Finite Group Databasebeta

← C31×#18537 #21475296

Subgroups — C31×#18537 #21475296

Order 7936.

1038 conjugacy classes of subgroups.

The subgroup lattice has 688 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3482C211yesmaximal, characteristic, complemented
2C31×#3138C211yesmaximal, characteristic, complemented
3C31×#3038C211yesmaximal, characteristic, complemented
4C31×#3038C211yesmaximal, characteristic, complemented
5C31×#1628C212yesmaximal, complemented
6C31×#1627C212yesmaximal, complemented
7C31×#1626C212yesmaximal, complemented
8C31×#1625C212yesmaximal, complemented
9C31×#1561C211yesmaximal, characteristic, complemented
10C31×#1489C211yesmaximal, characteristic, complemented
11C31×#1489C211yesmaximal, characteristic, complemented
12C2×C31×AGL(1,ℤ/8)—21no—
13C2×C31×AGL(1,ℤ/8)—21no—
14C31×#557C2211yescharacteristic, complemented
15C31×#556—21no—
16C31×#556C2211yescharacteristic, complemented
17C31×#552—22no—
18C31×#552—21no—
19D4×Q8×C31C2211yescharacteristic, complemented
20C31×#548—21no—
21C31×#547—21no—
22C31×#547C2211yescharacteristic, complemented
23C31×#533—21no—
24C31×#533C2211yescharacteristic
25C2×C31×#127C2211yescharacteristic
26C31×#529—21no—
27C31×#529—22no—
28C4×#41×C31—21no—
29C4×#41×C31C2211yescharacteristic
30C4×#41×C31C2211yescharacteristic
31C2×C4×Q8×C31—21no—
32C31×#490—22no—
33C31×#486C2212yes—
34C31×#486C2212yes—
35C31×#460—21no—
36C31×#460—21no—
37C31×#460C2212yes—
38C31×#460C2212yes—
39C31×#459—21no—
40C31×#459—21no—
41C31×#459C2212yes—
42C31×#459C2212yes—
43C31×#423C2211yescharacteristic
44C31×#423C2211yescharacteristic
45C31×#418—22no—
46C31×#418—21no—
47C31×#418—21no—
48C4×M16×C31C2211yescharacteristic
49C31×#332C2212yescomplemented
50C31×#332C2212yescomplemented
51C31×Q8⋊C8C2212yescomplemented
52C31×Q8⋊C8C2212yescomplemented
53C31×D4⋊C8C2212yescomplemented
54C31×D4⋊C8C2212yescomplemented
55C2×#41×C31—21no—
56C2×#41×C31D411yescharacteristic
57C2×#41×C31D411yescharacteristic
58C22×Q8×C31—21no—
59C22×D4×C31—21no—
60C22×D4×C31—21no—
61C22×D4×C31—21no—
62C31×AGL(1,ℤ/8)—44no—
63C31×AGL(1,ℤ/8)—44no—
64C2×SD16×C31—22no—
65C2×SD16×C31—22no—
66C2×D8×C31—22no—
67C2×D8×C31—22no—
68C2×M16×C31—21no—
69C2×M16×C31—21no—
70C2×M16×C31—21no—
71C31×C4⋊Q8—21no—
72C31×C4⋊Q8—21no—
73C31×C4⋊Q8C2311yescharacteristic
74C31×C4⋊Q8C2311yescharacteristic
75C31×#127—21no—
76C31×#127—21no—
77C31×#127—21no—
78C31×#127C2312yes—
79C31×#126—22no—
80C31×#126—22no—
81C31×#126—22no—
82C31×#125—22no—
83C31×#125—22no—
84C31×#125—21no—
85C31×#125D412yes—
86C31×#124—22no—
87C31×#124—21no—
88C31×#123—22no—
89C31×#123—22no—
90C31×#123—22no—
91C31×C22⋊Q8—22no—
92C31×C22⋊Q8—21no—
93C31×C22⋊Q8—21no—
94C31×C22⋊Q8—21no—
