Finite Group Databasebeta

← C31×#23882 #21480641

Subgroups — C31×#23882 #21480641

Order 7936.

1866 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3585C211yesmaximal, characteristic, complemented
2C31×#3484C211yesmaximal, characteristic, complemented
3C31×#3025C211yesmaximal, characteristic, complemented
4C31×#3021C211yesmaximal, characteristic, complemented
5C31×#3003C212yesmaximal, complemented
6C31×#2010C212yesmaximal, complemented
7C31×#2008C212yesmaximal, complemented
8C31×#1910C211yesmaximal, characteristic, complemented
9C31×#1904C212yesmaximal, complemented
10C31×#1891C211yesmaximal, characteristic, complemented
11C31×#1795C211yesmaximal, characteristic, complemented
12C31×#585C2211yescharacteristic, complemented
13C2×C31×H(5,𝔽2)C2211yescharacteristic
14C23×D4×C31C2211yescharacteristic, complemented
15C31×#577—24no—
16C31×#576—24no—
17C31×#575—22no—
18C31×#575C2212yescomplemented
19C2×C31×AGL(1,ℤ/8)—22no—
20C2×C31×AGL(1,ℤ/8)C2212yes—
21C2×C31×AGL(1,ℤ/8)C2212yescomplemented
22C31×#568C2211yescharacteristic, complemented
23C31×#546—22no—
24C31×#546—22no—
25D42×C31—22no—
26D42×C31—22no—
27C31×#535C2211yescharacteristic
28C31×#535C2211yescharacteristic, complemented
29C31×#534—22no—
30C31×#525C2211yescharacteristic
31C31×#525C2211yescharacteristic, complemented
32C31×#525C2212yescomplemented
33C2×C31×#120—22no—
34C31×#518C2211yescharacteristic, complemented
35C31×#458—22no—
36C31×B(4,𝔽2)—22no—
37C31×#454—22no—
38C31×#453—22no—
39C31×#450—24no—
40C31×#447—24no—
41C31×#421C2212yescomplemented
42C31×#421C2212yescomplemented
43C31×#418C2212yescomplemented
44C31×#418C2212yescomplemented
45C31×#413C2211yescharacteristic, complemented
46C31×#410C2211yescharacteristic, complemented
47C31×#410C2212yescomplemented
48C31×#407C2212yescomplemented
49C31×#344C2212yescomplemented
50C31×H(3,ℤ/4)C2212yescomplemented
51C25×C31—21no—
52C31×2−1+4—22no—
53C31×2−1+4—21no—
54C31×H(5,𝔽2)—24no—
55C31×H(5,𝔽2)—22no—
56C31×H(5,𝔽2)—22no—
57C31×H(5,𝔽2)—21no—
58C31×H(5,𝔽2)—42no—
59C2×#41×C31—21no—
60C2×#41×C31—22no—
61C2×#41×C31—42no—
62C2×#41×C31D412yescomplemented
63C2×#41×C31C2311yescharacteristic
64C2×#41×C31C2312yes—
65C2×#41×C31C2311yescharacteristic
66C22×D4×C31—24no—
67C22×D4×C31—22no—
68C22×D4×C31—21no—
69C22×D4×C31—22no—
70C22×D4×C31—22no—
71C22×D4×C31—24no—
72C22×D4×C31—21no—
73C22×D4×C31—42no—
74C22×D4×C31D412yescomplemented
75C22×D4×C31C2311yescharacteristic
76C22×D4×C31C2311yescharacteristic
77C23×C4×C31C2311yescharacteristic
78C31×#137—24no—
79C31×#137—22no—
80C31×#137—22no—
81C31×AGL(1,ℤ/8)—28no—
82C31×AGL(1,ℤ/8)—24no—
