Finite Group Databasebeta

← C131×#11018 #45696902

Subgroups — C131×#11018 #45696902

Order 33536.

1270 conjugacy classes of subgroups.

The subgroup lattice has 792 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#575×C131C211yesmaximal, characteristic
2C2×#421×C131C211yesmaximal, characteristic, complemented
3C2×#416×C131C211yesmaximal, characteristic, complemented
4#2879×C131C211yesmaximal, characteristic, complemented
5C2×#408×C131C211yesmaximal, characteristic, complemented
6C2×#344×C131C211yesmaximal, characteristic, complemented
7C2×#341×C131C211yesmaximal, characteristic, complemented
8C22×#41×C131C2211yescharacteristic
9C22×#41×C131C2211yescharacteristic
10#575×C131—22no—
11#575×C131—22no—
12#575×C131—22no—
13#575×C131—22no—
14C2×#137×C131—21no—
15C2×#137×C131C412yescomplemented
16C2×AGL(1,ℤ/8)×C131—21no—
17C2×AGL(1,ℤ/8)×C131C412yescomplemented
18C2×#135×C131—22no—
19C22×M16×C131C2211yescharacteristic
20C22×M16×C131C2211yescharacteristic
21C22×M16×C131C2211yescharacteristic
22C23×C8×C131C2211yescharacteristic
23C2×#117×C131C2211yescharacteristic
24#421×C131—22no—
25#421×C131—22no—
26C2×#104×C131—22no—
27#416×C131—22no—
28#416×C131—22no—
29C2×#103×C131—21no—
30C2×#102×C131—21no—
31#408×C131—22no—
32#408×C131—22no—
33#408×C131—22no—
34#408×C131—22no—
35#407×C131—22no—
36C2×C22⋊C8×C131—22no—
37#344×C131—22no—
38#341×C131—22no—
39C2×#41×C131—21no—
40C2×#41×C131—21no—
41C2×#41×C131—21no—
42C2×#41×C131—21no—
43C2×#41×C131—21no—
44C2×#41×C131—21no—
45C2×#41×C131—21no—
46C2×#41×C131—21no—
47C2×#41×C131—21no—
48C2×#41×C131—21no—
49C2×#41×C131—21no—
50C2×#41×C131—21no—
51C2×#41×C131—21no—
52C2×#41×C131—21no—
53C2×#41×C131—21no—
54C2×#41×C131—21no—
55C2×#41×C131—21no—
56C2×#41×C131—21no—
57C2×#41×C131—21no—
58C2×#41×C131—21no—
59C2×#41×C131C2×C412yes—
60C2×#41×C131D412yes—
61C2×#41×C131D412yes—
62C2×#41×C131D412yes—
63C22×Q8×C131C2×C411yescharacteristic
64C22×Q8×C131D411yescharacteristic
65C22×D4×C131—21no—
66C22×D4×C131—21no—
67C22×D4×C131C2×C411yescharacteristic
68C22×D4×C131D411yescharacteristic
69C23×C4×C131—21no—
70C23×C4×C131—21no—
71C23×C4×C131C2311yescharacteristic
72#137×C131—24no—
73#137×C131—24no—
74#137×C131—24no—
75#137×C131—24no—
76AGL(1,ℤ/8)×C131—24no—
77AGL(1,ℤ/8)×C131—24no—
78AGL(1,ℤ/8)×C131—24no—
79AGL(1,ℤ/8)×C131—24no—
80#135×C131—28no—
81#135×C131—28no—
82C2×Q16×C131—22no—
83C2×SD16×C131—22no—
84C2×SD16×C131—22no—
85C2×D8×C131—22no—
86C2×M16×C131—21no—
87C2×M16×C131—21no—
88C2×M16×C131—21no—
89C2×M16×C131—21no—
90C2×M16×C131—21no—
91C2×M16×C131—21no—
92C2×M16×C131—21no—
93C2×M16×C131—21no—
94C2×M16×C131—21no—
95C2×M16×C131—21no—
96C2×M16×C131—21no—
