Finite Group Databasebeta

← C131×#33560 #45719444

Subgroups — C131×#33560 #45719444

Order 33536.

1132 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3551×C131C211yesmaximal, characteristic, complemented
2#3028×C131C211yesmaximal, characteristic, complemented
3#3027×C131C211yesmaximal, characteristic, complemented
4#3018×C131C211yesmaximal, characteristic, complemented
5#2200×C131C214yesmaximal, complemented
6#2197×C131C214yesmaximal, complemented
7#2126×C131C211yesmaximal, characteristic, complemented
8#2123×C131C211yesmaximal, characteristic, complemented
9#2122×C131C211yesmaximal, characteristic, complemented
10#585×C131C2211yescharacteristic
11#575×C131—21no—
12#563×C131—21no—
13#560×C131C2212yescomplemented
14#555×C131—21no—
15#553×C131—21no—
16#552×C131—21no—
17#551×C131C2212yescomplemented
18#548×C131—21no—
19#546×C131—21no—
20#540×C131—22no—
21#538×C131—22no—
22#537×C131—21no—
23#536×C131—21no—
24#536×C131C2211yescharacteristic
25#535×C131—21no—
26#535×C131C2211yescharacteristic
27#532×C131C2211yescharacteristic
28#529×C131—21no—
29#458×C131—22no—
30#458×C131C2214yes—
31B(4,𝔽2)×C131—22no—
32B(4,𝔽2)×C131C2214yes—
33#456×C131—21no—
34#455×C131C2212yes—
35#454×C131—21no—
36#453×C131C2212yes—
37C2×#104×C131—21no—
38#413×C131C2211yescharacteristic
39#410×C131—21no—
40#410×C131—21no—
41#410×C131C2211yescharacteristic
42#410×C131C2211yescharacteristic
43#354×C131C2212yescomplemented
44#353×C131C2212yescomplemented
45#352×C131C2214yescomplemented
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×C131D411yescharacteristic, complemented
59C2×#41×C131C2311yescharacteristic
60C22×Q8×C131D411yescharacteristic, complemented
61C22×D4×C131D411yescharacteristic
62#137×C131—22no—
63#137×C131—41no—
64AGL(1,ℤ/8)×C131—22no—
65AGL(1,ℤ/8)×C131—41no—
66#135×C131—42no—
67C2×M16×C131—21no—
68C4⋊Q8×C131—21no—
69C4⋊Q8×C131—41no—
70C4⋊Q8×C131D411yescharacteristic, complemented
71#127×C131—21no—
72#127×C131—41no—
73#127×C131C2311yescharacteristic
74#126×C131—22no—
75#126×C131—22no—
76#126×C131—22no—
77#125×C131—21no—
78#125×C131—22no—
79#124×C131—21no—
80#124×C131—22no—
81#124×C131—21no—
82#124×C131—21no—
83#124×C131—41no—
84#124×C131—41no—
85#124×C131D411yescharacteristic, complemented
86#124×C131C2311yescharacteristic
87#123×C131—22no—
88#123×C131—22no—
89#123×C131—22no—
90#123×C131—22no—
91#123×C131—24no—
92#123×C131D412yescomplemented
93#123×C131C2312yes—
94C22⋊Q8×C131—21no—
95C22⋊Q8×C131—22no—
96C22⋊Q8×C131—22no—
97C22⋊Q8×C131—21no—
98C22⋊Q8×C131—21no—
99C22⋊Q8×C131—42no—
100#121×C131—22no—
101#121×C131—22no—
102#121×C131—21no—
103#121×C131—22no—
104#121×C131—21no—
105#121×C131—21no—
