Finite Group Databasebeta

← C31×#24056 #21480815

Subgroups — C31×#24056 #21480815

Order 7936.

1820 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3484C211yesmaximal, characteristic
2C31×#2849C212yesmaximal, complemented
3C2×C31×#386C211yesmaximal, characteristic, complemented
4C31×#2044C214yesmaximal, complemented
5C31×#1898C212yesmaximal, complemented
6C31×#1867C212yesmaximal, complemented
7C31×#1790C212yesmaximal, complemented
8C31×#1781C211yesmaximal, characteristic, complemented
9C2×C31×H(5,𝔽2)C2211yescharacteristic
10C23×D4×C31C2211yescharacteristic
11C24×C4×C31C2211yescharacteristic, complemented
12C31×#546—22no—
13C31×#546—22no—
14D42×C31—22no—
15D42×C31—22no—
16C31×#535—21no—
17C31×#534—21no—
18C31×#534C2212yes—
19C31×#525—21no—
20C2×C31×#123—22no—
21C2×C31×#120—21no—
22C2×C31×#120C2212yes—
23C31×#518C2211yescharacteristic
24C22×C22⋊C4×C31—21no—
25C22×C22⋊C4×C31C2211yescharacteristic, complemented
26C2×C31×#99C2212yes—
27C2×C31×#99C2214yescomplemented
28C2×C31×#99C2212yescomplemented
29C31×#386—22no—
30C31×#386—21no—
31C31×#386—21no—
32C31×#386C2212yes—
33C31×#386C2214yescomplemented
34C31×#386C2212yescomplemented
35C31×#385—22no—
36C31×#385C2214yescomplemented
37C31×#381—22no—
38C31×#379C2212yescomplemented
39C2×C31×#95—21no—
40C31×#342C2214yescomplemented
41C25×C31D411yescharacteristic
42C25×C31C2311yescharacteristic
43C31×H(5,𝔽2)—24no—
44C31×H(5,𝔽2)—42no—
45C2×#41×C31—21no—
46C2×#41×C31—22no—
47C22×D4×C31—21no—
48C22×D4×C31—22no—
49C22×D4×C31—22no—
50C22×D4×C31—22no—
51C22×D4×C31—21no—
52C22×D4×C31—21no—
53C22×D4×C31—24no—
54C22×D4×C31—42no—
55C22×D4×C31D411yescharacteristic
56C22×D4×C31D411yescharacteristic
57C22×D4×C31D412yes—
58C22×D4×C31D412yes—
59C22×D4×C31C2312yes—
60C22×D4×C31C2311yescharacteristic
61C22×D4×C31C2311yescharacteristic
62C23×C4×C31—21no—
63C23×C4×C31—22no—
64C23×C4×C31—21no—
65C23×C4×C31—22no—
66C23×C4×C31—21no—
67C23×C4×C31—44no—
68C23×C4×C31D411yescharacteristic
69C23×C4×C31C2312yes—
70C31×#127—22no—
71C31×#124—22no—
72C31×#123—22no—
73C31×#123—22no—
74C31×#123—22no—
75C31×#123—48no—
76C31×C22⋊Q8—21no—
77C31×C22⋊Q8—21no—
78C31×#121—21no—
79C31×#121—21no—
80C31×#121—22no—
81C31×#121—22no—
82C31×#121—22no—
83C31×#121—22no—
84C31×#121—22no—
85C31×#121—22no—
86C31×#120—22no—
87C31×#120—22no—
88C31×#120—22no—
89C31×#120—22no—
90C31×#120—22no—
91C31×#120—22no—
92C31×#120—22no—
93C31×#120—22no—
94C31×#120—22no—
95C4×D4×C31—22no—
96C4×D4×C31—22no—
97C4×D4×C31—22no—
98C4×D4×C31—22no—
99C31×#117—21no—
100C2×C4⋊C4×C31—24no—
101C2×C22⋊C4×C31—21no—
102C2×C22⋊C4×C31—21no—
103C2×C22⋊C4×C31—21no—
104C2×C22⋊C4×C31—22no—
105C2×C22⋊C4×C31—22no—
106C2×C22⋊C4×C31—21no—
107C2×C22⋊C4×C31—22no—
108C2×C22⋊C4×C31—24no—
109C2×C22⋊C4×C31—22no—
110C2×C22⋊C4×C31—42no—
111C2×C22⋊C4×C31—44no—
112C2×C22⋊C4×C31D412yes—
113C2×C22⋊C4×C31D412yes—
