Finite Group Databasebeta

← C31×#33560 #21490319

Subgroups — C31×#33560 #21490319

Order 7936.

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
1C31×#3551C211yesmaximal, characteristic, complemented
2C31×#3028C211yesmaximal, characteristic, complemented
3C31×#3027C211yesmaximal, characteristic, complemented
4C31×#3018C211yesmaximal, characteristic, complemented
5C31×#2200C214yesmaximal, complemented
6C31×#2197C214yesmaximal, complemented
7C31×#2126C211yesmaximal, characteristic, complemented
8C31×#2123C211yesmaximal, characteristic, complemented
9C31×#2122C211yesmaximal, characteristic, complemented
10C31×#585C2211yescharacteristic
11C31×#575—21no—
12C31×#563—21no—
13C31×#560C2212yescomplemented
14C31×#555—21no—
15C31×#553—21no—
16C31×#552—21no—
17C31×#551C2212yescomplemented
18C31×#548—21no—
19C31×#546—21no—
20C31×#540—22no—
21C31×#538—22no—
22C31×#537—21no—
23C31×#536—21no—
24C31×#536C2211yescharacteristic
25C31×#535—21no—
26C31×#535C2211yescharacteristic
27C31×#532C2211yescharacteristic
28C31×#529—21no—
29C31×#458—22no—
30C31×#458C2214yes—
31C31×B(4,𝔽2)—22no—
32C31×B(4,𝔽2)C2214yes—
33C31×#456—21no—
34C31×#455C2212yes—
35C31×#454—21no—
36C31×#453C2212yes—
37C2×C31×#104—21no—
38C31×#413C2211yescharacteristic
39C31×#410—21no—
40C31×#410—21no—
41C31×#410C2211yescharacteristic
42C31×#410C2211yescharacteristic
43C31×#354C2212yescomplemented
44C31×#353C2212yescomplemented
45C31×#352C2214yescomplemented
46C31×AΣL(1,𝔽16)C2214yescomplemented
47C31×2−1+4—21no—
48C31×2−1+4—41no—
49C31×H(5,𝔽2)—21no—
50C31×H(5,𝔽2)—21no—
51C31×H(5,𝔽2)—41no—
52C31×H(5,𝔽2)C2312yes—
53C2×#41×C31—21no—
54C2×#41×C31—21no—
55C2×#41×C31—21no—
56C2×#41×C31—21no—
57C2×#41×C31—42no—
58C2×#41×C31D411yescharacteristic, complemented
59C2×#41×C31C2311yescharacteristic
60C22×Q8×C31D411yescharacteristic, complemented
61C22×D4×C31D411yescharacteristic
62C31×#137—22no—
63C31×#137—41no—
64C31×AGL(1,ℤ/8)—22no—
65C31×AGL(1,ℤ/8)—41no—
66C31×#135—42no—
67C2×M16×C31—21no—
68C31×C4⋊Q8—21no—
69C31×C4⋊Q8—41no—
70C31×C4⋊Q8D411yescharacteristic, complemented
71C31×#127—21no—
72C31×#127—41no—
73C31×#127C2311yescharacteristic
74C31×#126—22no—
75C31×#126—22no—
76C31×#126—22no—
77C31×#125—21no—
78C31×#125—22no—
79C31×#124—21no—
80C31×#124—22no—
81C31×#124—21no—
82C31×#124—21no—
83C31×#124—41no—
84C31×#124—41no—
85C31×#124D411yescharacteristic, complemented
86C31×#124C2311yescharacteristic
87C31×#123—22no—
88C31×#123—22no—
89C31×#123—22no—
90C31×#123—22no—
91C31×#123—24no—
92C31×#123D412yescomplemented
93C31×#123C2312yes—
94C31×C22⋊Q8—21no—
95C31×C22⋊Q8—22no—
96C31×C22⋊Q8—22no—
97C31×C22⋊Q8—21no—
98C31×C22⋊Q8—21no—
99C31×C22⋊Q8—42no—
100C31×#121—22no—
101C31×#121—22no—
102C31×#121—21no—
103C31×#121—22no—
104C31×#121—21no—
105C31×#121—21no—
106C31×#121—22no—
107C31×#121—21no—
108C31×#121—21no—
109C31×#121—22no—
110C31×#121—22no—
111C31×#121—42no—
112C31×#120—22no—
113C31×#120—24no—
