Finite Group Databasebeta

← C47×#24056 #26063754

Subgroups — C47×#24056 #26063754

Order 12032.

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
1C47×#3484C211yesmaximal, characteristic
2C47×#2849C212yesmaximal, complemented
3C2×C47×#386C211yesmaximal, characteristic, complemented
4C47×#2044C214yesmaximal, complemented
5C47×#1898C212yesmaximal, complemented
6C47×#1867C212yesmaximal, complemented
7C47×#1790C212yesmaximal, complemented
8C47×#1781C211yesmaximal, characteristic, complemented
9C2×H(5,𝔽2)×C47C2211yescharacteristic
10C23×D4×C47C2211yescharacteristic
11C24×C4×C47C2211yescharacteristic, complemented
12C47×#546—22no—
13C47×#546—22no—
14D42×C47—22no—
15D42×C47—22no—
16C47×#535—21no—
17C47×#534—21no—
18C47×#534C2212yes—
19C47×#525—21no—
20C2×#123×C47—22no—
21C2×#120×C47—21no—
22C2×#120×C47C2212yes—
23C47×#518C2211yescharacteristic
24C22×C22⋊C4×C47—21no—
25C22×C22⋊C4×C47C2211yescharacteristic, complemented
26C2×#99×C47C2212yes—
27C2×#99×C47C2212yescomplemented
28C2×#99×C47C2214yescomplemented
29C47×#386—21no—
30C47×#386—21no—
31C47×#386—22no—
32C47×#386C2212yes—
33C47×#386C2212yescomplemented
34C47×#386C2214yescomplemented
35C47×#385—22no—
36C47×#385C2214yescomplemented
37C47×#381—22no—
38C47×#379C2212yescomplemented
39C2×#95×C47—21no—
40C47×#342C2214yescomplemented
41C25×C47D411yescharacteristic
42C25×C47C2311yescharacteristic
43H(5,𝔽2)×C47—24no—
44H(5,𝔽2)×C47—42no—
45C2×#41×C47—21no—
46C2×#41×C47—22no—
47C22×D4×C47—21no—
48C22×D4×C47—22no—
49C22×D4×C47—22no—
50C22×D4×C47—22no—
51C22×D4×C47—21no—
52C22×D4×C47—21no—
53C22×D4×C47—24no—
54C22×D4×C47—42no—
55C22×D4×C47D411yescharacteristic
56C22×D4×C47D411yescharacteristic
57C22×D4×C47D412yes—
58C22×D4×C47D412yes—
59C22×D4×C47C2312yes—
60C22×D4×C47C2311yescharacteristic
61C22×D4×C47C2311yescharacteristic
62C23×C4×C47—21no—
63C23×C4×C47—22no—
64C23×C4×C47—21no—
65C23×C4×C47—22no—
66C23×C4×C47—21no—
67C23×C4×C47—44no—
68C23×C4×C47D411yescharacteristic
69C23×C4×C47C2312yes—
70#127×C47—22no—
71#124×C47—22no—
72#123×C47—22no—
73#123×C47—22no—
74#123×C47—22no—
75#123×C47—48no—
76C22⋊Q8×C47—21no—
77C22⋊Q8×C47—21no—
78#121×C47—21no—
79#121×C47—21no—
80#121×C47—22no—
81#121×C47—22no—
82#121×C47—22no—
83#121×C47—22no—
84#121×C47—22no—
85#121×C47—22no—
86#120×C47—22no—
87#120×C47—22no—
88#120×C47—22no—
89#120×C47—22no—
90#120×C47—22no—
91#120×C47—22no—
92#120×C47—22no—
93#120×C47—22no—
94#120×C47—22no—
95C4×D4×C47—22no—
96C4×D4×C47—22no—
97C4×D4×C47—22no—
98C4×D4×C47—22no—
99#117×C47—21no—
100C2×C4⋊C4×C47—24no—
101C2×C22⋊C4×C47—21no—
102C2×C22⋊C4×C47—21no—
103C2×C22⋊C4×C47—21no—
104C2×C22⋊C4×C47—22no—
105C2×C22⋊C4×C47—22no—
106C2×C22⋊C4×C47—21no—
107C2×C22⋊C4×C47—22no—
108C2×C22⋊C4×C47—24no—
109C2×C22⋊C4×C47—22no—
110C2×C22⋊C4×C47—42no—
111C2×C22⋊C4×C47—44no—
112C2×C22⋊C4×C47D412yes—
113C2×C22⋊C4×C47D412yes—
114C2×C22⋊C4×C47C2312yes—
115C2×C22⋊C4×C47C2314yes—
116C2×C22⋊C4×C47C2312yes—
117#99×C47—24no—
118#99×C47—44no—
119#99×C47—42no—
120#95×C47—22no—
121#95×C47—22no—
122#95×C47—24no—
123#95×C47—24no—
124C24×C47—22no—
125C24×C47—22no—
126C24×C47—21no—
127C24×C47—22no—
128C24×C47—21no—
129C24×C47—21no—
130C24×C47—42no—
