Finite Group Databasebeta

← C131×#12753 #45698637

Subgroups — C131×#12753 #45698637

Order 33536.

936 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3532×C131C211yesmaximal, characteristic
2#2127×C131C211yesmaximal, characteristic, complemented
3#2121×C131C211yesmaximal, characteristic, complemented
4C2×AΣL(1,𝔽16)×C131C211yesmaximal, characteristic, complemented
5#1913×C131C211yesmaximal, characteristic, complemented
6#1911×C131C211yesmaximal, characteristic, complemented
7#1889×C131C211yesmaximal, characteristic, complemented
8H(3,𝔽4)×C131C411yescharacteristic, complemented
9#560×C131—21no—
10#560×C131C411yescharacteristic, complemented
11#551×C131—21no—
12#551×C131C411yescharacteristic, complemented
13#546×C131—21no—
14#546×C131—21no—
15#546×C131—21no—
16D42×C131—21no—
17D42×C131C411yescharacteristic, complemented
18#538×C131—21no—
19#538×C131—21no—
20#538×C131—21no—
21#535×C131—21no—
22#535×C131C2211yescharacteristic
23#534×C131—21no—
24#534×C131C2211yescharacteristic
25C2×#120×C131—21no—
26C2×#120×C131C2211yescharacteristic
27#518×C131C2211yescharacteristic, complemented
28#421×C131—21no—
29C2×#100×C131C2211yescharacteristic, complemented
30C2×#99×C131—21no—
31C2×#99×C131C2211yescharacteristic, complemented
32C2×#99×C131C2211yescharacteristic, complemented
33#379×C131—21no—
34#354×C131—21no—
35#353×C131—21no—
36#352×C131—21no—
37AΣL(1,𝔽16)×C131—21no—
38AΣL(1,𝔽16)×C131—21no—
39AΣL(1,𝔽16)×C131—21no—
40#342×C131—21no—
41#342×C131—21no—
42H(3,ℤ/4)×C131—21no—
43C25×C131D411yescharacteristic
44C2×#41×C131—21no—
45C2×#41×C131D411yescharacteristic
46C22×D4×C131—21no—
47C22×D4×C131—21no—
48C22×D4×C131—21no—
49C22×D4×C131—21no—
50C22×D4×C131—21no—
51C22×D4×C131D411yescharacteristic
52C22×D4×C131C2311yescharacteristic
53C2×M16×C131—21no—
54#127×C131—21no—
55#127×C131C2×C411yescharacteristic
56#127×C131D411yescharacteristic
57#126×C131—21no—
58#126×C131—21no—
59#126×C131—21no—
60#126×C131—21no—
61#124×C131—21no—
62#124×C131—21no—
63#124×C131—21no—
64#124×C131—21no—
65#124×C131—21no—
66#124×C131C2×C411yescharacteristic
67#124×C131D411yescharacteristic
68#123×C131—21no—
69#123×C131—21no—
70#123×C131—21no—
71#123×C131—21no—
72#123×C131—21no—
73#123×C131—21no—
74#123×C131—21no—
75#123×C131—21no—
76#123×C131C2×C411yescharacteristic
77#123×C131D411yescharacteristic
78C22⋊Q8×C131—21no—
79C22⋊Q8×C131—21no—
80C22⋊Q8×C131—21no—
81#121×C131—21no—
82#121×C131—21no—
83#121×C131—21no—
84#121×C131—21no—
85#121×C131—21no—
86#121×C131—21no—
87#121×C131—21no—
88#121×C131—21no—
89#121×C131—21no—
90#121×C131—21no—
91#121×C131—21no—
92#121×C131—21no—
93#121×C131—21no—
94#121×C131—21no—
95#121×C131—21no—
96#120×C131—21no—
97#120×C131—21no—
98#120×C131—21no—
99#120×C131—21no—
100#120×C131—21no—
101#120×C131—21no—
