Finite Group Databasebeta

← C31×#24083 #21480842

Subgroups — C31×#24083 #21480842

Order 7936.

1074 conjugacy classes of subgroups.

The subgroup lattice has 694 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3494C211yesmaximal, characteristic
2C31×#3092C211yesmaximal, characteristic, complemented
3C2×C31×#428C211yesmaximal, characteristic, complemented
4C31×#2504C211yesmaximal, characteristic, complemented
5C31×#2061C212yesmaximal, complemented
6C31×#2037C212yesmaximal, complemented
7C31×#1900C211yesmaximal, characteristic, complemented
8C31×#1871C211yesmaximal, characteristic, complemented
9C31×#1860C212yesmaximal, complemented
10C31×#1856C212yesmaximal, complemented
11C31×#1826C211yesmaximal, characteristic, complemented
12C22×M16×C31C2211yescharacteristic
13C31×#555—21no—
14C31×#553—21no—
15C31×#553—21no—
16C31×#551—22no—
17C31×#547—21no—
18C31×#546—22no—
19C31×#544C2211yescharacteristic
20C31×#542—21no—
21C31×#540—21no—
22C31×#535C2211yescharacteristic
23C31×#532—21no—
24C31×#529—21no—
25C31×#525C2211yescharacteristic
26C2×C31×#121C2211yescharacteristic
27C31×#520C2211yescharacteristic
28C31×#518C2211yescharacteristic
29C2×C31×#117C2211yescharacteristic
30C22×C4⋊C4×C31C2211yescharacteristic
31C31×#484—21no—
32C31×#483—21no—
33C31×#481—21no—
34C31×#480—21no—
35C31×#428—21no—
36C31×#428—21no—
37C31×#428C2212yes—
38C31×#428C2212yes—
39C31×#428C2212yes—
40C2×C31×#107—21no—
41C2×C31×#106—21no—
42C2×C31×#104C2212yes—
43C31×#417C2212yes—
44C2×C31×#100C2212yes—
45C31×#407C2211yescharacteristic
46C31×#397—22no—
47C31×#390C2212yes—
48C31×#386—22no—
49C31×#382C2212yes—
50C4×C22⋊C4×C31C2211yescharacteristic
51C31×#343C2212yes—
52C31×#339C2212yes—
53C31×#339C2212yes—
54C31×#339C2212yes—
55C2×#41×C31—22no—
56C2×#41×C31C2311yescharacteristic
57C22×D4×C31D412yes—
58C22×D4×C31C2311yescharacteristic
59C23×C4×C31—21no—
60C23×C4×C31C2311yescharacteristic
61C2×M16×C31—21no—
62C2×M16×C31—24no—
63C2×M16×C31C2312yes—
64C2×M16×C31C2312yes—
65C22×C8×C31—21no—
66C31×C4⋊Q8—21no—
67C31×C4⋊Q8—21no—
68C31×#127—21no—
69C31×#126—22no—
70C31×#126—22no—
71C31×#125—21no—
72C31×#125—21no—
73C31×#124—22no—
74C31×#124—22no—
75C31×#124—21no—
76C31×#123—22no—
77C31×#123—22no—
78C31×#123—22no—
79C31×#123—22no—
80C31×#123—21no—
81C31×C22⋊Q8—22no—
82C31×C22⋊Q8—22no—
83C31×C22⋊Q8D411yescharacteristic
84C31×C22⋊Q8D411yescharacteristic
85C31×#121—22no—
86C31×#121—22no—
87C31×#121—22no—
88C31×#121—21no—
89C31×#121—21no—
90C31×#121—21no—
91C31×#121—21no—
92C31×#121—21no—
93C31×#121—21no—
94C31×#121D411yescharacteristic
95C31×#121D411yescharacteristic
96C31×#120—21no—
