Finite Group Databasebeta

← C31×#18418 #21475177

Subgroups — C31×#18418 #21475177

Order 7936.

1176 conjugacy classes of subgroups.

The subgroup lattice has 766 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3537C211yesmaximal, characteristic, complemented
2C31×#3192C211yesmaximal, characteristic, complemented
3C31×#3188C211yesmaximal, characteristic, complemented
4C31×#2656C211yesmaximal, characteristic, complemented
5C31×#1618C212yesmaximal, complemented
6C31×#1613C212yesmaximal, complemented
7C31×#1600C212yesmaximal, complemented
8C31×#1595C212yesmaximal, complemented
9C31×#1504C211yesmaximal, characteristic, complemented
10C2×C31×#327C211yesmaximal, 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×#121—22no—
26C2×C31×#121C2211yescharacteristic
27C2×C31×#121C2211yescharacteristic
28C2×C31×#121C2211yescharacteristic, complemented
29C31×#484C2211yescharacteristic, complemented
30C31×#482—21no—
31C31×#481—21no—
32C31×#481C2211yescharacteristic, complemented
33C31×#481C2212yescomplemented
34C31×#469—22no—
35C31×#466—21no—
36C31×#465—21no—
37C31×#450C2211yescharacteristic, complemented
38C31×#449—21no—
39C31×#447—21no—
40C31×#447C2211yescharacteristic, complemented
41C31×#447C2212yescomplemented
42C31×#407C2211yescharacteristic, complemented
43C2×C31×C22⋊C8C2211yescharacteristic, complemented
44C31×#399—21no—
45C31×#399C2212yescomplemented
46C31×#392—21no—
47C31×#392C2212yescomplemented
48C2×C31×#95C2211yescharacteristic, 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×C31—21no—
67C23×C4×C31C2311yescharacteristic
68C2×SD16×C31—21no—
69C2×D8×C31—22no—
70C2×D8×C31—21no—
71C2×M16×C31—21no—
72C22×C8×C31—21no—
73C31×#127—22no—
74C31×#127—21no—
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×#121—21no—
101C31×#121—21no—
102C31×#121—21no—
103C31×#121—21no—
104C31×#121—48no—
105C31×#121D411yescharacteristic, complemented
106C31×#121D412yescomplemented
107C31×#121C2312yes—
108C31×#121C2311yescharacteristic
109C31×#120—22no—
110C31×#120—22no—
111C31×#120—22no—
112C31×#120—21no—
113C31×#120—22no—
114C31×#120—22no—
115C31×#120—22no—
116C4×D4×C31—22no—
117C4×D4×C31—21no—
118C4×D4×C31—21no—
119C4×D4×C31—21no—
120C4×D4×C31—21no—
121C4×D4×C31—22no—
122C31×#117—21no—
123C31×#117D411yescharacteristic, complemented
124C2×C4⋊C4×C31—22no—
125C2×C4⋊C4×C31D411yescharacteristic
126C2×C4⋊C4×C31D411yescharacteristic, complemented
127C2×C4⋊C4×C31C2311yescharacteristic
128C2×C22⋊C4×C31—21no—
129C2×C22⋊C4×C31—22no—
130C2×C22⋊C4×C31—22no—
131C2×C22⋊C4×C31—21no—
132C2×C22⋊C4×C31C2312yes—
133C31×#107—21no—
134C31×#106—21no—
135C31×#106—22no—
136C31×#103—21no—
137C31×#102—22no—
138C31×#102—21no—
139C31×#102—21no—
140C31×#102—22no—
141C31×#102—21no—
142C31×C22⋊C8—21no—
143C31×C22⋊C8—21no—
144C31×C22⋊C8C2311yescharacteristic
