Finite Group Databasebeta

← C131×#18418 #45704302

Subgroups — C131×#18418 #45704302

Order 33536.

1176 conjugacy classes of subgroups.

The subgroup lattice has 766 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3537×C131C211yesmaximal, characteristic, complemented
2#3192×C131C211yesmaximal, characteristic, complemented
3#3188×C131C211yesmaximal, characteristic, complemented
4#2656×C131C211yesmaximal, characteristic, complemented
5#1618×C131C212yesmaximal, complemented
6#1613×C131C212yesmaximal, complemented
7#1600×C131C212yesmaximal, complemented
8#1595×C131C212yesmaximal, complemented
9#1504×C131C211yesmaximal, characteristic, complemented
10C2×#327×C131C211yesmaximal, characteristic, complemented
11#1471×C131C211yesmaximal, characteristic, complemented
12#560×C131—22no—
13#553×C131—21no—
14#553×C131—21no—
15D42×C131—22no—
16D42×C131—21no—
17D42×C131—21no—
18#540×C131—21no—
19#538×C131—21no—
20#538×C131C2212yes—
21#535×C131—21no—
22#534×C131—21no—
23#534×C131C2212yes—
24#525×C131C2211yescharacteristic
25C2×#121×C131—22no—
26C2×#121×C131C2211yescharacteristic
27C2×#121×C131C2211yescharacteristic
28C2×#121×C131C2211yescharacteristic, complemented
29#484×C131C2211yescharacteristic, complemented
30#482×C131—21no—
31#481×C131—21no—
32#481×C131C2211yescharacteristic, complemented
33#481×C131C2212yescomplemented
34#469×C131—22no—
35#466×C131—21no—
36#465×C131—21no—
37#450×C131C2211yescharacteristic, complemented
38#449×C131—21no—
39#447×C131—21no—
40#447×C131C2211yescharacteristic, complemented
41#447×C131C2212yescomplemented
42#407×C131C2211yescharacteristic, complemented
43C2×C22⋊C8×C131C2211yescharacteristic, complemented
44#399×C131—21no—
45#399×C131C2212yescomplemented
46#392×C131—21no—
47#392×C131C2212yescomplemented
48C2×#95×C131C2211yescharacteristic, complemented
49#328×C131C2212yescomplemented
50#327×C131C2212yescomplemented
51#327×C131C2212yescomplemented
52#327×C131C2212yescomplemented
53#323×C131C2212yescomplemented
54#323×C131C2212yescomplemented
55C2×#41×C131D411yescharacteristic, complemented
56C22×D4×C131—22no—
57C22×D4×C131—21no—
58C22×D4×C131—21no—
59C22×D4×C131—22no—
60C22×D4×C131—21no—
61C22×D4×C131—22no—
62C22×D4×C131D412yes—
63C22×D4×C131D411yescharacteristic
64C22×D4×C131D411yescharacteristic, complemented
65C22×D4×C131C2311yescharacteristic
66C23×C4×C131—21no—
67C23×C4×C131C2311yescharacteristic
68C2×SD16×C131—21no—
69C2×D8×C131—22no—
70C2×D8×C131—21no—
71C2×M16×C131—21no—
72C22×C8×C131—21no—
73#127×C131—22no—
74#127×C131—21no—
75#126×C131—22no—
76#126×C131—22no—
77#125×C131—21no—
78#124×C131—22no—
79#123×C131—22no—
80#123×C131—21no—
81#123×C131—22no—
82#123×C131—22no—
83#123×C131—22no—
84C22⋊Q8×C131D411yescharacteristic, complemented
