Finite Group Databasebeta

← C131×#33555 #45719439

Subgroups — C131×#33555 #45719439

Order 33536.

1146 conjugacy classes of subgroups.

The subgroup lattice has 754 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3540×C131C211yesmaximal, characteristic, complemented
2#3027×C131C211yesmaximal, characteristic, complemented
3#3025×C131C211yesmaximal, characteristic, complemented
4#3022×C131C211yesmaximal, characteristic, complemented
5#2199×C131C214yesmaximal, complemented
6#2197×C131C214yesmaximal, complemented
7#2129×C131C211yesmaximal, characteristic, complemented
8#2122×C131C211yesmaximal, characteristic, complemented
9#2120×C131C211yesmaximal, characteristic, complemented
10#585×C131C2211yescharacteristic
11C2×#137×C131—21no—
12H(3,𝔽4)×C131C2212yescomplemented
13#560×C131—21no—
14#559×C131—21no—
15#556×C131—21no—
16#555×C131—21no—
17#551×C131C2212yescomplemented
18#548×C131—21no—
19#546×C131—21no—
20#542×C131—22no—
21#542×C131—21no—
22#538×C131—22no—
23#536×C131C2211yescharacteristic
24#535×C131—21no—
25#535×C131C2211yescharacteristic
26#525×C131—21no—
27#525×C131—21no—
28#525×C131C2211yescharacteristic
29#458×C131—21no—
30#458×C131C2212yes—
31B(4,𝔽2)×C131—21no—
32B(4,𝔽2)×C131—22no—
33B(4,𝔽2)×C131C2212yes—
34B(4,𝔽2)×C131C2214yes—
35#456×C131—22no—
36#455×C131C2214yes—
37#421×C131—21no—
38#413×C131C2211yescharacteristic
39#410×C131—21no—
40#410×C131—21no—
41#410×C131C2211yescharacteristic
42#410×C131C2211yescharacteristic
43#354×C131C2214yescomplemented
44#352×C131C2212yescomplemented
45AΣL(1,𝔽16)×C131C2212yescomplemented
46AΣL(1,𝔽16)×C131C2214yescomplemented
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, complemented
62#137×C131—24no—
63#137×C131—42no—
64C2×Q16×C131—41no—
65C2×SD16×C131—41no—
66C2×M16×C131—21no—
67C4⋊Q8×C131—21no—
68C4⋊Q8×C131D412yescomplemented
69#127×C131—21no—
70#127×C131—41no—
71#126×C131—22no—
72#126×C131—22no—
73#126×C131—22no—
74#124×C131—22no—
75#124×C131—21no—
76#124×C131—21no—
77#124×C131—22no—
78#124×C131—22no—
79#124×C131—22no—
80#124×C131—22no—
81#124×C131—41no—
82#124×C131C2312yes—
83#123×C131—22no—
84#123×C131—22no—
85#123×C131—21no—
86#123×C131—21no—
87#123×C131—22no—
88#123×C131—22no—
89#123×C131D411yescharacteristic, complemented
90#123×C131C2311yescharacteristic
91C22⋊Q8×C131—21no—
92C22⋊Q8×C131—22no—
93C22⋊Q8×C131—21no—
94C22⋊Q8×C131—22no—
95C22⋊Q8×C131—21no—
96C22⋊Q8×C131—21no—
97C22⋊Q8×C131—41no—
98#121×C131—21no—
99#121×C131—22no—
100#121×C131—22no—
101#121×C131—22no—
102#121×C131—21no—
103#121×C131—21no—
104#121×C131—21no—
105#121×C131—42no—
106#121×C131—41no—
107#120×C131—22no—
108#120×C131—22no—
109#120×C131—22no—
