Finite Group Databasebeta

← C131×#25665 #45711549

Subgroups — C131×#25665 #45711549

Order 33536.

1136 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3505×C131C211yesmaximal, characteristic
2#2591×C131C211yesmaximal, characteristic, complemented
3#2583×C131C211yesmaximal, characteristic, complemented
4#2579×C131C211yesmaximal, characteristic, complemented
5#2044×C131C212yesmaximal, complemented
6#2044×C131C212yesmaximal, complemented
7#1996×C131C211yesmaximal, characteristic, complemented
8#1964×C131C211yesmaximal, characteristic, complemented
9#1867×C131C212yesmaximal, complemented
10#1867×C131C212yesmaximal, complemented
11C4×#99×C131C211yesmaximal, characteristic, complemented
12#553×C131—22no—
13#553×C131—21no—
14#552×C131—21no—
15#551×C131—22no—
16#548×C131—21no—
17#546×C131—21no—
18#539×C131—21no—
19#538×C131—21no—
20#534×C131C2212yes—
21#529×C131—21no—
22#525×C131—21no—
23C2×C22⋊Q8×C131C2211yescharacteristic
24C2×#121×C131C2211yescharacteristic
25#518×C131C2212yes—
26C2×C4×D4×C131C2211yescharacteristic
27C22×C4⋊C4×C131C2211yescharacteristic
28C2×#99×C131C2212yes—
29C2×#99×C131C2212yes—
30C2×#99×C131C2212yes—
31#400×C131—21no—
32#398×C131—21no—
33#398×C131—21no—
34#396×C131—21no—
35#395×C131—21no—
36#394×C131—21no—
37#389×C131—22no—
38#388×C131—22no—
39#387×C131—21no—
40#386×C131C2211yescharacteristic
41#386×C131C2211yescharacteristic
42#386×C131C2212yes—
43#386×C131C2212yes—
44#385×C131—21no—
45#385×C131C2212yes—
46#385×C131C2212yes—
47#385×C131C2211yescharacteristic
48#385×C131C2211yescharacteristic
49#380×C131C2211yescharacteristic
50C4×C22⋊C4×C131C2211yescharacteristic
51C4×C22⋊C4×C131C2211yescharacteristic
52#342×C131C2212yes—
53#342×C131C2212yes—
54#342×C131C2212yes—
55C2×#41×C131—21no—
56C22×Q8×C131D411yescharacteristic
57C22×D4×C131D411yescharacteristic
58C22×D4×C131C2311yescharacteristic
59C22×D4×C131C2312yes—
60C23×C4×C131D411yescharacteristic
61C23×C4×C131C2311yescharacteristic
62C23×C4×C131C2311yescharacteristic
63C23×C4×C131C2311yescharacteristic
64#126×C131—22no—
65#126×C131—22no—
66#126×C131—22no—
67#125×C131—21no—
68#125×C131—22no—
69#124×C131—21no—
70#124×C131—22no—
71#123×C131—22no—
72#123×C131—22no—
73#123×C131—22no—
74#123×C131—22no—
75#123×C131—22no—
76C22⋊Q8×C131—21no—
77C22⋊Q8×C131—22no—
78C22⋊Q8×C131—21no—
79C22⋊Q8×C131—21no—
80C22⋊Q8×C131—21no—
81C22⋊Q8×C131—21no—
82#121×C131—21no—
83#121×C131—22no—
84#121×C131—21no—
85#121×C131—21no—
86#121×C131—21no—
87#121×C131—21no—
88#121×C131—22no—
89#121×C131—22no—
90#120×C131—22no—
91#120×C131—22no—
92C4×Q8×C131—21no—
93C4×D4×C131—22no—
94C4×D4×C131—21no—
95C4×D4×C131—21no—
96C4×D4×C131—21no—
97C4×D4×C131—21no—
98C4×D4×C131—21no—
99C4×D4×C131—22no—
100C4×D4×C131—22no—
101C4×D4×C131—22no—
102C4×D4×C131—22no—
103#117×C131—21no—
104#117×C131—22no—
105#117×C131—22no—
106C2×C4⋊C4×C131—21no—
107C2×C4⋊C4×C131—21no—