85C22⋊Q8×C131C2311yescharacteristic
86#121×C131—22no—
87#121×C131—21no—
88#121×C131—21no—
89#121×C131—22no—
90#121×C131—22no—
91#121×C131—22no—
92#121×C131—22no—
93#121×C131—21no—
94#121×C131—21no—
95#121×C131—21no—
96#121×C131—21no—
97#121×C131—21no—
98#121×C131—21no—
99#121×C131—22no—
100#121×C131—21no—
101#121×C131—21no—
102#121×C131—21no—
103#121×C131—21no—
104#121×C131—48no—
105#121×C131D411yescharacteristic, complemented
106#121×C131D412yescomplemented
107#121×C131C2312yes—
108#121×C131C2311yescharacteristic
109#120×C131—22no—
110#120×C131—22no—
111#120×C131—22no—
112#120×C131—21no—
113#120×C131—22no—
114#120×C131—22no—
115#120×C131—22no—
116C4×D4×C131—22no—
117C4×D4×C131—21no—
118C4×D4×C131—21no—
119C4×D4×C131—21no—
120C4×D4×C131—21no—
121C4×D4×C131—22no—
122#117×C131—21no—
123#117×C131D411yescharacteristic, complemented
124C2×C4⋊C4×C131—22no—
125C2×C4⋊C4×C131D411yescharacteristic
126C2×C4⋊C4×C131D411yescharacteristic, complemented
127C2×C4⋊C4×C131C2311yescharacteristic
128C2×C22⋊C4×C131—21no—
129C2×C22⋊C4×C131—22no—
130C2×C22⋊C4×C131—21no—
131C2×C22⋊C4×C131—22no—
132C2×C22⋊C4×C131C2312yes—
133#107×C131—21no—
134#106×C131—21no—
135#106×C131—22no—
136#103×C131—21no—
137#102×C131—22no—
138#102×C131—21no—
139#102×C131—21no—
140#102×C131—22no—
141#102×C131—21no—
142C22⋊C8×C131—21no—
143C22⋊C8×C131—21no—
144C22⋊C8×C131C2311yescharacteristic
145C22⋊C8×C131C2311yescharacteristic
146C22⋊C8×C131C2312yes—
147#95×C131—21no—
148#95×C131C2312yes—
149C24×C131—22no—
150C24×C131—21no—
151C24×C131—21no—
152C24×C131C2×D411yescharacteristic
153C24×C131C2×D412yes—
154#41×C131—81no—
155C2×Q8×C131C2×D411yescharacteristic
156C2×D4×C131—22no—
157C2×D4×C131—21no—
158C2×D4×C131—21no—
159C2×D4×C131—22no—
160C2×D4×C131—22no—
161C2×D4×C131—22no—
162C2×D4×C131—22no—
163C2×D4×C131—22no—
164C2×D4×C131—22no—
165C2×D4×C131—21no—
166C2×D4×C131—22no—
167C2×D4×C131—22no—
168C2×D4×C131—21no—
169C2×D4×C131—21no—
170C2×D4×C131—21no—
171C2×D4×C131—21no—
172C2×D4×C131—21no—
173C2×D4×C131—44no—
174C2×D4×C131—44no—
175C2×D4×C131—44no—
176C2×D4×C131—41no—
177C2×D4×C131—41no—
178C2×D4×C131—81no—
179C2×D4×C131—81no—
180C2×D4×C131—82no—
181C2×D4×C131—81no—
182C2×D4×C131—82no—
183C2×D4×C131—82no—
184C2×D4×C131—81no—
185C2×D4×C131—81no—
186C2×D4×C131—82no—
187C2×D4×C131—82no—
188C2×D4×C131—84no—
189C2×D4×C131C2×D411yescharacteristic
190C2×D4×C131C2×D412yes—
191C22×C4×C131—22no—
192C22×C4×C131—22no—
193C22×C4×C131—22no—
194C22×C4×C131—24no—
195C22×C4×C131—21no—
196C22×C4×C131—21no—
197C22×C4×C131—21no—
198C22×C4×C131—81no—
199C22×C4×C131—81no—
200C22×C4×C131—81no—
201C22×C4×C131C2×D412yes—
202C22×C4×C131C2×D411yescharacteristic
203C22×C4×C131C2×D411yescharacteristic
