Finite Group Databasebeta

← C31×#18450 #21475209

Subgroups — C31×#18450 #21475209

Order 7936.

1096 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3537C211yesmaximal, characteristic, complemented
2C31×#3194C211yesmaximal, characteristic, complemented
3C31×#3186C211yesmaximal, characteristic, complemented
4C31×#2815C211yesmaximal, characteristic, complemented
5C31×#1612C212yesmaximal, complemented
6C31×#1607C212yesmaximal, complemented
7C31×#1600C212yesmaximal, complemented
8C31×#1595C212yesmaximal, complemented
9C31×#1516C211yesmaximal, characteristic, complemented
10C31×#1510C211yesmaximal, characteristic, complemented
11C31×#1471C211yesmaximal, characteristic, complemented
12C31×#560—22no—
13C31×#553—21no—
14C31×#553—21no—
15D42×C31—22no—
16D42×C31—21no—
17D42×C31—21no—
18C31×#540—21no—
19C31×#538—21no—
20C31×#538C2212yes—
21C31×#535—21no—
22C31×#534—21no—
23C31×#534C2212yes—
24C31×#525C2211yescharacteristic
25C2×C31×#121C2211yescharacteristic
26C2×C31×#121C2211yescharacteristic
27C2×C31×#121C2211yescharacteristic, complemented
28C31×#483C2211yescharacteristic, complemented
29C31×#482—21no—
30C31×#480—21no—
31C31×#480C2211yescharacteristic, complemented
32C31×#480C2212yescomplemented
33C31×#469—21no—
34C31×#468—21no—
35C31×#466—22no—
36C31×#450C2211yescharacteristic, complemented
37C31×#449—21no—
38C31×#447—21no—
39C31×#447C2211yescharacteristic, complemented
40C31×#447C2212yescomplemented
41C31×#407C2211yescharacteristic, complemented
42C2×C31×C22⋊C8C2211yescharacteristic, complemented
43C31×#397—21no—
44C31×#397C2212yescomplemented
45C31×#392—22no—
46C31×#392—21no—
47C31×#392C2212yescomplemented
48C31×#381C2211yescharacteristic, complemented
49C31×#328C2212yescomplemented
50C31×#327C2212yescomplemented
51C31×#327C2212yescomplemented
52C31×#327C2212yescomplemented
53C31×#323C2212yescomplemented
54C31×#323C2212yescomplemented
55C2×#41×C31D411yescharacteristic, complemented
56C22×D4×C31—22no—
57C22×D4×C31—21no—
58C22×D4×C31—21no—
59C22×D4×C31—22no—
60C22×D4×C31—21no—
61C22×D4×C31—22no—
62C22×D4×C31D412yes—
63C22×D4×C31D411yescharacteristic
64C22×D4×C31D411yescharacteristic, complemented
65C22×D4×C31C2311yescharacteristic
66C23×C4×C31C2311yescharacteristic
67C2×SD16×C31—21no—
68C2×D8×C31—22no—
69C2×D8×C31—21no—
70C2×M16×C31—21no—
71C22×C8×C31—21no—
72C31×#127—22no—
73C31×#127—21no—
74C31×#126—22no—
75C31×#126—22no—
76C31×#125—21no—
77C31×#124—22no—
78C31×#123—22no—
79C31×#123—21no—
80C31×#123—22no—
81C31×#123—22no—
82C31×#123—22no—
83C31×C22⋊Q8D411yescharacteristic, complemented
84C31×C22⋊Q8C2311yescharacteristic
85C31×#121—22no—
86C31×#121—21no—
87C31×#121—21no—
88C31×#121—22no—
89C31×#121—22no—
90C31×#121—22no—
91C31×#121—22no—
92C31×#121—21no—
93C31×#121—21no—
94C31×#121—21no—
95C31×#121—21no—
96C31×#121—21no—
97C31×#121—21no—
98C31×#121—22no—
99C31×#121—21no—
100C31×#121—21no—
101C31×#121—21no—
102C31×#121—21no—
103C31×#121D412yescomplemented
104C31×#121D411yescharacteristic, complemented
