Finite Group Databasebeta

← C31×#14716 #21471475

Subgroups — C31×#14716 #21471475

Order 7936.

4878 conjugacy classes of subgroups.

The subgroup lattice has 784 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C31×#121C211yesmaximal, characteristic, complemented
2C22×C31×#120C212yesmaximal, complemented
3C23×C22⋊C4×C31C211yesmaximal, characteristic, complemented
4C2×C31×#392C212yesmaximal, complemented
5C2×C31×#386C212yesmaximal, complemented
6C31×#1439C212yesmaximal, complemented
7C31×#1438C214yesmaximal, complemented
8C31×C22⋊#95C211yesmaximal, characteristic, complemented
9C26×C31C2211yescharacteristic
10C23×D4×C31C2212yes—
11C23×D4×C31C2214yes—
12C23×D4×C31C2211yescharacteristic, complemented
13C24×C4×C31C2211yescharacteristic
14C24×C4×C31C2211yescharacteristic
15C2×C31×#121—28no—
16C2×C31×#121—24no—
17C2×C31×#120—28no—
18C2×C31×#120—28no—
19C2×C31×#120—28no—
20C22×C4⋊C4×C31C2211yescharacteristic, complemented
21C22×C22⋊C4×C31—24no—
22C22×C22⋊C4×C31—28no—
23C22×C22⋊C4×C31C2212yes—
24C22×C22⋊C4×C31C2214yes—
25C22×C22⋊C4×C31C2212yes—
26C22×C22⋊C4×C31C2212yes—
27C22×C22⋊C4×C31C2212yescomplemented
28C22×C22⋊C4×C31C2214yescomplemented
29C31×#392—28no—
30C31×#386—28no—
31C2×C31×#95C2212yescomplemented
32C2×C31×#95C2214yescomplemented
33C2×C31×#95C2212yescomplemented
34C25×C31—24no—
35C25×C31—22no—
36C25×C31—24no—
37C25×C31—22no—
38C25×C31—24no—
39C25×C31—24no—
40C25×C31—42no—
41C25×C31—42no—
42C25×C31D414yescomplemented
43C25×C31C2312yes—
44C25×C31C2312yes—
45C25×C31C2311yescharacteristic
46C22×D4×C31—28no—
47C22×D4×C31—28no—
48C22×D4×C31—24no—
49C22×D4×C31—24no—
50C22×D4×C31—24no—
51C22×D4×C31—24no—
52C22×D4×C31—24no—
53C22×D4×C31—24no—
54C22×D4×C31—24no—
55C22×D4×C31—28no—
56C22×D4×C31—28no—
57C22×D4×C31—28no—
58C22×D4×C31—22no—
59C22×D4×C31—24no—
60C22×D4×C31—44no—
61C22×D4×C31—44no—
62C22×D4×C31—42no—
63C22×D4×C31D418yescomplemented
64C23×C4×C31—22no—
65C23×C4×C31—24no—
66C23×C4×C31—24no—
67C23×C4×C31—24no—
68C23×C4×C31—24no—
69C23×C4×C31—42no—
70C23×C4×C31—42no—
71C23×C4×C31D414yescomplemented
72C23×C4×C31C2312yes—
73C23×C4×C31C2311yescharacteristic
74C23×C4×C31C2312yes—
75C23×C4×C31C2314yes—
76C23×C4×C31C2311yescharacteristic
77C31×#121—232no—
78C31×#120—264no—
79C2×C4⋊C4×C31—24no—
80C2×C4⋊C4×C31—22no—
81C2×C22⋊C4×C31—232no—
82C2×C22⋊C4×C31—24no—
83C2×C22⋊C4×C31—28no—
84C2×C22⋊C4×C31—24no—
85C2×C22⋊C4×C31—24no—
86C2×C22⋊C4×C31—24no—
87C2×C22⋊C4×C31—24no—
88C2×C22⋊C4×C31—24no—
89C2×C22⋊C4×C31—24no—
90C2×C22⋊C4×C31—24no—