83C31×AGL(1,ℤ/8)—22no—
84C31×AGL(1,ℤ/8)—24no—
85C31×AGL(1,ℤ/8)—24no—
86C31×AGL(1,ℤ/8)—22no—
87C31×AGL(1,ℤ/8)—24no—
88C31×AGL(1,ℤ/8)—42no—
89C31×#135—28no—
90C31×#135—24no—
91C2×SD16×C31—24no—
92C2×SD16×C31—22no—
93C2×SD16×C31D414yescomplemented
94C2×D8×C31—24no—
95C2×D8×C31—22no—
96C2×D8×C31D414yescomplemented
97C31×#131—24no—
98C2×M16×C31—22no—
99C2×M16×C31C2312yes—
100C2×M16×C31C2312yes—
101C31×#127—21no—
102C31×#127D412yescomplemented
103C31×#124—21no—
104C31×#124D412yescomplemented
105C31×#123—24no—
106C31×#123—21no—
107C31×#123—22no—
108C31×#123D412yes—
109C31×C22⋊Q8—21no—
110C31×C22⋊Q8—21no—
111C31×C22⋊Q8—22no—
112C31×#121—24no—
113C31×#121—24no—
114C31×#121—21no—
115C31×#121—21no—
116C31×#121—22no—
117C31×#121—22no—
118C31×#121—22no—
119C31×#120—24no—
120C31×#120—24no—
121C31×#120—24no—
122C31×#120—21no—
123C31×#120—22no—
124C31×#120—22no—
125C31×#120—22no—
126C31×#120D412yes—
127C4×D4×C31—22no—
128C4×D4×C31—22no—
129C4×D4×C31—22no—
130C4×D4×C31—22no—
131C4×D4×C31—42no—
132C31×#117C2312yes—
133C31×#117C2311yescharacteristic
134C31×#117C2311yescharacteristic
135C2×C22⋊C4×C31—24no—
136C2×C22⋊C4×C31—22no—
137C31×#104—24no—
138C31×#104—42no—
139C31×#102—24no—
140C31×#102—24no—
141C31×#101—21no—
142C31×#100—21no—
143C31×#99—22no—
144C31×#99—24no—
145C31×C22⋊C8—24no—
146C24×C31—21no—
147C24×C31—24no—
148C24×C31—22no—
149C24×C31—21no—
150C24×C31—44no—
151C24×C31—84no—
152C24×C31C2×D411yescharacteristic
153#41×C31—22no—
154#41×C31—22no—
155#41×C31—24no—
156#41×C31—24no—
157#41×C31—22no—
158#41×C31—22no—
159#41×C31—22no—
160#41×C31—22no—
161#41×C31—22no—
162#41×C31—22no—
163#41×C31—42no—
164#41×C31—44no—
165#41×C31—42no—
166#41×C31—44no—
167#41×C31—42no—
168#41×C31—42no—
169#41×C31—42no—
170C2×Q8×C31—22no—
171C2×Q8×C31—42no—
172C2×Q8×C31C2×D411yescharacteristic
173C2×Q8×C31C2×D411yescharacteristic
174C2×Q8×C31C2×D412yescomplemented
175C2×D4×C31—22no—
176C2×D4×C31—24no—
177C2×D4×C31—22no—
178C2×D4×C31—24no—
179C2×D4×C31—22no—
180C2×D4×C31—22no—
181C2×D4×C31—22no—
182C2×D4×C31—21no—
183C2×D4×C31—24no—
184C2×D4×C31—24no—
185C2×D4×C31—22no—
186C2×D4×C31—21no—
187C2×D4×C31—22no—
188C2×D4×C31—21no—
189C2×D4×C31—22no—
190C2×D4×C31—22no—
191C2×D4×C31—42no—
192C2×D4×C31—44no—
193C2×D4×C31—48no—
194C2×D4×C31—44no—
195C2×D4×C31—42no—
196C2×D4×C31—48no—
197C2×D4×C31—44no—
198C2×D4×C31—44no—
199C2×D4×C31—42no—
200C2×D4×C31—44no—
201C2×D4×C31—42no—
202C2×D4×C31—88no—
203C2×D4×C31C2×D412yes—
204C2×D4×C31C2×D412yes—
205C2×D4×C31C2×D411yescharacteristic
206C2×D4×C31C2×D411yescharacteristic
207C2×D4×C31C2×D414yes—
208C2×D4×C31C2×D412yes—