97C31×#120—22no—
98C4×Q8×C31—21no—
99C4×D4×C31—22no—
100C4×D4×C31—22no—
101C4×D4×C31—21no—
102C4×D4×C31—22no—
103C4×D4×C31—21no—
104C4×D4×C31—21no—
105C4×D4×C31—21no—
106C4×D4×C31—21no—
107C4×D4×C31—21no—
108C4×D4×C31—21no—
109C31×#117—22no—
110C31×#117—21no—
111C31×#117—21no—
112C31×#117—21no—
113C31×#117D411yescharacteristic
114C31×#117D411yescharacteristic
115C31×#117C2311yescharacteristic
116C31×#117C2311yescharacteristic
117C31×#117C2311yescharacteristic
118C2×C4⋊C4×C31—21no—
119C2×C4⋊C4×C31—21no—
120C2×C4⋊C4×C31—21no—
121C2×C4⋊C4×C31—21no—
122C2×C4⋊C4×C31—21no—
123C2×C4⋊C4×C31—21no—
124C2×C4⋊C4×C31D411yescharacteristic
125C2×C4⋊C4×C31D411yescharacteristic
126C2×C4⋊C4×C31C2312yes—
127C2×C4⋊C4×C31C2311yescharacteristic
128C2×C22⋊C4×C31—21no—
129C2×C22⋊C4×C31—22no—
130C2×C22⋊C4×C31—21no—
131C2×C22⋊C4×C31—24no—
132C2×C22⋊C4×C31D412yes—
133C2×C42×C31—21no—
134C2×C42×C31C2312yes—
135C31×#107—22no—
136C31×#107—22no—
137C31×#107—22no—
138C31×#106—22no—
139C31×#106—22no—
140C31×#106—22no—
141C31×#104—24no—
142C31×#103—22no—
143C31×#102—22no—
144C31×#100—24no—
145C31×C22⋊C8—21no—
146C31×C22⋊C8—21no—
147C31×#95—21no—
148C31×#95—24no—
149C24×C31C2×D411yescharacteristic
150C24×C31C2×D412yes—
151#41×C31—22no—
152#41×C31—22no—
153#41×C31—84no—
154C2×Q8×C31—22no—
155C2×Q8×C31C2×D411yescharacteristic
156C2×D4×C31—21no—
157C2×D4×C31—22no—
158C2×D4×C31—21no—
159C2×D4×C31—22no—
160C2×D4×C31—22no—
161C2×D4×C31—21no—
162C2×D4×C31—22no—
163C2×D4×C31—21no—
164C2×D4×C31—21no—
165C2×D4×C31—22no—
166C2×D4×C31—22no—
167C2×D4×C31—44no—
168C2×D4×C31C2×D411yescharacteristic
169C22×C4×C31—22no—
170C22×C4×C31—22no—
171C22×C4×C31—21no—
172C22×C4×C31—22no—
173C22×C4×C31—22no—
174C22×C4×C31—22no—
175C22×C4×C31—21no—
176C22×C4×C31—21no—
177C22×C4×C31—22no—
178C22×C4×C31—22no—
179C22×C4×C31—41no—
180C22×C4×C31—41no—
181C22×C4×C31—82no—
182C22×C4×C31C2×D411yescharacteristic
183C22×C4×C31C2×D411yescharacteristic
184C22×C4×C31C2×D411yescharacteristic
185C22×C4×C31C2×D411yescharacteristic
186C22×C4×C31C2×D411yescharacteristic
187C22×C4×C31C2×D412yes—
188C22×C4×C31C2411yescharacteristic
189M16×C31—24no—
190M16×C31—22no—
191M16×C31—22no—
192M16×C31—22no—
193M16×C31#4114yescomplemented
194C2×C8×C31—24no—
195C2×C8×C31—22no—
196C2×C8×C31—22no—
197C4⋊C4×C31—22no—
198C4⋊C4×C31—22no—
199C4⋊C4×C31—22no—
200C4⋊C4×C31—22no—
201C4⋊C4×C31—21no—
202C4⋊C4×C31—21no—
203C4⋊C4×C31—21no—
204C4⋊C4×C31—21no—
205C4⋊C4×C31—21no—
206C4⋊C4×C31—21no—
207C4⋊C4×C31—22no—
208C4⋊C4×C31—22no—
209C4⋊C4×C31—41no—
210C4⋊C4×C31—41no—
211C4⋊C4×C31C2×D411yescharacteristic
