Finite Group Databasebeta

← C131×#33556 #45719440

Subgroups — C131×#33556 #45719440

Order 33536.

1134 conjugacy classes of subgroups.

The subgroup lattice has 752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3540×C131C211yesmaximal, characteristic, complemented
2#3028×C131C211yesmaximal, characteristic, complemented
3#3025×C131C211yesmaximal, characteristic, complemented
4#3021×C131C211yesmaximal, characteristic, complemented
5#2200×C131C214yesmaximal, complemented
6#2198×C131C214yesmaximal, complemented
7#2128×C131C211yesmaximal, characteristic, complemented
8#2123×C131C211yesmaximal, characteristic, complemented
9#2120×C131C211yesmaximal, characteristic, complemented
10#585×C131C2211yescharacteristic
11C2×AGL(1,ℤ/8)×C131—21no—
12H(3,𝔽4)×C131—21no—
13#560×C131C2212yescomplemented
14#559×C131C2212yescomplemented
15#556×C131—21no—
16#555×C131—21no—
17#551×C131—21no—
18#548×C131—21no—
19#546×C131—21no—
20#542×C131—22no—
21#542×C131—21no—
22#538×C131—22no—
23#536×C131—21no—
24#536×C131C2211yescharacteristic
25#535×C131C2211yescharacteristic
26#525×C131—21no—
27#525×C131—21no—
28#525×C131C2211yescharacteristic
29#458×C131—21no—
30#458×C131—22no—
31#458×C131C2212yescomplemented
32#458×C131C2214yescomplemented
33B(4,𝔽2)×C131—21no—
34B(4,𝔽2)×C131C2212yescomplemented
35#454×C131—22no—
36#453×C131C2214yes—
37#421×C131—21no—
38#413×C131C2211yescharacteristic
39#410×C131—21no—
40#410×C131—21no—
41#410×C131C2211yescharacteristic
42#410×C131C2211yescharacteristic
43#353×C131C2214yescomplemented
44#352×C131C2212yescomplemented
45#352×C131C2214yescomplemented
46AΣL(1,𝔽16)×C131C2212yescomplemented
472−1+4×C131—21no—
482−1+4×C131—41no—
49H(5,𝔽2)×C131—21no—
50H(5,𝔽2)×C131—21no—
51H(5,𝔽2)×C131—41no—
52H(5,𝔽2)×C131C2312yes—
53C2×#41×C131—21no—
54C2×#41×C131—21no—
55C2×#41×C131—21no—
56C2×#41×C131—21no—
57C2×#41×C131—42no—
58C2×#41×C131C2311yescharacteristic
59C22×Q8×C131D411yescharacteristic, complemented
60C22×D4×C131D411yescharacteristic, complemented
61C23×C4×C131D411yescharacteristic
62AGL(1,ℤ/8)×C131—24no—
63AGL(1,ℤ/8)×C131—42no—
64C2×SD16×C131—41no—
65C2×D8×C131—41no—
66C2×M16×C131—21no—
67C4⋊Q8×C131—21no—
68C4⋊Q8×C131—21no—
69C4⋊Q8×C131—41no—
70#127×C131C2312yes—
71#126×C131—22no—
72#126×C131—22no—
73#126×C131—22no—
74#124×C131—22no—
75#124×C131—21no—
76#124×C131—22no—
77#124×C131—22no—
78#124×C131—21no—
79#124×C131—22no—
80#124×C131—22no—
81#124×C131—41no—
82#124×C131D412yescomplemented
83#123×C131—22no—
84#123×C131—22no—
85#123×C131—22no—
86#123×C131—22no—
87#123×C131—24no—
88#123×C131D411yescharacteristic
89#123×C131D412yescomplemented
90#123×C131C2311yescharacteristic
91#123×C131C2312yes—
92C22⋊Q8×C131—21no—
93C22⋊Q8×C131—22no—
94C22⋊Q8×C131—22no—
95C22⋊Q8×C131—21no—
96C22⋊Q8×C131—21no—
97C22⋊Q8×C131—21no—
98C22⋊Q8×C131—42no—
99C22⋊Q8×C131—41no—
100#121×C131—21no—
101#121×C131—21no—
102#121×C131—22no—
103#121×C131—21no—
104#121×C131—21no—
105#121×C131—22no—
106#121×C131—22no—
107#121×C131—41no—
108#120×C131—22no—
109#120×C131—22no—
110#120×C131—21no—
111#120×C131—21no—
112#120×C131—22no—
113#120×C131D411yescharacteristic
114#120×C131C2311yescharacteristic