209C2×D4×C31C2×D412yescomplemented
210C22×C4×C31—24no—
211C22×C4×C31—22no—
212C22×C4×C31—22no—
213C22×C4×C31—21no—
214C22×C4×C31—21no—
215C22×C4×C31—21no—
216C22×C4×C31—22no—
217C22×C4×C31—22no—
218C22×C4×C31—42no—
219C22×C4×C31C2×D411yescharacteristic
220C22×C4×C31C2×D412yes—
221C22×C4×C31C2411yescharacteristic
222Q16×C31—24no—
223SD16×C31—24no—
224SD16×C31—24no—
225SD16×C31—28no—
226SD16×C31—44no—
227D8×C31—24no—
228D8×C31—28no—
229D8×C31—44no—
230M16×C31—24no—
231M16×C31—22no—
232M16×C31—22no—
233M16×C31—22no—
234M16×C31—22no—
235C2×C8×C31—24no—
236C2×C8×C31—22no—
237C2×C8×C31C2×D414yescomplemented
238C4⋊C4×C31—22no—
239C4⋊C4×C31—22no—
240C4⋊C4×C31—21no—
241C4⋊C4×C31—21no—
242C4⋊C4×C31—22no—
243C4⋊C4×C31—42no—
244C22⋊C4×C31—22no—
245C22⋊C4×C31—24no—
246C22⋊C4×C31—24no—
247C22⋊C4×C31—22no—
248C22⋊C4×C31—22no—
249C22⋊C4×C31—21no—
250C22⋊C4×C31—22no—
251C22⋊C4×C31—24no—
252C22⋊C4×C31—22no—
253C22⋊C4×C31—42no—
254C22⋊C4×C31—42no—
255C22⋊C4×C31C2×D412yes—
256C42×C31—21no—
257C42×C31—22no—
258C42×C31C2×D412yes—
259#23882C3111yesmaximal, characteristic, direct product factor, Sylow
260C23×C31—21no—
261C23×C31—22no—
262C23×C31—22no—
263C23×C31—24no—
264C23×C31—22no—
265C23×C31—21no—
266C23×C31—22no—
267C23×C31—42no—
268C23×C31—44no—
269C23×C31—48no—
270C23×C31—48no—
271C23×C31—42no—
272C23×C31—42no—
273C23×C31—88no—
274C23×C31—82no—
275C23×C31—82no—
276C23×C31—84no—
277C23×C31—84no—
278C23×C31—88no—
279C23×C31#12012yes—
280C23×C31C22×D411yescharacteristic
281Q8×C31—22no—
282Q8×C31—22no—
283Q8×C31—21no—
284Q8×C31—21no—
285Q8×C31—22no—
286Q8×C31—42no—
287D4×C31—24no—
288D4×C31—22no—
289D4×C31—21no—
290D4×C31—22no—
291D4×C31—21no—
292D4×C31—24no—
293D4×C31—22no—
294D4×C31—22no—
295D4×C31—24no—
296D4×C31—44no—
297D4×C31—42no—
298D4×C31—44no—
299D4×C31—48no—
300D4×C31—44no—
301D4×C31—44no—
302D4×C31—44no—
303D4×C31—42no—
304D4×C31—42no—
305D4×C31—42no—
306D4×C31—41no—
307D4×C31—41no—
308D4×C31—84no—
309D4×C31—84no—
310D4×C31—84no—
311D4×C31#12014yes—
312C2×C4×C31—22no—
313C2×C4×C31—22no—
314C2×C4×C31—22no—
315C2×C4×C31—22no—
316C2×C4×C31—21no—
317C2×C4×C31—21no—
318C2×C4×C31—22no—
319C2×C4×C31—22no—
320C2×C4×C31—44no—
321C2×C4×C31—44no—
322C2×C4×C31—42no—
323C2×C4×C31—41no—
324C2×C4×C31—41no—
325C2×C4×C31—42no—
326C2×C4×C31—42no—
327C2×C4×C31—42no—
328C2×C4×C31—42no—
329C2×C4×C31—42no—
330C2×C4×C31—84no—
331C2×C4×C31#12012yes—
332C2×C4×C31C22×D411yescharacteristic
333C2×C4×C31C22×D412yes—
334C2×C4×C31C22×D411yescharacteristic
335C2×C4×C31H(5,𝔽2)12yes—
336C8×C31—24no—
337C8×C31—42no—
338#3585C2×C3111yescharacteristic, complemented