108C2×C4⋊C4×C131—22no—
109C2×C4⋊C4×C131—21no—
110C2×C4⋊C4×C131—21no—
111C2×C4⋊C4×C131—21no—
112C2×C4⋊C4×C131—21no—
113C2×C4⋊C4×C131—21no—
114C2×C4⋊C4×C131—22no—
115C2×C4⋊C4×C131—21no—
116C2×C4⋊C4×C131—21no—
117C2×C4⋊C4×C131D412yes—
118C2×C4⋊C4×C131D411yescharacteristic
119C2×C4⋊C4×C131D411yescharacteristic
120C2×C4⋊C4×C131D411yescharacteristic
121C2×C22⋊C4×C131—22no—
122C2×C22⋊C4×C131—22no—
123C2×C22⋊C4×C131—21no—
124C2×C22⋊C4×C131—22no—
125C2×C22⋊C4×C131—21no—
126C2×C22⋊C4×C131D412yes—
127C2×C22⋊C4×C131D411yescharacteristic
128C2×C22⋊C4×C131C2311yescharacteristic
129C2×C22⋊C4×C131C2311yescharacteristic
130C2×C22⋊C4×C131C2312yes—
131C2×C22⋊C4×C131C2311yescharacteristic
132C2×C22⋊C4×C131C2312yes—
133C2×C22⋊C4×C131C2312yes—
134C2×C42×C131—21no—
135C2×C42×C131—21no—
136C2×C42×C131D411yescharacteristic
137#99×C131—24no—
138#99×C131—24no—
139#99×C131—24no—
140#95×C131—22no—
141#95×C131—22no—
142#95×C131—22no—
143#95×C131—22no—
144#95×C131—21no—
145#95×C131—21no—
146#95×C131—21no—
147#95×C131—21no—
148#95×C131—21no—
149#95×C131—21no—
150#95×C131—21no—
151C24×C131C2×D412yes—
152C24×C131C2×D411yescharacteristic
153C24×C131C2411yescharacteristic
154#41×C131—82no—
155C2×Q8×C131—21no—
156C2×Q8×C131—21no—
157C2×Q8×C131—81no—
158C2×D4×C131—21no—
159C2×D4×C131—22no—
160C2×D4×C131—21no—
161C2×D4×C131—22no—
162C2×D4×C131—22no—
163C2×D4×C131—22no—
164C2×D4×C131—22no—
165C2×D4×C131—22no—
166C2×D4×C131—22no—
167C2×D4×C131—22no—
168C2×D4×C131—22no—
169C2×D4×C131—22no—
170C2×D4×C131—21no—
171C2×D4×C131—21no—
172C2×D4×C131—81no—
173C22×C4×C131—22no—
174C22×C4×C131—21no—
175C22×C4×C131—21no—
176C22×C4×C131—21no—
177C22×C4×C131—22no—
178C22×C4×C131—22no—
179C22×C4×C131—21no—
180C22×C4×C131—21no—
181C22×C4×C131—22no—
182C22×C4×C131—21no—
183C22×C4×C131—21no—
184C22×C4×C131—21no—
185C22×C4×C131—21no—
186C22×C4×C131—21no—
187C22×C4×C131—42no—
188C22×C4×C131—81no—
189C22×C4×C131—81no—
190C22×C4×C131—81no—
191C22×C4×C131C2×D411yescharacteristic
192C22×C4×C131C2×D412yes—
193C22×C4×C131C2×D411yescharacteristic
194C22×C4×C131C2×D412yes—
195C22×C4×C131C2×D411yescharacteristic
196C22×C4×C131C2×D412yes—
197C22×C4×C131C2×D411yescharacteristic
198C22×C4×C131C2×D411yescharacteristic
199C22×C4×C131C2×D411yescharacteristic
200C22×C4×C131C2×D411yescharacteristic
201C22×C4×C131C2×D411yescharacteristic
202C22×C4×C131C2×D411yescharacteristic
203C4⋊C4×C131—22no—
204C4⋊C4×C131—22no—
205C4⋊C4×C131—22no—
206C4⋊C4×C131—22no—
207C4⋊C4×C131—21no—
208C4⋊C4×C131—22no—
209C4⋊C4×C131—21no—
210C4⋊C4×C131—21no—
211C4⋊C4×C131—21no—
212C4⋊C4×C131—21no—
213C4⋊C4×C131—22no—
214C4⋊C4×C131—21no—
215C4⋊C4×C131—42no—
216C4⋊C4×C131—44no—
217C4⋊C4×C131—41no—
218C4⋊C4×C131—41no—
219C4⋊C4×C131—41no—
220C4⋊C4×C131—41no—
221C4⋊C4×C131—81no—
222C4⋊C4×C131—82no—
223C4⋊C4×C131—81no—
224C22⋊C4×C131—22no—
225C22⋊C4×C131—22no—
226C22⋊C4×C131—22no—
227C22⋊C4×C131—22no—