91C2×C22⋊C4×C31—28no—
92C2×C22⋊C4×C31—28no—
93C2×C22⋊C4×C31—24no—
94C2×C22⋊C4×C31—24no—
95C2×C22⋊C4×C31—28no—
96C2×C22⋊C4×C31—28no—
97C2×C22⋊C4×C31—44no—
98C2×C22⋊C4×C31D418yescomplemented
99C2×C22⋊C4×C31D418yescomplemented
100C31×#95—28no—
101C31×#95—24no—
102C31×#95—42no—
103C24×C31—22no—
104C24×C31—22no—
105C24×C31—22no—
106C24×C31—22no—
107C24×C31—28no—
108C24×C31—28no—
109C24×C31—216no—
110C24×C31—28no—
111C24×C31—216no—
112C24×C31—22no—
113C24×C31—22no—
114C24×C31—24no—
115C24×C31—24no—
116C24×C31—22no—
117C24×C31—22no—
118C24×C31—24no—
119C24×C31—24no—
120C24×C31—216no—
121C24×C31—22no—
122C24×C31—22no—
123C24×C31—22no—
124C24×C31—24no—
125C24×C31—22no—
126C24×C31—22no—
127C24×C31—22no—
128C24×C31—24no—
129C24×C31—24no—
130C24×C31—24no—
131C24×C31—48no—
132C24×C31—416no—
133C24×C31—416no—
134C24×C31—416no—
135C24×C31—416no—
136C24×C31—44no—
137C24×C31—44no—
138C24×C31—48no—
139C24×C31—44no—
140C24×C31—48no—
141C24×C31—44no—
142C24×C31C2×D414yes—
143C24×C31C2×D414yes—
144C24×C31C2×D414yes—
145C24×C31C2×D412yes—
146C24×C31C2×D414yes—
147C24×C31C2×D414yes—
148C24×C31C2×D412yes—
149C24×C31#4114yes—
150C24×C31#4112yes—
151C24×C31C2411yescharacteristic
152C2×D4×C31—232no—
153C2×D4×C31—28no—
154C2×D4×C31—216no—
155C2×D4×C31—216no—
156C2×D4×C31—216no—
157C2×D4×C31—416no—
158C2×D4×C31—416no—
159C2×D4×C31—416no—
160C2×D4×C31—44no—
161C2×D4×C31—416no—
162C2×D4×C31—416no—
163C2×D4×C31—416no—
164C2×D4×C31—48no—
165C2×D4×C31—48no—
166C2×D4×C31—48no—
167C2×D4×C31—416no—
168C2×D4×C31—48no—
169C2×D4×C31—44no—
170C22×C4×C31—22no—
171C22×C4×C31—22no—
172C22×C4×C31—28no—
173C22×C4×C31—28no—
174C22×C4×C31—22no—
175C22×C4×C31—24no—
176C22×C4×C31—24no—
177C22×C4×C31—22no—
178C22×C4×C31—22no—
179C22×C4×C31—22no—
180C22×C4×C31—22no—
181C22×C4×C31—22no—
182C22×C4×C31—22no—
183C22×C4×C31—24no—
184C22×C4×C31—24no—
185C22×C4×C31—22no—
186C22×C4×C31—22no—
187C22×C4×C31—22no—
188C22×C4×C31—24no—
189C22×C4×C31—22no—
190C22×C4×C31—24no—
191C22×C4×C31—24no—
192C22×C4×C31—24no—
193C22×C4×C31—28no—
194C22×C4×C31—44no—
195C22×C4×C31—416no—
196C22×C4×C31—416no—
197C22×C4×C31—44no—
198C22×C4×C31—44no—
199C22×C4×C31C2×D418yes—
200C22×C4×C31C2×D412yes—
201C22×C4×C31C2×D414yes—
202C22×C4×C31C2×D414yes—
203C22×C4×C31C2×D414yes—
204C22×C4×C31C2×D412yes—
205C4⋊C4×C31—28no—
206C22⋊C4×C31—216no—
207C22⋊C4×C31—232no—
208C22⋊C4×C31—216no—
209C22⋊C4×C31—216no—
210C22⋊C4×C31—216no—
211C22⋊C4×C31—416no—
212#14716C3111yesmaximal, characteristic, direct product factor, Sylow
213C23×C31—22no—