97C2×M16×C131—21no—
98C2×M16×C131—21no—
99C2×M16×C131—21no—
100C2×M16×C131C2×C412yes—
101C2×M16×C131D412yes—
102C2×M16×C131D412yes—
103C2×M16×C131D412yes—
104C22×C8×C131—21no—
105C22×C8×C131—21no—
106C22×C8×C131—21no—
107C22×C8×C131—21no—
108C22×C8×C131—21no—
109C22×C8×C131—21no—
110C22×C8×C131—21no—
111C22×C8×C131—21no—
112C22×C8×C131D412yes—
113C22×C8×C131D412yes—
114#117×C131—21no—
115#117×C131—21no—
116#117×C131—21no—
117#117×C131D412yes—
118C2×C4⋊C4×C131—21no—
119C2×C22⋊C4×C131—21no—
120C2×C42×C131—21no—
121#104×C131—28no—
122#103×C131—24no—
123#102×C131—24no—
124C22⋊C8×C131—28no—
125C22⋊C8×C131—28no—
126C24×C131—21no—
127C24×C131—21no—
128C24×C131#4111yescharacteristic
129#41×C131—22no—
130#41×C131—22no—
131#41×C131—22no—
132#41×C131—22no—
133#41×C131—22no—
134#41×C131—22no—
135#41×C131—22no—
136#41×C131—22no—
137#41×C131—22no—
138#41×C131—22no—
139#41×C131—22no—
140#41×C131—22no—
141#41×C131—22no—
142#41×C131—22no—
143#41×C131—22no—
144#41×C131—22no—
145#41×C131—41no—
146#41×C131—41no—
147#41×C131—41no—
148#41×C131—41no—
149#41×C131—41no—
150#41×C131—41no—
151#41×C131—41no—
152#41×C131—41no—
153#41×C131—41no—
154#41×C131—41no—
155#41×C131—41no—
156#41×C131—41no—
157#41×C131—41no—
158#41×C131—41no—
159#41×C131—41no—
160#41×C131—41no—
161C2×Q8×C131—21no—
162C2×Q8×C131—21no—
163C2×Q8×C131—21no—
164C2×Q8×C131—21no—
165C2×Q8×C131—21no—
166C2×Q8×C131—21no—
167C2×Q8×C131—21no—
168C2×Q8×C131—21no—
169C2×Q8×C131—21no—
170C2×Q8×C131—21no—
171C2×Q8×C131C22⋊C412yes—
172C2×Q8×C131C22⋊C412yes—
173C2×D4×C131—22no—
174C2×D4×C131—22no—
175C2×D4×C131—22no—
176C2×D4×C131—22no—
177C2×D4×C131—21no—
178C2×D4×C131—21no—
179C2×D4×C131—21no—
180C2×D4×C131—21no—
181C2×D4×C131—21no—
182C2×D4×C131—21no—
183C2×D4×C131—21no—
184C2×D4×C131—21no—
185C2×D4×C131—21no—
186C2×D4×C131—21no—
187C2×D4×C131—41no—
188C2×D4×C131—41no—
189C2×D4×C131—41no—
190C2×D4×C131—41no—
191C2×D4×C131—41no—
192C2×D4×C131—41no—
193C2×D4×C131—41no—
194C2×D4×C131—41no—
195C2×D4×C131C22⋊C412yes—
196C2×D4×C131C22⋊C412yes—
197C22×C4×C131—21no—
198C22×C4×C131—21no—
199C22×C4×C131—22no—
200C22×C4×C131—22no—
201C22×C4×C131—22no—
202C22×C4×C131—22no—
203C22×C4×C131—41no—
204C22×C4×C131—41no—
205C22×C4×C131—41no—
206C22×C4×C131—41no—
207C22×C4×C131—41no—
208C22×C4×C131—41no—
209C22×C4×C131—41no—
210C22×C4×C131—41no—
211C22×C4×C131—41no—
212C22×C4×C131C22×C411yescharacteristic
213C22×C4×C131C2×D411yescharacteristic
214C22×C4×C131C2×D411yescharacteristic
215C22×C4×C131C2×D411yescharacteristic
216C22×C4×C131C2×D411yescharacteristic
217C22×C4×C131C2×D411yescharacteristic
218C22×C4×C131C2×D411yescharacteristic