228C22⋊C4×C131—22no—
229C22⋊C4×C131—22no—
230C22⋊C4×C131—21no—
231C22⋊C4×C131—22no—
232C22⋊C4×C131—21no—
233C22⋊C4×C131—22no—
234C22⋊C4×C131—22no—
235C22⋊C4×C131—22no—
236C22⋊C4×C131—21no—
237C22⋊C4×C131—21no—
238C22⋊C4×C131—22no—
239C22⋊C4×C131—22no—
240C22⋊C4×C131—22no—
241C22⋊C4×C131—22no—
242C22⋊C4×C131—22no—
243C22⋊C4×C131—44no—
244C22⋊C4×C131—42no—
245C22⋊C4×C131—82no—
246C22⋊C4×C131—81no—
247C22⋊C4×C131#4114yescomplemented
248C42×C131—22no—
249C42×C131—22no—
250C42×C131—21no—
251C42×C131—21no—
252C42×C131—81no—
253C42×C131—81no—
254C23×C131—22no—
255C23×C131—21no—
256C23×C131—21no—
257C23×C131—21no—
258C23×C131—22no—
259C23×C131—22no—
260C23×C131—41no—
261C23×C131—41no—
262C23×C131—41no—
263C23×C131—41no—
264C23×C131—42no—
265C23×C131—42no—
266C23×C131C22×D411yescharacteristic
267C23×C131C22×D411yescharacteristic
268C23×C131C22×D411yescharacteristic
269C23×C131C2×#4112yes—
270C23×C1312−1+412yes—
271Q8×C131—42no—
272Q8×C131—81no—
273D4×C131—42no—
274D4×C131—42no—
275D4×C131—42no—
276D4×C131—42no—
277D4×C131—42no—
278D4×C131—42no—
279D4×C131—42no—
280D4×C131—81no—
281D4×C131—82no—
282D4×C131—82no—
283C2×C4×C131—22no—
284C2×C4×C131—22no—
285C2×C4×C131—22no—
286C2×C4×C131—21no—
287C2×C4×C131—22no—
288C2×C4×C131—21no—
289C2×C4×C131—21no—
290C2×C4×C131—22no—
291C2×C4×C131—22no—
292C2×C4×C131—21no—
293C2×C4×C131—21no—
294C2×C4×C131—22no—
295C2×C4×C131—22no—
296C2×C4×C131—24no—
297C2×C4×C131—41no—
298C2×C4×C131—41no—
299C2×C4×C131—41no—
300C2×C4×C131—41no—
301C2×C4×C131—41no—
302C2×C4×C131—41no—
303C2×C4×C131—42no—
304C2×C4×C131—42no—
305C2×C4×C131—42no—
306C2×C4×C131—41no—
307C2×C4×C131—41no—
308C2×C4×C131—41no—
309C2×C4×C131—41no—
310C2×C4×C131—41no—
311C2×C4×C131—42no—
312C2×C4×C131—41no—
313C2×C4×C131—42no—
314C2×C4×C131—42no—
315C2×C4×C131—41no—
316C2×C4×C131—42no—
317C2×C4×C131—41no—
318C2×C4×C131—41no—
319C2×C4×C131—42no—
320C2×C4×C131—41no—
321C2×C4×C131—41no—
322C2×C4×C131—42no—
323C2×C4×C131—41no—
324C2×C4×C131—41no—
325C2×C4×C131—41no—
326C2×C4×C131—41no—
327C2×C4×C131—42no—
328C2×C4×C131—81no—
329C2×C4×C131—82no—
330C2×C4×C131—82no—
331C2×C4×C131#12011yescharacteristic
332C2×C4×C131#12011yescharacteristic
333C2×C4×C131#12011yescharacteristic
334C2×C4×C131#12011yescharacteristic
335C22×C131—21no—
336C22×C131—21no—
337C22×C131—21no—
338C22×C131—21no—
339C22×C131—21no—
340C22×C131—21no—
341C22×C131—42no—
342C22×C131—42no—
343C22×C131—42no—
344C22×C131—41no—
345C22×C131—42no—
346C22×C131—42no—
347C22×C131—41no—
348C22×C131—41no—
349C22×C131—42no—
350C22×C131—81no—
351C22×C131—82no—
352C22×C131—82no—
353C22×C131C2×#12011yescharacteristic
354C22×C131#53211yescharacteristic
355C22×C131#53611yescharacteristic
356C22×C131#54712yes—
357C22×C131#54812yes—
358C4×C131—21no—
359C4×C131—21no—
360C4×C131—21no—
361C4×C131—21no—
362C4×C131—44no—
363C4×C131—41no—
364C4×C131—42no—
365C4×C131—42no—
