Finite Group Databasebeta

← C131×#18705 #45704589

Subgroups — C131×#18705 #45704589

Order 33536.

938 conjugacy classes of subgroups.

The subgroup lattice has 776 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3546×C131C211yesmaximal, characteristic
2#3252×C131C211yesmaximal, characteristic, complemented
3#3235×C131C211yesmaximal, characteristic, complemented
4#3167×C131C211yesmaximal, characteristic, complemented
5#1654×C131C211yesmaximal, characteristic, complemented
6#1652×C131C211yesmaximal, characteristic, complemented
7#1641×C131C211yesmaximal, characteristic, complemented
8#1639×C131C211yesmaximal, characteristic, complemented
9#1638×C131C211yesmaximal, characteristic, complemented
10#1635×C131C211yesmaximal, characteristic, complemented
11#1631×C131C211yesmaximal, characteristic, complemented
12#1629×C131C211yesmaximal, characteristic, complemented
13#1557×C131C211yesmaximal, characteristic, complemented
14#1494×C131C211yesmaximal, characteristic, complemented
15#1492×C131C211yesmaximal, characteristic, complemented
16#560×C131—22no—
17#556×C131C2211yescharacteristic
18#553×C131—21no—
19#550×C131—21no—
20#550×C131C2211yescharacteristic
21#547×C131C2211yescharacteristic
22#546×C131—21no—
23#546×C131—21no—
24D42×C131C2211yescharacteristic
25#542×C131—21no—
26#538×C131—22no—
27#537×C131—21no—
28#535×C131—21no—
29#535×C131—21no—
30#533×C131C2211yescharacteristic, complemented
31#532×C131C2211yescharacteristic
32#532×C131C2211yescharacteristic
33#529×C131C2211yescharacteristic
34#501×C131—21no—
35#498×C131C2211yescharacteristic, complemented
36#492×C131C2211yescharacteristic
37#490×C131—21no—
38#487×C131C2211yescharacteristic, complemented
39#486×C131C2211yescharacteristic
40#482×C131—21no—
41#482×C131—21no—
42#479×C131—21no—
43#477×C131C2211yescharacteristic, complemented
44#476×C131C2211yescharacteristic
45#476×C131C2211yescharacteristic
46#476×C131C2211yescharacteristic, complemented
47#474×C131C2211yescharacteristic
48#474×C131C2211yescharacteristic, complemented
49#470×C131—21no—
50#468×C131—21no—
51#465×C131—22no—
52#464×C131—21no—
53#462×C131C2211yescharacteristic, complemented
54#461×C131C2211yescharacteristic
55C4×SD16×C131—22no—
56#432×C131C2211yescharacteristic, complemented
57#423×C131C2211yescharacteristic, complemented
58C2×C4×C8×C131C2211yescharacteristic, complemented
59#332×C131C2211yescharacteristic, complemented
60#332×C131C2211yescharacteristic, complemented
61#331×C131C2211yescharacteristic
62#331×C131C2211yescharacteristic
63Q8⋊C8×C131C2211yescharacteristic, complemented
64Q8⋊C8×C131C2211yescharacteristic, complemented
65D4⋊C8×C131C2211yescharacteristic
66D4⋊C8×C131C2211yescharacteristic
67D4⋊C8×C131C2211yescharacteristic
68D4⋊C8×C131C2211yescharacteristic
69D4⋊C8×C131C2211yescharacteristic, complemented
70D4⋊C8×C131C2211yescharacteristic, complemented
71C2×#41×C131—21no—
