Finite Group Databasebeta

← C31×#18790 #21475549

Subgroups — C31×#18790 #21475549

Order 7936.

1054 conjugacy classes of subgroups.

The subgroup lattice has 694 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3480C211yesmaximal, characteristic, complemented
2C31×#3205C211yesmaximal, characteristic, complemented
3C31×#3038C211yesmaximal, characteristic, complemented
4C2×C31×#460C211yesmaximal, characteristic, complemented
5C31×#1628C212yesmaximal, complemented
6C31×#1626C212yesmaximal, complemented
7C31×#1621C212yesmaximal, complemented
8C31×#1620C212yesmaximal, complemented
9C31×#1547C211yesmaximal, characteristic, complemented
10C31×#1487C211yesmaximal, characteristic, complemented
11C31×#1477C211yesmaximal, characteristic, complemented
12C2×C31×AGL(1,ℤ/8)—21no—
13C22×SD16×C31—21no—
14C31×#559—21no—
15C31×#559C2211yescharacteristic, complemented
16C31×#557C2211yescharacteristic, complemented
17C31×#556—21no—
18C31×#556C2211yescharacteristic, complemented
19C31×#553—22no—
20C31×#553—21no—
21C31×#550C2211yescharacteristic, complemented
22C31×#548—21no—
23C31×#532—21no—
24C31×#532C2211yescharacteristic
25C2×C31×#127C2211yescharacteristic
26C31×#529—21no—
27C31×#529—22no—
28C4×#41×C31—21no—
29C4×#41×C31—21no—
30C4×#41×C31C2211yescharacteristic
31C2×C4×Q8×C31C2211yescharacteristic
32C31×#493C2212yes—
33C31×#486C2212yes—
34C31×#460—21no—
35C31×#460—21no—
36C31×#460—21no—
37C31×#460C2212yes—
38C31×#460C2212yes—
39C31×#460C2212yes—
40C31×#459—22no—
41C31×#459—21no—
42C31×#459C2212yes—
43C31×#447—22no—
44C31×#431C2211yescharacteristic
45C31×#423C2211yescharacteristic
46C2×C31×C4⋊C8C2211yescharacteristic
47C31×#418—21no—
48C2×C31×#102—21no—
49C31×#332C2212yescomplemented
50C31×#331C2212yescomplemented
51C31×Q8⋊C8C2212yescomplemented
52C31×Q8⋊C8C2212yescomplemented
53C31×Q8⋊C8C2212yescomplemented
54C31×D4⋊C8C2212yescomplemented
55C2×#41×C31—21no—
56C2×#41×C31—21no—
57C2×#41×C31D411yescharacteristic
58C22×Q8×C31D411yescharacteristic
59C22×D4×C31—21no—
60C22×D4×C31—21no—
61C22×D4×C31—21no—
62C31×AGL(1,ℤ/8)—44no—
63C2×SD16×C31—22no—
64C2×SD16×C31—22no—
65C2×SD16×C31—22no—
66C2×SD16×C31—44no—
67C2×D8×C31—22no—
68C2×D8×C31—24no—
69C2×M16×C31—21no—
70C22×C8×C31—21no—
71C31×C4⋊Q8—21no—
72C31×C4⋊Q8C2311yescharacteristic
73C31×#127—21no—
74C31×#127—21no—
75C31×#127—21no—
76C31×#127—21no—
77C31×#127C2312yes—
78C31×#127C2311yescharacteristic
79C31×#126—22no—
80C31×#126—22no—
81C31×#126—22no—
82C31×#125—22no—
83C31×#125—21no—
84C31×#124—22no—
85C31×#124—21no—
86C31×#124—21no—
87C31×#124—21no—
88C31×#124—21no—
89C31×#123—22no—
90C31×#123—22no—
91C31×#123—22no—
92C31×C22⋊Q8—22no—
93C31×C22⋊Q8—21no—
94C31×#121—22no—
95C31×#121—22no—
96C31×#121—22no—
97C31×#121—21no—
98C31×#121—21no—
99C31×#121D412yes—
100C4×Q8×C31—21no—