204C22×C4×C131C2×D411yescharacteristic
205C22×C4×C131C2×D411yescharacteristic
206C22×C4×C131C2×D411yescharacteristic
207C22×C4×C131C2411yescharacteristic
208SD16×C131—81no—
209D8×C131—81no—
210D8×C131—82no—
211M16×C131—81no—
212C2×C8×C131—21no—
213C2×C8×C131—22no—
214C2×C8×C131—21no—
215C2×C8×C131—81no—
216C4⋊C4×C131—22no—
217C4⋊C4×C131—22no—
218C4⋊C4×C131—21no—
219C4⋊C4×C131—21no—
220C4⋊C4×C131—21no—
221C4⋊C4×C131—21no—
222C4⋊C4×C131—21no—
223C4⋊C4×C131—21no—
224C4⋊C4×C131—21no—
225C4⋊C4×C131—44no—
226C4⋊C4×C131C2×D412yes—
227C4⋊C4×C131C2×D411yescharacteristic
228C4⋊C4×C131C2×D411yescharacteristic
229C22⋊C4×C131—22no—
230C22⋊C4×C131—22no—
231C22⋊C4×C131—22no—
232C22⋊C4×C131—22no—
233C22⋊C4×C131—22no—
234C22⋊C4×C131—21no—
235C22⋊C4×C131—21no—
236C22⋊C4×C131—21no—
237C22⋊C4×C131—22no—
238C22⋊C4×C131—21no—
239C22⋊C4×C131—22no—
240C22⋊C4×C131—22no—
241C22⋊C4×C131—22no—
242C22⋊C4×C131—21no—
243C22⋊C4×C131—44no—
244C22⋊C4×C131—44no—
245C22⋊C4×C131—41no—
246C22⋊C4×C131—41no—
247C42×C131—22no—
248C42×C131—21no—
249C23×C131—21no—
250C23×C131—21no—
251C23×C131—22no—
252C23×C131—22no—
253C23×C131—22no—
254C23×C131—21no—
255C23×C131—22no—
256C23×C131—22no—
257C23×C131—41no—
258C23×C131—42no—
259C23×C131—42no—
260C23×C131—42no—
261C23×C131—42no—
262C23×C131—42no—
263C23×C131—41no—
264C23×C131—41no—
265C23×C131—41no—
266C23×C131—81no—
267C23×C131—81no—
268C23×C131—82no—
269C23×C131—82no—
270C23×C131—82no—
271C23×C131#12011yescharacteristic
272C23×C131#12011yescharacteristic
273C23×C131C22×D411yescharacteristic
274Q8×C131—41no—
275D4×C131—42no—
276D4×C131—41no—
277D4×C131—42no—
278D4×C131—42no—
279D4×C131—42no—
280D4×C131—41no—
281D4×C131—41no—
282D4×C131—42no—
283D4×C131—41no—
284D4×C131—42no—
285D4×C131—41no—
286D4×C131—44no—
287D4×C131—42no—
288D4×C131—81no—
289D4×C131—82no—
290D4×C131—82no—
291D4×C131—81no—
292D4×C131—82no—
293D4×C131—82no—
294D4×C131—82no—
295D4×C131—82no—
296D4×C131—82no—
297D4×C131—88no—
298D4×C131—82no—
299D4×C131—82no—
300C2×C4×C131—24no—
301C2×C4×C131—21no—
302C2×C4×C131—22no—
303C2×C4×C131—22no—
304C2×C4×C131—21no—
305C2×C4×C131—21no—
306C2×C4×C131—41no—
307C2×C4×C131—41no—
308C2×C4×C131—41no—
309C2×C4×C131—41no—
310C2×C4×C131—41no—
311C2×C4×C131—41no—
312C2×C4×C131—42no—
313C2×C4×C131—42no—
314C2×C4×C131—42no—
315C2×C4×C131—42no—
316C2×C4×C131—42no—
317C2×C4×C131—41no—
318C2×C4×C131—81no—
319C2×C4×C131—84no—
320C2×C4×C131—82no—
321C2×C4×C131—82no—
322C2×C4×C131#12011yescharacteristic
323C2×C4×C131#12011yescharacteristic
324C2×C4×C131C22×D411yescharacteristic
325C2×C4×C131C22×D411yescharacteristic
326C8×C131—41no—
327C8×C131—41no—
328C8×C131—42no—
329C22×C131—21no—
330C22×C131—21no—
331C22×C131—21no—
332C22×C131—21no—
333C22×C131—21no—