72C2×#41×C131—21no—
73C2×#41×C131—21no—
74C2×#41×C131—21no—
75C22×D4×C131—21no—
76C22×D4×C131—21no—
77C2×Q16×C131—21no—
78C2×SD16×C131—22no—
79C2×SD16×C131—21no—
80C2×M16×C131—21no—
81C22×C8×C131—21no—
82C4⋊Q8×C131D411yescharacteristic
83C4⋊Q8×C131C2311yescharacteristic
84C4⋊Q8×C131C2311yescharacteristic
85C4⋊Q8×C131C2311yescharacteristic
86#127×C131—22no—
87#127×C131—21no—
88#127×C131D411yescharacteristic
89#127×C131C2311yescharacteristic
90#126×C131—22no—
91#126×C131—22no—
92#126×C131—21no—
93#125×C131—21no—
94#125×C131D411yescharacteristic
95#124×C131—22no—
96#124×C131—21no—
97#124×C131—21no—
98#124×C131—21no—
99#124×C131D411yescharacteristic
100#123×C131—22no—
101#123×C131—22no—
102#123×C131—21no—
103#123×C131—22no—
104C22⋊Q8×C131—22no—
105C22⋊Q8×C131—21no—
106C22⋊Q8×C131—21no—
107C22⋊Q8×C131—21no—
108C22⋊Q8×C131—21no—
109C22⋊Q8×C131D411yescharacteristic
110#121×C131—22no—
111#121×C131—22no—
112#121×C131—22no—
113#121×C131—22no—
114#121×C131—22no—
115#121×C131—21no—
116#121×C131—22no—
117#121×C131—21no—
118#121×C131—21no—
119#121×C131—21no—
120#121×C131—21no—
121#121×C131—21no—
122#121×C131D412yes—
123#121×C131D411yescharacteristic
124#121×C131D411yescharacteristic
125#121×C131D411yescharacteristic
126#120×C131—22no—
127#120×C131—22no—
128#120×C131—22no—
129#120×C131—22no—
130C4×Q8×C131—21no—
131C4×Q8×C131—21no—
132C4×Q8×C131—21no—
133C4×Q8×C131C2311yescharacteristic
134C4×D4×C131—22no—
135C4×D4×C131—21no—
136C4×D4×C131—21no—
137C4×D4×C131—21no—
138C4×D4×C131—21no—
139C4×D4×C131D412yes—
140C4×D4×C131C2311yescharacteristic
141C4×D4×C131C2311yescharacteristic
142C4×D4×C131C2311yescharacteristic
143#117×C131—21no—
144#117×C131—21no—
145#117×C131—21no—
146C2×C4⋊C4×C131—21no—
147C2×C22⋊C4×C131—22no—
148C2×C42×C131C2311yescharacteristic
149#107×C131—21no—
150#107×C131—21no—
151#107×C131—21no—
152#106×C131—22no—
153#106×C131—21no—
154#106×C131—21no—
155#106×C131—21no—
156C4⋊C8×C131—21no—
157C4⋊C8×C131C2311yescharacteristic
158C4⋊C8×C131C2311yescharacteristic
159C4⋊C8×C131C2311yescharacteristic
160C4⋊C8×C131C2311yescharacteristic
161#103×C131—21no—
162#103×C131—22no—
163#103×C131—21no—
164#103×C131—21no—
165#102×C131—22no—
166#102×C131—21no—
167#102×C131—21no—
168#102×C131—21no—
169#102×C131—21no—
170#102×C131—21no—
171C22⋊C8×C131—21no—
172#97×C131—21no—
173C4×C8×C131—21no—
174C4×C8×C131C2311yescharacteristic
175C4×C8×C131C2311yescharacteristic
176C24×C131—22no—
177#41×C131—81no—
178#41×C131—81no—
179#41×C131—81no—
180#41×C131—81no—
181#41×C131—81no—
182#41×C131—81no—
183#41×C131—81no—
184#41×C131—81no—
185C2×Q8×C131—21no—
186C2×Q8×C131—21no—
187C2×Q8×C131—21no—
188C2×Q8×C131—21no—
189C2×Q8×C131C2×D411yescharacteristic
190C2×D4×C131—22no—
191C2×D4×C131—22no—
192C2×D4×C131—22no—
193C2×D4×C131—22no—
194C2×D4×C131—22no—
195C2×D4×C131—21no—
196C2×D4×C131—21no—
197C2×D4×C131—22no—
198C2×D4×C131—21no—
199C2×D4×C131—21no—
200C2×D4×C131—21no—