366C4×C131—41no—
367C4×C131—42no—
368C4×C131—41no—
369C4×C131—42no—
370C4×C131—81no—
371C4×C131—81no—
372C4×C131—82no—
373C4×C131—81no—
374C2×C131—22no—
375C2×C131—21no—
376C2×C131—22no—
377C2×C131—21no—
378C2×C131—81no—
379C2×C131—82no—
380C2×C131#243211yescharacteristic
381C2×C131#302511yescharacteristic
382C2×C131#302611yescharacteristic
383#25665C13111yesmaximal, characteristic, direct product factor, Sylow
384C131#2566511yescharacteristic, direct product factor, Sylow
385#3505C2×C13111yescharacteristic
386#2591C2×C13111yescharacteristic, complemented
387#2583C2×C13111yescharacteristic, complemented
388#2579C2×C13111yescharacteristic, complemented
389#2044C2×C13112yescomplemented
390#2044C2×C13112yescomplemented
391#1996C2×C13111yescharacteristic, complemented
392#1964C2×C13111yescharacteristic, complemented
393#1867C2×C13112yescomplemented
394#1867C2×C13112yescomplemented
395C4×#99C2×C13111yescharacteristic, complemented
396#553—22no—
397#553—21no—
398#552—21no—
399#551—22no—
400#548—21no—
401#546—21no—
402#539—21no—
403#538—21no—
404#534C22×C13112yes—
405#529—21no—
406#525—21no—
407C2×C22⋊Q8C22×C13111yescharacteristic
408C2×#121C22×C13111yescharacteristic
409#518C22×C13112yes—
410C2×C4×D4C22×C13111yescharacteristic
411C22×C4⋊C4C22×C13111yescharacteristic
412C2×#99C22×C13112yes—
413C2×#99C22×C13112yes—
414C2×#99C22×C13112yes—
415#400—21no—
416#398—21no—
417#398—21no—
418#396—21no—
419#395—21no—
420#394—21no—
421#389—22no—
422#388—22no—
423#387—21no—
424#386C22×C13111yescharacteristic
425#386C22×C13111yescharacteristic
426#386C22×C13112yes—
427#386C22×C13112yes—
428#385—21no—
429#385C22×C13111yescharacteristic
430#385C22×C13111yescharacteristic
431#385C22×C13112yes—
432#385C22×C13112yes—
433#380C22×C13111yescharacteristic
434C4×C22⋊C4C22×C13111yescharacteristic
435C4×C22⋊C4C22×C13111yescharacteristic
436#342C22×C13112yes—
437#342C22×C13112yes—
438#342C22×C13112yes—
439C2×#41—21no—
440C22×Q8D4×C13111yescharacteristic
441C22×D4D4×C13111yescharacteristic
442C22×D4C23×C13111yescharacteristic
443C22×D4C23×C13112yes—
444C23×C4D4×C13111yescharacteristic
445C23×C4C23×C13111yescharacteristic
446C23×C4C23×C13111yescharacteristic
447C23×C4C23×C13111yescharacteristic
448#126—22no—
449#126—22no—
450#126—22no—
451#125—21no—
452#125—22no—
453#124—21no—
454#124—22no—
455#123—22no—
456#123—22no—
457#123—22no—
458#123—22no—
459#123—22no—
460C22⋊Q8—21no—
461C22⋊Q8—22no—
462C22⋊Q8—21no—
463C22⋊Q8—21no—
464C22⋊Q8—21no—
465C22⋊Q8—21no—
466#121—21no—
467#121—22no—
468#121—21no—
469#121—21no—
470#121—21no—
471#121—21no—
472#121—22no—
473#121—22no—
474#120—22no—
475#120—22no—
476C4×Q8—21no—
477C4×D4—22no—
478C4×D4—21no—
479C4×D4—21no—
480C4×D4—21no—
481C4×D4—21no—
482C4×D4—21no—
483C4×D4—22no—
484C4×D4—22no—
485C4×D4—22no—
486C4×D4—22no—
487#117—21no—
488#117—22no—
489#117—22no—
490C2×C4⋊C4—21no—
491C2×C4⋊C4—21no—
