Finite Group Databasebeta

← C31×#16032 #21472791

Subgroups — C31×#16032 #21472791

Order 7936.

2014 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C31×#124C211yesmaximal, characteristic
2C2×C31×#386C211yesmaximal, characteristic
3C2×C31×#385C211yesmaximal, characteristic, complemented
4C2×C31×#381C211yesmaximal, characteristic, complemented
5C31×#1446C212yesmaximal, complemented
6C31×#1440C212yesmaximal, complemented
7C31×#1440C211yesmaximal, characteristic, complemented
8C31×#1440C211yesmaximal, characteristic, complemented
9C31×#1439C212yesmaximal, complemented
10C31×#1438C211yesmaximal, characteristic
11C31×#1436C212yesmaximal, complemented
12C23×Q8×C31C2211yescharacteristic
13C23×D4×C31C2211yescharacteristic
14C24×C4×C31C2211yescharacteristic
15C2×C31×#124—24no—
16C2×C31×#124—24no—
17C2×C31×#124—24no—
18C22×C4⋊C4×C31C2212yes—
19C22×C22⋊C4×C31C2211yescharacteristic
20C22×C22⋊C4×C31C2211yescharacteristic
21C22×C22⋊C4×C31C2211yescharacteristic
22C22×C22⋊C4×C31C2212yes—
23C22×C22⋊C4×C31C2211yescharacteristic
24C22×C22⋊C4×C31C2211yescharacteristic
25C22×C22⋊C4×C31C2212yes—
26C22×C22⋊C4×C31C2211yescharacteristic
27C22×C22⋊C4×C31C2211yescharacteristic
28C22×C42×C31C2211yescharacteristic
29C31×#386—24no—
30C31×#385—24no—
31C31×#381—24no—
32C2×C31×#95C2212yes—
33C2×C31×#95C2212yes—
34C2×C31×#95C2212yes—
35C2×C31×#95C2212yes—
36C2×C31×#95C2212yes—
37C2×C31×#95C2212yes—
38C2×C31×#95C2212yes—
39C2×C31×#95C2212yes—
40C2×C31×#95C2212yes—
41C25×C31C2311yescharacteristic
42C25×C31C2311yescharacteristic
43C22×Q8×C31—22no—
44C22×Q8×C31—22no—
45C22×Q8×C31—22no—
46C22×Q8×C31—24no—
47C22×Q8×C31—42no—
48C22×D4×C31—22no—
49C22×D4×C31—22no—
50C22×D4×C31—24no—
51C22×D4×C31—42no—
52C22×D4×C31D414yes—
53C23×C4×C31—22no—
54C23×C4×C31—24no—
55C23×C4×C31—22no—
56C23×C4×C31—22no—
57C23×C4×C31—42no—
58C23×C4×C31C2312yes—
59C23×C4×C31C2312yes—
60C23×C4×C31C2311yescharacteristic
61C23×C4×C31C2311yescharacteristic
62C23×C4×C31C2311yescharacteristic
63C23×C4×C31C2311yescharacteristic
64C23×C4×C31C2312yes—
65C23×C4×C31C2312yes—
66C23×C4×C31C2311yescharacteristic
67C31×#124—232no—
68C2×C4⋊C4×C31—24no—
69C2×C4⋊C4×C31—24no—
70C2×C4⋊C4×C31—42no—
71C2×C22⋊C4×C31—22no—
72C2×C22⋊C4×C31—22no—
73C2×C22⋊C4×C31—22no—
74C2×C22⋊C4×C31—22no—
75C2×C22⋊C4×C31—22no—
76C2×C22⋊C4×C31—22no—
77C2×C22⋊C4×C31—22no—
78C2×C22⋊C4×C31—22no—
79C2×C22⋊C4×C31—22no—
80C2×C22⋊C4×C31—22no—
81C2×C22⋊C4×C31—22no—
82C2×C22⋊C4×C31—24no—
83C2×C22⋊C4×C31—22no—
84C2×C22⋊C4×C31—24no—
85C2×C22⋊C4×C31—22no—
86C2×C22⋊C4×C31—24no—
87C2×C22⋊C4×C31—24no—
88C2×C22⋊C4×C31—42no—