219C22×C4×C131C2×D411yescharacteristic
220C22×C4×C131C2×D411yescharacteristic
221C22×C4×C131C2×D411yescharacteristic
222C22×C4×C131C2×D411yescharacteristic
223C22×C4×C131#4111yescharacteristic
224C22×C4×C131#4111yescharacteristic
225C22×C4×C131#4111yescharacteristic
226Q16×C131—28no—
227SD16×C131—28no—
228SD16×C131—28no—
229D8×C131—28no—
230M16×C131—22no—
231M16×C131—22no—
232M16×C131—22no—
233M16×C131—22no—
234M16×C131—22no—
235M16×C131—41no—
236M16×C131—41no—
237M16×C131—41no—
238M16×C131—41no—
239M16×C131—41no—
240M16×C131—41no—
241M16×C131C22⋊C414yes—
242C2×C8×C131—22no—
243C2×C8×C131—22no—
244C2×C8×C131—22no—
245C2×C8×C131—22no—
246C2×C8×C131—22no—
247C2×C8×C131—22no—
248C2×C8×C131—22no—
249C2×C8×C131—22no—
250C2×C8×C131—22no—
251C2×C8×C131—22no—
252C2×C8×C131—41no—
253C2×C8×C131—41no—
254C2×C8×C131—41no—
255C2×C8×C131—41no—
256C2×C8×C131—41no—
257C2×C8×C131—41no—
258C4⋊C4×C131—22no—
259C4⋊C4×C131—41no—
260C22⋊C4×C131—22no—
261C22⋊C4×C131—41no—
262C42×C131—22no—
263C42×C131—41no—
264C23×C131—22no—
265C23×C131—22no—
266C23×C131—42no—
267C23×C131—44no—
268C23×C131—41no—
269C23×C131—41no—
270C23×C131—41no—
271C23×C131—41no—
272C23×C131—82no—
273C23×C131C4×D411yescharacteristic
274C23×C131#12111yescharacteristic
275C23×C131#12111yescharacteristic
276C23×C131#12111yescharacteristic
277C23×C131#12311yescharacteristic
278C23×C131#12311yescharacteristic
279C23×C131#12411yescharacteristic
280Q8×C131—22no—
281Q8×C131—22no—
282Q8×C131—22no—
283Q8×C131—22no—
284Q8×C131—41no—
285Q8×C131—41no—
286Q8×C131—41no—
287Q8×C131—41no—
288D4×C131—22no—
289D4×C131—22no—
290D4×C131—22no—
291D4×C131—22no—
292D4×C131—42no—
293D4×C131—42no—
294D4×C131—42no—
295D4×C131—42no—
296D4×C131—42no—
297D4×C131—42no—
298D4×C131—42no—
299D4×C131—42no—
300D4×C131—41no—
301D4×C131—41no—
302D4×C131—41no—
303D4×C131—41no—
304C2×C4×C131—22no—
305C2×C4×C131—22no—
306C2×C4×C131—41no—
307C2×C4×C131—41no—
308C2×C4×C131—41no—
309C2×C4×C131—41no—
310C2×C4×C131—42no—
311C2×C4×C131—42no—
312C2×C4×C131—42no—
313C2×C4×C131—42no—
314C2×C4×C131—42no—
315C2×C4×C131—42no—
316C2×C4×C131—42no—
317C2×C4×C131—42no—
318C2×C4×C131—42no—
319C2×C4×C131—82no—
320C2×C4×C131C2×C22⋊C411yescharacteristic
321C2×C4×C131C2×C22⋊C411yescharacteristic
322C2×C4×C131C2×C22⋊C411yescharacteristic
323C2×C4×C131C4×D411yescharacteristic
324C2×C4×C131C4×D411yescharacteristic
325C2×C4×C131C4×D411yescharacteristic
326C2×C4×C131#12011yescharacteristic
327C2×C4×C131#12011yescharacteristic
328C2×C4×C131#12011yescharacteristic
329C2×C4×C131#12011yescharacteristic
330C2×C4×C131#12011yescharacteristic
331C2×C4×C131#12011yescharacteristic
332C2×C4×C131#12011yescharacteristic
