Finite Group Databasebeta

← C31×#18788 #21475547

Subgroups — C31×#18788 #21475547

Order 7936.

1032 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1Q8×#41×C31C211yesmaximal, characteristic, complemented
2C31×#3208C211yesmaximal, characteristic, complemented
3C31×#3038C211yesmaximal, characteristic
4C2×C31×#460C211yesmaximal, characteristic, complemented
5C31×#1627C212yesmaximal, complemented
6C31×#1626C212yesmaximal, complemented
7C31×#1623C212yesmaximal, complemented
8C31×#1622C212yesmaximal, complemented
9C31×#1550C211yesmaximal, characteristic, complemented
10C31×#1487C211yesmaximal, characteristic, complemented
11C31×#1477C211yesmaximal, characteristic, complemented
12C2×C31×AGL(1,ℤ/8)—21no—
13C22×SD16×C31—21no—
14Q82×C31C2211yescharacteristic, complemented
15C31×#557—21no—
16C31×#557C2211yescharacteristic, complemented
17C31×#554—22no—
18C31×#554—21no—
19C31×#554—21no—
20C31×#554C2211yescharacteristic, complemented
21D4×Q8×C31—21no—
22D4×Q8×C31C2211yescharacteristic, complemented
23C31×#533—22no—
24C31×#533—21no—
25C31×#533—21no—
26C31×#533C2211yescharacteristic
27C2×C31×#127C2211yescharacteristic
28C4×#41×C31—21no—
29C4×#41×C31C2211yescharacteristic
30C2×C4×Q8×C31—21no—
31C2×C4×Q8×C31C2211yescharacteristic
32C31×#492C2212yes—
33C31×#486C2212yes—
34C31×#460—22no—
35C31×#460—21no—
36C31×#460—21no—
37C31×#460—21no—
38C31×#460C2212yes—
39C31×#460C2212yes—
40C31×#460C2212yes—
41C31×#459—21no—
42C31×#459C2212yes—
43C31×#450—22no—
44C31×#431C2211yescharacteristic
45C31×#423C2211yescharacteristic
46C2×C31×C4⋊C8C2211yescharacteristic
47C31×#418—21no—
48C2×C31×#102—21no—
49C31×#333C2212yescomplemented
50C31×#332C2212yescomplemented
51C31×Q8⋊C8C2212yescomplemented
52C31×Q8⋊C8C2212yescomplemented
53C31×Q8⋊C8C2212yescomplemented
54C31×D4⋊C8C2212yescomplemented
55C2×#41×C31D411yescharacteristic
56C22×Q8×C31—21no—
57C22×Q8×C31D411yescharacteristic
58C22×D4×C31—21no—
59C22×D4×C31—21no—
60C22×D4×C31—21no—
61C31×AGL(1,ℤ/8)—44no—
62C2×SD16×C31—22no—
63C2×SD16×C31—22no—
64C2×SD16×C31—22no—
65C2×SD16×C31—24no—
66C2×SD16×C31—44no—
67C2×D8×C31—22no—
68C2×M16×C31—21no—
69C22×C8×C31—21no—
70C31×C4⋊Q8—22no—
71C31×C4⋊Q8—21no—
72C31×C4⋊Q8—22no—
73C31×C4⋊Q8—21no—
74C31×C4⋊Q8—21no—
75C31×C4⋊Q8—21no—
76C31×C4⋊Q8C2311yescharacteristic
77C31×C4⋊Q8C2311yescharacteristic
78C31×#127—21no—
79C31×#127—21no—
80C31×#127—21no—
81C31×#127C2312yes—
82C31×#125—22no—
83C31×#125—22no—
84C31×#125—22no—
85C31×#125—21no—
86C31×#125—21no—
87C31×#125—21no—
88C31×C22⋊Q8—22no—
89C31×C22⋊Q8—22no—
90C31×C22⋊Q8—22no—
91C31×C22⋊Q8—22no—
92C31×C22⋊Q8—22no—
93C31×C22⋊Q8—21no—
94C31×C22⋊Q8—22no—
95C31×C22⋊Q8—21no—
96C31×C22⋊Q8—21no—
97C31×C22⋊Q8—22no—