89C2×C22⋊C4×C31—42no—
90C2×C22⋊C4×C31—42no—
91C2×C22⋊C4×C31—42no—
92C2×C22⋊C4×C31—42no—
93C2×C22⋊C4×C31D414yes—
94C2×C22⋊C4×C31D414yes—
95C2×C42×C31—22no—
96C2×C42×C31—22no—
97C2×C42×C31—22no—
98C31×#95—24no—
99C31×#95—24no—
100C31×#95—24no—
101C31×#95—24no—
102C31×#95—24no—
103C31×#95—24no—
104C31×#95—42no—
105C31×#95—42no—
106C31×#95—42no—
107C24×C31—22no—
108C24×C31—22no—
109C24×C31—22no—
110C24×C31—22no—
111C24×C31—22no—
112C24×C31—22no—
113C24×C31—21no—
114C24×C31—21no—
115C24×C31—22no—
116C24×C31—22no—
117C24×C31—22no—
118C24×C31—22no—
119C24×C31—22no—
120C24×C31—22no—
121C24×C31C2×D412yes—
122C24×C31C2×D412yes—
123C24×C31C2×D412yes—
124C24×C31C2×D412yes—
125C24×C31C2411yescharacteristic
126C2×Q8×C31—28no—
127C2×Q8×C31—48no—
128C2×Q8×C31—48no—
129C2×Q8×C31—44no—
130C2×Q8×C31—44no—
131C2×D4×C31—28no—
132C2×D4×C31—28no—
133C2×D4×C31—44no—
134C2×D4×C31—48no—
135C2×D4×C31—48no—
136C22×C4×C31—21no—
137C22×C4×C31—21no—
138C22×C4×C31—22no—
139C22×C4×C31—28no—
140C22×C4×C31—22no—
141C22×C4×C31—22no—
142C22×C4×C31—22no—
143C22×C4×C31—22no—
144C22×C4×C31—21no—
145C22×C4×C31—21no—
146C22×C4×C31—21no—
147C22×C4×C31—21no—
148C22×C4×C31—21no—
149C22×C4×C31—21no—
150C22×C4×C31—21no—
151C22×C4×C31—21no—
152C22×C4×C31—22no—
153C22×C4×C31—22no—
154C22×C4×C31—22no—
155C22×C4×C31—22no—
156C22×C4×C31—22no—
157C22×C4×C31—22no—
158C22×C4×C31—22no—
159C22×C4×C31—22no—
160C22×C4×C31—22no—
161C22×C4×C31—22no—
162C22×C4×C31—22no—
163C22×C4×C31—22no—
164C22×C4×C31—22no—
165C22×C4×C31—22no—
166C22×C4×C31—22no—
167C22×C4×C31—22no—
168C22×C4×C31—22no—
169C22×C4×C31—22no—
170C22×C4×C31—22no—
171C22×C4×C31—22no—
172C22×C4×C31—22no—
173C22×C4×C31—22no—
174C22×C4×C31—22no—
175C22×C4×C31—22no—
176C22×C4×C31—22no—
177C22×C4×C31—22no—
178C22×C4×C31—22no—
179C22×C4×C31—22no—
180C22×C4×C31—22no—
181C22×C4×C31—22no—
182C22×C4×C31—48no—
183C22×C4×C31—48no—
184C22×C4×C31—44no—
185C22×C4×C31—44no—
186C22×C4×C31C2×D412yes—
187C22×C4×C31C2×D412yes—
188C22×C4×C31C2×D412yes—
189C22×C4×C31C2×D412yes—
190C22×C4×C31C2×D412yes—
191C22×C4×C31#4114yes—
192C22×C4×C31#4114yes—
193C22×C4×C31#4114yes—
194C4⋊C4×C31—48no—
195C22⋊C4×C31—28no—
196C22⋊C4×C31—28no—
197C22⋊C4×C31—28no—
198C22⋊C4×C31—28no—
199C22⋊C4×C31—28no—
200C22⋊C4×C31—48no—
201C22⋊C4×C31—48no—
202C22⋊C4×C31—44no—
203C22⋊C4×C31—44no—
204C42×C31—28no—
205#16032C3111yesmaximal, characteristic, direct product factor, Sylow
206C23×C31—22no—
207C23×C31—22no—
208C23×C31—22no—
209C23×C31—22no—
210C23×C31—22no—
211C23×C31—22no—
212C23×C31—24no—
213C23×C31—24no—
214C23×C31—24no—
215C23×C31—24no—
