Finite Group Databasebeta

← #26137881

Subgroups — #26137881

Order 12032.

2390 conjugacy classes of subgroups.

The subgroup lattice has 754 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689026C211yesmaximal, characteristic
2C2×#15689003C211yesmaximal, characteristic
3C2×C22⋊C4×Dic47C212yesmaximal, complemented
4C2×C4×C22⋊Dic47C212yesmaximal, complemented
5#20241625C212yesmaximal, complemented
6#20241625C212yesmaximal, complemented
7#20241622C212yesmaximal, complemented
8#95×Dic47C212yesmaximal, complemented
9C2×C47×#386C211yesmaximal, characteristic
10C24×Dic47C2211yescharacteristic
11C22×C4⋊Dic47C2211yescharacteristic
12C22×C22⋊Dic47C2212yes—
13C22×C22⋊Dic47C2212yes—
14C22×C22⋊Dic47C2212yes—
15C22×C22⋊Dic47C2211yescharacteristic
16C22×C4×Dic47C2212yes—
17C22×C4×Dic47C2212yes—
18C22×C4×Dic47C2212yes—
19C22×C4×Dic47C2211yescharacteristic
20#15689026C418yescomplemented
21#15689003C418yescomplemented
22C22⋊C4×Dic47—28no—
23C4×C22⋊Dic47—28no—
24C2×C47⋊#95C2212yes—
25C2×C47⋊#95C2212yes—
26C2×C47⋊#95C2212yes—
27C2×C47⋊#95C2212yes—
28C2×C47⋊#95C2212yes—
29C2×C47⋊#95C2212yes—
30C23×D4×C47C2211yescharacteristic
31C24×C4×C47C2211yescharacteristic
32C22×C22⋊C4×C47C2212yes—
33C22×C22⋊C4×C47C2211yescharacteristic
34C47×#386C418yescomplemented
35C2×#95×C47C2212yes—
36C23×Dic47—24no—
37C23×Dic47—24no—
38C23×Dic47—41no—
39C23×Dic47—41no—
40C23×Dic47C2×C414yescomplemented
41C23×Dic47C2312yes—
42C23×Dic47C2312yes—
43C23×Dic47C2312yes—
44C23×Dic47C2312yes—
45C2×C4⋊Dic47—41no—
46C2×C4⋊Dic47—41no—
47C2×C4⋊Dic47C2×C414yescomplemented
48C2×C22⋊Dic47—24no—
49C2×C22⋊Dic47—24no—
50C2×C22⋊Dic47—24no—
51C2×C22⋊Dic47—24no—
52C2×C22⋊Dic47—24no—
53C2×C22⋊Dic47—24no—
54C2×C22⋊Dic47—41no—
55C2×C22⋊Dic47—41no—
56C2×C22⋊Dic47C2×C418yes—
57C2×C22⋊Dic47C2×C418yescomplemented
58C2×C22⋊Dic47C2×C418yescomplemented
59C2×C22⋊Dic47C2×C414yescomplemented
60C2×C4×Dic47—24no—
61C2×C4×Dic47—24no—
62C2×C4×Dic47—24no—
63C2×C4×Dic47—24no—
64C2×C4×Dic47—24no—
65C2×C4×Dic47—24no—
66C2×C4×Dic47—41no—
67C2×C4×Dic47—41no—
68C2×C4×Dic47—42no—
69C2×C4×Dic47—42no—
70C2×C4×Dic47—42no—
71C2×C4×Dic47C2×C414yescomplemented
72C47⋊#95—24no—
73C47⋊#95—24no—
74C47⋊#95—24no—
75C47⋊#95—42no—
76C47⋊#95C2×C418yescomplemented
77C47⋊#95D418yescomplemented
78C25×C47C2311yescharacteristic
79C25×C47C2311yescharacteristic
80C22×D4×C47—41no—
81C22×D4×C47—41no—
82C22×D4×C47—41no—
83C22×D4×C47—41no—
84C22×D4×C47C2×C414yes—
85C22×D4×C47C2×C414yes—
86C22×D4×C47C2×C414yes—
87C23×C4×C47—24no—
88C23×C4×C47—24no—
89C23×C4×C47—41no—
90C23×C4×C47—41no—
91C23×C4×C47C2×C414yescomplemented
92C23×C4×C47C2312yes—