114C2×C22⋊C4×C31C2314yes—
115C2×C22⋊C4×C31C2312yes—
116C2×C22⋊C4×C31C2312yes—
117C31×#99—24no—
118C31×#99—42no—
119C31×#99—44no—
120C31×#95—22no—
121C31×#95—22no—
122C31×#95—24no—
123C31×#95—24no—
124C24×C31—22no—
125C24×C31—22no—
126C24×C31—21no—
127C24×C31—22no—
128C24×C31—21no—
129C24×C31—21no—
130C24×C31—42no—
131C24×C31—42no—
132C24×C31—41no—
133C24×C31—42no—
134C24×C31—42no—
135C24×C31C2×D411yescharacteristic
136C24×C31C2×D412yes—
137C24×C31C2×D412yes—
138C24×C31C2×D411yescharacteristic
139C24×C31C2×D412yes—
140C24×C31C2×D411yescharacteristic
141C24×C31C2×D411yescharacteristic
142C24×C31C2411yescharacteristic
143#41×C31—48no—
144#41×C31—42no—
145#41×C31—42no—
146C2×Q8×C31—21no—
147C2×D4×C31—22no—
148C2×D4×C31—22no—
149C2×D4×C31—22no—
150C2×D4×C31—21no—
151C2×D4×C31—22no—
152C2×D4×C31—22no—
153C2×D4×C31—22no—
154C2×D4×C31—22no—
155C2×D4×C31—22no—
156C2×D4×C31—22no—
157C2×D4×C31—22no—
158C2×D4×C31—22no—
159C2×D4×C31—22no—
160C2×D4×C31—24no—
161C2×D4×C31—22no—
162C2×D4×C31—24no—
163C2×D4×C31—22no—
164C2×D4×C31—22no—
165C2×D4×C31—22no—
166C2×D4×C31—22no—
167C2×D4×C31—22no—
168C2×D4×C31—41no—
169C2×D4×C31—41no—
170C2×D4×C31—48no—
171C2×D4×C31—48no—
172C2×D4×C31—48no—
173C2×D4×C31—42no—
174C2×D4×C31—42no—
175C2×D4×C31—44no—
176C2×D4×C31—44no—
177C2×D4×C31—82no—
178C2×D4×C31—82no—
179C2×D4×C31#4114yes—
180C22×C4×C31—21no—
181C22×C4×C31—24no—
182C22×C4×C31—22no—
183C22×C4×C31—28no—
184C22×C4×C31—21no—
185C22×C4×C31—21no—
186C22×C4×C31—22no—
187C22×C4×C31—24no—
188C22×C4×C31—21no—
189C22×C4×C31—21no—
190C22×C4×C31—22no—
191C22×C4×C31—24no—
192C22×C4×C31—22no—
193C22×C4×C31—44no—
194C22×C4×C31—41no—
195C22×C4×C31—44no—
196C22×C4×C31—48no—
197C22×C4×C31—42no—
198C22×C4×C31—44no—
199C22×C4×C31—42no—
200C22×C4×C31—41no—
201C22×C4×C31—41no—
202C22×C4×C31—42no—
203C22×C4×C31—42no—
204C22×C4×C31—42no—
205C22×C4×C31C2×D412yes—
206C22×C4×C31C2×D411yescharacteristic
207C22×C4×C31C2×D411yescharacteristic
208C22×C4×C31C2×D412yes—
209C22×C4×C31C2×D412yes—
210C4⋊C4×C31—21no—
211C4⋊C4×C31—21no—
212C4⋊C4×C31—22no—
213C4⋊C4×C31—22no—
214C4⋊C4×C31—48no—
215C22⋊C4×C31—22no—
216C22⋊C4×C31—22no—
217C22⋊C4×C31—22no—
218C22⋊C4×C31—22no—
219C22⋊C4×C31—22no—
220C22⋊C4×C31—22no—
221C22⋊C4×C31—22no—
222C22⋊C4×C31—22no—
223C22⋊C4×C31—22no—
224C22⋊C4×C31—22no—
225C22⋊C4×C31—22no—
226C22⋊C4×C31—24no—
227C22⋊C4×C31—24no—
228C22⋊C4×C31—24no—
229C22⋊C4×C31—44no—
230C22⋊C4×C31—44no—
231C22⋊C4×C31—48no—
232C22⋊C4×C31—44no—
233C22⋊C4×C31—42no—
234C22⋊C4×C31—44no—
235C42×C31—22no—
236#24056C3111yesmaximal, characteristic, direct product factor, Sylow
237C23×C31—21no—
238C23×C31—21no—
239C23×C31—22no—
240C23×C31—22no—
241C23×C31—21no—
242C23×C31—21no—
243C23×C31—21no—
244C23×C31—24no—
245C23×C31—24no—
246C23×C31—24no—
247C23×C31—24no—
248C23×C31—21no—
249C23×C31—21no—
250C23×C31—22no—