145C31×C22⋊C8C2311yescharacteristic
146C31×C22⋊C8C2312yes—
147C31×#95—21no—
148C31×#95C2312yes—
149C24×C31—22no—
150C24×C31—21no—
151C24×C31—21no—
152C24×C31C2×D411yescharacteristic
153C24×C31C2×D412yes—
154#41×C31—81no—
155C2×Q8×C31C2×D411yescharacteristic
156C2×D4×C31—22no—
157C2×D4×C31—21no—
158C2×D4×C31—21no—
159C2×D4×C31—22no—
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—22no—
167C2×D4×C31—22no—
168C2×D4×C31—21no—
169C2×D4×C31—21no—
170C2×D4×C31—21no—
171C2×D4×C31—21no—
172C2×D4×C31—21no—
173C2×D4×C31—44no—
174C2×D4×C31—44no—
175C2×D4×C31—44no—
176C2×D4×C31—41no—
177C2×D4×C31—41no—
178C2×D4×C31—81no—
179C2×D4×C31—81no—
180C2×D4×C31—82no—
181C2×D4×C31—81no—
182C2×D4×C31—82no—
183C2×D4×C31—82no—
184C2×D4×C31—81no—
185C2×D4×C31—81no—
186C2×D4×C31—82no—
187C2×D4×C31—82no—
188C2×D4×C31—84no—
189C2×D4×C31C2×D411yescharacteristic
190C2×D4×C31C2×D412yes—
191C22×C4×C31—22no—
192C22×C4×C31—22no—
193C22×C4×C31—22no—
194C22×C4×C31—24no—
195C22×C4×C31—21no—
196C22×C4×C31—21no—
197C22×C4×C31—21no—
198C22×C4×C31—81no—
199C22×C4×C31—81no—
200C22×C4×C31—81no—
201C22×C4×C31C2×D412yes—
202C22×C4×C31C2×D411yescharacteristic
203C22×C4×C31C2×D411yescharacteristic
204C22×C4×C31C2×D411yescharacteristic
205C22×C4×C31C2×D411yescharacteristic
206C22×C4×C31C2×D411yescharacteristic
207C22×C4×C31C2411yescharacteristic
208SD16×C31—81no—
209D8×C31—81no—
210D8×C31—82no—
211M16×C31—81no—
212C2×C8×C31—21no—
213C2×C8×C31—22no—
214C2×C8×C31—21no—
215C2×C8×C31—81no—
216C4⋊C4×C31—22no—
217C4⋊C4×C31—22no—
218C4⋊C4×C31—21no—
219C4⋊C4×C31—21no—
220C4⋊C4×C31—21no—
221C4⋊C4×C31—21no—
222C4⋊C4×C31—21no—
223C4⋊C4×C31—21no—
224C4⋊C4×C31—21no—
225C4⋊C4×C31—44no—
226C4⋊C4×C31C2×D412yes—
227C4⋊C4×C31C2×D411yescharacteristic
228C4⋊C4×C31C2×D411yescharacteristic
229C22⋊C4×C31—22no—
230C22⋊C4×C31—22no—
231C22⋊C4×C31—22no—
232C22⋊C4×C31—22no—
233C22⋊C4×C31—22no—
234C22⋊C4×C31—21no—
235C22⋊C4×C31—21no—
236C22⋊C4×C31—21no—
237C22⋊C4×C31—22no—
238C22⋊C4×C31—21no—
239C22⋊C4×C31—22no—
240C22⋊C4×C31—22no—
241C22⋊C4×C31—22no—
242C22⋊C4×C31—21no—
243C22⋊C4×C31—44no—
244C22⋊C4×C31—44no—
245C22⋊C4×C31—41no—
246C22⋊C4×C31—41no—
247C42×C31—22no—
248C42×C31—21no—
249#18418C3111yesmaximal, characteristic, direct product factor, Sylow
250C23×C31—21no—
251C23×C31—21no—
252C23×C31—22no—
253C23×C31—22no—
254C23×C31—22no—
255C23×C31—21no—
256C23×C31—22no—
257C23×C31—22no—
258C23×C31—41no—
259C23×C31—42no—
260C23×C31—42no—
261C23×C31—42no—
262C23×C31—42no—
263C23×C31—42no—
264C23×C31—41no—
265C23×C31—41no—
266C23×C31—41no—
267C23×C31—81no—
268C23×C31—81no—
269C23×C31—82no—
270C23×C31—82no—
271C23×C31—82no—
272C23×C31#12011yescharacteristic
273C23×C31#12011yescharacteristic
274C23×C31C22×D411yescharacteristic
275Q8×C31—41no—
276D4×C31—42no—
277D4×C31—41no—
278D4×C31—42no—
279D4×C31—42no—