131C24×C47—42no—
132C24×C47—41no—
133C24×C47—42no—
134C24×C47—42no—
135C24×C47C2×D411yescharacteristic
136C24×C47C2×D412yes—
137C24×C47C2×D412yes—
138C24×C47C2×D411yescharacteristic
139C24×C47C2×D412yes—
140C24×C47C2×D411yescharacteristic
141C24×C47C2×D411yescharacteristic
142C24×C47C2411yescharacteristic
143#41×C47—48no—
144#41×C47—42no—
145#41×C47—42no—
146C2×Q8×C47—21no—
147C2×D4×C47—22no—
148C2×D4×C47—22no—
149C2×D4×C47—22no—
150C2×D4×C47—21no—
151C2×D4×C47—22no—
152C2×D4×C47—22no—
153C2×D4×C47—22no—
154C2×D4×C47—22no—
155C2×D4×C47—22no—
156C2×D4×C47—22no—
157C2×D4×C47—22no—
158C2×D4×C47—22no—
159C2×D4×C47—22no—
160C2×D4×C47—24no—
161C2×D4×C47—22no—
162C2×D4×C47—24no—
163C2×D4×C47—22no—
164C2×D4×C47—22no—
165C2×D4×C47—22no—
166C2×D4×C47—22no—
167C2×D4×C47—22no—
168C2×D4×C47—41no—
169C2×D4×C47—41no—
170C2×D4×C47—48no—
171C2×D4×C47—48no—
172C2×D4×C47—48no—
173C2×D4×C47—42no—
174C2×D4×C47—42no—
175C2×D4×C47—44no—
176C2×D4×C47—44no—
177C2×D4×C47—82no—
178C2×D4×C47—82no—
179C2×D4×C47#4114yes—
180C22×C4×C47—21no—
181C22×C4×C47—24no—
182C22×C4×C47—22no—
183C22×C4×C47—28no—
184C22×C4×C47—21no—
185C22×C4×C47—21no—
186C22×C4×C47—22no—
187C22×C4×C47—24no—
188C22×C4×C47—21no—
189C22×C4×C47—21no—
190C22×C4×C47—22no—
191C22×C4×C47—24no—
192C22×C4×C47—22no—
193C22×C4×C47—44no—
194C22×C4×C47—41no—
195C22×C4×C47—44no—
196C22×C4×C47—48no—
197C22×C4×C47—42no—
198C22×C4×C47—44no—
199C22×C4×C47—42no—
200C22×C4×C47—41no—
201C22×C4×C47—41no—
202C22×C4×C47—42no—
203C22×C4×C47—42no—
204C22×C4×C47—42no—
205C22×C4×C47C2×D412yes—
206C22×C4×C47C2×D411yescharacteristic
207C22×C4×C47C2×D411yescharacteristic
208C22×C4×C47C2×D412yes—
209C22×C4×C47C2×D412yes—
210C4⋊C4×C47—21no—
211C4⋊C4×C47—21no—
212C4⋊C4×C47—22no—
213C4⋊C4×C47—22no—
214C4⋊C4×C47—48no—
215C22⋊C4×C47—22no—
216C22⋊C4×C47—22no—
217C22⋊C4×C47—22no—
218C22⋊C4×C47—22no—
219C22⋊C4×C47—22no—
220C22⋊C4×C47—22no—
221C22⋊C4×C47—22no—
222C22⋊C4×C47—22no—
223C22⋊C4×C47—22no—
224C22⋊C4×C47—22no—
225C22⋊C4×C47—22no—
226C22⋊C4×C47—24no—
227C22⋊C4×C47—24no—
228C22⋊C4×C47—24no—
229C22⋊C4×C47—44no—
230C22⋊C4×C47—44no—
231C22⋊C4×C47—48no—
232C22⋊C4×C47—44no—
233C22⋊C4×C47—42no—
234C22⋊C4×C47—44no—
235C42×C47—22no—
236C23×C47—21no—
237C23×C47—21no—
238C23×C47—22no—
239C23×C47—22no—
240C23×C47—21no—
241C23×C47—21no—
242C23×C47—21no—
243C23×C47—24no—
244C23×C47—24no—
245C23×C47—24no—
246C23×C47—24no—
247C23×C47—21no—
248C23×C47—21no—
249C23×C47—22no—
250C23×C47—21no—
251C23×C47—21no—
252C23×C47—24no—
253C23×C47—42no—
254C23×C47—41no—
255C23×C47—41no—
256C23×C47—42no—
257C23×C47—41no—
258C23×C47—41no—
259C23×C47—42no—
260C23×C47—42no—
261C23×C47—48no—
262C23×C47—48no—
263C23×C47—41no—
264C23×C47—41no—
265C23×C47—41no—
266C23×C47—41no—
267C23×C47—48no—
268C23×C47—42no—
269C23×C47—42no—
270C23×C47—42no—
271C23×C47—42no—
272C23×C47—42no—
273C23×C47—81no—
274C23×C47—81no—
275C23×C47—84no—
276C23×C47—81no—
277C23×C47—81no—
278C23×C47#12012yes—
279C23×C47#12011yescharacteristic
280C23×C47#12011yescharacteristic
281C23×C47#12312yescomplemented
282C23×C47C22×D411yescharacteristic
283C23×C47C22×D412yes—
284C23×C47C2×#4112yes—
285C23×C47H(5,𝔽2)12yes—
286Q8×C47—42no—