201C2×D4×C131—21no—
202C2×D4×C131—21no—
203C2×D4×C131—81no—
204C2×D4×C131—81no—
205C2×D4×C131—81no—
206C2×D4×C131—81no—
207C2×D4×C131C2×D411yescharacteristic
208C2×D4×C131C2×D411yescharacteristic
209C2×D4×C131C2×D411yescharacteristic
210C2×D4×C131C2×D412yes—
211C22×C4×C131—22no—
212C22×C4×C131—22no—
213C22×C4×C131—21no—
214C22×C4×C131—21no—
215C22×C4×C131—21no—
216C22×C4×C131—22no—
217C22×C4×C131C2×D411yescharacteristic
218C22×C4×C131C2×D411yescharacteristic
219C22×C4×C131C2×D411yescharacteristic
220Q16×C131—81no—
221SD16×C131—44no—
222SD16×C131—81no—
223M16×C131—81no—
224C2×C8×C131—21no—
225C2×C8×C131—21no—
226C2×C8×C131—21no—
227C2×C8×C131—21no—
228C2×C8×C131—21no—
229C2×C8×C131—21no—
230C2×C8×C131—42no—
231C4⋊C4×C131—22no—
232C4⋊C4×C131—22no—
233C4⋊C4×C131—21no—
234C4⋊C4×C131—21no—
235C4⋊C4×C131—21no—
236C4⋊C4×C131—21no—
237C4⋊C4×C131—21no—
238C4⋊C4×C131—21no—
239C4⋊C4×C131—21no—
240C4⋊C4×C131—21no—
241C4⋊C4×C131—21no—
242C4⋊C4×C131—21no—
243C4⋊C4×C131—41no—
244C4⋊C4×C131—41no—
245C4⋊C4×C131C2×D411yescharacteristic
246C4⋊C4×C131C2×D412yes—
247C4⋊C4×C131C2×D411yescharacteristic
248C4⋊C4×C131C2×D411yescharacteristic
249C4⋊C4×C131C2×D411yescharacteristic
250C22⋊C4×C131—22no—
251C22⋊C4×C131—22no—
252C22⋊C4×C131—22no—
253C22⋊C4×C131—22no—
254C22⋊C4×C131—22no—
255C22⋊C4×C131—21no—
256C22⋊C4×C131—21no—
257C22⋊C4×C131—21no—
258C22⋊C4×C131—21no—
259C22⋊C4×C131—21no—
260C22⋊C4×C131—21no—
261C22⋊C4×C131—22no—
262C22⋊C4×C131—22no—
263C22⋊C4×C131—21no—
264C22⋊C4×C131—21no—
265C22⋊C4×C131—21no—
266C22⋊C4×C131—41no—
267C42×C131—22no—
268C42×C131—21no—
269C42×C131—41no—
270C42×C131C2×D411yescharacteristic
271C42×C131C2×D411yescharacteristic
272C42×C131C2×D411yescharacteristic
273C42×C131C2411yescharacteristic
274C23×C131—21no—
275C23×C131—21no—
276C23×C131—22no—
277C23×C131—21no—
278C23×C131—82no—
279C23×C131—82no—
280C23×C131—82no—
281C23×C131#12011yescharacteristic
282Q8×C131—21no—
283Q8×C131—21no—
284Q8×C131—42no—
285Q8×C131—41no—
286Q8×C131—41no—
287Q8×C131—41no—
288Q8×C131—41no—
289Q8×C131—81no—
290D4×C131—21no—
291D4×C131—21no—
292D4×C131—21no—
293D4×C131—21no—
294D4×C131—21no—
295D4×C131—21no—
296D4×C131—42no—
297D4×C131—41no—
298D4×C131—41no—
299D4×C131—41no—
300D4×C131—41no—
301D4×C131—81no—
302D4×C131—81no—
303D4×C131—81no—
304D4×C131—82no—
305D4×C131—81no—
306D4×C131—81no—
307D4×C131—82no—
308D4×C131—82no—
309D4×C131—82no—
310D4×C131—82no—
311D4×C131—82no—
312C2×C4×C131—21no—
313C2×C4×C131—21no—
314C2×C4×C131—21no—
315C2×C4×C131—21no—
316C2×C4×C131—21no—
317C2×C4×C131—21no—
318C2×C4×C131—21no—
319C2×C4×C131—22no—
320C2×C4×C131—21no—
321C2×C4×C131—21no—
322C2×C4×C131—41no—
323C2×C4×C131—41no—
324C2×C4×C131—41no—
325C2×C4×C131—41no—
326C2×C4×C131—41no—
327C2×C4×C131—41no—
328C2×C4×C131—41no—
329C2×C4×C131—41no—
330C2×C4×C131—41no—
331C2×C4×C131—82no—
332C2×C4×C131—82no—
333C2×C4×C131—82no—
334C2×C4×C131#12011yescharacteristic
