Finite Group Databasebeta

← C31×#18254 #21475013

Subgroups — C31×#18254 #21475013

Order 7936.

1508 conjugacy classes of subgroups.

The subgroup lattice has 734 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3537C211yesmaximal, characteristic, complemented
2C31×#3003C211yesmaximal, characteristic, complemented
3C2×C31×#447C211yesmaximal, characteristic, complemented
4C31×#2433C211yesmaximal, characteristic, complemented
5C31×#1600C214yesmaximal, complemented
6C31×#1595C214yesmaximal, complemented
7C31×#1507C211yesmaximal, characteristic, complemented
8C31×#1501C211yesmaximal, characteristic, complemented
9C31×#1471C211yesmaximal, characteristic, complemented
10C23×D4×C31C2211yescharacteristic, complemented
11C2×C31×AGL(1,ℤ/8)—21no—
12C22×D8×C31—21no—
13C31×#560—22no—
14C31×#553—21no—
15C31×#553—21no—
16D42×C31—22no—
17D42×C31—21no—
18D42×C31—21no—
19C31×#540—21no—
20C31×#538—21no—
21C31×#538C2212yescomplemented
22C31×#535—21no—
23C31×#534—21no—
24C31×#534C2212yescomplemented
25C2×C31×#127—21no—
26C31×#525C2211yescharacteristic
27C2×C31×#121C2211yescharacteristic
28C2×C31×#121C2211yescharacteristic
29C2×C31×#120—22no—
30C31×#450—21no—
31C31×#450C2212yescomplemented
32C31×#447—22no—
33C31×#447—21no—
34C31×#447C2212yescomplemented
35C31×#447C2214yescomplemented
36C31×#418—21no—
37C2×C31×#102—21no—
38C31×#407C2211yescharacteristic, complemented
39C2×C31×C22⋊C8C2211yescharacteristic, complemented
40C31×#392C2214yescomplemented
41C31×#390—21no—
42C4×C22⋊C4×C31C2211yescharacteristic, complemented
43C31×#328C2212yescomplemented
44C31×#327C2212yescomplemented
45C31×#327C2214yescomplemented
46C31×#323C2214yescomplemented
47C25×C31—21no—
48C2×#41×C31D411yescharacteristic, complemented
49C22×D4×C31—22no—
50C22×D4×C31—21no—
51C22×D4×C31—21no—
52C22×D4×C31—22no—
53C22×D4×C31—24no—
54C22×D4×C31—21no—
55C22×D4×C31—21no—
56C22×D4×C31—21no—
57C22×D4×C31—21no—
58C22×D4×C31—21no—
59C22×D4×C31—44no—
60C22×D4×C31D412yes—
61C22×D4×C31D411yescharacteristic
62C22×D4×C31D411yescharacteristic, complemented
63C22×D4×C31C2312yes—
64C23×C4×C31C2311yescharacteristic
65C31×AGL(1,ℤ/8)—44no—
66C2×SD16×C31—22no—
67C2×D8×C31—24no—
68C2×D8×C31—22no—
69C2×D8×C31—44no—
70C2×M16×C31—21no—
71C22×C8×C31—21no—
72C31×#127—22no—
73C31×#127—21no—
74C31×#127—44no—
75C31×#126—22no—
76C31×#126—22no—
77C31×#125—21no—
78C31×#124—22no—
79C31×#123—22no—
80C31×#123—21no—
81C31×#123—22no—
82C31×#123—22no—
83C31×#123—22no—
84C31×C22⋊Q8D411yescharacteristic, complemented
85C31×C22⋊Q8C2311yescharacteristic
86C31×#121—22no—
87C31×#121—21no—
88C31×#121—21no—
89C31×#121—22no—
90C31×#121—22no—
91C31×#121—22no—
92C31×#121—22no—
93C31×#121—21no—
94C31×#121—21no—
95C31×#121—21no—
96C31×#121—21no—
97C31×#121—21no—
98C31×#121—21no—
99C31×#121—22no—
100C31×#121D412yescomplemented