106#121×C131—22no—
107#121×C131—21no—
108#121×C131—21no—
109#121×C131—22no—
110#121×C131—22no—
111#121×C131—42no—
112#120×C131—22no—
113#120×C131—24no—
114#120×C131D412yes—
115#120×C131C2312yes—
116C4×Q8×C131—21no—
117C4×D4×C131—22no—
118C4×D4×C131—21no—
119C4×D4×C131—22no—
120C4×D4×C131—21no—
121C4×D4×C131—21no—
122C4×D4×C131—22no—
123#117×C131—22no—
124#117×C131—22no—
125#117×C131—21no—
126#117×C131—21no—
127#117×C131D411yescharacteristic
128#117×C131D411yescharacteristic, complemented
129C2×C4⋊C4×C131—21no—
130C2×C22⋊C4×C131—22no—
131C2×C42×C131D411yescharacteristic, complemented
132#104×C131—22no—
133#104×C131—22no—
134#101×C131—21no—
135#100×C131C2312yes—
136#99×C131—21no—
137#99×C131—21no—
138#99×C131—24no—
139#99×C131—24no—
140#99×C131C2312yes—
141#99×C131C2312yes—
142C24×C131C2×D412yes—
143#41×C131—22no—
144#41×C131—22no—
145#41×C131—41no—
146#41×C131—41no—
147#41×C131—42no—
148#41×C131—41no—
149#41×C131—41no—
150#41×C131—41no—
151#41×C131—41no—
152#41×C131—41no—
153#41×C131—42no—
154#41×C131—42no—
155#41×C131—41no—
156#41×C131—41no—
157#41×C131—42no—
158#41×C131—41no—
159#41×C131—41no—
160#41×C131—41no—
161#41×C131—81no—
162#41×C131—81no—
163C2×Q8×C131—21no—
164C2×Q8×C131—21no—
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×Q8×C131C2×D411yescharacteristic
173C2×D4×C131—21no—
174C2×D4×C131—21no—
175C2×D4×C131—21no—
176C2×D4×C131—22no—
177C2×D4×C131—22no—
178C2×D4×C131—22no—
179C2×D4×C131—22no—
180C2×D4×C131—22no—
181C2×D4×C131—21no—
182C2×D4×C131—21no—
183C2×D4×C131—22no—
184C2×D4×C131—21no—
185C2×D4×C131—21no—
186C2×D4×C131—21no—
187C2×D4×C131—41no—
188C2×D4×C131—41no—
189C2×D4×C131—42no—
190C2×D4×C131—42no—
191C2×D4×C131—42no—
192C2×D4×C131—41no—
193C2×D4×C131—44no—
194C2×D4×C131C2×D411yescharacteristic
195C2×D4×C131C2×D411yescharacteristic
196C2×D4×C131C2×D411yescharacteristic
197C2×D4×C131C2411yescharacteristic
198C22×C4×C131—22no—
199C22×C4×C131—22no—
200C22×C4×C131—22no—
201C22×C4×C131—22no—
202C22×C4×C131—22no—
203C22×C4×C131—21no—
204C22×C4×C131—21no—
205C22×C4×C131—41no—
206C22×C4×C131C2×D411yescharacteristic
207C22×C4×C131C2×D411yescharacteristic
208C22×C4×C131C2×D411yescharacteristic
209C22×C4×C131C2×D412yes—
210Q16×C131—42no—
211SD16×C131—42no—
212SD16×C131—42no—
213D8×C131—42no—
214M16×C131—22no—
215M16×C131—41no—
216C2×C8×C131—41no—
217C4⋊C4×C131—22no—
218C4⋊C4×C131—22no—
219C4⋊C4×C131—22no—
220C4⋊C4×C131—22no—
221C4⋊C4×C131—22no—
222C4⋊C4×C131—22no—
223C4⋊C4×C131—21no—
224C4⋊C4×C131—21no—
225C4⋊C4×C131—21no—
226C4⋊C4×C131—21no—
227C4⋊C4×C131—22no—
228C4⋊C4×C131—41no—
229C4⋊C4×C131—41no—
230C4⋊C4×C131—44no—
231C22⋊C4×C131—22no—
232C22⋊C4×C131—22no—
