Finite Group Databasebeta

← C31×#24039 #21480798

Subgroups — C31×#24039 #21480798

Order 7936.

1484 conjugacy classes of subgroups.

The subgroup lattice has 648 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#546C211yesmaximal, characteristic
2C2×C31×#484C211yesmaximal, characteristic, complemented
3C22×C31×#102C211yesmaximal, characteristic, complemented
4C31×#2487C211yesmaximal, characteristic, complemented
5C31×#2042C212yesmaximal, complemented
6C31×#2033C212yesmaximal, complemented
7C31×#1892C211yesmaximal, characteristic, complemented
8C31×#1869C211yesmaximal, characteristic, complemented
9C31×#1862C212yesmaximal, complemented
10C31×#1788C212yesmaximal, complemented
11C31×#1786C211yesmaximal, characteristic, complemented
12C22×#41×C31C2211yescharacteristic
13C23×D4×C31C2211yescharacteristic
14C23×C8×C31C2211yescharacteristic
15C31×#546—24no—
16C31×#546—24no—
17C2×C31×#124C2211yescharacteristic
18C2×C31×#123—21no—
19C2×C31×C22⋊Q8C2211yescharacteristic
20C2×C31×#121—21no—
21C2×C31×#121C2211yescharacteristic
22C2×C31×#120—21no—
23C2×C4×D4×C31C2211yescharacteristic
24C2×C4×D4×C31C2211yescharacteristic
25C22×C4⋊C4×C31C2211yescharacteristic
26C22×C22⋊C4×C31—21no—
27C31×#484—24no—
28C2×C31×#107C2212yescomplemented
29C2×C31×#103C2212yescomplemented
30C2×C31×#103C2212yescomplemented
31C2×C31×#102—24no—
32C2×C31×#102C2212yes—
33C2×C31×#102C2212yes—
34C2×C31×#102C2212yes—
35C2×C31×#102C2212yes—
36C2×C31×C22⋊C8C2211yescharacteristic
37C2×C31×C22⋊C8C2212yescomplemented
38C31×#400—21no—
39C31×#399—21no—
40C31×#389C2212yescomplemented
41C31×#386—21no—
42C31×#385—21no—
43C31×#380C2211yescharacteristic
44C31×#380C2212yescomplemented
45C31×#340C2212yescomplemented
46C31×#336C2212yescomplemented
47C25×C31—21no—
48C2×#41×C31—22no—
49C2×#41×C31—22no—
50C2×#41×C31—24no—
51C2×#41×C31—42no—
52C22×Q8×C31C2311yescharacteristic
53C22×D4×C31—24no—
54C22×D4×C31—21no—
55C22×D4×C31—21no—
56C22×D4×C31—21no—
57C22×D4×C31—22no—
58C22×D4×C31—42no—
59C22×D4×C31D411yescharacteristic
60C22×D4×C31D414yes—
61C22×D4×C31C2311yescharacteristic
62C22×D4×C31C2311yescharacteristic
63C23×C4×C31—21no—
64C23×C4×C31—21no—
65C23×C4×C31—21no—
66C23×C4×C31C2311yescharacteristic
67C23×C4×C31C2311yescharacteristic
68C22×C8×C31—22no—
69C22×C8×C31—42no—
70C22×C8×C31C2312yes—
71C22×C8×C31C2312yes—
72C31×#124—22no—
73C31×#124—22no—
74C31×#123—28no—
75C31×C22⋊Q8—22no—
76C31×C22⋊Q8D414yes—
77C31×#121—28no—
78C31×#121—22no—
79C31×#121—22no—
80C31×#120—28no—
81C4×D4×C31—22no—
82C4×D4×C31—22no—
83C4×D4×C31—22no—
84C4×D4×C31—22no—
85C2×C4⋊C4×C31—21no—