335C2×C4×C131#12011yescharacteristic
336C2×C4×C131#12011yescharacteristic
337C2×C4×C131C22×D411yescharacteristic
338C2×C4×C131C22×D411yescharacteristic
339C2×C4×C131C22×D411yescharacteristic
340C8×C131—22no—
341C8×C131—41no—
342C8×C131—41no—
343C8×C131—41no—
344C8×C131—41no—
345C8×C131—41no—
346C22×C131—21no—
347C22×C131—21no—
348C22×C131—21no—
349C22×C131—41no—
350C22×C131—41no—
351C22×C131—42no—
352C22×C131—41no—
353C22×C131—41no—
354C22×C131—41no—
355C22×C131—42no—
356C22×C131—41no—
357C22×C131—42no—
358C22×C131—41no—
359C22×C131—41no—
360C22×C131—41no—
361C22×C131—164no—
362C22×C131C2×#12011yescharacteristic
363C4×C131—21no—
364C4×C131—21no—
365C4×C131—21no—
366C4×C131—21no—
367C4×C131—41no—
368C4×C131—42no—
369C4×C131—41no—
370C4×C131—41no—
371C4×C131—41no—
372C4×C131—41no—
373C4×C131—81no—
374C4×C131—81no—
375C4×C131#57611yescharacteristic
376C4×C131#57711yescharacteristic
377C4×C131#57711yescharacteristic
378C4×C131#57711yescharacteristic
379C2×C131—41no—
380C2×C131—81no—
381C2×C131—82no—
382C2×C131—81no—
383C2×C131—81no—
384C2×C131#300911yescharacteristic
385C2×C131#301211yescharacteristic
386C2×C131#301811yescharacteristic
387#18705C13111yesmaximal, characteristic, direct product factor, Sylow
388C131#1870511yescharacteristic, direct product factor, Sylow
389#3546C2×C13111yescharacteristic
390#3252C2×C13111yescharacteristic, complemented
391#3235C2×C13111yescharacteristic, complemented
392#3167C2×C13111yescharacteristic, complemented
393#1654C2×C13111yescharacteristic, complemented
394#1652C2×C13111yescharacteristic, complemented
395#1641C2×C13111yescharacteristic, complemented
396#1639C2×C13111yescharacteristic, complemented
397#1638C2×C13111yescharacteristic, complemented
398#1635C2×C13111yescharacteristic, complemented
399#1631C2×C13111yescharacteristic, complemented
400#1629C2×C13111yescharacteristic, complemented
401#1557C2×C13111yescharacteristic, complemented
402#1494C2×C13111yescharacteristic, complemented
403#1492C2×C13111yescharacteristic, complemented
404#560—22no—
405#556C22×C13111yescharacteristic
406#553—21no—
407#550—21no—
408#550C22×C13111yescharacteristic
409#547C22×C13111yescharacteristic
410#546—21no—
411#546—21no—
412D42C22×C13111yescharacteristic
413#542—21no—
414#538—22no—
415#537—21no—
416#535—21no—
417#535—21no—
418#533C22×C13111yescharacteristic, complemented
419#532C22×C13111yescharacteristic
420#532C22×C13111yescharacteristic
421#529C22×C13111yescharacteristic
422#501—21no—
423#498C22×C13111yescharacteristic, complemented
424#492C22×C13111yescharacteristic
425#490—21no—
426#487C22×C13111yescharacteristic, complemented
427#486C22×C13111yescharacteristic
428#482—21no—
429#482—21no—
430#479—21no—
431#477C22×C13111yescharacteristic, complemented
432#476C22×C13111yescharacteristic
433#476C22×C13111yescharacteristic
434#476C22×C13111yescharacteristic, complemented
