Finite Group Databasebeta

← C31×#24398 #21481157

Subgroups — C31×#24398 #21481157

Order 7936.

1476 conjugacy classes of subgroups.

The subgroup lattice has 730 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C31×AGL(1,ℤ/8)C211yesmaximal, characteristic, complemented
2C2×C31×#472C212yesmaximal, complemented
3C31×#3006C211yesmaximal, characteristic, complemented
4C2×C31×#447C211yesmaximal, characteristic, complemented
5C31×#2880C211yesmaximal, characteristic, complemented
6C31×#2051C212yesmaximal, complemented
7C31×#2018C212yesmaximal, complemented
8C31×#1907C212yesmaximal, complemented
9C31×#1900C211yesmaximal, characteristic, complemented
10C31×#1855C211yesmaximal, characteristic, complemented
11C31×#1783C211yesmaximal, characteristic, complemented
12C22×#41×C31C2211yescharacteristic
13C23×D4×C31C2211yescharacteristic
14C2×C31×AGL(1,ℤ/8)—21no—
15C2×C31×AGL(1,ℤ/8)—21no—
16C2×C31×AGL(1,ℤ/8)—28no—
17C2×C31×AGL(1,ℤ/8)C2212yes—
18C2×C31×AGL(1,ℤ/8)C2212yes—
19C2×C31×AGL(1,ℤ/8)C2211yescharacteristic, complemented
20C2×C31×AGL(1,ℤ/8)C2211yescharacteristic, complemented
21C22×SD16×C31—21no—
22C22×D8×C31—21no—
23C22×D8×C31C2212yescomplemented
24C2×C31×#131C2212yescomplemented
25C22×M16×C31C2211yescharacteristic
26C2×C31×#121C2211yescharacteristic
27C31×#472—28no—
28C31×#449—21no—
29C31×#449—21no—
30C31×#448—21no—
31C31×#447—21no—
32C31×#447—21no—
33C31×#447—21no—
34C31×#447—22no—
35C2×C31×#108C2212yescomplemented
36C31×#417C2211yescharacteristic, complemented
37C31×#417C2211yescharacteristic, complemented
38C2×C31×#102C2212yescomplemented
39C2×C31×#100C2212yescomplemented
40C2×C31×#100C2212yescomplemented
41C2×C31×#100C2212yescomplemented
42C31×#408—22no—
43C31×#408C2212yescomplemented
44C31×#407—21no—
45C31×#407C2211yescharacteristic
46C31×#407C2211yescharacteristic
47C2×C31×C22⋊C8—21no—
48C2×C31×C22⋊C8C2211yescharacteristic
49C31×#343C2212yescomplemented
50C31×#341C2212yescomplemented
51C25×C31—21no—
52C2×#41×C31—21no—
53C2×#41×C31—21no—
54C2×#41×C31—24no—
55C2×#41×C31—42no—
56C2×#41×C31D411yescharacteristic
57C2×#41×C31D411yescharacteristic
58C2×#41×C31C2311yescharacteristic
59C2×#41×C31C2311yescharacteristic
60C22×Q8×C31D411yescharacteristic
61C22×D4×C31—24no—
62C22×D4×C31—21no—
63C22×D4×C31—21no—
64C22×D4×C31—21no—
65C22×D4×C31—21no—
66C22×D4×C31—21no—
67C22×D4×C31—21no—
68C22×D4×C31—21no—
69C22×D4×C31—42no—
70C22×D4×C31D411yescharacteristic
71C22×D4×C31C2311yescharacteristic
72C22×D4×C31C2312yes—
73C23×C4×C31—21no—
74C23×C4×C31C2311yescharacteristic
