Finite Group Databasebeta

← C31×#24146 #21480905

Subgroups — C31×#24146 #21480905

Order 7936.

1142 conjugacy classes of subgroups.

The subgroup lattice has 662 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3508C211yesmaximal, characteristic
2C31×#3078C211yesmaximal, characteristic, complemented
3C4×C31×#137C211yesmaximal, characteristic, complemented
4C31×#2548C211yesmaximal, characteristic, complemented
5C31×#2037C212yesmaximal, complemented
6C31×#2004C212yesmaximal, complemented
7C31×#1986C211yesmaximal, characteristic, complemented
8C31×#1965C211yesmaximal, characteristic, complemented
9C31×#1885C212yesmaximal, complemented
10C31×#1856C212yesmaximal, complemented
11C31×#1806C211yesmaximal, characteristic, complemented
12C2×C31×#137C2211yescharacteristic
13C31×#559—21no—
14C31×#559—21no—
15C31×#550—21no—
16C31×#550—21no—
17C31×#546—22no—
18C31×#546—22no—
19C31×#540—22no—
20C31×#535C2212yes—
21C31×#533C2211yescharacteristic
22C31×#532—21no—
23C31×#532—21no—
24C2×C31×#127C2211yescharacteristic
25C2×C31×#124C2212yes—
26C31×#518C2212yes—
27C4×#41×C31C2211yescharacteristic
28C2×C4×Q8×C31C2211yescharacteristic
29C31×#479—22no—
30C31×#477—21no—
31C31×#475—21no—
32C31×#441—21no—
33C31×#440—21no—
34C4×Q16×C31—21no—
35C4×SD16×C31—21no—
36C31×#428C2212yes—
37C31×#428C2211yescharacteristic
38C31×#423C2211yescharacteristic
39C2×C31×#104C2212yes—
40C31×#419C2212yes—
41C31×#419C2211yescharacteristic
42C31×#417C2211yescharacteristic
43C2×C31×#100C2212yes—
44C2×C31×#100C2212yes—
45C4×M16×C31C2211yescharacteristic
46C31×#394—22no—
47C31×#390—22no—
48C31×#390C2212yes—
49C4×C4⋊C4×C31C2211yescharacteristic
50C31×#339C2212yes—
51C31×#339C2212yes—
52C31×#339C2212yes—
53C2×#41×C31—22no—
54C2×#41×C31—22no—
55C2×#41×C31C2311yescharacteristic
56C22×Q8×C31C2311yescharacteristic
57C22×D4×C31D412yes—
58C22×D4×C31D412yes—
59C22×D4×C31C2312yes—
60C31×#137—22no—
61C31×#137—22no—
62C2×Q16×C31—21no—
63C2×SD16×C31—21no—
64C2×M16×C31C2311yescharacteristic
65C2×M16×C31C2312yes—
66C2×M16×C31C2311yescharacteristic
67C31×C4⋊Q8D411yescharacteristic
68C31×C4⋊Q8D411yescharacteristic
69C31×#127—22no—
70C31×#127—21no—
71C31×#127—21no—
72C31×#127—21no—
73C31×#127—21no—
74C31×#125D412yes—
75C31×#124—22no—
76C31×#124—22no—
77C31×#124—22no—
78C31×#124—24no—
79C31×#124—42no—
80C31×#123—24no—
81C31×#123—24no—
82C31×C22⋊Q8—21no—
83C31×C22⋊Q8—21no—
84C31×#121—22no—
85C31×#121—22no—
86C31×#121—24no—
87C31×#121—24no—
88C31×#121—22no—
89C31×#121—22no—
90C31×#120—24no—
91C4×Q8×C31—21no—
92C4×Q8×C31—21no—
93C4×Q8×C31—21no—