95C31×C22⋊Q8—21no—
96C31×C22⋊Q8—22no—
97C31×C22⋊Q8—21no—
98C31×#121—22no—
99C31×#121—21no—
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×C31D411yescharacteristic
108C4×Q8×C31D411yescharacteristic
109C4×Q8×C31C2311yescharacteristic
110C4×Q8×C31C2311yescharacteristic
111C4×D4×C31—22no—
112C4×D4×C31—22no—
113C4×D4×C31—21no—
114C4×D4×C31—21no—
115C4×D4×C31—21no—
116C4×D4×C31—21no—
117C4×D4×C31—21no—
118C4×D4×C31D411yescharacteristic
119C4×D4×C31D411yescharacteristic
120C4×D4×C31C2311yescharacteristic
121C4×D4×C31C2311yescharacteristic
122C31×#117—22no—
123C31×#117—22no—
124C31×#117—21no—
125C31×#117—21no—
126C31×#117—21no—
127C31×#117D411yescharacteristic
128C31×#117D411yescharacteristic
129C31×#117D412yes—
130C2×C4⋊C4×C31—22no—
131C2×C4⋊C4×C31—21no—
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⋊C8C2312yes—
139C31×C4⋊C8C2312yes—
140C31×#102—22no—
141C31×#102—22no—
142C31×#102—22no—
143C31×#102—22no—
144C31×#102—24no—
145C31×#102—24no—
146C31×#97—21no—
147C4×C8×C31C2312yes—
148C24×C31—41no—
149#41×C31—22no—
150#41×C31—22no—
151#41×C31—41no—
152#41×C31—41no—
153#41×C31—42no—
154#41×C31—42no—
155C2×Q8×C31—22no—
156C2×Q8×C31—21no—
157C2×Q8×C31—21no—
158C2×Q8×C31—42no—
159C2×Q8×C31—42no—
160C2×Q8×C31C2×D411yescharacteristic
161C2×Q8×C31C2×D411yescharacteristic
162C2×D4×C31—22no—
163C2×D4×C31—21no—
164C2×D4×C31—21no—
165C2×D4×C31—22no—
166C2×D4×C31—22no—
167C2×D4×C31—22no—
168C2×D4×C31—42no—
169C2×D4×C31—42no—
170C2×D4×C31—42no—
171C2×D4×C31—42no—
172C2×D4×C31—44no—
173C2×D4×C31—41no—
174C2×D4×C31—41no—
175C2×D4×C31—41no—
176C2×D4×C31C2×D411yescharacteristic
177C2×D4×C31C2×D411yescharacteristic
178C22×C4×C31—22no—
179C22×C4×C31—22no—
180C22×C4×C31—21no—
181C22×C4×C31—21no—
182C22×C4×C31—21no—
183C22×C4×C31—21no—
184C22×C4×C31—21no—
185C22×C4×C31—21no—
186C22×C4×C31C2×D411yescharacteristic
187C22×C4×C31C2×D411yescharacteristic
188C22×C4×C31C2×D411yescharacteristic
189SD16×C31—44no—
190SD16×C31—44no—
191D8×C31—44no—
192D8×C31—44no—
193M16×C31—42no—
194M16×C31—42no—
195M16×C31—42no—
196C2×C8×C31—22no—
197C2×C8×C31—22no—
198C2×C8×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—22no—
205C4⋊C4×C31—21no—
206C4⋊C4×C31—22no—
207C4⋊C4×C31—22no—
208C4⋊C4×C31—21no—
209C4⋊C4×C31—21no—
210C4⋊C4×C31—21no—
211C4⋊C4×C31—21no—
212C4⋊C4×C31—21no—
213C4⋊C4×C31C2×D411yescharacteristic
214C4⋊C4×C31C2×D411yescharacteristic
215C4⋊C4×C31C2×D411yescharacteristic
216C4⋊C4×C31C2×D411yescharacteristic
217C4⋊C4×C31C2×D412yes—
218C4⋊C4×C31C2×D412yes—
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—22no—
226C22⋊C4×C31—21no—
227C22⋊C4×C31—21no—
228C22⋊C4×C31—21no—
229C22⋊C4×C31—21no—
230C42×C31—22no—
231C42×C31—22no—
232C42×C31—21no—