75C31×AGL(1,ℤ/8)—28no—
76C31×AGL(1,ℤ/8)—28no—
77C31×AGL(1,ℤ/8)—24no—
78C31×AGL(1,ℤ/8)—24no—
79C31×AGL(1,ℤ/8)—24no—
80C31×AGL(1,ℤ/8)—24no—
81C31×AGL(1,ℤ/8)—42no—
82C31×AGL(1,ℤ/8)D418yescomplemented
83C2×SD16×C31—28no—
84C2×SD16×C31—22no—
85C2×SD16×C31—22no—
86C2×SD16×C31—21no—
87C2×SD16×C31—21no—
88C2×D8×C31—28no—
89C2×D8×C31—22no—
90C2×D8×C31—22no—
91C2×D8×C31—21no—
92C2×D8×C31—21no—
93C2×D8×C31—24no—
94C2×D8×C31—22no—
95C2×D8×C31—22no—
96C2×D8×C31—42no—
97C31×#131—24no—
98C31×#131—42no—
99C2×M16×C31—21no—
100C2×M16×C31—24no—
101C2×M16×C31—22no—
102C2×M16×C31C2312yes—
103C2×M16×C31C2311yescharacteristic
104C2×M16×C31C2311yescharacteristic
105C2×M16×C31C2312yes—
106C22×C8×C31—21no—
107C22×C8×C31—22no—
108C22×C8×C31C2312yes—
109C31×#121—21no—
110C31×#121—21no—
111C31×#121—21no—
112C31×#121—21no—
113C2×C4⋊C4×C31C2311yescharacteristic
114C2×C22⋊C4×C31—21no—
115C31×#108—24no—
116C31×#103—21no—
117C31×#103—21no—
118C31×#102—21no—
119C31×#102—21no—
120C31×#102—22no—
121C31×#102—22no—
122C31×#100—24no—
123C31×#100—24no—
124C31×#100—42no—
125C31×C22⋊C8—21no—
126C31×C22⋊C8—21no—
127C31×C22⋊C8—21no—
128C31×C22⋊C8—21no—
129C31×C22⋊C8—22no—
130C31×C22⋊C8—22no—
131C31×C22⋊C8D411yescharacteristic
132C31×C22⋊C8D411yescharacteristic
133C31×C22⋊C8D412yes—
134C24×C31—21no—
135C24×C31—22no—
136C24×C31—21no—
137C24×C31—44no—
138C24×C31—41no—
139C24×C31—41no—
140C24×C31—82no—
141C24×C31—82no—
142C24×C31#4111yescharacteristic
143#41×C31—22no—
144#41×C31—22no—
145#41×C31—22no—
146#41×C31—22no—
147#41×C31—22no—
148#41×C31—44no—
149#41×C31—41no—
150#41×C31—41no—
151#41×C31—44no—
152#41×C31C2×D414yes—
153C2×Q8×C31—21no—
154C2×Q8×C31—22no—
155C2×Q8×C31—41no—
156C2×Q8×C31C2×D411yescharacteristic
157C2×Q8×C31C2×D411yescharacteristic
158C2×D4×C31—21no—
159C2×D4×C31—24no—
160C2×D4×C31—24no—
161C2×D4×C31—22no—
162C2×D4×C31—21no—
163C2×D4×C31—21no—
164C2×D4×C31—21no—
165C2×D4×C31—21no—
166C2×D4×C31—22no—
167C2×D4×C31—22no—
168C2×D4×C31—22no—
169C2×D4×C31—22no—
170C2×D4×C31—21no—
171C2×D4×C31—21no—
172C2×D4×C31—22no—
173C2×D4×C31—22no—
174C2×D4×C31—22no—
175C2×D4×C31—41no—
176C2×D4×C31—44no—
177C2×D4×C31—44no—
178C2×D4×C31—44no—
179C2×D4×C31—42no—
180C2×D4×C31—42no—
181C2×D4×C31—44no—
182C2×D4×C31—41no—
183C2×D4×C31—41no—
184C2×D4×C31—41no—
185C2×D4×C31—41no—
186C2×D4×C31—82no—
187C2×D4×C31C2×D414yes—
188C2×D4×C31C2×D411yescharacteristic
189C2×D4×C31C2×D411yescharacteristic
190C22×C4×C31—21no—
191C22×C4×C31—22no—
192C22×C4×C31—22no—
193C22×C4×C31—21no—