105C31×#121C2312yes—
106C31×#121C2311yescharacteristic
107C31×#120—22no—
108C31×#120—22no—
109C31×#120—22no—
110C31×#120—21no—
111C31×#120—22no—
112C31×#120—22no—
113C31×#120—22no—
114C4×D4×C31—22no—
115C4×D4×C31—21no—
116C4×D4×C31—21no—
117C4×D4×C31—21no—
118C4×D4×C31—21no—
119C4×D4×C31—22no—
120C31×#117—21no—
121C31×#117D411yescharacteristic, complemented
122C2×C4⋊C4×C31D411yescharacteristic
123C2×C4⋊C4×C31D411yescharacteristic, complemented
124C2×C4⋊C4×C31C2311yescharacteristic
125C2×C22⋊C4×C31—21no—
126C2×C22⋊C4×C31—21no—
127C2×C22⋊C4×C31—22no—
128C2×C22⋊C4×C31—21no—
129C2×C22⋊C4×C31—22no—
130C2×C22⋊C4×C31C2312yes—
131C31×#107—22no—
132C31×#107—21no—
133C31×#106—21no—
134C31×#103—21no—
135C31×#102—22no—
136C31×#102—21no—
137C31×#102—22no—
138C31×#102—21no—
139C31×#102—21no—
140C31×C22⋊C8—21no—
141C31×C22⋊C8—21no—
142C31×C22⋊C8C2312yes—
143C31×C22⋊C8C2311yescharacteristic
144C31×C22⋊C8C2311yescharacteristic
145C31×#95—22no—
146C31×#95—21no—
147C31×#95C2312yes—
148C24×C31—22no—
149C24×C31—21no—
150C24×C31—21no—
151C24×C31C2×D412yes—
152C24×C31C2×D411yescharacteristic
153#41×C31—81no—
154C2×Q8×C31C2×D411yescharacteristic
155C2×D4×C31—22no—
156C2×D4×C31—21no—
157C2×D4×C31—21no—
158C2×D4×C31—22no—
159C2×D4×C31—22no—
160C2×D4×C31—22no—
161C2×D4×C31—22no—
162C2×D4×C31—22no—
163C2×D4×C31—22no—
164C2×D4×C31—21no—
165C2×D4×C31—22no—
166C2×D4×C31—22no—
167C2×D4×C31—21no—
168C2×D4×C31—21no—
169C2×D4×C31—21no—
170C2×D4×C31—21no—
171C2×D4×C31—21no—
172C2×D4×C31—41no—
173C2×D4×C31—41no—
174C2×D4×C31—81no—
175C2×D4×C31—81no—
176C2×D4×C31—82no—
177C2×D4×C31—81no—
178C2×D4×C31—82no—
179C2×D4×C31—82no—
180C2×D4×C31—82no—
181C2×D4×C31—82no—
182C2×D4×C31—82no—
183C2×D4×C31—82no—
184C2×D4×C31—82no—
185C2×D4×C31—82no—
186C2×D4×C31—84no—
187C2×D4×C31C2×D411yescharacteristic
188C2×D4×C31C2×D412yes—
189C22×C4×C31—22no—
190C22×C4×C31—22no—
191C22×C4×C31—21no—
192C22×C4×C31—21no—
193C22×C4×C31—22no—
194C22×C4×C31—21no—
195C22×C4×C31—81no—
196C22×C4×C31C2×D412yes—
197C22×C4×C31C2×D411yescharacteristic
198C22×C4×C31C2×D411yescharacteristic
199C22×C4×C31C2×D411yescharacteristic
200C22×C4×C31C2×D411yescharacteristic
201C22×C4×C31C2×D411yescharacteristic
202C22×C4×C31C2411yescharacteristic
203SD16×C31—81no—
204D8×C31—82no—
205D8×C31—81no—
206M16×C31—81no—
207C2×C8×C31—22no—
208C2×C8×C31—21no—
209C2×C8×C31—21no—
210C2×C8×C31—81no—
211C4⋊C4×C31—22no—
212C4⋊C4×C31—22no—
213C4⋊C4×C31—21no—
214C4⋊C4×C31—21no—
215C4⋊C4×C31—21no—
216C4⋊C4×C31—21no—
217C4⋊C4×C31—21no—
218C4⋊C4×C31—21no—
219C4⋊C4×C31—21no—
220C4⋊C4×C31C2×D411yescharacteristic
221C4⋊C4×C31C2×D412yes—
222C4⋊C4×C31C2×D411yescharacteristic
223C22⋊C4×C31—22no—
224C22⋊C4×C31—22no—
225C22⋊C4×C31—22no—
226C22⋊C4×C31—22no—
227C22⋊C4×C31—22no—
228C22⋊C4×C31—21no—
229C22⋊C4×C31—21no—
230C22⋊C4×C31—21no—
231C22⋊C4×C31—22no—
232C22⋊C4×C31—21no—
233C22⋊C4×C31—22no—
234C22⋊C4×C31—22no—
235C22⋊C4×C31—22no—
236C22⋊C4×C31—21no—
237C22⋊C4×C31—41no—
238C22⋊C4×C31—41no—
