Finite Group Databasebeta

← C131×#25587 #45711471

Subgroups — C131×#25587 #45711471

Order 33536.

1332 conjugacy classes of subgroups.

The subgroup lattice has 850 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3505×C131C211yesmaximal, characteristic, complemented
2#2561×C131C211yesmaximal, characteristic, complemented
3#2539×C131C211yesmaximal, characteristic, complemented
4#2534×C131C211yesmaximal, characteristic, complemented
5#2022×C131C212yesmaximal, complemented
6#2021×C131C212yesmaximal, complemented
7#1996×C131C211yesmaximal, characteristic, complemented
8#1964×C131C211yesmaximal, characteristic, complemented
9#1890×C131C212yesmaximal, complemented
10#1889×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×#123×C131C2212yes—
24C2×#123×C131C2211yescharacteristic
25C2×C22⋊Q8×C131C2211yescharacteristic
26C2×#121×C131C2211yescharacteristic
27C2×#120×C131C2212yes—
28C2×#120×C131C2211yescharacteristic
29#518×C131C2212yes—
30C2×C4×D4×C131C2211yescharacteristic
31C22×C22⋊C4×C131C2211yescharacteristic
32C2×#99×C131C2212yes—
33C2×#99×C131C2212yes—
34C2×#99×C131C2212yes—
35#399×C131—21no—
36#397×C131—21no—
37#396×C131—21no—
38#394×C131—21no—
39#393×C131—21no—
40#392×C131—21no—
41#390×C131—22no—
42#388×C131—22no—
43#388×C131—21no—
44#386×C131—21no—
45#381×C131C2212yes—
46#381×C131C2211yescharacteristic
47#380×C131C2211yescharacteristic
48#379×C131C2212yes—
49#379×C131C2211yescharacteristic
50C4×C22⋊C4×C131C2211yescharacteristic
51C4×C22⋊C4×C131C2211yescharacteristic
52#342×C131C2212yes—
53#342×C131C2212yes—
54#342×C131C2212yes—
55C25×C131C2311yescharacteristic
56C2×#41×C131—21no—
57C22×Q8×C131D411yescharacteristic, complemented
58C22×D4×C131—22no—
59C22×D4×C131—21no—
60C22×D4×C131D411yescharacteristic, complemented
61C22×D4×C131C2311yescharacteristic
62C22×D4×C131C2312yes—
63C23×C4×C131D411yescharacteristic, complemented
64C23×C4×C131C2311yescharacteristic
65C23×C4×C131C2311yescharacteristic
66#126×C131—22no—
67#126×C131—22no—
68#126×C131—22no—
69#125×C131—21no—
70#125×C131—22no—
71#124×C131—21no—
72#124×C131—22no—
73#123×C131—22no—
74#123×C131—22no—
75#123×C131—22no—
76#123×C131—22no—
77#123×C131—22no—
78#123×C131—24no—
79#123×C131—42no—
80#123×C131—42no—
81C22⋊Q8×C131—21no—
82C22⋊Q8×C131—22no—
83C22⋊Q8×C131—21no—
84C22⋊Q8×C131—21no—
85C22⋊Q8×C131—21no—
86C22⋊Q8×C131—21no—
87#121×C131—21no—
88#121×C131—22no—
89#121×C131—21no—
90#121×C131—21no—
91#121×C131—21no—
92#121×C131—21no—
93#121×C131—22no—
94#121×C131—22no—
95#120×C131—22no—
96#120×C131—22no—
97#120×C131—24no—
98#120×C131—42no—
99#120×C131—42no—
100C4×Q8×C131—21no—
101C4×D4×C131—22no—
102C4×D4×C131—21no—
103C4×D4×C131—21no—
104C4×D4×C131—21no—
105C4×D4×C131—21no—
106C4×D4×C131—21no—
107C4×D4×C131—22no—