233C22⋊C4×C131—22no—
234C22⋊C4×C131—22no—
235C22⋊C4×C131—22no—
236C22⋊C4×C131—22no—
237C22⋊C4×C131—21no—
238C22⋊C4×C131—22no—
239C22⋊C4×C131—21no—
240C22⋊C4×C131—21no—
241C22⋊C4×C131—21no—
242C22⋊C4×C131—22no—
243C22⋊C4×C131—22no—
244C22⋊C4×C131—22no—
245C22⋊C4×C131—22no—
246C22⋊C4×C131—44no—
247C22⋊C4×C131—44no—
248C22⋊C4×C131C2×D412yes—
249C22⋊C4×C131C2×D412yes—
250C42×C131—22no—
251C42×C131—21no—
252C42×C131—21no—
253C42×C131—21no—
254C42×C131—41no—
255C42×C131—41no—
256C42×C131C2×D411yescharacteristic
257C42×C131C2×D411yescharacteristic
258C23×C131—22no—
259C23×C131—22no—
260C23×C131—22no—
261C23×C131—21no—
262C23×C131—41no—
263C23×C131—42no—
264C23×C131—82no—
265C23×C131#12011yescharacteristic
266C23×C131C22×D411yescharacteristic
267C23×C131C22×D411yescharacteristic
268Q8×C131—22no—
269Q8×C131—41no—
270Q8×C131—41no—
271Q8×C131—41no—
272Q8×C131—41no—
273Q8×C131—41no—
274Q8×C131—41no—
275Q8×C131—41no—
276Q8×C131—81no—
277D4×C131—22no—
278D4×C131—41no—
279D4×C131—41no—
280D4×C131—41no—
281D4×C131—41no—
282D4×C131—41no—
283D4×C131—41no—
284D4×C131—42no—
285D4×C131—42no—
286D4×C131—42no—
287D4×C131—42no—
288D4×C131—41no—
289D4×C131—41no—
290D4×C131—41no—
291D4×C131—81no—
292D4×C131—81no—
293D4×C131—82no—
294D4×C131—82no—
295D4×C131—82no—
296D4×C131—81no—
297D4×C131—81no—
298D4×C131—82no—
299D4×C131—164no—
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—21no—
311C2×C4×C131—22no—
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—42no—
322C2×C4×C131—42no—
323C2×C4×C131—42no—
324C2×C4×C131—82no—
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—41no—
340C22×C131—42no—
341C22×C131—41no—
342C22×C131—42no—
343C22×C131—42no—
344C22×C131—41no—
345C22×C131—42no—
346C22×C131—82no—
347C22×C131—84no—
348C22×C131—82no—
349C22×C131—161no—
350C22×C131C2×#12011yescharacteristic
351C4×C131—21no—
352C4×C131—21no—
353C4×C131—21no—
354C4×C131—41no—
355C4×C131—42no—
356C4×C131—42no—
357C4×C131—41no—
358C4×C131—42no—
359C4×C131—41no—
360C4×C131—42no—
361C4×C131—82no—
362C4×C131—82no—
363C4×C131B(4,𝔽2)11yescharacteristic
364C4×C131B(4,𝔽2)11yescharacteristic
365C2×C131—21no—
366C2×C131—41no—
367C2×C131—41no—
368C2×C131—41no—
369C2×C131—81no—
370C2×C131—82no—
371C2×C131—82no—
372C2×C131C2×B(4,𝔽2)11yescharacteristic
373#33560C13111yesmaximal, characteristic, direct product factor, Sylow
374C131#3356011yescharacteristic, direct product factor, Sylow
375#3551C2×C13111yescharacteristic, complemented
376#3028C2×C13111yescharacteristic, complemented
377#3027C2×C13111yescharacteristic, complemented
378#3018C2×C13111yescharacteristic, complemented
379#2200C2×C13114yescomplemented