280D4×C31—42no—
281D4×C31—41no—
282D4×C31—41no—
283D4×C31—42no—
284D4×C31—41no—
285D4×C31—42no—
286D4×C31—41no—
287D4×C31—44no—
288D4×C31—42no—
289D4×C31—81no—
290D4×C31—82no—
291D4×C31—82no—
292D4×C31—81no—
293D4×C31—82no—
294D4×C31—82no—
295D4×C31—82no—
296D4×C31—82no—
297D4×C31—82no—
298D4×C31—88no—
299D4×C31—82no—
300D4×C31—82no—
301C2×C4×C31—24no—
302C2×C4×C31—21no—
303C2×C4×C31—22no—
304C2×C4×C31—22no—
305C2×C4×C31—21no—
306C2×C4×C31—21no—
307C2×C4×C31—41no—
308C2×C4×C31—41no—
309C2×C4×C31—41no—
310C2×C4×C31—41no—
311C2×C4×C31—41no—
312C2×C4×C31—41no—
313C2×C4×C31—42no—
314C2×C4×C31—42no—
315C2×C4×C31—42no—
316C2×C4×C31—42no—
317C2×C4×C31—42no—
318C2×C4×C31—41no—
319C2×C4×C31—81no—
320C2×C4×C31—84no—
321C2×C4×C31—82no—
322C2×C4×C31—82no—
323C2×C4×C31#12011yescharacteristic
324C2×C4×C31#12011yescharacteristic
325C2×C4×C31C22×D411yescharacteristic
326C2×C4×C31C22×D411yescharacteristic
327C8×C31—41no—
328C8×C31—41no—
329C8×C31—42no—
330#3537C2×C3111yescharacteristic, complemented
331#3192C2×C3111yescharacteristic, complemented
332#3188C2×C3111yescharacteristic, complemented
333#2656C2×C3111yescharacteristic, complemented
334#1618C2×C3112yescomplemented
335#1613C2×C3112yescomplemented
336#1600C2×C3112yescomplemented
337#1595C2×C3112yescomplemented
338#1504C2×C3111yescharacteristic, complemented
339C2×#327C2×C3111yescharacteristic, complemented
340#1471C2×C3111yescharacteristic, complemented
341C22×C31—21no—
342C22×C31—21no—
343C22×C31—21no—
344C22×C31—21no—
345C22×C31—21no—
346C22×C31—21no—
347C22×C31—21no—
348C22×C31—42no—
349C22×C31—42no—
350C22×C31—42no—
351C22×C31—42no—
352C22×C31—41no—
353C22×C31—42no—
354C22×C31—42no—
355C22×C31—41no—
356C22×C31—41no—
357C22×C31—42no—
358C22×C31—42no—
359C22×C31—82no—
360C22×C31—82no—
361C22×C31—82no—
362C22×C31—82no—
363C22×C31—81no—
364C22×C31—81no—
365C22×C31—81no—
366C22×C31—162no—
367C22×C31—164no—
368C22×C31#45312yes—
369C22×C31C2×#12011yescharacteristic
370C22×C31#57611yescharacteristic
371C22×C31#57711yescharacteristic
372C4×C31—21no—
373C4×C31—21no—
374C4×C31—21no—
375C4×C31—21no—
376C4×C31—44no—
377C4×C31—42no—
378C4×C31—41no—
379C4×C31—42no—
380C4×C31—41no—
381C4×C31—41no—
382C4×C31—81no—
383#560—22no—
384#553—21no—
385#553—21no—
386D42—22no—
387D42—21no—
388D42—21no—
389#540—21no—
390#538—21no—
391#538C22×C3112yes—
392#535—21no—
393#534—21no—
394#534C22×C3112yes—
395#525C22×C3111yescharacteristic
396C2×#121—22no—
397C2×#121C22×C3111yescharacteristic
398C2×#121C22×C3111yescharacteristic
399C2×#121C22×C3111yescharacteristic, complemented
400#484C22×C3111yescharacteristic, complemented
401#482—21no—
402#481—21no—
403#481C22×C3111yescharacteristic, complemented
404#481C22×C3112yescomplemented
405#469—22no—
406#466—21no—
407#465—21no—
408#450C22×C3111yescharacteristic, complemented