94C4×Q8×C31—21no—
95C4×Q8×C31—21no—
96C4×Q8×C31—21no—
97C4×Q8×C31D411yescharacteristic
98C4×Q8×C31D411yescharacteristic
99C4×D4×C31—22no—
100C4×D4×C31—22no—
101C4×D4×C31—21no—
102C4×D4×C31—21no—
103C4×D4×C31—22no—
104C4×D4×C31—22no—
105C4×D4×C31—22no—
106C4×D4×C31—22no—
107C4×D4×C31D411yescharacteristic
108C4×D4×C31D411yescharacteristic
109C31×#117—21no—
110C31×#117C2311yescharacteristic
111C31×#117C2312yes—
112C2×C4⋊C4×C31—21no—
113C2×C4⋊C4×C31—21no—
114C2×C4⋊C4×C31C2311yescharacteristic
115C2×C22⋊C4×C31—24no—
116C2×C22⋊C4×C31—24no—
117C2×C22⋊C4×C31—24no—
118C2×C42×C31—21no—
119C2×C42×C31—21no—
120C2×C42×C31C2312yes—
121C2×C42×C31C2311yescharacteristic
122C31×#107—21no—
123C31×#107—22no—
124C31×#106—21no—
125C31×#106—22no—
126C31×C4⋊C8—21no—
127C31×C4⋊C8—21no—
128C31×#104—42no—
129C31×#103—21no—
130C31×#103—21no—
131C31×#103—21no—
132C31×#103—22no—
133C31×#103—22no—
134C31×#102—21no—
135C31×#100—24no—
136C31×#100—42no—
137C31×#97—21no—
138C4×C8×C31—21no—
139C31×#95—21no—
140C24×C31C2×D414yes—
141#41×C31—21no—
142#41×C31—21no—
143#41×C31—21no—
144#41×C31—21no—
145#41×C31—84no—
146#41×C31—84no—
147C2×Q8×C31—21no—
148C2×Q8×C31—21no—
149C2×Q8×C31—21no—
150C2×Q8×C31—21no—
151C2×Q8×C31—21no—
152C2×Q8×C31—21no—
153C2×Q8×C31—21no—
154C2×Q8×C31C2×D411yescharacteristic
155C2×Q8×C31#4112yescomplemented
156C2×D4×C31—21no—
157C2×D4×C31—24no—
158C2×D4×C31—24no—
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—22no—
166C2×D4×C31—22no—
167C2×D4×C31—22no—
168C2×D4×C31—22no—
169C2×D4×C31—44no—
170C2×D4×C31—82no—
171C2×D4×C31C2×D411yescharacteristic
172C22×C4×C31—21no—
173C22×C4×C31—24no—
174C22×C4×C31—24no—
175C22×C4×C31—21no—
176C22×C4×C31—21no—
177C22×C4×C31—21no—
178C22×C4×C31—22no—
179C22×C4×C31—21no—
180C22×C4×C31C2×D411yescharacteristic
181C22×C4×C31C2×D411yescharacteristic
182C22×C4×C31C2411yescharacteristic
183Q16×C31—24no—
184SD16×C31—24no—
185M16×C31—21no—
186M16×C31—22no—
187M16×C31—21no—
188M16×C31—22no—
189M16×C31—21no—
190M16×C31#4112yescomplemented
191C2×C8×C31—21no—
192C2×C8×C31—21no—
193C2×C8×C31—22no—
194C4⋊C4×C31—21no—
195C4⋊C4×C31—21no—
196C4⋊C4×C31—21no—
197C4⋊C4×C31—21no—
198C4⋊C4×C31—22no—
199C4⋊C4×C31—22no—
200C4⋊C4×C31—21no—
201C4⋊C4×C31—21no—
202C4⋊C4×C31—42no—
203C4⋊C4×C31—41no—
204C4⋊C4×C31—41no—
205C4⋊C4×C31C2×D411yescharacteristic
206C4⋊C4×C31C2×D412yes—
207C4⋊C4×C31C2×D411yescharacteristic
208C4⋊C4×C31C2×D412yes—
209C22⋊C4×C31—24no—
210C22⋊C4×C31—24no—
211C22⋊C4×C31—24no—
212C22⋊C4×C31—24no—
213C22⋊C4×C31—21no—
214C22⋊C4×C31—22no—
215C22⋊C4×C31—21no—