194C22×C4×C31—21no—
195C22×C4×C31—21no—
196C22×C4×C31—21no—
197C22×C4×C31—21no—
198C22×C4×C31—44no—
199C22×C4×C31C2×D411yescharacteristic
200C22×C4×C31C2×D411yescharacteristic
201C22×C4×C31C2×D411yescharacteristic
202C22×C4×C31C2×D411yescharacteristic
203C22×C4×C31#4111yescharacteristic
204C22×C4×C31C2411yescharacteristic
205SD16×C31—28no—
206SD16×C31—28no—
207SD16×C31—42no—
208SD16×C31—42no—
209D8×C31—28no—
210D8×C31—28no—
211D8×C31—44no—
212D8×C31—44no—
213D8×C31—42no—
214D8×C31—42no—
215M16×C31—24no—
216M16×C31—22no—
217M16×C31—22no—
218M16×C31—22no—
219M16×C31—22no—
220M16×C31—22no—
221M16×C31—44no—
222M16×C31C2×D414yes—
223C2×C8×C31—24no—
224C2×C8×C31—22no—
225C2×C8×C31—22no—
226C2×C8×C31—22no—
227C2×C8×C31—22no—
228C2×C8×C31—21no—
229C2×C8×C31—21no—
230C2×C8×C31—44no—
231C2×C8×C31C2×D412yes—
232C2×C8×C31C2×D412yes—
233C4⋊C4×C31—21no—
234C4⋊C4×C31—21no—
235C22⋊C4×C31—41no—
236C22⋊C4×C31—41no—
237#24398C3111yesmaximal, characteristic, direct product factor, Sylow
238C23×C31—21no—
239C23×C31—22no—
240C23×C31—22no—
241C23×C31—21no—
242C23×C31—24no—
243C23×C31—41no—
244C23×C31—42no—
245C23×C31—44no—
246C23×C31—44no—
247C23×C31—42no—
248C23×C31—42no—
249C23×C31—42no—
250C23×C31—41no—
251C23×C31—42no—
252C23×C31—81no—
253C23×C31—82no—
254C23×C31—82no—
255C23×C31—82no—
256C23×C31—82no—
257C23×C31—82no—
258C23×C31—81no—
259C23×C31—81no—
260C23×C31—816no—
261C23×C31—82no—
262C23×C31#12111yescharacteristic
263C23×C31#12111yescharacteristic
264C23×C31C2×#4111yescharacteristic
265Q8×C31—21no—
266Q8×C31—21no—
267Q8×C31—21no—
268Q8×C31—42no—
269Q8×C31#12012yes—
270D4×C31—24no—
271D4×C31—21no—
272D4×C31—24no—
273D4×C31—21no—
274D4×C31—21no—
275D4×C31—24no—
276D4×C31—42no—
277D4×C31—42no—
278D4×C31—44no—
279D4×C31—44no—
280D4×C31—42no—
281D4×C31—42no—
282D4×C31—41no—
283D4×C31—42no—
284D4×C31—41no—
285D4×C31—42no—
286D4×C31—42no—
287D4×C31—82no—
288D4×C31—82no—
289D4×C31#12012yes—
290C2×C4×C31—21no—
291C2×C4×C31—22no—
292C2×C4×C31—21no—
293C2×C4×C31—21no—
294C2×C4×C31—21no—
295C2×C4×C31—21no—
296C2×C4×C31—24no—
297C2×C4×C31—22no—
298C2×C4×C31—22no—
299C2×C4×C31—21no—
300C2×C4×C31—42no—
301C2×C4×C31—42no—
302C2×C4×C31—42no—
303C2×C4×C31—42no—
304C2×C4×C31—41no—
305C2×C4×C31—81no—
306C2×C4×C31#12111yescharacteristic
307C2×C4×C31#12111yescharacteristic
308C2×C4×C31C22×D411yescharacteristic
309C2×C4×C31C22×D412yes—
310C2×C4×C31C22×D411yescharacteristic
311C2×C4×C31H(5,𝔽2)12yes—
312C8×C31—24no—
313C8×C31—22no—
314C8×C31—22no—
315C8×C31—41no—
316C8×C31—41no—
317C8×C31—42no—