98C31×C22⋊Q8D412yes—
99C4×Q8×C31—22no—
100C4×Q8×C31—22no—
101C4×Q8×C31—22no—
102C4×Q8×C31—21no—
103C4×Q8×C31—21no—
104C4×Q8×C31—21no—
105C4×Q8×C31—21no—
106C4×Q8×C31—21no—
107C4×Q8×C31—21no—
108C4×Q8×C31—21no—
109C4×Q8×C31D411yescharacteristic
110C4×Q8×C31D411yescharacteristic
111C4×Q8×C31D411yescharacteristic
112C4×Q8×C31D412yes—
113C4×Q8×C31C2311yescharacteristic
114C4×Q8×C31C2311yescharacteristic
115C4×Q8×C31C2311yescharacteristic
116C4×D4×C31—22no—
117C4×D4×C31—22no—
118C4×D4×C31—21no—
119C4×D4×C31—21no—
120C4×D4×C31—21no—
121C4×D4×C31—21no—
122C4×D4×C31D411yescharacteristic
123C4×D4×C31C2311yescharacteristic
124C31×#117—22no—
125C31×#117—21no—
126C31×#117—21no—
127C31×#117D411yescharacteristic
128C2×C4⋊C4×C31—22no—
129C2×C4⋊C4×C31—21no—
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×C31SD1614yescomplemented
151C2×Q8×C31—22no—
152C2×Q8×C31—22no—
153C2×Q8×C31—21no—
154C2×Q8×C31—21no—
155C2×Q8×C31—22no—
156C2×Q8×C31—41no—
157C2×Q8×C31—42no—
158C2×Q8×C31—42no—
159C2×Q8×C31C2×D411yescharacteristic
160C2×Q8×C31C2×D411yescharacteristic
161C2×Q8×C31C2×D411yescharacteristic
162C2×Q8×C31C2×D412yes—
163C2×D4×C31—21no—
164C2×D4×C31—22no—
165C2×D4×C31—22no—
166C2×D4×C31—22no—
167C2×D4×C31—42no—
168C2×D4×C31—42no—
169C2×D4×C31—41no—
170C2×D4×C31—41no—
171C2×D4×C31—41no—
172C2×D4×C31—42no—
173C2×D4×C31—42no—
174C2×D4×C31—82no—
175C2×D4×C31C2×D411yescharacteristic
176C22×C4×C31—21no—
177C22×C4×C31—22no—
178C22×C4×C31—21no—
179C22×C4×C31—22no—
180C22×C4×C31—21no—
181C22×C4×C31—21no—
182C22×C4×C31—21no—
183C22×C4×C31C2×D411yescharacteristic
184C22×C4×C31C2×D411yescharacteristic
185C22×C4×C31C2×D411yescharacteristic
186SD16×C31—44no—
187SD16×C31—44no—
188SD16×C31—44no—
189SD16×C31—84no—
190D8×C31—44no—
191M16×C31—42no—
192C2×C8×C31—22no—
193C2×C8×C31—22no—
194C2×C8×C31—22no—
195C2×C8×C31—42no—
196C4⋊C4×C31—22no—
197C4⋊C4×C31—22no—
198C4⋊C4×C31—22no—
199C4⋊C4×C31—22no—
200C4⋊C4×C31—22no—
201C4⋊C4×C31—22no—
202C4⋊C4×C31—22no—
203C4⋊C4×C31—22no—
204C4⋊C4×C31—21no—
205C4⋊C4×C31—22no—
206C4⋊C4×C31—21no—
207C4⋊C4×C31—21no—
208C4⋊C4×C31—21no—
209C4⋊C4×C31—22no—
210C4⋊C4×C31—21no—
211C4⋊C4×C31—21no—
212C4⋊C4×C31—21no—
213C4⋊C4×C31—21no—
214C4⋊C4×C31—21no—
215C4⋊C4×C31—21no—
216C4⋊C4×C31C2×D411yescharacteristic
217C4⋊C4×C31C2×D411yescharacteristic
218C4⋊C4×C31C2×D411yescharacteristic
219C4⋊C4×C31C2×D411yescharacteristic
220C4⋊C4×C31C2×D412yes—
221C22⋊C4×C31—22no—
222C22⋊C4×C31—22no—
223C22⋊C4×C31—22no—
224C22⋊C4×C31—21no—
225C22⋊C4×C31—21no—
226C22⋊C4×C31—21no—
227C42×C31—22no—
228C42×C31—22no—
229C42×C31—21no—
230C42×C31—22no—
231C42×C31—21no—
232C42×C31—21no—
233C42×C31—21no—
234C42×C31—21no—
235C42×C31—21no—
236C42×C31—21no—