216C22⋊C4×C31—21no—
217C22⋊C4×C31—48no—
218C22⋊C4×C31—84no—
219C42×C31—21no—
220C42×C31—21no—
221C42×C31—21no—
222C42×C31—22no—
223C42×C31—22no—
224C42×C31—22no—
225C42×C31—41no—
226C42×C31—41no—
227C42×C31C2×D411yescharacteristic
228C42×C31C2×D411yescharacteristic
229C42×C31C2×D411yescharacteristic
230C42×C31C2×D411yescharacteristic
231#24146C3111yesmaximal, characteristic, direct product factor, Sylow
232C23×C31—24no—
233C23×C31—21no—
234C23×C31—24no—
235C23×C31—24no—
236C23×C31—44no—
237C23×C31—44no—
238C23×C31C22×D411yescharacteristic
239Q8×C31—22no—
240Q8×C31—21no—
241Q8×C31—21no—
242Q8×C31—22no—
243Q8×C31—42no—
244Q8×C31—41no—
245Q8×C31—41no—
246Q8×C31—42no—
247D4×C31—21no—
248D4×C31—21no—
249D4×C31—44no—
250D4×C31—41no—
251D4×C31—41no—
252D4×C31—42no—
253D4×C31—42no—
254D4×C31—42no—
255D4×C31—42no—
256D4×C31—44no—
257D4×C31—82no—
258D4×C31—82no—
259D4×C31—84no—
260D4×C31—84no—
261C2×C4×C31—22no—
262C2×C4×C31—21no—
263C2×C4×C31—21no—
264C2×C4×C31—21no—
265C2×C4×C31—22no—
266C2×C4×C31—22no—
267C2×C4×C31—22no—
268C2×C4×C31—41no—
269C2×C4×C31—42no—
270C2×C4×C31—41no—
271C2×C4×C31—41no—
272C2×C4×C31—41no—
273C2×C4×C31—41no—
274C2×C4×C31—42no—
275C2×C4×C31—42no—
276C2×C4×C31—42no—
277C2×C4×C31—42no—
278C2×C4×C31—41no—
279C2×C4×C31—42no—
280C2×C4×C31—84no—
281C2×C4×C31—84no—
282C2×C4×C31#12011yescharacteristic
283C2×C4×C31#12011yescharacteristic
284C2×C4×C31#12011yescharacteristic
285C2×C4×C31#12011yescharacteristic
286C2×C4×C31C22×D411yescharacteristic
287C2×C4×C31C22×D411yescharacteristic
288C2×C4×C31C2×#4111yescharacteristic
289C2×C4×C31C2×#4111yescharacteristic
290C2×C4×C31H(5,𝔽2)11yescharacteristic
291C2×C4×C312−1+411yescharacteristic
292C8×C31—22no—
293C8×C31—41no—
294C8×C31—42no—
295#3508C2×C3111yescharacteristic
296#3078C2×C3111yescharacteristic, complemented
297C4×#137C2×C3111yescharacteristic, complemented
298#2548C2×C3111yescharacteristic, complemented
299#2037C2×C3112yescomplemented
300#2004C2×C3112yescomplemented
301#1986C2×C3111yescharacteristic, complemented
302#1965C2×C3111yescharacteristic, complemented
303#1885C2×C3112yescomplemented
304#1856C2×C3112yescomplemented
305#1806C2×C3111yescharacteristic, complemented
306C22×C31—21no—
307C22×C31—21no—
308C22×C31—41no—
309C22×C31—44no—
310C22×C31—41no—
311C22×C31—44no—
312C22×C31—41no—
313C22×C31—44no—
314C22×C31—84no—
315C22×C31—84no—
316C22×C31C2×#12011yescharacteristic
317C22×C31#54611yescharacteristic
318C22×C31#54711yescharacteristic
319C4×C31—21no—
320C4×C31—21no—
321C4×C31—21no—
322C4×C31—41no—
323C4×C31—42no—