102#120×C131—21no—
103#120×C131—21no—
104#120×C131—21no—
105#120×C131—21no—
106#120×C131—21no—
107#120×C131—21no—
108#120×C131—21no—
109#120×C131—21no—
110#120×C131C2×C411yescharacteristic
111#120×C131C2×C411yescharacteristic
112#120×C131C2×C411yescharacteristic
113#120×C131D411yescharacteristic
114#120×C131D411yescharacteristic
115#120×C131D411yescharacteristic
116C4×D4×C131—21no—
117C4×D4×C131—21no—
118C4×D4×C131—21no—
119C4×D4×C131—21no—
120C4×D4×C131—21no—
121C4×D4×C131—21no—
122C4×D4×C131—42no—
123#117×C131—21no—
124#117×C131—21no—
125#117×C131D411yescharacteristic
126C2×C22⋊C4×C131—21no—
127C2×C22⋊C4×C131—21no—
128C2×C22⋊C4×C131—21no—
129C2×C22⋊C4×C131—21no—
130C2×C22⋊C4×C131—21no—
131C2×C22⋊C4×C131—21no—
132C2×C22⋊C4×C131—21no—
133C2×C22⋊C4×C131—21no—
134C2×C22⋊C4×C131—21no—
135C2×C22⋊C4×C131—42no—
136C2×C22⋊C4×C131D411yescharacteristic
137C2×C22⋊C4×C131D411yescharacteristic
138#104×C131—42no—
139#100×C131—21no—
140#100×C131—21no—
141#99×C131—21no—
142#99×C131—21no—
143#99×C131—21no—
144#99×C131—21no—
145#99×C131—42no—
146C24×C131—21no—
147C24×C131—21no—
148C24×C131—21no—
149C24×C131—41no—
150C24×C131—41no—
151C24×C131—82no—
152C24×C131C22⋊C411yescharacteristic
153C24×C131C22⋊C411yescharacteristic
154C24×C131C22⋊C411yescharacteristic, complemented
155C24×C131C2×D411yescharacteristic
156C24×C131C2×D411yescharacteristic
157#41×C131—41no—
158#41×C131—41no—
159#41×C131—82no—
160C2×Q8×C131—21no—
161C2×Q8×C131C22⋊C411yescharacteristic, complemented
162C2×D4×C131—21no—
163C2×D4×C131—21no—
164C2×D4×C131—21no—
165C2×D4×C131—21no—
166C2×D4×C131—21no—
167C2×D4×C131—21no—
168C2×D4×C131—21no—
169C2×D4×C131—21no—
170C2×D4×C131—21no—
171C2×D4×C131—21no—
172C2×D4×C131—21no—
173C2×D4×C131—21no—
174C2×D4×C131—21no—
175C2×D4×C131—21no—
176C2×D4×C131—21no—
177C2×D4×C131—21no—
178C2×D4×C131—21no—
179C2×D4×C131—21no—
180C2×D4×C131—21no—
181C2×D4×C131—21no—
182C2×D4×C131—41no—
183C2×D4×C131—41no—
184C2×D4×C131—41no—
185C2×D4×C131—41no—
186C2×D4×C131—82no—
187C2×D4×C131—82no—
188C2×D4×C131—82no—
189C2×D4×C131—82no—
190C2×D4×C131—81no—
191C2×D4×C131—81no—
192C2×D4×C131C22⋊C411yescharacteristic, complemented
193C2×D4×C131C22×C411yescharacteristic
194C2×D4×C131C2×D411yescharacteristic
195C2×D4×C131C2×D411yescharacteristic
196C2×D4×C131C2×D411yescharacteristic
197C22×C4×C131—21no—
198C22×C4×C131—21no—
199C22×C4×C131—21no—
200C22×C4×C131—21no—
201C22×C4×C131—21no—
202C22×C4×C131—21no—
203C22×C4×C131—21no—
204C22×C4×C131—21no—
205C22×C4×C131—22no—
206C22×C4×C131—41no—
207C22×C4×C131—41no—
208C22×C4×C131—41no—
209C22×C4×C131C22⋊C411yescharacteristic, complemented
210C22×C4×C131C2×D411yescharacteristic
211M16×C131—41no—
212M16×C131—41no—
213C2×C8×C131—41no—
214C4⋊C4×C131—21no—
215C4⋊C4×C131—21no—
216C4⋊C4×C131—21no—