233C42×C31—21no—
234C42×C31—21no—
235C42×C31—22no—
236C42×C31—21no—
237C42×C31—21no—
238C42×C31—21no—
239C42×C31C2×D411yescharacteristic
240C42×C31C2×D411yescharacteristic
241C42×C31C2×D411yescharacteristic
242C42×C31C2411yescharacteristic
243#18537C3111yesmaximal, characteristic, direct product factor, Sylow
244C23×C31—21no—
245C23×C31—21no—
246C23×C31—42no—
247C23×C31—82no—
248C23×C31—82no—
249C23×C31—82no—
250C23×C31#12011yescharacteristic
251Q8×C31—21no—
252Q8×C31—21no—
253Q8×C31—21no—
254Q8×C31—44no—
255Q8×C31—41no—
256Q8×C31—41no—
257Q8×C31—41no—
258Q8×C31—41no—
259Q8×C31AGL(1,ℤ/8)12yescomplemented
260D4×C31—21no—
261D4×C31—21no—
262D4×C31—21no—
263D4×C31—42no—
264D4×C31—44no—
265D4×C31—42no—
266D4×C31—44no—
267D4×C31—42no—
268D4×C31—42no—
269D4×C31—42no—
270D4×C31—42no—
271D4×C31—82no—
272D4×C31—82no—
273D4×C31—82no—
274D4×C31AGL(1,ℤ/8)12yescomplemented
275C2×C4×C31—21no—
276C2×C4×C31—21no—
277C2×C4×C31—21no—
278C2×C4×C31—21no—
279C2×C4×C31—21no—
280C2×C4×C31—22no—
281C2×C4×C31—21no—
282C2×C4×C31—21no—
283C2×C4×C31—21no—
284C2×C4×C31—22no—
285C2×C4×C31—21no—
286C2×C4×C31—21no—
287C2×C4×C31—22no—
288C2×C4×C31—42no—
289C2×C4×C31—42no—
290C2×C4×C31—44no—
291C2×C4×C31—44no—
292C2×C4×C31—41no—
293C2×C4×C31—41no—
294C2×C4×C31—41no—
295C2×C4×C31—41no—
296C2×C4×C31—42no—
297C2×C4×C31—42no—
298C2×C4×C31#12011yescharacteristic
299C2×C4×C31#12011yescharacteristic
300C2×C4×C31#12011yescharacteristic
301C2×C4×C31C22×D411yescharacteristic
302C2×C4×C31C22×D411yescharacteristic
303C2×C4×C31C22×D411yescharacteristic
304C8×C31—42no—
305C8×C31—42no—
306C8×C31—42no—
307#3482C2×C3111yescharacteristic, complemented
308#3138C2×C3111yescharacteristic, complemented
309#3038C2×C3111yescharacteristic, complemented
310#3038C2×C3111yescharacteristic, complemented
311#1628C2×C3112yescomplemented
312#1627C2×C3112yescomplemented
313#1626C2×C3112yescomplemented
314#1625C2×C3112yescomplemented
315#1561C2×C3111yescharacteristic, complemented
316#1489C2×C3111yescharacteristic, complemented
317#1489C2×C3111yescharacteristic, complemented
318C22×C31—21no—
319C22×C31—21no—
320C22×C31—22no—
321C22×C31—21no—
322C22×C31—41no—
323C22×C31—41no—
324C22×C31—41no—
325C22×C31—41no—
326C22×C31—41no—
327C22×C31—82no—
328C22×C31—82no—
329C22×C31—82no—
330C22×C31—164no—
331C22×C31C2×#12011yescharacteristic
332C4×C31—21no—
333C4×C31—21no—
334C4×C31—22no—
335C4×C31—21no—
336C4×C31—41no—
337C4×C31—41no—
338C4×C31—42no—
339C4×C31—42no—
340C4×C31—41no—
341C4×C31—41no—
342C4×C31—41no—
343C4×C31#45412yes—
344C4×C31C2×AGL(1,ℤ/8)11yescharacteristic
345C4×C31C2×AGL(1,ℤ/8)11yescharacteristic
346C4×C31#57511yescharacteristic
347C4×C31#57511yescharacteristic