251C23×C31—21no—
252C23×C31—21no—
253C23×C31—24no—
254C23×C31—42no—
255C23×C31—41no—
256C23×C31—41no—
257C23×C31—42no—
258C23×C31—41no—
259C23×C31—41no—
260C23×C31—42no—
261C23×C31—42no—
262C23×C31—48no—
263C23×C31—48no—
264C23×C31—41no—
265C23×C31—41no—
266C23×C31—41no—
267C23×C31—41no—
268C23×C31—48no—
269C23×C31—42no—
270C23×C31—42no—
271C23×C31—42no—
272C23×C31—42no—
273C23×C31—42no—
274C23×C31—81no—
275C23×C31—81no—
276C23×C31—84no—
277C23×C31—81no—
278C23×C31—81no—
279C23×C31#12012yes—
280C23×C31#12011yescharacteristic
281C23×C31#12011yescharacteristic
282C23×C31#12312yescomplemented
283C23×C31C22×D411yescharacteristic
284C23×C31C22×D412yes—
285C23×C31C2×#4112yes—
286C23×C31H(5,𝔽2)12yes—
287Q8×C31—42no—
288D4×C31—28no—
289D4×C31—44no—
290D4×C31—42no—
291D4×C31—44no—
292D4×C31—44no—
293D4×C31—42no—
294D4×C31—42no—
295D4×C31—44no—
296D4×C31—44no—
297D4×C31—44no—
298D4×C31—44no—
299D4×C31—82no—
300D4×C31—82no—
301D4×C31—82no—
302D4×C31—82no—
303C2×C4×C31—21no—
304C2×C4×C31—21no—
305C2×C4×C31—24no—
306C2×C4×C31—28no—
307C2×C4×C31—22no—
308C2×C4×C31—22no—
309C2×C4×C31—22no—
310C2×C4×C31—21no—
311C2×C4×C31—21no—
312C2×C4×C31—21no—
313C2×C4×C31—24no—
314C2×C4×C31—42no—
315C2×C4×C31—42no—
316C2×C4×C31—44no—
317C2×C4×C31—44no—
318C2×C4×C31—42no—
319C2×C4×C31—44no—
320C2×C4×C31—48no—
321C2×C4×C31—42no—
322C2×C4×C31—42no—
323C2×C4×C31—44no—
324C2×C4×C31—42no—
325C2×C4×C31—42no—
326C2×C4×C31—44no—
327C2×C4×C31—42no—
328C2×C4×C31—44no—
329C2×C4×C31—42no—
330C2×C4×C31—42no—
331C2×C4×C31—44no—
332C2×C4×C31—81no—
333C2×C4×C31—81no—
334C2×C4×C31—84no—
335C2×C4×C31#12312yescomplemented
336#3484C2×C3111yescharacteristic
337#2849C2×C3112yescomplemented
338C2×#386C2×C3111yescharacteristic, complemented
339#2044C2×C3114yescomplemented
340#1898C2×C3112yescomplemented
341#1867C2×C3112yescomplemented
342#1790C2×C3112yescomplemented
343#1781C2×C3111yescharacteristic, complemented
344C22×C31—24no—
345C22×C31—24no—
346C22×C31—21no—
347C22×C31—21no—
348C22×C31—22no—
349C22×C31—21no—
350C22×C31—21no—
351C22×C31—22no—
352C22×C31—21no—
353C22×C31—21no—
354C22×C31—22no—
355C22×C31—22no—
356C22×C31—22no—
357C22×C31—22no—
358C22×C31—42no—
359C22×C31—42no—
360C22×C31—48no—
361C22×C31—48no—
362C22×C31—42no—
363C22×C31—42no—
364C22×C31—42no—
365C22×C31—42no—
366C22×C31—41no—
367C22×C31—41no—
368C22×C31—42no—
369C22×C31—41no—
370C22×C31—42no—
371C22×C31—41no—
372C22×C31—42no—
373C22×C31—41no—
374C22×C31—81no—
375C22×C31—84no—
376C22×C31—84no—
377C22×C31—84no—
378C22×C31—81no—
379C22×C31—162no—
380C22×C31B(4,𝔽2)12yes—
381C22×C31#45812yes—
382C22×C31C2×#12011yescharacteristic
383C22×C31C2×#12311yescharacteristic
384C22×C31#53411yescharacteristic
385C22×C31#54614yes—
386C4×C31—22no—
387C4×C31—41no—
388C4×C31—42no—
389C4×C31—44no—
390C4×C31—42no—
391C4×C31—42no—
392C4×C31—84no—