239C22⋊C4×C31—82no—
240C22⋊C4×C31—82no—
241C22⋊C4×C31—81no—
242C42×C31—22no—
243C42×C31—21no—
244#18450C3111yesmaximal, characteristic, direct product factor, Sylow
245C23×C31—22no—
246C23×C31—22no—
247C23×C31—22no—
248C23×C31—21no—
249C23×C31—22no—
250C23×C31—22no—
251C23×C31—41no—
252C23×C31—41no—
253C23×C31—42no—
254C23×C31—42no—
255C23×C31—42no—
256C23×C31—41no—
257C23×C31—41no—
258C23×C31—42no—
259C23×C31—41no—
260C23×C31—42no—
261C23×C31—81no—
262C23×C31—81no—
263C23×C31—82no—
264C23×C31—82no—
265C23×C31—82no—
266C23×C31#12011yescharacteristic
267C23×C31#12011yescharacteristic
268C23×C31C22×D411yescharacteristic
269Q8×C31—41no—
270D4×C31—42no—
271D4×C31—41no—
272D4×C31—42no—
273D4×C31—42no—
274D4×C31—42no—
275D4×C31—41no—
276D4×C31—41no—
277D4×C31—44no—
278D4×C31—42no—
279D4×C31—42no—
280D4×C31—42no—
281D4×C31—42no—
282D4×C31—81no—
283D4×C31—82no—
284D4×C31—82no—
285D4×C31—81no—
286D4×C31—82no—
287D4×C31—82no—
288D4×C31—82no—
289D4×C31—82no—
290D4×C31—82no—
291D4×C31—82no—
292D4×C31—82no—
293D4×C31—88no—
294C2×C4×C31—21no—
295C2×C4×C31—22no—
296C2×C4×C31—22no—
297C2×C4×C31—21no—
298C2×C4×C31—21no—
299C2×C4×C31—41no—
300C2×C4×C31—41no—
301C2×C4×C31—41no—
302C2×C4×C31—41no—
303C2×C4×C31—41no—
304C2×C4×C31—41no—
305C2×C4×C31—42no—
306C2×C4×C31—42no—
307C2×C4×C31—42no—
308C2×C4×C31—42no—
309C2×C4×C31—41no—
310C2×C4×C31—42no—
311C2×C4×C31—42no—
312C2×C4×C31—81no—
313C2×C4×C31—82no—
314C2×C4×C31—82no—
315C2×C4×C31#12011yescharacteristic
316C2×C4×C31#12011yescharacteristic
317C2×C4×C31C22×D411yescharacteristic
318C2×C4×C31C22×D411yescharacteristic
319C8×C31—42no—
320C8×C31—41no—
321C8×C31—41no—
322#3537C2×C3111yescharacteristic, complemented
323#3194C2×C3111yescharacteristic, complemented
324#3186C2×C3111yescharacteristic, complemented
325#2815C2×C3111yescharacteristic, complemented
326#1612C2×C3112yescomplemented
327#1607C2×C3112yescomplemented
328#1600C2×C3112yescomplemented
329#1595C2×C3112yescomplemented
330#1516C2×C3111yescharacteristic, complemented
331#1510C2×C3111yescharacteristic, complemented
332#1471C2×C3111yescharacteristic, complemented
333C22×C31—21no—
334C22×C31—21no—
335C22×C31—21no—
336C22×C31—21no—
337C22×C31—21no—
338C22×C31—21no—
339C22×C31—21no—
340C22×C31—21no—
341C22×C31—42no—
342C22×C31—42no—
343C22×C31—41no—
344C22×C31—42no—
345C22×C31—42no—
346C22×C31—41no—
347C22×C31—41no—
348C22×C31—42no—
349C22×C31—42no—
350C22×C31—82no—
351C22×C31—82no—
352C22×C31—82no—
353C22×C31—82no—
354C22×C31—82no—
355C22×C31—81no—
356C22×C31—81no—
357C22×C31—81no—
358C22×C31—162no—
359C22×C31—164no—
360C22×C31C2×#12011yescharacteristic
361C22×C31#57612yes—
362C4×C31—21no—
363C4×C31—21no—
364C4×C31—21no—
365C4×C31—21no—
366C4×C31—42no—
367C4×C31—41no—
368C4×C31—42no—
369C4×C31—41no—
370C4×C31—41no—
371C4×C31—82no—
372C4×C31—81no—
373#560—22no—
374#553—21no—
375#553—21no—
376D42—22no—
377D42—21no—
378D42—21no—
379#540—21no—
380#538—21no—
381#538C22×C3112yes—
382#535—21no—
383#534—21no—
384#534C22×C3112yes—