101C31×#121D411yescharacteristic, complemented
102C31×#121C2312yes—
103C31×#121C2311yescharacteristic
104C31×#120—22no—
105C31×#120—22no—
106C31×#120—22no—
107C31×#120—21no—
108C31×#120—22no—
109C31×#120—22no—
110C31×#120—22no—
111C31×#120—48no—
112C4×D4×C31—22no—
113C4×D4×C31—21no—
114C4×D4×C31—21no—
115C4×D4×C31—21no—
116C4×D4×C31—21no—
117C4×D4×C31—22no—
118C31×#117—21no—
119C31×#117D411yescharacteristic, complemented
120C2×C4⋊C4×C31D411yescharacteristic
121C2×C4⋊C4×C31D411yescharacteristic, complemented
122C2×C22⋊C4×C31—21no—
123C2×C22⋊C4×C31—21no—
124C2×C22⋊C4×C31—24no—
125C2×C22⋊C4×C31C2312yes—
126C2×C42×C31—21no—
127C31×#102—24no—
128C31×#102—22no—
129C31×#102—22no—
130C31×C22⋊C8—21no—
131C31×C22⋊C8—21no—
132C31×C22⋊C8C2312yes—
133C31×C22⋊C8C2312yes—
134C31×#95C2312yes—
135C24×C31—22no—
136C24×C31—22no—
137C24×C31—21no—
138C24×C31—44no—
139C24×C31—44no—
140C24×C31—41no—
141C24×C31—41no—
142C24×C31—82no—
143C24×C31C2×D411yescharacteristic
144C24×C31C2×D412yes—
145#41×C31—42no—
146C2×Q8×C31C2×D411yescharacteristic
147C2×D4×C31—24no—
148C2×D4×C31—24no—
149C2×D4×C31—24no—
150C2×D4×C31—22no—
151C2×D4×C31—21no—
152C2×D4×C31—21no—
153C2×D4×C31—22no—
154C2×D4×C31—22no—
155C2×D4×C31—22no—
156C2×D4×C31—22no—
157C2×D4×C31—22no—
158C2×D4×C31—22no—
159C2×D4×C31—21no—
160C2×D4×C31—22no—
161C2×D4×C31—22no—
162C2×D4×C31—21no—
163C2×D4×C31—21no—
164C2×D4×C31—21no—
165C2×D4×C31—22no—
166C2×D4×C31—22no—
167C2×D4×C31—42no—
168C2×D4×C31—42no—
169C2×D4×C31—42no—
170C2×D4×C31—42no—
171C2×D4×C31—42no—
172C2×D4×C31—48no—
173C2×D4×C31—44no—
174C2×D4×C31—44no—
175C2×D4×C31—44no—
176C2×D4×C31—44no—
177C2×D4×C31—48no—
178C2×D4×C31—41no—
179C2×D4×C31—41no—
180C2×D4×C31—82no—
181C2×D4×C31—84no—
182C2×D4×C31—82no—
183C2×D4×C31—84no—
184C2×D4×C31—84no—
185C2×D4×C31C2×D411yescharacteristic
186C2×D4×C31C2×D412yes—
187C22×C4×C31—22no—
188C22×C4×C31—22no—
189C22×C4×C31—22no—
190C22×C4×C31—21no—
191C22×C4×C31—21no—
192C22×C4×C31—42no—
193C22×C4×C31C2×D411yescharacteristic
194C22×C4×C31C2×D411yescharacteristic
195C22×C4×C31C2×D411yescharacteristic
196C22×C4×C31C2×D412yes—
197C22×C4×C31C2×D411yescharacteristic
198C22×C4×C31C2×D411yescharacteristic
199C22×C4×C31C2411yescharacteristic
200SD16×C31—44no—
201D8×C31—48no—
202D8×C31—44no—
203M16×C31—42no—
204C2×C8×C31—22no—
205C2×C8×C31—22no—
206C2×C8×C31—42no—
207C4⋊C4×C31—22no—
208C4⋊C4×C31—22no—
209C4⋊C4×C31—21no—
210C4⋊C4×C31—21no—
211C4⋊C4×C31—21no—
212C4⋊C4×C31—21no—
213C4⋊C4×C31—21no—
214C4⋊C4×C31C2×D412yes—
215C4⋊C4×C31C2×D411yescharacteristic
216C4⋊C4×C31C2×D411yescharacteristic
217C22⋊C4×C31—24no—
218C22⋊C4×C31—22no—
219C22⋊C4×C31—22no—
220C22⋊C4×C31—22no—
221C22⋊C4×C31—22no—
222C22⋊C4×C31—22no—
223C22⋊C4×C31—21no—
224C22⋊C4×C31—21no—
225C22⋊C4×C31—21no—
226C22⋊C4×C31—22no—
227C22⋊C4×C31—21no—
