Finite Group Databasebeta

← C31×#18240 #21474999

Subgroups — C31×#18240 #21474999

Order 7936.

1056 conjugacy classes of subgroups.

The subgroup lattice has 698 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3558C211yesmaximal, characteristic, complemented
2C31×#3114C211yesmaximal, characteristic, complemented
3C31×#3100C211yesmaximal, characteristic, complemented
4C31×#2631C211yesmaximal, characteristic, complemented
5C31×#1612C212yesmaximal, complemented
6C31×#1607C212yesmaximal, complemented
7C31×#1600C212yesmaximal, complemented
8C31×#1595C212yesmaximal, complemented
9C31×#1521C211yesmaximal, characteristic, complemented
10C31×#1514C211yesmaximal, characteristic, complemented
11C31×#1469C211yesmaximal, characteristic, complemented
12C31×#562—21no—
13C31×H(3,𝔽4)—21no—
14C31×#559—21no—
15C31×#548—21no—
16C31×#546—21no—
17C31×#546—22no—
18D42×C31—21no—
19C31×#542—21no—
20C31×#538—22no—
21C31×#538C2212yes—
22C31×#535—21no—
23C31×#534C2212yes—
24C31×#532C2211yescharacteristic
25C31×#529C2211yescharacteristic
26C2×C31×#124C2211yescharacteristic
27C2×C4×D4×C31C2211yescharacteristic, complemented
28C31×#483C2211yescharacteristic, complemented
29C31×#480C2211yescharacteristic
30C31×#480C2212yescomplemented
31C31×#478—21no—
32C31×#474—21no—
33C31×#463—21no—
34C31×#459—21no—
35C31×#450C2211yescharacteristic, complemented
36C31×#447C2211yescharacteristic
37C31×#447C2212yescomplemented
38C31×#442—21no—
39C31×#440—21no—
40C4×D8×C31—22no—
41C31×#432C2211yescharacteristic, complemented
42C31×#431C2211yescharacteristic, complemented
43C31×#397C2212yescomplemented
44C31×#393—21no—
45C31×#392—21no—
46C31×#392C2212yescomplemented
47C31×#386—22no—
48C31×#383C2211yescharacteristic, complemented
49C31×#328C2212yescomplemented
50C31×#327C2212yes—
51C31×#327C2212yescomplemented
52C31×#327C2212yescomplemented
53C31×#323C2212yescomplemented
54C31×#323C2212yescomplemented
55C2×#41×C31—21no—
56C2×#41×C31—21no—
57C22×Q8×C31D411yescharacteristic
58C22×D4×C31—21no—
59C22×D4×C31—22no—
60C22×D4×C31—22no—
61C22×D4×C31D411yescharacteristic
62C22×D4×C31C2311yescharacteristic
63C23×C4×C31—21no—
64C2×SD16×C31—21no—
65C2×D8×C31—22no—
66C2×D8×C31—21no—
67C31×C4⋊Q8D411yescharacteristic, complemented
68C31×#127—21no—
69C31×#127D411yescharacteristic, complemented
70C31×#126—22no—
71C31×#126—21no—
72C31×#125D411yescharacteristic, complemented
73C31×#124—21no—
74C31×#124—22no—
75C31×#124—22no—
76C31×#124—22no—
77C31×#124—21no—
78C31×#124—21no—
79C31×#124—21no—
80C31×#124—21no—
81C31×#124—21no—
82C31×#124D411yescharacteristic, complemented
83C31×#123—22no—
84C31×#123—21no—
85C31×#123—22no—
86C31×#123—22no—
87C31×#123—22no—
88C31×C22⋊Q8—22no—
89C31×C22⋊Q8—21no—
90C31×C22⋊Q8—22no—
91C31×C22⋊Q8C2311yescharacteristic
92C31×#121—22no—
93C31×#121—22no—
94C31×#121—22no—
95C31×#121—21no—
96C31×#121—22no—