212C4⋊C4×C31C2×D411yescharacteristic
213C4⋊C4×C31C2×D411yescharacteristic
214C4⋊C4×C31C2×D411yescharacteristic
215C4⋊C4×C31C2×D411yescharacteristic
216C4⋊C4×C31C2×D411yescharacteristic
217C22⋊C4×C31—22no—
218C22⋊C4×C31—22no—
219C22⋊C4×C31—22no—
220C22⋊C4×C31—22no—
221C22⋊C4×C31—22no—
222C22⋊C4×C31—21no—
223C22⋊C4×C31—21no—
224C22⋊C4×C31—21no—
225C22⋊C4×C31—21no—
226C22⋊C4×C31—21no—
227C22⋊C4×C31—21no—
228C22⋊C4×C31—21no—
229C22⋊C4×C31—22no—
230C22⋊C4×C31—22no—
231C22⋊C4×C31—21no—
232C22⋊C4×C31—21no—
233C22⋊C4×C31—42no—
234C22⋊C4×C31—84no—
235C42×C31—22no—
236C42×C31—21no—
237C42×C31—21no—
238C42×C31—21no—
239C42×C31—21no—
240C42×C31—21no—
241C42×C31—22no—
242C42×C31—22no—
243#24083C3111yesmaximal, characteristic, direct product factor, Sylow
244C23×C31—22no—
245C23×C31—22no—
246C23×C31—22no—
247C23×C31—21no—
248C23×C31—24no—
249C23×C31—41no—
250C23×C31—42no—
251C23×C31—42no—
252C23×C31#12011yescharacteristic
253C23×C31#12011yescharacteristic
254C23×C31C22×D411yescharacteristic
255Q8×C31—22no—
256Q8×C31—82no—
257D4×C31—22no—
258D4×C31—42no—
259D4×C31—44no—
260D4×C31—42no—
261D4×C31—41no—
262D4×C31—41no—
263D4×C31—42no—
264D4×C31—81no—
265D4×C31—82no—
266D4×C31—82no—
267D4×C31—82no—
268C2×C4×C31—22no—
269C2×C4×C31—21no—
270C2×C4×C31—21no—
271C2×C4×C31—21no—
272C2×C4×C31—21no—
273C2×C4×C31—22no—
274C2×C4×C31—22no—
275C2×C4×C31—21no—
276C2×C4×C31—21no—
277C2×C4×C31—21no—
278C2×C4×C31—21no—
279C2×C4×C31—21no—
280C2×C4×C31—21no—
281C2×C4×C31—21no—
282C2×C4×C31—22no—
283C2×C4×C31—42no—
284C2×C4×C31—41no—
285C2×C4×C31—41no—
286C2×C4×C31—42no—
287C2×C4×C31—42no—
288C2×C4×C31—42no—
289C2×C4×C31—44no—
290C2×C4×C31—42no—
291C2×C4×C31—42no—
292C2×C4×C31—81no—
293C2×C4×C31—82no—
294C2×C4×C31—82no—
295C2×C4×C31—82no—
296C2×C4×C31—82no—
297C2×C4×C31—82no—
298C2×C4×C31#12011yescharacteristic
299C2×C4×C31#12011yescharacteristic
300C2×C4×C31C22×D411yescharacteristic
301C2×C4×C31C22×D411yescharacteristic
302C2×C4×C31C2×#4112yes—
303C2×C4×C312−1+412yes—
304C8×C31—24no—
305C8×C31—42no—
306#3494C2×C3111yescharacteristic
307#3092C2×C3111yescharacteristic, complemented
308C2×#428C2×C3111yescharacteristic, complemented
309#2504C2×C3111yescharacteristic, complemented
310#2061C2×C3112yescomplemented
311#2037C2×C3112yescomplemented
312#1900C2×C3111yescharacteristic, complemented
313#1871C2×C3111yescharacteristic, complemented
314#1860C2×C3112yescomplemented
315#1856C2×C3112yescomplemented
316#1826C2×C3111yescharacteristic, complemented
317C22×C31—21no—
318C22×C31—21no—
319C22×C31—21no—
320C22×C31—21no—
321C22×C31—21no—
322C22×C31—21no—
323C22×C31—21no—
324C22×C31—44no—