339#3484C2×C3111yescharacteristic, complemented
340#3025C2×C3111yescharacteristic, complemented
341#3021C2×C3111yescharacteristic, complemented
342#3003C2×C3112yescomplemented
343#2010C2×C3112yescomplemented
344#2008C2×C3112yescomplemented
345#1910C2×C3111yescharacteristic, complemented
346#1904C2×C3112yescomplemented
347#1891C2×C3111yescharacteristic, complemented
348#1795C2×C3111yescharacteristic, complemented
349C22×C31—22no—
350C22×C31—24no—
351C22×C31—22no—
352C22×C31—24no—
353C22×C31—41no—
354C22×C31—42no—
355C22×C31—44no—
356C22×C31—41no—
357C22×C31—42no—
358C22×C31—42no—
359C22×C31—44no—
360C22×C31—41no—
361C22×C31—42no—
362C22×C31—41no—
363C22×C31—42no—
364C22×C31—84no—
365C22×C31—82no—
366C22×C31—84no—
367C22×C31—816no—
368C22×C31—164no—
369C22×C31—162no—
370C22×C31C2×#12011yescharacteristic
371C22×C31D4212yes—
372C4×C31—22no—
373C4×C31—42no—
374C4×C31—42no—
375C4×C31—41no—
376C4×C31—41no—
377C4×C31—42no—
378C4×C31—82no—
379C4×C31C2×#12011yescharacteristic
380C4×C31#53411yescharacteristic
381C4×C31D4212yes—
382#585C22×C3111yescharacteristic, complemented
383C2×H(5,𝔽2)C22×C3111yescharacteristic
384C23×D4C22×C3111yescharacteristic, complemented
385#577—24no—
386#576—24no—
387#575—22no—
388#575C22×C3112yescomplemented
389C2×AGL(1,ℤ/8)—22no—
390C2×AGL(1,ℤ/8)C22×C3112yes—
391C2×AGL(1,ℤ/8)C22×C3112yescomplemented
392#568C22×C3111yescharacteristic, complemented
393#546—22no—
394#546—22no—
395D42—22no—
396D42—22no—
397#535C22×C3111yescharacteristic
398#535C22×C3111yescharacteristic, complemented
399#534—22no—
400#525C22×C3111yescharacteristic
401#525C22×C3111yescharacteristic, complemented
402#525C22×C3112yescomplemented
403C2×#120—22no—
404#518C22×C3111yescharacteristic, complemented
405#458—22no—
406B(4,𝔽2)—22no—
407#454—22no—
408#453—22no—
409#450—24no—
410#447—24no—
411#421C22×C3112yescomplemented
412#421C22×C3112yescomplemented
413#418C22×C3112yescomplemented
414#418C22×C3112yescomplemented
415#413C22×C3111yescharacteristic, complemented
416#410C22×C3111yescharacteristic, complemented
417#410C22×C3112yescomplemented
418#407C22×C3112yescomplemented
419#344C22×C3112yescomplemented
420H(3,ℤ/4)C22×C3112yescomplemented
421C2×C31—21no—
422C2×C31—22no—
423C2×C31—42no—
424C2×C31—44no—
425C2×C31—42no—
426C2×C31—82no—
427C2×C31—81no—
428C2×C31—82no—
429C2×C31#240311yescharacteristic
430C25—21no—
4312−1+4—22no—
4322−1+4—21no—
433H(5,𝔽2)—24no—
434H(5,𝔽2)—22no—
435H(5,𝔽2)—22no—
436H(5,𝔽2)—21no—
437H(5,𝔽2)—42no—
438C2×#41—21no—
439C2×#41—22no—
440C2×#41—42no—
441C2×#41D4×C3112yescomplemented