492C2×C4⋊C4—21no—
493C2×C4⋊C4—21no—
494C2×C4⋊C4—21no—
495C2×C4⋊C4—21no—
496C2×C4⋊C4—21no—
497C2×C4⋊C4—22no—
498C2×C4⋊C4—21no—
499C2×C4⋊C4—21no—
500C2×C4⋊C4—22no—
501C2×C4⋊C4D4×C13111yescharacteristic
502C2×C4⋊C4D4×C13111yescharacteristic
503C2×C4⋊C4D4×C13112yes—
504C2×C4⋊C4D4×C13111yescharacteristic
505C2×C22⋊C4—22no—
506C2×C22⋊C4—21no—
507C2×C22⋊C4—22no—
508C2×C22⋊C4—21no—
509C2×C22⋊C4—22no—
510C2×C22⋊C4D4×C13111yescharacteristic
511C2×C22⋊C4D4×C13112yes—
512C2×C22⋊C4C23×C13112yes—
513C2×C22⋊C4C23×C13111yescharacteristic
514C2×C22⋊C4C23×C13111yescharacteristic
515C2×C22⋊C4C23×C13111yescharacteristic
516C2×C22⋊C4C23×C13112yes—
517C2×C22⋊C4C23×C13112yes—
518C2×C42—21no—
519C2×C42—21no—
520C2×C42D4×C13111yescharacteristic
521#99—24no—
522#99—24no—
523#99—24no—
524#95—21no—
525#95—21no—
526#95—21no—
527#95—21no—
528#95—21no—
529#95—22no—
530#95—22no—
531#95—21no—
532#95—21no—
533#95—22no—
534#95—22no—
535C24C2×D4×C13112yes—
536C24C2×D4×C13111yescharacteristic
537C24C24×C13111yescharacteristic
538#41—82no—
539C2×Q8—21no—
540C2×Q8—21no—
541C2×Q8—81no—
542C2×D4—21no—
543C2×D4—22no—
544C2×D4—21no—
545C2×D4—22no—
546C2×D4—22no—
547C2×D4—22no—
548C2×D4—22no—
549C2×D4—22no—
550C2×D4—22no—
551C2×D4—22no—
552C2×D4—22no—
553C2×D4—22no—
554C2×D4—21no—
555C2×D4—21no—
556C2×D4—81no—
557C22×C4—22no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—22no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—42no—
572C22×C4—81no—
573C22×C4—81no—
574C22×C4—81no—
575C22×C4C2×D4×C13111yescharacteristic
576C22×C4C2×D4×C13112yes—
577C22×C4C2×D4×C13111yescharacteristic
578C22×C4C2×D4×C13112yes—
579C22×C4C2×D4×C13111yescharacteristic
580C22×C4C2×D4×C13112yes—
581C22×C4C2×D4×C13111yescharacteristic
582C22×C4C2×D4×C13111yescharacteristic
583C22×C4C2×D4×C13111yescharacteristic
584C22×C4C2×D4×C13111yescharacteristic
585C22×C4C2×D4×C13111yescharacteristic
586C22×C4C2×D4×C13111yescharacteristic
587C4⋊C4—22no—
588C4⋊C4—22no—
589C4⋊C4—22no—
590C4⋊C4—22no—
591C4⋊C4—21no—
592C4⋊C4—22no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—21no—
596C4⋊C4—21no—
597C4⋊C4—22no—
598C4⋊C4—21no—
599C4⋊C4—42no—
600C4⋊C4—44no—
601C4⋊C4—41no—
602C4⋊C4—41no—
603C4⋊C4—41no—
604C4⋊C4—41no—
605C4⋊C4—81no—
606C4⋊C4—82no—
607C4⋊C4—81no—
608C22⋊C4—22no—
609C22⋊C4—22no—
610C22⋊C4—22no—
611C22⋊C4—22no—
612C22⋊C4—22no—
613C22⋊C4—22no—
614C22⋊C4—21no—
615C22⋊C4—22no—
616C22⋊C4—21no—
617C22⋊C4—22no—
618C22⋊C4—22no—
619C22⋊C4—22no—
620C22⋊C4—21no—
621C22⋊C4—21no—
622C22⋊C4—22no—
623C22⋊C4—22no—
624C22⋊C4—22no—
625C22⋊C4—22no—
626C22⋊C4—22no—
627C22⋊C4—44no—
628C22⋊C4—42no—
629C22⋊C4—82no—
630C22⋊C4—81no—
631C22⋊C4#41×C13114yescomplemented
632C42—22no—
633C42—22no—
634C42—21no—
635C42—21no—
636C42—81no—
637C42—81no—
638C23—22no—
639C23—21no—
640C23—21no—
641C23—21no—
642C23—22no—
643C23—22no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—42no—
649C23—42no—