114C31×#120D412yes—
115C31×#120C2312yes—
116C4×Q8×C31—21no—
117C4×D4×C31—22no—
118C4×D4×C31—21no—
119C4×D4×C31—22no—
120C4×D4×C31—21no—
121C4×D4×C31—21no—
122C4×D4×C31—22no—
123C31×#117—22no—
124C31×#117—22no—
125C31×#117—21no—
126C31×#117—21no—
127C31×#117D411yescharacteristic
128C31×#117D411yescharacteristic, complemented
129C2×C4⋊C4×C31—21no—
130C2×C22⋊C4×C31—22no—
131C2×C42×C31D411yescharacteristic, complemented
132C31×#104—22no—
133C31×#104—22no—
134C31×#101—21no—
135C31×#100C2312yes—
136C31×#99—21no—
137C31×#99—21no—
138C31×#99—24no—
139C31×#99—24no—
140C31×#99C2312yes—
141C31×#99C2312yes—
142C24×C31C2×D412yes—
143#41×C31—22no—
144#41×C31—22no—
145#41×C31—41no—
146#41×C31—41no—
147#41×C31—42no—
148#41×C31—41no—
149#41×C31—41no—
150#41×C31—41no—
151#41×C31—41no—
152#41×C31—41no—
153#41×C31—42no—
154#41×C31—42no—
155#41×C31—41no—
156#41×C31—41no—
157#41×C31—42no—
158#41×C31—41no—
159#41×C31—41no—
160#41×C31—41no—
161#41×C31—81no—
162#41×C31—81no—
163C2×Q8×C31—21no—
164C2×Q8×C31—21no—
165C2×Q8×C31—21no—
166C2×Q8×C31—21no—
167C2×Q8×C31—21no—
168C2×Q8×C31—41no—
169C2×Q8×C31—41no—
170C2×Q8×C31—42no—
171C2×Q8×C31C2×D411yescharacteristic
172C2×Q8×C31C2×D411yescharacteristic
173C2×D4×C31—21no—
174C2×D4×C31—21no—
175C2×D4×C31—21no—
176C2×D4×C31—22no—
177C2×D4×C31—22no—
178C2×D4×C31—22no—
179C2×D4×C31—22no—
180C2×D4×C31—22no—
181C2×D4×C31—21no—
182C2×D4×C31—21no—
183C2×D4×C31—22no—
184C2×D4×C31—21no—
185C2×D4×C31—21no—
186C2×D4×C31—21no—
187C2×D4×C31—41no—
188C2×D4×C31—41no—
189C2×D4×C31—42no—
190C2×D4×C31—42no—
191C2×D4×C31—42no—
192C2×D4×C31—41no—
193C2×D4×C31—44no—
194C2×D4×C31C2×D411yescharacteristic
195C2×D4×C31C2×D411yescharacteristic
196C2×D4×C31C2×D411yescharacteristic
197C2×D4×C31C2411yescharacteristic
198C22×C4×C31—22no—
199C22×C4×C31—22no—
200C22×C4×C31—22no—
201C22×C4×C31—22no—
202C22×C4×C31—22no—
203C22×C4×C31—21no—
204C22×C4×C31—21no—
205C22×C4×C31—41no—
206C22×C4×C31C2×D411yescharacteristic
207C22×C4×C31C2×D411yescharacteristic
208C22×C4×C31C2×D411yescharacteristic
209C22×C4×C31C2×D412yes—
210Q16×C31—42no—
211SD16×C31—42no—
212SD16×C31—42no—
213D8×C31—42no—
214M16×C31—22no—
215M16×C31—41no—
216C2×C8×C31—41no—
217C4⋊C4×C31—22no—
218C4⋊C4×C31—22no—
219C4⋊C4×C31—22no—
220C4⋊C4×C31—22no—
221C4⋊C4×C31—22no—
222C4⋊C4×C31—22no—
223C4⋊C4×C31—21no—
224C4⋊C4×C31—21no—
225C4⋊C4×C31—21no—
226C4⋊C4×C31—21no—
227C4⋊C4×C31—22no—
228C4⋊C4×C31—41no—
229C4⋊C4×C31—41no—
230C4⋊C4×C31—44no—
231C22⋊C4×C31—22no—
232C22⋊C4×C31—22no—
233C22⋊C4×C31—22no—
234C22⋊C4×C31—22no—
235C22⋊C4×C31—22no—
236C22⋊C4×C31—22no—
237C22⋊C4×C31—21no—
238C22⋊C4×C31—22no—
239C22⋊C4×C31—21no—
240C22⋊C4×C31—21no—
241C22⋊C4×C31—21no—
242C22⋊C4×C31—22no—
243C22⋊C4×C31—22no—
244C22⋊C4×C31—22no—
245C22⋊C4×C31—22no—
246C22⋊C4×C31—44no—
247C22⋊C4×C31—44no—
248C22⋊C4×C31C2×D412yes—
249C22⋊C4×C31C2×D412yes—
250C42×C31—22no—
251C42×C31—21no—
252C42×C31—21no—
253C42×C31—21no—