442C2×#41C23×C3111yescharacteristic
443C2×#41C23×C3112yes—
444C2×#41C23×C3111yescharacteristic
445C22×D4—24no—
446C22×D4—22no—
447C22×D4—21no—
448C22×D4—22no—
449C22×D4—22no—
450C22×D4—24no—
451C22×D4—21no—
452C22×D4—42no—
453C22×D4D4×C3112yescomplemented
454C22×D4C23×C3111yescharacteristic
455C22×D4C23×C3111yescharacteristic
456C23×C4C23×C3111yescharacteristic
457#137—24no—
458#137—22no—
459#137—22no—
460AGL(1,ℤ/8)—28no—
461AGL(1,ℤ/8)—24no—
462AGL(1,ℤ/8)—22no—
463AGL(1,ℤ/8)—24no—
464AGL(1,ℤ/8)—24no—
465AGL(1,ℤ/8)—22no—
466AGL(1,ℤ/8)—24no—
467AGL(1,ℤ/8)—42no—
468#135—28no—
469#135—24no—
470C2×SD16—24no—
471C2×SD16—22no—
472C2×SD16D4×C3114yescomplemented
473C2×D8—24no—
474C2×D8—22no—
475C2×D8D4×C3114yescomplemented
476#131—24no—
477C2×M16—22no—
478C2×M16C23×C3112yes—
479C2×M16C23×C3112yes—
480#127—21no—
481#127D4×C3112yescomplemented
482#124—21no—
483#124D4×C3112yescomplemented
484#123—24no—
485#123—21no—
486#123—22no—
487#123D4×C3112yes—
488C22⋊Q8—21no—
489C22⋊Q8—21no—
490C22⋊Q8—22no—
491#121—24no—
492#121—24no—
493#121—21no—
494#121—21no—
495#121—22no—
496#121—22no—
497#121—22no—
498#120—24no—
499#120—24no—
500#120—24no—
501#120—21no—
502#120—22no—
503#120—22no—
504#120—22no—
505#120D4×C3112yes—
506C4×D4—22no—
507C4×D4—22no—
508C4×D4—22no—
509C4×D4—22no—
510C4×D4—42no—
511#117C23×C3112yes—
512#117C23×C3111yescharacteristic
513#117C23×C3111yescharacteristic
514C2×C22⋊C4—24no—
515C2×C22⋊C4—22no—
516#104—24no—
517#104—42no—
518#102—24no—
519#102—24no—
520#101—21no—
521#100—21no—
522#99—22no—
523#99—24no—
524C22⋊C8—24no—
525C31#2388211yescharacteristic, direct product factor, Sylow
526C24—21no—
527C24—24no—
528C24—22no—
529C24—21no—
530C24—44no—
531C24—84no—
532C24C2×D4×C3111yescharacteristic
533#41—22no—
534#41—22no—
535#41—24no—
536#41—24no—
537#41—22no—
538#41—22no—
539#41—22no—
540#41—22no—
541#41—22no—
542#41—22no—
543#41—42no—
544#41—44no—
545#41—42no—
546#41—44no—
547#41—42no—
548#41—42no—
549#41—42no—
550C2×Q8—22no—
551C2×Q8—42no—
552C2×Q8C2×D4×C3111yescharacteristic
553C2×Q8C2×D4×C3111yescharacteristic
554C2×Q8C2×D4×C3112yescomplemented
555C2×D4—22no—
556C2×D4—24no—
557C2×D4—22no—
558C2×D4—24no—
559C2×D4—22no—
560C2×D4—22no—
561C2×D4—22no—
562C2×D4—21no—
563C2×D4—24no—
564C2×D4—24no—
565C2×D4—22no—
566C2×D4—21no—
567C2×D4—22no—
568C2×D4—21no—
569C2×D4—22no—
570C2×D4—22no—
571C2×D4—42no—
572C2×D4—44no—
573C2×D4—48no—
574C2×D4—44no—
575C2×D4—42no—
576C2×D4—48no—
577C2×D4—44no—
578C2×D4—44no—
579C2×D4—42no—
580C2×D4—44no—
581C2×D4—42no—
582C2×D4—88no—
583C2×D4C2×D4×C3112yes—
584C2×D4C2×D4×C3112yes—
585C2×D4C2×D4×C3111yescharacteristic