333C2×C4×C131#12011yescharacteristic
334C2×C4×C131#12111yescharacteristic
335C2×C4×C131#12111yescharacteristic
336C2×C4×C131#12111yescharacteristic
337C2×C4×C131#12111yescharacteristic
338C2×C4×C131#12111yescharacteristic
339C2×C4×C131#12111yescharacteristic
340C2×C4×C131#12111yescharacteristic
341C2×C4×C131#12111yescharacteristic
342C2×C4×C131#12111yescharacteristic
343C2×C4×C131#12311yescharacteristic
344C2×C4×C131#12311yescharacteristic
345C2×C4×C131#12411yescharacteristic
346C2×C4×C131#12711yescharacteristic
347C2×C4×C131#12711yescharacteristic
348C8×C131—24no—
349C8×C131—42no—
350C8×C131—42no—
351C8×C131—42no—
352C22×C131—22no—
353C22×C131—22no—
354C22×C131—22no—
355C22×C131—41no—
356C22×C131—41no—
357C22×C131—41no—
358C22×C131—41no—
359C22×C131—44no—
360C22×C131—44no—
361C22×C131—42no—
362C22×C131—42no—
363C22×C131—82no—
364C22×C131—82no—
365C22×C131—82no—
366C22×C131—82no—
367C22×C131#38611yescharacteristic
368C22×C131#38611yescharacteristic
369C22×C131#39011yescharacteristic
370C22×C131#39211yescharacteristic
371C22×C131#39411yescharacteristic
372C22×C131#39411yescharacteristic
373C22×C131#39411yescharacteristic
374C4×C131—42no—
375C4×C131—42no—
376C4×C131—82no—
377C4×C131#37911yescharacteristic
378C4×C131#38611yescharacteristic
379C4×C131#38611yescharacteristic
380C4×C131#39011yescharacteristic
381C4×C131#39211yescharacteristic
382C4×C131#39211yescharacteristic
383C4×C131#39211yescharacteristic
384C4×C131#39411yescharacteristic
385C2×C131—21no—
386C2×C131—21no—
387C2×C131—21no—
388C2×C131—21no—
389C2×C131—21no—
390C2×C131—21no—
391C2×C131—82no—
392C2×C131—82no—
393C2×C131#143811yescharacteristic
394C2×C131#188112yes—
395#11018C13111yesmaximal, characteristic, direct product factor, Sylow
396C131#1101811yescharacteristic, direct product factor, Sylow
397C2×#575C2×C13111yescharacteristic
398C2×#421C2×C13111yescharacteristic, complemented
399C2×#416C2×C13111yescharacteristic, complemented
400#2879C2×C13111yescharacteristic, complemented
401C2×#408C2×C13111yescharacteristic, complemented
402C2×#344C2×C13111yescharacteristic, complemented
403C2×#341C2×C13111yescharacteristic, complemented
404C22×#41C22×C13111yescharacteristic
405C22×#41C22×C13111yescharacteristic
406#575—22no—
407#575—22no—
408#575—22no—
409#575—22no—
410C2×#137—21no—
411C2×#137C4×C13112yescomplemented
412C2×AGL(1,ℤ/8)—21no—
413C2×AGL(1,ℤ/8)C4×C13112yescomplemented
414C2×#135—22no—
415C22×M16C22×C13111yescharacteristic
416C22×M16C22×C13111yescharacteristic
417C22×M16C22×C13111yescharacteristic
418C23×C8C22×C13111yescharacteristic
419C2×#117C22×C13111yescharacteristic
420#421—22no—
