C4×C131—21no—
169C4⋊C4×C131—21no—
170C4⋊C4×C131—21no—
171C4⋊C4×C131—21no—
172C4⋊C4×C131—21no—
173C4⋊C4×C131—21no—
174C4⋊C4×C131—21no—
175C4⋊C4×C131—21no—
176C4⋊C4×C131—21no—
177C4⋊C4×C131—21no—
178C4⋊C4×C131—42no—
179C4⋊C4×C131—42no—
180C4⋊C4×C131—42no—
181C4⋊C4×C131—81no—
182C4⋊C4×C131—81no—
183C4⋊C4×C131C2×D412yes—
184C4⋊C4×C131C2×D412yes—
185C22⋊C4×C131—24no—
186C22⋊C4×C131—22no—
187C22⋊C4×C131—41no—
188C22⋊C4×C131—42no—
189C22⋊C4×C131—42no—
190C22⋊C4×C131—81no—
191C42×C131—24no—
192C42×C131—21no—
193C42×C131—21no—
194C42×C131—21no—
195C42×C131—21no—
196C42×C131—42no—
197C42×C131—42no—
198C42×C131—42no—
199C23×C131—21no—
200C23×C131—21no—
201C23×C131—21no—
202C23×C131—21no—
203C23×C131—21no—
204C23×C131—21no—
205C23×C131#12112yes—
206C23×C131C22×D411yescharacteristic
207Q8×C131—41no—
208Q8×C131—41no—
209Q8×C131—41no—
210Q8×C131—41no—
211C2×C4×C131—21no—
212C2×C4×C131—21no—
213C2×C4×C131—21no—
214C2×C4×C131—21no—
215C2×C4×C131—22no—
216C2×C4×C131—22no—
217C2×C4×C131—22no—
218C2×C4×C131—22no—
219C2×C4×C131—22no—
220C2×C4×C131—22no—
221C2×C4×C131—21no—
222C2×C4×C131—21no—
223C2×C4×C131—21no—
224C2×C4×C131—21no—
225C2×C4×C131—21no—
226C2×C4×C131—21no—
227C2×C4×C131—21no—
228C2×C4×C131—21no—
229C2×C4×C131—21no—
230C2×C4×C131—41no—
231C2×C4×C131—41no—
232C2×C4×C131—41no—
233C2×C4×C131—41no—
234C2×C4×C131—41no—
235C2×C4×C131—41no—
236C2×C4×C131—41no—
237C2×C4×C131—41no—
238C2×C4×C131—41no—
239C2×C4×C131—41no—
240C2×C4×C131—41no—
241C2×C4×C131—41no—
242C2×C4×C131—41no—
243C2×C4×C131—41no—
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—41no—
252C2×C4×C131#12112yes—
253C2×C4×C131#13512yes—
254C2×C4×C131C22×D411yescharacteristic
255C2×C4×C131C2×#4111yescharacteristic
256C2×C4×C131C2×#4111yescharacteristic
257C2×C4×C131C2×#4111yescharacteristic
258C2×C4×C1312−1+411yescharacteristic
259C2×C4×C1312−1+411yescharacteristic
260C8×C131—22no—
261C8×C131—22no—
262C8×C131—41no—
263C8×C131—41no—
264C22×C131—22no—
265C22×C131—22no—
266C22×C131—22no—
267C22×C131—41no—
268C22×C131—41no—
269C22×C131—41no—
270C22×C131—41no—
271C22×C131C2×#12111yescharacteristic
272C22×C131#54711yescharacteristic
273C22×C131#54711yescharacteristic
274C22×C131C2×#13511yescharacteristic
275C22×C131#57511yescharacteristic
276C22×C131#57711yescharacteristic
277C22×C131#57811yescharacteristic
278C4×C131—22no—
279C4×C131—22no—
280C4×C131—41no—
281C4×C131—41no—
282C4×C131—41no—
283C4×C131—42no—
284C4×C131—42no—
285C4×C131—81no—
286C4×C131—81no—
287C4×C131—81no—
288C4×C131—81no—
289C4×C131—81no—
290C4×C131—81no—
291C4×C131#52511yescharacteristic
292C4×C131#53611yescharacteristic
293C4×C131#55211yescharacteristic
294C4×C131#55211yescharacteristic
295C2×C131—42no—
296C2×C131#241311yescharacteristic
297C2×C131#303511yescharacteristic
298C2×C131#304611yescharacteristic
299C2×C131#333611yescharacteristic
300C2×C131#334011yescharacteristic
301C2×C131#334811yescharacteristic
302C2×C131#334911yescharacteristic
303#24586C13111yesmaximal, characteristic, direct product factor, Sylow
304C131#2458611yescharacteristic, direct product factor, Sylow
305C2×#485C2×C13111yescharacteristic
306C2×#427C2×C13111yescharacteristic
307#2499C2×C13111yescharacteristic
308#2346C2×C13111yescharacteristic
309#2085C2×C13111yescharacteristic, complemented
310#2084C2×C13111yescharacteristic, complemented
311#2068C2×C13111yescharacteristic, complemented
312#2066C2×C13111yescharacteristic, complemented