110#120×C131—24no—
111#120×C131D411yescharacteristic, complemented
112#120×C131D412yescomplemented
113#120×C131C2311yescharacteristic
114#120×C131C2312yes—
115C4×Q8×C131—21no—
116C4×Q8×C131—22no—
117C4×D4×C131—22no—
118C4×D4×C131—22no—
119C4×D4×C131—21no—
120C4×D4×C131—22no—
121C4×D4×C131—21no—
122C4×D4×C131—21no—
123C4×D4×C131—42no—
124#117×C131—21no—
125#117×C131—22no—
126#117×C131—21no—
127#117×C131—21no—
128#117×C131D411yescharacteristic, complemented
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—24no—
138#99×C131—22no—
139#99×C131—22no—
140#99×C131C2312yes—
141#99×C131C2312yes—
142C24×C131C2×D412yes—
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—41no—
168C2×Q8×C131—41no—
169C2×Q8×C131—42no—
170C2×Q8×C131C2×D412yes—
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—21no—
182C2×D4×C131—22no—
183C2×D4×C131—21no—
184C2×D4×C131—21no—
185C2×D4×C131—41no—
186C2×D4×C131—41no—
187C2×D4×C131—42no—
188C2×D4×C131—42no—
189C2×D4×C131—42no—
190C2×D4×C131—41no—
191C2×D4×C131—42no—
192C2×D4×C131—44no—
193C2×D4×C131C2×D411yescharacteristic
194C2×D4×C131C2×D411yescharacteristic
195C2×D4×C131C2411yescharacteristic
196C22×C4×C131—22no—
197C22×C4×C131—22no—
198C22×C4×C131—22no—
199C22×C4×C131—22no—
200C22×C4×C131—21no—
201C22×C4×C131—21no—
202C22×C4×C131—21no—
203C22×C4×C131—41no—
204C22×C4×C131—41no—
205C22×C4×C131—41no—
206C22×C4×C131C2×D411yescharacteristic
207C22×C4×C131C2×D411yescharacteristic
208C22×C4×C131C2×D411yescharacteristic
209C22×C4×C131C2×D411yescharacteristic
210Q16×C131—44no—
211SD16×C131—44no—
212M16×C131—22no—
213M16×C131—41no—
214C2×C8×C131—41no—
215C4⋊C4×C131—22no—
216C4⋊C4×C131—22no—
217C4⋊C4×C131—22no—
218C4⋊C4×C131—21no—
219C4⋊C4×C131—21no—
220C4⋊C4×C131—22no—
221C4⋊C4×C131—22no—
222C4⋊C4×C131—21no—
223C4⋊C4×C131—21no—
224C4⋊C4×C131—21no—
225C4⋊C4×C131—41no—
226C4⋊C4×C131—41no—
227C4⋊C4×C131—42no—
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—21no—
236C22⋊C4×C131—21no—
237C22⋊C4×C131—22no—
238C22⋊C4×C131—22no—
239C22⋊C4×C131—21no—
240C22⋊C4×C131—22no—
241C22⋊C4×C131—22no—
242C22⋊C4×C131—21no—
243C22⋊C4×C131—22no—
244C22⋊C4×C131—22no—
245C22⋊C4×C131—42no—
246C22⋊C4×C131—44no—
247C22⋊C4×C131—42no—
248C22⋊C4×C131C2×D412yes—
249C22⋊C4×C131C2×D411yescharacteristic
250C22⋊C4×C131C2×D411yescharacteristic
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—22no—
261C23×C131—21no—
262C23×C131—41no—
263C23×C131—41no—
264C23×C131—42no—
265C23×C131—81no—
266C23×C131—82no—
267C23×C131#12011yescharacteristic
268C23×C131C22×D411yescharacteristic
269C23×C131C22×D411yescharacteristic
270Q8×C131—22no—
271Q8×C131—41no—
272Q8×C131—42no—
273Q8×C131—41no—
274Q8×C131—41no—