650C23C22×D4×C13111yescharacteristic
651C23C22×D4×C13111yescharacteristic
652C23C22×D4×C13111yescharacteristic
653C23C2×#41×C13112yes—
654C232−1+4×C13112yes—
655Q8—42no—
656Q8—81no—
657D4—42no—
658D4—42no—
659D4—42no—
660D4—42no—
661D4—42no—
662D4—42no—
663D4—42no—
664D4—81no—
665D4—82no—
666D4—82no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—21no—
671C2×C4—22no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—24no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—42no—
696C2×C4—41no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—41no—
700C2×C4—42no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—42no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—42no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—42no—
712C2×C4—81no—
713C2×C4—82no—
714C2×C4—82no—
715C2×C4#120×C13111yescharacteristic
716C2×C4#120×C13111yescharacteristic
717C2×C4#120×C13111yescharacteristic
718C2×C4#120×C13111yescharacteristic
719C22—21no—
720C22—21no—
721C22—21no—
722C22—21no—
723C22—21no—
724C22—21no—
725C22—42no—
726C22—42no—
727C22—42no—
728C22—42no—
729C22—41no—
730C22—41no—
731C22—42no—
732C22—41no—
733C22—42no—
734C22—81no—
735C22—82no—
736C22—82no—
737C22C2×#120×C13111yescharacteristic
738C22#532×C13111yescharacteristic
739C22#536×C13111yescharacteristic
740C22#547×C13112yes—
741C22#548×C13112yes—
742C4—21no—
743C4—21no—
744C4—21no—
745C4—21no—
746C4—44no—
747C4—42no—
748C4—41no—
749C4—42no—
750C4—41no—
751C4—42no—
752C4—41no—
753C4—42no—
754C4—81no—
755C4—81no—
756C4—82no—
757C4—81no—
758C2—22no—
759C2—21no—
760C2—22no—
761C2—21no—
762C2—81no—
763C2—82no—
764C2#2432×C13111yescharacteristic
765C2#3025×C13111yescharacteristic
766C2#3026×C13111yescharacteristic
subgroupG/H
center, socleC22×C131C2×#120
commutator, Frattini, cosocleC24C24×C131
prime radical#3505×C131C2
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C131 ◁ C23×C4×C131 ◁ G

Complements

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

NH ≅ G/Ntype
2. #2591×C131C2semidirect
3. #2583×C131C2semidirect
4. #2579×C131C2semidirect
5. #2044×C131C2semidirect
6. #2044×C131C2semidirect
7. #1996×C131C2semidirect
8. #1964×C131C2semidirect
9. #1867×C131C2semidirect
10. #1867×C131C2semidirect
11. C4×#99×C131C2semidirect
247. C22⋊C4×C131#41semidirect
383. #25665C131direct (N × H)
384. C131#25665direct (N × H)
386. #2591C2×C131semidirect
387. #2583C2×C131semidirect
388. #2579C2×C131semidirect
389. #2044C2×C131semidirect
390. #2044C2×C131semidirect
391. #1996C2×C131semidirect
392. #1964C2×C131semidirect
393. #1867C2×C131semidirect
394. #1867C2×C131semidirect
395. C4×#99C2×C131semidirect
631. C22⋊C4#41×C131semidirect

Maximal subgroups

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

subgroupindex
#3505×C1312
#2591×C1312
#2583×C1312
#2579×C1312
#2044×C1312
#1996×C1312
#1964×C1312
#1867×C1312
C4×#99×C1312
#25665131