313#1949C2×C13111yescharacteristic, complemented
314#1947C2×C13111yescharacteristic, complemented
315#1928C2×C13111yescharacteristic, complemented
316#1927C2×C13111yescharacteristic, complemented
317#1892C2×C13111yescharacteristic
318#1850C2×C13111yescharacteristic
319#1825C2×C13111yescharacteristic
320C23×C8C22×C13111yescharacteristic
321C2×C22⋊Q8C22×C13111yescharacteristic
322C2×#117C22×C13111yescharacteristic
323C2×#117C22×C13111yescharacteristic
324#485—24no—
325#427—24no—
326C2×#107C22×C13111yescharacteristic
327C2×#107C22×C13111yescharacteristic
328C2×#107C22×C13111yescharacteristic
329C2×#106C22×C13111yescharacteristic
330C2×#106C22×C13111yescharacteristic
331C2×#106C22×C13111yescharacteristic
332C2×C4⋊C8C22×C13111yescharacteristic
333C2×C4⋊C8C22×C13111yescharacteristic
334C2×#103C22×C13111yescharacteristic
335C2×#103C22×C13111yescharacteristic
336C2×#103C22×C13111yescharacteristic
337C2×#103C22×C13111yescharacteristic
338C2×C22⋊C8C22×C13111yescharacteristic
339#397—21no—
340#397—21no—
341#391C22×C13111yescharacteristic
342#391C22×C13111yescharacteristic
343#389C22×C13111yescharacteristic
344#389C22×C13111yescharacteristic
345#388—21no—
346#388—21no—
347#387—21no—
348#387—21no—
349#384C22×C13111yescharacteristic
350#382—21no—
351#382C22×C13111yescharacteristic
352#380C22×C13111yescharacteristic
353C4×C4⋊C4C22×C13111yescharacteristic
354C4×C4⋊C4C22×C13111yescharacteristic
355C4×C22⋊C4C22×C13111yescharacteristic
356#376—21no—
357#340C22×C13111yescharacteristic
358#340C22×C13111yescharacteristic
359#340C22×C13111yescharacteristic
360#340C22×C13111yescharacteristic
361#340C22×C13111yescharacteristic
362#340C22×C13111yescharacteristic
363#336C22×C13111yescharacteristic
364#336C22×C13111yescharacteristic
365C22×Q8C23×C13111yescharacteristic
366C23×C4C23×C13111yescharacteristic
367C22×C8—22no—
368C22×C8—22no—
369C22×C8—22no—
370C22×C8C23×C13111yescharacteristic
371C22×C8C23×C13111yescharacteristic
372C22×C8C23×C13111yescharacteristic
373C22×C8C23×C13111yescharacteristic
374C22⋊Q8—22no—
375C22⋊Q8—22no—
376#117—22no—
377#117—22no—
378#117—22no—
379#117D4×C13114yes—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4C23×C13111yescharacteristic
386C2×C4⋊C4C23×C13111yescharacteristic
387C2×C4⋊C4C23×C13111yescharacteristic
388C2×C4⋊C4C23×C13111yescharacteristic
389C2×C4⋊C4C23×C13111yescharacteristic
390C2×C4⋊C4C23×C13111yescharacteristic
391C2×C4⋊C4C23×C13111yescharacteristic
392C2×C22⋊C4—21no—
393C2×C22⋊C4—21no—
394C2×C22⋊C4—21no—
395C2×C22⋊C4—21no—
396C2×C22⋊C4D4×C13111yescharacteristic
397C2×C22⋊C4D4×C13111yescharacteristic
398C2×C42—21no—
399C2×C42—21no—
400C2×C42—21no—
401C2×C42—21no—
402C2×C42C23×C13111yescharacteristic
403C2×C42C23×C13111yescharacteristic
404#107—22no—
405#107—22no—
406#107—22no—
407#106—22no—
408#106—22no—
409#106—22no—
410C4⋊C8—22no—
411C4⋊C8—22no—
412#103—22no—
413#103—22no—
414#103—22no—
415#103—22no—
416C22⋊C8—22no—
417#95—21no—
418#95—21no—
419#95—21no—
420#95—21no—
421#95—21no—
422#95—21no—
423#95—21no—
424#95—21no—
425#95—21no—
426#95—21no—
427#95—21no—
428#95D4×C13111yescharacteristic
429#95D4×C13111yescharacteristic
430C24C2×D4×C13111yescharacteristic
431C2×Q8—21no—
432C2×Q8—21no—
433C2×Q8—21no—
434C2×Q8—21no—
435C2×Q8—21no—
436C2×Q8—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4C2×D4×C13111yescharacteristic
450C22×C4C2×D4×C13111yescharacteristic
