Finite Group Databasebeta

← C31×#24041 #21480800

Subgroups — C31×#24041 #21480800

Order 7936.

1338 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×Q8×C31C211yesmaximal, characteristic
2C2×C31×#483C211yesmaximal, characteristic, complemented
3C22×C31×#103C211yesmaximal, characteristic, complemented
4C31×#2486C211yesmaximal, characteristic
5C31×#2043C212yesmaximal, complemented
6C31×#2035C212yesmaximal, complemented
7C31×#1892C211yesmaximal, characteristic, complemented
8C31×#1869C211yesmaximal, characteristic
9C31×#1865C212yesmaximal, complemented
10C31×#1787C211yesmaximal, characteristic, complemented
11C31×#1787C212yesmaximal, complemented
12C23×Q8×C31C2211yescharacteristic
13C23×Q8×C31C2211yescharacteristic
14C23×C8×C31C2211yescharacteristic
15D4×Q8×C31—24no—
16D4×Q8×C31—24no—
17C2×C31×C4⋊Q8—21no—
18C2×C31×C4⋊Q8C2211yescharacteristic
19C2×C31×#123—21no—
20C2×C31×C22⋊Q8—21no—
21C2×C31×C22⋊Q8—21no—
22C2×C31×C22⋊Q8C2211yescharacteristic
23C2×C31×C22⋊Q8C2211yescharacteristic
24C2×C4×Q8×C31C2211yescharacteristic
25C2×C4×D4×C31—21no—
26C2×C4×D4×C31C2211yescharacteristic
27C22×C4⋊C4×C31C2211yescharacteristic
28C31×#483—24no—
29C2×C31×#106C2212yes—
30C2×C31×#103—24no—
31C2×C31×#103C2212yes—
32C2×C31×#103C2212yes—
33C2×C31×#103C2212yes—
34C2×C31×#103C2212yes—
35C2×C31×#103C2212yes—
36C2×C31×#103C2212yes—
37C2×C31×C22⋊C8C2211yescharacteristic
38C2×C31×C22⋊C8C2212yes—
39C31×#398—21no—
40C31×#397—21no—
41C31×#389C2212yes—
42C31×#381—21no—
43C31×#380C2211yescharacteristic
44C31×#380C2212yes—
45C31×#340C2212yes—
46C31×#336C2212yes—
47C22×Q8×C31—22no—
48C22×Q8×C31—22no—
49C22×Q8×C31—21no—
50C22×Q8×C31—21no—
51C22×Q8×C31—22no—
52C22×Q8×C31—24no—
53C22×Q8×C31—24no—
54C22×Q8×C31—42no—
55C22×Q8×C31—42no—
56C22×Q8×C31D414yes—
57C22×Q8×C31C2311yescharacteristic
58C22×Q8×C31C2311yescharacteristic
59C22×Q8×C31C2311yescharacteristic
60C22×D4×C31D411yescharacteristic
61C23×C4×C31—21no—
62C23×C4×C31—21no—
63C23×C4×C31—21no—
64C23×C4×C31C2311yescharacteristic
65C23×C4×C31C2311yescharacteristic
66C22×C8×C31—22no—
67C22×C8×C31—42no—
68C22×C8×C31C2312yes—
69C22×C8×C31C2312yes—
70C31×C4⋊Q8—28no—
71C31×C4⋊Q8—22no—
72C31×C4⋊Q8—22no—
73C31×#123—44no—
74C31×C22⋊Q8—28no—
75C31×C22⋊Q8—28no—
76C31×C22⋊Q8—22no—
77C31×C22⋊Q8—22no—
78C31×C22⋊Q8—22no—
79C31×C22⋊Q8D414yes—
80C4×Q8×C31—22no—
81C4×Q8×C31—22no—
82C4×D4×C31—28no—
83C4×D4×C31—22no—
84C4×D4×C31—22no—
85C2×C4⋊C4×C31—21no—
86C2×C4⋊C4×C31—21no—
87C2×C4⋊C4×C31—21no—
88C2×C4⋊C4×C31—21no—
89C2×C4⋊C4×C31—21no—
90C2×C4⋊C4×C31—22no—
91C2×C4⋊C4×C31—22no—
92C2×C4⋊C4×C31—21no—
93C2×C4⋊C4×C31—22no—
94C2×C4⋊C4×C31D411yescharacteristic
95C2×C4⋊C4×C31C2312yes—
96C2×C4⋊C4×C31C2312yes—
97C2×C4⋊C4×C31C2311yescharacteristic
98C2×C22⋊C4×C31—21no—
99C2×C22⋊C4×C31—21no—