216C23×C31—24no—
217C23×C31—24no—
218C23×C31—22no—
219C23×C31—22no—
220C23×C31—22no—
221C23×C31—24no—
222C23×C31—24no—
223C23×C31—42no—
224C23×C31—42no—
225C23×C31—42no—
226C23×C31—42no—
227C23×C31—42no—
228C23×C31—42no—
229C23×C31—42no—
230C23×C31—42no—
231C23×C31—41no—
232C23×C31—41no—
233C23×C31—42no—
234C23×C31—41no—
235C23×C31—41no—
236C23×C31—42no—
237C23×C31—42no—
238C23×C31—42no—
239C23×C31—42no—
240C23×C31—42no—
241C23×C31—42no—
242C23×C31—42no—
243C23×C31—42no—
244C23×C31—42no—
245C23×C31—42no—
246C23×C31—42no—
247C23×C31#12014yes—
248C23×C31C22×D411yescharacteristic
249C23×C31C22×D411yescharacteristic
250C23×C31C22×D411yescharacteristic
251C23×C31C2×#4112yes—
252C23×C31C2×#4112yes—
253C23×C31C2×#4112yes—
254C23×C31H(5,𝔽2)12yes—
255C23×C31H(5,𝔽2)12yes—
256C23×C312−1+412yes—
257Q8×C31—416no—
258D4×C31—416no—
259C2×C4×C31—22no—
260C2×C4×C31—22no—
261C2×C4×C31—24no—
262C2×C4×C31—24no—
263C2×C4×C31—22no—
264C2×C4×C31—22no—
265C2×C4×C31—22no—
266C2×C4×C31—22no—
267C2×C4×C31—24no—
268C2×C4×C31—24no—
269C2×C4×C31—24no—
270C2×C4×C31—24no—
271C2×C4×C31—24no—
272C2×C4×C31—24no—
273C2×C4×C31—24no—
274C2×C4×C31—24no—
275C2×C4×C31—24no—
276C2×C4×C31—24no—
277C2×C4×C31—416no—
278C2×C4×C31—42no—
279C2×C4×C31—41no—
280C2×C4×C31—41no—
281C2×C4×C31—41no—
282C2×C4×C31—41no—
283C2×C4×C31—41no—
284C2×C4×C31—41no—
285C2×C4×C31—41no—
286C2×C4×C31—42no—
287C2×C4×C31—41no—
288C2×C4×C31—42no—
289C2×C4×C31—42no—
290C2×C4×C31—42no—
291C2×C4×C31—42no—
292C2×C4×C31—42no—
293C2×C4×C31—42no—
294C2×C4×C31—42no—
295C2×C4×C31—42no—
296C2×C4×C31—42no—
297C2×C4×C31—42no—
298C2×C4×C31—42no—
299C2×C4×C31—42no—
300C2×C4×C31—42no—
301C2×C4×C31—42no—
302C2×C4×C31—42no—
303C2×C4×C31—42no—
304C2×C4×C31—42no—
305C2×C4×C31—42no—
306C2×C4×C31—42no—
307C2×C4×C31—42no—
308C2×C4×C31—42no—
309C2×C4×C31—42no—
310C2×C4×C31—42no—
311C2×C4×C31—42no—
312C2×C4×C31#12314yes—
313C22×#124C2×C3111yescharacteristic
314C2×#386C2×C3111yescharacteristic
315C2×#385C2×C3111yescharacteristic, complemented
316C2×#381C2×C3111yescharacteristic, complemented
317#1446C2×C3112yescomplemented
318#1440C2×C3112yescomplemented
319#1440C2×C3111yescharacteristic, complemented
320#1440C2×C3111yescharacteristic, complemented
321#1439C2×C3112yescomplemented
322#1438C2×C3111yescharacteristic
323#1436C2×C3112yescomplemented
324C22×C31—24no—
325C22×C31—24no—
326C22×C31—24no—
327C22×C31—44no—
328C22×C31—44no—
329C22×C31—44no—
330C22×C31—44no—
331C22×C31—44no—
332C22×C31—44no—
333C22×C31—42no—
334C22×C31—42no—
335C22×C31—42no—
336C22×C31—44no—
337C22×C31—44no—
338C22×C31—82no—