86C2×C4⋊C4×C31—22no—
87C2×C4⋊C4×C31—22no—
88C2×C4⋊C4×C31—21no—
89C2×C4⋊C4×C31—22no—
90C2×C4⋊C4×C31D411yescharacteristic
91C2×C4⋊C4×C31C2312yes—
92C2×C4⋊C4×C31C2312yes—
93C2×C4⋊C4×C31C2311yescharacteristic
94C2×C22⋊C4×C31—28no—
95C2×C22⋊C4×C31—21no—
96C2×C22⋊C4×C31—21no—
97C2×C22⋊C4×C31—21no—
98C2×C22⋊C4×C31—21no—
99C2×C22⋊C4×C31—21no—
100C2×C22⋊C4×C31—21no—
101C2×C22⋊C4×C31—22no—
102C2×C22⋊C4×C31D411yescharacteristic
103C2×C22⋊C4×C31D411yescharacteristic
104C2×C42×C31C2311yescharacteristic
105C31×#107—24no—
106C31×#103—24no—
107C31×#103—42no—
108C31×#102—24no—
109C31×#102—24no—
110C31×#102—24no—
111C31×#102—42no—
112C31×C22⋊C8—22no—
113C31×C22⋊C8—42no—
114C31×#95—21no—
115C31×#95—22no—
116C31×#95—22no—
117C24×C31—21no—
118C24×C31—21no—
119C24×C31—24no—
120C24×C31—44no—
121C24×C31—42no—
122C24×C31—42no—
123C24×C31—82no—
124C24×C31C2×D411yescharacteristic
125C24×C31C2×D411yescharacteristic
126#41×C31—48no—
127#41×C31—44no—
128#41×C31—44no—
129C2×Q8×C31—21no—
130C2×Q8×C31—22no—
131C2×Q8×C31—22no—
132C2×Q8×C31C2×D412yes—
133C2×D4×C31—28no—
134C2×D4×C31—24no—
135C2×D4×C31—22no—
136C2×D4×C31—22no—
137C2×D4×C31—22no—
138C2×D4×C31—24no—
139C2×D4×C31—24no—
140C2×D4×C31—21no—
141C2×D4×C31—21no—
142C2×D4×C31—22no—
143C2×D4×C31—22no—
144C2×D4×C31—22no—
145C2×D4×C31—44no—
146C2×D4×C31—48no—
147C2×D4×C31—44no—
148C2×D4×C31—44no—
149C2×D4×C31—82no—
150C2×D4×C31C2×D412yes—
151C2×D4×C31C2×D412yes—
152C2×D4×C31#4114yes—
153C22×C4×C31—22no—
154C22×C4×C31—22no—
155C22×C4×C31—24no—
156C22×C4×C31—21no—
157C22×C4×C31—21no—
158C22×C4×C31—24no—
159C22×C4×C31—21no—
160C22×C4×C31—21no—
161C22×C4×C31—22no—
162C22×C4×C31—22no—
163C22×C4×C31—22no—
164C22×C4×C31—22no—
165C22×C4×C31—44no—
166C22×C4×C31—42no—
167C22×C4×C31—82no—
168C22×C4×C31—82no—
169C22×C4×C31C2×D411yescharacteristic
170C22×C4×C31C2×D411yescharacteristic
171C22×C4×C31C2×D411yescharacteristic
172C22×C4×C31C2×D411yescharacteristic
173C22×C4×C31C2×D412yes—
174C22×C4×C31C2×D412yes—
175C22×C4×C31C2411yescharacteristic
176C2×C8×C31—22no—
177C2×C8×C31—22no—
178C2×C8×C31—22no—
179C2×C8×C31—22no—
180C2×C8×C31—22no—
181C2×C8×C31—22no—
182C2×C8×C31—44no—
183C4⋊C4×C31—24no—
184C4⋊C4×C31—22no—
185C4⋊C4×C31—21no—
186C4⋊C4×C31—22no—
187C4⋊C4×C31—22no—
188C4⋊C4×C31—22no—
189C4⋊C4×C31—22no—
190C4⋊C4×C31—42no—
191C4⋊C4×C31—82no—
192C4⋊C4×C31C2×D412yes—
193C22⋊C4×C31—24no—
194C22⋊C4×C31—24no—
195C22⋊C4×C31—24no—
196C22⋊C4×C31—24no—
197C22⋊C4×C31—22no—
198C22⋊C4×C31—24no—
199C22⋊C4×C31—22no—
200C22⋊C4×C31—42no—
201C22⋊C4×C31—82no—
202C42×C31—21no—
203C42×C31—21no—