97C31×#121—21no—
98C31×#121—22no—
99C31×#121C2311yescharacteristic
100C31×#121C2312yes—
101C31×#120—22no—
102C31×#120—22no—
103C31×#120—22no—
104C31×#120—22no—
105C31×#120—22no—
106C4×Q8×C31—21no—
107C4×Q8×C31D411yescharacteristic, complemented
108C4×D4×C31—22no—
109C4×D4×C31—21no—
110C4×D4×C31—21no—
111C4×D4×C31—22no—
112C4×D4×C31—21no—
113C4×D4×C31—21no—
114C4×D4×C31—21no—
115C4×D4×C31—21no—
116C4×D4×C31—21no—
117C4×D4×C31D412yescomplemented
118C4×D4×C31D411yescharacteristic, complemented
119C31×#117—21no—
120C2×C4⋊C4×C31C2311yescharacteristic
121C2×C22⋊C4×C31—22no—
122C2×C22⋊C4×C31—21no—
123C2×C22⋊C4×C31—22no—
124C2×C22⋊C4×C31—22no—
125C2×C22⋊C4×C31D412yes—
126C2×C22⋊C4×C31C2312yes—
127C2×C42×C31C2311yescharacteristic
128C31×#107—22no—
129C31×#107—21no—
130C31×#106—21no—
131C31×C4⋊C8—21no—
132C31×C4⋊C8—21no—
133C31×#103—21no—
134C31×#102—22no—
135C31×#102—21no—
136C31×#102—22no—
137C31×#102—21no—
138C31×#102—21no—
139C31×C22⋊C8C2312yes—
140C31×C22⋊C8C2311yescharacteristic
141C31×C22⋊C8C2311yescharacteristic
142C31×#97—21no—
143C4×C8×C31—21no—
144C31×#95—22no—
145C31×#95—21no—
146C31×#95—21no—
147C31×#95C2312yes—
148C24×C31—22no—
149C24×C31—21no—
150C24×C31C2×D412yes—
151#41×C31—82no—
152#41×C31—82no—
153C2×Q8×C31—21no—
154C2×Q8×C31—21no—
155C2×Q8×C31—21no—
156C2×Q8×C31—81no—
157C2×Q8×C31C2×D411yescharacteristic
158C2×D4×C31—22no—
159C2×D4×C31—21no—
160C2×D4×C31—22no—
161C2×D4×C31—22no—
162C2×D4×C31—22no—
163C2×D4×C31—22no—
164C2×D4×C31—22no—
165C2×D4×C31—21no—
166C2×D4×C31—21no—
167C2×D4×C31—21no—
168C2×D4×C31—21no—
169C2×D4×C31—21no—
170C2×D4×C31—21no—
171C2×D4×C31—42no—
172C2×D4×C31—44no—
173C2×D4×C31—82no—
174C2×D4×C31—81no—
175C2×D4×C31—82no—
176C2×D4×C31—82no—
177C2×D4×C31—82no—
178C2×D4×C31—82no—
179C2×D4×C31C2×D411yescharacteristic
180C2×D4×C31C2×D412yes—
181C22×C4×C31—22no—
182C22×C4×C31—22no—
183C22×C4×C31—21no—
184C22×C4×C31—22no—
185C22×C4×C31—22no—
186C22×C4×C31—21no—
187C22×C4×C31—41no—
188C22×C4×C31—41no—
189C22×C4×C31—82no—
190C22×C4×C31C2×D411yescharacteristic
191C22×C4×C31C2×D412yes—
192C22×C4×C31C2×D411yescharacteristic
193C22×C4×C31C2411yescharacteristic
194SD16×C31—42no—
195D8×C31—44no—
196D8×C31—42no—
197C2×C8×C31—22no—
198C2×C8×C31—21no—
199C2×C8×C31—21no—
200C4⋊C4×C31—22no—
201C4⋊C4×C31—22no—
202C4⋊C4×C31—21no—
203C4⋊C4×C31—21no—
204C4⋊C4×C31—21no—
205C4⋊C4×C31—21no—
206C4⋊C4×C31—21no—
207C4⋊C4×C31—21no—
208C4⋊C4×C31—21no—
209C4⋊C4×C31C2×D411yescharacteristic
210C4⋊C4×C31C2×D412yes—
211C4⋊C4×C31C2×D411yescharacteristic
212C22⋊C4×C31—22no—
213C22⋊C4×C31—22no—
214C22⋊C4×C31—22no—
215C22⋊C4×C31—22no—
216C22⋊C4×C31—22no—
217C22⋊C4×C31—21no—
218C22⋊C4×C31—21no—
219C22⋊C4×C31—22no—
220C22⋊C4×C31—22no—
221C22⋊C4×C31—21no—
222C22⋊C4×C31—21no—
223C22⋊C4×C31—22no—
224C22⋊C4×C31—22no—
225C22⋊C4×C31—22no—
226C22⋊C4×C31—21no—
227C22⋊C4×C31—22no—