275Q8×C131—41no—
276Q8×C131—41no—
277Q8×C131—41no—
278Q8×C131—82no—
279D4×C131—22no—
280D4×C131—41no—
281D4×C131—41no—
282D4×C131—41no—
283D4×C131—41no—
284D4×C131—41no—
285D4×C131—42no—
286D4×C131—42no—
287D4×C131—42no—
288D4×C131—42no—
289D4×C131—41no—
290D4×C131—41no—
291D4×C131—41no—
292D4×C131—81no—
293D4×C131—81no—
294D4×C131—82no—
295D4×C131—82no—
296D4×C131—82no—
297D4×C131—81no—
298D4×C131—82no—
299D4×C131—84no—
300D4×C131—164no—
301C2×C4×C131—21no—
302C2×C4×C131—21no—
303C2×C4×C131—21no—
304C2×C4×C131—21no—
305C2×C4×C131—21no—
306C2×C4×C131—21no—
307C2×C4×C131—22no—
308C2×C4×C131—22no—
309C2×C4×C131—21no—
310C2×C4×C131—22no—
311C2×C4×C131—21no—
312C2×C4×C131—22no—
313C2×C4×C131—22no—
314C2×C4×C131—21no—
315C2×C4×C131—42no—
316C2×C4×C131—42no—
317C2×C4×C131—42no—
318C2×C4×C131—41no—
319C2×C4×C131—42no—
320C2×C4×C131—41no—
321C2×C4×C131—41no—
322C2×C4×C131—41no—
323C2×C4×C131—42no—
324C2×C4×C131—42no—
325C2×C4×C131—81no—
326C2×C4×C131—81no—
327C2×C4×C131—82no—
328C2×C4×C131—82no—
329C2×C4×C131#12011yescharacteristic
330C2×C4×C131#12011yescharacteristic
331C2×C4×C131#12011yescharacteristic
332C2×C4×C131C22×D411yescharacteristic
333C8×C131—42no—
334C22×C131—21no—
335C22×C131—21no—
336C22×C131—21no—
337C22×C131—41no—
338C22×C131—41no—
339C22×C131—41no—
340C22×C131—42no—
341C22×C131—41no—
342C22×C131—41no—
343C22×C131—42no—
344C22×C131—42no—
345C22×C131—42no—
346C22×C131—41no—
347C22×C131—42no—
348C22×C131—82no—
349C22×C131—82no—
350C22×C131—84no—
351C22×C131—81no—
352C22×C131—161no—
353C22×C131C2×#12011yescharacteristic
354C4×C131—21no—
355C4×C131—21no—
356C4×C131—21no—
357C4×C131—41no—
358C4×C131—42no—
359C4×C131—42no—
360C4×C131—41no—
361C4×C131—42no—
362C4×C131—41no—
363C4×C131—42no—
364C4×C131—82no—
365C4×C131—82no—
366C4×C131B(4,𝔽2)11yescharacteristic
367C4×C131B(4,𝔽2)11yescharacteristic
368C2×C131—21no—
369C2×C131—41no—
370C2×C131—41no—
371C2×C131—41no—
372C2×C131—81no—
373C2×C131—82no—
374C2×C131—82no—
375C2×C131C2×B(4,𝔽2)11yescharacteristic
376#33555C13111yesmaximal, characteristic, direct product factor, Sylow
377C131#3355511yescharacteristic, direct product factor, Sylow
378#3540C2×C13111yescharacteristic, complemented
379#3027C2×C13111yescharacteristic, complemented
380#3025C2×C13111yescharacteristic, complemented
381#3022C2×C13111yescharacteristic, complemented
382#2199C2×C13114yescomplemented
383#2197C2×C13114yescomplemented
384#2129C2×C13111yescharacteristic, complemented
385#2122C2×C13111yescharacteristic, complemented
386#2120C2×C13111yescharacteristic, complemented
387#585C22×C13111yescharacteristic
388C2×#137—21no—
389H(3,𝔽4)C22×C13112yescomplemented