237C42×C31C2×D411yescharacteristic
238C42×C31C2×D411yescharacteristic
239C42×C31C2×D411yescharacteristic
240C42×C31C2411yescharacteristic
241#18788C3111yesmaximal, characteristic, direct product factor, Sylow
242C23×C31—21no—
243C23×C31—42no—
244C23×C31—82no—
245C23×C31—82no—
246C23×C31—82no—
247C23×C31#12011yescharacteristic
248Q8×C31—21no—
249Q8×C31—21no—
250Q8×C31—21no—
251Q8×C31—21no—
252Q8×C31—42no—
253Q8×C31—42no—
254Q8×C31—44no—
255Q8×C31—41no—
256Q8×C31—41no—
257Q8×C31—82no—
258Q8×C31C2×SD1612yescomplemented
259Q8×C31AGL(1,ℤ/8)12yescomplemented
260D4×C31—24no—
261D4×C31—21no—
262D4×C31—44no—
263D4×C31—42no—
264D4×C31—42no—
265D4×C31—42no—
266D4×C31—42no—
267D4×C31—82no—
268D4×C31—82no—
269D4×C31—82no—
270D4×C31C2×SD1612yescomplemented
271C2×C4×C31—21no—
272C2×C4×C31—21no—
273C2×C4×C31—21no—
274C2×C4×C31—21no—
275C2×C4×C31—24no—
276C2×C4×C31—21no—
277C2×C4×C31—21no—
278C2×C4×C31—22no—
279C2×C4×C31—22no—
280C2×C4×C31—21no—
281C2×C4×C31—21no—
282C2×C4×C31—21no—
283C2×C4×C31—41no—
284C2×C4×C31—42no—
285C2×C4×C31—44no—
286C2×C4×C31—41no—
287C2×C4×C31—41no—
288C2×C4×C31—81no—
289C2×C4×C31—81no—
290C2×C4×C31—82no—
291C2×C4×C31#12011yescharacteristic
292C2×C4×C31#12011yescharacteristic
293C2×C4×C31#12011yescharacteristic
294C2×C4×C31C2×SD1612yes—
295C2×C4×C31#13712yes—
296C2×C4×C31C22×D411yescharacteristic
297C2×C4×C31C22×D411yescharacteristic
298C2×C4×C31C22×D411yescharacteristic
299C8×C31—42no—
300C8×C31—42no—
301C8×C31—42no—
302Q8×#41C2×C3111yescharacteristic, complemented
303#3208C2×C3111yescharacteristic, complemented
304#3038C2×C3111yescharacteristic
305C2×#460C2×C3111yescharacteristic, complemented
306#1627C2×C3112yescomplemented
307#1626C2×C3112yescomplemented
308#1623C2×C3112yescomplemented
309#1622C2×C3112yescomplemented
310#1550C2×C3111yescharacteristic, complemented
311#1487C2×C3111yescharacteristic, complemented
312#1477C2×C3111yescharacteristic, complemented
313C22×C31—21no—
314C22×C31—21no—
315C22×C31—22no—
316C22×C31—41no—
317C22×C31—41no—
318C22×C31—82no—
319C22×C31—82no—
320C22×C31—82no—
321C22×C31—164no—
322C22×C31#44812yes—
323C22×C31C2×#12011yescharacteristic
324C4×C31—22no—
325C4×C31—21no—
326C4×C31—22no—
327C4×C31—21no—
328C4×C31—21no—
329C4×C31—41no—
330C4×C31—42no—
331C4×C31—41no—
332C4×C31—41no—
333C4×C31—42no—
334C4×C31—41no—
335C4×C31—41no—
336C4×C31#44812yes—
337C4×C31C22×SD1611yescharacteristic
338C4×C31C2×AGL(1,ℤ/8)11yescharacteristic
339C4×C31C2×#13711yescharacteristic
340C4×C31#57511yescharacteristic
341C2×AGL(1,ℤ/8)—21no—
342C22×SD16—21no—
343Q82C22×C3111yescharacteristic, complemented
344#557—21no—
345#557C22×C3111yescharacteristic, complemented
346#554—22no—
347#554—21no—
348#554—21no—