435#474C22×C13111yescharacteristic
436#474C22×C13111yescharacteristic, complemented
437#470—21no—
438#468—21no—
439#465—22no—
440#464—21no—
441#462C22×C13111yescharacteristic, complemented
442#461C22×C13111yescharacteristic
443C4×SD16—22no—
444#432C22×C13111yescharacteristic, complemented
445#423C22×C13111yescharacteristic, complemented
446C2×C4×C8C22×C13111yescharacteristic, complemented
447#332C22×C13111yescharacteristic, complemented
448#332C22×C13111yescharacteristic, complemented
449#331C22×C13111yescharacteristic
450#331C22×C13111yescharacteristic
451Q8⋊C8C22×C13111yescharacteristic, complemented
452Q8⋊C8C22×C13111yescharacteristic, complemented
453D4⋊C8C22×C13111yescharacteristic
454D4⋊C8C22×C13111yescharacteristic
455D4⋊C8C22×C13111yescharacteristic
456D4⋊C8C22×C13111yescharacteristic
457D4⋊C8C22×C13111yescharacteristic, complemented
458D4⋊C8C22×C13111yescharacteristic, complemented
459C2×#41—21no—
460C2×#41—21no—
461C2×#41—21no—
462C2×#41—21no—
463C22×D4—21no—
464C22×D4—21no—
465C2×Q16—21no—
466C2×SD16—22no—
467C2×SD16—21no—
468C2×M16—21no—
469C22×C8—21no—
470C4⋊Q8D4×C13111yescharacteristic
471C4⋊Q8C23×C13111yescharacteristic
472C4⋊Q8C23×C13111yescharacteristic
473C4⋊Q8C23×C13111yescharacteristic
474#127—22no—
475#127—21no—
476#127D4×C13111yescharacteristic
477#127C23×C13111yescharacteristic
478#126—22no—
479#126—22no—
480#126—21no—
481#125—21no—
482#125D4×C13111yescharacteristic
483#124—22no—
484#124—21no—
485#124—21no—
486#124—21no—
487#124D4×C13111yescharacteristic
488#123—22no—
489#123—22no—
490#123—21no—
491#123—22no—
492C22⋊Q8—22no—
493C22⋊Q8—21no—
494C22⋊Q8—21no—
495C22⋊Q8—21no—
496C22⋊Q8—21no—
497C22⋊Q8D4×C13111yescharacteristic
498#121—22no—
499#121—22no—
500#121—22no—
501#121—22no—
502#121—22no—
503#121—21no—
504#121—22no—
505#121—21no—
506#121—21no—
507#121—21no—
508#121—21no—
509#121—21no—
510#121D4×C13111yescharacteristic
511#121D4×C13111yescharacteristic
512#121D4×C13111yescharacteristic
513#121D4×C13112yes—
514#120—22no—
515#120—22no—
516#120—22no—
517#120—22no—
518C4×Q8—21no—
519C4×Q8—21no—
520C4×Q8—21no—
521C4×Q8C23×C13111yescharacteristic
522C4×D4—22no—
523C4×D4—21no—
524C4×D4—21no—
525C4×D4—21no—
526C4×D4—21no—
527C4×D4D4×C13112yes—
528C4×D4C23×C13111yescharacteristic
529C4×D4C23×C13111yescharacteristic
530C4×D4C23×C13111yescharacteristic
531#117—21no—
532#117—21no—
533#117—21no—
534C2×C4⋊C4—21no—
535C2×C22⋊C4—22no—
536C2×C42C23×C13111yescharacteristic
537#107—21no—
538#107—21no—
539#107—21no—
540#106—22no—
541#106—21no—
542#106—21no—
543#106—21no—
544C4⋊C8—21no—
545C4⋊C8C23×C13111yescharacteristic
546C4⋊C8C23×C13111yescharacteristic
547C4⋊C8C23×C13111yescharacteristic
548C4⋊C8C23×C13111yescharacteristic
549#103—21no—
550#103—22no—
551#103—21no—
552#103—21no—
553#102—22no—
554#102—21no—
555#102—21no—
556#102—21no—
557#102—21no—
558#102—21no—
559C22⋊C8—21no—
560#97—21no—
561C4×C8—21no—