228C22⋊C4×C31—22no—
229C22⋊C4×C31—22no—
230C22⋊C4×C31—22no—
231C22⋊C4×C31—21no—
232C22⋊C4×C31—48no—
233C42×C31—22no—
234C42×C31—21no—
235C42×C31—42no—
236#18254C3111yesmaximal, characteristic, direct product factor, Sylow
237C23×C31—22no—
238C23×C31—22no—
239C23×C31—24no—
240C23×C31—22no—
241C23×C31—22no—
242C23×C31—21no—
243C23×C31—24no—
244C23×C31—41no—
245C23×C31—44no—
246C23×C31—44no—
247C23×C31—44no—
248C23×C31—42no—
249C23×C31—42no—
250C23×C31—42no—
251C23×C31—42no—
252C23×C31—44no—
253C23×C31—42no—
254C23×C31—81no—
255C23×C31—81no—
256C23×C31—82no—
257C23×C31—82no—
258C23×C31—82no—
259C23×C31—82no—
260C23×C31—82no—
261C23×C31—82no—
262C23×C31—816no—
263C23×C31—82no—
264C23×C31#12011yescharacteristic
265C23×C31#12011yescharacteristic
266C23×C31C22×D411yescharacteristic
267Q8×C31—41no—
268D4×C31—24no—
269D4×C31—24no—
270D4×C31—42no—
271D4×C31—41no—
272D4×C31—42no—
273D4×C31—42no—
274D4×C31—44no—
275D4×C31—44no—
276D4×C31—42no—
277D4×C31—44no—
278D4×C31—42no—
279D4×C31—44no—
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—816no—
292C2×C4×C31—22no—
293C2×C4×C31—22no—
294C2×C4×C31—22no—
295C2×C4×C31—24no—
296C2×C4×C31—21no—
297C2×C4×C31—22no—
298C2×C4×C31—22no—
299C2×C4×C31—21no—
300C2×C4×C31—21no—
301C2×C4×C31—41no—
302C2×C4×C31—41no—
303C2×C4×C31—41no—
304C2×C4×C31—42no—
305C2×C4×C31—42no—
306C2×C4×C31—42no—
307C2×C4×C31—42no—
308C2×C4×C31—81no—
309C2×C4×C31—82no—
310C2×C4×C31—82no—
311C2×C4×C31#12011yescharacteristic
312C2×C4×C31#12011yescharacteristic
313C2×C4×C31C22×D411yescharacteristic
314C2×C4×C31C22×D411yescharacteristic
315C8×C31—42no—
316C8×C31—42no—
317#3537C2×C3111yescharacteristic, complemented
318#3003C2×C3111yescharacteristic, complemented
319C2×#447C2×C3111yescharacteristic, complemented
320#2433C2×C3111yescharacteristic, complemented
321#1600C2×C3114yescomplemented
322#1595C2×C3114yescomplemented
323#1507C2×C3111yescharacteristic, complemented
324#1501C2×C3111yescharacteristic, complemented
325#1471C2×C3111yescharacteristic, complemented
326C22×C31—21no—
327C22×C31—21no—
328C22×C31—21no—
329C22×C31—21no—
330C22×C31—21no—
331C22×C31—21no—
332C22×C31—21no—
333C22×C31—44no—
334C22×C31—48no—
335C22×C31—42no—
336C22×C31—42no—
337C22×C31—41no—
338C22×C31—42no—
339C22×C31—42no—
340C22×C31—41no—
341C22×C31—41no—
342C22×C31—44no—
343C22×C31—42no—
344C22×C31—42no—
345C22×C31—84no—
346C22×C31—84no—
347C22×C31—88no—
348C22×C31—88no—
349C22×C31—82no—
350C22×C31—82no—
351C22×C31—162no—
352C22×C31—164no—
353C22×C31#45312yes—
354C22×C31C2×#12011yescharacteristic
355C22×C31#57612yes—
356C4×C31—21no—
357C4×C31—21no—
358C4×C31—21no—
359C4×C31—44no—
360C4×C31—42no—
361C4×C31—41no—
362C4×C31—42no—
363C4×C31—41no—
364C4×C31—41no—
365C4×C31B(4,𝔽2)12yes—
366C23×D4C22×C3111yescharacteristic, complemented
367C2×AGL(1,ℤ/8)—21no—