287D4×C47—28no—
288D4×C47—44no—
289D4×C47—42no—
290D4×C47—44no—
291D4×C47—44no—
292D4×C47—42no—
293D4×C47—42no—
294D4×C47—44no—
295D4×C47—44no—
296D4×C47—44no—
297D4×C47—44no—
298D4×C47—82no—
299D4×C47—82no—
300D4×C47—82no—
301D4×C47—82no—
302C2×C4×C47—21no—
303C2×C4×C47—21no—
304C2×C4×C47—24no—
305C2×C4×C47—28no—
306C2×C4×C47—22no—
307C2×C4×C47—22no—
308C2×C4×C47—22no—
309C2×C4×C47—21no—
310C2×C4×C47—21no—
311C2×C4×C47—21no—
312C2×C4×C47—24no—
313C2×C4×C47—42no—
314C2×C4×C47—42no—
315C2×C4×C47—44no—
316C2×C4×C47—44no—
317C2×C4×C47—42no—
318C2×C4×C47—44no—
319C2×C4×C47—48no—
320C2×C4×C47—42no—
321C2×C4×C47—42no—
322C2×C4×C47—44no—
323C2×C4×C47—42no—
324C2×C4×C47—42no—
325C2×C4×C47—44no—
326C2×C4×C47—42no—
327C2×C4×C47—44no—
328C2×C4×C47—42no—
329C2×C4×C47—42no—
330C2×C4×C47—44no—
331C2×C4×C47—81no—
332C2×C4×C47—81no—
333C2×C4×C47—84no—
334C2×C4×C47#12312yescomplemented
335#24056C4711yesmaximal, characteristic, direct product factor, Sylow
336C22×C47—24no—
337C22×C47—24no—
338C22×C47—21no—
339C22×C47—21no—
340C22×C47—22no—
341C22×C47—21no—
342C22×C47—21no—
343C22×C47—22no—
344C22×C47—21no—
345C22×C47—21no—
346C22×C47—22no—
347C22×C47—22no—
348C22×C47—22no—
349C22×C47—22no—
350C22×C47—42no—
351C22×C47—42no—
352C22×C47—48no—
353C22×C47—48no—
354C22×C47—42no—
355C22×C47—42no—
356C22×C47—42no—
357C22×C47—42no—
358C22×C47—41no—
359C22×C47—41no—
360C22×C47—42no—
361C22×C47—41no—
362C22×C47—42no—
363C22×C47—41no—
364C22×C47—42no—
365C22×C47—41no—
366C22×C47—81no—
367C22×C47—84no—
368C22×C47—84no—
369C22×C47—84no—
370C22×C47—81no—
371C22×C47—162no—
372C22×C47B(4,𝔽2)12yes—
373C22×C47#45812yes—
374C22×C47C2×#12011yescharacteristic
375C22×C47C2×#12311yescharacteristic
376C22×C47#53411yescharacteristic
377C22×C47#54614yes—
378C4×C47—22no—
379C4×C47—41no—
380C4×C47—42no—
381C4×C47—44no—
382C4×C47—42no—
383C4×C47—42no—
384C4×C47—84no—
385C4×C47—82no—
386#3484C2×C4711yescharacteristic
387#2849C2×C4712yescomplemented
388C2×#386C2×C4711yescharacteristic, complemented
389#2044C2×C4714yescomplemented
390#1898C2×C4712yescomplemented
391#1867C2×C4712yescomplemented
392#1790C2×C4712yescomplemented
393#1781C2×C4711yescharacteristic, complemented
394C2×C47—21no—
395C2×C47—24no—
396C2×C47—21no—
397C2×C47—22no—
398C2×C47—22no—
399C2×C47—42no—
400C2×C47—42no—
401C2×C47—81no—
402C2×C47—82no—
403C2×C47#240511yescharacteristic
404C2×C47C2×B(4,𝔽2)11yescharacteristic
405C2×C47C2×#45811yescharacteristic
406C2×H(5,𝔽2)C22×C4711yescharacteristic
407C23×D4C22×C4711yescharacteristic
408C24×C4C22×C4711yescharacteristic, complemented
409#546—22no—
410#546—22no—
411D42—22no—
412D42—22no—
413#535—21no—
414#534—21no—
415#534C22×C4712yes—
416#525—21no—
417C2×#123—22no—
418C2×#120—21no—
419C2×#120C22×C4712yes—
420#518C22×C4711yescharacteristic
421C22×C22⋊C4—21no—
422C22×C22⋊C4C22×C4711yescharacteristic, complemented
423C2×#99C22×C4712yes—
424C2×#99C22×C4714yescomplemented
425C2×#99C22×C4712yescomplemented
426#386—22no—
427#386—21no—
428#386—21no—
429#386C22×C4712yes—
430#386C22×C4714yescomplemented
431#386C22×C4712yescomplemented
432#385—22no—
433#385C22×C4714yescomplemented
434#381—22no—