214C23×C31—24no—
215C23×C31—22no—
216C23×C31—24no—
217C23×C31—22no—
218C23×C31—24no—
219C23×C31—22no—
220C23×C31—24no—
221C23×C31—28no—
222C23×C31—28no—
223C23×C31—28no—
224C23×C31—28no—
225C23×C31—232no—
226C23×C31—24no—
227C23×C31—28no—
228C23×C31—24no—
229C23×C31—24no—
230C23×C31—24no—
231C23×C31—24no—
232C23×C31—24no—
233C23×C31—28no—
234C23×C31—28no—
235C23×C31—28no—
236C23×C31—28no—
237C23×C31—28no—
238C23×C31—24no—
239C23×C31—24no—
240C23×C31—24no—
241C23×C31—28no—
242C23×C31—28no—
243C23×C31—464no—
244C23×C31—416no—
245C23×C31—416no—
246C23×C31—416no—
247C23×C31—464no—
248C23×C31—416no—
249C23×C31—416no—
250C23×C31—42no—
251C23×C31—44no—
252C23×C31—42no—
253C23×C31—42no—
254C23×C31—42no—
255C23×C31—44no—
256C23×C31—44no—
257C23×C31—44no—
258C23×C31—44no—
259C23×C31—44no—
260C23×C31—416no—
261C23×C31—42no—
262C23×C31—42no—
263C23×C31—42no—
264C23×C31—42no—
265C23×C31—44no—
266C23×C31—42no—
267C23×C31—44no—
268C23×C31—42no—
269C23×C31—42no—
270C23×C31—44no—
271C23×C31—42no—
272C23×C31—44no—
273C23×C31—44no—
274C23×C31—44no—
275C23×C31—44no—
276C23×C31—44no—
277C23×C31—44no—
278C23×C31—44no—
279C23×C31#12018yes—
280C23×C31#12014yes—
281C23×C31#12118yes—
282C23×C31#12114yes—
283C23×C31#12118yescomplemented
284C23×C31#12714yes—
285C23×C31C22×D411yescharacteristic
286C23×C31C22×D411yescharacteristic
287C23×C31C22×D412yes—
288C23×C31C22×D412yes—
289C23×C31C22×D412yes—
290C23×C31C2×#4111yescharacteristic
291C23×C31C2×#4112yes—
292C23×C31H(5,𝔽2)12yes—
293C23×C31H(5,𝔽2)12yes—
294D4×C31—416no—
295D4×C31—464no—
296D4×C31—432no—
297C2×C4×C31—22no—
298C2×C4×C31—22no—
299C2×C4×C31—28no—
300C2×C4×C31—22no—
301C2×C4×C31—22no—
302C2×C4×C31—24no—
303C2×C4×C31—24no—
304C2×C4×C31—28no—
305C2×C4×C31—24no—
306C2×C4×C31—24no—
307C2×C4×C31—22no—
308C2×C4×C31—28no—
309C2×C4×C31—28no—
310C2×C4×C31—28no—
311C2×C4×C31—416no—
312C2×C4×C31—416no—
313C2×C4×C31—42no—
314C2×C4×C31—42no—
315C2×C4×C31—42no—
316C2×C4×C31—44no—
317C2×C4×C31—42no—
318C2×C4×C31—42no—
319C2×C4×C31—44no—
320C2×C4×C31—42no—
321C2×C4×C31—44no—
322C2×C4×C31—44no—
323C2×C4×C31—44no—
324C2×C4×C31—44no—
325C2×C4×C31#12014yescomplemented
326C22×#121C2×C3111yescharacteristic, complemented
327C22×#120C2×C3112yescomplemented
328C23×C22⋊C4C2×C3111yescharacteristic, complemented
329C2×#392C2×C3112yescomplemented
330C2×#386C2×C3112yescomplemented
331#1439C2×C3112yescomplemented
332#1438C2×C3114yescomplemented
333C22⋊#95C2×C3111yescharacteristic, complemented
334C22×C31—24no—
335C22×C31—24no—