385#525C22×C3111yescharacteristic
386C2×#121C22×C3111yescharacteristic
387C2×#121C22×C3111yescharacteristic
388C2×#121C22×C3111yescharacteristic, complemented
389#483C22×C3111yescharacteristic, complemented
390#482—21no—
391#480—21no—
392#480C22×C3111yescharacteristic, complemented
393#480C22×C3112yescomplemented
394#469—21no—
395#468—21no—
396#466—22no—
397#450C22×C3111yescharacteristic, complemented
398#449—21no—
399#447—21no—
400#447C22×C3111yescharacteristic, complemented
401#447C22×C3112yescomplemented
402#407C22×C3111yescharacteristic, complemented
403C2×C22⋊C8C22×C3111yescharacteristic, complemented
404#397—21no—
405#397C22×C3112yescomplemented
406#392—21no—
407#392—22no—
408#392C22×C3112yescomplemented
409#381C22×C3111yescharacteristic, complemented
410#328C22×C3112yescomplemented
411#327C22×C3112yescomplemented
412#327C22×C3112yescomplemented
413#327C22×C3112yescomplemented
414#323C22×C3112yescomplemented
415#323C22×C3112yescomplemented
416C2×C31—22no—
417C2×C31—41no—
418C2×C31—41no—
419C2×C31—82no—
420C2×C31—82no—
421C2×C31—81no—
422C2×C31—161no—
423C2×C31#300811yescharacteristic
424C2×C31#301911yescharacteristic
425C2×C31#302611yescharacteristic
426C2×#41D4×C3111yescharacteristic, complemented
427C22×D4—22no—
428C22×D4—21no—
429C22×D4—21no—
430C22×D4—22no—
431C22×D4—21no—
432C22×D4—22no—
433C22×D4D4×C3112yes—
434C22×D4D4×C3111yescharacteristic
435C22×D4D4×C3111yescharacteristic, complemented
436C22×D4C23×C3111yescharacteristic
437C23×C4C23×C3111yescharacteristic
438C2×SD16—21no—
439C2×D8—22no—
440C2×D8—21no—
441C2×M16—21no—
442C22×C8—21no—
443#127—22no—
444#127—21no—
445#126—22no—
446#126—22no—
447#125—21no—
448#124—22no—
449#123—22no—
450#123—21no—
451#123—22no—
452#123—22no—
453#123—22no—
454C22⋊Q8D4×C3111yescharacteristic, complemented
455C22⋊Q8C23×C3111yescharacteristic
456#121—22no—
457#121—21no—
458#121—21no—
459#121—22no—
460#121—22no—
461#121—22no—
462#121—22no—
463#121—21no—
464#121—21no—
465#121—21no—
466#121—21no—
467#121—21no—
468#121—21no—
469#121—22no—
470#121—21no—
471#121—21no—
472#121—21no—
473#121—21no—
474#121D4×C3112yescomplemented
475#121D4×C3111yescharacteristic, complemented
476#121C23×C3112yes—
477#121C23×C3111yescharacteristic
478#120—22no—
479#120—22no—
480#120—22no—
481#120—21no—
482#120—22no—
483#120—22no—
484#120—22no—
485C4×D4—22no—
486C4×D4—21no—
487C4×D4—21no—
488C4×D4—21no—
489C4×D4—21no—
490C4×D4—22no—
491#117—21no—
492#117D4×C3111yescharacteristic, complemented
493C2×C4⋊C4D4×C3111yescharacteristic
494C2×C4⋊C4D4×C3111yescharacteristic, complemented
495C2×C4⋊C4C23×C3111yescharacteristic
496C2×C22⋊C4—21no—
497C2×C22⋊C4—21no—
498C2×C22⋊C4—21no—
499C2×C22⋊C4—22no—
500C2×C22⋊C4—22no—
501C2×C22⋊C4C23×C3112yes—
502#107—22no—
503#107—21no—
504#106—21no—
505#103—21no—
506#102—22no—
507#102—21no—
508#102—22no—
509#102—21no—
510#102—21no—
511C22⋊C8—21no—
512C22⋊C8—21no—
513C22⋊C8C23×C3111yescharacteristic
514C22⋊C8C23×C3111yescharacteristic
515C22⋊C8C23×C3112yes—