217C4⋊C4×C131—21no—
218C4⋊C4×C131—21no—
219C4⋊C4×C131—21no—
220C4⋊C4×C131—21no—
221C4⋊C4×C131—21no—
222C4⋊C4×C131—21no—
223C4⋊C4×C131—41no—
224C22⋊C4×C131—21no—
225C22⋊C4×C131—21no—
226C22⋊C4×C131—21no—
227C22⋊C4×C131—21no—
228C22⋊C4×C131—21no—
229C22⋊C4×C131—21no—
230C22⋊C4×C131—21no—
231C22⋊C4×C131—21no—
232C22⋊C4×C131—21no—
233C22⋊C4×C131—21no—
234C22⋊C4×C131—21no—
235C22⋊C4×C131—21no—
236C22⋊C4×C131—21no—
237C22⋊C4×C131—21no—
238C22⋊C4×C131—21no—
239C22⋊C4×C131—21no—
240C22⋊C4×C131—21no—
241C22⋊C4×C131—21no—
242C22⋊C4×C131—21no—
243C22⋊C4×C131—21no—
244C22⋊C4×C131—21no—
245C22⋊C4×C131—21no—
246C22⋊C4×C131—21no—
247C22⋊C4×C131—21no—
248C22⋊C4×C131—21no—
249C22⋊C4×C131—22no—
250C22⋊C4×C131—41no—
251C22⋊C4×C131—41no—
252C22⋊C4×C131—41no—
253C22⋊C4×C131—41no—
254C22⋊C4×C131—41no—
255C22⋊C4×C131—41no—
256C22⋊C4×C131—84no—
257C22⋊C4×C131C22⋊C411yescharacteristic
258C22⋊C4×C131C22⋊C411yescharacteristic
259C22⋊C4×C131C22⋊C411yescharacteristic, complemented
260C22⋊C4×C131C22⋊C411yescharacteristic, complemented
261C42×C131—21no—
262C42×C131—21no—
263C42×C131—22no—
264C42×C131C22⋊C411yescharacteristic, complemented
265C42×C131C22⋊C411yescharacteristic, complemented
266C23×C131—21no—
267C23×C131—21no—
268C23×C131—21no—
269C23×C131—21no—
270C23×C131—21no—
271C23×C131—21no—
272C23×C131—21no—
273C23×C131—21no—
274C23×C131—42no—
275C23×C131—41no—
276C23×C131—41no—
277C23×C131—42no—
278C23×C131—42no—
279C23×C131—42no—
280C23×C131—41no—
281C23×C131—44no—
282C23×C131—41no—
283C23×C131—41no—
284C23×C131—81no—
285C23×C131—81no—
286C23×C131—81no—
287C23×C131—81no—
288C23×C131—81no—
289C23×C131—81no—
290C23×C131—81no—
291C23×C131—81no—
292C23×C131—81no—
293C23×C131—82no—
294C23×C131—82no—
295C23×C131—82no—
296C23×C131C2×C22⋊C411yescharacteristic
297C23×C131C2×C22⋊C411yescharacteristic
298C23×C131#12011yescharacteristic
299C23×C131#12011yescharacteristic
300C23×C131#12011yescharacteristic
301Q8×C131—41no—
302Q8×C131—81no—
303D4×C131—41no—
304D4×C131—41no—
305D4×C131—41no—
306D4×C131—41no—
307D4×C131—41no—
308D4×C131—42no—
309D4×C131—42no—
310D4×C131—42no—
311D4×C131—42no—
312D4×C131—41no—
313D4×C131—41no—
314D4×C131—41no—
315D4×C131—41no—
316D4×C131—81no—
317D4×C131—81no—
318D4×C131—81no—
319D4×C131—81no—
320D4×C131—81no—
321D4×C131—81no—
322D4×C131—81no—
323D4×C131—81no—
324D4×C131—81no—
325D4×C131—81no—
326D4×C131—81no—
327D4×C131—81no—
328D4×C131—81no—
329D4×C131—81no—
330C2×C4×C131—21no—
331C2×C4×C131—21no—
332C2×C4×C131—21no—
333C2×C4×C131—21no—
334C2×C4×C131—21no—
335C2×C4×C131—21no—
336C2×C4×C131—21no—
337C2×C4×C131—21no—
338C2×C4×C131—21no—
339C2×C4×C131—21no—
340C2×C4×C131—42no—
341C2×C4×C131—41no—
342C2×C4×C131—42no—
343C2×C4×C131—81no—
344C2×C4×C131—81no—
345C2×C4×C131—81no—
346C2×C4×C131—81no—