101C4×Q8×C31—21no—
102C4×Q8×C31—21no—
103C4×Q8×C31—21no—
104C4×Q8×C31—21no—
105C4×Q8×C31D411yescharacteristic
106C4×Q8×C31D411yescharacteristic
107C4×Q8×C31D411yescharacteristic
108C4×Q8×C31C2311yescharacteristic
109C4×Q8×C31C2311yescharacteristic
110C4×Q8×C31C2311yescharacteristic
111C4×D4×C31—22no—
112C4×D4×C31—22no—
113C4×D4×C31—22no—
114C4×D4×C31—22no—
115C4×D4×C31—22no—
116C4×D4×C31—21no—
117C4×D4×C31—21no—
118C4×D4×C31—21no—
119C4×D4×C31—21no—
120C4×D4×C31—21no—
121C4×D4×C31—21no—
122C4×D4×C31D411yescharacteristic
123C4×D4×C31D412yes—
124C4×D4×C31C2311yescharacteristic
125C31×#117—22no—
126C31×#117—22no—
127C31×#117—21no—
128C31×#117—21no—
129C31×#117D411yescharacteristic
130C2×C4⋊C4×C31—21no—
131C2×C4⋊C4×C31D411yescharacteristic
132C2×C42×C31—22no—
133C2×C42×C31—21no—
134C2×C42×C31—21no—
135C2×C42×C31C2311yescharacteristic
136C31×C4⋊C8—21no—
137C31×C4⋊C8—21no—
138C31×C4⋊C8—21no—
139C31×C4⋊C8C2312yes—
140C31×C4⋊C8C2312yes—
141C31×#102—22no—
142C31×#102—22no—
143C31×#102—22no—
144C31×#102—22no—
145C31×#102—24no—
146C31×C22⋊C8—21no—
147C4×C8×C31C2312yes—
148C24×C31—41no—
149#41×C31—22no—
150#41×C31—22no—
151#41×C31—42no—
152#41×C31—42no—
153#41×C31—42no—
154#41×C31—42no—
155C2×Q8×C31—21no—
156C2×Q8×C31—21no—
157C2×Q8×C31—22no—
158C2×Q8×C31—41no—
159C2×Q8×C31C2×D411yescharacteristic
160C2×Q8×C31C2×D411yescharacteristic
161C2×Q8×C31C2×D411yescharacteristic
162C2×D4×C31—22no—
163C2×D4×C31—21no—
164C2×D4×C31—22no—
165C2×D4×C31—22no—
166C2×D4×C31—21no—
167C2×D4×C31—21no—
168C2×D4×C31—22no—
169C2×D4×C31—22no—
170C2×D4×C31—22no—
171C2×D4×C31—42no—
172C2×D4×C31—42no—
173C2×D4×C31—41no—
174C2×D4×C31—41no—
175C2×D4×C31—41no—
176C2×D4×C31—42no—
177C2×D4×C31—42no—
178C2×D4×C31—82no—
179C2×D4×C31C2×D411yescharacteristic
180C2×D4×C31C2×D412yes—
181C22×C4×C31—22no—
182C22×C4×C31—21no—
183C22×C4×C31—22no—
184C22×C4×C31—21no—
185C22×C4×C31—21no—
186C22×C4×C31—22no—
187C22×C4×C31—21no—
188C22×C4×C31—21no—
189C22×C4×C31C2×D411yescharacteristic
190C22×C4×C31C2×D411yescharacteristic
191C22×C4×C31C2×D411yescharacteristic
192SD16×C31—44no—
193SD16×C31—44no—
194SD16×C31—44no—
195D8×C31—44no—
196D8×C31—84no—
197M16×C31—42no—
198C2×C8×C31—22no—
199C2×C8×C31—22no—
200C2×C8×C31—22no—
201C2×C8×C31—42no—
202C4⋊C4×C31—22no—
203C4⋊C4×C31—22no—
204C4⋊C4×C31—22no—
205C4⋊C4×C31—22no—
206C4⋊C4×C31—21no—
207C4⋊C4×C31—21no—
208C4⋊C4×C31—21no—
209C4⋊C4×C31—21no—
210C4⋊C4×C31—21no—
211C4⋊C4×C31—21no—
212C4⋊C4×C31—21no—
213C4⋊C4×C31—21no—
214C4⋊C4×C31C2×D411yescharacteristic
215C4⋊C4×C31C2×D411yescharacteristic
216C4⋊C4×C31C2×D411yescharacteristic
217C4⋊C4×C31C2×D411yescharacteristic
218C4⋊C4×C31C2×D412yes—
219C22⋊C4×C31—22no—
220C22⋊C4×C31—22no—
221C22⋊C4×C31—22no—
222C22⋊C4×C31—22no—
223C22⋊C4×C31—22no—
224C22⋊C4×C31—22no—