93C23×C4×C47C2311yescharacteristic
94C23×C4×C47C2312yes—
95C2×C22⋊C4×C47—24no—
96C2×C22⋊C4×C47—24no—
97C2×C22⋊C4×C47—41no—
98C2×C22⋊C4×C47—41no—
99C2×C22⋊C4×C47C2×C418yes—
100C2×C22⋊C4×C47C2×C414yescomplemented
101#95×C47C2×C418yescomplemented
102C24×C47—22no—
103C24×C47—22no—
104C24×C47—22no—
105C24×C47—22no—
106C24×C47—22no—
107C24×C47—22no—
108C24×C47—22no—
109C24×C47—22no—
110C24×C47—21no—
111C24×C47—21no—
112C24×C47—21no—
113C24×C47—21no—
114C24×C47—21no—
115C24×C47—21no—
116C24×C47—21no—
117C24×C47—21no—
118C24×C47C22×C412yes—
119C24×C47C22×C412yes—
120C24×C47C22×C412yes—
121C24×C47C22×C412yes—
122C24×C47C22×C412yes—
123C24×C47C22×C412yes—
124C24×C47C2411yescharacteristic
125C2×D4×C47—44no—
126C2×D4×C47—44no—
127C2×D4×C47—44no—
128C2×D4×C47—44no—
129C2×D4×C47—44no—
130C2×D4×C47—44no—
131C2×D4×C47C42116yescomplemented
132C22×C4×C47—22no—
133C22×C4×C47—22no—
134C22×C4×C47—22no—
135C22×C4×C47—22no—
136C22×C4×C47—21no—
137C22×C4×C47—21no—
138C22×C4×C47—21no—
139C22×C4×C47—21no—
140C22×C4×C47—22no—
141C22×C4×C47—22no—
142C22×C4×C47—22no—
143C22×C4×C47—22no—
144C22×C4×C47—22no—
145C22×C4×C47—22no—
146C22×C4×C47—216no—
147C22×C4×C47—44no—
148C22×C4×C47—44no—
149C22×C4×C47—48no—
150C22×C4×C47—44no—
151C22×C4×C47C22×C414yes—
152C22×C4×C47C22×C412yes—
153C22×C4×C47C22×C412yes—
154C22×C4×C47C22×C412yes—
155C22×C4×C47C22×C414yes—
156C22×C4×C47C2×D414yes—
157C22×C4×C47#4114yes—
158C22×Dic47—22no—
159C22×Dic47—22no—
160C22×Dic47—22no—
161C22×Dic47—22no—
162C22×Dic47—22no—
163C22×Dic47—22no—
164C22×Dic47—22no—
165C22×Dic47—22no—
166C22×Dic47—22no—
167C22×Dic47—22no—
168C22×Dic47—22no—
169C22×Dic47—22no—
170C22×Dic47—22no—
171C22×Dic47—22no—
172C22×Dic47—22no—
173C22×Dic47—22no—
174C22×Dic47—22no—
175C22×Dic47—22no—
176C22×Dic47—22no—
177C22×Dic47—22no—
178C22×Dic47—216no—
179C22×Dic47—44no—
180C22×Dic47—44no—
181C22×Dic47—48no—
182C22×Dic47—44no—
183C22×Dic47C22×C414yes—
184C22×Dic47C22×C414yes—
185C22×Dic47C22×C414yes—
186C22×Dic47C22×C414yes—
187C22×Dic47C2×D414yes—
188C22×Dic47C2×D414yes—
189C22×Dic47#4114yes—
190C22×Dic47#4114yes—
191C22⋊C4×C47—216no—
192C22⋊C4×C47—44no—
193C22⋊Dic47—216no—
194C22⋊Dic47—216no—
195C22⋊Dic47—216no—
196C22⋊Dic47—44no—
197C4⋊Dic47—44no—
198C4×Dic47—44no—
199C4×Dic47—48no—
200C4×Dic47—48no—
201C4×Dic47—48no—
202C23×C47—24no—
203C23×C47—24no—
204C23×C47—24no—
205C23×C47—24no—
206C23×C47—24no—
207C23×C47—24no—
208C23×C47—24no—
209C23×C47—24no—
210C23×C47—24no—
211C23×C47—24no—
212C23×C47—24no—
213C23×C47—24no—
214C23×C47—22no—
215C23×C47—22no—
216C23×C47—22no—
217C23×C47—22no—
218C23×C47—22no—
219C23×C47—22no—
220C23×C47—22no—