100C2×C22⋊C4×C31—22no—
101C2×C22⋊C4×C31—21no—
102C2×C22⋊C4×C31D411yescharacteristic
103C2×C22⋊C4×C31D411yescharacteristic
104C2×C42×C31—21no—
105C2×C42×C31C2311yescharacteristic
106C31×#106—24no—
107C31×#103—24no—
108C31×#103—24no—
109C31×#103—24no—
110C31×#103—24no—
111C31×#103—42no—
112C31×#103—42no—
113C31×C22⋊C8—22no—
114C31×C22⋊C8—42no—
115C31×#95—21no—
116C31×#95—22no—
117C31×#95—22no—
118C24×C31C2×D411yescharacteristic
119C24×C31C2×D411yescharacteristic
120C2×Q8×C31—24no—
121C2×Q8×C31—24no—
122C2×Q8×C31—21no—
123C2×Q8×C31—21no—
124C2×Q8×C31—21no—
125C2×Q8×C31—22no—
126C2×Q8×C31—28no—
127C2×Q8×C31—22no—
128C2×Q8×C31—22no—
129C2×Q8×C31—22no—
130C2×Q8×C31—22no—
131C2×Q8×C31—44no—
132C2×Q8×C31—44no—
133C2×Q8×C31—44no—
134C2×Q8×C31—48no—
135C2×Q8×C31—48no—
136C2×Q8×C31—44no—
137C2×Q8×C31—44no—
138C2×Q8×C31C2×D412yes—
139C2×Q8×C31C2×D412yes—
140C2×Q8×C31C2×D412yes—
141C2×Q8×C31#4114yes—
142C2×D4×C31—22no—
143C2×D4×C31—22no—
144C2×D4×C31SD1614yes—
145C22×C4×C31—21no—
146C22×C4×C31—22no—
147C22×C4×C31—22no—
148C22×C4×C31—24no—
149C22×C4×C31—24no—
150C22×C4×C31—21no—
151C22×C4×C31—21no—
152C22×C4×C31—21no—
153C22×C4×C31—21no—
154C22×C4×C31—21no—
155C22×C4×C31—22no—
156C22×C4×C31—22no—
157C22×C4×C31—22no—
158C22×C4×C31—22no—
159C22×C4×C31—44no—
160C22×C4×C31—44no—
161C22×C4×C31—42no—
162C22×C4×C31—42no—
163C22×C4×C31—42no—
164C22×C4×C31C2×D411yescharacteristic
165C22×C4×C31C2×D411yescharacteristic
166C22×C4×C31C2×D411yescharacteristic
167C22×C4×C31C2×D412yes—
168C22×C4×C31C2×D412yes—
169C22×C4×C31C2×D411yescharacteristic
170C22×C4×C31C2411yescharacteristic
171C2×C8×C31—22no—
172C2×C8×C31—22no—
173C2×C8×C31—22no—
174C2×C8×C31—22no—
175C2×C8×C31—22no—
176C2×C8×C31—22no—
177C2×C8×C31—44no—
178C4⋊C4×C31—24no—
179C4⋊C4×C31—24no—
180C4⋊C4×C31—24no—
181C4⋊C4×C31—24no—
182C4⋊C4×C31—24no—
183C4⋊C4×C31—22no—
184C4⋊C4×C31—21no—
185C4⋊C4×C31—22no—
186C4⋊C4×C31—22no—
187C4⋊C4×C31—22no—
188C4⋊C4×C31—22no—
189C4⋊C4×C31—42no—
190C4⋊C4×C31—44no—
191C4⋊C4×C31C2×D412yes—
192C22⋊C4×C31—24no—
193C22⋊C4×C31—24no—
194C22⋊C4×C31—22no—
195C22⋊C4×C31—22no—
196C22⋊C4×C31—42no—
197C22⋊C4×C31—44no—
198C42×C31—24no—
199C42×C31—21no—
200C42×C31—21no—
201#24041C3111yesmaximal, characteristic, direct product factor, Sylow
202C23×C31—22no—
203C23×C31—22no—
204C23×C31—21no—
205C23×C31—22no—
206C23×C31—21no—
207C23×C31—22no—
208C23×C31#12012yes—
209C23×C31C2×SD1612yes—
210C23×C31C2×SD1612yes—
211C23×C31#13712yes—
212C23×C31C22×D411yescharacteristic
213Q8×C31—22no—
214Q8×C31—24no—
215Q8×C31—22no—
216Q8×C31—22no—
217Q8×C31—24no—
218Q8×C31—48no—
219Q8×C31—48no—
220Q8×C31—41no—
221Q8×C31—41no—
222Q8×C31—42no—
223Q8×C31#12314yescomplemented
224D4×C31—28no—
225C2×C4×C31—21no—
226C2×C4×C31—22no—
227C2×C4×C31—22no—
228C2×C4×C31—24no—