336C22×C31—24no—
337C22×C31—24no—
338C22×C31—216no—
339C22×C31—216no—
340C22×C31—24no—
341C22×C31—24no—
342C22×C31—28no—
343C22×C31—216no—
344C22×C31—464no—
345C22×C31—44no—
346C22×C31—44no—
347C22×C31—44no—
348C22×C31—44no—
349C22×C31—48no—
350C22×C31—48no—
351C22×C31—48no—
352C22×C31—44no—
353C22×C31—44no—
354C22×C31—44no—
355C22×C31—44no—
356C22×C31—44no—
357C22×C31—48no—
358C22×C31—48no—
359C22×C31—82no—
360C22×C31—82no—
361C22×C31—84no—
362C22×C31—84no—
363C22×C31—82no—
364C22×C31—82no—
365C22×C31#39218yescomplemented
366C22×C31C2×#12011yescharacteristic
367C22×C31C2×#12011yescharacteristic
368C22×C31C2×#12012yes—
369C22×C31C2×#12111yescharacteristic
370C22×C31C2×#12112yes—
371C22×C31C2×#12112yes—
372C22×C31#52511yescharacteristic
373C22×C31#52512yes—
374C22×C31C2×#12711yescharacteristic
375C22×C31#53411yescharacteristic
376C22×C31#53412yes—
377C22×C31#53511yescharacteristic
378C22×C31#53812yes—
379C22×C31D4214yes—
380C22×C31D4214yes—
381C22×C31#54614yes—
382C22×C31#54614yes—
383C4×C31—24no—
384C4×C31—44no—
385C4×C31—42no—
386C4×C31—48no—
387C4×C31—44no—
388C26C22×C3111yescharacteristic
389C23×D4C22×C3112yes—
390C23×D4C22×C3114yes—
391C23×D4C22×C3111yescharacteristic, complemented
392C24×C4C22×C3111yescharacteristic
393C24×C4C22×C3111yescharacteristic
394C2×#121—28no—
395C2×#121—24no—
396C2×#120—28no—
397C2×#120—28no—
398C2×#120—28no—
399C22×C4⋊C4C22×C3111yescharacteristic, complemented
400C22×C22⋊C4—24no—
401C22×C22⋊C4—28no—
402C22×C22⋊C4C22×C3112yes—
403C22×C22⋊C4C22×C3114yes—
404C22×C22⋊C4C22×C3112yes—
405C22×C22⋊C4C22×C3112yes—
406C22×C22⋊C4C22×C3112yescomplemented
407C22×C22⋊C4C22×C3114yescomplemented
408#392—28no—
409#386—28no—
410C2×#95C22×C3112yescomplemented
411C2×#95C22×C3114yescomplemented
412C2×#95C22×C3112yescomplemented
413C2×C31—28no—
414C2×C31—48no—
415C2×C31—84no—
416C2×C31C2×#39211yescharacteristic
417C2×C31#240311yescharacteristic
418C2×C31#240411yescharacteristic
419C2×C31#241014yes—
420C2×C31#242414yes—
421C2×C31#243311yescharacteristic
422C2×C31#253911yescharacteristic
423C2×C31#261711yescharacteristic
424C2×C31#284711yescharacteristic
425C25—24no—
426C25—22no—
427C25—24no—
428C25—22no—
429C25—24no—
430C25—24no—
431C25—42no—
432C25—42no—
433C25D4×C3114yescomplemented
434C25C23×C3112yes—
435C25C23×C3112yes—
436C25C23×C3111yescharacteristic
437C22×D4—28no—
438C22×D4—28no—
439C22×D4—24no—
440C22×D4—24no—
441C22×D4—24no—
442C22×D4—24no—
443C22×D4—24no—
444C22×D4—24no—
445C22×D4—24no—
446C22×D4—28no—
447C22×D4—28no—