334C22×C131—21no—
335C22×C131—21no—
336C22×C131—42no—
337C22×C131—42no—
338C22×C131—42no—
339C22×C131—42no—
340C22×C131—41no—
341C22×C131—42no—
342C22×C131—42no—
343C22×C131—41no—
344C22×C131—41no—
345C22×C131—42no—
346C22×C131—42no—
347C22×C131—82no—
348C22×C131—82no—
349C22×C131—82no—
350C22×C131—82no—
351C22×C131—81no—
352C22×C131—81no—
353C22×C131—81no—
354C22×C131—162no—
355C22×C131—164no—
356C22×C131#45312yes—
357C22×C131C2×#12011yescharacteristic
358C22×C131#57611yescharacteristic
359C22×C131#57711yescharacteristic
360C4×C131—21no—
361C4×C131—21no—
362C4×C131—21no—
363C4×C131—21no—
364C4×C131—44no—
365C4×C131—42no—
366C4×C131—41no—
367C4×C131—42no—
368C4×C131—41no—
369C4×C131—41no—
370C4×C131—81no—
371C2×C131—21no—
372C2×C131—21no—
373C2×C131—22no—
374C2×C131—41no—
375C2×C131—82no—
376C2×C131—82no—
377C2×C131—81no—
378C2×C131—161no—
379C2×C131#301211yescharacteristic
380C2×C131C2×#45311yescharacteristic
381C2×C131#302611yescharacteristic
382#18418C13111yesmaximal, characteristic, direct product factor, Sylow
383C131#1841811yescharacteristic, direct product factor, Sylow
384#3537C2×C13111yescharacteristic, complemented
385#3192C2×C13111yescharacteristic, complemented
386#3188C2×C13111yescharacteristic, complemented
387#2656C2×C13111yescharacteristic, complemented
388#1618C2×C13112yescomplemented
389#1613C2×C13112yescomplemented
390#1600C2×C13112yescomplemented
391#1595C2×C13112yescomplemented
392#1504C2×C13111yescharacteristic, complemented
393C2×#327C2×C13111yescharacteristic, complemented
394#1471C2×C13111yescharacteristic, complemented
395#560—22no—
396#553—21no—
397#553—21no—
398D42—22no—
399D42—21no—
400D42—21no—
401#540—21no—
402#538—21no—
403#538C22×C13112yes—
404#535—21no—
405#534—21no—
406#534C22×C13112yes—
407#525C22×C13111yescharacteristic
408C2×#121—22no—
409C2×#121C22×C13111yescharacteristic
410C2×#121C22×C13111yescharacteristic
411C2×#121C22×C13111yescharacteristic, complemented
412#484C22×C13111yescharacteristic, complemented
413#482—21no—
414#481—21no—
415#481C22×C13111yescharacteristic, complemented
416#481C22×C13112yescomplemented
417#469—22no—
418#466—21no—
419#465—21no—
420#450C22×C13111yescharacteristic, complemented
421#449—21no—
422#447—21no—
423#447C22×C13111yescharacteristic, complemented
424#447C22×C13112yescomplemented
425#407C22×C13111yescharacteristic, complemented
426C2×C22⋊C8C22×C13111yescharacteristic, complemented
427#399—21no—
428#399C22×C13112yescomplemented
429#392—21no—
430#392C22×C13112yescomplemented
431C2×#95C22×C13111yescharacteristic, complemented
432#328C22×C13112yescomplemented
433#327C22×C13112yescomplemented
434#327C22×C13112yescomplemented
435#327C22×C13112yescomplemented
436#323C22×C13112yescomplemented