225C22⋊C4×C31—21no—
226C22⋊C4×C31—22no—
227C22⋊C4×C31—21no—
228C22⋊C4×C31—22no—
229C22⋊C4×C31—21no—
230C42×C31—22no—
231C42×C31—22no—
232C42×C31—21no—
233C42×C31—21no—
234C42×C31—21no—
235C42×C31—21no—
236C42×C31—21no—
237C42×C31—21no—
238C42×C31—21no—
239C42×C31C2×D411yescharacteristic
240C42×C31C2×D411yescharacteristic
241C42×C31C2×D411yescharacteristic
242C42×C31C2411yescharacteristic
243#18790C3111yesmaximal, characteristic, direct product factor, Sylow
244C23×C31—21no—
245C23×C31—22no—
246C23×C31—42no—
247C23×C31—82no—
248C23×C31—82no—
249C23×C31—82no—
250C23×C31#12011yescharacteristic
251Q8×C31—21no—
252Q8×C31—21no—
253Q8×C31—21no—
254Q8×C31—21no—
255Q8×C31—21no—
256Q8×C31—42no—
257Q8×C31—41no—
258Q8×C31—41no—
259Q8×C31AGL(1,ℤ/8)12yescomplemented
260D4×C31—21no—
261D4×C31—21no—
262D4×C31—42no—
263D4×C31—44no—
264D4×C31—44no—
265D4×C31—42no—
266D4×C31—44no—
267D4×C31—41no—
268D4×C31—42no—
269D4×C31—41no—
270D4×C31—41no—
271D4×C31—42no—
272D4×C31—42no—
273D4×C31—41no—
274D4×C31—42no—
275D4×C31—82no—
276D4×C31—82no—
277D4×C31—82no—
278D4×C31—82no—
279C2×C4×C31—21no—
280C2×C4×C31—21no—
281C2×C4×C31—21no—
282C2×C4×C31—21no—
283C2×C4×C31—21no—
284C2×C4×C31—21no—
285C2×C4×C31—21no—
286C2×C4×C31—21no—
287C2×C4×C31—22no—
288C2×C4×C31—21no—
289C2×C4×C31—41no—
290C2×C4×C31—42no—
291C2×C4×C31—44no—
292C2×C4×C31—41no—
293C2×C4×C31—41no—
294C2×C4×C31—42no—
295C2×C4×C31—44no—
296C2×C4×C31—81no—
297C2×C4×C31—81no—
298C2×C4×C31—82no—
299C2×C4×C31#12011yescharacteristic
300C2×C4×C31#12011yescharacteristic
301C2×C4×C31#12011yescharacteristic
302C2×C4×C31#13512yes—
303C2×C4×C31AGL(1,ℤ/8)12yes—
304C2×C4×C31C22×D411yescharacteristic
305C2×C4×C31C22×D411yescharacteristic
306C2×C4×C31C22×D411yescharacteristic
307C8×C31—42no—
308C8×C31—42no—
309C8×C31—42no—
310#3480C2×C3111yescharacteristic, complemented
311#3205C2×C3111yescharacteristic, complemented
312#3038C2×C3111yescharacteristic, complemented
313C2×#460C2×C3111yescharacteristic, complemented
314#1628C2×C3112yescomplemented
315#1626C2×C3112yescomplemented
316#1621C2×C3112yescomplemented
317#1620C2×C3112yescomplemented
318#1547C2×C3111yescharacteristic, complemented
319#1487C2×C3111yescharacteristic, complemented
320#1477C2×C3111yescharacteristic, complemented
321C22×C31—21no—
322C22×C31—21no—
323C22×C31—41no—
324C22×C31—42no—
325C22×C31—42no—
326C22×C31—41no—
327C22×C31—42no—
328C22×C31—41no—
329C22×C31—82no—
330C22×C31—82no—
331C22×C31—82no—
332C22×C31—164no—
333C22×C31#44912yes—
334C22×C31C2×#12011yescharacteristic
335C4×C31—21no—
336C4×C31—22no—
337C4×C31—21no—
338C4×C31—21no—
339C4×C31—41no—
340C4×C31—42no—
341C4×C31—41no—
342C4×C31—41no—
343C4×C31—41no—
344C4×C31—41no—
345C4×C31—41no—
346C4×C31#44912yes—
347C4×C31C2×#13511yescharacteristic