586C2×D4C2×D4×C3111yescharacteristic
587C2×D4C2×D4×C3114yes—
588C2×D4C2×D4×C3112yes—
589C2×D4C2×D4×C3112yescomplemented
590C22×C4—24no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—42no—
599C22×C4C2×D4×C3111yescharacteristic
600C22×C4C2×D4×C3112yes—
601C22×C4C24×C3111yescharacteristic
602Q16—24no—
603SD16—24no—
604SD16—24no—
605SD16—28no—
606SD16—44no—
607D8—24no—
608D8—28no—
609D8—44no—
610M16—24no—
611M16—22no—
612M16—22no—
613M16—22no—
614M16—22no—
615C2×C8—24no—
616C2×C8—22no—
617C2×C8C2×D4×C3114yescomplemented
618C4⋊C4—22no—
619C4⋊C4—22no—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—22no—
623C4⋊C4—42no—
624C22⋊C4—22no—
625C22⋊C4—24no—
626C22⋊C4—24no—
627C22⋊C4—22no—
628C22⋊C4—22no—
629C22⋊C4—21no—
630C22⋊C4—22no—
631C22⋊C4—24no—
632C22⋊C4—22no—
633C22⋊C4—42no—
634C22⋊C4—42no—
635C22⋊C4C2×D4×C3112yes—
636C42—21no—
637C42—22no—
638C42C2×D4×C3112yes—
639C23—21no—
640C23—22no—
641C23—22no—
642C23—24no—
643C23—22no—
644C23—21no—
645C23—22no—
646C23—42no—
647C23—44no—
648C23—48no—
649C23—48no—
650C23—42no—
651C23—42no—
652C23—88no—
653C23—82no—
654C23—82no—
655C23—84no—
656C23—84no—
657C23—88no—
658C23C31×#12012yes—
659C23C22×D4×C3111yescharacteristic
660Q8—22no—
661Q8—22no—
662Q8—21no—
663Q8—21no—
664Q8—22no—
665Q8—42no—
666D4—24no—
667D4—22no—
668D4—21no—
669D4—22no—
670D4—21no—
671D4—24no—
672D4—22no—
673D4—22no—
674D4—24no—
675D4—44no—
676D4—42no—
677D4—44no—
678D4—48no—
679D4—44no—
680D4—44no—
681D4—44no—
682D4—42no—
683D4—42no—
684D4—42no—
685D4—41no—
686D4—41no—
687D4—84no—
688D4—84no—
689D4—84no—
690D4C31×#12014yes—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—44no—
700C2×C4—44no—
701C2×C4—42no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—84no—
710C2×C4C31×#12012yes—
711C2×C4C22×D4×C3111yescharacteristic
712C2×C4C22×D4×C3112yes—
713C2×C4C22×D4×C3111yescharacteristic
714C2×C4C31×H(5,𝔽2)12yes—
715C8—24no—
716C8—42no—
717C22—22no—
718C22—24no—
719C22—22no—
720C22—24no—
721C22—41no—
722C22—42no—
723C22—44no—
724C22—41no—
725C22—42no—
726C22—42no—
727C22—44no—
728C22—41no—
729C22—42no—
730C22—41no—
731C22—42no—
732C22—84no—
733C22—82no—
734C22—84no—
735C22—816no—
736C22—164no—
737C22—162no—
738C22C2×C31×#12011yescharacteristic
739C22D42×C3112yes—
740C4—22no—
741C4—42no—
742C4—42no—
743C4—41no—
744C4—41no—
745C4—42no—
746C4—82no—
747C4C2×C31×#12011yescharacteristic
748C4C31×#53411yescharacteristic
749C4D42×C3112yes—
750C2—21no—
751C2—22no—
752C2—42no—
753C2—44no—
754C2—42no—
755C2—82no—
756C2—81no—
757C2—82no—
758C2C31×#240311yescharacteristic
subgroupG/H
center, socleC2×C31#2403