204#24039C3111yesmaximal, characteristic, direct product factor, Sylow
205C23×C31—22no—
206C23×C31—22no—
207C23×C31—22no—
208C23×C31—24no—
209C23×C31—22no—
210C23×C31—21no—
211C23×C31—22no—
212C23×C31—21no—
213C23×C31—21no—
214C23×C31—22no—
215C23×C31—48no—
216C23×C31—41no—
217C23×C31—41no—
218C23×C31—42no—
219C23×C31—42no—
220C23×C31—41no—
221C23×C31—41no—
222C23×C31—42no—
223C23×C31—48no—
224C23×C31—84no—
225C23×C31—88no—
226C23×C31—88no—
227C23×C31#12012yes—
228C23×C31#13512yes—
229C23×C31#13712yes—
230C23×C31C22×D411yescharacteristic
231Q8×C31—24no—
232Q8×C31—41no—
233Q8×C31—41no—
234D4×C31—22no—
235D4×C31—22no—
236D4×C31—22no—
237D4×C31—24no—
238D4×C31—48no—
239D4×C31—48no—
240D4×C31—44no—
241D4×C31—42no—
242D4×C31—84no—
243D4×C31#12314yes—
244C2×C4×C31—22no—
245C2×C4×C31—22no—
246C2×C4×C31—22no—
247C2×C4×C31—24no—
248C2×C4×C31—21no—
249C2×C4×C31—21no—
250C2×C4×C31—22no—
251C2×C4×C31—21no—
252C2×C4×C31—22no—
253C2×C4×C31—22no—
254C2×C4×C31—21no—
255C2×C4×C31—21no—
256C2×C4×C31—22no—
257C2×C4×C31—48no—
258C2×C4×C31—42no—
259C2×C4×C31—42no—
260C2×C4×C31—41no—
261C2×C4×C31—41no—
262C2×C4×C31—42no—
263C2×C4×C31—42no—
264C2×C4×C31—42no—
265C2×C4×C31—42no—
266C2×C4×C31—42no—
267C2×C4×C31—42no—
268C2×C4×C31—42no—
269C2×C4×C31—84no—
270C2×C4×C31—84no—
271C2×C4×C31#12012yes—
272C2×C4×C31C22×D411yescharacteristic
273C2×C4×C31C22×D411yescharacteristic
274C2×C4×C31C2×#4112yes—
275C2×C4×C31H(5,𝔽2)12yes—
276C8×C31—42no—
277C8×C31—42no—
278C2×#546C2×C3111yescharacteristic
279C2×#484C2×C3111yescharacteristic, complemented
280C22×#102C2×C3111yescharacteristic, complemented
281#2487C2×C3111yescharacteristic, complemented
282#2042C2×C3112yescomplemented
283#2033C2×C3112yescomplemented
284#1892C2×C3111yescharacteristic, complemented
285#1869C2×C3111yescharacteristic, complemented
286#1862C2×C3112yescomplemented
287#1788C2×C3112yescomplemented
288#1786C2×C3111yescharacteristic, complemented
289C22×C31—22no—
290C22×C31—22no—
291C22×C31—24no—
292C22×C31—24no—
293C22×C31—24no—
294C22×C31—42no—
295C22×C31—42no—
296C22×C31—44no—
297C22×C31—44no—
298C22×C31—41no—
299C22×C31—42no—
300C22×C31—41no—
301C22×C31—42no—
302C22×C31—41no—
303C22×C31—42no—
304C22×C31—42no—
305C22×C31—42no—
306C22×C31—816no—
307C22×C31—82no—
308C22×C31—82no—
309C22×C31#45214yes—
310C22×C31C2×#12011yescharacteristic
311C22×C31#54612yes—
312C22×C31C2×#13511yescharacteristic
313C22×C31C2×#13711yescharacteristic
314C22×C31#57612yes—
315C4×C31—22no—
316C4×C31—41no—
317C4×C31—42no—
318C4×C31—41no—
319C4×C31—41no—
320C4×C31—42no—
321C4×C31—82no—
322C4×C31—82no—