347C2×C4×C131—81no—
348C2×C4×C131—81no—
349C2×C4×C131—81no—
350C2×C4×C131—82no—
351C2×C4×C131—81no—
352C2×C4×C131—81no—
353C2×C4×C131—82no—
354C2×C4×C131—161no—
355C2×C4×C131—161no—
356C2×C4×C131C2×C22⋊C411yescharacteristic
357C2×C4×C131#12011yescharacteristic
358C8×C131—81no—
359C22×C131—22no—
360C22×C131—21no—
361C22×C131—21no—
362C22×C131—21no—
363C22×C131—21no—
364C22×C131—41no—
365C22×C131—41no—
366C22×C131—41no—
367C22×C131—41no—
368C22×C131—41no—
369C22×C131—42no—
370C22×C131—41no—
371C22×C131—41no—
372C22×C131—41no—
373C22×C131—41no—
374C22×C131—41no—
375C22×C131—41no—
376C22×C131—41no—
377C22×C131—42no—
378C22×C131—41no—
379C22×C131—42no—
380C22×C131—41no—
381C22×C131—41no—
382C22×C131—41no—
383C22×C131—81no—
384C22×C131—81no—
385C22×C131—81no—
386C22×C131—82no—
387C22×C131—82no—
388C22×C131—81no—
389C22×C131—84no—
390C22×C131—81no—
391C22×C131—161no—
392C22×C131—162no—
393C22×C131#37911yescharacteristic
394C22×C131B(4,𝔽2)11yescharacteristic
395C22×C131#45811yescharacteristic
396C4×C131—21no—
397C4×C131—21no—
398C4×C131—41no—
399C4×C131—41no—
400C4×C131—41no—
401C4×C131—41no—
402C4×C131—41no—
403C4×C131—41no—
404C4×C131—41no—
405C4×C131—41no—
406C4×C131—82no—
407C4×C131—161no—
408C4×C131—161no—
409C2×C131—21no—
410C2×C131—21no—
411C2×C131—21no—
412C2×C131—41no—
413C2×C131—41no—
414C2×C131—41no—
415C2×C131—42no—
416C2×C131—41no—
417C2×C131—81no—
418C2×C131—81no—
419C2×C131—81no—
420C2×C131#179011yescharacteristic
421#12753C13111yesmaximal, characteristic, direct product factor, Sylow
422C131#1275311yescharacteristic, direct product factor, Sylow
423#3532C2×C13111yescharacteristic
424#2127C2×C13111yescharacteristic, complemented
425#2121C2×C13111yescharacteristic, complemented
426C2×AΣL(1,𝔽16)C2×C13111yescharacteristic, complemented
427#1913C2×C13111yescharacteristic, complemented
428#1911C2×C13111yescharacteristic, complemented
429#1889C2×C13111yescharacteristic, complemented
430H(3,𝔽4)C4×C13111yescharacteristic, complemented
431#560—21no—
432#560C4×C13111yescharacteristic, complemented
433#551—21no—
434#551C4×C13111yescharacteristic, complemented
435#546—21no—
436#546—21no—
437#546—21no—
438D42—21no—
439D42C4×C13111yescharacteristic, complemented
440#538—21no—
441#538—21no—
442#538—21no—
443#535—21no—
444#535C22×C13111yescharacteristic
445#534—21no—
446#534C22×C13111yescharacteristic
447C2×#120—21no—
448C2×#120C22×C13111yescharacteristic
449#518C22×C13111yescharacteristic, complemented
450#421—21no—
451C2×#100C22×C13111yescharacteristic, complemented
452C2×#99—21no—
453C2×#99C22×C13111yescharacteristic, complemented
454C2×#99C22×C13111yescharacteristic, complemented
455#379—21no—
456#354—21no—
457#353—21no—
458#352—21no—
459AΣL(1,𝔽16)—21no—
460AΣL(1,𝔽16)—21no—
461AΣL(1,𝔽16)—21no—