108C4×D4×C131—22no—
109C4×D4×C131—22no—
110C4×D4×C131—22no—
111#117×C131—21no—
112#117×C131—22no—
113#117×C131—22no—
114C2×C4⋊C4×C131—21no—
115C2×C4⋊C4×C131—22no—
116C2×C4⋊C4×C131—21no—
117C2×C4⋊C4×C131D412yescomplemented
118C2×C4⋊C4×C131D411yescharacteristic, complemented
119C2×C4⋊C4×C131D411yescharacteristic, complemented
120C2×C4⋊C4×C131D411yescharacteristic, complemented
121C2×C22⋊C4×C131—22no—
122C2×C22⋊C4×C131—22no—
123C2×C22⋊C4×C131—21no—
124C2×C22⋊C4×C131—21no—
125C2×C22⋊C4×C131—21no—
126C2×C22⋊C4×C131—21no—
127C2×C22⋊C4×C131—22no—
128C2×C22⋊C4×C131—21no—
129C2×C22⋊C4×C131—21no—
130C2×C22⋊C4×C131—22no—
131C2×C22⋊C4×C131—21no—
132C2×C22⋊C4×C131—21no—
133C2×C22⋊C4×C131—21no—
134C2×C22⋊C4×C131—22no—
135C2×C22⋊C4×C131—21no—
136C2×C22⋊C4×C131D412yescomplemented
137C2×C22⋊C4×C131D411yescharacteristic, complemented
138C2×C22⋊C4×C131C2312yes—
139C2×C22⋊C4×C131C2311yescharacteristic
140C2×C22⋊C4×C131C2311yescharacteristic
141C2×C22⋊C4×C131C2311yescharacteristic
142C2×C22⋊C4×C131C2312yes—
143C2×C22⋊C4×C131C2312yes—
144C2×C42×C131—21no—
145C2×C42×C131—21no—
146C2×C42×C131D411yescharacteristic, complemented
147#99×C131—24no—
148#99×C131—42no—
149#99×C131—42no—
150#95×C131—22no—
151#95×C131—21no—
152#95×C131—22no—
153#95×C131—21no—
154#95×C131—21no—
155#95×C131—21no—
156#95×C131—21no—
157C24×C131—21no—
158C24×C131—21no—
159C24×C131—21no—
160C24×C131—22no—
161C24×C131—22no—
162C24×C131—42no—
163C24×C131—81no—
164C24×C131C2×D412yes—
165C24×C131C2×D411yescharacteristic
166C24×C131C2411yescharacteristic
167#41×C131—82no—
168C2×Q8×C131—21no—
169C2×Q8×C131—21no—
170C2×Q8×C131—81no—
171C2×D4×C131—21no—
172C2×D4×C131—22no—
173C2×D4×C131—21no—
174C2×D4×C131—22no—
175C2×D4×C131—22no—
176C2×D4×C131—22no—
177C2×D4×C131—22no—
178C2×D4×C131—22no—
179C2×D4×C131—22no—
180C2×D4×C131—22no—
181C2×D4×C131—22no—
182C2×D4×C131—22no—
183C2×D4×C131—21no—
184C2×D4×C131—21no—
185C2×D4×C131—44no—
186C2×D4×C131—42no—
187C2×D4×C131—44no—
188C2×D4×C131—42no—
189C2×D4×C131—81no—
190C2×D4×C131—82no—
191C2×D4×C131—81no—
192C22×C4×C131—22no—
193C22×C4×C131—22no—
194C22×C4×C131—22no—
195C22×C4×C131—21no—
196C22×C4×C131—21no—
197C22×C4×C131—21no—
198C22×C4×C131—22no—
199C22×C4×C131—21no—
200C22×C4×C131—21no—
201C22×C4×C131—21no—
202C22×C4×C131—21no—
203C22×C4×C131—22no—
204C22×C4×C131—22no—
205C22×C4×C131—81no—
206C22×C4×C131—81no—
207C22×C4×C131C2×D411yescharacteristic
208C22×C4×C131C2×D412yes—
209C22×C4×C131C2×D411yescharacteristic
210C22×C4×C131C2×D412yes—
211C22×C4×C131C2×D411yescharacteristic
212C22×C4×C131C2×D412yes—
213C22×C4×C131C2×D411yescharacteristic
214C22×C4×C131C2×D411yescharacteristic
215C22×C4×C131C2×D411yescharacteristic
216C22×C4×C131C2×D411yescharacteristic
217C22×C4×C131C2×D411yescharacteristic