421#421—22no—
422C2×#104—22no—
423#416—22no—
424#416—22no—
425C2×#103—21no—
426C2×#102—21no—
427#408—22no—
428#408—22no—
429#408—22no—
430#408—22no—
431#407—22no—
432C2×C22⋊C8—22no—
433#344—22no—
434#341—22no—
435C2×#41—21no—
436C2×#41—21no—
437C2×#41—21no—
438C2×#41—21no—
439C2×#41—21no—
440C2×#41—21no—
441C2×#41—21no—
442C2×#41—21no—
443C2×#41—21no—
444C2×#41—21no—
445C2×#41—21no—
446C2×#41—21no—
447C2×#41—21no—
448C2×#41—21no—
449C2×#41—21no—
450C2×#41—21no—
451C2×#41—21no—
452C2×#41—21no—
453C2×#41—21no—
454C2×#41—21no—
455C2×#41C2×C4×C13112yes—
456C2×#41D4×C13112yes—
457C2×#41D4×C13112yes—
458C2×#41D4×C13112yes—
459C22×Q8C2×C4×C13111yescharacteristic
460C22×Q8D4×C13111yescharacteristic
461C22×D4—21no—
462C22×D4—21no—
463C22×D4C2×C4×C13111yescharacteristic
464C22×D4D4×C13111yescharacteristic
465C23×C4—21no—
466C23×C4—21no—
467C23×C4C23×C13111yescharacteristic
468#137—24no—
469#137—24no—
470#137—24no—
471#137—24no—
472AGL(1,ℤ/8)—24no—
473AGL(1,ℤ/8)—24no—
474AGL(1,ℤ/8)—24no—
475AGL(1,ℤ/8)—24no—
476#135—28no—
477#135—28no—
478C2×Q16—22no—
479C2×SD16—22no—
480C2×SD16—22no—
481C2×D8—22no—
482C2×M16—21no—
483C2×M16—21no—
484C2×M16—21no—
485C2×M16—21no—
486C2×M16—21no—
487C2×M16—21no—
488C2×M16—21no—
489C2×M16—21no—
490C2×M16—21no—
491C2×M16—21no—
492C2×M16—21no—
493C2×M16—21no—
494C2×M16—21no—
495C2×M16—21no—
496C2×M16C2×C4×C13112yes—
497C2×M16D4×C13112yes—
498C2×M16D4×C13112yes—
499C2×M16D4×C13112yes—
500C22×C8—21no—
501C22×C8—21no—
502C22×C8—21no—
503C22×C8—21no—
504C22×C8—21no—
505C22×C8—21no—
506C22×C8—21no—
507C22×C8—21no—
508C22×C8D4×C13112yes—
509C22×C8D4×C13112yes—
510#117—21no—
511#117—21no—
512#117—21no—
513#117D4×C13112yes—
514C2×C4⋊C4—21no—
515C2×C22⋊C4—21no—
516C2×C42—21no—
517#104—28no—
518#103—24no—
519#102—24no—
520C22⋊C8—28no—
521C22⋊C8—28no—
522C24—21no—
523C24—21no—
524C24#41×C13111yescharacteristic
525#41—22no—
526#41—22no—
527#41—22no—
528#41—22no—
529#41—22no—
530#41—22no—
531#41—22no—
532#41—22no—
533#41—22no—
534#41—22no—
535#41—22no—
536#41—22no—
537#41—22no—
538#41—22no—
539#41—22no—
540#41—22no—
541#41—41no—
542#41—41no—
543#41—41no—
544#41—41no—
545#41—41no—
546#41—41no—
547#41—41no—
548#41—41no—
549#41—41no—
550#41—41no—
551#41—41no—
552#41—41no—
553#41—41no—
554#41—41no—
555#41—41no—
556#41—41no—
557C2×Q8—21no—
558C2×Q8—21no—
559C2×Q8—21no—
560C2×Q8—21no—
561C2×Q8—21no—
562C2×Q8—21no—
563C2×Q8—21no—
564C2×Q8—21no—
565C2×Q8—21no—
566C2×Q8—21no—
567C2×Q8C22⋊C4×C13112yes—
568C2×Q8C22⋊C4×C13112yes—
569C2×D4—22no—
570C2×D4—22no—
571C2×D4—22no—
572C2×D4—22no—
573C2×D4—21no—
574C2×D4—21no—
575C2×D4—21no—
576C2×D4—21no—