462#342—21no—
463#342—21no—
464H(3,ℤ/4)—21no—
465C25D4×C13111yescharacteristic
466C2×#41—21no—
467C2×#41D4×C13111yescharacteristic
468C22×D4—21no—
469C22×D4—21no—
470C22×D4—21no—
471C22×D4—21no—
472C22×D4—21no—
473C22×D4D4×C13111yescharacteristic
474C22×D4C23×C13111yescharacteristic
475C2×M16—21no—
476#127—21no—
477#127C2×C4×C13111yescharacteristic
478#127D4×C13111yescharacteristic
479#126—21no—
480#126—21no—
481#126—21no—
482#126—21no—
483#124—21no—
484#124—21no—
485#124—21no—
486#124—21no—
487#124—21no—
488#124C2×C4×C13111yescharacteristic
489#124D4×C13111yescharacteristic
490#123—21no—
491#123—21no—
492#123—21no—
493#123—21no—
494#123—21no—
495#123—21no—
496#123—21no—
497#123—21no—
498#123C2×C4×C13111yescharacteristic
499#123D4×C13111yescharacteristic
500C22⋊Q8—21no—
501C22⋊Q8—21no—
502C22⋊Q8—21no—
503#121—21no—
504#121—21no—
505#121—21no—
506#121—21no—
507#121—21no—
508#121—21no—
509#121—21no—
510#121—21no—
511#121—21no—
512#121—21no—
513#121—21no—
514#121—21no—
515#121—21no—
516#121—21no—
517#121—21no—
518#120—21no—
519#120—21no—
520#120—21no—
521#120—21no—
522#120—21no—
523#120—21no—
524#120—21no—
525#120—21no—
526#120—21no—
527#120—21no—
528#120—21no—
529#120—21no—
530#120—21no—
531#120—21no—
532#120C2×C4×C13111yescharacteristic
533#120C2×C4×C13111yescharacteristic
534#120C2×C4×C13111yescharacteristic
535#120D4×C13111yescharacteristic
536#120D4×C13111yescharacteristic
537#120D4×C13111yescharacteristic
538C4×D4—21no—
539C4×D4—21no—
540C4×D4—21no—
541C4×D4—21no—
542C4×D4—21no—
543C4×D4—21no—
544C4×D4—42no—
545#117—21no—
546#117—21no—
547#117D4×C13111yescharacteristic
548C2×C22⋊C4—21no—
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—21no—
557C2×C22⋊C4—42no—
558C2×C22⋊C4D4×C13111yescharacteristic
559C2×C22⋊C4D4×C13111yescharacteristic
560#104—42no—
561#100—21no—
562#100—21no—
563#99—21no—
564#99—21no—
565#99—21no—
566#99—21no—
567#99—42no—
568C24—21no—
569C24—21no—
570C24—21no—
571C24—41no—
572C24—41no—
573C24—82no—
574C24C22⋊C4×C13111yescharacteristic
575C24C22⋊C4×C13111yescharacteristic
576C24C22⋊C4×C13111yescharacteristic, complemented
577C24C2×D4×C13111yescharacteristic
578C24C2×D4×C13111yescharacteristic
579#41—41no—
580#41—41no—
581#41—82no—
582C2×Q8—21no—
583C2×Q8C22⋊C4×C13111yescharacteristic, complemented
584C2×D4—21no—
585C2×D4—21no—
586C2×D4—21no—
587C2×D4—21no—
588C2×D4—21no—
589C2×D4—21no—
590C2×D4—21no—
591C2×D4—21no—
592C2×D4—21no—
593C2×D4—21no—
594C2×D4—21no—
595C2×D4—21no—
596C2×D4—21no—
597C2×D4—21no—
598C2×D4—21no—
599C2×D4—21no—
600C2×D4—21no—
601C2×D4—21no—
602C2×D4—21no—
603C2×D4—21no—
604C2×D4—41no—
605C2×D4—41no—
606C2×D4—41no—
607C2×D4—41no—
608C2×D4—82no—
609C2×D4—82no—
610C2×D4—82no—
611C2×D4—82no—
612C2×D4—81no—
613C2×D4—81no—