218C22×C4×C131C2×D411yescharacteristic
219C4⋊C4×C131—22no—
220C4⋊C4×C131—22no—
221C4⋊C4×C131—22no—
222C4⋊C4×C131—22no—
223C4⋊C4×C131—21no—
224C4⋊C4×C131—22no—
225C4⋊C4×C131—21no—
226C4⋊C4×C131—21no—
227C4⋊C4×C131—21no—
228C4⋊C4×C131—21no—
229C4⋊C4×C131—22no—
230C4⋊C4×C131—21no—
231C4⋊C4×C131—44no—
232C4⋊C4×C131—42no—
233C4⋊C4×C131—81no—
234C22⋊C4×C131—22no—
235C22⋊C4×C131—22no—
236C22⋊C4×C131—22no—
237C22⋊C4×C131—22no—
238C22⋊C4×C131—22no—
239C22⋊C4×C131—22no—
240C22⋊C4×C131—21no—
241C22⋊C4×C131—22no—
242C22⋊C4×C131—21no—
243C22⋊C4×C131—22no—
244C22⋊C4×C131—22no—
245C22⋊C4×C131—22no—
246C22⋊C4×C131—21no—
247C22⋊C4×C131—21no—
248C22⋊C4×C131—22no—
249C22⋊C4×C131—22no—
250C22⋊C4×C131—22no—
251C22⋊C4×C131—22no—
252C22⋊C4×C131—22no—
253C22⋊C4×C131—44no—
254C22⋊C4×C131—44no—
255C22⋊C4×C131—42no—
256C22⋊C4×C131—44no—
257C22⋊C4×C131—42no—
258C22⋊C4×C131—42no—
259C22⋊C4×C131—41no—
260C22⋊C4×C131—41no—
261C22⋊C4×C131—41no—
262C22⋊C4×C131—41no—
263C22⋊C4×C131—81no—
264C22⋊C4×C131—82no—
265C22⋊C4×C131#4114yescomplemented
266C42×C131—22no—
267C42×C131—22no—
268C42×C131—21no—
269C42×C131—21no—
270C42×C131—81no—
271C42×C131—81no—
272C23×C131—22no—
273C23×C131—22no—
274C23×C131—22no—
275C23×C131—22no—
276C23×C131—21no—
277C23×C131—21no—
278C23×C131—21no—
279C23×C131—22no—
280C23×C131—22no—
281C23×C131—41no—
282C23×C131—41no—
283C23×C131—41no—
284C23×C131—41no—
285C23×C131—42no—
286C23×C131—41no—
287C23×C131—41no—
288C23×C131—42no—
289C23×C131—41no—
290C23×C131—41no—
291C23×C131—41no—
292C23×C131—42no—
293C23×C131—42no—
294C23×C131—41no—
295C23×C131—41no—
296C23×C131—41no—
297C23×C131—42no—
298C23×C131—42no—
299C23×C131—84no—
300C23×C131—84no—
301C23×C131C22×D411yescharacteristic
302C23×C131C22×D411yescharacteristic
303C23×C131C22×D411yescharacteristic
304C23×C131C2×#4112yes—
305C23×C131H(5,𝔽2)12yes—
306Q8×C131—42no—
307Q8×C131—81no—
308D4×C131—42no—
309D4×C131—42no—
310D4×C131—42no—
311D4×C131—42no—
312D4×C131—42no—
313D4×C131—42no—
314D4×C131—42no—
315D4×C131—81no—
316D4×C131—82no—
317D4×C131—82no—
318D4×C131—88no—
319D4×C131—84no—
320C2×C4×C131—21no—
321C2×C4×C131—22no—
322C2×C4×C131—21no—
323C2×C4×C131—21no—
324C2×C4×C131—22no—
325C2×C4×C131—22no—
326C2×C4×C131—21no—
327C2×C4×C131—21no—
328C2×C4×C131—24no—
329C2×C4×C131—22no—
330C2×C4×C131—22no—
331C2×C4×C131—41no—
332C2×C4×C131—41no—
333C2×C4×C131—41no—
334C2×C4×C131—41no—
335C2×C4×C131—41no—
336C2×C4×C131—41no—
337C2×C4×C131—42no—
338C2×C4×C131—42no—
339C2×C4×C131—42no—
340C2×C4×C131—41no—
341C2×C4×C131—42no—
342C2×C4×C131—41no—
343C2×C4×C131—42no—
344C2×C4×C131—42no—
345C2×C4×C131—42no—
346C2×C4×C131—41no—
347C2×C4×C131—41no—
348C2×C4×C131—41no—
349C2×C4×C131—41no—
350C2×C4×C131—41no—
351C2×C4×C131—41no—
352C2×C4×C131—41no—
353C2×C4×C131—41no—