562C4×C8C23×C13111yescharacteristic
563C4×C8C23×C13111yescharacteristic
564C24—22no—
565#41—81no—
566#41—81no—
567#41—81no—
568#41—81no—
569#41—81no—
570#41—81no—
571#41—81no—
572#41—81no—
573C2×Q8—21no—
574C2×Q8—21no—
575C2×Q8—21no—
576C2×Q8—21no—
577C2×Q8C2×D4×C13111yescharacteristic
578C2×D4—22no—
579C2×D4—22no—
580C2×D4—22no—
581C2×D4—22no—
582C2×D4—22no—
583C2×D4—21no—
584C2×D4—21no—
585C2×D4—22no—
586C2×D4—21no—
587C2×D4—21no—
588C2×D4—21no—
589C2×D4—21no—
590C2×D4—21no—
591C2×D4—81no—
592C2×D4—81no—
593C2×D4—81no—
594C2×D4—81no—
595C2×D4C2×D4×C13111yescharacteristic
596C2×D4C2×D4×C13111yescharacteristic
597C2×D4C2×D4×C13111yescharacteristic
598C2×D4C2×D4×C13112yes—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—22no—
605C22×C4C2×D4×C13111yescharacteristic
606C22×C4C2×D4×C13111yescharacteristic
607C22×C4C2×D4×C13111yescharacteristic
608Q16—81no—
609SD16—44no—
610SD16—81no—
611M16—81no—
612C2×C8—21no—
613C2×C8—21no—
614C2×C8—21no—
615C2×C8—21no—
616C2×C8—21no—
617C2×C8—21no—
618C2×C8—42no—
619C4⋊C4—22no—
620C4⋊C4—22no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4—21no—
625C4⋊C4—21no—
626C4⋊C4—21no—
627C4⋊C4—21no—
628C4⋊C4—21no—
629C4⋊C4—21no—
630C4⋊C4—21no—
631C4⋊C4—41no—
632C4⋊C4—41no—
633C4⋊C4C2×D4×C13111yescharacteristic
634C4⋊C4C2×D4×C13112yes—
635C4⋊C4C2×D4×C13111yescharacteristic
636C4⋊C4C2×D4×C13111yescharacteristic
637C4⋊C4C2×D4×C13111yescharacteristic
638C22⋊C4—22no—
639C22⋊C4—22no—
640C22⋊C4—22no—
641C22⋊C4—22no—
642C22⋊C4—22no—
643C22⋊C4—21no—
644C22⋊C4—21no—
645C22⋊C4—21no—
646C22⋊C4—21no—
647C22⋊C4—21no—
648C22⋊C4—21no—
649C22⋊C4—22no—
650C22⋊C4—22no—
651C22⋊C4—21no—
652C22⋊C4—21no—
653C22⋊C4—21no—
654C22⋊C4—41no—
655C42—22no—
656C42—21no—
657C42—41no—
658C42C2×D4×C13111yescharacteristic
659C42C2×D4×C13111yescharacteristic
660C42C2×D4×C13111yescharacteristic
661C42C24×C13111yescharacteristic
662C23—21no—
663C23—21no—
664C23—22no—
665C23—21no—
666C23—82no—
667C23—82no—
668C23—82no—
669C23#120×C13111yescharacteristic
670Q8—21no—
671Q8—21no—
672Q8—42no—
673Q8—41no—
674Q8—41no—
675Q8—41no—
676Q8—41no—
677Q8—81no—
678D4—21no—
679D4—21no—
680D4—21no—
681D4—21no—
682D4—21no—
683D4—21no—
684D4—42no—
685D4—41no—
686D4—41no—
687D4—41no—
688D4—41no—
689D4—81no—
690D4—81no—
691D4—82no—
692D4—81no—
693D4—81no—
694D4—81no—
695D4—82no—
696D4—82no—
697D4—82no—
698D4—82no—
699D4—82no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—22no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—82no—
720C2×C4—82no—
721C2×C4—82no—
722C2×C4#120×C13111yescharacteristic
723C2×C4#120×C13111yescharacteristic
724C2×C4#120×C13111yescharacteristic
725C2×C4C22×D4×C13111yescharacteristic
726C2×C4C22×D4×C13111yescharacteristic
727C2×C4C22×D4×C13111yescharacteristic
728C8—22no—
729C8—41no—
730C8—41no—
731C8—41no—
732C8—41no—
733C8—41no—
734C22—21no—
735C22—21no—
736C22—21no—
737C22—41no—
738C22—41no—
739C22—42no—
740C22—41no—