516#95—21no—
517#95—22no—
518#95C23×C3112yes—
519C31#1845011yescharacteristic, direct product factor, Sylow
520C24—22no—
521C24—21no—
522C24—21no—
523C24C2×D4×C3112yes—
524C24C2×D4×C3111yescharacteristic
525#41—81no—
526C2×Q8C2×D4×C3111yescharacteristic
527C2×D4—22no—
528C2×D4—21no—
529C2×D4—21no—
530C2×D4—22no—
531C2×D4—22no—
532C2×D4—22no—
533C2×D4—22no—
534C2×D4—22no—
535C2×D4—22no—
536C2×D4—21no—
537C2×D4—22no—
538C2×D4—22no—
539C2×D4—21no—
540C2×D4—21no—
541C2×D4—21no—
542C2×D4—21no—
543C2×D4—21no—
544C2×D4—41no—
545C2×D4—41no—
546C2×D4—81no—
547C2×D4—81no—
548C2×D4—82no—
549C2×D4—81no—
550C2×D4—82no—
551C2×D4—82no—
552C2×D4—82no—
553C2×D4—82no—
554C2×D4—82no—
555C2×D4—82no—
556C2×D4—82no—
557C2×D4—82no—
558C2×D4—84no—
559C2×D4C2×D4×C3111yescharacteristic
560C2×D4C2×D4×C3112yes—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—22no—
566C22×C4—21no—
567C22×C4—81no—
568C22×C4C2×D4×C3112yes—
569C22×C4C2×D4×C3111yescharacteristic
570C22×C4C2×D4×C3111yescharacteristic
571C22×C4C2×D4×C3111yescharacteristic
572C22×C4C2×D4×C3111yescharacteristic
573C22×C4C2×D4×C3111yescharacteristic
574C22×C4C24×C3111yescharacteristic
575SD16—81no—
576D8—82no—
577D8—81no—
578M16—81no—
579C2×C8—22no—
580C2×C8—21no—
581C2×C8—21no—
582C2×C8—81no—
583C4⋊C4—22no—
584C4⋊C4—22no—
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—21no—
590C4⋊C4—21no—
591C4⋊C4—21no—
592C4⋊C4C2×D4×C3111yescharacteristic
593C4⋊C4C2×D4×C3112yes—
594C4⋊C4C2×D4×C3111yescharacteristic
595C22⋊C4—22no—
596C22⋊C4—22no—
597C22⋊C4—22no—
598C22⋊C4—22no—
599C22⋊C4—22no—
600C22⋊C4—21no—
601C22⋊C4—21no—
602C22⋊C4—21no—
603C22⋊C4—22no—
604C22⋊C4—21no—
605C22⋊C4—22no—
606C22⋊C4—22no—
607C22⋊C4—22no—
608C22⋊C4—21no—
609C22⋊C4—41no—
610C22⋊C4—41no—
611C22⋊C4—82no—
612C22⋊C4—82no—
613C22⋊C4—81no—
614C42—22no—
615C42—21no—
616C23—22no—
617C23—22no—
618C23—22no—
619C23—21no—
620C23—22no—
621C23—22no—
622C23—41no—
623C23—41no—
624C23—42no—
625C23—42no—
626C23—42no—
627C23—41no—
628C23—41no—
629C23—42no—
630C23—41no—
631C23—42no—
632C23—81no—
633C23—81no—
634C23—82no—
635C23—82no—
636C23—82no—
637C23C31×#12011yescharacteristic
638C23C31×#12011yescharacteristic
639C23C22×D4×C3111yescharacteristic
640Q8—41no—
641D4—42no—
642D4—41no—
643D4—42no—
644D4—42no—
645D4—42no—
646D4—41no—
647D4—41no—
648D4—44no—
649D4—42no—
650D4—42no—
651D4—42no—
652D4—42no—
653D4—81no—
654D4—82no—
655D4—82no—
656D4—81no—
657D4—82no—
658D4—82no—
659D4—82no—
660D4—82no—
661D4—82no—
662D4—82no—
663D4—82no—
664D4—88no—
665C2×C4—21no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—41no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—81no—
684C2×C4—82no—
685C2×C4—82no—
686C2×C4C31×#12011yescharacteristic
687C2×C4C31×#12011yescharacteristic
688C2×C4C22×D4×C3111yescharacteristic
689C2×C4C22×D4×C3111yescharacteristic
690C8—42no—
691C8—41no—
692C8—41no—
693C22—21no—
694C22—21no—
695C22—21no—
696C22—21no—
697C22—21no—
698C22—21no—
699C22—21no—
700C22—21no—
701C22—42no—
702C22—42no—