435#379C22×C4712yescomplemented
436C2×#95—21no—
437#342C22×C4714yescomplemented
438C47#2405611yescharacteristic, direct product factor, Sylow
439C25D4×C4711yescharacteristic
440C25C23×C4711yescharacteristic
441H(5,𝔽2)—24no—
442H(5,𝔽2)—42no—
443C2×#41—21no—
444C2×#41—22no—
445C22×D4—21no—
446C22×D4—22no—
447C22×D4—22no—
448C22×D4—22no—
449C22×D4—21no—
450C22×D4—21no—
451C22×D4—24no—
452C22×D4—42no—
453C22×D4D4×C4711yescharacteristic
454C22×D4D4×C4711yescharacteristic
455C22×D4D4×C4712yes—
456C22×D4D4×C4712yes—
457C22×D4C23×C4712yes—
458C22×D4C23×C4711yescharacteristic
459C22×D4C23×C4711yescharacteristic
460C23×C4—21no—
461C23×C4—22no—
462C23×C4—21no—
463C23×C4—22no—
464C23×C4—21no—
465C23×C4—44no—
466C23×C4D4×C4711yescharacteristic
467C23×C4C23×C4712yes—
468#127—22no—
469#124—22no—
470#123—22no—
471#123—22no—
472#123—22no—
473#123—48no—
474C22⋊Q8—21no—
475C22⋊Q8—21no—
476#121—21no—
477#121—21no—
478#121—22no—
479#121—22no—
480#121—22no—
481#121—22no—
482#121—22no—
483#121—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—
492#120—22no—
493C4×D4—22no—
494C4×D4—22no—
495C4×D4—22no—
496C4×D4—22no—
497#117—21no—
498C2×C4⋊C4—24no—
499C2×C22⋊C4—21no—
500C2×C22⋊C4—21no—
501C2×C22⋊C4—21no—
502C2×C22⋊C4—22no—
503C2×C22⋊C4—22no—
504C2×C22⋊C4—21no—
505C2×C22⋊C4—22no—
506C2×C22⋊C4—24no—
507C2×C22⋊C4—22no—
508C2×C22⋊C4—42no—
509C2×C22⋊C4—44no—
510C2×C22⋊C4D4×C4712yes—
511C2×C22⋊C4D4×C4712yes—
512C2×C22⋊C4C23×C4712yes—
513C2×C22⋊C4C23×C4714yes—
514C2×C22⋊C4C23×C4712yes—
515#99—24no—
516#99—42no—
517#99—44no—
518#95—22no—
519#95—22no—
520#95—24no—
521#95—24no—
522C24—22no—
523C24—22no—
524C24—21no—
525C24—22no—
526C24—21no—
527C24—21no—
528C24—42no—
529C24—42no—
530C24—41no—
531C24—42no—
532C24—42no—
533C24C2×D4×C4711yescharacteristic
534C24C2×D4×C4712yes—
535C24C2×D4×C4712yes—
536C24C2×D4×C4711yescharacteristic
537C24C2×D4×C4712yes—
538C24C2×D4×C4711yescharacteristic
539C24C2×D4×C4711yescharacteristic
540C24C24×C4711yescharacteristic
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×C4714yes—
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×C4712yes—
604C22×C4C2×D4×C4711yescharacteristic
605C22×C4C2×D4×C4711yescharacteristic
606C22×C4C2×D4×C4712yes—
607C22×C4C2×D4×C4712yes—
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—
676C23#120×C4712yes—
677C23#120×C4711yescharacteristic
678C23#120×C4711yescharacteristic
679C23#123×C4712yescomplemented
680C23C22×D4×C4711yescharacteristic
681C23C22×D4×C4712yes—
682C23C2×#41×C4712yes—
683C23H(5,𝔽2)×C4712yes—
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×C4#123×C4712yescomplemented
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—
769C22C47×B(4,𝔽2)12yes—
770C22C47×#45812yes—
771C22C2×#120×C4711yescharacteristic
772C22C2×#123×C4711yescharacteristic
773C22C47×#53411yescharacteristic
774C22C47×#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—
792C2C47×#240511yescharacteristic
793C2C2×C47×B(4,𝔽2)11yescharacteristic
794C2C2×C47×#45811yescharacteristic
subgroupG/H
center, socleC22×C47C2×#120
commutator, Frattini, cosocleC24C24×C47
prime radicalC47×#3484C2
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C47 ◁ C25×C47 ◁ G