228C22⋊C4×C31—41no—
229C22⋊C4×C31—41no—
230C22⋊C4×C31—82no—
231C22⋊C4×C31—82no—
232C42×C31—22no—
233C42×C31—21no—
234C42×C31C2×D411yescharacteristic
235C42×C31C2×D411yescharacteristic
236C42×C31C2×D411yescharacteristic
237C42×C31C2×D411yescharacteristic
238#18240C3111yesmaximal, characteristic, direct product factor, Sylow
239C23×C31—22no—
240C23×C31—22no—
241C23×C31—21no—
242C23×C31—22no—
243C23×C31—22no—
244C23×C31—22no—
245C23×C31—42no—
246C23×C31—41no—
247C23×C31—42no—
248C23×C31—42no—
249C23×C31—41no—
250C23×C31—42no—
251C23×C31—82no—
252C23×C31—82no—
253C23×C31—82no—
254C23×C31C22×D411yescharacteristic
255Q8×C31—41no—
256Q8×C31—42no—
257Q8×C31—81no—
258Q8×C31—81no—
259D4×C31—22no—
260D4×C31—22no—
261D4×C31—42no—
262D4×C31—41no—
263D4×C31—41no—
264D4×C31—41no—
265D4×C31—42no—
266D4×C31—42no—
267D4×C31—42no—
268D4×C31—42no—
269D4×C31—42no—
270D4×C31—81no—
271D4×C31—81no—
272D4×C31—82no—
273D4×C31—82no—
274D4×C31—82no—
275D4×C31—82no—
276D4×C31—82no—
277D4×C31—88no—
278C2×C4×C31—22no—
279C2×C4×C31—21no—
280C2×C4×C31—22no—
281C2×C4×C31—22no—
282C2×C4×C31—21no—
283C2×C4×C31—21no—
284C2×C4×C31—41no—
285C2×C4×C31—41no—
286C2×C4×C31—42no—
287C2×C4×C31—42no—
288C2×C4×C31—42no—
289C2×C4×C31—42no—
290C2×C4×C31—41no—
291C2×C4×C31—42no—
292C2×C4×C31—42no—
293C2×C4×C31—82no—
294C2×C4×C31—82no—
295C2×C4×C31—82no—
296C2×C4×C31—82no—
297C2×C4×C31—82no—
298C2×C4×C31#12011yescharacteristic
299C2×C4×C31#12011yescharacteristic
300C2×C4×C31#12011yescharacteristic
301C2×C4×C31#12011yescharacteristic
302C2×C4×C31C22×D411yescharacteristic
303C2×C4×C31C22×D411yescharacteristic
304C8×C31—42no—
305C8×C31—41no—
306C8×C31—41no—
307#3558C2×C3111yescharacteristic, complemented
308#3114C2×C3111yescharacteristic, complemented
309#3100C2×C3111yescharacteristic, complemented
310#2631C2×C3111yescharacteristic, complemented
311#1612C2×C3112yescomplemented
312#1607C2×C3112yescomplemented
313#1600C2×C3112yescomplemented
314#1595C2×C3112yescomplemented
315#1521C2×C3111yescharacteristic, complemented
316#1514C2×C3111yescharacteristic, complemented
317#1469C2×C3111yescharacteristic, complemented
318C22×C31—21no—
319C22×C31—21no—
320C22×C31—44no—
321C22×C31—42no—
322C22×C31—42no—
323C22×C31—41no—
324C22×C31—41no—
325C22×C31—42no—
326C22×C31—42no—
327C22×C31—42no—
328C22×C31—42no—
329C22×C31—41no—
330C22×C31—42no—
331C22×C31—82no—
332C22×C31—82no—
333C22×C31—82no—
334C22×C31—81no—
335C22×C31—81no—
336C22×C31—164no—
337C22×C31C2×#12011yescharacteristic
338C22×C31#57612yes—
339C4×C31—21no—
340C4×C31—21no—
341C4×C31—21no—
342C4×C31—21no—
343C4×C31—21no—
344C4×C31—21no—
345C4×C31—41no—
346C4×C31—42no—
347C4×C31—41no—
348C4×C31—42no—
349C4×C31—41no—
350C4×C31—82no—
351C4×C31—81no—
352#562—21no—
353H(3,𝔽4)—21no—
354#559—21no—
355#548—21no—
356#546—21no—
357#546—22no—
358D42—21no—
359#542—21no—
360#538—22no—