115C4×Q8×C131—21no—
116C4×Q8×C131—22no—
117C4×D4×C131—22no—
118C4×D4×C131—21no—
119C4×D4×C131—22no—
120C4×D4×C131—21no—
121C4×D4×C131—21no—
122C4×D4×C131—22no—
123C4×D4×C131—42no—
124#117×C131—21no—
125#117×C131—22no—
126#117×C131—21no—
127#117×C131—21no—
128#117×C131D411yescharacteristic
129#117×C131D411yescharacteristic, complemented
130#117×C131D411yescharacteristic, complemented
131C2×C22⋊C4×C131—22no—
132#104×C131—24no—
133#101×C131—21no—
134#100×C131C2312yes—
135#99×C131—21no—
136#99×C131—21no—
137#99×C131—22no—
138#99×C131—22no—
139#99×C131—24no—
140#99×C131C2312yes—
141#99×C131C2312yes—
142C24×C131—21no—
143C24×C131C2×D411yescharacteristic
144#41×C131—22no—
145#41×C131—22no—
146#41×C131—41no—
147#41×C131—41no—
148#41×C131—42no—
149#41×C131—41no—
150#41×C131—41no—
151#41×C131—41no—
152#41×C131—41no—
153#41×C131—41no—
154#41×C131—42no—
155#41×C131—42no—
156#41×C131—42no—
157#41×C131—41no—
158#41×C131—41no—
159#41×C131—41no—
160#41×C131—81no—
161#41×C131—81no—
162C2×Q8×C131—21no—
163C2×Q8×C131—21no—
164C2×Q8×C131—22no—
165C2×Q8×C131—21no—
166C2×Q8×C131—21no—
167C2×Q8×C131—21no—
168C2×Q8×C131—41no—
169C2×Q8×C131—41no—
170C2×Q8×C131—42no—
171C2×Q8×C131C2×D411yescharacteristic
172C2×D4×C131—21no—
173C2×D4×C131—21no—
174C2×D4×C131—21no—
175C2×D4×C131—22no—
176C2×D4×C131—22no—
177C2×D4×C131—22no—
178C2×D4×C131—22no—
179C2×D4×C131—21no—
180C2×D4×C131—22no—
181C2×D4×C131—22no—
182C2×D4×C131—21no—
183C2×D4×C131—21no—
184C2×D4×C131—41no—
185C2×D4×C131—41no—
186C2×D4×C131—42no—
187C2×D4×C131—42no—
188C2×D4×C131—42no—
189C2×D4×C131—41no—
190C2×D4×C131—42no—
191C2×D4×C131C2×D411yescharacteristic
192C2×D4×C131C2×D411yescharacteristic
193C2×D4×C131C2×D412yes—
194C2×D4×C131C2411yescharacteristic
195C22×C4×C131—22no—
196C22×C4×C131—22no—
197C22×C4×C131—22no—
198C22×C4×C131—22no—
199C22×C4×C131—21no—
200C22×C4×C131—21no—
201C22×C4×C131—41no—
202C22×C4×C131—41no—
203C22×C4×C131—41no—
204C22×C4×C131C2×D411yescharacteristic
205C22×C4×C131C2×D411yescharacteristic
206C22×C4×C131C2×D411yescharacteristic
207C22×C4×C131C2×D411yescharacteristic
208C22×C4×C131C2×D412yes—
209SD16×C131—44no—
210D8×C131—44no—
211M16×C131—22no—
212M16×C131—41no—
213C2×C8×C131—41no—
214C4⋊C4×C131—22no—
215C4⋊C4×C131—22no—
216C4⋊C4×C131—22no—
217C4⋊C4×C131—21no—
218C4⋊C4×C131—21no—
219C4⋊C4×C131—22no—
220C4⋊C4×C131—21no—
221C4⋊C4×C131—21no—
222C4⋊C4×C131—21no—
223C4⋊C4×C131—22no—
224C4⋊C4×C131—41no—
225C4⋊C4×C131—41no—
226C4⋊C4×C131—42no—
227C4⋊C4×C131—44no—
228C22⋊C4×C131—22no—
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—22no—
236C22⋊C4×C131—21no—
237C22⋊C4×C131—21no—
238C22⋊C4×C131—22no—
239C22⋊C4×C131—22no—
240C22⋊C4×C131—22no—
241C22⋊C4×C131—21no—
242C22⋊C4×C131—21no—
243C22⋊C4×C131—22no—
244C22⋊C4×C131—22no—
245C22⋊C4×C131—42no—
246C22⋊C4×C131—42no—
247C22⋊C4×C131—44no—
248C22⋊C4×C131C2×D411yescharacteristic
249C22⋊C4×C131C2×D411yescharacteristic
250C22⋊C4×C131C2×D412yes—
251C42×C131—22no—
252C42×C131—22no—
253C42×C131—21no—
254C42×C131—21no—
255C42×C131—41no—
256C42×C131—41no—
257C42×C131C2×D412yes—
258C23×C131—22no—
259C23×C131—22no—
260C23×C131—21no—