348C4×C31C2×AGL(1,ℤ/8)11yescharacteristic
349C4×C31C2×AGL(1,ℤ/8)11yescharacteristic
350C4×C31#57511yescharacteristic
351C2×AGL(1,ℤ/8)—21no—
352C22×SD16—21no—
353#559—21no—
354#559C22×C3111yescharacteristic, complemented
355#557C22×C3111yescharacteristic, complemented
356#556—21no—
357#556C22×C3111yescharacteristic, complemented
358#553—22no—
359#553—21no—
360#550C22×C3111yescharacteristic, complemented
361#548—21no—
362#532—21no—
363#532C22×C3111yescharacteristic
364C2×#127C22×C3111yescharacteristic
365#529—21no—
366#529—22no—
367C4×#41—21no—
368C4×#41—21no—
369C4×#41C22×C3111yescharacteristic
370C2×C4×Q8C22×C3111yescharacteristic
371#493C22×C3112yes—
372#486C22×C3112yes—
373#460—21no—
374#460—21no—
375#460—21no—
376#460C22×C3112yes—
377#460C22×C3112yes—
378#460C22×C3112yes—
379#459—22no—
380#459—21no—
381#459C22×C3112yes—
382#447—22no—
383#431C22×C3111yescharacteristic
384#423C22×C3111yescharacteristic
385C2×C4⋊C8C22×C3111yescharacteristic
386#418—21no—
387C2×#102—21no—
388#332C22×C3112yescomplemented
389#331C22×C3112yescomplemented
390Q8⋊C8C22×C3112yescomplemented
391Q8⋊C8C22×C3112yescomplemented
392Q8⋊C8C22×C3112yescomplemented
393D4⋊C8C22×C3112yescomplemented
394C2×C31—22no—
395C2×C31—81no—
396C2×C31—82no—
397C2×C31—162no—
398C2×C31C2×#44911yescharacteristic
399C2×C31#300611yescharacteristic
400C2×C31#302111yescharacteristic
401C2×#41—21no—
402C2×#41—21no—
403C2×#41D4×C3111yescharacteristic
404C22×Q8D4×C3111yescharacteristic
405C22×D4—21no—
406C22×D4—21no—
407C22×D4—21no—
408AGL(1,ℤ/8)—44no—
409C2×SD16—22no—
410C2×SD16—22no—
411C2×SD16—22no—
412C2×SD16—44no—
413C2×D8—22no—
414C2×D8—24no—
415C2×M16—21no—
416C22×C8—21no—
417C4⋊Q8—21no—
418C4⋊Q8C23×C3111yescharacteristic
419#127—21no—
420#127—21no—
421#127—21no—
422#127—21no—
423#127C23×C3112yes—
424#127C23×C3111yescharacteristic
425#126—22no—
426#126—22no—
427#126—22no—
428#125—22no—
429#125—21no—
430#124—22no—
431#124—21no—
432#124—21no—
433#124—21no—
434#124—21no—
435#123—22no—
436#123—22no—
437#123—22no—
438C22⋊Q8—22no—
439C22⋊Q8—21no—
440#121—22no—
441#121—22no—
442#121—22no—
443#121—21no—
444#121—21no—
445#121D4×C3112yes—
446C4×Q8—21no—
447C4×Q8—21no—
448C4×Q8—21no—
449C4×Q8—21no—
450C4×Q8—21no—
451C4×Q8D4×C3111yescharacteristic
452C4×Q8D4×C3111yescharacteristic
453C4×Q8D4×C3111yescharacteristic
454C4×Q8C23×C3111yescharacteristic
455C4×Q8C23×C3111yescharacteristic
456C4×Q8C23×C3111yescharacteristic
457C4×D4—22no—
458C4×D4—22no—
459C4×D4—22no—
460C4×D4—22no—
461C4×D4—22no—
462C4×D4—21no—
463C4×D4—21no—
464C4×D4—21no—
465C4×D4—21no—
466C4×D4—21no—
467C4×D4—21no—
468C4×D4D4×C3111yescharacteristic
469C4×D4D4×C3112yes—
470C4×D4C23×C3111yescharacteristic
471#117—22no—
472#117—22no—
473#117—21no—
474#117—21no—
475#117D4×C3111yescharacteristic
476C2×C4⋊C4—21no—