361#538C22×C3112yes—
362#535—21no—
363#534C22×C3112yes—
364#532C22×C3111yescharacteristic
365#529C22×C3111yescharacteristic
366C2×#124C22×C3111yescharacteristic
367C2×C4×D4C22×C3111yescharacteristic, complemented
368#483C22×C3111yescharacteristic, complemented
369#480C22×C3111yescharacteristic
370#480C22×C3112yescomplemented
371#478—21no—
372#474—21no—
373#463—21no—
374#459—21no—
375#450C22×C3111yescharacteristic, complemented
376#447C22×C3111yescharacteristic
377#447C22×C3112yescomplemented
378#442—21no—
379#440—21no—
380C4×D8—22no—
381#432C22×C3111yescharacteristic, complemented
382#431C22×C3111yescharacteristic, complemented
383#397C22×C3112yescomplemented
384#393—21no—
385#392—21no—
386#392C22×C3112yescomplemented
387#386—22no—
388#383C22×C3111yescharacteristic, complemented
389#328C22×C3112yescomplemented
390#327C22×C3112yes—
391#327C22×C3112yescomplemented
392#327C22×C3112yescomplemented
393#323C22×C3112yescomplemented
394#323C22×C3112yescomplemented
395C2×C31—22no—
396C2×C31—82no—
397C2×C31—82no—
398C2×C31—82no—
399C2×C31—81no—
400C2×C31#300811yescharacteristic
401C2×C31#301911yescharacteristic
402C2×C31#302511yescharacteristic
403C2×#41—21no—
404C2×#41—21no—
405C22×Q8D4×C3111yescharacteristic
406C22×D4—21no—
407C22×D4—22no—
408C22×D4—22no—
409C22×D4D4×C3111yescharacteristic
410C22×D4C23×C3111yescharacteristic
411C23×C4—21no—
412C2×SD16—21no—
413C2×D8—22no—
414C2×D8—21no—
415C4⋊Q8D4×C3111yescharacteristic, complemented
416#127—21no—
417#127D4×C3111yescharacteristic, complemented
418#126—22no—
419#126—21no—
420#125D4×C3111yescharacteristic, complemented
421#124—21no—
422#124—22no—
423#124—22no—
424#124—22no—
425#124—21no—
426#124—21no—
427#124—21no—
428#124—21no—
429#124—21no—
430#124D4×C3111yescharacteristic, complemented
431#123—22no—
432#123—21no—
433#123—22no—
434#123—22no—
435#123—22no—
436C22⋊Q8—22no—
437C22⋊Q8—21no—
438C22⋊Q8—22no—
439C22⋊Q8C23×C3111yescharacteristic
440#121—22no—
441#121—22no—
442#121—22no—
443#121—21no—
444#121—22no—
445#121—21no—
446#121—22no—
447#121C23×C3111yescharacteristic
448#121C23×C3112yes—
449#120—22no—
450#120—22no—
451#120—22no—
452#120—22no—
453#120—22no—
454C4×Q8—21no—
455C4×Q8D4×C3111yescharacteristic, complemented
456C4×D4—22no—
457C4×D4—21no—
458C4×D4—21no—
459C4×D4—22no—
460C4×D4—21no—
461C4×D4—21no—
462C4×D4—21no—
463C4×D4—21no—
464C4×D4—21no—
465C4×D4D4×C3111yescharacteristic, complemented
466C4×D4D4×C3112yescomplemented
467#117—21no—
468C2×C4⋊C4C23×C3111yescharacteristic
469C2×C22⋊C4—22no—
470C2×C22⋊C4—21no—
471C2×C22⋊C4—22no—
472C2×C22⋊C4—22no—
473C2×C22⋊C4D4×C3112yes—
474C2×C22⋊C4C23×C3112yes—
475C2×C42C23×C3111yescharacteristic
476#107—22no—
477#107—21no—
478#106—21no—
479C4⋊C8—21no—
480C4⋊C8—21no—
481#103—21no—
482#102—22no—
483#102—21no—
484#102—22no—
485#102—21no—
486#102—21no—
487C22⋊C8C23×C3112yes—