614C2×D4C22⋊C4×C13111yescharacteristic, complemented
615C2×D4C22×C4×C13111yescharacteristic
616C2×D4C2×D4×C13111yescharacteristic
617C2×D4C2×D4×C13111yescharacteristic
618C2×D4C2×D4×C13111yescharacteristic
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—22no—
628C22×C4—41no—
629C22×C4—41no—
630C22×C4—41no—
631C22×C4C22⋊C4×C13111yescharacteristic, complemented
632C22×C4C2×D4×C13111yescharacteristic
633M16—41no—
634M16—41no—
635C2×C8—41no—
636C4⋊C4—21no—
637C4⋊C4—21no—
638C4⋊C4—21no—
639C4⋊C4—21no—
640C4⋊C4—21no—
641C4⋊C4—21no—
642C4⋊C4—21no—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—41no—
646C22⋊C4—21no—
647C22⋊C4—21no—
648C22⋊C4—21no—
649C22⋊C4—21no—
650C22⋊C4—21no—
651C22⋊C4—21no—
652C22⋊C4—21no—
653C22⋊C4—21no—
654C22⋊C4—21no—
655C22⋊C4—21no—
656C22⋊C4—21no—
657C22⋊C4—21no—
658C22⋊C4—21no—
659C22⋊C4—21no—
660C22⋊C4—21no—
661C22⋊C4—21no—
662C22⋊C4—21no—
663C22⋊C4—21no—
664C22⋊C4—21no—
665C22⋊C4—21no—
666C22⋊C4—21no—
667C22⋊C4—21no—
668C22⋊C4—21no—
669C22⋊C4—21no—
670C22⋊C4—21no—
671C22⋊C4—22no—
672C22⋊C4—41no—
673C22⋊C4—41no—
674C22⋊C4—41no—
675C22⋊C4—41no—
676C22⋊C4—41no—
677C22⋊C4—41no—
678C22⋊C4—84no—
679C22⋊C4C22⋊C4×C13111yescharacteristic
680C22⋊C4C22⋊C4×C13111yescharacteristic
681C22⋊C4C22⋊C4×C13111yescharacteristic, complemented
682C22⋊C4C22⋊C4×C13111yescharacteristic, complemented
683C42—21no—
684C42—21no—
685C42—22no—
686C42C22⋊C4×C13111yescharacteristic, complemented
687C42C22⋊C4×C13111yescharacteristic, complemented
688C23—21no—
689C23—21no—
690C23—21no—
691C23—21no—
692C23—21no—
693C23—21no—
694C23—21no—
695C23—21no—
696C23—42no—
697C23—41no—
698C23—41no—
699C23—42no—
700C23—42no—
701C23—42no—
702C23—41no—
703C23—44no—
704C23—41no—
705C23—41no—
706C23—81no—
707C23—81no—
708C23—81no—
709C23—81no—
710C23—81no—
711C23—81no—
712C23—81no—
713C23—81no—
714C23—81no—
715C23—82no—
716C23—82no—
717C23—82no—
718C23C2×C22⋊C4×C13111yescharacteristic
719C23C2×C22⋊C4×C13111yescharacteristic
720C23#120×C13111yescharacteristic
721C23#120×C13111yescharacteristic
722C23#120×C13111yescharacteristic
723Q8—41no—
724Q8—81no—
725D4—41no—
726D4—41no—
727D4—41no—
728D4—41no—
729D4—41no—
730D4—42no—
731D4—42no—
732D4—42no—
733D4—42no—
734D4—41no—
735D4—41no—
736D4—41no—
737D4—41no—
738D4—81no—
739D4—81no—
740D4—81no—
741D4—81no—
742D4—81no—
743D4—81no—
744D4—81no—
745D4—81no—
746D4—81no—
747D4—81no—
748D4—81no—
749D4—81no—
750D4—81no—
751D4—81no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—42no—
763C2×C4—41no—
764C2×C4—42no—
765C2×C4—81no—
766C2×C4—81no—
767C2×C4—81no—
768C2×C4—81no—
769C2×C4—81no—
770C2×C4—81no—
771C2×C4—81no—
772C2×C4—82no—
773C2×C4—81no—
774C2×C4—81no—
775C2×C4—82no—
776C2×C4—161no—
777C2×C4—161no—
778C2×C4C2×C22⋊C4×C13111yescharacteristic
779C2×C4#120×C13111yescharacteristic