348C2×AGL(1,ℤ/8)—21no—
349C2×AGL(1,ℤ/8)—21no—
350#557C22×C3111yescharacteristic, complemented
351#556—21no—
352#556C22×C3111yescharacteristic, complemented
353#552—22no—
354#552—21no—
355D4×Q8C22×C3111yescharacteristic, complemented
356#548—21no—
357#547—21no—
358#547C22×C3111yescharacteristic, complemented
359#533—21no—
360#533C22×C3111yescharacteristic
361C2×#127C22×C3111yescharacteristic
362#529—21no—
363#529—22no—
364C4×#41—21no—
365C4×#41C22×C3111yescharacteristic
366C4×#41C22×C3111yescharacteristic
367C2×C4×Q8—21no—
368#490—22no—
369#486C22×C3112yes—
370#486C22×C3112yes—
371#460—21no—
372#460—21no—
373#460C22×C3112yes—
374#460C22×C3112yes—
375#459—21no—
376#459—21no—
377#459C22×C3112yes—
378#459C22×C3112yes—
379#423C22×C3111yescharacteristic
380#423C22×C3111yescharacteristic
381#418—22no—
382#418—21no—
383#418—21no—
384C4×M16C22×C3111yescharacteristic
385#332C22×C3112yescomplemented
386#332C22×C3112yescomplemented
387Q8⋊C8C22×C3112yescomplemented
388Q8⋊C8C22×C3112yescomplemented
389D4⋊C8C22×C3112yescomplemented
390D4⋊C8C22×C3112yescomplemented
391C2×C31—41no—
392C2×C31—42no—
393C2×C31—81no—
394C2×C31—162no—
395C2×C31#300611yescharacteristic
396C2×C31#300611yescharacteristic
397C2×C31C2×#45411yescharacteristic
398C2×#41—21no—
399C2×#41D4×C3111yescharacteristic
400C2×#41D4×C3111yescharacteristic
401C22×Q8—21no—
402C22×D4—21no—
403C22×D4—21no—
404C22×D4—21no—
405AGL(1,ℤ/8)—44no—
406AGL(1,ℤ/8)—44no—
407C2×SD16—22no—
408C2×SD16—22no—
409C2×D8—22no—
410C2×D8—22no—
411C2×M16—21no—
412C2×M16—21no—
413C2×M16—21no—
414C4⋊Q8—21no—
415C4⋊Q8—21no—
416C4⋊Q8C23×C3111yescharacteristic
417C4⋊Q8C23×C3111yescharacteristic
418#127—21no—
419#127—21no—
420#127—21no—
421#127C23×C3112yes—
422#126—22no—
423#126—22no—
424#126—22no—
425#125—22no—
426#125—22no—
427#125—21no—
428#125D4×C3112yes—
429#124—22no—
430#124—21no—
431#123—22no—
432#123—22no—
433#123—22no—
434C22⋊Q8—22no—
435C22⋊Q8—21no—
436C22⋊Q8—21no—
437C22⋊Q8—21no—
438C22⋊Q8—21no—
439C22⋊Q8—22no—
440C22⋊Q8—21no—
441#121—22no—
442#121—21no—
443C4×Q8—22no—
444C4×Q8—22no—
445C4×Q8—21no—
446C4×Q8—21no—
447C4×Q8—21no—
448C4×Q8—21no—
449C4×Q8—21no—
450C4×Q8D4×C3111yescharacteristic
451C4×Q8D4×C3111yescharacteristic
452C4×Q8C23×C3111yescharacteristic
453C4×Q8C23×C3111yescharacteristic
454C4×D4—22no—
455C4×D4—22no—
456C4×D4—21no—
457C4×D4—21no—
458C4×D4—21no—
459C4×D4—21no—
460C4×D4—21no—
461C4×D4D4×C3111yescharacteristic
462C4×D4D4×C3111yescharacteristic
463C4×D4C23×C3111yescharacteristic
464C4×D4C23×C3111yescharacteristic
465#117—22no—
466#117—22no—
467#117—21no—
468#117—21no—
469#117—21no—
470#117D4×C3111yescharacteristic
471#117D4×C3111yescharacteristic
472#117D4×C3112yes—
473C2×C4⋊C4—22no—