390#560—21no—
391#559—21no—
392#556—21no—
393#555—21no—
394#551C22×C13112yescomplemented
395#548—21no—
396#546—21no—
397#542—22no—
398#542—21no—
399#538—22no—
400#536C22×C13111yescharacteristic
401#535—21no—
402#535C22×C13111yescharacteristic
403#525—21no—
404#525—21no—
405#525C22×C13111yescharacteristic
406#458—21no—
407#458C22×C13112yes—
408B(4,𝔽2)—21no—
409B(4,𝔽2)—22no—
410B(4,𝔽2)C22×C13114yes—
411B(4,𝔽2)C22×C13112yes—
412#456—22no—
413#455C22×C13114yes—
414#421—21no—
415#413C22×C13111yescharacteristic
416#410—21no—
417#410—21no—
418#410C22×C13111yescharacteristic
419#410C22×C13111yescharacteristic
420#354C22×C13114yescomplemented
421#352C22×C13112yescomplemented
422AΣL(1,𝔽16)C22×C13112yescomplemented
423AΣL(1,𝔽16)C22×C13114yescomplemented
4242−1+4—21no—
4252−1+4—41no—
426H(5,𝔽2)—21no—
427H(5,𝔽2)—21no—
428H(5,𝔽2)—41no—
429H(5,𝔽2)C23×C13112yes—
430C2×#41—21no—
431C2×#41—21no—
432C2×#41—21no—
433C2×#41—21no—
434C2×#41—42no—
435C2×#41C23×C13111yescharacteristic
436C22×Q8D4×C13111yescharacteristic, complemented
437C22×D4D4×C13111yescharacteristic, complemented
438C23×C4D4×C13111yescharacteristic, complemented
439#137—24no—
440#137—42no—
441C2×Q16—41no—
442C2×SD16—41no—
443C2×M16—21no—
444C4⋊Q8—21no—
445C4⋊Q8D4×C13112yescomplemented
446#127—21no—
447#127—41no—
448#126—22no—
449#126—22no—
450#126—22no—
451#124—22no—
452#124—21no—
453#124—21no—
454#124—22no—
455#124—22no—
456#124—22no—
457#124—22no—
458#124—41no—
459#124C23×C13112yes—
460#123—22no—
461#123—22no—
462#123—21no—
463#123—21no—
464#123—22no—
465#123—22no—
466#123D4×C13111yescharacteristic, complemented
467#123C23×C13111yescharacteristic
468C22⋊Q8—21no—
469C22⋊Q8—22no—
470C22⋊Q8—21no—
471C22⋊Q8—22no—
472C22⋊Q8—21no—
473C22⋊Q8—21no—
474C22⋊Q8—41no—
475#121—21no—
476#121—22no—
477#121—22no—
478#121—22no—
479#121—21no—
480#121—21no—
481#121—21no—
482#121—42no—
483#121—41no—
484#120—22no—
485#120—22no—
486#120—22no—
487#120—24no—
488#120D4×C13111yescharacteristic, complemented
489#120D4×C13112yescomplemented
490#120C23×C13111yescharacteristic
491#120C23×C13112yes—
492C4×Q8—21no—
493C4×Q8—22no—
494C4×D4—22no—
495C4×D4—22no—
496C4×D4—21no—
497C4×D4—22no—
498C4×D4—21no—
499C4×D4—21no—
500C4×D4—42no—
501#117—21no—
502#117—22no—
503#117—21no—
504#117—21no—
505#117D4×C13111yescharacteristic, complemented
506#117D4×C13111yescharacteristic, complemented
507#117D4×C13111yescharacteristic, complemented
508C2×C22⋊C4—22no—
509#104—24no—
510#101—21no—
511#100C23×C13112yes—
512#99—21no—
513#99—21no—
514#99—24no—
515#99—22no—
516#99—22no—
517#99C23×C13112yes—
518#99C23×C13112yes—
519C24C2×D4×C13112yes—
520C24C2×D4×C13111yescharacteristic