354C2×C4×C131—41no—
355C2×C4×C131—42no—
356C2×C4×C131—42no—
357C2×C4×C131—42no—
358C2×C4×C131—81no—
359C2×C4×C131—82no—
360C2×C4×C131—82no—
361C2×C4×C131#12011yescharacteristic
362C2×C4×C131#12011yescharacteristic
363C2×C4×C131#12011yescharacteristic
364C2×C4×C131#12011yescharacteristic
365C22×C131—21no—
366C22×C131—21no—
367C22×C131—21no—
368C22×C131—21no—
369C22×C131—21no—
370C22×C131—21no—
371C22×C131—42no—
372C22×C131—42no—
373C22×C131—42no—
374C22×C131—44no—
375C22×C131—42no—
376C22×C131—44no—
377C22×C131—42no—
378C22×C131—41no—
379C22×C131—42no—
380C22×C131—42no—
381C22×C131—41no—
382C22×C131—42no—
383C22×C131—41no—
384C22×C131—42no—
385C22×C131—82no—
386C22×C131—82no—
387C22×C131—81no—
388C22×C131—82no—
389C22×C131—81no—
390C22×C131—82no—
391C22×C131—81no—
392C22×C131—81no—
393C22×C131—81no—
394C22×C131C2×#12011yescharacteristic
395C22×C131#53211yescharacteristic
396C22×C131#53511yescharacteristic
397C22×C131#54612yes—
398C22×C131#55012yes—
399C4×C131—21no—
400C4×C131—21no—
401C4×C131—21no—
402C4×C131—21no—
403C4×C131—44no—
404C4×C131—41no—
405C4×C131—42no—
406C4×C131—41no—
407C4×C131—42no—
408C4×C131—41no—
409C4×C131—42no—
410C4×C131—81no—
411C4×C131—82no—
412C4×C131—81no—
413C4×C131—81no—
414C2×C131—22no—
415C2×C131—21no—
416C2×C131—22no—
417C2×C131—21no—
418C2×C131—82no—
419C2×C131—81no—
420C2×C131—82no—
421C2×C131#243111yescharacteristic
422C2×C131#302511yescharacteristic
423C2×C131#302611yescharacteristic
424#25587C13111yesmaximal, characteristic, direct product factor, Sylow
425C131#2558711yescharacteristic, direct product factor, Sylow
426#3505C2×C13111yescharacteristic, complemented
427#2561C2×C13111yescharacteristic, complemented
428#2539C2×C13111yescharacteristic, complemented
429#2534C2×C13111yescharacteristic, complemented
430#2022C2×C13112yescomplemented
431#2021C2×C13112yescomplemented
432#1996C2×C13111yescharacteristic, complemented
433#1964C2×C13111yescharacteristic, complemented
434#1890C2×C13112yescomplemented
435#1889C2×C13112yescomplemented
436C4×#99C2×C13111yescharacteristic, complemented
437#553—22no—
438#553—21no—
439#552—21no—
440#551—22no—
441#548—21no—
442#546—21no—
443#539—21no—
444#538—21no—
445#534C22×C13112yes—
446#529—21no—
447#525—21no—
448C2×#123C22×C13112yes—
449C2×#123C22×C13111yescharacteristic
450C2×C22⋊Q8C22×C13111yescharacteristic
451C2×#121C22×C13111yescharacteristic
452C2×#120C22×C13112yes—
453C2×#120C22×C13111yescharacteristic
454#518C22×C13112yes—
455C2×C4×D4C22×C13111yescharacteristic
456C22×C22⋊C4C22×C13111yescharacteristic
457C2×#99C22×C13112yes—
458C2×#99C22×C13112yes—
459C2×#99C22×C13112yes—
460#399—21no—
461#397—21no—
462#396—21no—
463#394—21no—
464#393—21no—
465#392—21no—
466#390—22no—
467#388—22no—
468#388—21no—
469#386—21no—