325C22×C31—41no—
326C22×C31—42no—
327C22×C31—41no—
328C22×C31—42no—
329C22×C31—42no—
330C22×C31—41no—
331C22×C31—84no—
332C22×C31#45512yes—
333C22×C31C2×#12011yescharacteristic
334C22×C31#54712yes—
335C4×C31—21no—
336C4×C31—21no—
337C4×C31—41no—
338C4×C31—41no—
339C4×C31—41no—
340C4×C31—42no—
341C4×C31—41no—
342C4×C31—41no—
343C4×C31—41no—
344C4×C31—41no—
345C4×C31—82no—
346C4×C31—82no—
347C4×C31#52511yescharacteristic
348C4×C31#53611yescharacteristic
349C4×C31#54712yes—
350C22×M16C22×C3111yescharacteristic
351#555—21no—
352#553—21no—
353#553—21no—
354#551—22no—
355#547—21no—
356#546—22no—
357#544C22×C3111yescharacteristic
358#542—21no—
359#540—21no—
360#535C22×C3111yescharacteristic
361#532—21no—
362#529—21no—
363#525C22×C3111yescharacteristic
364C2×#121C22×C3111yescharacteristic
365#520C22×C3111yescharacteristic
366#518C22×C3111yescharacteristic
367C2×#117C22×C3111yescharacteristic
368C22×C4⋊C4C22×C3111yescharacteristic
369#484—21no—
370#483—21no—
371#481—21no—
372#480—21no—
373#428—21no—
374#428—21no—
375#428C22×C3112yes—
376#428C22×C3112yes—
377#428C22×C3112yes—
378C2×#107—21no—
379C2×#106—21no—
380C2×#104C22×C3112yes—
381#417C22×C3112yes—
382C2×#100C22×C3112yes—
383#407C22×C3111yescharacteristic
384#397—22no—
385#390C22×C3112yes—
386#386—22no—
387#382C22×C3112yes—
388C4×C22⋊C4C22×C3111yescharacteristic
389#343C22×C3112yes—
390#339C22×C3112yes—
391#339C22×C3112yes—
392#339C22×C3112yes—
393C2×C31—22no—
394C2×C31—22no—
395C2×C31—41no—
396C2×C31—81no—
397C2×C31—82no—
398C2×C31#240611yescharacteristic
399C2×C31C2×#45511yescharacteristic
400C2×C31#302111yescharacteristic
401C2×#41—22no—
402C2×#41C23×C3111yescharacteristic
403C22×D4D4×C3112yes—
404C22×D4C23×C3111yescharacteristic
405C23×C4—21no—
406C23×C4C23×C3111yescharacteristic
407C2×M16—21no—
408C2×M16—24no—
409C2×M16C23×C3112yes—
410C2×M16C23×C3112yes—
411C22×C8—21no—
412C4⋊Q8—21no—
413C4⋊Q8—21no—
414#127—21no—
415#126—22no—
416#126—22no—
417#125—21no—
418#125—21no—
419#124—22no—
420#124—22no—
421#124—21no—
422#123—22no—
423#123—22no—
424#123—22no—
425#123—22no—
426#123—21no—
427C22⋊Q8—22no—
428C22⋊Q8—22no—
429C22⋊Q8D4×C3111yescharacteristic
430C22⋊Q8D4×C3111yescharacteristic
431#121—22no—
432#121—22no—
433#121—22no—
434#121—21no—
435#121—21no—
436#121—21no—
437#121—21no—
438#121—21no—
439#121—21no—
440#121D4×C3111yescharacteristic
441#121D4×C3111yescharacteristic
442#120—21no—
443#120—22no—
444C4×Q8—21no—
445C4×D4—22no—
446C4×D4—22no—
447C4×D4—21no—
448C4×D4—22no—
449C4×D4—21no—
450C4×D4—21no—
451C4×D4—21no—
452C4×D4—21no—
453C4×D4—21no—
454C4×D4—21no—
455#117—22no—
456#117—21no—