521#41—22no—
522#41—22no—
523#41—41no—
524#41—41no—
525#41—42no—
526#41—41no—
527#41—41no—
528#41—41no—
529#41—41no—
530#41—41no—
531#41—42no—
532#41—42no—
533#41—42no—
534#41—41no—
535#41—41no—
536#41—41no—
537#41—81no—
538#41—81no—
539C2×Q8—21no—
540C2×Q8—21no—
541C2×Q8—22no—
542C2×Q8—21no—
543C2×Q8—21no—
544C2×Q8—41no—
545C2×Q8—41no—
546C2×Q8—42no—
547C2×Q8C2×D4×C13112yes—
548C2×Q8C2×D4×C13111yescharacteristic
549C2×D4—21no—
550C2×D4—21no—
551C2×D4—21no—
552C2×D4—22no—
553C2×D4—22no—
554C2×D4—22no—
555C2×D4—22no—
556C2×D4—21no—
557C2×D4—22no—
558C2×D4—21no—
559C2×D4—22no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—41no—
563C2×D4—41no—
564C2×D4—42no—
565C2×D4—42no—
566C2×D4—42no—
567C2×D4—41no—
568C2×D4—42no—
569C2×D4—44no—
570C2×D4C2×D4×C13111yescharacteristic
571C2×D4C2×D4×C13111yescharacteristic
572C2×D4C24×C13111yescharacteristic
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—41no—
581C22×C4—41no—
582C22×C4—41no—
583C22×C4C2×D4×C13111yescharacteristic
584C22×C4C2×D4×C13111yescharacteristic
585C22×C4C2×D4×C13111yescharacteristic
586C22×C4C2×D4×C13111yescharacteristic
587Q16—44no—
588SD16—44no—
589M16—22no—
590M16—41no—
591C2×C8—41no—
592C4⋊C4—22no—
593C4⋊C4—22no—
594C4⋊C4—22no—
595C4⋊C4—21no—
596C4⋊C4—21no—
597C4⋊C4—21no—
598C4⋊C4—21no—
599C4⋊C4—22no—
600C4⋊C4—22no—
601C4⋊C4—21no—
602C4⋊C4—41no—
603C4⋊C4—41no—
604C4⋊C4—42no—
605C22⋊C4—22no—
606C22⋊C4—22no—
607C22⋊C4—22no—
608C22⋊C4—22no—
609C22⋊C4—22no—
610C22⋊C4—22no—
611C22⋊C4—21no—
612C22⋊C4—21no—
613C22⋊C4—21no—
614C22⋊C4—22no—
615C22⋊C4—22no—
616C22⋊C4—21no—
617C22⋊C4—22no—
618C22⋊C4—22no—
619C22⋊C4—21no—
620C22⋊C4—22no—
621C22⋊C4—22no—
622C22⋊C4—42no—
623C22⋊C4—44no—
624C22⋊C4—42no—
625C22⋊C4C2×D4×C13112yes—
626C22⋊C4C2×D4×C13111yescharacteristic
627C22⋊C4C2×D4×C13111yescharacteristic
628C42—22no—
629C42—22no—
630C42—21no—
631C42—21no—
632C42—41no—
633C42—41no—
634C42C2×D4×C13112yes—
635C23—22no—
636C23—22no—
637C23—22no—
638C23—21no—
639C23—41no—
640C23—41no—
641C23—42no—
642C23—81no—
643C23—82no—
644C23#120×C13111yescharacteristic
645C23C22×D4×C13111yescharacteristic
646C23C22×D4×C13111yescharacteristic
647Q8—22no—
648Q8—41no—
649Q8—42no—
650Q8—41no—
651Q8—41no—
652Q8—41no—
653Q8—41no—
654Q8—41no—
655Q8—82no—
656D4—22no—
657D4—41no—
658D4—41no—
659D4—41no—
660D4—41no—
661D4—41no—
662D4—42no—
663D4—42no—
664D4—42no—
665D4—42no—
666D4—41no—
667D4—41no—
668D4—41no—
669D4—81no—
670D4—82no—
671D4—81no—
672D4—82no—
673D4—82no—
674D4—82no—
675D4—81no—
676D4—84no—
677D4—164no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—21no—
687C2×C4—22no—
688C2×C4—21no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—21no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—41no—