339C22×C31—82no—
340C22×C31—82no—
341C22×C31—82no—
342C22×C31C2×#12011yescharacteristic
343C22×C31C2×#12311yescharacteristic
344C22×C31#52511yescharacteristic
345C22×C31#52511yescharacteristic
346C22×C31#52912yes—
347C22×C31#53411yescharacteristic
348C22×C31#53511yescharacteristic
349C22×C31#53611yescharacteristic
350C22×C31#53812yes—
351C22×C31#54212yes—
352C22×C31#54212yes—
353C22×C31#54612yes—
354C22×C31#54612yes—
355C22×C31#54612yes—
356C22×C31#54612yes—
357C22×C31#54712yes—
358C22×C31#54712yes—
359C22×C31#55512yes—
360C22×C31#55612yes—
361C22×C31#55912yes—
362C22×C31#56212yes—
363C4×C31—24no—
364C4×C31—42no—
365C4×C31—44no—
366C4×C31—42no—
367C4×C31—42no—
368C4×C31—42no—
369C4×C31—44no—
370C4×C31—82no—
371C4×C31—82no—
372C23×Q8C22×C3111yescharacteristic
373C23×D4C22×C3111yescharacteristic
374C24×C4C22×C3111yescharacteristic
375C2×#124—24no—
376C2×#124—24no—
377C2×#124—24no—
378C22×C4⋊C4C22×C3112yes—
379C22×C22⋊C4C22×C3111yescharacteristic
380C22×C22⋊C4C22×C3111yescharacteristic
381C22×C22⋊C4C22×C3111yescharacteristic
382C22×C22⋊C4C22×C3112yes—
383C22×C22⋊C4C22×C3111yescharacteristic
384C22×C22⋊C4C22×C3111yescharacteristic
385C22×C22⋊C4C22×C3112yes—
386C22×C22⋊C4C22×C3111yescharacteristic
387C22×C22⋊C4C22×C3111yescharacteristic
388C22×C42C22×C3111yescharacteristic
389#386—24no—
390#385—24no—
391#381—24no—
392C2×#95C22×C3112yes—
393C2×#95C22×C3112yes—
394C2×#95C22×C3112yes—
395C2×#95C22×C3112yes—
396C2×#95C22×C3112yes—
397C2×#95C22×C3112yes—
398C2×#95C22×C3112yes—
399C2×#95C22×C3112yes—
400C2×#95C22×C3112yes—
401C2×C31—44no—
402C2×C31—82no—
403C2×C31#240411yescharacteristic
404C2×C31#240511yescharacteristic
405C2×C31#240611yescharacteristic
406C2×C31#244712yes—
407C2×C31#245912yes—
408C2×C31#247412yes—
409C2×C31#268612yes—
410C2×C31#270012yes—
411C2×C31#271012yes—
412C25C23×C3111yescharacteristic
413C25C23×C3111yescharacteristic
414C22×Q8—22no—
415C22×Q8—22no—
416C22×Q8—22no—
417C22×Q8—24no—
418C22×Q8—42no—
419C22×D4—22no—
420C22×D4—22no—
421C22×D4—24no—
422C22×D4—42no—
423C22×D4D4×C3114yes—
424C23×C4—22no—
425C23×C4—24no—
426C23×C4—22no—
427C23×C4—22no—
428C23×C4—42no—
429C23×C4C23×C3112yes—
430C23×C4C23×C3112yes—
431C23×C4C23×C3111yescharacteristic
432C23×C4C23×C3111yescharacteristic
433C23×C4C23×C3111yescharacteristic
434C23×C4C23×C3111yescharacteristic
435C23×C4C23×C3112yes—
436C23×C4C23×C3112yes—
437C23×C4C23×C3111yescharacteristic
438#124—232no—
439C2×C4⋊C4—24no—
440C2×C4⋊C4—24no—
441C2×C4⋊C4—42no—
442C2×C22⋊C4—22no—
443C2×C22⋊C4—22no—
444C2×C22⋊C4—22no—
445C2×C22⋊C4—22no—
446C2×C22⋊C4—22no—