349#554C22×C3111yescharacteristic, complemented
350D4×Q8—21no—
351D4×Q8C22×C3111yescharacteristic, complemented
352#533—22no—
353#533—21no—
354#533—21no—
355#533C22×C3111yescharacteristic
356C2×#127C22×C3111yescharacteristic
357C4×#41—21no—
358C4×#41C22×C3111yescharacteristic
359C2×C4×Q8—21no—
360C2×C4×Q8C22×C3111yescharacteristic
361#492C22×C3112yes—
362#486C22×C3112yes—
363#460—22no—
364#460—21no—
365#460—21no—
366#460—21no—
367#460C22×C3112yes—
368#460C22×C3112yes—
369#460C22×C3112yes—
370#459—21no—
371#459C22×C3112yes—
372#450—22no—
373#431C22×C3111yescharacteristic
374#423C22×C3111yescharacteristic
375C2×C4⋊C8C22×C3111yescharacteristic
376#418—21no—
377C2×#102—21no—
378#333C22×C3112yescomplemented
379#332C22×C3112yescomplemented
380Q8⋊C8C22×C3112yescomplemented
381Q8⋊C8C22×C3112yescomplemented
382Q8⋊C8C22×C3112yescomplemented
383D4⋊C8C22×C3112yescomplemented
384C2×C31—22no—
385C2×C31—42no—
386C2×C31—162no—
387C2×C31C2×#44811yescharacteristic
388C2×C31#300611yescharacteristic
389C2×C31#302111yescharacteristic
390C2×#41D4×C3111yescharacteristic
391C22×Q8—21no—
392C22×Q8D4×C3111yescharacteristic
393C22×D4—21no—
394C22×D4—21no—
395C22×D4—21no—
396AGL(1,ℤ/8)—44no—
397C2×SD16—22no—
398C2×SD16—22no—
399C2×SD16—22no—
400C2×SD16—24no—
401C2×SD16—44no—
402C2×D8—22no—
403C2×M16—21no—
404C22×C8—21no—
405C4⋊Q8—22no—
406C4⋊Q8—21no—
407C4⋊Q8—22no—
408C4⋊Q8—21no—
409C4⋊Q8—21no—
410C4⋊Q8—21no—
411C4⋊Q8C23×C3111yescharacteristic
412C4⋊Q8C23×C3111yescharacteristic
413#127—21no—
414#127—21no—
415#127—21no—
416#127C23×C3112yes—
417#125—22no—
418#125—22no—
419#125—22no—
420#125—21no—
421#125—21no—
422#125—21no—
423C22⋊Q8—22no—
424C22⋊Q8—22no—
425C22⋊Q8—22no—
426C22⋊Q8—22no—
427C22⋊Q8—22no—
428C22⋊Q8—21no—
429C22⋊Q8—22no—
430C22⋊Q8—21no—
431C22⋊Q8—21no—
432C22⋊Q8—22no—
433C22⋊Q8D4×C3112yes—
434C4×Q8—22no—
435C4×Q8—22no—
436C4×Q8—22no—
437C4×Q8—21no—
438C4×Q8—21no—
439C4×Q8—21no—
440C4×Q8—21no—
441C4×Q8—21no—
442C4×Q8—21no—
443C4×Q8—21no—
444C4×Q8D4×C3111yescharacteristic
445C4×Q8D4×C3111yescharacteristic
446C4×Q8D4×C3111yescharacteristic
447C4×Q8D4×C3112yes—
448C4×Q8C23×C3111yescharacteristic
449C4×Q8C23×C3111yescharacteristic
450C4×Q8C23×C3111yescharacteristic
451C4×D4—22no—
452C4×D4—22no—
453C4×D4—21no—
454C4×D4—21no—
455C4×D4—21no—
456C4×D4—21no—
457C4×D4D4×C3111yescharacteristic
458C4×D4C23×C3111yescharacteristic
459#117—22no—
460#117—21no—
461#117—21no—
462#117D4×C3111yescharacteristic
463C2×C4⋊C4—22no—
464C2×C4⋊C4—21no—
465C2×C4⋊C4—21no—
466C2×C4⋊C4D4×C3111yescharacteristic
467C2×C42—22no—
468C2×C42—21no—
469C2×C42—21no—
470C2×C42C23×C3111yescharacteristic
471C4⋊C8—21no—
472C4⋊C8—21no—
473C4⋊C8—21no—
474C4⋊C8C23×C3112yes—