368C22×D8—21no—
369#560—22no—
370#553—21no—
371#553—21no—
372D42—22no—
373D42—21no—
374D42—21no—
375#540—21no—
376#538—21no—
377#538C22×C3112yescomplemented
378#535—21no—
379#534—21no—
380#534C22×C3112yescomplemented
381C2×#127—21no—
382#525C22×C3111yescharacteristic
383C2×#121C22×C3111yescharacteristic
384C2×#121C22×C3111yescharacteristic
385C2×#120—22no—
386#450—21no—
387#450C22×C3112yescomplemented
388#447—22no—
389#447—21no—
390#447C22×C3112yescomplemented
391#447C22×C3114yescomplemented
392#418—21no—
393C2×#102—21no—
394#407C22×C3111yescharacteristic, complemented
395C2×C22⋊C8C22×C3111yescharacteristic, complemented
396#392C22×C3114yescomplemented
397#390—21no—
398C4×C22⋊C4C22×C3111yescharacteristic, complemented
399#328C22×C3112yescomplemented
400#327C22×C3112yescomplemented
401#327C22×C3114yescomplemented
402#323C22×C3114yescomplemented
403C2×C31—22no—
404C2×C31—22no—
405C2×C31—41no—
406C2×C31—84no—
407C2×C31—82no—
408C2×C31—82no—
409C2×C31—81no—
410C2×C31#300811yescharacteristic
411C2×C31C2×#45311yescharacteristic
412C2×C31C2×B(4,𝔽2)11yescharacteristic
413C25—21no—
414C2×#41D4×C3111yescharacteristic, complemented
415C22×D4—22no—
416C22×D4—21no—
417C22×D4—21no—
418C22×D4—22no—
419C22×D4—24no—
420C22×D4—21no—
421C22×D4—21no—
422C22×D4—21no—
423C22×D4—21no—
424C22×D4—21no—
425C22×D4—44no—
426C22×D4D4×C3112yes—
427C22×D4D4×C3111yescharacteristic
428C22×D4D4×C3111yescharacteristic, complemented
429C22×D4C23×C3112yes—
430C23×C4C23×C3111yescharacteristic
431AGL(1,ℤ/8)—44no—
432C2×SD16—22no—
433C2×D8—24no—
434C2×D8—22no—
435C2×D8—44no—
436C2×M16—21no—
437C22×C8—21no—
438#127—22no—
439#127—21no—
440#127—44no—
441#126—22no—
442#126—22no—
443#125—21no—
444#124—22no—
445#123—22no—
446#123—21no—
447#123—22no—
448#123—22no—
449#123—22no—
450C22⋊Q8D4×C3111yescharacteristic, complemented
451C22⋊Q8C23×C3111yescharacteristic
452#121—22no—
453#121—21no—
454#121—21no—
455#121—22no—
456#121—22no—
457#121—22no—
458#121—22no—
459#121—21no—
460#121—21no—
461#121—21no—
462#121—21no—
463#121—21no—
464#121—21no—
465#121—22no—
466#121D4×C3112yescomplemented
467#121D4×C3111yescharacteristic, complemented
468#121C23×C3112yes—
469#121C23×C3111yescharacteristic
470#120—22no—
471#120—22no—
472#120—22no—
473#120—21no—
474#120—22no—
475#120—22no—
476#120—22no—
477#120—48no—
478C4×D4—22no—
479C4×D4—21no—
480C4×D4—21no—
481C4×D4—21no—
482C4×D4—21no—
483C4×D4—22no—
484#117—21no—
485#117D4×C3111yescharacteristic, complemented
486C2×C4⋊C4D4×C3111yescharacteristic
487C2×C4⋊C4D4×C3111yescharacteristic, complemented
488C2×C22⋊C4—21no—
489C2×C22⋊C4—21no—
490C2×C22⋊C4—24no—
491C2×C22⋊C4C23×C3112yes—
492C2×C42—21no—
493#102—24no—
494#102—22no—
495#102—22no—
496C22⋊C8—21no—
497C22⋊C8—21no—
498C22⋊C8C23×C3112yes—
499C22⋊C8C23×C3112yes—
500#95C23×C3112yes—