409#449—21no—
410#447—21no—
411#447C22×C3111yescharacteristic, complemented
412#447C22×C3112yescomplemented
413#407C22×C3111yescharacteristic, complemented
414C2×C22⋊C8C22×C3111yescharacteristic, complemented
415#399—21no—
416#399C22×C3112yescomplemented
417#392—21no—
418#392C22×C3112yescomplemented
419C2×#95C22×C3111yescharacteristic, complemented
420#328C22×C3112yescomplemented
421#327C22×C3112yescomplemented
422#327C22×C3112yescomplemented
423#327C22×C3112yescomplemented
424#323C22×C3112yescomplemented
425#323C22×C3112yescomplemented
426C2×C31—21no—
427C2×C31—21no—
428C2×C31—22no—
429C2×C31—41no—
430C2×C31—82no—
431C2×C31—82no—
432C2×C31—81no—
433C2×C31—161no—
434C2×C31#301211yescharacteristic
435C2×C31C2×#45311yescharacteristic
436C2×C31#302611yescharacteristic
437C2×#41D4×C3111yescharacteristic, complemented
438C22×D4—22no—
439C22×D4—21no—
440C22×D4—21no—
441C22×D4—22no—
442C22×D4—21no—
443C22×D4—22no—
444C22×D4D4×C3112yes—
445C22×D4D4×C3111yescharacteristic
446C22×D4D4×C3111yescharacteristic, complemented
447C22×D4C23×C3111yescharacteristic
448C23×C4—21no—
449C23×C4C23×C3111yescharacteristic
450C2×SD16—21no—
451C2×D8—22no—
452C2×D8—21no—
453C2×M16—21no—
454C22×C8—21no—
455#127—22no—
456#127—21no—
457#126—22no—
458#126—22no—
459#125—21no—
460#124—22no—
461#123—22no—
462#123—21no—
463#123—22no—
464#123—22no—
465#123—22no—
466C22⋊Q8D4×C3111yescharacteristic, complemented
467C22⋊Q8C23×C3111yescharacteristic
468#121—22no—
469#121—21no—
470#121—21no—
471#121—22no—
472#121—22no—
473#121—22no—
474#121—22no—
475#121—21no—
476#121—21no—
477#121—21no—
478#121—21no—
479#121—21no—
480#121—21no—
481#121—22no—
482#121—21no—
483#121—21no—
484#121—21no—
485#121—21no—
486#121—48no—
487#121D4×C3112yescomplemented
488#121D4×C3111yescharacteristic, complemented
489#121C23×C3112yes—
490#121C23×C3111yescharacteristic
491#120—22no—
492#120—22no—
493#120—22no—
494#120—21no—
495#120—22no—
496#120—22no—
497#120—22no—
498C4×D4—22no—
499C4×D4—21no—
500C4×D4—21no—
501C4×D4—21no—
502C4×D4—21no—
503C4×D4—22no—
504#117—21no—
505#117D4×C3111yescharacteristic, complemented
506C2×C4⋊C4—22no—
507C2×C4⋊C4D4×C3111yescharacteristic
508C2×C4⋊C4D4×C3111yescharacteristic, complemented
509C2×C4⋊C4C23×C3111yescharacteristic
510C2×C22⋊C4—21no—
511C2×C22⋊C4—22no—
512C2×C22⋊C4—22no—
513C2×C22⋊C4—21no—
514C2×C22⋊C4C23×C3112yes—
515#107—21no—
516#106—21no—
517#106—22no—
518#103—21no—
519#102—22no—
520#102—21no—
521#102—21no—
522#102—22no—
523#102—21no—
524C22⋊C8—21no—
525C22⋊C8—21no—
526C22⋊C8C23×C3111yescharacteristic
527C22⋊C8C23×C3111yescharacteristic
528C22⋊C8C23×C3112yes—
529#95—21no—
530#95C23×C3112yes—
531C31#1841811yescharacteristic, direct product factor, Sylow
532C24—22no—
533C24—21no—
534C24—21no—
535C24C2×D4×C3111yescharacteristic