475C4⋊C8C23×C3112yes—
476#102—22no—
477#102—22no—
478#102—22no—
479#102—22no—
480#102—24no—
481C22⋊C8—21no—
482C4×C8C23×C3112yes—
483C31#1878811yescharacteristic, direct product factor, Sylow
484C24—41no—
485#41—22no—
486#41SD16×C3114yescomplemented
487C2×Q8—22no—
488C2×Q8—22no—
489C2×Q8—21no—
490C2×Q8—21no—
491C2×Q8—22no—
492C2×Q8—41no—
493C2×Q8—42no—
494C2×Q8—42no—
495C2×Q8C2×D4×C3111yescharacteristic
496C2×Q8C2×D4×C3111yescharacteristic
497C2×Q8C2×D4×C3111yescharacteristic
498C2×Q8C2×D4×C3112yes—
499C2×D4—21no—
500C2×D4—22no—
501C2×D4—22no—
502C2×D4—22no—
503C2×D4—42no—
504C2×D4—42no—
505C2×D4—41no—
506C2×D4—41no—
507C2×D4—41no—
508C2×D4—42no—
509C2×D4—42no—
510C2×D4—82no—
511C2×D4C2×D4×C3111yescharacteristic
512C22×C4—21no—
513C22×C4—22no—
514C22×C4—21no—
515C22×C4—22no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4C2×D4×C3111yescharacteristic
520C22×C4C2×D4×C3111yescharacteristic
521C22×C4C2×D4×C3111yescharacteristic
522SD16—44no—
523SD16—44no—
524SD16—44no—
525SD16—84no—
526D8—44no—
527M16—42no—
528C2×C8—22no—
529C2×C8—22no—
530C2×C8—22no—
531C2×C8—42no—
532C4⋊C4—22no—
533C4⋊C4—22no—
534C4⋊C4—22no—
535C4⋊C4—22no—
536C4⋊C4—22no—
537C4⋊C4—22no—
538C4⋊C4—22no—
539C4⋊C4—22no—
540C4⋊C4—21no—
541C4⋊C4—22no—
542C4⋊C4—21no—
543C4⋊C4—21no—
544C4⋊C4—21no—
545C4⋊C4—22no—
546C4⋊C4—21no—
547C4⋊C4—21no—
548C4⋊C4—21no—
549C4⋊C4—21no—
550C4⋊C4—21no—
551C4⋊C4—21no—
552C4⋊C4C2×D4×C3111yescharacteristic
553C4⋊C4C2×D4×C3111yescharacteristic
554C4⋊C4C2×D4×C3111yescharacteristic
555C4⋊C4C2×D4×C3111yescharacteristic
556C4⋊C4C2×D4×C3112yes—
557C22⋊C4—22no—
558C22⋊C4—22no—
559C22⋊C4—22no—
560C22⋊C4—21no—
561C22⋊C4—21no—
562C22⋊C4—21no—
563C42—22no—
564C42—22no—
565C42—21no—
566C42—22no—
567C42—21no—
568C42—21no—
569C42—21no—
570C42—21no—
571C42—21no—
572C42—21no—
573C42C2×D4×C3111yescharacteristic
574C42C2×D4×C3111yescharacteristic
575C42C2×D4×C3111yescharacteristic
576C42C24×C3111yescharacteristic
577C23—21no—
578C23—42no—
579C23—82no—
580C23—82no—
581C23—82no—
582C23C31×#12011yescharacteristic
583Q8—21no—
584Q8—21no—
585Q8—21no—
586Q8—21no—
587Q8—42no—
588Q8—42no—
589Q8—44no—
590Q8—41no—
591Q8—41no—
592Q8—82no—
593Q8C2×SD16×C3112yescomplemented
594Q8C31×AGL(1,ℤ/8)12yescomplemented
595D4—24no—
596D4—21no—
597D4—44no—
598D4—42no—
599D4—42no—
600D4—42no—
601D4—42no—
602D4—82no—
603D4—82no—
604D4—82no—
605D4C2×SD16×C3112yescomplemented
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—24no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—22no—
614C2×C4—22no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—41no—
619C2×C4—42no—
620C2×C4—44no—
621C2×C4—41no—
622C2×C4—41no—
623C2×C4—81no—
624C2×C4—81no—
625C2×C4—82no—