229C2×C4×C31—21no—
230C2×C4×C31—22no—
231C2×C4×C31—22no—
232C2×C4×C31—24no—
233C2×C4×C31—21no—
234C2×C4×C31—22no—
235C2×C4×C31—22no—
236C2×C4×C31—22no—
237C2×C4×C31—21no—
238C2×C4×C31—22no—
239C2×C4×C31—22no—
240C2×C4×C31—48no—
241C2×C4×C31—48no—
242C2×C4×C31—42no—
243C2×C4×C31—42no—
244C2×C4×C31—42no—
245C2×C4×C31—41no—
246C2×C4×C31—41no—
247C2×C4×C31—42no—
248C2×C4×C31—42no—
249C2×C4×C31—42no—
250C2×C4×C31—42no—
251C2×C4×C31—42no—
252C2×C4×C31—42no—
253C2×C4×C31—42no—
254C2×C4×C31—84no—
255C2×C4×C31#12012yes—
256C2×C4×C31C2×SD1612yes—
257C2×C4×C31C22×D411yescharacteristic
258C2×C4×C31C22×D411yescharacteristic
259C2×C4×C31C2×#4112yes—
260C2×C4×C31H(5,𝔽2)12yes—
261C8×C31—42no—
262C8×C31—42no—
263C2×D4×Q8C2×C3111yescharacteristic
264C2×#483C2×C3111yescharacteristic, complemented
265C22×#103C2×C3111yescharacteristic, complemented
266#2486C2×C3111yescharacteristic
267#2043C2×C3112yescomplemented
268#2035C2×C3112yescomplemented
269#1892C2×C3111yescharacteristic, complemented
270#1869C2×C3111yescharacteristic
271#1865C2×C3112yescomplemented
272#1787C2×C3112yescomplemented
273#1787C2×C3111yescharacteristic, complemented
274C22×C31—22no—
275C22×C31—22no—
276C22×C31—24no—
277C22×C31—24no—
278C22×C31—22no—
279C22×C31—24no—
280C22×C31—41no—
281C22×C31—41no—
282C22×C31—42no—
283C22×C31#44814yes—
284C22×C31C2×#12011yescharacteristic
285C22×C31#54612yes—
286C22×C31C22×SD1611yescharacteristic
287C22×C31C2×#13711yescharacteristic
288C22×C31#57812yes—
289C4×C31—22no—
290C4×C31—24no—
291C4×C31—22no—
292C4×C31—41no—
293C4×C31—42no—
294C4×C31—42no—
295C4×C31—41no—
296C4×C31—42no—
297C4×C31—82no—
298C4×C31—82no—
299C4×C31C2×#12311yescharacteristic
300C4×C31#53411yescharacteristic
301C4×C31#54612yes—
302C23×Q8C22×C3111yescharacteristic
303C23×Q8C22×C3111yescharacteristic
304C23×C8C22×C3111yescharacteristic
305D4×Q8—24no—
306D4×Q8—24no—
307C2×C4⋊Q8—21no—
308C2×C4⋊Q8C22×C3111yescharacteristic
309C2×#123—21no—
310C2×C22⋊Q8—21no—
311C2×C22⋊Q8—21no—
312C2×C22⋊Q8C22×C3111yescharacteristic
313C2×C22⋊Q8C22×C3111yescharacteristic
314C2×C4×Q8C22×C3111yescharacteristic
315C2×C4×D4—21no—
316C2×C4×D4C22×C3111yescharacteristic
317C22×C4⋊C4C22×C3111yescharacteristic
318#483—24no—
319C2×#106C22×C3112yes—
320C2×#103—24no—
321C2×#103C22×C3112yes—
322C2×#103C22×C3112yes—
323C2×#103C22×C3112yes—
324C2×#103C22×C3112yes—
325C2×#103C22×C3112yes—
326C2×#103C22×C3112yes—
327C2×C22⋊C8C22×C3111yescharacteristic
328C2×C22⋊C8C22×C3112yes—
329#398—21no—
330#397—21no—
331#389C22×C3112yes—
332#381—21no—
333#380C22×C3111yescharacteristic
334#380C22×C3112yes—
335#340C22×C3112yes—
336#336C22×C3112yes—
337C2×C31—24no—
338C2×C31—42no—
339C2×C31#240511yescharacteristic
340C2×C31C2×#44811yescharacteristic
341C2×C31#301111yescharacteristic