536C24C2×D4×C3112yes—
537#41—81no—
538C2×Q8C2×D4×C3111yescharacteristic
539C2×D4—22no—
540C2×D4—21no—
541C2×D4—21no—
542C2×D4—22no—
543C2×D4—22no—
544C2×D4—22no—
545C2×D4—22no—
546C2×D4—22no—
547C2×D4—22no—
548C2×D4—21no—
549C2×D4—22no—
550C2×D4—22no—
551C2×D4—21no—
552C2×D4—21no—
553C2×D4—21no—
554C2×D4—21no—
555C2×D4—21no—
556C2×D4—44no—
557C2×D4—44no—
558C2×D4—44no—
559C2×D4—41no—
560C2×D4—41no—
561C2×D4—81no—
562C2×D4—81no—
563C2×D4—82no—
564C2×D4—81no—
565C2×D4—82no—
566C2×D4—82no—
567C2×D4—81no—
568C2×D4—81no—
569C2×D4—82no—
570C2×D4—82no—
571C2×D4—84no—
572C2×D4C2×D4×C3111yescharacteristic
573C2×D4C2×D4×C3112yes—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—24no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—81no—
582C22×C4—81no—
583C22×C4—81no—
584C22×C4C2×D4×C3112yes—
585C22×C4C2×D4×C3111yescharacteristic
586C22×C4C2×D4×C3111yescharacteristic
587C22×C4C2×D4×C3111yescharacteristic
588C22×C4C2×D4×C3111yescharacteristic
589C22×C4C2×D4×C3111yescharacteristic
590C22×C4C24×C3111yescharacteristic
591SD16—81no—
592D8—81no—
593D8—82no—
594M16—81no—
595C2×C8—21no—
596C2×C8—22no—
597C2×C8—21no—
598C2×C8—81no—
599C4⋊C4—22no—
600C4⋊C4—22no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—21no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—44no—
609C4⋊C4C2×D4×C3112yes—
610C4⋊C4C2×D4×C3111yescharacteristic
611C4⋊C4C2×D4×C3111yescharacteristic
612C22⋊C4—22no—
613C22⋊C4—22no—
614C22⋊C4—22no—
615C22⋊C4—22no—
616C22⋊C4—22no—
617C22⋊C4—21no—
618C22⋊C4—21no—
619C22⋊C4—21no—
620C22⋊C4—22no—
621C22⋊C4—21no—
622C22⋊C4—22no—
623C22⋊C4—22no—
624C22⋊C4—22no—
625C22⋊C4—21no—
626C22⋊C4—44no—
627C22⋊C4—44no—
628C22⋊C4—41no—
629C22⋊C4—41no—
630C42—22no—
631C42—21no—
632C23—22no—
633C23—21no—
634C23—21no—
635C23—22no—
636C23—22no—
637C23—21no—
638C23—22no—
639C23—22no—
640C23—41no—
641C23—42no—
642C23—42no—
643C23—42no—
644C23—42no—
645C23—42no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—81no—
650C23—81no—
651C23—82no—
652C23—82no—
653C23—82no—
654C23C31×#12011yescharacteristic
655C23C31×#12011yescharacteristic
656C23C22×D4×C3111yescharacteristic
657Q8—41no—
658D4—42no—
659D4—41no—
660D4—42no—
661D4—42no—
662D4—42no—
663D4—41no—
664D4—41no—
665D4—44no—
666D4—42no—
667D4—42no—
668D4—41no—
669D4—42no—
670D4—41no—
671D4—81no—
672D4—82no—
673D4—82no—
674D4—81no—
675D4—82no—
676D4—82no—
677D4—82no—
678D4—82no—
679D4—82no—
680D4—88no—
681D4—82no—
682D4—82no—
683C2×C4—24no—
684C2×C4—21no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—41no—
701C2×C4—81no—
702C2×C4—84no—
703C2×C4—82no—
704C2×C4—82no—
705C2×C4C31×#12011yescharacteristic
706C2×C4C31×#12011yescharacteristic
707C2×C4C22×D4×C3111yescharacteristic
708C2×C4C22×D4×C3111yescharacteristic
709C8—41no—
710C8—41no—
711C8—42no—
712C22—21no—
713C22—21no—
714C22—21no—