380#2197C2×C13114yescomplemented
381#2126C2×C13111yescharacteristic, complemented
382#2123C2×C13111yescharacteristic, complemented
383#2122C2×C13111yescharacteristic, complemented
384#585C22×C13111yescharacteristic
385#575—21no—
386#563—21no—
387#560C22×C13112yescomplemented
388#555—21no—
389#553—21no—
390#552—21no—
391#551C22×C13112yescomplemented
392#548—21no—
393#546—21no—
394#540—22no—
395#538—22no—
396#537—21no—
397#536—21no—
398#536C22×C13111yescharacteristic
399#535—21no—
400#535C22×C13111yescharacteristic
401#532C22×C13111yescharacteristic
402#529—21no—
403#458—22no—
404#458C22×C13114yes—
405B(4,𝔽2)—22no—
406B(4,𝔽2)C22×C13114yes—
407#456—21no—
408#455C22×C13112yes—
409#454—21no—
410#453C22×C13112yes—
411C2×#104—21no—
412#413C22×C13111yescharacteristic
413#410—21no—
414#410—21no—
415#410C22×C13111yescharacteristic
416#410C22×C13111yescharacteristic
417#354C22×C13112yescomplemented
418#353C22×C13112yescomplemented
419#352C22×C13114yescomplemented
420AΣL(1,𝔽16)C22×C13114yescomplemented
4212−1+4—21no—
4222−1+4—41no—
423H(5,𝔽2)—21no—
424H(5,𝔽2)—21no—
425H(5,𝔽2)—41no—
426H(5,𝔽2)C23×C13112yes—
427C2×#41—21no—
428C2×#41—21no—
429C2×#41—21no—
430C2×#41—21no—
431C2×#41—42no—
432C2×#41D4×C13111yescharacteristic, complemented
433C2×#41C23×C13111yescharacteristic
434C22×Q8D4×C13111yescharacteristic, complemented
435C22×D4D4×C13111yescharacteristic
436#137—22no—
437#137—41no—
438AGL(1,ℤ/8)—22no—
439AGL(1,ℤ/8)—41no—
440#135—42no—
441C2×M16—21no—
442C4⋊Q8—21no—
443C4⋊Q8—41no—
444C4⋊Q8D4×C13111yescharacteristic, complemented
445#127—21no—
446#127—41no—
447#127C23×C13111yescharacteristic
448#126—22no—
449#126—22no—
450#126—22no—
451#125—21no—
452#125—22no—
453#124—21no—
454#124—22no—
455#124—21no—
456#124—21no—
457#124—41no—
458#124—41no—
459#124D4×C13111yescharacteristic, complemented
460#124C23×C13111yescharacteristic
461#123—22no—
462#123—22no—
463#123—22no—
464#123—22no—
465#123—24no—
466#123D4×C13112yescomplemented
467#123C23×C13112yes—
468C22⋊Q8—21no—
469C22⋊Q8—22no—
470C22⋊Q8—22no—
471C22⋊Q8—21no—
472C22⋊Q8—21no—
473C22⋊Q8—42no—
474#121—22no—
475#121—22no—
476#121—21no—
477#121—22no—
478#121—21no—
479#121—21no—
480#121—22no—
481#121—21no—
482#121—21no—
483#121—22no—
484#121—22no—
485#121—42no—
486#120—22no—
487#120—24no—
488#120D4×C13112yes—
489#120C23×C13112yes—
490C4×Q8—21no—
491C4×D4—22no—
492C4×D4—21no—
493C4×D4—22no—
494C4×D4—21no—
495C4×D4—21no—
496C4×D4—22no—
497#117—22no—
498#117—22no—
499#117—21no—
500#117—21no—
501#117D4×C13111yescharacteristic
502#117D4×C13111yescharacteristic, complemented
503C2×C4⋊C4—21no—
504C2×C22⋊C4—22no—
505C2×C42D4×C13111yescharacteristic, complemented