261C23×C131—22no—
262C23×C131—41no—
263C23×C131—41no—
264C23×C131—81no—
265C23×C131—81no—
266C23×C131—82no—
267C23×C131#12011yescharacteristic
268C23×C131C22×D411yescharacteristic
269C23×C131C22×D411yescharacteristic
270Q8×C131—22no—
271Q8×C131—41no—
272Q8×C131—41no—
273Q8×C131—41no—
274Q8×C131—41no—
275Q8×C131—41no—
276Q8×C131—41no—
277Q8×C131—81no—
278Q8×C131—82no—
279D4×C131—22no—
280D4×C131—41no—
281D4×C131—41no—
282D4×C131—41no—
283D4×C131—42no—
284D4×C131—41no—
285D4×C131—41no—
286D4×C131—42no—
287D4×C131—42no—
288D4×C131—42no—
289D4×C131—42no—
290D4×C131—41no—
291D4×C131—41no—
292D4×C131—41no—
293D4×C131—81no—
294D4×C131—82no—
295D4×C131—82no—
296D4×C131—82no—
297D4×C131—81no—
298D4×C131—82no—
299D4×C131—84no—
300C2×C4×C131—21no—
301C2×C4×C131—21no—
302C2×C4×C131—21no—
303C2×C4×C131—21no—
304C2×C4×C131—21no—
305C2×C4×C131—21no—
306C2×C4×C131—22no—
307C2×C4×C131—22no—
308C2×C4×C131—21no—
309C2×C4×C131—22no—
310C2×C4×C131—22no—
311C2×C4×C131—21no—
312C2×C4×C131—22no—
313C2×C4×C131—21no—
314C2×C4×C131—42no—
315C2×C4×C131—42no—
316C2×C4×C131—42no—
317C2×C4×C131—41no—
318C2×C4×C131—42no—
319C2×C4×C131—41no—
320C2×C4×C131—41no—
321C2×C4×C131—41no—
322C2×C4×C131—42no—
323C2×C4×C131—42no—
324C2×C4×C131—42no—
325C2×C4×C131—81no—
326C2×C4×C131—82no—
327C2×C4×C131—82no—
328C2×C4×C131#12011yescharacteristic
329C2×C4×C131#12011yescharacteristic
330C2×C4×C131#12011yescharacteristic
331C2×C4×C131C22×D411yescharacteristic
332C8×C131—42no—
333C22×C131—21no—
334C22×C131—21no—
335C22×C131—21no—
336C22×C131—41no—
337C22×C131—41no—
338C22×C131—41no—
339C22×C131—42no—
340C22×C131—41no—
341C22×C131—41no—
342C22×C131—42no—
343C22×C131—42no—
344C22×C131—42no—
345C22×C131—41no—
346C22×C131—42no—
347C22×C131—82no—
348C22×C131—82no—
349C22×C131—81no—
350C22×C131—161no—
351C22×C131—162no—
352C22×C131C2×#12011yescharacteristic
353C4×C131—21no—
354C4×C131—21no—
355C4×C131—21no—
356C4×C131—41no—
357C4×C131—42no—
358C4×C131—42no—
359C4×C131—41no—
360C4×C131—42no—
361C4×C131—41no—
362C4×C131—42no—
363C4×C131—82no—
364C4×C131—82no—
365C4×C131B(4,𝔽2)11yescharacteristic
366C4×C131B(4,𝔽2)11yescharacteristic
367C2×C131—21no—
368C2×C131—41no—
369C2×C131—41no—
370C2×C131—41no—
371C2×C131—81no—
372C2×C131—82no—
373C2×C131—82no—
374C2×C131C2×B(4,𝔽2)11yescharacteristic
375#33556C13111yesmaximal, characteristic, direct product factor, Sylow
376C131#3355611yescharacteristic, direct product factor, Sylow
377#3540C2×C13111yescharacteristic, complemented
378#3028C2×C13111yescharacteristic, complemented
379#3025C2×C13111yescharacteristic, complemented
380#3021C2×C13111yescharacteristic, complemented
381#2200C2×C13114yescomplemented
382#2198C2×C13114yescomplemented
383#2128C2×C13111yescharacteristic, complemented
384#2123C2×C13111yescharacteristic, complemented
385#2120C2×C13111yescharacteristic, complemented
386#585C22×C13111yescharacteristic
387C2×AGL(1,ℤ/8)—21no—
388H(3,𝔽4)—21no—
389#560C22×C13112yescomplemented
390#559C22×C13112yescomplemented
391#556—21no—
392#555—21no—
393#551—21no—
394#548—21no—
395#546—21no—
396#542—22no—
397#542—21no—
398#538—22no—
399#536—21no—
400#536C22×C13111yescharacteristic