448C22×D4—28no—
449C22×D4—22no—
450C22×D4—24no—
451C22×D4—44no—
452C22×D4—44no—
453C22×D4—42no—
454C22×D4D4×C3118yescomplemented
455C23×C4—22no—
456C23×C4—24no—
457C23×C4—24no—
458C23×C4—24no—
459C23×C4—24no—
460C23×C4—42no—
461C23×C4—42no—
462C23×C4D4×C3114yescomplemented
463C23×C4C23×C3112yes—
464C23×C4C23×C3111yescharacteristic
465C23×C4C23×C3112yes—
466C23×C4C23×C3114yes—
467C23×C4C23×C3111yescharacteristic
468#121—232no—
469#120—264no—
470C2×C4⋊C4—24no—
471C2×C4⋊C4—22no—
472C2×C22⋊C4—232no—
473C2×C22⋊C4—24no—
474C2×C22⋊C4—28no—
475C2×C22⋊C4—24no—
476C2×C22⋊C4—24no—
477C2×C22⋊C4—24no—
478C2×C22⋊C4—24no—
479C2×C22⋊C4—24no—
480C2×C22⋊C4—24no—
481C2×C22⋊C4—24no—
482C2×C22⋊C4—28no—
483C2×C22⋊C4—28no—
484C2×C22⋊C4—24no—
485C2×C22⋊C4—24no—
486C2×C22⋊C4—28no—
487C2×C22⋊C4—28no—
488C2×C22⋊C4—44no—
489C2×C22⋊C4D4×C3118yescomplemented
490C2×C22⋊C4D4×C3118yescomplemented
491#95—28no—
492#95—24no—
493#95—42no—
494C31#1471611yescharacteristic, direct product factor, Sylow
495C24—22no—
496C24—22no—
497C24—22no—
498C24—22no—
499C24—28no—
500C24—28no—
501C24—216no—
502C24—28no—
503C24—216no—
504C24—22no—
505C24—22no—
506C24—24no—
507C24—24no—
508C24—22no—
509C24—22no—
510C24—24no—
511C24—24no—
512C24—216no—
513C24—22no—
514C24—22no—
515C24—22no—
516C24—24no—
517C24—22no—
518C24—22no—
519C24—22no—
520C24—24no—
521C24—24no—
522C24—24no—
523C24—48no—
524C24—416no—
525C24—416no—
526C24—416no—
527C24—416no—
528C24—44no—
529C24—44no—
530C24—48no—
531C24—44no—
532C24—48no—
533C24—44no—
534C24C2×D4×C3114yes—
535C24C2×D4×C3114yes—
536C24C2×D4×C3114yes—
537C24C2×D4×C3112yes—
538C24C2×D4×C3114yes—
539C24C2×D4×C3114yes—
540C24C2×D4×C3112yes—
541C24#41×C3114yes—
542C24#41×C3112yes—
543C24C24×C3111yescharacteristic
544C2×D4—232no—
545C2×D4—28no—
546C2×D4—216no—
547C2×D4—216no—
548C2×D4—216no—
549C2×D4—416no—
550C2×D4—416no—
551C2×D4—416no—
552C2×D4—44no—
553C2×D4—416no—
554C2×D4—416no—
555C2×D4—416no—
556C2×D4—48no—
557C2×D4—48no—
558C2×D4—48no—
559C2×D4—416no—
560C2×D4—48no—
561C2×D4—44no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—28no—
565C22×C4—28no—
566C22×C4—22no—
567C22×C4—24no—
568C22×C4—24no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—24no—
576C22×C4—24no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—24no—
581C22×C4—22no—
582C22×C4—24no—
583C22×C4—24no—
584C22×C4—24no—
585C22×C4—28no—
586C22×C4—44no—
587C22×C4—416no—
588C22×C4—416no—
589C22×C4—44no—
590C22×C4—44no—
591C22×C4C2×D4×C3118yes—
592C22×C4C2×D4×C3112yes—
593C22×C4C2×D4×C3114yes—