437#323C22×C13112yescomplemented
438C2×#41D4×C13111yescharacteristic, complemented
439C22×D4—22no—
440C22×D4—21no—
441C22×D4—21no—
442C22×D4—22no—
443C22×D4—21no—
444C22×D4—22no—
445C22×D4D4×C13112yes—
446C22×D4D4×C13111yescharacteristic
447C22×D4D4×C13111yescharacteristic, complemented
448C22×D4C23×C13111yescharacteristic
449C23×C4—21no—
450C23×C4C23×C13111yescharacteristic
451C2×SD16—21no—
452C2×D8—22no—
453C2×D8—21no—
454C2×M16—21no—
455C22×C8—21no—
456#127—22no—
457#127—21no—
458#126—22no—
459#126—22no—
460#125—21no—
461#124—22no—
462#123—22no—
463#123—21no—
464#123—22no—
465#123—22no—
466#123—22no—
467C22⋊Q8D4×C13111yescharacteristic, complemented
468C22⋊Q8C23×C13111yescharacteristic
469#121—22no—
470#121—21no—
471#121—21no—
472#121—22no—
473#121—22no—
474#121—22no—
475#121—22no—
476#121—21no—
477#121—21no—
478#121—21no—
479#121—21no—
480#121—21no—
481#121—21no—
482#121—22no—
483#121—21no—
484#121—21no—
485#121—21no—
486#121—21no—
487#121—48no—
488#121D4×C13112yescomplemented
489#121D4×C13111yescharacteristic, complemented
490#121C23×C13112yes—
491#121C23×C13111yescharacteristic
492#120—22no—
493#120—22no—
494#120—22no—
495#120—21no—
496#120—22no—
497#120—22no—
498#120—22no—
499C4×D4—22no—
500C4×D4—21no—
501C4×D4—21no—
502C4×D4—21no—
503C4×D4—21no—
504C4×D4—22no—
505#117—21no—
506#117D4×C13111yescharacteristic, complemented
507C2×C4⋊C4—22no—
508C2×C4⋊C4D4×C13111yescharacteristic
509C2×C4⋊C4D4×C13111yescharacteristic, complemented
510C2×C4⋊C4C23×C13111yescharacteristic
511C2×C22⋊C4—21no—
512C2×C22⋊C4—22no—
513C2×C22⋊C4—22no—
514C2×C22⋊C4—21no—
515C2×C22⋊C4C23×C13112yes—
516#107—21no—
517#106—21no—
518#106—22no—
519#103—21no—
520#102—22no—
521#102—21no—
522#102—21no—
523#102—22no—
524#102—21no—
525C22⋊C8—21no—
526C22⋊C8—21no—
527C22⋊C8C23×C13111yescharacteristic
528C22⋊C8C23×C13111yescharacteristic
529C22⋊C8C23×C13112yes—
530#95—21no—
531#95C23×C13112yes—
532C24—22no—
533C24—21no—
534C24—21no—
535C24C2×D4×C13111yescharacteristic
536C24C2×D4×C13112yes—
537#41—81no—
538C2×Q8C2×D4×C13111yescharacteristic
539C2×D4—22no—
540C2×D4—21no—
541C2×D4—21no—
542C2×D4—22no—
543C2×D4—22no—
544C2×D4—22no—
545C2×D4—22no—
546C2×D4—22no—
547C2×D4—22no—
548C2×D4—21no—
549C2×D4—22no—
550C2×D4—22no—
551C2×D4—21no—
552C2×D4—21no—
553C2×D4—21no—
554C2×D4—21no—
555C2×D4—21no—
556C2×D4—44no—
557C2×D4—44no—
558C2×D4—44no—
559C2×D4—41no—
560C2×D4—41no—
561C2×D4—81no—
562C2×D4—81no—
563C2×D4—82no—
564C2×D4—81no—
565C2×D4—82no—
566C2×D4—82no—
567C2×D4—81no—
568C2×D4—81no—
569C2×D4—82no—
570C2×D4—82no—
571C2×D4—84no—
572C2×D4C2×D4×C13111yescharacteristic
573C2×D4C2×D4×C13112yes—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—24no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—81no—