488C22⋊C8C23×C3111yescharacteristic
489C22⋊C8C23×C3111yescharacteristic
490#97—21no—
491C4×C8—21no—
492#95—21no—
493#95—21no—
494#95—22no—
495#95C23×C3112yes—
496C31#1824011yescharacteristic, direct product factor, Sylow
497C24—22no—
498C24—21no—
499C24C2×D4×C3112yes—
500#41—82no—
501#41—82no—
502C2×Q8—21no—
503C2×Q8—21no—
504C2×Q8—21no—
505C2×Q8—81no—
506C2×Q8C2×D4×C3111yescharacteristic
507C2×D4—22no—
508C2×D4—21no—
509C2×D4—22no—
510C2×D4—22no—
511C2×D4—22no—
512C2×D4—22no—
513C2×D4—22no—
514C2×D4—21no—
515C2×D4—21no—
516C2×D4—21no—
517C2×D4—21no—
518C2×D4—21no—
519C2×D4—21no—
520C2×D4—42no—
521C2×D4—44no—
522C2×D4—82no—
523C2×D4—81no—
524C2×D4—82no—
525C2×D4—82no—
526C2×D4—82no—
527C2×D4—82no—
528C2×D4C2×D4×C3111yescharacteristic
529C2×D4C2×D4×C3112yes—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—21no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—21no—
536C22×C4—41no—
537C22×C4—41no—
538C22×C4—82no—
539C22×C4C2×D4×C3111yescharacteristic
540C22×C4C2×D4×C3112yes—
541C22×C4C2×D4×C3111yescharacteristic
542C22×C4C24×C3111yescharacteristic
543SD16—42no—
544D8—44no—
545D8—42no—
546C2×C8—22no—
547C2×C8—21no—
548C2×C8—21no—
549C4⋊C4—22no—
550C4⋊C4—22no—
551C4⋊C4—21no—
552C4⋊C4—21no—
553C4⋊C4—21no—
554C4⋊C4—21no—
555C4⋊C4—21no—
556C4⋊C4—21no—
557C4⋊C4—21no—
558C4⋊C4C2×D4×C3111yescharacteristic
559C4⋊C4C2×D4×C3112yes—
560C4⋊C4C2×D4×C3111yescharacteristic
561C22⋊C4—22no—
562C22⋊C4—22no—
563C22⋊C4—22no—
564C22⋊C4—22no—
565C22⋊C4—22no—
566C22⋊C4—21no—
567C22⋊C4—21no—
568C22⋊C4—22no—
569C22⋊C4—22no—
570C22⋊C4—21no—
571C22⋊C4—21no—
572C22⋊C4—22no—
573C22⋊C4—22no—
574C22⋊C4—22no—
575C22⋊C4—21no—
576C22⋊C4—22no—
577C22⋊C4—41no—
578C22⋊C4—41no—
579C22⋊C4—82no—
580C22⋊C4—82no—
581C42—22no—
582C42—21no—
583C42C2×D4×C3111yescharacteristic
584C42C2×D4×C3111yescharacteristic
585C42C2×D4×C3111yescharacteristic
586C42C2×D4×C3111yescharacteristic
587C23—22no—
588C23—22no—
589C23—21no—
590C23—22no—
591C23—22no—
592C23—22no—
593C23—42no—
594C23—41no—
595C23—42no—
596C23—42no—
597C23—41no—
598C23—42no—
599C23—82no—
600C23—82no—
601C23—82no—
602C23C22×D4×C3111yescharacteristic
603Q8—41no—
604Q8—42no—
605Q8—81no—
606Q8—81no—
607D4—22no—
608D4—22no—
609D4—42no—
610D4—41no—
611D4—41no—
612D4—41no—
613D4—42no—
614D4—42no—
615D4—42no—
616D4—42no—
617D4—42no—
618D4—81no—
619D4—81no—
620D4—82no—
621D4—82no—
622D4—82no—
623D4—82no—
624D4—82no—
625D4—88no—
626C2×C4—22no—
627C2×C4—21no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—42no—
635C2×C4—42no—
636C2×C4—42no—
637C2×C4—42no—
638C2×C4—41no—
639C2×C4—42no—
640C2×C4—42no—
641C2×C4—82no—
642C2×C4—82no—
643C2×C4—82no—
644C2×C4—82no—
645C2×C4—82no—
646C2×C4C31×#12011yescharacteristic
647C2×C4C31×#12011yescharacteristic
648C2×C4C31×#12011yescharacteristic
649C2×C4C31×#12011yescharacteristic
650C2×C4C22×D4×C3111yescharacteristic