324C4×C31—41no—
325C4×C31—42no—
326C4×C31—41no—
327C4×C31—42no—
328C4×C31—82no—
329C4×C31—81no—
330C4×C31#45512yes—
331C4×C31#52511yescharacteristic
332C4×C31#53711yescharacteristic
333C4×C31#54811yescharacteristic
334C4×C31#55011yescharacteristic
335C2×#137C22×C3111yescharacteristic
336#559—21no—
337#559—21no—
338#550—21no—
339#550—21no—
340#546—22no—
341#546—22no—
342#540—22no—
343#535C22×C3112yes—
344#533C22×C3111yescharacteristic
345#532—21no—
346#532—21no—
347C2×#127C22×C3111yescharacteristic
348C2×#124C22×C3112yes—
349#518C22×C3112yes—
350C4×#41C22×C3111yescharacteristic
351C2×C4×Q8C22×C3111yescharacteristic
352#479—22no—
353#477—21no—
354#475—21no—
355#441—21no—
356#440—21no—
357C4×Q16—21no—
358C4×SD16—21no—
359#428C22×C3112yes—
360#428C22×C3111yescharacteristic
361#423C22×C3111yescharacteristic
362C2×#104C22×C3112yes—
363#419C22×C3112yes—
364#419C22×C3111yescharacteristic
365#417C22×C3111yescharacteristic
366C2×#100C22×C3112yes—
367C2×#100C22×C3112yes—
368C4×M16C22×C3111yescharacteristic
369#394—22no—
370#390—22no—
371#390C22×C3112yes—
372C4×C4⋊C4C22×C3111yescharacteristic
373#339C22×C3112yes—
374#339C22×C3112yes—
375#339C22×C3112yes—
376C2×C31—21no—
377C2×C31—21no—
378C2×C31—81no—
379C2×C31—84no—
380C2×C31#240711yescharacteristic
381C2×C31C2×#45511yescharacteristic
382C2×C31#301911yescharacteristic
383C2×#41—22no—
384C2×#41—22no—
385C2×#41C23×C3111yescharacteristic
386C22×Q8C23×C3111yescharacteristic
387C22×D4D4×C3112yes—
388C22×D4D4×C3112yes—
389C22×D4C23×C3112yes—
390#137—22no—
391#137—22no—
392C2×Q16—21no—
393C2×SD16—21no—
394C2×M16C23×C3111yescharacteristic
395C2×M16C23×C3112yes—
396C2×M16C23×C3111yescharacteristic
397C4⋊Q8D4×C3111yescharacteristic
398C4⋊Q8D4×C3111yescharacteristic
399#127—22no—
400#127—21no—
401#127—21no—
402#127—21no—
403#127—21no—
404#125D4×C3112yes—
405#124—22no—
406#124—22no—
407#124—22no—
408#124—24no—
409#124—42no—
410#123—24no—
411#123—24no—
412C22⋊Q8—21no—
413C22⋊Q8—21no—
414#121—22no—
415#121—22no—
416#121—24no—
417#121—24no—
418#121—22no—
419#121—22no—
420#120—24no—
421C4×Q8—21no—
422C4×Q8—21no—
423C4×Q8—21no—
424C4×Q8—21no—
425C4×Q8—21no—
426C4×Q8—21no—
427C4×Q8D4×C3111yescharacteristic
428C4×Q8D4×C3111yescharacteristic
429C4×D4—22no—
430C4×D4—22no—
431C4×D4—21no—
432C4×D4—21no—
433C4×D4—22no—
434C4×D4—22no—
435C4×D4—22no—
436C4×D4—22no—
437C4×D4D4×C3111yescharacteristic
438C4×D4D4×C3111yescharacteristic
439#117—21no—
440#117C23×C3111yescharacteristic
441#117C23×C3112yes—
442C2×C4⋊C4—21no—
443C2×C4⋊C4—21no—
444C2×C4⋊C4C23×C3111yescharacteristic