715C22—21no—
716C22—21no—
717C22—21no—
718C22—21no—
719C22—42no—
720C22—42no—
721C22—42no—
722C22—42no—
723C22—41no—
724C22—42no—
725C22—42no—
726C22—41no—
727C22—41no—
728C22—42no—
729C22—42no—
730C22—82no—
731C22—82no—
732C22—82no—
733C22—82no—
734C22—81no—
735C22—81no—
736C22—81no—
737C22—162no—
738C22—164no—
739C22C31×#45312yes—
740C22C2×C31×#12011yescharacteristic
741C22C31×#57611yescharacteristic
742C22C31×#57711yescharacteristic
743C4—21no—
744C4—21no—
745C4—21no—
746C4—21no—
747C4—44no—
748C4—42no—
749C4—41no—
750C4—42no—
751C4—41no—
752C4—41no—
753C4—81no—
754C2—21no—
755C2—21no—
756C2—22no—
757C2—41no—
758C2—82no—
759C2—82no—
760C2—81no—
761C2—161no—
762C2C31×#301211yescharacteristic
763C2C2×C31×#45311yescharacteristic
764C2C31×#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×#3192C2semidirect
3. C31×#3188C2semidirect
4. C31×#2656C2semidirect
5. C31×#1618C2semidirect
6. C31×#1613C2semidirect
7. C31×#1600C2semidirect
8. C31×#1595C2semidirect
9. C31×#1504C2semidirect
10. C2×C31×#327C2semidirect
11. C31×#1471C2semidirect
28. C2×C31×#121C22semidirect
29. C31×#484C22semidirect
32. C31×#481C22semidirect
33. C31×#481C22semidirect
37. C31×#450C22semidirect
40. C31×#447C22semidirect
41. C31×#447C22semidirect
42. C31×#407C22semidirect
43. C2×C31×C22⋊C8C22semidirect
45. C31×#399C22semidirect
47. C31×#392C22semidirect
48. C2×C31×#95C22semidirect
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
84. C31×C22⋊Q8D4semidirect
105. C31×#121D4semidirect
106. C31×#121D4semidirect
123. C31×#117D4semidirect
126. C2×C4⋊C4×C31D4semidirect
249. #18418C31direct (N × H)
330. #3537C2×C31semidirect
331. #3192C2×C31semidirect
332. #3188C2×C31semidirect
333. #2656C2×C31semidirect
334. #1618C2×C31semidirect
335. #1613C2×C31semidirect
336. #1600C2×C31semidirect
337. #1595C2×C31semidirect
338. #1504C2×C31semidirect
339. C2×#327C2×C31semidirect
340. #1471C2×C31semidirect
399. C2×#121C22×C31semidirect
400. #484C22×C31semidirect
403. #481C22×C31semidirect
404. #481C22×C31semidirect
408. #450C22×C31semidirect
411. #447C22×C31semidirect
412. #447C22×C31semidirect
413. #407C22×C31semidirect
414. C2×C22⋊C8C22×C31semidirect
416. #399C22×C31semidirect
418. #392C22×C31semidirect
419. C2×#95C22×C31semidirect
420. #328C22×C31semidirect
421. #327C22×C31semidirect
422. #327C22×C31semidirect
423. #327C22×C31semidirect
424. #323C22×C31semidirect
425. #323C22×C31semidirect
437. C2×#41D4×C31semidirect
446. C22×D4D4×C31semidirect
466. C22⋊Q8D4×C31semidirect
487. #121D4×C31semidirect
488. #121D4×C31semidirect
505. #117D4×C31semidirect
508. C2×C4⋊C4D4×C31semidirect
531. C31#18418direct (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×#31922
C31×#31882
C31×#26562
C31×#16182
C31×#16132
C31×#16002
C31×#15952
C31×#15042
C2×C31×#3272
C31×#14712
#1841831