323C4×C31C2×#12311yescharacteristic
324C4×C31#53411yescharacteristic
325C4×C31#54612yes—
326C22×#41C22×C3111yescharacteristic
327C23×D4C22×C3111yescharacteristic
328C23×C8C22×C3111yescharacteristic
329#546—24no—
330#546—24no—
331C2×#124C22×C3111yescharacteristic
332C2×#123—21no—
333C2×C22⋊Q8C22×C3111yescharacteristic
334C2×#121—21no—
335C2×#121C22×C3111yescharacteristic
336C2×#120—21no—
337C2×C4×D4C22×C3111yescharacteristic
338C2×C4×D4C22×C3111yescharacteristic
339C22×C4⋊C4C22×C3111yescharacteristic
340C22×C22⋊C4—21no—
341#484—24no—
342C2×#107C22×C3112yescomplemented
343C2×#103C22×C3112yescomplemented
344C2×#103C22×C3112yescomplemented
345C2×#102—24no—
346C2×#102C22×C3112yes—
347C2×#102C22×C3112yes—
348C2×#102C22×C3112yes—
349C2×#102C22×C3112yes—
350C2×C22⋊C8C22×C3111yescharacteristic
351C2×C22⋊C8C22×C3112yescomplemented
352#400—21no—
353#399—21no—
354#389C22×C3112yescomplemented
355#386—21no—
356#385—21no—
357#380C22×C3111yescharacteristic
358#380C22×C3112yescomplemented
359#340C22×C3112yescomplemented
360#336C22×C3112yescomplemented
361C2×C31—24no—
362C2×C31—44no—
363C2×C31—81no—
364C2×C31—82no—
365C2×C31#240511yescharacteristic
366C2×C31C2×#45211yescharacteristic
367C2×C31#300811yescharacteristic
368C2×C31#329712yes—
369C2×C31#331412yes—
370C25—21no—
371C2×#41—22no—
372C2×#41—22no—
373C2×#41—24no—
374C2×#41—42no—
375C22×Q8C23×C3111yescharacteristic
376C22×D4—24no—
377C22×D4—21no—
378C22×D4—21no—
379C22×D4—21no—
380C22×D4—22no—
381C22×D4—42no—
382C22×D4D4×C3111yescharacteristic
383C22×D4D4×C3114yes—
384C22×D4C23×C3111yescharacteristic
385C22×D4C23×C3111yescharacteristic
386C23×C4—21no—
387C23×C4—21no—
388C23×C4—21no—
389C23×C4C23×C3111yescharacteristic
390C23×C4C23×C3111yescharacteristic
391C22×C8—22no—
392C22×C8—42no—
393C22×C8C23×C3112yes—
394C22×C8C23×C3112yes—
395#124—22no—
396#124—22no—
397#123—28no—
398C22⋊Q8—22no—
399C22⋊Q8D4×C3114yes—
400#121—28no—
401#121—22no—
402#121—22no—
403#120—28no—
404C4×D4—22no—
405C4×D4—22no—
406C4×D4—22no—
407C4×D4—22no—
408C2×C4⋊C4—21no—
409C2×C4⋊C4—22no—
410C2×C4⋊C4—22no—
411C2×C4⋊C4—21no—
412C2×C4⋊C4—22no—
413C2×C4⋊C4D4×C3111yescharacteristic
414C2×C4⋊C4C23×C3112yes—
415C2×C4⋊C4C23×C3112yes—
416C2×C4⋊C4C23×C3111yescharacteristic
417C2×C22⋊C4—28no—
418C2×C22⋊C4—21no—
419C2×C22⋊C4—21no—
420C2×C22⋊C4—21no—
421C2×C22⋊C4—21no—
422C2×C22⋊C4—21no—
423C2×C22⋊C4—21no—
424C2×C22⋊C4—22no—
425C2×C22⋊C4D4×C3111yescharacteristic
426C2×C22⋊C4D4×C3111yescharacteristic
427C2×C42C23×C3111yescharacteristic
428#107—24no—
429#103—24no—
430#103—42no—
431#102—24no—
432#102—24no—