696C2×C4—42no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—81no—
703C2×C4—81no—
704C2×C4—82no—
705C2×C4—82no—
706C2×C4#120×C13111yescharacteristic
707C2×C4#120×C13111yescharacteristic
708C2×C4#120×C13111yescharacteristic
709C2×C4C22×D4×C13111yescharacteristic
710C8—42no—
711C22—21no—
712C22—21no—
713C22—21no—
714C22—41no—
715C22—41no—
716C22—41no—
717C22—42no—
718C22—41no—
719C22—41no—
720C22—42no—
721C22—42no—
722C22—42no—
723C22—41no—
724C22—42no—
725C22—82no—
726C22—82no—
727C22—84no—
728C22—81no—
729C22—161no—
730C22C2×#120×C13111yescharacteristic
731C4—21no—
732C4—21no—
733C4—21no—
734C4—41no—
735C4—42no—
736C4—42no—
737C4—41no—
738C4—42no—
739C4—41no—
740C4—42no—
741C4—82no—
742C4—82no—
743C4B(4,𝔽2)×C13111yescharacteristic
744C4B(4,𝔽2)×C13111yescharacteristic
745C2—21no—
746C2—41no—
747C2—41no—
748C2—41no—
749C2—81no—
750C2—82no—
751C2—82no—
752C2C2×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. #3027×C131C2semidirect
3. #3025×C131C2semidirect
4. #3022×C131C2semidirect
5. #2199×C131C2semidirect
6. #2197×C131C2semidirect
7. #2129×C131C2semidirect
8. #2122×C131C2semidirect
9. #2120×C131C2semidirect
12. H(3,𝔽4)×C131C22semidirect
17. #551×C131C22semidirect
43. #354×C131C22semidirect
44. #352×C131C22semidirect
45. AΣL(1,𝔽16)×C131C22semidirect
46. AΣL(1,𝔽16)×C131C22semidirect
59. C22×Q8×C131D4semidirect
60. C22×D4×C131D4semidirect
61. C23×C4×C131D4semidirect
68. C4⋊Q8×C131D4semidirect
89. #123×C131D4semidirect
111. #120×C131D4semidirect
112. #120×C131D4semidirect
128. #117×C131D4semidirect
129. #117×C131D4semidirect
130. #117×C131D4semidirect
376. #33555C131direct (N × H)
377. C131#33555direct (N × H)
378. #3540C2×C131semidirect
379. #3027C2×C131semidirect
380. #3025C2×C131semidirect
381. #3022C2×C131semidirect
382. #2199C2×C131semidirect
383. #2197C2×C131semidirect
384. #2129C2×C131semidirect
385. #2122C2×C131semidirect
386. #2120C2×C131semidirect
389. H(3,𝔽4)C22×C131semidirect
394. #551C22×C131semidirect
420. #354C22×C131semidirect
421. #352C22×C131semidirect
422. AΣL(1,𝔽16)C22×C131semidirect
423. AΣL(1,𝔽16)C22×C131semidirect
436. C22×Q8D4×C131semidirect
437. C22×D4D4×C131semidirect
438. C23×C4D4×C131semidirect
445. C4⋊Q8D4×C131semidirect
466. #123D4×C131semidirect
488. #120D4×C131semidirect
489. #120D4×C131semidirect
505. #117D4×C131semidirect
506. #117D4×C131semidirect
507. #117D4×C131semidirect

Maximal subgroups

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

subgroupindex
#3540×C1312
#3027×C1312
#3025×C1312
#3022×C1312
#2199×C1312
#2197×C1312
#2129×C1312
#2122×C1312
#2120×C1312
#33555131