393C4×C31—82no—
394C2×H(5,𝔽2)C22×C3111yescharacteristic
395C23×D4C22×C3111yescharacteristic
396C24×C4C22×C3111yescharacteristic, complemented
397#546—22no—
398#546—22no—
399D42—22no—
400D42—22no—
401#535—21no—
402#534—21no—
403#534C22×C3112yes—
404#525—21no—
405C2×#123—22no—
406C2×#120—21no—
407C2×#120C22×C3112yes—
408#518C22×C3111yescharacteristic
409C22×C22⋊C4—21no—
410C22×C22⋊C4C22×C3111yescharacteristic, complemented
411C2×#99C22×C3112yes—
412C2×#99C22×C3114yescomplemented
413C2×#99C22×C3112yescomplemented
414#386—22no—
415#386—21no—
416#386—21no—
417#386C22×C3112yes—
418#386C22×C3114yescomplemented
419#386C22×C3112yescomplemented
420#385—22no—
421#385C22×C3114yescomplemented
422#381—22no—
423#379C22×C3112yescomplemented
424C2×#95—21no—
425#342C22×C3114yescomplemented
426C2×C31—21no—
427C2×C31—24no—
428C2×C31—21no—
429C2×C31—22no—
430C2×C31—22no—
431C2×C31—42no—
432C2×C31—42no—
433C2×C31—81no—
434C2×C31—82no—
435C2×C31#240511yescharacteristic
436C2×C31C2×B(4,𝔽2)11yescharacteristic
437C2×C31C2×#45811yescharacteristic
438C25D4×C3111yescharacteristic
439C25C23×C3111yescharacteristic
440H(5,𝔽2)—24no—
441H(5,𝔽2)—42no—
442C2×#41—21no—
443C2×#41—22no—
444C22×D4—21no—
445C22×D4—22no—
446C22×D4—22no—
447C22×D4—22no—
448C22×D4—21no—
449C22×D4—21no—
450C22×D4—24no—
451C22×D4—42no—
452C22×D4D4×C3111yescharacteristic
453C22×D4D4×C3111yescharacteristic
454C22×D4D4×C3112yes—
455C22×D4D4×C3112yes—
456C22×D4C23×C3112yes—
457C22×D4C23×C3111yescharacteristic
458C22×D4C23×C3111yescharacteristic
459C23×C4—21no—
460C23×C4—22no—
461C23×C4—21no—
462C23×C4—22no—
463C23×C4—21no—
464C23×C4—44no—
465C23×C4D4×C3111yescharacteristic
466C23×C4C23×C3112yes—
467#127—22no—
468#124—22no—
469#123—22no—
470#123—22no—
471#123—22no—
472#123—48no—
473C22⋊Q8—21no—
474C22⋊Q8—21no—
475#121—21no—
476#121—21no—
477#121—22no—
478#121—22no—
479#121—22no—
480#121—22no—
481#121—22no—
482#121—22no—
483#120—22no—
484#120—22no—
485#120—22no—
486#120—22no—
487#120—22no—
488#120—22no—
489#120—22no—
490#120—22no—
491#120—22no—
492C4×D4—22no—
493C4×D4—22no—
494C4×D4—22no—
495C4×D4—22no—
496#117—21no—
497C2×C4⋊C4—24no—
498C2×C22⋊C4—21no—
499C2×C22⋊C4—21no—
500C2×C22⋊C4—21no—
501C2×C22⋊C4—22no—
502C2×C22⋊C4—22no—
503C2×C22⋊C4—21no—
504C2×C22⋊C4—22no—
505C2×C22⋊C4—24no—
506C2×C22⋊C4—22no—
507C2×C22⋊C4—42no—
508C2×C22⋊C4—44no—
509C2×C22⋊C4D4×C3112yes—
510C2×C22⋊C4D4×C3112yes—
511C2×C22⋊C4C23×C3112yes—
512C2×C22⋊C4C23×C3114yes—
513C2×C22⋊C4C23×C3112yes—
514#99—24no—
515#99—42no—
516#99—44no—
517#95—22no—
518#95—22no—
519#95—24no—
520#95—24no—
521C31#2405611yescharacteristic, direct product factor, Sylow
522C24—22no—
523C24—22no—
524C24—21no—
525C24—22no—
526C24—21no—
527C24—21no—
528C24—42no—
529C24—42no—
530C24—41no—
531C24—42no—
532C24—42no—
533C24C2×D4×C3111yescharacteristic
534C24C2×D4×C3112yes—