651C2×C4C22×D4×C3111yescharacteristic
652C8—42no—
653C8—41no—
654C8—41no—
655C22—21no—
656C22—21no—
657C22—44no—
658C22—42no—
659C22—42no—
660C22—41no—
661C22—41no—
662C22—42no—
663C22—42no—
664C22—42no—
665C22—42no—
666C22—41no—
667C22—42no—
668C22—82no—
669C22—82no—
670C22—82no—
671C22—81no—
672C22—81no—
673C22—164no—
674C22C2×C31×#12011yescharacteristic
675C22C31×#57612yes—
676C4—21no—
677C4—21no—
678C4—21no—
679C4—21no—
680C4—21no—
681C4—21no—
682C4—41no—
683C4—42no—
684C4—41no—
685C4—42no—
686C4—41no—
687C4—82no—
688C4—81no—
689C2—22no—
690C2—82no—
691C2—82no—
692C2—81no—
693C2—82no—
694C2C31×#300811yescharacteristic
695C2C31×#301911yescharacteristic
696C2C31×#302511yescharacteristic
subgroupG/H
center, socleC22×C31C2×#120
commutator, Frattini, cosocleC22×C4C24×C31
LCSG ▷ C22×C4 ▷ 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×#3558C2semidirect
2. C31×#3114C2semidirect
3. C31×#3100C2semidirect
4. C31×#2631C2semidirect
5. C31×#1612C2semidirect
6. C31×#1607C2semidirect
7. C31×#1600C2semidirect
8. C31×#1595C2semidirect
9. C31×#1521C2semidirect
10. C31×#1514C2semidirect
11. C31×#1469C2semidirect
27. C2×C4×D4×C31C22semidirect
28. C31×#483C22semidirect
30. C31×#480C22semidirect
35. C31×#450C22semidirect
37. C31×#447C22semidirect
41. C31×#432C22semidirect
42. C31×#431C22semidirect
43. C31×#397C22semidirect
46. C31×#392C22semidirect
48. C31×#383C22semidirect
49. C31×#328C22semidirect
51. C31×#327C22semidirect
52. C31×#327C22semidirect
53. C31×#323C22semidirect
54. C31×#323C22semidirect
67. C31×C4⋊Q8D4semidirect
69. C31×#127D4semidirect
72. C31×#125D4semidirect
82. C31×#124D4semidirect
107. C4×Q8×C31D4semidirect
117. C4×D4×C31D4semidirect
118. C4×D4×C31D4semidirect
238. #18240C31direct (N × H)
307. #3558C2×C31semidirect
308. #3114C2×C31semidirect
309. #3100C2×C31semidirect
310. #2631C2×C31semidirect
311. #1612C2×C31semidirect
312. #1607C2×C31semidirect
313. #1600C2×C31semidirect
314. #1595C2×C31semidirect
315. #1521C2×C31semidirect
316. #1514C2×C31semidirect
317. #1469C2×C31semidirect
367. C2×C4×D4C22×C31semidirect
368. #483C22×C31semidirect
370. #480C22×C31semidirect
375. #450C22×C31semidirect
377. #447C22×C31semidirect
381. #432C22×C31semidirect
382. #431C22×C31semidirect
383. #397C22×C31semidirect
386. #392C22×C31semidirect
388. #383C22×C31semidirect
389. #328C22×C31semidirect
391. #327C22×C31semidirect
392. #327C22×C31semidirect
393. #323C22×C31semidirect
394. #323C22×C31semidirect
415. C4⋊Q8D4×C31semidirect
417. #127D4×C31semidirect
420. #125D4×C31semidirect
430. #124D4×C31semidirect
455. C4×Q8D4×C31semidirect
465. C4×D4D4×C31semidirect
466. C4×D4D4×C31semidirect
496. C31#18240direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#35582
C31×#31142
C31×#31002
C31×#26312
C31×#16122
C31×#16072
C31×#16002
C31×#15952
C31×#15212
C31×#15142
C31×#14692
#1824031