254C42×C31—41no—
255C42×C31—41no—
256C42×C31C2×D411yescharacteristic
257C42×C31C2×D411yescharacteristic
258#33560C3111yesmaximal, characteristic, direct product factor, Sylow
259C23×C31—22no—
260C23×C31—22no—
261C23×C31—22no—
262C23×C31—21no—
263C23×C31—41no—
264C23×C31—42no—
265C23×C31—82no—
266C23×C31#12011yescharacteristic
267C23×C31C22×D411yescharacteristic
268C23×C31C22×D411yescharacteristic
269Q8×C31—22no—
270Q8×C31—41no—
271Q8×C31—41no—
272Q8×C31—41no—
273Q8×C31—41no—
274Q8×C31—41no—
275Q8×C31—41no—
276Q8×C31—41no—
277Q8×C31—81no—
278D4×C31—22no—
279D4×C31—41no—
280D4×C31—41no—
281D4×C31—41no—
282D4×C31—41no—
283D4×C31—41no—
284D4×C31—41no—
285D4×C31—42no—
286D4×C31—42no—
287D4×C31—42no—
288D4×C31—42no—
289D4×C31—41no—
290D4×C31—41no—
291D4×C31—41no—
292D4×C31—81no—
293D4×C31—81no—
294D4×C31—82no—
295D4×C31—82no—
296D4×C31—82no—
297D4×C31—81no—
298D4×C31—81no—
299D4×C31—82no—
300D4×C31—164no—
301C2×C4×C31—21no—
302C2×C4×C31—21no—
303C2×C4×C31—21no—
304C2×C4×C31—21no—
305C2×C4×C31—21no—
306C2×C4×C31—21no—
307C2×C4×C31—22no—
308C2×C4×C31—22no—
309C2×C4×C31—21no—
310C2×C4×C31—22no—
311C2×C4×C31—21no—
312C2×C4×C31—22no—
313C2×C4×C31—22no—
314C2×C4×C31—21no—
315C2×C4×C31—42no—
316C2×C4×C31—42no—
317C2×C4×C31—42no—
318C2×C4×C31—41no—
319C2×C4×C31—42no—
320C2×C4×C31—41no—
321C2×C4×C31—41no—
322C2×C4×C31—42no—
323C2×C4×C31—42no—
324C2×C4×C31—42no—
325C2×C4×C31—82no—
326C2×C4×C31—81no—
327C2×C4×C31—82no—
328C2×C4×C31—82no—
329C2×C4×C31#12011yescharacteristic
330C2×C4×C31#12011yescharacteristic
331C2×C4×C31#12011yescharacteristic
332C2×C4×C31C22×D411yescharacteristic
333C8×C31—42no—
334#3551C2×C3111yescharacteristic, complemented
335#3028C2×C3111yescharacteristic, complemented
336#3027C2×C3111yescharacteristic, complemented
337#3018C2×C3111yescharacteristic, complemented
338#2200C2×C3114yescomplemented
339#2197C2×C3114yescomplemented
340#2126C2×C3111yescharacteristic, complemented
341#2123C2×C3111yescharacteristic, complemented
342#2122C2×C3111yescharacteristic, complemented
343C22×C31—21no—
344C22×C31—21no—
345C22×C31—21no—
346C22×C31—41no—
347C22×C31—41no—
348C22×C31—41no—
349C22×C31—41no—
350C22×C31—42no—
351C22×C31—41no—
352C22×C31—42no—
353C22×C31—42no—
354C22×C31—41no—
355C22×C31—42no—
356C22×C31—82no—
357C22×C31—84no—
358C22×C31—82no—
359C22×C31—161no—
360C22×C31C2×#12011yescharacteristic
361C4×C31—21no—
362C4×C31—21no—
363C4×C31—21no—
364C4×C31—41no—
365C4×C31—42no—
366C4×C31—42no—
367C4×C31—41no—
368C4×C31—42no—
369C4×C31—41no—
370C4×C31—42no—
371C4×C31—82no—
372C4×C31—82no—
373C4×C31B(4,𝔽2)11yescharacteristic
374C4×C31B(4,𝔽2)11yescharacteristic
375#585C22×C3111yescharacteristic
376#575—21no—
377#563—21no—
378#560C22×C3112yescomplemented
379#555—21no—
380#553—21no—
381#552—21no—
382#551C22×C3112yescomplemented
383#548—21no—
384#546—21no—
385#540—22no—
386#538—22no—
387#537—21no—
388#536—21no—
389#536C22×C3111yescharacteristic