221C23×C47—22no—
222C23×C47—22no—
223C23×C47—22no—
224C23×C47—22no—
225C23×C47—22no—
226C23×C47—41no—
227C23×C47—41no—
228C23×C47—42no—
229C23×C47—42no—
230C23×C47—42no—
231C23×C47—42no—
232C23×C47—42no—
233C23×C47—42no—
234C23×C47—41no—
235C23×C47—41no—
236C23×C47—41no—
237C23×C47—41no—
238C23×C47—42no—
239C23×C47—42no—
240C23×C47—42no—
241C23×C47—42no—
242C23×C47—42no—
243C23×C47—42no—
244C23×C47—41no—
245C23×C47—41no—
246C23×C47C2×C4214yes—
247C23×C47C2×C4214yes—
248C23×C47C23×C411yescharacteristic
249C23×C47C23×C411yescharacteristic
250C23×C47C23×C411yescharacteristic
251C23×C47C22×D412yes—
252C23×C47C2×#4112yes—
253C23×C47C2×#4112yes—
254C23×C47C2×#4112yes—
255C23×C47H(5,𝔽2)11yescharacteristic
256C23×C47H(5,𝔽2)11yescharacteristic
257C23×C47H(5,𝔽2)11yescharacteristic
258C23×C47H(5,𝔽2)11yescharacteristic
259D4×C47—416no—
260C2×C4×C47—24no—
261C2×C4×C47—22no—
262C2×C4×C47—22no—
263C2×C4×C47—24no—
264C2×C4×C47—22no—
265C2×C4×C47—22no—
266C2×C4×C47—22no—
267C2×C4×C47—22no—
268C2×C4×C47—24no—
269C2×C4×C47—24no—
270C2×C4×C47—24no—
271C2×C4×C47—24no—
272C2×C4×C47—24no—
273C2×C4×C47—24no—
274C2×C4×C47—24no—
275C2×C4×C47—416no—
276C2×C4×C47—42no—
277C2×C4×C47—42no—
278C2×C4×C47—42no—
279C2×C4×C47—42no—
280C2×C4×C47C2×C4214yes—
281C2×C4×C47C4×D418yes—
282C2×Dic47—24no—
283C2×Dic47—24no—
284C2×Dic47—24no—
285C2×Dic47—24no—
286C2×Dic47—24no—
287C2×Dic47—24no—
288C2×Dic47—24no—
289C2×Dic47—24no—
290C2×Dic47—24no—
291C2×Dic47—24no—
292C2×Dic47—24no—
293C2×Dic47—24no—
294C2×Dic47—24no—
295C2×Dic47—24no—
296C2×Dic47—24no—
297C2×Dic47—24no—
298C2×Dic47—24no—
299C2×Dic47—24no—
300C2×Dic47—416no—
301C2×Dic47—42no—
302C2×Dic47—42no—
303C2×Dic47—42no—
304C2×Dic47—42no—
305C2×Dic47—42no—
306C2×Dic47—42no—
307C2×Dic47—42no—
308C2×Dic47—42no—
309C2×Dic47C4×D418yes—
310C2×Dic47C4×D418yes—
311#13824—471nomaximal, Sylow
312C22×C47—28no—
313C22×C47—28no—
314C22×C47—24no—
315C22×C47—24no—
316C22×C47—42no—
317C22×C47—42no—
318C22×C47—42no—
319C22×C47—42no—
320C22×C47—44no—
321C22×C47—44no—
322C22×C47—44no—
323C22×C47—44no—
324C22×C47—44no—
325C22×C47—44no—
326C22×C47—42no—
327C22×C47—42no—
328C22×C47—42no—
329C22×C47—42no—
330C22×C47—42no—
331C22×C47—42no—
332C22×C47—42no—
333C22×C47—42no—
334C22×C47C22×C4211yescharacteristic
335C22×C47C2×C4×D412yes—
336C22×C47C2×C4×D412yes—
337C22×C47C2×C4×D412yes—
338C22×C47C4×#4112yes—
339C22×C47C4×#4112yes—
340C22×C47C4×#4112yes—
341C22×C47#51811yescharacteristic
342C22×C47#51811yescharacteristic
343C22×C47#51811yescharacteristic
344C22×C47#51811yescharacteristic
345C22×C47#51811yescharacteristic
346C22×C47#51811yescharacteristic