Complements

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

NH ≅ G/Ntype
2. C47×#2849C2semidirect
3. C2×C47×#386C2semidirect
4. C47×#2044C2semidirect
5. C47×#1898C2semidirect
6. C47×#1867C2semidirect
7. C47×#1790C2semidirect
8. C47×#1781C2semidirect
11. C24×C4×C47C22semidirect
25. C22×C22⋊C4×C47C22semidirect
27. C2×#99×C47C22semidirect
28. C2×#99×C47C22semidirect
33. C47×#386C22semidirect
34. C47×#386C22semidirect
36. C47×#385C22semidirect
38. C47×#379C22semidirect
40. C47×#342C22semidirect
281. C23×C47#123semidirect
334. C2×C4×C47#123semidirect
335. #24056C47direct (N × H)
387. #2849C2×C47semidirect
388. C2×#386C2×C47semidirect
389. #2044C2×C47semidirect
390. #1898C2×C47semidirect
391. #1867C2×C47semidirect
392. #1790C2×C47semidirect
393. #1781C2×C47semidirect
408. C24×C4C22×C47semidirect
422. C22×C22⋊C4C22×C47semidirect
424. C2×#99C22×C47semidirect
425. C2×#99C22×C47semidirect
430. #386C22×C47semidirect
431. #386C22×C47semidirect
433. #385C22×C47semidirect
435. #379C22×C47semidirect
437. #342C22×C47semidirect
438. C47#24056direct (N × H)
679. C23#123×C47semidirect
732. C2×C4#123×C47semidirect

Maximal subgroups

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

subgroupindex
C47×#34842
C47×#28492
C2×C47×#3862
C47×#20442
C47×#18982
C47×#18672
C47×#17902
C47×#17812
#2405647