594C22×C4C2×D4×C3114yes—
595C22×C4C2×D4×C3114yes—
596C22×C4C2×D4×C3112yes—
597C4⋊C4—28no—
598C22⋊C4—216no—
599C22⋊C4—232no—
600C22⋊C4—216no—
601C22⋊C4—216no—
602C22⋊C4—216no—
603C22⋊C4—416no—
604C23—22no—
605C23—24no—
606C23—22no—
607C23—24no—
608C23—22no—
609C23—24no—
610C23—22no—
611C23—24no—
612C23—28no—
613C23—28no—
614C23—28no—
615C23—28no—
616C23—232no—
617C23—24no—
618C23—28no—
619C23—24no—
620C23—24no—
621C23—24no—
622C23—24no—
623C23—24no—
624C23—28no—
625C23—28no—
626C23—28no—
627C23—28no—
628C23—28no—
629C23—24no—
630C23—24no—
631C23—24no—
632C23—28no—
633C23—28no—
634C23—464no—
635C23—416no—
636C23—416no—
637C23—416no—
638C23—464no—
639C23—416no—
640C23—416no—
641C23—42no—
642C23—44no—
643C23—42no—
644C23—42no—
645C23—42no—
646C23—44no—
647C23—44no—
648C23—44no—
649C23—44no—
650C23—44no—
651C23—416no—
652C23—42no—
653C23—42no—
654C23—42no—
655C23—42no—
656C23—44no—
657C23—42no—
658C23—44no—
659C23—42no—
660C23—42no—
661C23—44no—
662C23—42no—
663C23—44no—
664C23—44no—
665C23—44no—
666C23—44no—
667C23—44no—
668C23—44no—
669C23—44no—
670C23C31×#12018yes—
671C23C31×#12014yes—
672C23C31×#12118yes—
673C23C31×#12114yes—
674C23C31×#12118yescomplemented
675C23C31×#12714yes—
676C23C22×D4×C3111yescharacteristic
677C23C22×D4×C3111yescharacteristic
678C23C22×D4×C3112yes—
679C23C22×D4×C3112yes—
680C23C22×D4×C3112yes—
681C23C2×#41×C3111yescharacteristic
682C23C2×#41×C3112yes—
683C23C31×H(5,𝔽2)12yes—
684C23C31×H(5,𝔽2)12yes—
685D4—416no—
686D4—464no—
687D4—432no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—28no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—24no—
694C2×C4—24no—
695C2×C4—28no—
696C2×C4—24no—
697C2×C4—24no—
698C2×C4—22no—
699C2×C4—28no—
700C2×C4—28no—
701C2×C4—28no—
702C2×C4—416no—
703C2×C4—416no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—44no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—44no—
711C2×C4—42no—
712C2×C4—44no—
713C2×C4—44no—
714C2×C4—44no—
715C2×C4—44no—
716C2×C4C31×#12014yescomplemented
717C22—24no—
718C22—24no—
719C22—24no—
720C22—24no—
721C22—216no—
722C22—216no—
723C22—24no—
724C22—24no—
725C22—28no—
726C22—216no—
727C22—464no—
728C22—44no—
729C22—44no—
730C22—44no—
731C22—44no—
732C22—48no—
733C22—48no—
734C22—48no—
735C22—44no—
736C22—44no—
737C22—44no—
738C22—44no—
739C22—44no—
740C22—48no—
741C22—48no—
742C22—82no—
743C22—82no—
744C22—84no—
745C22—84no—
746C22—82no—
747C22—82no—
748C22C31×#39218yescomplemented
749C22C2×C31×#12011yescharacteristic
750C22C2×C31×#12011yescharacteristic