318C22×AGL(1,ℤ/8)C2×C3111yescharacteristic, complemented
319C2×#472C2×C3112yescomplemented
320#3006C2×C3111yescharacteristic, complemented
321C2×#447C2×C3111yescharacteristic, complemented
322#2880C2×C3111yescharacteristic, complemented
323#2051C2×C3112yescomplemented
324#2018C2×C3112yescomplemented
325#1907C2×C3112yescomplemented
326#1900C2×C3111yescharacteristic, complemented
327#1855C2×C3111yescharacteristic, complemented
328#1783C2×C3111yescharacteristic, complemented
329C22×C31—21no—
330C22×C31—21no—
331C22×C31—21no—
332C22×C31—21no—
333C22×C31—21no—
334C22×C31—22no—
335C22×C31—21no—
336C22×C31—21no—
337C22×C31—44no—
338C22×C31—41no—
339C22×C31—41no—
340C22×C31—41no—
341C22×C31—44no—
342C22×C31—41no—
343C22×C31—41no—
344C22×C31—84no—
345C22×C31—84no—
346C22×C31—88no—
347C22×C31—84no—
348C22×C31—88no—
349C22×C31—82no—
350C22×C31—82no—
351C22×C31—81no—
352C22×C31—81no—
353C22×C31—81no—
354C22×C31—162no—
355C22×C31#47212yescomplemented
356C22×C31C2×#12111yescharacteristic
357C22×C31#54612yes—
358C4×C31—21no—
359C4×C31—21no—
360C4×C31—22no—
361C4×C31—41no—
362C4×C31—81no—
363C4×C31C2×#12011yescharacteristic
364C4×C31#53411yescharacteristic
365C4×C31D4212yes—
366C22×#41C22×C3111yescharacteristic
367C23×D4C22×C3111yescharacteristic
368C2×AGL(1,ℤ/8)—21no—
369C2×AGL(1,ℤ/8)—21no—
370C2×AGL(1,ℤ/8)—28no—
371C2×AGL(1,ℤ/8)C22×C3112yes—
372C2×AGL(1,ℤ/8)C22×C3112yes—
373C2×AGL(1,ℤ/8)C22×C3111yescharacteristic, complemented
374C2×AGL(1,ℤ/8)C22×C3111yescharacteristic, complemented
375C22×SD16—21no—
376C22×D8—21no—
377C22×D8C22×C3112yescomplemented
378C2×#131C22×C3112yescomplemented
379C22×M16C22×C3111yescharacteristic
380C2×#121C22×C3111yescharacteristic
381#472—28no—
382#449—21no—
383#449—21no—
384#448—21no—
385#447—21no—
386#447—21no—
387#447—21no—
388#447—22no—
389C2×#108C22×C3112yescomplemented
390#417C22×C3111yescharacteristic, complemented
391#417C22×C3111yescharacteristic, complemented
392C2×#102C22×C3112yescomplemented
393C2×#100C22×C3112yescomplemented
394C2×#100C22×C3112yescomplemented
395C2×#100C22×C3112yescomplemented
396#408—22no—
397#408C22×C3112yescomplemented
398#407—21no—
399#407C22×C3111yescharacteristic
400#407C22×C3111yescharacteristic
401C2×C22⋊C8—21no—
402C2×C22⋊C8C22×C3111yescharacteristic
403#343C22×C3112yescomplemented
404#341C22×C3112yescomplemented
405C2×C31—22no—
406C2×C31—22no—
407C2×C31—41no—
408C2×C31—42no—
409C2×C31—81no—
410C2×C31—84no—
411C2×C31—161no—
412C2×C31#241011yescharacteristic
413C2×C31C2×#47211yescharacteristic