535C24C2×D4×C3112yes—
536C24C2×D4×C3111yescharacteristic
537C24C2×D4×C3112yes—
538C24C2×D4×C3111yescharacteristic
539C24C2×D4×C3111yescharacteristic
540C24C24×C3111yescharacteristic
541#41—48no—
542#41—42no—
543#41—42no—
544C2×Q8—21no—
545C2×D4—22no—
546C2×D4—22no—
547C2×D4—22no—
548C2×D4—21no—
549C2×D4—22no—
550C2×D4—22no—
551C2×D4—22no—
552C2×D4—22no—
553C2×D4—22no—
554C2×D4—22no—
555C2×D4—22no—
556C2×D4—22no—
557C2×D4—22no—
558C2×D4—24no—
559C2×D4—22no—
560C2×D4—24no—
561C2×D4—22no—
562C2×D4—22no—
563C2×D4—22no—
564C2×D4—22no—
565C2×D4—22no—
566C2×D4—41no—
567C2×D4—41no—
568C2×D4—48no—
569C2×D4—48no—
570C2×D4—48no—
571C2×D4—42no—
572C2×D4—42no—
573C2×D4—44no—
574C2×D4—44no—
575C2×D4—82no—
576C2×D4—82no—
577C2×D4#41×C3114yes—
578C22×C4—21no—
579C22×C4—24no—
580C22×C4—22no—
581C22×C4—28no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—22no—
585C22×C4—24no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—22no—
589C22×C4—24no—
590C22×C4—22no—
591C22×C4—44no—
592C22×C4—41no—
593C22×C4—44no—
594C22×C4—48no—
595C22×C4—42no—
596C22×C4—44no—
597C22×C4—42no—
598C22×C4—41no—
599C22×C4—41no—
600C22×C4—42no—
601C22×C4—42no—
602C22×C4—42no—
603C22×C4C2×D4×C3112yes—
604C22×C4C2×D4×C3111yescharacteristic
605C22×C4C2×D4×C3111yescharacteristic
606C22×C4C2×D4×C3112yes—
607C22×C4C2×D4×C3112yes—
608C4⋊C4—21no—
609C4⋊C4—21no—
610C4⋊C4—22no—
611C4⋊C4—22no—
612C4⋊C4—48no—
613C22⋊C4—22no—
614C22⋊C4—22no—
615C22⋊C4—22no—
616C22⋊C4—22no—
617C22⋊C4—22no—
618C22⋊C4—22no—
619C22⋊C4—22no—
620C22⋊C4—22no—
621C22⋊C4—22no—
622C22⋊C4—22no—
623C22⋊C4—22no—
624C22⋊C4—24no—
625C22⋊C4—24no—
626C22⋊C4—24no—
627C22⋊C4—44no—
628C22⋊C4—44no—
629C22⋊C4—48no—
630C22⋊C4—44no—
631C22⋊C4—42no—
632C22⋊C4—44no—
633C42—22no—
634C23—22no—
635C23—22no—
636C23—21no—
637C23—21no—
638C23—24no—
639C23—24no—
640C23—21no—
641C23—21no—
642C23—21no—
643C23—24no—
644C23—24no—
645C23—21no—
646C23—21no—
647C23—22no—
648C23—21no—
649C23—21no—
650C23—24no—
651C23—42no—
652C23—41no—
653C23—41no—
654C23—42no—
655C23—41no—
656C23—41no—
657C23—42no—
658C23—42no—
659C23—48no—
660C23—48no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23—48no—
666C23—42no—
667C23—42no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—81no—
672C23—81no—
673C23—84no—
674C23—81no—
675C23—81no—
676C23C31×#12012yes—
677C23C31×#12011yescharacteristic
678C23C31×#12011yescharacteristic
679C23C31×#12312yescomplemented
680C23C22×D4×C3111yescharacteristic
681C23C22×D4×C3112yes—
682C23C2×#41×C3112yes—
683C23C31×H(5,𝔽2)12yes—
684Q8—42no—
685D4—28no—
686D4—44no—
687D4—42no—
688D4—44no—
689D4—44no—
690D4—44no—
691D4—44no—
692D4—42no—
693D4—42no—
694D4—44no—
695D4—44no—
696D4—82no—
697D4—82no—
698D4—82no—
699D4—82no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—24no—