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—21no—
580C2×D4—21no—
581C2×D4—21no—
582C2×D4—21no—
583C2×D4—41no—
584C2×D4—41no—
585C2×D4—41no—
586C2×D4—41no—
587C2×D4—41no—
588C2×D4—41no—
589C2×D4—41no—
590C2×D4—41no—
591C2×D4C22⋊C4×C13112yes—
592C2×D4C22⋊C4×C13112yes—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—41no—
600C22×C4—41no—
601C22×C4—41no—
602C22×C4—41no—
603C22×C4—41no—
604C22×C4—41no—
605C22×C4—41no—
606C22×C4—41no—
607C22×C4—41no—
608C22×C4C22×C4×C13111yescharacteristic
609C22×C4C2×D4×C13111yescharacteristic
610C22×C4C2×D4×C13111yescharacteristic
611C22×C4C2×D4×C13111yescharacteristic
612C22×C4C2×D4×C13111yescharacteristic
613C22×C4C2×D4×C13111yescharacteristic
614C22×C4C2×D4×C13111yescharacteristic
615C22×C4C2×D4×C13111yescharacteristic
616C22×C4C2×D4×C13111yescharacteristic
617C22×C4C2×D4×C13111yescharacteristic
618C22×C4C2×D4×C13111yescharacteristic
619C22×C4#41×C13111yescharacteristic
620C22×C4#41×C13111yescharacteristic
621C22×C4#41×C13111yescharacteristic
622Q16—28no—
623SD16—28no—
624SD16—28no—
625D8—28no—
626M16—22no—
627M16—22no—
628M16—22no—
629M16—22no—
630M16—22no—
631M16—41no—
632M16—41no—
633M16—41no—
634M16—41no—
635M16—41no—
636M16—41no—
637M16C22⋊C4×C13114yes—
638C2×C8—22no—
639C2×C8—22no—
640C2×C8—22no—
641C2×C8—22no—
642C2×C8—22no—
643C2×C8—22no—
644C2×C8—22no—
645C2×C8—22no—
646C2×C8—22no—
647C2×C8—22no—
648C2×C8—41no—
649C2×C8—41no—
650C2×C8—41no—
651C2×C8—41no—
652C2×C8—41no—
653C2×C8—41no—
654C4⋊C4—22no—
655C4⋊C4—41no—
656C22⋊C4—22no—
657C22⋊C4—41no—
658C42—22no—
659C42—41no—
660C23—22no—
661C23—22no—
662C23—42no—
663C23—44no—
664C23—41no—
665C23—41no—
666C23—41no—
667C23—41no—
668C23—82no—
669C23C4×D4×C13111yescharacteristic
670C23#121×C13111yescharacteristic
671C23#121×C13111yescharacteristic
672C23#121×C13111yescharacteristic
673C23#123×C13111yescharacteristic
674C23#123×C13111yescharacteristic
675C23#124×C13111yescharacteristic
676Q8—22no—
677Q8—22no—
678Q8—22no—
679Q8—22no—
680Q8—41no—
681Q8—41no—
682Q8—41no—
683Q8—41no—
684D4—22no—
685D4—22no—
686D4—22no—
687D4—22no—
688D4—42no—
689D4—42no—
690D4—42no—
691D4—42no—
692D4—42no—
693D4—42no—
694D4—42no—
695D4—42no—
696D4—41no—
697D4—41no—
698D4—41no—
699D4—41no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—82no—
716C2×C4C2×C22⋊C4×C13111yescharacteristic
717C2×C4C2×C22⋊C4×C13111yescharacteristic
718C2×C4C2×C22⋊C4×C13111yescharacteristic
719C2×C4C4×D4×C13111yescharacteristic
720C2×C4C4×D4×C13111yescharacteristic
721C2×C4C4×D4×C13111yescharacteristic
722C2×C4#120×C13111yescharacteristic
723C2×C4#120×C13111yescharacteristic
724C2×C4#120×C13111yescharacteristic
725C2×C4#120×C13111yescharacteristic