501C31#1825411yescharacteristic, direct product factor, Sylow
502C24—22no—
503C24—22no—
504C24—21no—
505C24—44no—
506C24—44no—
507C24—41no—
508C24—41no—
509C24—82no—
510C24C2×D4×C3111yescharacteristic
511C24C2×D4×C3112yes—
512#41—42no—
513C2×Q8C2×D4×C3111yescharacteristic
514C2×D4—24no—
515C2×D4—24no—
516C2×D4—24no—
517C2×D4—22no—
518C2×D4—21no—
519C2×D4—21no—
520C2×D4—22no—
521C2×D4—22no—
522C2×D4—22no—
523C2×D4—22no—
524C2×D4—22no—
525C2×D4—22no—
526C2×D4—21no—
527C2×D4—22no—
528C2×D4—22no—
529C2×D4—21no—
530C2×D4—21no—
531C2×D4—21no—
532C2×D4—22no—
533C2×D4—22no—
534C2×D4—42no—
535C2×D4—42no—
536C2×D4—42no—
537C2×D4—42no—
538C2×D4—42no—
539C2×D4—48no—
540C2×D4—44no—
541C2×D4—44no—
542C2×D4—44no—
543C2×D4—44no—
544C2×D4—48no—
545C2×D4—41no—
546C2×D4—41no—
547C2×D4—82no—
548C2×D4—84no—
549C2×D4—82no—
550C2×D4—84no—
551C2×D4—84no—
552C2×D4C2×D4×C3111yescharacteristic
553C2×D4C2×D4×C3112yes—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—42no—
560C22×C4C2×D4×C3111yescharacteristic
561C22×C4C2×D4×C3111yescharacteristic
562C22×C4C2×D4×C3111yescharacteristic
563C22×C4C2×D4×C3112yes—
564C22×C4C2×D4×C3111yescharacteristic
565C22×C4C2×D4×C3111yescharacteristic
566C22×C4C24×C3111yescharacteristic
567SD16—44no—
568D8—48no—
569D8—44no—
570M16—42no—
571C2×C8—22no—
572C2×C8—22no—
573C2×C8—42no—
574C4⋊C4—22no—
575C4⋊C4—22no—
576C4⋊C4—21no—
577C4⋊C4—21no—
578C4⋊C4—21no—
579C4⋊C4—21no—
580C4⋊C4—21no—
581C4⋊C4C2×D4×C3112yes—
582C4⋊C4C2×D4×C3111yescharacteristic
583C4⋊C4C2×D4×C3111yescharacteristic
584C22⋊C4—24no—
585C22⋊C4—22no—
586C22⋊C4—22no—
587C22⋊C4—22no—
588C22⋊C4—22no—
589C22⋊C4—22no—
590C22⋊C4—21no—
591C22⋊C4—21no—
592C22⋊C4—21no—
593C22⋊C4—22no—
594C22⋊C4—21no—
595C22⋊C4—22no—
596C22⋊C4—22no—
597C22⋊C4—22no—
598C22⋊C4—21no—
599C22⋊C4—48no—
600C42—22no—
601C42—21no—
602C42—42no—
603C23—22no—
604C23—22no—
605C23—24no—
606C23—22no—
607C23—22no—
608C23—21no—
609C23—24no—
610C23—41no—
611C23—44no—
612C23—44no—
613C23—44no—
614C23—42no—
615C23—42no—
616C23—42no—
617C23—42no—
618C23—44no—
619C23—42no—
620C23—81no—
621C23—81no—
622C23—82no—
623C23—82no—
624C23—82no—
625C23—82no—
626C23—82no—
627C23—82no—
628C23—816no—
629C23—82no—
630C23C31×#12011yescharacteristic
631C23C31×#12011yescharacteristic
632C23C22×D4×C3111yescharacteristic
633Q8—41no—
634D4—24no—
635D4—24no—
636D4—42no—
637D4—41no—
638D4—42no—
639D4—42no—
640D4—44no—
641D4—44no—
642D4—42no—
643D4—44no—
644D4—42no—
645D4—44no—
646D4—42no—
647D4—42no—
648D4—81no—
649D4—82no—
650D4—82no—
651D4—81no—
652D4—82no—
653D4—82no—
654D4—82no—
655D4—82no—
656D4—82no—
657D4—816no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—24no—
662C2×C4—21no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—42no—
671C2×C4—42no—
672C2×C4—42no—
673C2×C4—42no—
674C2×C4—81no—
675C2×C4—82no—
676C2×C4—82no—