474C2×C4⋊C4—21no—
475C2×C42—22no—
476C2×C42—21no—
477C2×C42—21no—
478C2×C42C23×C3111yescharacteristic
479C4⋊C8—21no—
480C4⋊C8—21no—
481C4⋊C8C23×C3112yes—
482C4⋊C8C23×C3112yes—
483#102—22no—
484#102—22no—
485#102—22no—
486#102—22no—
487#102—24no—
488#102—24no—
489#97—21no—
490C4×C8C23×C3112yes—
491C31#1853711yescharacteristic, direct product factor, Sylow
492C24—41no—
493#41—22no—
494#41—22no—
495#41—41no—
496#41—41no—
497#41—42no—
498#41—42no—
499C2×Q8—22no—
500C2×Q8—21no—
501C2×Q8—21no—
502C2×Q8—42no—
503C2×Q8—42no—
504C2×Q8C2×D4×C3111yescharacteristic
505C2×Q8C2×D4×C3111yescharacteristic
506C2×D4—22no—
507C2×D4—21no—
508C2×D4—21no—
509C2×D4—22no—
510C2×D4—22no—
511C2×D4—22no—
512C2×D4—42no—
513C2×D4—42no—
514C2×D4—44no—
515C2×D4—42no—
516C2×D4—42no—
517C2×D4—41no—
518C2×D4—41no—
519C2×D4—41no—
520C2×D4C2×D4×C3111yescharacteristic
521C2×D4C2×D4×C3111yescharacteristic
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4C2×D4×C3111yescharacteristic
531C22×C4C2×D4×C3111yescharacteristic
532C22×C4C2×D4×C3111yescharacteristic
533SD16—44no—
534SD16—44no—
535D8—44no—
536D8—44no—
537M16—42no—
538M16—42no—
539M16—42no—
540C2×C8—22no—
541C2×C8—22no—
542C2×C8—22no—
543C4⋊C4—22no—
544C4⋊C4—22no—
545C4⋊C4—22no—
546C4⋊C4—22no—
547C4⋊C4—22no—
548C4⋊C4—22no—
549C4⋊C4—21no—
550C4⋊C4—22no—
551C4⋊C4—22no—
552C4⋊C4—21no—
553C4⋊C4—21no—
554C4⋊C4—21no—
555C4⋊C4—21no—
556C4⋊C4—21no—
557C4⋊C4C2×D4×C3111yescharacteristic
558C4⋊C4C2×D4×C3111yescharacteristic
559C4⋊C4C2×D4×C3111yescharacteristic
560C4⋊C4C2×D4×C3111yescharacteristic
561C4⋊C4C2×D4×C3112yes—
562C4⋊C4C2×D4×C3112yes—
563C22⋊C4—22no—
564C22⋊C4—22no—
565C22⋊C4—22no—
566C22⋊C4—22no—
567C22⋊C4—21no—
568C22⋊C4—21no—
569C22⋊C4—22no—
570C22⋊C4—21no—
571C22⋊C4—21no—
572C22⋊C4—21no—
573C22⋊C4—21no—
574C42—22no—
575C42—22no—
576C42—21no—
577C42—21no—
578C42—21no—
579C42—22no—
580C42—21no—
581C42—21no—
582C42—21no—
583C42C2×D4×C3111yescharacteristic
584C42C2×D4×C3111yescharacteristic
585C42C2×D4×C3111yescharacteristic
586C42C24×C3111yescharacteristic
587C23—21no—
588C23—21no—
589C23—42no—
590C23—82no—
591C23—82no—
592C23—82no—
593C23C31×#12011yescharacteristic
594Q8—21no—
595Q8—21no—
596Q8—21no—
597Q8—44no—
598Q8—41no—
599Q8—41no—
600Q8—41no—
601Q8—41no—
602Q8C31×AGL(1,ℤ/8)12yescomplemented
603D4—21no—
604D4—21no—
605D4—21no—
606D4—42no—
607D4—44no—
608D4—42no—
609D4—44no—
610D4—42no—
611D4—42no—
612D4—42no—
613D4—42no—
614D4—82no—
615D4—82no—
616D4—82no—
617D4C31×AGL(1,ℤ/8)12yescomplemented
618C2×C4—21no—
619C2×C4—22no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—22no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—22no—
631C2×C4—42no—
632C2×C4—42no—
633C2×C4—44no—