342C2×C31#329812yes—
343C2×C31#331212yes—
344C22×Q8—22no—
345C22×Q8—22no—
346C22×Q8—21no—
347C22×Q8—21no—
348C22×Q8—22no—
349C22×Q8—24no—
350C22×Q8—24no—
351C22×Q8—42no—
352C22×Q8—42no—
353C22×Q8D4×C3114yes—
354C22×Q8C23×C3111yescharacteristic
355C22×Q8C23×C3111yescharacteristic
356C22×Q8C23×C3111yescharacteristic
357C22×D4D4×C3111yescharacteristic
358C23×C4—21no—
359C23×C4—21no—
360C23×C4—21no—
361C23×C4C23×C3111yescharacteristic
362C23×C4C23×C3111yescharacteristic
363C22×C8—22no—
364C22×C8—42no—
365C22×C8C23×C3112yes—
366C22×C8C23×C3112yes—
367C4⋊Q8—28no—
368C4⋊Q8—22no—
369C4⋊Q8—22no—
370#123—44no—
371C22⋊Q8—28no—
372C22⋊Q8—28no—
373C22⋊Q8—22no—
374C22⋊Q8—22no—
375C22⋊Q8—22no—
376C22⋊Q8D4×C3114yes—
377C4×Q8—22no—
378C4×Q8—22no—
379C4×D4—28no—
380C4×D4—22no—
381C4×D4—22no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—22no—
388C2×C4⋊C4—22no—
389C2×C4⋊C4—21no—
390C2×C4⋊C4—22no—
391C2×C4⋊C4D4×C3111yescharacteristic
392C2×C4⋊C4C23×C3112yes—
393C2×C4⋊C4C23×C3112yes—
394C2×C4⋊C4C23×C3111yescharacteristic
395C2×C22⋊C4—21no—
396C2×C22⋊C4—21no—
397C2×C22⋊C4—21no—
398C2×C22⋊C4—22no—
399C2×C22⋊C4D4×C3111yescharacteristic
400C2×C22⋊C4D4×C3111yescharacteristic
401C2×C42—21no—
402C2×C42C23×C3111yescharacteristic
403#106—24no—
404#103—24no—
405#103—24no—
406#103—24no—
407#103—24no—
408#103—42no—
409#103—42no—
410C22⋊C8—22no—
411C22⋊C8—42no—
412#95—22no—
413#95—21no—
414#95—22no—
415C31#2404111yescharacteristic, direct product factor, Sylow
416C24C2×D4×C3111yescharacteristic
417C24C2×D4×C3111yescharacteristic
418C2×Q8—24no—
419C2×Q8—24no—
420C2×Q8—21no—
421C2×Q8—21no—
422C2×Q8—21no—
423C2×Q8—22no—
424C2×Q8—28no—
425C2×Q8—22no—
426C2×Q8—22no—
427C2×Q8—22no—
428C2×Q8—22no—
429C2×Q8—44no—
430C2×Q8—44no—
431C2×Q8—44no—
432C2×Q8—48no—
433C2×Q8—48no—
434C2×Q8—44no—
435C2×Q8—44no—
436C2×Q8C2×D4×C3112yes—
437C2×Q8C2×D4×C3112yes—
438C2×Q8C2×D4×C3112yes—
439C2×Q8#41×C3114yes—
440C2×D4—22no—
441C2×D4—22no—
442C2×D4SD16×C3114yes—
443C22×C4—21no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—24no—
447C22×C4—24no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—44no—
458C22×C4—44no—
459C22×C4—42no—
460C22×C4—42no—
461C22×C4—42no—
462C22×C4C2×D4×C3111yescharacteristic
463C22×C4C2×D4×C3111yescharacteristic
464C22×C4C2×D4×C3111yescharacteristic
465C22×C4C2×D4×C3112yes—
466C22×C4C2×D4×C3112yes—
467C22×C4C2×D4×C3111yescharacteristic
468C22×C4C24×C3111yescharacteristic
469C2×C8—22no—
470C2×C8—22no—
471C2×C8—22no—
472C2×C8—22no—
473C2×C8—22no—
474C2×C8—22no—
475C2×C8—44no—
476C4⋊C4—24no—
477C4⋊C4—24no—
478C4⋊C4—24no—
479C4⋊C4—24no—
480C4⋊C4—24no—
481C4⋊C4—22no—
482C4⋊C4—21no—
483C4⋊C4—22no—
484C4⋊C4—22no—
485C4⋊C4—22no—
486C4⋊C4—22no—
487C4⋊C4—42no—
488C4⋊C4—44no—
489C4⋊C4C2×D4×C3112yes—
490C22⋊C4—24no—