457#117—21no—
458#117—21no—
459#117D4×C3111yescharacteristic
460#117D4×C3111yescharacteristic
461#117C23×C3111yescharacteristic
462#117C23×C3111yescharacteristic
463#117C23×C3111yescharacteristic
464C2×C4⋊C4—21no—
465C2×C4⋊C4—21no—
466C2×C4⋊C4—21no—
467C2×C4⋊C4—21no—
468C2×C4⋊C4—21no—
469C2×C4⋊C4—21no—
470C2×C4⋊C4D4×C3111yescharacteristic
471C2×C4⋊C4D4×C3111yescharacteristic
472C2×C4⋊C4C23×C3112yes—
473C2×C4⋊C4C23×C3111yescharacteristic
474C2×C22⋊C4—21no—
475C2×C22⋊C4—22no—
476C2×C22⋊C4—21no—
477C2×C22⋊C4—24no—
478C2×C22⋊C4D4×C3112yes—
479C2×C42—21no—
480C2×C42C23×C3112yes—
481#107—22no—
482#107—22no—
483#107—22no—
484#106—22no—
485#106—22no—
486#106—22no—
487#104—24no—
488#103—22no—
489#102—22no—
490#100—24no—
491C22⋊C8—21no—
492C22⋊C8—21no—
493#95—21no—
494#95—24no—
495C31#2408311yescharacteristic, direct product factor, Sylow
496C24C2×D4×C3111yescharacteristic
497C24C2×D4×C3112yes—
498#41—22no—
499#41—22no—
500#41—84no—
501C2×Q8—22no—
502C2×Q8C2×D4×C3111yescharacteristic
503C2×D4—21no—
504C2×D4—22no—
505C2×D4—21no—
506C2×D4—22no—
507C2×D4—22no—
508C2×D4—21no—
509C2×D4—22no—
510C2×D4—21no—
511C2×D4—21no—
512C2×D4—22no—
513C2×D4—22no—
514C2×D4—44no—
515C2×D4C2×D4×C3111yescharacteristic
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—21no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—41no—
527C22×C4—41no—
528C22×C4—82no—
529C22×C4C2×D4×C3111yescharacteristic
530C22×C4C2×D4×C3111yescharacteristic
531C22×C4C2×D4×C3111yescharacteristic
532C22×C4C2×D4×C3111yescharacteristic
533C22×C4C2×D4×C3111yescharacteristic
534C22×C4C2×D4×C3112yes—
535C22×C4C24×C3111yescharacteristic
536M16—24no—
537M16—22no—
538M16—22no—
539M16—22no—
540M16#41×C3114yescomplemented
541C2×C8—24no—
542C2×C8—22no—
543C2×C8—22no—
544C4⋊C4—22no—
545C4⋊C4—22no—
546C4⋊C4—22no—
547C4⋊C4—22no—
548C4⋊C4—21no—
549C4⋊C4—21no—
550C4⋊C4—21no—
551C4⋊C4—21no—
552C4⋊C4—21no—
553C4⋊C4—21no—
554C4⋊C4—22no—
555C4⋊C4—22no—
556C4⋊C4—41no—
557C4⋊C4—41no—
558C4⋊C4C2×D4×C3111yescharacteristic
559C4⋊C4C2×D4×C3111yescharacteristic
560C4⋊C4C2×D4×C3111yescharacteristic
561C4⋊C4C2×D4×C3111yescharacteristic
562C4⋊C4C2×D4×C3111yescharacteristic
563C4⋊C4C2×D4×C3111yescharacteristic
564C22⋊C4—22no—
565C22⋊C4—22no—
566C22⋊C4—22no—
567C22⋊C4—22no—
568C22⋊C4—22no—
569C22⋊C4—21no—
570C22⋊C4—21no—
571C22⋊C4—21no—
572C22⋊C4—21no—
573C22⋊C4—21no—
574C22⋊C4—21no—
575C22⋊C4—21no—
576C22⋊C4—22no—
577C22⋊C4—22no—
578C22⋊C4—21no—
579C22⋊C4—21no—
580C22⋊C4—42no—
581C22⋊C4—84no—
582C42—22no—
583C42—21no—
584C42—21no—
585C42—21no—
586C42—21no—
587C42—21no—
588C42—22no—
589C42—22no—
590C23—22no—