470#381C22×C13112yes—
471#381C22×C13111yescharacteristic
472#380C22×C13111yescharacteristic
473#379C22×C13112yes—
474#379C22×C13111yescharacteristic
475C4×C22⋊C4C22×C13111yescharacteristic
476C4×C22⋊C4C22×C13111yescharacteristic
477#342C22×C13112yes—
478#342C22×C13112yes—
479#342C22×C13112yes—
480C25C23×C13111yescharacteristic
481C2×#41—21no—
482C22×Q8D4×C13111yescharacteristic, complemented
483C22×D4—21no—
484C22×D4—22no—
485C22×D4D4×C13111yescharacteristic, complemented
486C22×D4C23×C13111yescharacteristic
487C22×D4C23×C13112yes—
488C23×C4D4×C13111yescharacteristic, complemented
489C23×C4C23×C13111yescharacteristic
490C23×C4C23×C13111yescharacteristic
491#126—22no—
492#126—22no—
493#126—22no—
494#125—21no—
495#125—22no—
496#124—21no—
497#124—22no—
498#123—22no—
499#123—22no—
500#123—22no—
501#123—22no—
502#123—22no—
503#123—24no—
504#123—42no—
505#123—42no—
506C22⋊Q8—21no—
507C22⋊Q8—22no—
508C22⋊Q8—21no—
509C22⋊Q8—21no—
510C22⋊Q8—21no—
511C22⋊Q8—21no—
512#121—21no—
513#121—22no—
514#121—21no—
515#121—21no—
516#121—21no—
517#121—21no—
518#121—22no—
519#121—22no—
520#120—22no—
521#120—22no—
522#120—24no—
523#120—42no—
524#120—42no—
525C4×Q8—21no—
526C4×D4—22no—
527C4×D4—21no—
528C4×D4—21no—
529C4×D4—21no—
530C4×D4—21no—
531C4×D4—21no—
532C4×D4—22no—
533C4×D4—22no—
534C4×D4—22no—
535C4×D4—22no—
536#117—21no—
537#117—22no—
538#117—22no—
539C2×C4⋊C4—21no—
540C2×C4⋊C4—22no—
541C2×C4⋊C4—21no—
542C2×C4⋊C4D4×C13111yescharacteristic, complemented
543C2×C4⋊C4D4×C13111yescharacteristic, complemented
544C2×C4⋊C4D4×C13112yescomplemented
545C2×C4⋊C4D4×C13111yescharacteristic, complemented
546C2×C22⋊C4—22no—
547C2×C22⋊C4—21no—
548C2×C22⋊C4—22no—
549C2×C22⋊C4—21no—
550C2×C22⋊C4—21no—
551C2×C22⋊C4—21no—
552C2×C22⋊C4—21no—
553C2×C22⋊C4—21no—
554C2×C22⋊C4—21no—
555C2×C22⋊C4—21no—
556C2×C22⋊C4—22no—
557C2×C22⋊C4—21no—
558C2×C22⋊C4—22no—
559C2×C22⋊C4—21no—
560C2×C22⋊C4—22no—
561C2×C22⋊C4D4×C13111yescharacteristic, complemented
562C2×C22⋊C4D4×C13112yescomplemented
563C2×C22⋊C4C23×C13111yescharacteristic
564C2×C22⋊C4C23×C13111yescharacteristic
565C2×C22⋊C4C23×C13112yes—
566C2×C22⋊C4C23×C13111yescharacteristic
567C2×C22⋊C4C23×C13112yes—
568C2×C22⋊C4C23×C13112yes—
569C2×C42—21no—
570C2×C42—21no—
571C2×C42D4×C13111yescharacteristic, complemented
572#99—24no—
573#99—42no—
574#99—42no—
575#95—21no—
576#95—21no—
577#95—21no—
578#95—21no—
579#95—22no—
580#95—21no—
581#95—22no—
582C24—21no—
583C24—21no—
584C24—21no—
585C24—22no—
586C24—22no—
587C24—42no—
588C24—81no—
589C24C2×D4×C13112yes—
590C24C2×D4×C13111yescharacteristic
591C24C24×C13111yescharacteristic
592#41—82no—
593C2×Q8—21no—
594C2×Q8—21no—
595C2×Q8—81no—
596C2×D4—21no—
597C2×D4—22no—
598C2×D4—21no—
599C2×D4—22no—
600C2×D4—22no—
601C2×D4—22no—