414C2×C31#306811yescharacteristic
415C25—21no—
416C2×#41—21no—
417C2×#41—21no—
418C2×#41—24no—
419C2×#41—42no—
420C2×#41D4×C3111yescharacteristic
421C2×#41D4×C3111yescharacteristic
422C2×#41C23×C3111yescharacteristic
423C2×#41C23×C3111yescharacteristic
424C22×Q8D4×C3111yescharacteristic
425C22×D4—24no—
426C22×D4—21no—
427C22×D4—21no—
428C22×D4—21no—
429C22×D4—21no—
430C22×D4—21no—
431C22×D4—21no—
432C22×D4—21no—
433C22×D4—42no—
434C22×D4D4×C3111yescharacteristic
435C22×D4C23×C3111yescharacteristic
436C22×D4C23×C3112yes—
437C23×C4—21no—
438C23×C4C23×C3111yescharacteristic
439AGL(1,ℤ/8)—28no—
440AGL(1,ℤ/8)—28no—
441AGL(1,ℤ/8)—24no—
442AGL(1,ℤ/8)—24no—
443AGL(1,ℤ/8)—24no—
444AGL(1,ℤ/8)—24no—
445AGL(1,ℤ/8)—42no—
446AGL(1,ℤ/8)D4×C3118yescomplemented
447C2×SD16—28no—
448C2×SD16—22no—
449C2×SD16—22no—
450C2×SD16—21no—
451C2×SD16—21no—
452C2×D8—28no—
453C2×D8—22no—
454C2×D8—22no—
455C2×D8—24no—
456C2×D8—21no—
457C2×D8—21no—
458C2×D8—22no—
459C2×D8—22no—
460C2×D8—42no—
461#131—24no—
462#131—42no—
463C2×M16—21no—
464C2×M16—24no—
465C2×M16—22no—
466C2×M16C23×C3112yes—
467C2×M16C23×C3111yescharacteristic
468C2×M16C23×C3111yescharacteristic
469C2×M16C23×C3112yes—
470C22×C8—21no—
471C22×C8—22no—
472C22×C8C23×C3112yes—
473#121—21no—
474#121—21no—
475#121—21no—
476#121—21no—
477C2×C4⋊C4C23×C3111yescharacteristic
478C2×C22⋊C4—21no—
479#108—24no—
480#103—21no—
481#103—21no—
482#102—21no—
483#102—21no—
484#102—22no—
485#102—22no—
486#100—24no—
487#100—24no—
488#100—42no—
489C22⋊C8—21no—
490C22⋊C8—21no—
491C22⋊C8—21no—
492C22⋊C8—21no—
493C22⋊C8—22no—
494C22⋊C8—22no—
495C22⋊C8D4×C3111yescharacteristic
496C22⋊C8D4×C3111yescharacteristic
497C22⋊C8D4×C3112yes—
498C31#2439811yescharacteristic, direct product factor, Sylow
499C24—21no—
500C24—22no—
501C24—21no—
502C24—44no—
503C24—41no—
504C24—41no—
505C24—82no—
506C24—82no—
507C24#41×C3111yescharacteristic
508#41—22no—
509#41—22no—
510#41—22no—
511#41—22no—
512#41—22no—
513#41—44no—
514#41—41no—
515#41—41no—
516#41—44no—
517#41C2×D4×C3114yes—
518C2×Q8—21no—
519C2×Q8—22no—
520C2×Q8—41no—
521C2×Q8C2×D4×C3111yescharacteristic
522C2×Q8C2×D4×C3111yescharacteristic
523C2×D4—21no—
524C2×D4—24no—
525C2×D4—24no—
526C2×D4—22no—
527C2×D4—21no—
528C2×D4—21no—
529C2×D4—21no—
530C2×D4—21no—
531C2×D4—22no—
532C2×D4—22no—
533C2×D4—22no—
534C2×D4—22no—
535C2×D4—21no—
536C2×D4—21no—
537C2×D4—22no—
538C2×D4—22no—
539C2×D4—22no—
540C2×D4—41no—
541C2×D4—44no—
542C2×D4—44no—
543C2×D4—44no—
544C2×D4—42no—
545C2×D4—42no—
546C2×D4—44no—