401#535C22×C13111yescharacteristic
402#525—21no—
403#525—21no—
404#525C22×C13111yescharacteristic
405#458—21no—
406#458—22no—
407#458C22×C13112yescomplemented
408#458C22×C13114yescomplemented
409B(4,𝔽2)—21no—
410B(4,𝔽2)C22×C13112yescomplemented
411#454—22no—
412#453C22×C13114yes—
413#421—21no—
414#413C22×C13111yescharacteristic
415#410—21no—
416#410—21no—
417#410C22×C13111yescharacteristic
418#410C22×C13111yescharacteristic
419#353C22×C13114yescomplemented
420#352C22×C13112yescomplemented
421#352C22×C13114yescomplemented
422AΣL(1,𝔽16)C22×C13112yescomplemented
4232−1+4—21no—
4242−1+4—41no—
425H(5,𝔽2)—21no—
426H(5,𝔽2)—21no—
427H(5,𝔽2)—41no—
428H(5,𝔽2)C23×C13112yes—
429C2×#41—21no—
430C2×#41—21no—
431C2×#41—21no—
432C2×#41—21no—
433C2×#41—42no—
434C2×#41C23×C13111yescharacteristic
435C22×Q8D4×C13111yescharacteristic, complemented
436C22×D4D4×C13111yescharacteristic, complemented
437C23×C4D4×C13111yescharacteristic
438AGL(1,ℤ/8)—24no—
439AGL(1,ℤ/8)—42no—
440C2×SD16—41no—
441C2×D8—41no—
442C2×M16—21no—
443C4⋊Q8—21no—
444C4⋊Q8—21no—
445C4⋊Q8—41no—
446#127C23×C13112yes—
447#126—22no—
448#126—22no—
449#126—22no—
450#124—22no—
451#124—21no—
452#124—22no—
453#124—22no—
454#124—21no—
455#124—22no—
456#124—22no—
457#124—41no—
458#124D4×C13112yescomplemented
459#123—22no—
460#123—22no—
461#123—22no—
462#123—22no—
463#123—24no—
464#123D4×C13111yescharacteristic
465#123D4×C13112yescomplemented
466#123C23×C13111yescharacteristic
467#123C23×C13112yes—
468C22⋊Q8—21no—
469C22⋊Q8—22no—
470C22⋊Q8—22no—
471C22⋊Q8—21no—
472C22⋊Q8—21no—
473C22⋊Q8—21no—
474C22⋊Q8—42no—
475C22⋊Q8—41no—
476#121—21no—
477#121—21no—
478#121—22no—
479#121—21no—
480#121—21no—
481#121—22no—
482#121—22no—
483#121—41no—
484#120—22no—
485#120—22no—
486#120—21no—
487#120—21no—
488#120—22no—
489#120D4×C13111yescharacteristic
490#120C23×C13111yescharacteristic
491C4×Q8—21no—
492C4×Q8—22no—
493C4×D4—22no—
494C4×D4—21no—
495C4×D4—22no—
496C4×D4—21no—
497C4×D4—21no—
498C4×D4—22no—
499C4×D4—42no—
500#117—21no—
501#117—22no—
502#117—21no—
503#117—21no—
504#117D4×C13111yescharacteristic
505#117D4×C13111yescharacteristic, complemented
506#117D4×C13111yescharacteristic, complemented
507C2×C22⋊C4—22no—
508#104—24no—
509#101—21no—
510#100C23×C13112yes—
511#99—21no—
512#99—21no—
513#99—22no—
514#99—22no—
515#99—24no—
516#99C23×C13112yes—
517#99C23×C13112yes—
518C24—21no—
519C24C2×D4×C13111yescharacteristic
520#41—22no—
521#41—22no—
522#41—41no—
523#41—41no—
524#41—42no—
525#41—41no—
526#41—41no—
527#41—41no—
528#41—41no—
529#41—41no—
530#41—42no—
531#41—42no—
532#41—42no—
533#41—41no—
534#41—41no—
535#41—41no—
536#41—81no—
537#41—81no—
538C2×Q8—21no—
539C2×Q8—21no—
540C2×Q8—22no—
541C2×Q8—21no—
542C2×Q8—21no—
543C2×Q8—21no—
544C2×Q8—41no—
545C2×Q8—41no—
546C2×Q8—42no—
547C2×Q8C2×D4×C13111yescharacteristic
548C2×D4—21no—
549C2×D4—21no—
550C2×D4—21no—
551C2×D4—22no—
552C2×D4—22no—
553C2×D4—22no—
554C2×D4—22no—
555C2×D4—21no—
556C2×D4—22no—
557C2×D4—22no—
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—41no—
561C2×D4—41no—
562C2×D4—42no—
563C2×D4—42no—
564C2×D4—42no—
565C2×D4—41no—
566C2×D4—42no—