602C2×D4—22no—
603C2×D4—22no—
604C2×D4—22no—
605C2×D4—22no—
606C2×D4—22no—
607C2×D4—22no—
608C2×D4—21no—
609C2×D4—21no—
610C2×D4—44no—
611C2×D4—42no—
612C2×D4—44no—
613C2×D4—42no—
614C2×D4—81no—
615C2×D4—82no—
616C2×D4—81no—
617C22×C4—22no—
618C22×C4—22no—
619C22×C4—22no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—22no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—22no—
629C22×C4—22no—
630C22×C4—81no—
631C22×C4—81no—
632C22×C4C2×D4×C13111yescharacteristic
633C22×C4C2×D4×C13112yes—
634C22×C4C2×D4×C13111yescharacteristic
635C22×C4C2×D4×C13112yes—
636C22×C4C2×D4×C13111yescharacteristic
637C22×C4C2×D4×C13112yes—
638C22×C4C2×D4×C13111yescharacteristic
639C22×C4C2×D4×C13111yescharacteristic
640C22×C4C2×D4×C13111yescharacteristic
641C22×C4C2×D4×C13111yescharacteristic
642C22×C4C2×D4×C13111yescharacteristic
643C22×C4C2×D4×C13111yescharacteristic
644C4⋊C4—22no—
645C4⋊C4—22no—
646C4⋊C4—22no—
647C4⋊C4—22no—
648C4⋊C4—21no—
649C4⋊C4—22no—
650C4⋊C4—21no—
651C4⋊C4—21no—
652C4⋊C4—21no—
653C4⋊C4—21no—
654C4⋊C4—22no—
655C4⋊C4—21no—
656C4⋊C4—44no—
657C4⋊C4—42no—
658C4⋊C4—81no—
659C22⋊C4—22no—
660C22⋊C4—22no—
661C22⋊C4—22no—
662C22⋊C4—22no—
663C22⋊C4—22no—
664C22⋊C4—22no—
665C22⋊C4—21no—
666C22⋊C4—22no—
667C22⋊C4—21no—
668C22⋊C4—22no—
669C22⋊C4—22no—
670C22⋊C4—22no—
671C22⋊C4—21no—
672C22⋊C4—21no—
673C22⋊C4—22no—
674C22⋊C4—22no—
675C22⋊C4—22no—
676C22⋊C4—22no—
677C22⋊C4—22no—
678C22⋊C4—44no—
679C22⋊C4—44no—
680C22⋊C4—42no—
681C22⋊C4—44no—
682C22⋊C4—42no—
683C22⋊C4—42no—
684C22⋊C4—41no—
685C22⋊C4—41no—
686C22⋊C4—41no—
687C22⋊C4—41no—
688C22⋊C4—81no—
689C22⋊C4—82no—
690C22⋊C4#41×C13114yescomplemented
691C42—22no—
692C42—22no—
693C42—21no—
694C42—21no—
695C42—81no—
696C42—81no—
697C23—22no—
698C23—22no—
699C23—22no—
700C23—22no—
701C23—21no—
702C23—21no—
703C23—21no—
704C23—22no—
705C23—22no—
706C23—41no—
707C23—41no—
708C23—41no—
709C23—41no—
710C23—42no—
711C23—41no—
712C23—41no—
713C23—42no—
714C23—41no—
715C23—41no—
716C23—41no—
717C23—42no—
718C23—42no—
719C23—41no—
720C23—41no—
721C23—41no—
722C23—42no—
723C23—42no—
724C23—84no—
725C23—84no—
726C23C22×D4×C13111yescharacteristic
727C23C22×D4×C13111yescharacteristic
728C23C22×D4×C13111yescharacteristic
729C23C2×#41×C13112yes—
730C23H(5,𝔽2)×C13112yes—
731Q8—42no—
732Q8—81no—
733D4—42no—
734D4—42no—
735D4—42no—
736D4—42no—
737D4—42no—
738D4—42no—
739D4—42no—
740D4—81no—
741D4—82no—
742D4—82no—
743D4—88no—
744D4—84no—
745C2×C4—21no—
746C2×C4—22no—
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—24no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—41no—
766C2×C4—42no—
767C2×C4—41no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—42no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—42no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—81no—