547C2×D4—41no—
548C2×D4—41no—
549C2×D4—41no—
550C2×D4—41no—
551C2×D4—82no—
552C2×D4C2×D4×C3114yes—
553C2×D4C2×D4×C3111yescharacteristic
554C2×D4C2×D4×C3111yescharacteristic
555C22×C4—21no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—44no—
564C22×C4C2×D4×C3111yescharacteristic
565C22×C4C2×D4×C3111yescharacteristic
566C22×C4C2×D4×C3111yescharacteristic
567C22×C4C2×D4×C3111yescharacteristic
568C22×C4#41×C3111yescharacteristic
569C22×C4C24×C3111yescharacteristic
570SD16—28no—
571SD16—28no—
572SD16—42no—
573SD16—42no—
574D8—28no—
575D8—28no—
576D8—44no—
577D8—44no—
578D8—42no—
579D8—42no—
580M16—24no—
581M16—22no—
582M16—22no—
583M16—22no—
584M16—22no—
585M16—22no—
586M16—44no—
587M16C2×D4×C3114yes—
588C2×C8—24no—
589C2×C8—22no—
590C2×C8—22no—
591C2×C8—22no—
592C2×C8—22no—
593C2×C8—21no—
594C2×C8—21no—
595C2×C8—44no—
596C2×C8C2×D4×C3112yes—
597C2×C8C2×D4×C3112yes—
598C4⋊C4—21no—
599C4⋊C4—21no—
600C22⋊C4—41no—
601C22⋊C4—41no—
602C23—22no—
603C23—21no—
604C23—22no—
605C23—21no—
606C23—24no—
607C23—41no—
608C23—42no—
609C23—44no—
610C23—44no—
611C23—42no—
612C23—42no—
613C23—42no—
614C23—41no—
615C23—42no—
616C23—81no—
617C23—82no—
618C23—82no—
619C23—82no—
620C23—82no—
621C23—82no—
622C23—81no—
623C23—81no—
624C23—816no—
625C23—82no—
626C23C31×#12111yescharacteristic
627C23C31×#12111yescharacteristic
628C23C2×#41×C3111yescharacteristic
629Q8—21no—
630Q8—21no—
631Q8—21no—
632Q8—42no—
633Q8C31×#12012yes—
634D4—24no—
635D4—21no—
636D4—24no—
637D4—21no—
638D4—21no—
639D4—24no—
640D4—42no—
641D4—42no—
642D4—44no—
643D4—44no—
644D4—42no—
645D4—42no—
646D4—41no—
647D4—42no—
648D4—41no—
649D4—42no—
650D4—42no—
651D4—82no—
652D4—82no—
653D4C31×#12012yes—
654C2×C4—21no—
655C2×C4—22no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—24no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—21no—
664C2×C4—42no—
665C2×C4—42no—
666C2×C4—42no—
667C2×C4—42no—
668C2×C4—41no—
669C2×C4—81no—
670C2×C4C31×#12111yescharacteristic
671C2×C4C31×#12111yescharacteristic
672C2×C4C22×D4×C3111yescharacteristic
673C2×C4C22×D4×C3112yes—
674C2×C4C22×D4×C3111yescharacteristic
675C2×C4C31×H(5,𝔽2)12yes—
676C8—24no—
677C8—22no—
678C8—22no—
679C8—41no—
680C8—41no—
681C8—42no—
682C22—21no—
683C22—21no—
684C22—21no—
685C22—21no—
686C22—21no—
687C22—22no—
688C22—21no—
689C22—21no—
690C22—44no—
691C22—41no—
692C22—41no—
693C22—41no—
694C22—44no—
695C22—41no—
696C22—41no—
697C22—84no—
698C22—84no—
699C22—88no—
700C22—84no—
701C22—88no—
702C22—82no—
703C22—82no—
704C22—81no—