491C22⋊C4—24no—
492C22⋊C4—22no—
493C22⋊C4—22no—
494C22⋊C4—42no—
495C22⋊C4—44no—
496C42—24no—
497C42—21no—
498C42—21no—
499C23—22no—
500C23—22no—
501C23—21no—
502C23—22no—
503C23—21no—
504C23—22no—
505C23C31×#12012yes—
506C23C2×SD16×C3112yes—
507C23C2×SD16×C3112yes—
508C23C31×#13712yes—
509C23C22×D4×C3111yescharacteristic
510Q8—22no—
511Q8—24no—
512Q8—22no—
513Q8—22no—
514Q8—24no—
515Q8—48no—
516Q8—48no—
517Q8—41no—
518Q8—41no—
519Q8—42no—
520Q8C31×#12314yescomplemented
521D4—28no—
522C2×C4—21no—
523C2×C4—22no—
524C2×C4—22no—
525C2×C4—24no—
526C2×C4—21no—
527C2×C4—22no—
528C2×C4—22no—
529C2×C4—24no—
530C2×C4—21no—
531C2×C4—22no—
532C2×C4—22no—
533C2×C4—22no—
534C2×C4—21no—
535C2×C4—22no—
536C2×C4—22no—
537C2×C4—48no—
538C2×C4—48no—
539C2×C4—42no—
540C2×C4—42no—
541C2×C4—42no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—42no—
545C2×C4—42no—
546C2×C4—42no—
547C2×C4—42no—
548C2×C4—42no—
549C2×C4—42no—
550C2×C4—42no—
551C2×C4—84no—
552C2×C4C31×#12012yes—
553C2×C4C2×SD16×C3112yes—
554C2×C4C22×D4×C3111yescharacteristic
555C2×C4C22×D4×C3111yescharacteristic
556C2×C4C2×#41×C3112yes—
557C2×C4C31×H(5,𝔽2)12yes—
558C8—42no—
559C8—42no—
560C22—22no—
561C22—22no—
562C22—24no—
563C22—24no—
564C22—22no—
565C22—24no—
566C22—41no—
567C22—41no—
568C22—42no—
569C22C31×#44814yes—
570C22C2×C31×#12011yescharacteristic
571C22C31×#54612yes—
572C22C22×SD16×C3111yescharacteristic
573C22C2×C31×#13711yescharacteristic
574C22C31×#57812yes—
575C4—22no—
576C4—24no—
577C4—22no—
578C4—41no—
579C4—42no—
580C4—42no—
581C4—41no—
582C4—42no—
583C4—82no—
584C4—82no—
585C4C2×C31×#12311yescharacteristic
586C4C31×#53411yescharacteristic
587C4C31×#54612yes—
588C2—24no—
589C2—42no—
590C2C31×#240511yescharacteristic
591C2C2×C31×#44811yescharacteristic
592C2C31×#301111yescharacteristic
593C2C31×#329812yes—
594C2C31×#331212yes—
subgroupG/H
center, socleC23×C31C22×D4
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC22×D4×C31D4
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×#483C2semidirect
3. C22×C31×#103C2semidirect
5. C31×#2043C2semidirect
6. C31×#2035C2semidirect
7. C31×#1892C2semidirect
9. C31×#1865C2semidirect
10. C31×#1787C2semidirect
11. C31×#1787C2semidirect
201. #24041C31direct (N × H)
223. Q8×C31#123semidirect
264. C2×#483C2×C31semidirect
265. C22×#103C2×C31semidirect
267. #2043C2×C31semidirect
268. #2035C2×C31semidirect
269. #1892C2×C31semidirect
271. #1865C2×C31semidirect
272. #1787C2×C31semidirect
273. #1787C2×C31semidirect
415. C31#24041direct (N × H)
520. Q8C31×#123semidirect

Maximal subgroups

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

subgroupindex
C2×D4×Q8×C312
C2×C31×#4832
C22×C31×#1032
C31×#24862
C31×#20432
C31×#20352
C31×#18922
C31×#18692
C31×#18652
C31×#17872
#2404131