751C22C2×C31×#12012yes—
752C22C2×C31×#12111yescharacteristic
753C22C2×C31×#12112yes—
754C22C2×C31×#12112yes—
755C22C31×#52511yescharacteristic
756C22C31×#52512yes—
757C22C2×C31×#12711yescharacteristic
758C22C31×#53411yescharacteristic
759C22C31×#53412yes—
760C22C31×#53511yescharacteristic
761C22C31×#53812yes—
762C22D42×C3114yes—
763C22D42×C3114yes—
764C22C31×#54614yes—
765C22C31×#54614yes—
766C4—24no—
767C4—44no—
768C4—42no—
769C4—48no—
770C4—44no—
771C2—28no—
772C2—48no—
773C2—84no—
774C2C2×C31×#39211yescharacteristic
775C2C31×#240311yescharacteristic
776C2C31×#240411yescharacteristic
777C2C31×#241014yes—
778C2C31×#242414yes—
779C2C31×#243311yescharacteristic
780C2C31×#253911yescharacteristic
781C2C31×#261711yescharacteristic
782C2C31×#284711yescharacteristic
subgroupG/H
center, socleC24×C31C24
commutator, Frattini, cosocleC24C24×C31
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C31×#121C2semidirect
2. C22×C31×#120C2semidirect
3. C23×C22⋊C4×C31C2semidirect
4. C2×C31×#392C2semidirect
5. C2×C31×#386C2semidirect
6. C31×#1439C2semidirect
7. C31×#1438C2semidirect
8. C31×C22⋊#95C2semidirect
12. C23×D4×C31C22semidirect
20. C22×C4⋊C4×C31C22semidirect
27. C22×C22⋊C4×C31C22semidirect
28. C22×C22⋊C4×C31C22semidirect
31. C2×C31×#95C22semidirect
32. C2×C31×#95C22semidirect
33. C2×C31×#95C22semidirect
42. C25×C31D4semidirect
63. C22×D4×C31D4semidirect
71. C23×C4×C31D4semidirect
98. C2×C22⋊C4×C31D4semidirect
99. C2×C22⋊C4×C31D4semidirect
212. #14716C31direct (N × H)
283. C23×C31#121semidirect
325. C2×C4×C31#120semidirect
326. C22×#121C2×C31semidirect
327. C22×#120C2×C31semidirect
328. C23×C22⋊C4C2×C31semidirect
329. C2×#392C2×C31semidirect
330. C2×#386C2×C31semidirect
331. #1439C2×C31semidirect
332. #1438C2×C31semidirect
333. C22⋊#95C2×C31semidirect
365. C22×C31#392semidirect
391. C23×D4C22×C31semidirect
399. C22×C4⋊C4C22×C31semidirect
406. C22×C22⋊C4C22×C31semidirect
407. C22×C22⋊C4C22×C31semidirect
410. C2×#95C22×C31semidirect
411. C2×#95C22×C31semidirect
412. C2×#95C22×C31semidirect
433. C25D4×C31semidirect
454. C22×D4D4×C31semidirect
462. C23×C4D4×C31semidirect
489. C2×C22⋊C4D4×C31semidirect
490. C2×C22⋊C4D4×C31semidirect
494. C31#14716direct (N × H)
674. C23C31×#121semidirect
716. C2×C4C31×#120semidirect
748. C22C31×#392semidirect

Maximal subgroups

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

subgroupindex
C22×C31×#1212
C22×C31×#1202
C23×C22⋊C4×C312
C2×C31×#3922
C2×C31×#3862
C31×#14392
C31×#14382
C31×C22⋊#952
#1471631