582C22×C4—81no—
583C22×C4—81no—
584C22×C4C2×D4×C13112yes—
585C22×C4C2×D4×C13111yescharacteristic
586C22×C4C2×D4×C13111yescharacteristic
587C22×C4C2×D4×C13111yescharacteristic
588C22×C4C2×D4×C13111yescharacteristic
589C22×C4C2×D4×C13111yescharacteristic
590C22×C4C24×C13111yescharacteristic
591SD16—81no—
592D8—81no—
593D8—82no—
594M16—81no—
595C2×C8—21no—
596C2×C8—22no—
597C2×C8—21no—
598C2×C8—81no—
599C4⋊C4—22no—
600C4⋊C4—22no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—21no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—44no—
609C4⋊C4C2×D4×C13112yes—
610C4⋊C4C2×D4×C13111yescharacteristic
611C4⋊C4C2×D4×C13111yescharacteristic
612C22⋊C4—22no—
613C22⋊C4—22no—
614C22⋊C4—22no—
615C22⋊C4—22no—
616C22⋊C4—22no—
617C22⋊C4—21no—
618C22⋊C4—21no—
619C22⋊C4—21no—
620C22⋊C4—22no—
621C22⋊C4—21no—
622C22⋊C4—22no—
623C22⋊C4—22no—
624C22⋊C4—22no—
625C22⋊C4—21no—
626C22⋊C4—44no—
627C22⋊C4—44no—
628C22⋊C4—41no—
629C22⋊C4—41no—
630C42—22no—
631C42—21no—
632C23—22no—
633C23—21no—
634C23—21no—
635C23—22no—
636C23—22no—
637C23—21no—
638C23—22no—
639C23—22no—
640C23—41no—
641C23—42no—
642C23—42no—
643C23—42no—
644C23—42no—
645C23—42no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—81no—
650C23—81no—
651C23—82no—
652C23—82no—
653C23—82no—
654C23#120×C13111yescharacteristic
655C23#120×C13111yescharacteristic
656C23C22×D4×C13111yescharacteristic
657Q8—41no—
658D4—42no—
659D4—41no—
660D4—42no—
661D4—42no—
662D4—42no—
663D4—41no—
664D4—41no—
665D4—44no—
666D4—42no—
667D4—42no—
668D4—41no—
669D4—42no—
670D4—41no—
671D4—81no—
672D4—82no—
673D4—82no—
674D4—81no—
675D4—82no—
676D4—82no—
677D4—82no—
678D4—82no—
679D4—82no—
680D4—88no—
681D4—82no—
682D4—82no—
683C2×C4—24no—
684C2×C4—21no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—41no—
701C2×C4—81no—
702C2×C4—84no—
703C2×C4—82no—
704C2×C4—82no—
705C2×C4#120×C13111yescharacteristic
706C2×C4#120×C13111yescharacteristic
707C2×C4C22×D4×C13111yescharacteristic
708C2×C4C22×D4×C13111yescharacteristic
709C8—41no—
710C8—41no—
711C8—42no—
712C22—21no—
713C22—21no—
714C22—21no—
715C22—21no—
716C22—21no—
717C22—21no—
718C22—21no—
719C22—42no—
720C22—42no—
721C22—42no—
722C22—42no—
723C22—41no—
724C22—42no—
725C22—42no—
726C22—41no—
727C22—41no—
728C22—42no—
729C22—42no—
730C22—82no—
731C22—82no—
732C22—82no—
733C22—82no—
734C22—81no—
735C22—81no—
736C22—81no—
737C22—162no—
738C22—164no—
739C22#453×C13112yes—
740C22C2×#120×C13111yescharacteristic
741C22#576×C13111yescharacteristic
742C22#577×C13111yescharacteristic
743C4—21no—
744C4—21no—
745C4—21no—
746C4—21no—
747C4—44no—
748C4—42no—
749C4—41no—
750C4—42no—
751C4—41no—
752C4—41no—
753C4—81no—
754C2—21no—
755C2—21no—
756C2—22no—
757C2—41no—