447C2×C22⋊C4—22no—
448C2×C22⋊C4—22no—
449C2×C22⋊C4—22no—
450C2×C22⋊C4—22no—
451C2×C22⋊C4—22no—
452C2×C22⋊C4—22no—
453C2×C22⋊C4—24no—
454C2×C22⋊C4—22no—
455C2×C22⋊C4—24no—
456C2×C22⋊C4—22no—
457C2×C22⋊C4—24no—
458C2×C22⋊C4—24no—
459C2×C22⋊C4—42no—
460C2×C22⋊C4—42no—
461C2×C22⋊C4—42no—
462C2×C22⋊C4—42no—
463C2×C22⋊C4—42no—
464C2×C22⋊C4D4×C3114yes—
465C2×C22⋊C4D4×C3114yes—
466C2×C42—22no—
467C2×C42—22no—
468C2×C42—22no—
469#95—24no—
470#95—24no—
471#95—24no—
472#95—24no—
473#95—24no—
474#95—24no—
475#95—42no—
476#95—42no—
477#95—42no—
478C31#1603211yescharacteristic, direct product factor, Sylow
479C24—22no—
480C24—22no—
481C24—22no—
482C24—22no—
483C24—22no—
484C24—22no—
485C24—21no—
486C24—21no—
487C24—22no—
488C24—22no—
489C24—22no—
490C24—22no—
491C24—22no—
492C24—22no—
493C24C2×D4×C3112yes—
494C24C2×D4×C3112yes—
495C24C2×D4×C3112yes—
496C24C2×D4×C3112yes—
497C24C24×C3111yescharacteristic
498C2×Q8—28no—
499C2×Q8—48no—
500C2×Q8—48no—
501C2×Q8—44no—
502C2×Q8—44no—
503C2×D4—28no—
504C2×D4—28no—
505C2×D4—44no—
506C2×D4—48no—
507C2×D4—48no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—22no—
511C22×C4—28no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—48no—
555C22×C4—48no—
556C22×C4—44no—
557C22×C4—44no—
558C22×C4C2×D4×C3112yes—
559C22×C4C2×D4×C3112yes—
560C22×C4C2×D4×C3112yes—
561C22×C4C2×D4×C3112yes—
562C22×C4C2×D4×C3112yes—
563C22×C4#41×C3114yes—
564C22×C4#41×C3114yes—
565C22×C4#41×C3114yes—
566C4⋊C4—48no—
567C22⋊C4—28no—
568C22⋊C4—28no—
569C22⋊C4—28no—
570C22⋊C4—28no—
571C22⋊C4—28no—
572C22⋊C4—48no—
573C22⋊C4—48no—
574C22⋊C4—44no—
575C22⋊C4—44no—
576C42—28no—
577C23—22no—
578C23—22no—
579C23—22no—
580C23—22no—
581C23—22no—
582C23—22no—
583C23—24no—
584C23—24no—
585C23—24no—
586C23—24no—
587C23—24no—
588C23—24no—
589C23—22no—
590C23—22no—
591C23—22no—
592C23—24no—
593C23—24no—
594C23—42no—
595C23—42no—
596C23—42no—
597C23—42no—
598C23—42no—
599C23—42no—
600C23—42no—
601C23—42no—
602C23—41no—
603C23—41no—
604C23—42no—
605C23—41no—
606C23—41no—
607C23—42no—
608C23—42no—
609C23—42no—
610C23—42no—
611C23—42no—
612C23—42no—
613C23—42no—
614C23—42no—
615C23—42no—
616C23—42no—
617C23—42no—
618C23C31×#12014yes—
619C23C22×D4×C3111yescharacteristic
620C23C22×D4×C3111yescharacteristic
621C23C22×D4×C3111yescharacteristic
622C23C2×#41×C3112yes—
623C23C2×#41×C3112yes—
624C23C2×#41×C3112yes—
625C23C31×H(5,𝔽2)12yes—
626C23C31×H(5,𝔽2)12yes—
627C23C31×2−1+412yes—
628Q8—416no—
629D4—416no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—24no—
633C2×C4—24no—
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—24no—