433#102—24no—
434#102—42no—
435C22⋊C8—22no—
436C22⋊C8—42no—
437#95—21no—
438#95—22no—
439#95—22no—
440C31#2403911yescharacteristic, direct product factor, Sylow
441C24—21no—
442C24—21no—
443C24—24no—
444C24—44no—
445C24—42no—
446C24—42no—
447C24—82no—
448C24C2×D4×C3111yescharacteristic
449C24C2×D4×C3111yescharacteristic
450#41—48no—
451#41—44no—
452#41—44no—
453C2×Q8—21no—
454C2×Q8—22no—
455C2×Q8—22no—
456C2×Q8C2×D4×C3112yes—
457C2×D4—28no—
458C2×D4—24no—
459C2×D4—22no—
460C2×D4—22no—
461C2×D4—22no—
462C2×D4—24no—
463C2×D4—24no—
464C2×D4—21no—
465C2×D4—21no—
466C2×D4—22no—
467C2×D4—22no—
468C2×D4—22no—
469C2×D4—44no—
470C2×D4—48no—
471C2×D4—44no—
472C2×D4—44no—
473C2×D4—82no—
474C2×D4C2×D4×C3112yes—
475C2×D4C2×D4×C3112yes—
476C2×D4#41×C3114yes—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—24no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—24no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—44no—
490C22×C4—42no—
491C22×C4—82no—
492C22×C4—82no—
493C22×C4C2×D4×C3111yescharacteristic
494C22×C4C2×D4×C3111yescharacteristic
495C22×C4C2×D4×C3111yescharacteristic
496C22×C4C2×D4×C3111yescharacteristic
497C22×C4C2×D4×C3112yes—
498C22×C4C2×D4×C3112yes—
499C22×C4C24×C3111yescharacteristic
500C2×C8—22no—
501C2×C8—22no—
502C2×C8—22no—
503C2×C8—22no—
504C2×C8—22no—
505C2×C8—22no—
506C2×C8—44no—
507C4⋊C4—24no—
508C4⋊C4—22no—
509C4⋊C4—21no—
510C4⋊C4—22no—
511C4⋊C4—22no—
512C4⋊C4—22no—
513C4⋊C4—22no—
514C4⋊C4—42no—
515C4⋊C4—82no—
516C4⋊C4C2×D4×C3112yes—
517C22⋊C4—24no—
518C22⋊C4—24no—
519C22⋊C4—24no—
520C22⋊C4—24no—
521C22⋊C4—22no—
522C22⋊C4—24no—
523C22⋊C4—22no—
524C22⋊C4—42no—
525C22⋊C4—82no—
526C42—21no—
527C42—21no—
528C23—22no—
529C23—22no—
530C23—22no—
531C23—24no—
532C23—22no—
533C23—21no—
534C23—22no—
535C23—21no—
536C23—21no—
537C23—22no—
538C23—48no—
539C23—41no—
540C23—41no—
541C23—42no—
542C23—48no—
543C23—42no—
544C23—41no—
545C23—41no—
546C23—42no—
547C23—84no—
548C23—88no—
549C23—88no—
550C23C31×#12012yes—
551C23C31×#13512yes—
552C23C31×#13712yes—
553C23C22×D4×C3111yescharacteristic
554Q8—24no—
555Q8—41no—
556Q8—41no—
557D4—22no—
558D4—22no—
559D4—22no—
560D4—24no—
561D4—48no—
562D4—48no—
563D4—44no—
564D4—42no—
565D4—84no—
566D4C31×#12314yes—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—22no—
570C2×C4—24no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—22no—
574C2×C4—21no—
575C2×C4—22no—
576C2×C4—22no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—22no—
580C2×C4—48no—
581C2×C4—42no—
582C2×C4—42no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—42no—