477C2×C4⋊C4D4×C3111yescharacteristic
478C2×C42—22no—
479C2×C42—21no—
480C2×C42—21no—
481C2×C42C23×C3111yescharacteristic
482C4⋊C8—21no—
483C4⋊C8—21no—
484C4⋊C8—21no—
485C4⋊C8C23×C3112yes—
486C4⋊C8C23×C3112yes—
487#102—22no—
488#102—22no—
489#102—22no—
490#102—22no—
491#102—24no—
492C22⋊C8—21no—
493C4×C8C23×C3112yes—
494C31#1879011yescharacteristic, direct product factor, Sylow
495C24—41no—
496#41—22no—
497#41—22no—
498#41—42no—
499#41—42no—
500#41—42no—
501#41—42no—
502C2×Q8—21no—
503C2×Q8—21no—
504C2×Q8—22no—
505C2×Q8—41no—
506C2×Q8C2×D4×C3111yescharacteristic
507C2×Q8C2×D4×C3111yescharacteristic
508C2×Q8C2×D4×C3111yescharacteristic
509C2×D4—22no—
510C2×D4—21no—
511C2×D4—22no—
512C2×D4—22no—
513C2×D4—21no—
514C2×D4—21no—
515C2×D4—22no—
516C2×D4—22no—
517C2×D4—22no—
518C2×D4—42no—
519C2×D4—42no—
520C2×D4—41no—
521C2×D4—41no—
522C2×D4—41no—
523C2×D4—42no—
524C2×D4—42no—
525C2×D4—82no—
526C2×D4C2×D4×C3111yescharacteristic
527C2×D4C2×D4×C3112yes—
528C22×C4—22no—
529C22×C4—21no—
530C22×C4—22no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—22no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4C2×D4×C3111yescharacteristic
537C22×C4C2×D4×C3111yescharacteristic
538C22×C4C2×D4×C3111yescharacteristic
539SD16—44no—
540SD16—44no—
541SD16—44no—
542D8—44no—
543D8—84no—
544M16—42no—
545C2×C8—22no—
546C2×C8—22no—
547C2×C8—22no—
548C2×C8—42no—
549C4⋊C4—22no—
550C4⋊C4—22no—
551C4⋊C4—22no—
552C4⋊C4—22no—
553C4⋊C4—21no—
554C4⋊C4—21no—
555C4⋊C4—21no—
556C4⋊C4—21no—
557C4⋊C4—21no—
558C4⋊C4—21no—
559C4⋊C4—21no—
560C4⋊C4—21no—
561C4⋊C4C2×D4×C3111yescharacteristic
562C4⋊C4C2×D4×C3111yescharacteristic
563C4⋊C4C2×D4×C3111yescharacteristic
564C4⋊C4C2×D4×C3111yescharacteristic
565C4⋊C4C2×D4×C3112yes—
566C22⋊C4—22no—
567C22⋊C4—22no—
568C22⋊C4—22no—
569C22⋊C4—22no—
570C22⋊C4—22no—
571C22⋊C4—22no—
572C22⋊C4—21no—
573C22⋊C4—22no—
574C22⋊C4—21no—
575C22⋊C4—22no—
576C22⋊C4—21no—
577C42—22no—
578C42—22no—
579C42—21no—
580C42—21no—
581C42—21no—
582C42—21no—
583C42—21no—
584C42—21no—
585C42—21no—
586C42C2×D4×C3111yescharacteristic
587C42C2×D4×C3111yescharacteristic
588C42C2×D4×C3111yescharacteristic
589C42C24×C3111yescharacteristic
590C23—21no—
591C23—22no—
592C23—42no—
593C23—82no—
594C23—82no—
595C23—82no—
596C23C31×#12011yescharacteristic
597Q8—21no—
598Q8—21no—
599Q8—21no—
600Q8—21no—
601Q8—21no—
602Q8—42no—
603Q8—41no—
604Q8—41no—
605Q8C31×AGL(1,ℤ/8)12yescomplemented
606D4—21no—
607D4—21no—
608D4—42no—
609D4—44no—
610D4—44no—
611D4—42no—
612D4—44no—
613D4—41no—
614D4—42no—
615D4—41no—
616D4—41no—
617D4—42no—
618D4—42no—
619D4—41no—
620D4—42no—
621D4—82no—
622D4—82no—
623D4—82no—
624D4—82no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—22no—
634C2×C4—21no—
635C2×C4—41no—
636C2×C4—42no—
637C2×C4—44no—
638C2×C4—42no—