commutator, Frattini, cosocleC22×C4C24×C31
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C31 ◁ C22×C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C31×#3585C2semidirect
2. C31×#3484C2semidirect
3. C31×#3025C2semidirect
4. C31×#3021C2semidirect
5. C31×#3003C2semidirect
6. C31×#2010C2semidirect
7. C31×#2008C2semidirect
8. C31×#1910C2semidirect
9. C31×#1904C2semidirect
10. C31×#1891C2semidirect
11. C31×#1795C2semidirect
12. C31×#585C22semidirect
14. C23×D4×C31C22semidirect
18. C31×#575C22semidirect
21. C2×C31×AGL(1,ℤ/8)C22semidirect
22. C31×#568C22semidirect
28. C31×#535C22semidirect
31. C31×#525C22semidirect
32. C31×#525C22semidirect
34. C31×#518C22semidirect
41. C31×#421C22semidirect
42. C31×#421C22semidirect
43. C31×#418C22semidirect
44. C31×#418C22semidirect
45. C31×#413C22semidirect
46. C31×#410C22semidirect
47. C31×#410C22semidirect
48. C31×#407C22semidirect
49. C31×#344C22semidirect
50. C31×H(3,ℤ/4)C22semidirect
62. C2×#41×C31D4semidirect
74. C22×D4×C31D4semidirect
93. C2×SD16×C31D4semidirect
96. C2×D8×C31D4semidirect
102. C31×#127D4semidirect
104. C31×#124D4semidirect
174. C2×Q8×C31C2×D4semidirect
209. C2×D4×C31C2×D4semidirect
237. C2×C8×C31C2×D4semidirect
259. #23882C31direct (N × H)
338. #3585C2×C31semidirect
339. #3484C2×C31semidirect
340. #3025C2×C31semidirect
341. #3021C2×C31semidirect
342. #3003C2×C31semidirect
343. #2010C2×C31semidirect
344. #2008C2×C31semidirect
345. #1910C2×C31semidirect
346. #1904C2×C31semidirect
347. #1891C2×C31semidirect
348. #1795C2×C31semidirect
382. #585C22×C31semidirect
384. C23×D4C22×C31semidirect
388. #575C22×C31semidirect
391. C2×AGL(1,ℤ/8)C22×C31semidirect
392. #568C22×C31semidirect
398. #535C22×C31semidirect
401. #525C22×C31semidirect
402. #525C22×C31semidirect
404. #518C22×C31semidirect
411. #421C22×C31semidirect
412. #421C22×C31semidirect
413. #418C22×C31semidirect
414. #418C22×C31semidirect
415. #413C22×C31semidirect
416. #410C22×C31semidirect
417. #410C22×C31semidirect
418. #407C22×C31semidirect
419. #344C22×C31semidirect
420. H(3,ℤ/4)C22×C31semidirect
441. C2×#41D4×C31semidirect
453. C22×D4D4×C31semidirect
472. C2×SD16D4×C31semidirect
475. C2×D8D4×C31semidirect
481. #127D4×C31semidirect
483. #124D4×C31semidirect
525. C31#23882direct (N × H)
554. C2×Q8C2×D4×C31semidirect
589. C2×D4C2×D4×C31semidirect
617. C2×C8C2×D4×C31semidirect

Maximal subgroups

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

subgroupindex
C31×#35852
C31×#34842
C31×#30252
C31×#30212
C31×#30032
C31×#20102
C31×#20082
C31×#19102
C31×#19042
C31×#18912
C31×#17952
#2388231