506#104—22no—
507#104—22no—
508#101—21no—
509#100C23×C13112yes—
510#99—21no—
511#99—21no—
512#99—24no—
513#99—24no—
514#99C23×C13112yes—
515#99C23×C13112yes—
516C24C2×D4×C13112yes—
517#41—22no—
518#41—22no—
519#41—41no—
520#41—41no—
521#41—42no—
522#41—41no—
523#41—41no—
524#41—41no—
525#41—41no—
526#41—41no—
527#41—42no—
528#41—42no—
529#41—41no—
530#41—41no—
531#41—42no—
532#41—41no—
533#41—41no—
534#41—41no—
535#41—81no—
536#41—81no—
537C2×Q8—21no—
538C2×Q8—21no—
539C2×Q8—21no—
540C2×Q8—21no—
541C2×Q8—21no—
542C2×Q8—41no—
543C2×Q8—41no—
544C2×Q8—42no—
545C2×Q8C2×D4×C13111yescharacteristic
546C2×Q8C2×D4×C13111yescharacteristic
547C2×D4—21no—
548C2×D4—21no—
549C2×D4—21no—
550C2×D4—22no—
551C2×D4—22no—
552C2×D4—22no—
553C2×D4—22no—
554C2×D4—22no—
555C2×D4—21no—
556C2×D4—21no—
557C2×D4—22no—
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—41no—
562C2×D4—41no—
563C2×D4—42no—
564C2×D4—42no—
565C2×D4—42no—
566C2×D4—41no—
567C2×D4—44no—
568C2×D4C2×D4×C13111yescharacteristic
569C2×D4C2×D4×C13111yescharacteristic
570C2×D4C2×D4×C13111yescharacteristic
571C2×D4C24×C13111yescharacteristic
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—41no—
580C22×C4C2×D4×C13111yescharacteristic
581C22×C4C2×D4×C13111yescharacteristic
582C22×C4C2×D4×C13111yescharacteristic
583C22×C4C2×D4×C13112yes—
584Q16—42no—
585SD16—42no—
586SD16—42no—
587D8—42no—
588M16—22no—
589M16—41no—
590C2×C8—41no—
591C4⋊C4—22no—
592C4⋊C4—22no—
593C4⋊C4—22no—
594C4⋊C4—22no—
595C4⋊C4—22no—
596C4⋊C4—21no—
597C4⋊C4—21no—
598C4⋊C4—22no—
599C4⋊C4—21no—
600C4⋊C4—21no—
601C4⋊C4—22no—
602C4⋊C4—41no—
603C4⋊C4—41no—
604C4⋊C4—44no—
605C22⋊C4—22no—
606C22⋊C4—22no—
607C22⋊C4—22no—
608C22⋊C4—22no—
609C22⋊C4—22no—
610C22⋊C4—22no—
611C22⋊C4—21no—
612C22⋊C4—22no—
613C22⋊C4—21no—
614C22⋊C4—21no—
615C22⋊C4—21no—
616C22⋊C4—22no—
617C22⋊C4—22no—
618C22⋊C4—22no—
619C22⋊C4—22no—
620C22⋊C4—44no—
621C22⋊C4—44no—
622C22⋊C4C2×D4×C13112yes—
623C22⋊C4C2×D4×C13112yes—
624C42—22no—
625C42—21no—
626C42—21no—
627C42—21no—
628C42—41no—
629C42—41no—
630C42C2×D4×C13111yescharacteristic
631C42C2×D4×C13111yescharacteristic
632C23—22no—
633C23—22no—
634C23—22no—
635C23—21no—
636C23—41no—
637C23—42no—
638C23—82no—
639C23#120×C13111yescharacteristic
640C23C22×D4×C13111yescharacteristic
641C23C22×D4×C13111yescharacteristic
642Q8—22no—
643Q8—41no—
644Q8—41no—
645Q8—41no—
646Q8—41no—
647Q8—41no—
648Q8—41no—
649Q8—41no—
650Q8—81no—
651D4—22no—
652D4—41no—
653D4—41no—
654D4—41no—
655D4—41no—
656D4—41no—
657D4—41no—
658D4—42no—
659D4—42no—
660D4—42no—
661D4—42no—
662D4—41no—
663D4—41no—
664D4—41no—
665D4—81no—
666D4—81no—
667D4—82no—
668D4—82no—
669D4—82no—
670D4—82no—