445C2×C22⋊C4—24no—
446C2×C22⋊C4—24no—
447C2×C22⋊C4—24no—
448C2×C42—21no—
449C2×C42—21no—
450C2×C42C23×C3112yes—
451C2×C42C23×C3111yescharacteristic
452#107—21no—
453#107—22no—
454#106—21no—
455#106—22no—
456C4⋊C8—21no—
457C4⋊C8—21no—
458#104—42no—
459#103—21no—
460#103—21no—
461#103—21no—
462#103—22no—
463#103—22no—
464#102—21no—
465#100—24no—
466#100—42no—
467#97—21no—
468C4×C8—21no—
469#95—21no—
470C31#2414611yescharacteristic, direct product factor, Sylow
471C24C2×D4×C3114yes—
472#41—21no—
473#41—21no—
474#41—21no—
475#41—21no—
476#41—84no—
477#41—84no—
478C2×Q8—21no—
479C2×Q8—21no—
480C2×Q8—21no—
481C2×Q8—21no—
482C2×Q8—21no—
483C2×Q8—21no—
484C2×Q8—21no—
485C2×Q8C2×D4×C3111yescharacteristic
486C2×Q8#41×C3112yescomplemented
487C2×D4—21no—
488C2×D4—24no—
489C2×D4—24no—
490C2×D4—22no—
491C2×D4—22no—
492C2×D4—22no—
493C2×D4—22no—
494C2×D4—22no—
495C2×D4—22no—
496C2×D4—22no—
497C2×D4—22no—
498C2×D4—22no—
499C2×D4—22no—
500C2×D4—44no—
501C2×D4—82no—
502C2×D4C2×D4×C3111yescharacteristic
503C22×C4—21no—
504C22×C4—24no—
505C22×C4—24no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—22no—
510C22×C4—21no—
511C22×C4C2×D4×C3111yescharacteristic
512C22×C4C2×D4×C3111yescharacteristic
513C22×C4C24×C3111yescharacteristic
514Q16—24no—
515SD16—24no—
516M16—21no—
517M16—22no—
518M16—21no—
519M16—22no—
520M16—21no—
521M16#41×C3112yescomplemented
522C2×C8—21no—
523C2×C8—21no—
524C2×C8—22no—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—21no—
529C4⋊C4—22no—
530C4⋊C4—22no—
531C4⋊C4—21no—
532C4⋊C4—21no—
533C4⋊C4—42no—
534C4⋊C4—41no—
535C4⋊C4—41no—
536C4⋊C4C2×D4×C3111yescharacteristic
537C4⋊C4C2×D4×C3112yes—
538C4⋊C4C2×D4×C3111yescharacteristic
539C4⋊C4C2×D4×C3112yes—
540C22⋊C4—24no—
541C22⋊C4—24no—
542C22⋊C4—24no—
543C22⋊C4—24no—
544C22⋊C4—21no—
545C22⋊C4—22no—
546C22⋊C4—21no—
547C22⋊C4—21no—
548C22⋊C4—48no—
549C22⋊C4—84no—
550C42—21no—
551C42—21no—
552C42—21no—
553C42—22no—
554C42—22no—
555C42—22no—
556C42—41no—
557C42—41no—
558C42C2×D4×C3111yescharacteristic
559C42C2×D4×C3111yescharacteristic
560C42C2×D4×C3111yescharacteristic
561C42C2×D4×C3111yescharacteristic
562C23—24no—
563C23—21no—
564C23—24no—
565C23—24no—
566C23—44no—
567C23—44no—
568C23C22×D4×C3111yescharacteristic
569Q8—22no—
570Q8—21no—
571Q8—21no—
572Q8—22no—
573Q8—42no—
574Q8—42no—
575Q8—41no—
576Q8—41no—
577D4—21no—
578D4—21no—
579D4—44no—
580D4—41no—
581D4—41no—
582D4—44no—
583D4—42no—
584D4—42no—
585D4—42no—
586D4—42no—
587D4—82no—
588D4—82no—
589D4—84no—
590D4—84no—