703C22—41no—
704C22—42no—
705C22—42no—
706C22—41no—
707C22—41no—
708C22—42no—
709C22—42no—
710C22—82no—
711C22—82no—
712C22—82no—
713C22—82no—
714C22—82no—
715C22—81no—
716C22—81no—
717C22—81no—
718C22—162no—
719C22—164no—
720C22C2×C31×#12011yescharacteristic
721C22C31×#57612yes—
722C4—21no—
723C4—21no—
724C4—21no—
725C4—21no—
726C4—42no—
727C4—41no—
728C4—42no—
729C4—41no—
730C4—41no—
731C4—82no—
732C4—81no—
733C2—22no—
734C2—41no—
735C2—41no—
736C2—82no—
737C2—82no—
738C2—81no—
739C2—161no—
740C2C31×#300811yescharacteristic
741C2C31×#301911yescharacteristic
742C2C31×#302611yescharacteristic
subgroupG/H
center, socleC22×C31C2×#120
commutator, Frattini, cosocleC22×C4C24×C31
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C31 ◁ C23×C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C31×#3537C2semidirect
2. C31×#3194C2semidirect
3. C31×#3186C2semidirect
4. C31×#2815C2semidirect
5. C31×#1612C2semidirect
6. C31×#1607C2semidirect
7. C31×#1600C2semidirect
8. C31×#1595C2semidirect
9. C31×#1516C2semidirect
10. C31×#1510C2semidirect
11. C31×#1471C2semidirect
27. C2×C31×#121C22semidirect
28. C31×#483C22semidirect
31. C31×#480C22semidirect
32. C31×#480C22semidirect
36. C31×#450C22semidirect
39. C31×#447C22semidirect
40. C31×#447C22semidirect
41. C31×#407C22semidirect
42. C2×C31×C22⋊C8C22semidirect
44. C31×#397C22semidirect
47. C31×#392C22semidirect
48. C31×#381C22semidirect
49. C31×#328C22semidirect
50. C31×#327C22semidirect
51. C31×#327C22semidirect
52. C31×#327C22semidirect
53. C31×#323C22semidirect
54. C31×#323C22semidirect
55. C2×#41×C31D4semidirect
64. C22×D4×C31D4semidirect
83. C31×C22⋊Q8D4semidirect
103. C31×#121D4semidirect
104. C31×#121D4semidirect
121. C31×#117D4semidirect
123. C2×C4⋊C4×C31D4semidirect
244. #18450C31direct (N × H)
322. #3537C2×C31semidirect
323. #3194C2×C31semidirect
324. #3186C2×C31semidirect
325. #2815C2×C31semidirect
326. #1612C2×C31semidirect
327. #1607C2×C31semidirect
328. #1600C2×C31semidirect
329. #1595C2×C31semidirect
330. #1516C2×C31semidirect
331. #1510C2×C31semidirect
332. #1471C2×C31semidirect
388. C2×#121C22×C31semidirect
389. #483C22×C31semidirect
392. #480C22×C31semidirect
393. #480C22×C31semidirect
397. #450C22×C31semidirect
400. #447C22×C31semidirect
401. #447C22×C31semidirect
402. #407C22×C31semidirect
403. C2×C22⋊C8C22×C31semidirect
405. #397C22×C31semidirect
408. #392C22×C31semidirect
409. #381C22×C31semidirect
410. #328C22×C31semidirect
411. #327C22×C31semidirect
412. #327C22×C31semidirect
413. #327C22×C31semidirect
414. #323C22×C31semidirect
415. #323C22×C31semidirect
426. C2×#41D4×C31semidirect
435. C22×D4D4×C31semidirect
454. C22⋊Q8D4×C31semidirect
474. #121D4×C31semidirect
475. #121D4×C31semidirect
492. #117D4×C31semidirect
494. C2×C4⋊C4D4×C31semidirect
519. C31#18450direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#35372
C31×#31942
C31×#31862
C31×#28152
C31×#16122
C31×#16072
C31×#16002
C31×#15952
C31×#15162
C31×#15102
C31×#14712
#1845031