567C2×D4C2×D4×C13111yescharacteristic
568C2×D4C2×D4×C13111yescharacteristic
569C2×D4C2×D4×C13112yes—
570C2×D4C24×C13111yescharacteristic
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—41no—
578C22×C4—41no—
579C22×C4—41no—
580C22×C4C2×D4×C13111yescharacteristic
581C22×C4C2×D4×C13111yescharacteristic
582C22×C4C2×D4×C13111yescharacteristic
583C22×C4C2×D4×C13111yescharacteristic
584C22×C4C2×D4×C13112yes—
585SD16—44no—
586D8—44no—
587M16—22no—
588M16—41no—
589C2×C8—41no—
590C4⋊C4—22no—
591C4⋊C4—22no—
592C4⋊C4—22no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—21no—
596C4⋊C4—21no—
597C4⋊C4—22no—
598C4⋊C4—21no—
599C4⋊C4—22no—
600C4⋊C4—41no—
601C4⋊C4—41no—
602C4⋊C4—42no—
603C4⋊C4—44no—
604C22⋊C4—22no—
605C22⋊C4—22no—
606C22⋊C4—22no—
607C22⋊C4—22no—
608C22⋊C4—22no—
609C22⋊C4—22no—
610C22⋊C4—21no—
611C22⋊C4—22no—
612C22⋊C4—21no—
613C22⋊C4—21no—
614C22⋊C4—22no—
615C22⋊C4—22no—
616C22⋊C4—22no—
617C22⋊C4—21no—
618C22⋊C4—21no—
619C22⋊C4—22no—
620C22⋊C4—22no—
621C22⋊C4—42no—
622C22⋊C4—42no—
623C22⋊C4—44no—
624C22⋊C4C2×D4×C13111yescharacteristic
625C22⋊C4C2×D4×C13111yescharacteristic
626C22⋊C4C2×D4×C13112yes—
627C42—22no—
628C42—22no—
629C42—21no—
630C42—21no—
631C42—41no—
632C42—41no—
633C42C2×D4×C13112yes—
634C23—22no—
635C23—22no—
636C23—21no—
637C23—22no—
638C23—41no—
639C23—41no—
640C23—81no—
641C23—81no—
642C23—82no—
643C23#120×C13111yescharacteristic
644C23C22×D4×C13111yescharacteristic
645C23C22×D4×C13111yescharacteristic
646Q8—22no—
647Q8—41no—
648Q8—41no—
649Q8—41no—
650Q8—41no—
651Q8—41no—
652Q8—41no—
653Q8—81no—
654Q8—82no—
655D4—22no—
656D4—41no—
657D4—41no—
658D4—41no—
659D4—42no—
660D4—41no—
661D4—41no—
662D4—42no—
663D4—42no—
664D4—42no—
665D4—42no—
666D4—41no—
667D4—41no—
668D4—41no—
669D4—82no—
670D4—81no—
671D4—82no—
672D4—82no—
673D4—82no—
674D4—81no—
675D4—84no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—21no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—21no—
688C2×C4—22no—
689C2×C4—21no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—41no—
694C2×C4—42no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—81no—
702C2×C4—82no—
703C2×C4—82no—
704C2×C4#120×C13111yescharacteristic
705C2×C4#120×C13111yescharacteristic
706C2×C4#120×C13111yescharacteristic
707C2×C4C22×D4×C13111yescharacteristic
708C8—42no—
709C22—21no—
710C22—21no—
711C22—21no—
712C22—41no—
713C22—41no—
714C22—41no—
715C22—42no—
716C22—41no—
717C22—41no—
718C22—42no—
719C22—42no—
720C22—42no—
721C22—41no—
722C22—42no—
723C22—82no—
724C22—82no—
725C22—81no—
726C22—161no—
727C22—162no—
728C22C2×#120×C13111yescharacteristic
729C4—21no—
730C4—21no—
731C4—21no—
732C4—41no—
733C4—42no—
734C4—42no—
735C4—41no—
736C4—42no—
737C4—41no—
738C4—42no—
739C4—82no—
740C4—82no—
741C4B(4,𝔽2)×C13111yescharacteristic
742C4B(4,𝔽2)×C13111yescharacteristic
743C2—21no—
744C2—41no—
745C2—41no—
746C2—41no—
747C2—81no—
748C2—82no—
749C2—82no—
750C2C2×B(4,𝔽2)×C13111yescharacteristic
subgroupG/H
center, socleC2×C131C2×B(4,𝔽2)
commutator, Frattini, cosocleC2×D4C24×C131
LCSG ▷ C2×D4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C131 ◁ C2×C4×C131 ◁ C2×#41×C131 ◁ G