677C2×C4C31×#12011yescharacteristic
678C2×C4C31×#12011yescharacteristic
679C2×C4C22×D4×C3111yescharacteristic
680C2×C4C22×D4×C3111yescharacteristic
681C8—42no—
682C8—42no—
683C22—21no—
684C22—21no—
685C22—21no—
686C22—21no—
687C22—21no—
688C22—21no—
689C22—21no—
690C22—44no—
691C22—48no—
692C22—42no—
693C22—42no—
694C22—41no—
695C22—42no—
696C22—42no—
697C22—41no—
698C22—41no—
699C22—44no—
700C22—42no—
701C22—42no—
702C22—84no—
703C22—84no—
704C22—88no—
705C22—88no—
706C22—82no—
707C22—82no—
708C22—162no—
709C22—164no—
710C22C31×#45312yes—
711C22C2×C31×#12011yescharacteristic
712C22C31×#57612yes—
713C4—21no—
714C4—21no—
715C4—21no—
716C4—44no—
717C4—42no—
718C4—41no—
719C4—42no—
720C4—41no—
721C4—41no—
722C4C31×B(4,𝔽2)12yes—
723C2—22no—
724C2—22no—
725C2—41no—
726C2—84no—
727C2—82no—
728C2—82no—
729C2—81no—
730C2C31×#300811yescharacteristic
731C2C2×C31×#45311yescharacteristic
732C2C2×C31×B(4,𝔽2)11yescharacteristic
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×#3003C2semidirect
3. C2×C31×#447C2semidirect
4. C31×#2433C2semidirect
5. C31×#1600C2semidirect
6. C31×#1595C2semidirect
7. C31×#1507C2semidirect
8. C31×#1501C2semidirect
9. C31×#1471C2semidirect
10. C23×D4×C31C22semidirect
21. C31×#538C22semidirect
24. C31×#534C22semidirect
31. C31×#450C22semidirect
34. C31×#447C22semidirect
35. C31×#447C22semidirect
38. C31×#407C22semidirect
39. C2×C31×C22⋊C8C22semidirect
40. C31×#392C22semidirect
42. C4×C22⋊C4×C31C22semidirect
43. C31×#328C22semidirect
44. C31×#327C22semidirect
45. C31×#327C22semidirect
46. C31×#323C22semidirect
48. C2×#41×C31D4semidirect
62. C22×D4×C31D4semidirect
84. C31×C22⋊Q8D4semidirect
100. C31×#121D4semidirect
101. C31×#121D4semidirect
119. C31×#117D4semidirect
121. C2×C4⋊C4×C31D4semidirect
236. #18254C31direct (N × H)
317. #3537C2×C31semidirect
318. #3003C2×C31semidirect
319. C2×#447C2×C31semidirect
320. #2433C2×C31semidirect
321. #1600C2×C31semidirect
322. #1595C2×C31semidirect
323. #1507C2×C31semidirect
324. #1501C2×C31semidirect
325. #1471C2×C31semidirect
366. C23×D4C22×C31semidirect
377. #538C22×C31semidirect
380. #534C22×C31semidirect
387. #450C22×C31semidirect
390. #447C22×C31semidirect
391. #447C22×C31semidirect
394. #407C22×C31semidirect
395. C2×C22⋊C8C22×C31semidirect
396. #392C22×C31semidirect
398. C4×C22⋊C4C22×C31semidirect
399. #328C22×C31semidirect
400. #327C22×C31semidirect
401. #327C22×C31semidirect
402. #323C22×C31semidirect
414. C2×#41D4×C31semidirect
428. C22×D4D4×C31semidirect
450. C22⋊Q8D4×C31semidirect
466. #121D4×C31semidirect
467. #121D4×C31semidirect
485. #117D4×C31semidirect
487. C2×C4⋊C4D4×C31semidirect
501. C31#18254direct (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×#30032
C2×C31×#4472
C31×#24332
C31×#16002
C31×#15952
C31×#15072
C31×#15012
C31×#14712
#1825431