634C2×C4—44no—
635C2×C4—42no—
636C2×C4—42no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—41no—
640C2×C4—41no—
641C2×C4C31×#12011yescharacteristic
642C2×C4C31×#12011yescharacteristic
643C2×C4C31×#12011yescharacteristic
644C2×C4C22×D4×C3111yescharacteristic
645C2×C4C22×D4×C3111yescharacteristic
646C2×C4C22×D4×C3111yescharacteristic
647C8—42no—
648C8—42no—
649C8—42no—
650C22—21no—
651C22—21no—
652C22—22no—
653C22—21no—
654C22—41no—
655C22—41no—
656C22—41no—
657C22—41no—
658C22—41no—
659C22—82no—
660C22—82no—
661C22—82no—
662C22—164no—
663C22C2×C31×#12011yescharacteristic
664C4—21no—
665C4—21no—
666C4—22no—
667C4—21no—
668C4—41no—
669C4—41no—
670C4—42no—
671C4—42no—
672C4—41no—
673C4—41no—
674C4—41no—
675C4C31×#45412yes—
676C4C2×C31×AGL(1,ℤ/8)11yescharacteristic
677C4C2×C31×AGL(1,ℤ/8)11yescharacteristic
678C4C31×#57511yescharacteristic
679C4C31×#57511yescharacteristic
680C2—41no—
681C2—42no—
682C2—81no—
683C2—162no—
684C2C31×#300611yescharacteristic
685C2C31×#300611yescharacteristic
686C2C2×C31×#45411yescharacteristic
subgroupG/H
center, socleC22×C31C2×#120
commutator, Frattini, cosocleC42C24×C31
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. C31×#3482C2semidirect
2. C31×#3138C2semidirect
3. C31×#3038C2semidirect
4. C31×#3038C2semidirect
5. C31×#1628C2semidirect
6. C31×#1627C2semidirect
7. C31×#1626C2semidirect
8. C31×#1625C2semidirect
9. C31×#1561C2semidirect
10. C31×#1489C2semidirect
11. C31×#1489C2semidirect
14. C31×#557C22semidirect
16. C31×#556C22semidirect
19. D4×Q8×C31C22semidirect
22. C31×#547C22semidirect
49. C31×#332C22semidirect
50. C31×#332C22semidirect
51. C31×Q8⋊C8C22semidirect
52. C31×Q8⋊C8C22semidirect
53. C31×D4⋊C8C22semidirect
54. C31×D4⋊C8C22semidirect
243. #18537C31direct (N × H)
259. Q8×C31AGL(1,ℤ/8)semidirect
274. D4×C31AGL(1,ℤ/8)semidirect
307. #3482C2×C31semidirect
308. #3138C2×C31semidirect
309. #3038C2×C31semidirect
310. #3038C2×C31semidirect
311. #1628C2×C31semidirect
312. #1627C2×C31semidirect
313. #1626C2×C31semidirect
314. #1625C2×C31semidirect
315. #1561C2×C31semidirect
316. #1489C2×C31semidirect
317. #1489C2×C31semidirect
350. #557C22×C31semidirect
352. #556C22×C31semidirect
355. D4×Q8C22×C31semidirect
358. #547C22×C31semidirect
385. #332C22×C31semidirect
386. #332C22×C31semidirect
387. Q8⋊C8C22×C31semidirect
388. Q8⋊C8C22×C31semidirect
389. D4⋊C8C22×C31semidirect
390. D4⋊C8C22×C31semidirect
491. C31#18537direct (N × H)
602. Q8C31×AGL(1,ℤ/8)semidirect
617. D4C31×AGL(1,ℤ/8)semidirect

Maximal subgroups

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

subgroupindex
C31×#34822
C31×#31382
C31×#30382
C31×#16282
C31×#16272
C31×#16262
C31×#16252
C31×#15612
C31×#14892
#1853731