780C8—81no—
781C22—22no—
782C22—21no—
783C22—21no—
784C22—21no—
785C22—21no—
786C22—41no—
787C22—41no—
788C22—41no—
789C22—41no—
790C22—41no—
791C22—42no—
792C22—41no—
793C22—41no—
794C22—41no—
795C22—41no—
796C22—41no—
797C22—41no—
798C22—41no—
799C22—42no—
800C22—41no—
801C22—42no—
802C22—41no—
803C22—41no—
804C22—41no—
805C22—81no—
806C22—81no—
807C22—81no—
808C22—82no—
809C22—82no—
810C22—81no—
811C22—84no—
812C22—81no—
813C22—161no—
814C22—162no—
815C22#379×C13111yescharacteristic
816C22B(4,𝔽2)×C13111yescharacteristic
817C22#458×C13111yescharacteristic
818C4—21no—
819C4—21no—
820C4—41no—
821C4—41no—
822C4—41no—
823C4—41no—
824C4—41no—
825C4—41no—
826C4—41no—
827C4—41no—
828C4—82no—
829C4—161no—
830C4—161no—
831C2—21no—
832C2—21no—
833C2—21no—
834C2—41no—
835C2—41no—
836C2—41no—
837C2—42no—
838C2—41no—
839C2—81no—
840C2—81no—
841C2—81no—
842C2#1790×C13111yescharacteristic
subgroupG/H
center, socleC2×C131#1790
commutatorC2×D4C22×C4×C131
Frattini, cosocleC22×D4C23×C131
prime radical#3532×C131C2
LCSG ▷ C2×D4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C131 ◁ C23×C131 ◁ C22×D4×C131 ◁ G

Complements

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

NH ≅ G/Ntype
2. #2127×C131C2semidirect
3. #2121×C131C2semidirect
4. C2×AΣL(1,𝔽16)×C131C2semidirect
5. #1913×C131C2semidirect
6. #1911×C131C2semidirect
7. #1889×C131C2semidirect
8. H(3,𝔽4)×C131C4semidirect
10. #560×C131C4semidirect
12. #551×C131C4semidirect
17. D42×C131C4semidirect
27. #518×C131C22semidirect
29. C2×#100×C131C22semidirect
31. C2×#99×C131C22semidirect
32. C2×#99×C131C22semidirect
154. C24×C131C22⋊C4semidirect
161. C2×Q8×C131C22⋊C4semidirect
192. C2×D4×C131C22⋊C4semidirect
209. C22×C4×C131C22⋊C4semidirect
259. C22⋊C4×C131C22⋊C4semidirect
260. C22⋊C4×C131C22⋊C4semidirect
264. C42×C131C22⋊C4semidirect
265. C42×C131C22⋊C4semidirect
421. #12753C131direct (N × H)
422. C131#12753direct (N × H)
424. #2127C2×C131semidirect
425. #2121C2×C131semidirect
426. C2×AΣL(1,𝔽16)C2×C131semidirect
427. #1913C2×C131semidirect
428. #1911C2×C131semidirect
429. #1889C2×C131semidirect
430. H(3,𝔽4)C4×C131semidirect
432. #560C4×C131semidirect
434. #551C4×C131semidirect
439. D42C4×C131semidirect
449. #518C22×C131semidirect
451. C2×#100C22×C131semidirect
453. C2×#99C22×C131semidirect
454. C2×#99C22×C131semidirect
576. C24C22⋊C4×C131semidirect
583. C2×Q8C22⋊C4×C131semidirect
614. C2×D4C22⋊C4×C131semidirect
631. C22×C4C22⋊C4×C131semidirect
681. C22⋊C4C22⋊C4×C131semidirect
682. C22⋊C4C22⋊C4×C131semidirect
686. C42C22⋊C4×C131semidirect
687. C42C22⋊C4×C131semidirect

Maximal subgroups

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

subgroupindex
#3532×C1312
#2127×C1312
#2121×C1312
C2×AΣL(1,𝔽16)×C1312
#1913×C1312
#1911×C1312
#1889×C1312
#12753131