591C23—22no—
592C23—22no—
593C23—21no—
594C23—24no—
595C23—41no—
596C23—42no—
597C23—42no—
598C23C31×#12011yescharacteristic
599C23C31×#12011yescharacteristic
600C23C22×D4×C3111yescharacteristic
601Q8—22no—
602Q8—82no—
603D4—22no—
604D4—44no—
605D4—42no—
606D4—42no—
607D4—41no—
608D4—41no—
609D4—42no—
610D4—81no—
611D4—82no—
612D4—82no—
613D4—82no—
614C2×C4—22no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—22no—
629C2×C4—42no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—42no—
633C2×C4—42no—
634C2×C4—42no—
635C2×C4—44no—
636C2×C4—42no—
637C2×C4—42no—
638C2×C4—81no—
639C2×C4—82no—
640C2×C4—82no—
641C2×C4—82no—
642C2×C4—82no—
643C2×C4—82no—
644C2×C4C31×#12011yescharacteristic
645C2×C4C31×#12011yescharacteristic
646C2×C4C22×D4×C3111yescharacteristic
647C2×C4C22×D4×C3111yescharacteristic
648C2×C4C2×#41×C3112yes—
649C2×C4C31×2−1+412yes—
650C8—24no—
651C8—42no—
652C22—21no—
653C22—21no—
654C22—21no—
655C22—21no—
656C22—21no—
657C22—21no—
658C22—21no—
659C22—44no—
660C22—41no—
661C22—42no—
662C22—41no—
663C22—42no—
664C22—42no—
665C22—41no—
666C22—84no—
667C22C31×#45512yes—
668C22C2×C31×#12011yescharacteristic
669C22C31×#54712yes—
670C4—21no—
671C4—21no—
672C4—41no—
673C4—41no—
674C4—41no—
675C4—42no—
676C4—41no—
677C4—41no—
678C4—41no—
679C4—41no—
680C4—82no—
681C4—82no—
682C4C31×#52511yescharacteristic
683C4C31×#53611yescharacteristic
684C4C31×#54712yes—
685C2—22no—
686C2—22no—
687C2—41no—
688C2—82no—
689C2—81no—
690C2C31×#240611yescharacteristic
691C2C2×C31×#45511yescharacteristic
692C2C31×#302111yescharacteristic
subgroupG/H
center, socleC22×C31C2×#120
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC31×#3494C2
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
2. C31×#3092C2semidirect
3. C2×C31×#428C2semidirect
4. C31×#2504C2semidirect
5. C31×#2061C2semidirect
6. C31×#2037C2semidirect
7. C31×#1900C2semidirect
8. C31×#1871C2semidirect
9. C31×#1860C2semidirect
10. C31×#1856C2semidirect
11. C31×#1826C2semidirect
193. M16×C31#41semidirect
243. #24083C31direct (N × H)
307. #3092C2×C31semidirect
308. C2×#428C2×C31semidirect
309. #2504C2×C31semidirect
310. #2061C2×C31semidirect
311. #2037C2×C31semidirect
312. #1900C2×C31semidirect
313. #1871C2×C31semidirect
314. #1860C2×C31semidirect
315. #1856C2×C31semidirect
316. #1826C2×C31semidirect
495. C31#24083direct (N × H)
540. M16#41×C31semidirect

Maximal subgroups

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

subgroupindex
C31×#34942
C31×#30922
C2×C31×#4282
C31×#25042
C31×#20612
C31×#20372
C31×#19002
C31×#18712
C31×#18602
C31×#18562
C31×#18262
#2408331