671D4—81no—
672D4—81no—
673D4—164no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—21no—
683C2×C4—22no—
684C2×C4—21no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—21no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—41no—
692C2×C4—42no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—82no—
699C2×C4—82no—
700C2×C4—81no—
701C2×C4—82no—
702C2×C4#120×C13111yescharacteristic
703C2×C4#120×C13111yescharacteristic
704C2×C4#120×C13111yescharacteristic
705C2×C4C22×D4×C13111yescharacteristic
706C8—42no—
707C22—21no—
708C22—21no—
709C22—21no—
710C22—41no—
711C22—41no—
712C22—41no—
713C22—41no—
714C22—42no—
715C22—41no—
716C22—42no—
717C22—42no—
718C22—41no—
719C22—42no—
720C22—82no—
721C22—84no—
722C22—82no—
723C22—161no—
724C22C2×#120×C13111yescharacteristic
725C4—21no—
726C4—21no—
727C4—21no—
728C4—41no—
729C4—42no—
730C4—42no—
731C4—41no—
732C4—42no—
733C4—41no—
734C4—42no—
735C4—82no—
736C4—82no—
737C4B(4,𝔽2)×C13111yescharacteristic
738C4B(4,𝔽2)×C13111yescharacteristic
739C2—21no—
740C2—41no—
741C2—41no—
742C2—41no—
743C2—82no—
744C2—81no—
745C2—82no—
746C2C2×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. #3551×C131C2semidirect
2. #3028×C131C2semidirect
3. #3027×C131C2semidirect
4. #3018×C131C2semidirect
5. #2200×C131C2semidirect
6. #2197×C131C2semidirect
7. #2126×C131C2semidirect
8. #2123×C131C2semidirect
9. #2122×C131C2semidirect
13. #560×C131C22semidirect
17. #551×C131C22semidirect
43. #354×C131C22semidirect
44. #353×C131C22semidirect
45. #352×C131C22semidirect
46. AΣL(1,𝔽16)×C131C22semidirect
58. C2×#41×C131D4semidirect
60. C22×Q8×C131D4semidirect
70. C4⋊Q8×C131D4semidirect
85. #124×C131D4semidirect
92. #123×C131D4semidirect
128. #117×C131D4semidirect
131. C2×C42×C131D4semidirect
373. #33560C131direct (N × H)
374. C131#33560direct (N × H)
375. #3551C2×C131semidirect
376. #3028C2×C131semidirect
377. #3027C2×C131semidirect
378. #3018C2×C131semidirect
379. #2200C2×C131semidirect
380. #2197C2×C131semidirect
381. #2126C2×C131semidirect
382. #2123C2×C131semidirect
383. #2122C2×C131semidirect
387. #560C22×C131semidirect
391. #551C22×C131semidirect
417. #354C22×C131semidirect
418. #353C22×C131semidirect
419. #352C22×C131semidirect
420. AΣL(1,𝔽16)C22×C131semidirect
432. C2×#41D4×C131semidirect
434. C22×Q8D4×C131semidirect
444. C4⋊Q8D4×C131semidirect
459. #124D4×C131semidirect
466. #123D4×C131semidirect
502. #117D4×C131semidirect
505. C2×C42D4×C131semidirect

Maximal subgroups

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

subgroupindex
#3551×C1312
#3028×C1312
#3027×C1312
#3018×C1312
#2200×C1312
#2197×C1312
#2126×C1312
#2123×C1312
#2122×C1312
#33560131