703C2×C4—28no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—24no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—44no—
714C2×C4—44no—
715C2×C4—42no—
716C2×C4—44no—
717C2×C4—48no—
718C2×C4—42no—
719C2×C4—44no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—44no—
724C2×C4—42no—
725C2×C4—44no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—44no—
729C2×C4—81no—
730C2×C4—81no—
731C2×C4—84no—
732C2×C4C31×#12312yescomplemented
733C22—24no—
734C22—24no—
735C22—21no—
736C22—21no—
737C22—22no—
738C22—21no—
739C22—21no—
740C22—22no—
741C22—21no—
742C22—21no—
743C22—22no—
744C22—22no—
745C22—22no—
746C22—22no—
747C22—42no—
748C22—42no—
749C22—48no—
750C22—48no—
751C22—42no—
752C22—42no—
753C22—42no—
754C22—42no—
755C22—41no—
756C22—41no—
757C22—42no—
758C22—41no—
759C22—42no—
760C22—41no—
761C22—42no—
762C22—41no—
763C22—81no—
764C22—84no—
765C22—84no—
766C22—81no—
767C22—84no—
768C22—162no—
769C22C31×B(4,𝔽2)12yes—
770C22C31×#45812yes—
771C22C2×C31×#12011yescharacteristic
772C22C2×C31×#12311yescharacteristic
773C22C31×#53411yescharacteristic
774C22C31×#54614yes—
775C4—22no—
776C4—41no—
777C4—42no—
778C4—44no—
779C4—42no—
780C4—42no—
781C4—82no—
782C4—84no—
783C2—21no—
784C2—24no—
785C2—21no—
786C2—22no—
787C2—22no—
788C2—42no—
789C2—42no—
790C2—81no—
791C2—82no—
792C2C31×#240511yescharacteristic
793C2C2×C31×B(4,𝔽2)11yescharacteristic
794C2C2×C31×#45811yescharacteristic
subgroupG/H
center, socleC22×C31C2×#120
commutator, Frattini, cosocleC24C24×C31
prime radicalC31×#3484C2
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C31 ◁ C25×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C31×#2849C2semidirect
3. C2×C31×#386C2semidirect
4. C31×#2044C2semidirect
5. C31×#1898C2semidirect
6. C31×#1867C2semidirect
7. C31×#1790C2semidirect
8. C31×#1781C2semidirect
11. C24×C4×C31C22semidirect
25. C22×C22⋊C4×C31C22semidirect
27. C2×C31×#99C22semidirect
28. C2×C31×#99C22semidirect
33. C31×#386C22semidirect
34. C31×#386C22semidirect
36. C31×#385C22semidirect
38. C31×#379C22semidirect
40. C31×#342C22semidirect
236. #24056C31direct (N × H)
282. C23×C31#123semidirect
335. C2×C4×C31#123semidirect
337. #2849C2×C31semidirect
338. C2×#386C2×C31semidirect
339. #2044C2×C31semidirect
340. #1898C2×C31semidirect
341. #1867C2×C31semidirect
342. #1790C2×C31semidirect
343. #1781C2×C31semidirect
396. C24×C4C22×C31semidirect
410. C22×C22⋊C4C22×C31semidirect
412. C2×#99C22×C31semidirect
413. C2×#99C22×C31semidirect
418. #386C22×C31semidirect
419. #386C22×C31semidirect
421. #385C22×C31semidirect
423. #379C22×C31semidirect
425. #342C22×C31semidirect
521. C31#24056direct (N × H)
679. C23C31×#123semidirect
732. C2×C4C31×#123semidirect

Maximal subgroups

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

subgroupindex
C31×#34842
C31×#28492
C2×C31×#3862
C31×#20442
C31×#18982
C31×#18672
C31×#17902
C31×#17812
#2405631