705C22—81no—
706C22—81no—
707C22—162no—
708C22C31×#47212yescomplemented
709C22C2×C31×#12111yescharacteristic
710C22C31×#54612yes—
711C4—21no—
712C4—21no—
713C4—22no—
714C4—41no—
715C4—81no—
716C4C2×C31×#12011yescharacteristic
717C4C31×#53411yescharacteristic
718C4D42×C3112yes—
719C2—22no—
720C2—22no—
721C2—41no—
722C2—42no—
723C2—81no—
724C2—84no—
725C2—161no—
726C2C31×#241011yescharacteristic
727C2C2×C31×#47211yescharacteristic
728C2C31×#306811yescharacteristic
subgroupG/H
center, socleC22×C31C2×#121
commutator, Frattini, cosocleC22×C4C24×C31
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C31 ◁ C23×C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C31×AGL(1,ℤ/8)C2semidirect
2. C2×C31×#472C2semidirect
3. C31×#3006C2semidirect
4. C2×C31×#447C2semidirect
5. C31×#2880C2semidirect
6. C31×#2051C2semidirect
7. C31×#2018C2semidirect
8. C31×#1907C2semidirect
9. C31×#1900C2semidirect
10. C31×#1855C2semidirect
11. C31×#1783C2semidirect
19. C2×C31×AGL(1,ℤ/8)C22semidirect
20. C2×C31×AGL(1,ℤ/8)C22semidirect
23. C22×D8×C31C22semidirect
24. C2×C31×#131C22semidirect
35. C2×C31×#108C22semidirect
36. C31×#417C22semidirect
37. C31×#417C22semidirect
38. C2×C31×#102C22semidirect
39. C2×C31×#100C22semidirect
40. C2×C31×#100C22semidirect
41. C2×C31×#100C22semidirect
43. C31×#408C22semidirect
49. C31×#343C22semidirect
50. C31×#341C22semidirect
82. C31×AGL(1,ℤ/8)D4semidirect
237. #24398C31direct (N × H)
318. C22×AGL(1,ℤ/8)C2×C31semidirect
319. C2×#472C2×C31semidirect
320. #3006C2×C31semidirect
321. C2×#447C2×C31semidirect
322. #2880C2×C31semidirect
323. #2051C2×C31semidirect
324. #2018C2×C31semidirect
325. #1907C2×C31semidirect
326. #1900C2×C31semidirect
327. #1855C2×C31semidirect
328. #1783C2×C31semidirect
355. C22×C31#472semidirect
373. C2×AGL(1,ℤ/8)C22×C31semidirect
374. C2×AGL(1,ℤ/8)C22×C31semidirect
377. C22×D8C22×C31semidirect
378. C2×#131C22×C31semidirect
389. C2×#108C22×C31semidirect
390. #417C22×C31semidirect
391. #417C22×C31semidirect
392. C2×#102C22×C31semidirect
393. C2×#100C22×C31semidirect
394. C2×#100C22×C31semidirect
395. C2×#100C22×C31semidirect
397. #408C22×C31semidirect
403. #343C22×C31semidirect
404. #341C22×C31semidirect
446. AGL(1,ℤ/8)D4×C31semidirect
498. C31#24398direct (N × H)
708. C22C31×#472semidirect

Maximal subgroups

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

subgroupindex
C22×C31×AGL(1,ℤ/8)2
C2×C31×#4722
C31×#30062
C2×C31×#4472
C31×#28802
C31×#20512
C31×#20182
C31×#19072
C31×#19002
C31×#18552
C31×#17832
#2439831