784C2×C4—82no—
785C2×C4—82no—
786C2×C4#120×C13111yescharacteristic
787C2×C4#120×C13111yescharacteristic
788C2×C4#120×C13111yescharacteristic
789C2×C4#120×C13111yescharacteristic
790C22—21no—
791C22—21no—
792C22—21no—
793C22—21no—
794C22—21no—
795C22—21no—
796C22—42no—
797C22—42no—
798C22—44no—
799C22—42no—
800C22—42no—
801C22—44no—
802C22—42no—
803C22—42no—
804C22—41no—
805C22—42no—
806C22—41no—
807C22—42no—
808C22—41no—
809C22—42no—
810C22—82no—
811C22—82no—
812C22—81no—
813C22—82no—
814C22—81no—
815C22—82no—
816C22—81no—
817C22—81no—
818C22—81no—
819C22C2×#120×C13111yescharacteristic
820C22#532×C13111yescharacteristic
821C22#535×C13111yescharacteristic
822C22#546×C13112yes—
823C22#550×C13112yes—
824C4—21no—
825C4—21no—
826C4—21no—
827C4—21no—
828C4—44no—
829C4—41no—
830C4—42no—
831C4—41no—
832C4—42no—
833C4—41no—
834C4—42no—
835C4—81no—
836C4—81no—
837C4—82no—
838C4—81no—
839C2—22no—
840C2—21no—
841C2—22no—
842C2—21no—
843C2—82no—
844C2—81no—
845C2—82no—
846C2#2431×C13111yescharacteristic
847C2#3025×C13111yescharacteristic
848C2#3026×C13111yescharacteristic
subgroupG/H
center, socleC22×C131C2×#120
commutator, Frattini, cosocleC24C24×C131
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
1. #3505×C131C2semidirect
2. #2561×C131C2semidirect
3. #2539×C131C2semidirect
4. #2534×C131C2semidirect
5. #2022×C131C2semidirect
6. #2021×C131C2semidirect
7. #1996×C131C2semidirect
8. #1964×C131C2semidirect
9. #1890×C131C2semidirect
10. #1889×C131C2semidirect
11. C4×#99×C131C2semidirect
57. C22×Q8×C131D4semidirect
60. C22×D4×C131D4semidirect
63. C23×C4×C131D4semidirect
117. C2×C4⋊C4×C131D4semidirect
118. C2×C4⋊C4×C131D4semidirect
119. C2×C4⋊C4×C131D4semidirect
120. C2×C4⋊C4×C131D4semidirect
136. C2×C22⋊C4×C131D4semidirect
137. C2×C22⋊C4×C131D4semidirect
146. C2×C42×C131D4semidirect
265. C22⋊C4×C131#41semidirect
424. #25587C131direct (N × H)
425. C131#25587direct (N × H)
426. #3505C2×C131semidirect
427. #2561C2×C131semidirect
428. #2539C2×C131semidirect
429. #2534C2×C131semidirect
430. #2022C2×C131semidirect
431. #2021C2×C131semidirect
432. #1996C2×C131semidirect
433. #1964C2×C131semidirect
434. #1890C2×C131semidirect
435. #1889C2×C131semidirect
436. C4×#99C2×C131semidirect
482. C22×Q8D4×C131semidirect
485. C22×D4D4×C131semidirect
488. C23×C4D4×C131semidirect
542. C2×C4⋊C4D4×C131semidirect
543. C2×C4⋊C4D4×C131semidirect
544. C2×C4⋊C4D4×C131semidirect
545. C2×C4⋊C4D4×C131semidirect
561. C2×C22⋊C4D4×C131semidirect
562. C2×C22⋊C4D4×C131semidirect
571. C2×C42D4×C131semidirect
690. 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
#2561×C1312
#2539×C1312
#2534×C1312
#2022×C1312
#2021×C1312
#1996×C1312
#1964×C1312
#1890×C1312
#1889×C1312
C4×#99×C1312
#25587131