639C2×C4—44no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—81no—
643C2×C4—81no—
644C2×C4—82no—
645C2×C4C31×#12011yescharacteristic
646C2×C4C31×#12011yescharacteristic
647C2×C4C31×#12011yescharacteristic
648C2×C4C31×#13512yes—
649C2×C4C31×AGL(1,ℤ/8)12yes—
650C2×C4C22×D4×C3111yescharacteristic
651C2×C4C22×D4×C3111yescharacteristic
652C2×C4C22×D4×C3111yescharacteristic
653C8—42no—
654C8—42no—
655C8—42no—
656C22—21no—
657C22—21no—
658C22—41no—
659C22—42no—
660C22—42no—
661C22—41no—
662C22—42no—
663C22—41no—
664C22—82no—
665C22—82no—
666C22—82no—
667C22—164no—
668C22C31×#44912yes—
669C22C2×C31×#12011yescharacteristic
670C4—21no—
671C4—22no—
672C4—21no—
673C4—21no—
674C4—41no—
675C4—42no—
676C4—41no—
677C4—41no—
678C4—41no—
679C4—41no—
680C4—41no—
681C4C31×#44912yes—
682C4C2×C31×#13511yescharacteristic
683C4C2×C31×AGL(1,ℤ/8)11yescharacteristic
684C4C2×C31×AGL(1,ℤ/8)11yescharacteristic
685C4C31×#57511yescharacteristic
686C2—22no—
687C2—81no—
688C2—82no—
689C2—162no—
690C2C2×C31×#44911yescharacteristic
691C2C31×#300611yescharacteristic
692C2C31×#302111yescharacteristic
subgroupG/H
center, socleC22×C31C2×#120
commutator, Frattini, cosocleC42C24×C31
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C31 ◁ C2×C42×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C31×#3480C2semidirect
2. C31×#3205C2semidirect
3. C31×#3038C2semidirect
4. C2×C31×#460C2semidirect
5. C31×#1628C2semidirect
6. C31×#1626C2semidirect
7. C31×#1621C2semidirect
8. C31×#1620C2semidirect
9. C31×#1547C2semidirect
10. C31×#1487C2semidirect
11. C31×#1477C2semidirect
15. C31×#559C22semidirect
16. C31×#557C22semidirect
18. C31×#556C22semidirect
21. C31×#550C22semidirect
49. C31×#332C22semidirect
50. C31×#331C22semidirect
51. C31×Q8⋊C8C22semidirect
52. C31×Q8⋊C8C22semidirect
53. C31×Q8⋊C8C22semidirect
54. C31×D4⋊C8C22semidirect
243. #18790C31direct (N × H)
259. Q8×C31AGL(1,ℤ/8)semidirect
310. #3480C2×C31semidirect
311. #3205C2×C31semidirect
312. #3038C2×C31semidirect
313. C2×#460C2×C31semidirect
314. #1628C2×C31semidirect
315. #1626C2×C31semidirect
316. #1621C2×C31semidirect
317. #1620C2×C31semidirect
318. #1547C2×C31semidirect
319. #1487C2×C31semidirect
320. #1477C2×C31semidirect
354. #559C22×C31semidirect
355. #557C22×C31semidirect
357. #556C22×C31semidirect
360. #550C22×C31semidirect
388. #332C22×C31semidirect
389. #331C22×C31semidirect
390. Q8⋊C8C22×C31semidirect
391. Q8⋊C8C22×C31semidirect
392. Q8⋊C8C22×C31semidirect
393. D4⋊C8C22×C31semidirect
494. C31#18790direct (N × H)
605. Q8C31×AGL(1,ℤ/8)semidirect

Maximal subgroups

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

subgroupindex
C31×#34802
C31×#32052
C31×#30382
C2×C31×#4602
C31×#16282
C31×#16262
C31×#16212
C31×#16202
C31×#15472
C31×#14872
C31×#14772
#1879031