639C2×C4—24no—
640C2×C4—24no—
641C2×C4—24no—
642C2×C4—24no—
643C2×C4—24no—
644C2×C4—24no—
645C2×C4—24no—
646C2×C4—24no—
647C2×C4—24no—
648C2×C4—416no—
649C2×C4—42no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—42no—
658C2×C4—41no—
659C2×C4—42no—
660C2×C4—42no—
661C2×C4—42no—
662C2×C4—42no—
663C2×C4—42no—
664C2×C4—42no—
665C2×C4—42no—
666C2×C4—42no—
667C2×C4—42no—
668C2×C4—42no—
669C2×C4—42no—
670C2×C4—42no—
671C2×C4—42no—
672C2×C4—42no—
673C2×C4—42no—
674C2×C4—42no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4C31×#12314yes—
684C22—24no—
685C22—24no—
686C22—24no—
687C22—44no—
688C22—44no—
689C22—44no—
690C22—44no—
691C22—44no—
692C22—44no—
693C22—42no—
694C22—42no—
695C22—42no—
696C22—44no—
697C22—44no—
698C22—82no—
699C22—82no—
700C22—82no—
701C22—82no—
702C22C2×C31×#12011yescharacteristic
703C22C2×C31×#12311yescharacteristic
704C22C31×#52511yescharacteristic
705C22C31×#52511yescharacteristic
706C22C31×#52912yes—
707C22C31×#53411yescharacteristic
708C22C31×#53511yescharacteristic
709C22C31×#53611yescharacteristic
710C22C31×#53812yes—
711C22C31×#54212yes—
712C22C31×#54212yes—
713C22C31×#54612yes—
714C22C31×#54612yes—
715C22C31×#54612yes—
716C22C31×#54612yes—
717C22C31×#54712yes—
718C22C31×#54712yes—
719C22C31×#55512yes—
720C22C31×#55612yes—
721C22C31×#55912yes—
722C22C31×#56212yes—
723C4—24no—
724C4—44no—
725C4—42no—
726C4—42no—
727C4—42no—
728C4—42no—
729C4—44no—
730C4—82no—
731C4—82no—
732C2—44no—
733C2—82no—
734C2C31×#240411yescharacteristic
735C2C31×#240511yescharacteristic
736C2C31×#240611yescharacteristic
737C2C31×#244712yes—
738C2C31×#245912yes—
739C2C31×#247412yes—
740C2C31×#268612yes—
741C2C31×#270012yes—
742C2C31×#271012yes—
subgroupG/H
center, socleC24×C31C24
commutator, Frattini, cosocleC24C24×C31
prime radicalC23×D4×C31C22
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C31 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×C31×#385C2semidirect
4. C2×C31×#381C2semidirect
5. C31×#1446C2semidirect
6. C31×#1440C2semidirect
7. C31×#1440C2semidirect
8. C31×#1440C2semidirect
9. C31×#1439C2semidirect
11. C31×#1436C2semidirect
205. #16032C31direct (N × H)
315. C2×#385C2×C31semidirect
316. C2×#381C2×C31semidirect
317. #1446C2×C31semidirect
318. #1440C2×C31semidirect
319. #1440C2×C31semidirect
320. #1440C2×C31semidirect
321. #1439C2×C31semidirect
323. #1436C2×C31semidirect
478. C31#16032direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C31×#1242
C2×C31×#3862
C2×C31×#3852
C2×C31×#3812
C31×#14462
C31×#14402
C31×#14392
C31×#14382
C31×#14362
#1603231