591C2×C4—22no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—22no—
596C2×C4—22no—
597C2×C4—22no—
598C2×C4—41no—
599C2×C4—42no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—42no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—42no—
606C2×C4—42no—
607C2×C4—42no—
608C2×C4—41no—
609C2×C4—42no—
610C2×C4—84no—
611C2×C4—84no—
612C2×C4C31×#12011yescharacteristic
613C2×C4C31×#12011yescharacteristic
614C2×C4C31×#12011yescharacteristic
615C2×C4C31×#12011yescharacteristic
616C2×C4C22×D4×C3111yescharacteristic
617C2×C4C22×D4×C3111yescharacteristic
618C2×C4C2×#41×C3111yescharacteristic
619C2×C4C2×#41×C3111yescharacteristic
620C2×C4C31×H(5,𝔽2)11yescharacteristic
621C2×C4C31×2−1+411yescharacteristic
622C8—22no—
623C8—41no—
624C8—42no—
625C22—21no—
626C22—21no—
627C22—41no—
628C22—44no—
629C22—41no—
630C22—44no—
631C22—41no—
632C22—44no—
633C22—84no—
634C22—84no—
635C22C2×C31×#12011yescharacteristic
636C22C31×#54611yescharacteristic
637C22C31×#54711yescharacteristic
638C4—21no—
639C4—21no—
640C4—21no—
641C4—41no—
642C4—42no—
643C4—41no—
644C4—42no—
645C4—41no—
646C4—42no—
647C4—82no—
648C4—81no—
649C4C31×#45512yes—
650C4C31×#52511yescharacteristic
651C4C31×#53711yescharacteristic
652C4C31×#54811yescharacteristic
653C4C31×#55011yescharacteristic
654C2—21no—
655C2—21no—
656C2—84no—
657C2—81no—
658C2C31×#240711yescharacteristic
659C2C2×C31×#45511yescharacteristic
660C2C31×#301911yescharacteristic
subgroupG/H
center, socleC22×C31C2×#120
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC31×#3508C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C31 ◁ C2×C42×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C31×#3078C2semidirect
3. C4×C31×#137C2semidirect
4. C31×#2548C2semidirect
5. C31×#2037C2semidirect
6. C31×#2004C2semidirect
7. C31×#1986C2semidirect
8. C31×#1965C2semidirect
9. C31×#1885C2semidirect
10. C31×#1856C2semidirect
11. C31×#1806C2semidirect
155. C2×Q8×C31#41semidirect
190. M16×C31#41semidirect
231. #24146C31direct (N × H)
296. #3078C2×C31semidirect
297. C4×#137C2×C31semidirect
298. #2548C2×C31semidirect
299. #2037C2×C31semidirect
300. #2004C2×C31semidirect
301. #1986C2×C31semidirect
302. #1965C2×C31semidirect
303. #1885C2×C31semidirect
304. #1856C2×C31semidirect
305. #1806C2×C31semidirect
470. C31#24146direct (N × H)
486. C2×Q8#41×C31semidirect
521. M16#41×C31semidirect

Maximal subgroups

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

subgroupindex
C31×#35082
C31×#30782
C4×C31×#1372
C31×#25482
C31×#20372
C31×#20042
C31×#19862
C31×#19652
C31×#18852
C31×#18562
C31×#18062
#2414631