741C22—41no—
742C22—41no—
743C22—42no—
744C22—41no—
745C22—42no—
746C22—41no—
747C22—41no—
748C22—41no—
749C22—164no—
750C22C2×#120×C13111yescharacteristic
751C4—21no—
752C4—21no—
753C4—21no—
754C4—21no—
755C4—41no—
756C4—42no—
757C4—41no—
758C4—41no—
759C4—41no—
760C4—41no—
761C4—81no—
762C4—81no—
763C4#576×C13111yescharacteristic
764C4#577×C13111yescharacteristic
765C4#577×C13111yescharacteristic
766C4#577×C13111yescharacteristic
767C2—41no—
768C2—81no—
769C2—81no—
770C2—82no—
771C2—81no—
772C2#3009×C13111yescharacteristic
773C2#3012×C13111yescharacteristic
774C2#3018×C13111yescharacteristic
subgroupG/H
center, socleC22×C131C2×#120
commutator, Frattini, cosocleC42C24×C131
prime radical#3546×C131C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C131 ◁ C2×C42×C131 ◁ G

Complements

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

NH ≅ G/Ntype
2. #3252×C131C2semidirect
3. #3235×C131C2semidirect
4. #3167×C131C2semidirect
5. #1654×C131C2semidirect
6. #1652×C131C2semidirect
7. #1641×C131C2semidirect
8. #1639×C131C2semidirect
9. #1638×C131C2semidirect
10. #1635×C131C2semidirect
11. #1631×C131C2semidirect
12. #1629×C131C2semidirect
13. #1557×C131C2semidirect
14. #1494×C131C2semidirect
15. #1492×C131C2semidirect
30. #533×C131C22semidirect
35. #498×C131C22semidirect
38. #487×C131C22semidirect
43. #477×C131C22semidirect
46. #476×C131C22semidirect
48. #474×C131C22semidirect
53. #462×C131C22semidirect
56. #432×C131C22semidirect
57. #423×C131C22semidirect
58. C2×C4×C8×C131C22semidirect
59. #332×C131C22semidirect
60. #332×C131C22semidirect
63. Q8⋊C8×C131C22semidirect
64. Q8⋊C8×C131C22semidirect
69. D4⋊C8×C131C22semidirect
70. D4⋊C8×C131C22semidirect
387. #18705C131direct (N × H)
388. C131#18705direct (N × H)
390. #3252C2×C131semidirect
391. #3235C2×C131semidirect
392. #3167C2×C131semidirect
393. #1654C2×C131semidirect
394. #1652C2×C131semidirect
395. #1641C2×C131semidirect
396. #1639C2×C131semidirect
397. #1638C2×C131semidirect
398. #1635C2×C131semidirect
399. #1631C2×C131semidirect
400. #1629C2×C131semidirect
401. #1557C2×C131semidirect
402. #1494C2×C131semidirect
403. #1492C2×C131semidirect
418. #533C22×C131semidirect
423. #498C22×C131semidirect
426. #487C22×C131semidirect
431. #477C22×C131semidirect
434. #476C22×C131semidirect
436. #474C22×C131semidirect
441. #462C22×C131semidirect
444. #432C22×C131semidirect
445. #423C22×C131semidirect
446. C2×C4×C8C22×C131semidirect
447. #332C22×C131semidirect
448. #332C22×C131semidirect
451. Q8⋊C8C22×C131semidirect
452. Q8⋊C8C22×C131semidirect
457. D4⋊C8C22×C131semidirect
458. D4⋊C8C22×C131semidirect

Maximal subgroups

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

subgroupindex
#3546×C1312
#3252×C1312
#3235×C1312
#3167×C1312
#1654×C1312
#1652×C1312
#1641×C1312
#1639×C1312
#1638×C1312
#1635×C1312
#1631×C1312
#1629×C1312
#1557×C1312
#1494×C1312
#1492×C1312
#18705131