390#535—21no—
391#535C22×C3111yescharacteristic
392#532C22×C3111yescharacteristic
393#529—21no—
394#458—22no—
395#458C22×C3114yes—
396B(4,𝔽2)—22no—
397B(4,𝔽2)C22×C3114yes—
398#456—21no—
399#455C22×C3112yes—
400#454—21no—
401#453C22×C3112yes—
402C2×#104—21no—
403#413C22×C3111yescharacteristic
404#410—21no—
405#410—21no—
406#410C22×C3111yescharacteristic
407#410C22×C3111yescharacteristic
408#354C22×C3112yescomplemented
409#353C22×C3112yescomplemented
410#352C22×C3114yescomplemented
411AΣL(1,𝔽16)C22×C3114yescomplemented
412C2×C31—21no—
413C2×C31—41no—
414C2×C31—41no—
415C2×C31—41no—
416C2×C31—81no—
417C2×C31—82no—
418C2×C31—82no—
419C2×C31C2×B(4,𝔽2)11yescharacteristic
4202−1+4—21no—
4212−1+4—41no—
422H(5,𝔽2)—21no—
423H(5,𝔽2)—21no—
424H(5,𝔽2)—41no—
425H(5,𝔽2)C23×C3112yes—
426C2×#41—21no—
427C2×#41—21no—
428C2×#41—21no—
429C2×#41—21no—
430C2×#41—42no—
431C2×#41D4×C3111yescharacteristic, complemented
432C2×#41C23×C3111yescharacteristic
433C22×Q8D4×C3111yescharacteristic, complemented
434C22×D4D4×C3111yescharacteristic
435#137—22no—
436#137—41no—
437AGL(1,ℤ/8)—22no—
438AGL(1,ℤ/8)—41no—
439#135—42no—
440C2×M16—21no—
441C4⋊Q8—21no—
442C4⋊Q8—41no—
443C4⋊Q8D4×C3111yescharacteristic, complemented
444#127—21no—
445#127—41no—
446#127C23×C3111yescharacteristic
447#126—22no—
448#126—22no—
449#126—22no—
450#125—21no—
451#125—22no—
452#124—21no—
453#124—22no—
454#124—21no—
455#124—21no—
456#124—41no—
457#124—41no—
458#124D4×C3111yescharacteristic, complemented
459#124C23×C3111yescharacteristic
460#123—22no—
461#123—22no—
462#123—22no—
463#123—22no—
464#123—24no—
465#123D4×C3112yescomplemented
466#123C23×C3112yes—
467C22⋊Q8—21no—
468C22⋊Q8—22no—
469C22⋊Q8—22no—
470C22⋊Q8—21no—
471C22⋊Q8—21no—
472C22⋊Q8—42no—
473#121—22no—
474#121—22no—
475#121—21no—
476#121—22no—
477#121—21no—
478#121—21no—
479#121—22no—
480#121—21no—
481#121—21no—
482#121—22no—
483#121—22no—
484#121—42no—
485#120—22no—
486#120—24no—
487#120D4×C3112yes—
488#120C23×C3112yes—
489C4×Q8—21no—
490C4×D4—22no—
491C4×D4—21no—
492C4×D4—22no—
493C4×D4—21no—
494C4×D4—21no—
495C4×D4—22no—
496#117—22no—
497#117—22no—
498#117—21no—
499#117—21no—
500#117D4×C3111yescharacteristic
501#117D4×C3111yescharacteristic, complemented
502C2×C4⋊C4—21no—
503C2×C22⋊C4—22no—
504C2×C42D4×C3111yescharacteristic, complemented
505#104—22no—
506#104—22no—
507#101—21no—
508#100C23×C3112yes—
509#99—21no—
510#99—21no—
511#99—24no—
512#99—24no—
513#99C23×C3112yes—
514#99C23×C3112yes—
515C31#3356011yescharacteristic, direct product factor, Sylow
516C24C2×D4×C3112yes—
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×C3111yescharacteristic
546C2×Q8C2×D4×C3111yescharacteristic
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×C3111yescharacteristic
569C2×D4C2×D4×C3111yescharacteristic
570C2×D4C2×D4×C3111yescharacteristic
571C2×D4C24×C3111yescharacteristic
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×C3111yescharacteristic