626C2×C4C31×#12011yescharacteristic
627C2×C4C31×#12011yescharacteristic
628C2×C4C31×#12011yescharacteristic
629C2×C4C2×SD16×C3112yes—
630C2×C4C31×#13712yes—
631C2×C4C22×D4×C3111yescharacteristic
632C2×C4C22×D4×C3111yescharacteristic
633C2×C4C22×D4×C3111yescharacteristic
634C8—42no—
635C8—42no—
636C8—42no—
637C22—21no—
638C22—21no—
639C22—22no—
640C22—41no—
641C22—41no—
642C22—82no—
643C22—82no—
644C22—82no—
645C22—164no—
646C22C31×#44812yes—
647C22C2×C31×#12011yescharacteristic
648C4—22no—
649C4—21no—
650C4—22no—
651C4—21no—
652C4—21no—
653C4—41no—
654C4—42no—
655C4—41no—
656C4—41no—
657C4—42no—
658C4—41no—
659C4—41no—
660C4C31×#44812yes—
661C4C22×SD16×C3111yescharacteristic
662C4C2×C31×AGL(1,ℤ/8)11yescharacteristic
663C4C2×C31×#13711yescharacteristic
664C4C31×#57511yescharacteristic
665C2—22no—
666C2—42no—
667C2—162no—
668C2C2×C31×#44811yescharacteristic
669C2C31×#300611yescharacteristic
670C2C31×#302111yescharacteristic
subgroupG/H
center, socleC22×C31C2×#120
commutator, Frattini, cosocleC42C24×C31
prime radicalC31×#3038C2
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. Q8×#41×C31C2semidirect
2. C31×#3208C2semidirect
4. C2×C31×#460C2semidirect
5. C31×#1627C2semidirect
6. C31×#1626C2semidirect
7. C31×#1623C2semidirect
8. C31×#1622C2semidirect
9. C31×#1550C2semidirect
10. C31×#1487C2semidirect
11. C31×#1477C2semidirect
14. Q82×C31C22semidirect
16. C31×#557C22semidirect
20. C31×#554C22semidirect
22. D4×Q8×C31C22semidirect
49. C31×#333C22semidirect
50. C31×#332C22semidirect
51. C31×Q8⋊C8C22semidirect
52. C31×Q8⋊C8C22semidirect
53. C31×Q8⋊C8C22semidirect
54. C31×D4⋊C8C22semidirect
150. #41×C31SD16semidirect
241. #18788C31direct (N × H)
258. Q8×C31C2×SD16semidirect
259. Q8×C31AGL(1,ℤ/8)semidirect
270. D4×C31C2×SD16semidirect
302. Q8×#41C2×C31semidirect
303. #3208C2×C31semidirect
305. C2×#460C2×C31semidirect
306. #1627C2×C31semidirect
307. #1626C2×C31semidirect
308. #1623C2×C31semidirect
309. #1622C2×C31semidirect
310. #1550C2×C31semidirect
311. #1487C2×C31semidirect
312. #1477C2×C31semidirect
343. Q82C22×C31semidirect
345. #557C22×C31semidirect
349. #554C22×C31semidirect
351. D4×Q8C22×C31semidirect
378. #333C22×C31semidirect
379. #332C22×C31semidirect
380. Q8⋊C8C22×C31semidirect
381. Q8⋊C8C22×C31semidirect
382. Q8⋊C8C22×C31semidirect
383. D4⋊C8C22×C31semidirect
483. C31#18788direct (N × H)
486. #41SD16×C31semidirect
593. Q8C2×SD16×C31semidirect
594. Q8C31×AGL(1,ℤ/8)semidirect
605. D4C2×SD16×C31semidirect

Maximal subgroups

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

subgroupindex
Q8×#41×C312
C31×#32082
C31×#30382
C2×C31×#4602
C31×#16272
C31×#16262
C31×#16232
C31×#16222
C31×#15502
C31×#14872
C31×#14772
#1878831