451C22×C4C2×D4×C13111yescharacteristic
452C22×C4C2×D4×C13111yescharacteristic
453C22×C4C2×D4×C13112yes—
454C22×C4C2×D4×C13111yescharacteristic
455C22×C4#41×C13112yes—
456C22×C4C24×C13111yescharacteristic
457C2×C8—28no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—21no—
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8#41×C13112yes—
469C2×C8#41×C13112yes—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—42no—
483C4⋊C4—42no—
484C4⋊C4—42no—
485C4⋊C4—81no—
486C4⋊C4—81no—
487C4⋊C4C2×D4×C13112yes—
488C4⋊C4C2×D4×C13112yes—
489C22⋊C4—24no—
490C22⋊C4—22no—
491C22⋊C4—41no—
492C22⋊C4—42no—
493C22⋊C4—42no—
494C22⋊C4—81no—
495C42—24no—
496C42—21no—
497C42—21no—
498C42—21no—
499C42—21no—
500C42—42no—
501C42—42no—
502C42—42no—
503C23—21no—
504C23—21no—
505C23—21no—
506C23—21no—
507C23—21no—
508C23—21no—
509C23#121×C13112yes—
510C23C22×D4×C13111yescharacteristic
511Q8—41no—
512Q8—41no—
513Q8—41no—
514Q8—41no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—22no—
520C2×C4—22no—
521C2×C4—22no—
522C2×C4—22no—
523C2×C4—22no—
524C2×C4—22no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4#121×C13112yes—
557C2×C4#135×C13112yes—
558C2×C4C22×D4×C13111yescharacteristic
559C2×C4C2×#41×C13111yescharacteristic
560C2×C4C2×#41×C13111yescharacteristic
561C2×C4C2×#41×C13111yescharacteristic
562C2×C42−1+4×C13111yescharacteristic
563C2×C42−1+4×C13111yescharacteristic
564C8—22no—
565C8—22no—
566C8—41no—
567C8—41no—
568C22—22no—
569C22—22no—
570C22—22no—
571C22—41no—
572C22—41no—
573C22—41no—
574C22—41no—
575C22C2×#121×C13111yescharacteristic
576C22#547×C13111yescharacteristic
577C22#547×C13111yescharacteristic
578C22C2×#135×C13111yescharacteristic
579C22#575×C13111yescharacteristic
580C22#577×C13111yescharacteristic
581C22#578×C13111yescharacteristic
582C4—22no—
583C4—22no—
584C4—42no—
585C4—42no—
586C4—41no—
587C4—41no—
588C4—41no—
589C4—81no—
590C4—81no—
591C4—81no—
592C4—81no—
593C4—81no—
594C4—81no—
595C4#525×C13111yescharacteristic
596C4#536×C13111yescharacteristic
597C4#552×C13111yescharacteristic
598C4#552×C13111yescharacteristic
599C2—42no—
600C2#2413×C13111yescharacteristic
601C2#3035×C13111yescharacteristic
602C2#3046×C13111yescharacteristic
603C2#3336×C13111yescharacteristic
604C2#3340×C13111yescharacteristic
605C2#3348×C13111yescharacteristic
606C2#3349×C13111yescharacteristic
subgroupG/H
center, socleC23×C131C22×D4
commutator, Frattini, cosocleC22×C4C24×C131
prime radicalC24×C131C2×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C131 ◁ C4×C22⋊C4×C131 ◁ G

Complements

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

NH ≅ G/Ntype
5. #2085×C131C2semidirect
6. #2084×C131C2semidirect
7. #2068×C131C2semidirect
8. #2066×C131C2semidirect
9. #1949×C131C2semidirect
10. #1947×C131C2semidirect
11. #1928×C131C2semidirect
12. #1927×C131C2semidirect
303. #24586C131direct (N × H)
304. C131#24586direct (N × H)
309. #2085C2×C131semidirect
310. #2084C2×C131semidirect
311. #2068C2×C131semidirect
312. #2066C2×C131semidirect
313. #1949C2×C131semidirect
314. #1947C2×C131semidirect
315. #1928C2×C131semidirect
316. #1927C2×C131semidirect

Maximal subgroups

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

subgroupindex
C2×#485×C1312
C2×#427×C1312
#2499×C1312
#2346×C1312
#2085×C1312
#2084×C1312
#2068×C1312
#2066×C1312
#1949×C1312
#1947×C1312
#1928×C1312
#1927×C1312
#1892×C1312
#1850×C1312
#1825×C1312
#24586131