581C22×C4C2×D4×C3111yescharacteristic
582C22×C4C2×D4×C3111yescharacteristic
583C22×C4C2×D4×C3112yes—
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×C3112yes—
623C22⋊C4C2×D4×C3112yes—
624C42—22no—
625C42—21no—
626C42—21no—
627C42—21no—
628C42—41no—
629C42—41no—
630C42C2×D4×C3111yescharacteristic
631C42C2×D4×C3111yescharacteristic
632C23—22no—
633C23—22no—
634C23—22no—
635C23—21no—
636C23—41no—
637C23—42no—
638C23—82no—
639C23C31×#12011yescharacteristic
640C23C22×D4×C3111yescharacteristic
641C23C22×D4×C3111yescharacteristic
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—81no—
671D4—81no—
672D4—82no—
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—81no—
700C2×C4—82no—
701C2×C4—82no—
702C2×C4C31×#12011yescharacteristic
703C2×C4C31×#12011yescharacteristic
704C2×C4C31×#12011yescharacteristic
705C2×C4C22×D4×C3111yescharacteristic
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×C31×#12011yescharacteristic
725C4—21no—
726C4—21no—
727C4—21no—
728C4—41no—
729C4—42no—
730C4—42no—
731C4—41no—
732C4—42no—
733C4—41no—
734C4—42no—
735C4—82no—
736C4—82no—
737C4C31×B(4,𝔽2)11yescharacteristic
738C4C31×B(4,𝔽2)11yescharacteristic
739C2—21no—
740C2—41no—
741C2—41no—
742C2—41no—
743C2—82no—
744C2—81no—
745C2—82no—
746C2C2×C31×B(4,𝔽2)11yescharacteristic
subgroupG/H
center, socleC2×C31C2×B(4,𝔽2)
commutator, Frattini, cosocleC2×D4C24×C31
LCSG ▷ C2×D4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C31 ◁ C2×C4×C31 ◁ C2×#41×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C31×#3551C2semidirect
2. C31×#3028C2semidirect
3. C31×#3027C2semidirect
4. C31×#3018C2semidirect
5. C31×#2200C2semidirect
6. C31×#2197C2semidirect
7. C31×#2126C2semidirect
8. C31×#2123C2semidirect
9. C31×#2122C2semidirect
13. C31×#560C22semidirect
17. C31×#551C22semidirect
43. C31×#354C22semidirect
44. C31×#353C22semidirect
45. C31×#352C22semidirect
46. C31×AΣL(1,𝔽16)C22semidirect
58. C2×#41×C31D4semidirect
60. C22×Q8×C31D4semidirect
70. C31×C4⋊Q8D4semidirect
85. C31×#124D4semidirect
92. C31×#123D4semidirect
128. C31×#117D4semidirect
131. C2×C42×C31D4semidirect
258. #33560C31direct (N × H)
334. #3551C2×C31semidirect
335. #3028C2×C31semidirect
336. #3027C2×C31semidirect
337. #3018C2×C31semidirect
338. #2200C2×C31semidirect
339. #2197C2×C31semidirect
340. #2126C2×C31semidirect
341. #2123C2×C31semidirect
342. #2122C2×C31semidirect
378. #560C22×C31semidirect
382. #551C22×C31semidirect
408. #354C22×C31semidirect
409. #353C22×C31semidirect
410. #352C22×C31semidirect
411. AΣL(1,𝔽16)C22×C31semidirect
431. C2×#41D4×C31semidirect
433. C22×Q8D4×C31semidirect
443. C4⋊Q8D4×C31semidirect
458. #124D4×C31semidirect
465. #123D4×C31semidirect
501. #117D4×C31semidirect
504. C2×C42D4×C31semidirect
515. C31#33560direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#35512
C31×#30282
C31×#30272
C31×#30182
C31×#22002
C31×#21972
C31×#21262
C31×#21232
C31×#21222
#3356031