586C2×C4—42no—
587C2×C4—42no—
588C2×C4—42no—
589C2×C4—42no—
590C2×C4—42no—
591C2×C4—42no—
592C2×C4—84no—
593C2×C4—84no—
594C2×C4C31×#12012yes—
595C2×C4C22×D4×C3111yescharacteristic
596C2×C4C22×D4×C3111yescharacteristic
597C2×C4C2×#41×C3112yes—
598C2×C4C31×H(5,𝔽2)12yes—
599C8—42no—
600C8—42no—
601C22—22no—
602C22—22no—
603C22—24no—
604C22—24no—
605C22—24no—
606C22—42no—
607C22—42no—
608C22—44no—
609C22—44no—
610C22—41no—
611C22—42no—
612C22—41no—
613C22—42no—
614C22—41no—
615C22—42no—
616C22—42no—
617C22—42no—
618C22—816no—
619C22—82no—
620C22—82no—
621C22C31×#45214yes—
622C22C2×C31×#12011yescharacteristic
623C22C31×#54612yes—
624C22C2×C31×#13511yescharacteristic
625C22C2×C31×#13711yescharacteristic
626C22C31×#57612yes—
627C4—22no—
628C4—41no—
629C4—42no—
630C4—41no—
631C4—41no—
632C4—42no—
633C4—82no—
634C4—82no—
635C4C2×C31×#12311yescharacteristic
636C4C31×#53411yescharacteristic
637C4C31×#54612yes—
638C2—24no—
639C2—44no—
640C2—81no—
641C2—82no—
642C2C31×#240511yescharacteristic
643C2C2×C31×#45211yescharacteristic
644C2C31×#300811yescharacteristic
645C2C31×#329712yes—
646C2C31×#331412yes—
subgroupG/H
center, socleC23×C31C22×D4
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC2×C31×#546C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C31 ◁ C2×C4×D4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C31×#484C2semidirect
3. C22×C31×#102C2semidirect
4. C31×#2487C2semidirect
5. C31×#2042C2semidirect
6. C31×#2033C2semidirect
7. C31×#1892C2semidirect
8. C31×#1869C2semidirect
9. C31×#1862C2semidirect
10. C31×#1788C2semidirect
11. C31×#1786C2semidirect
28. C2×C31×#107C22semidirect
29. C2×C31×#103C22semidirect
30. C2×C31×#103C22semidirect
37. C2×C31×C22⋊C8C22semidirect
40. C31×#389C22semidirect
44. C31×#380C22semidirect
45. C31×#340C22semidirect
46. C31×#336C22semidirect
204. #24039C31direct (N × H)
279. C2×#484C2×C31semidirect
280. C22×#102C2×C31semidirect
281. #2487C2×C31semidirect
282. #2042C2×C31semidirect
283. #2033C2×C31semidirect
284. #1892C2×C31semidirect
285. #1869C2×C31semidirect
286. #1862C2×C31semidirect
287. #1788C2×C31semidirect
288. #1786C2×C31semidirect
342. C2×#107C22×C31semidirect
343. C2×#103C22×C31semidirect
344. C2×#103C22×C31semidirect
351. C2×C22⋊C8C22×C31semidirect
354. #389C22×C31semidirect
358. #380C22×C31semidirect
359. #340C22×C31semidirect
360. #336C22×C31semidirect
440. C31#24039direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#5462
C2×C31×#4842
C22×C31×#1022
C31×#24872
C31×#20422
C31×#20332
C31×#18922
C31×#18692
C31×#18622
C31×#17882
C31×#17862
#2403931