Complements

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

NH ≅ G/Ntype
1. #3540×C131C2semidirect
2. #3028×C131C2semidirect
3. #3025×C131C2semidirect
4. #3021×C131C2semidirect
5. #2200×C131C2semidirect
6. #2198×C131C2semidirect
7. #2128×C131C2semidirect
8. #2123×C131C2semidirect
9. #2120×C131C2semidirect
13. #560×C131C22semidirect
14. #559×C131C22semidirect
31. #458×C131C22semidirect
32. #458×C131C22semidirect
34. B(4,𝔽2)×C131C22semidirect
43. #353×C131C22semidirect
44. #352×C131C22semidirect
45. #352×C131C22semidirect
46. AΣL(1,𝔽16)×C131C22semidirect
59. C22×Q8×C131D4semidirect
60. C22×D4×C131D4semidirect
82. #124×C131D4semidirect
89. #123×C131D4semidirect
129. #117×C131D4semidirect
130. #117×C131D4semidirect
375. #33556C131direct (N × H)
376. C131#33556direct (N × H)
377. #3540C2×C131semidirect
378. #3028C2×C131semidirect
379. #3025C2×C131semidirect
380. #3021C2×C131semidirect
381. #2200C2×C131semidirect
382. #2198C2×C131semidirect
383. #2128C2×C131semidirect
384. #2123C2×C131semidirect
385. #2120C2×C131semidirect
389. #560C22×C131semidirect
390. #559C22×C131semidirect
407. #458C22×C131semidirect
408. #458C22×C131semidirect
410. B(4,𝔽2)C22×C131semidirect
419. #353C22×C131semidirect
420. #352C22×C131semidirect
421. #352C22×C131semidirect
422. AΣL(1,𝔽16)C22×C131semidirect
435. C22×Q8D4×C131semidirect
436. C22×D4D4×C131semidirect
458. #124D4×C131semidirect
465. #123D4×C131semidirect
505. #117D4×C131semidirect
506. #117D4×C131semidirect

Maximal subgroups

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

subgroupindex
#3540×C1312
#3028×C1312
#3025×C1312
#3021×C1312
#2200×C1312
#2198×C1312
#2128×C1312
#2123×C1312
#2120×C1312
#33556131