726C2×C4#120×C13111yescharacteristic
727C2×C4#120×C13111yescharacteristic
728C2×C4#120×C13111yescharacteristic
729C2×C4#120×C13111yescharacteristic
730C2×C4#121×C13111yescharacteristic
731C2×C4#121×C13111yescharacteristic
732C2×C4#121×C13111yescharacteristic
733C2×C4#121×C13111yescharacteristic
734C2×C4#121×C13111yescharacteristic
735C2×C4#121×C13111yescharacteristic
736C2×C4#121×C13111yescharacteristic
737C2×C4#121×C13111yescharacteristic
738C2×C4#121×C13111yescharacteristic
739C2×C4#123×C13111yescharacteristic
740C2×C4#123×C13111yescharacteristic
741C2×C4#124×C13111yescharacteristic
742C2×C4#127×C13111yescharacteristic
743C2×C4#127×C13111yescharacteristic
744C8—24no—
745C8—42no—
746C8—42no—
747C8—42no—
748C22—22no—
749C22—22no—
750C22—22no—
751C22—41no—
752C22—41no—
753C22—41no—
754C22—41no—
755C22—44no—
756C22—44no—
757C22—42no—
758C22—42no—
759C22—82no—
760C22—82no—
761C22—82no—
762C22—82no—
763C22#386×C13111yescharacteristic
764C22#386×C13111yescharacteristic
765C22#390×C13111yescharacteristic
766C22#392×C13111yescharacteristic
767C22#394×C13111yescharacteristic
768C22#394×C13111yescharacteristic
769C22#394×C13111yescharacteristic
770C4—42no—
771C4—42no—
772C4—82no—
773C4#379×C13111yescharacteristic
774C4#386×C13111yescharacteristic
775C4#386×C13111yescharacteristic
776C4#390×C13111yescharacteristic
777C4#392×C13111yescharacteristic
778C4#392×C13111yescharacteristic
779C4#392×C13111yescharacteristic
780C4#394×C13111yescharacteristic
781C2—21no—
782C2—21no—
783C2—21no—
784C2—21no—
785C2—21no—
786C2—21no—
787C2—82no—
788C2—82no—
789C2#1438×C13111yescharacteristic
790C2#1881×C13112yes—
subgroupG/H
centerC2×C4×C131#120
commutatorC22×C4C22×C4×C131
Frattini, cosocleC23×C4C23×C131
socleC22×C131#386
prime radicalC2×#575×C131C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C131 ◁ C23×C4×C131 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#421×C131C2semidirect
3. C2×#416×C131C2semidirect
4. #2879×C131C2semidirect
5. C2×#408×C131C2semidirect
6. C2×#344×C131C2semidirect
7. C2×#341×C131C2semidirect
15. C2×#137×C131C4semidirect
17. C2×AGL(1,ℤ/8)×C131C4semidirect
395. #11018C131direct (N × H)
396. C131#11018direct (N × H)
398. C2×#421C2×C131semidirect
399. C2×#416C2×C131semidirect
400. #2879C2×C131semidirect
401. C2×#408C2×C131semidirect
402. C2×#344C2×C131semidirect
403. C2×#341C2×C131semidirect
411. C2×#137C4×C131semidirect
413. C2×AGL(1,ℤ/8)C4×C131semidirect

Maximal subgroups

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

subgroupindex
C2×#575×C1312
C2×#421×C1312
C2×#416×C1312
#2879×C1312
C2×#408×C1312
C2×#344×C1312
C2×#341×C1312
#11018131