758C2—82no—
759C2—82no—
760C2—81no—
761C2—161no—
762C2#3012×C13111yescharacteristic
763C2C2×#453×C13111yescharacteristic
764C2#3026×C13111yescharacteristic
subgroupG/H
center, socleC22×C131C2×#120
commutator, Frattini, cosocleC22×C4C24×C131
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C131 ◁ C23×C4×C131 ◁ G

Complements

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

NH ≅ G/Ntype
1. #3537×C131C2semidirect
2. #3192×C131C2semidirect
3. #3188×C131C2semidirect
4. #2656×C131C2semidirect
5. #1618×C131C2semidirect
6. #1613×C131C2semidirect
7. #1600×C131C2semidirect
8. #1595×C131C2semidirect
9. #1504×C131C2semidirect
10. C2×#327×C131C2semidirect
11. #1471×C131C2semidirect
28. C2×#121×C131C22semidirect
29. #484×C131C22semidirect
32. #481×C131C22semidirect
33. #481×C131C22semidirect
37. #450×C131C22semidirect
40. #447×C131C22semidirect
41. #447×C131C22semidirect
42. #407×C131C22semidirect
43. C2×C22⋊C8×C131C22semidirect
45. #399×C131C22semidirect
47. #392×C131C22semidirect
48. C2×#95×C131C22semidirect
49. #328×C131C22semidirect
50. #327×C131C22semidirect
51. #327×C131C22semidirect
52. #327×C131C22semidirect
53. #323×C131C22semidirect
54. #323×C131C22semidirect
55. C2×#41×C131D4semidirect
64. C22×D4×C131D4semidirect
84. C22⋊Q8×C131D4semidirect
105. #121×C131D4semidirect
106. #121×C131D4semidirect
123. #117×C131D4semidirect
126. C2×C4⋊C4×C131D4semidirect
382. #18418C131direct (N × H)
383. C131#18418direct (N × H)
384. #3537C2×C131semidirect
385. #3192C2×C131semidirect
386. #3188C2×C131semidirect
387. #2656C2×C131semidirect
388. #1618C2×C131semidirect
389. #1613C2×C131semidirect
390. #1600C2×C131semidirect
391. #1595C2×C131semidirect
392. #1504C2×C131semidirect
393. C2×#327C2×C131semidirect
394. #1471C2×C131semidirect
411. C2×#121C22×C131semidirect
412. #484C22×C131semidirect
415. #481C22×C131semidirect
416. #481C22×C131semidirect
420. #450C22×C131semidirect
423. #447C22×C131semidirect
424. #447C22×C131semidirect
425. #407C22×C131semidirect
426. C2×C22⋊C8C22×C131semidirect
428. #399C22×C131semidirect
430. #392C22×C131semidirect
431. C2×#95C22×C131semidirect
432. #328C22×C131semidirect
433. #327C22×C131semidirect
434. #327C22×C131semidirect
435. #327C22×C131semidirect
436. #323C22×C131semidirect
437. #323C22×C131semidirect
438. C2×#41D4×C131semidirect
447. C22×D4D4×C131semidirect
467. C22⋊Q8D4×C131semidirect
488. #121D4×C131semidirect
489. #121D4×C131semidirect
506. #117D4×C131semidirect
509. C2×C4⋊C4D4×C131semidirect

Maximal subgroups

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

subgroupindex
#3537×C1312
#3192×C1312
#3188×C1312
#2656×C1312
#1618×C1312
#1613×C1312
#1600×C1312
#1595×C1312
#1504×C1312
C2×#327×C1312
#1471×C1312
#18418131