347C22×C47D4211yescharacteristic
348C22×C47#54612yes—
349C22×C47#54612yes—
350C22×C47#55012yes—
351C22×C47#55111yescharacteristic
352C22×C47#55111yescharacteristic
353C22×C47#55312yes—
354C22×C47#55312yes—
355C22×C47#55512yes—
356C22×C47#55911yescharacteristic
357C4×C47—28no—
358C4×C47—24no—
359C4×C47—44no—
360Dic47—28no—
361Dic47—28no—
362Dic47—44no—
363Dic47—44no—
364C2×#390—471no—
365C2×#386—471no—
366C2×#386D4711yescharacteristic
367C2×C4×C22⋊C4—472no—
368C2×C4×C22⋊C4—472no—
369#1437—472no—
370#1437—472no—
371#1436—472no—
372C4×#95—472no—
373C2×C47—44no—
374C2×C47—44no—
375C2×C47C42×D412yes—
376C2×C47#227311yescharacteristic
377C2×C47#235811yescharacteristic
378C2×C47#235811yescharacteristic
379C2×C47#236312yes—
380C2×C47#236312yes—
381C2×C47#236412yes—
382C2×C47#236611yescharacteristic
383C2×C47#237211yescharacteristic
384C2×C47#237411yescharacteristic
385C2×C47#237411yescharacteristic
386C23×D4C2×D4711yescharacteristic
387C24×C4—471no—
388C24×C4C2×D4711yescharacteristic
389C22×C4⋊C4—471no—
390C22×C22⋊C4—472no—
391C22×C22⋊C4—472no—
392C22×C22⋊C4—472no—
393C22×C22⋊C4—471no—
394C22×C22⋊C4C2×D4712yes—
395C22×C22⋊C4C2×D4711yescharacteristic
396C22×C42—471no—
397C22×C42—472no—
398C22×C42—472no—
399C22×C42—472no—
400#390—478no—
401#386—478no—
402#386Dic4718yescomplemented
403C4×C22⋊C4—948no—
404C4×C22⋊C4—948no—
405C2×#95—472no—
406C2×#95—472no—
407C2×#95—472no—
408C2×#95—472no—
409C2×#95—472no—
410C2×#95—472no—
411C2×#95C2×D4712yes—
412C47#1382411yescharacteristic, complemented, Sylow
413C25C22×D4711yescharacteristic
414C25C22×D4711yescharacteristic
415C22×D4—41no—
416C22×D4—41no—
417C22×D4—41no—
418C22×D4—41no—
419C22×D4C4×D4714yes—
420C22×D4C4×D4714yes—
421C22×D4C2×Dic4714yes—
422C23×C4—24no—
423C23×C4—24no—
424C23×C4—41no—
425C23×C4—41no—
426C23×C4—472no—
427C23×C4—472no—
428C23×C4—472no—
429C23×C4—472no—
430C23×C4—474no—
431C23×C4—944no—
432C23×C4—944no—
433C23×C4—1881no—
434C23×C4—1881no—
435C23×C4C2×Dic4714yescomplemented
436C23×C4C22×D4712yes—
437C23×C4C22×D4711yescharacteristic
438C23×C4C22×D4712yes—
439C2×C4⋊C4—474no—
440C2×C4⋊C4—1881no—
441C2×C4⋊C4—1881no—
442C2×C22⋊C4—24no—
443C2×C22⋊C4—24no—
444C2×C22⋊C4—41no—
445C2×C22⋊C4—41no—
446C2×C22⋊C4—478no—
447C2×C22⋊C4—478no—
448C2×C22⋊C4—478no—
449C2×C22⋊C4—474no—
450C2×C22⋊C4—944no—
451C2×C22⋊C4—944no—
452C2×C22⋊C4—944no—
453C2×C22⋊C4—944no—
454C2×C22⋊C4—944no—
455C2×C22⋊C4—944no—
456C2×C22⋊C4—1881no—
457C2×C22⋊C4—1881no—
458C2×C22⋊C4C2×Dic4718yes—
459C2×C22⋊C4C2×Dic4714yescomplemented
460C2×C42—474no—
461C2×C42—944no—
462C2×C42—944no—
463C2×C42—944no—
464C2×C42—944no—
465C2×C42—944no—
466C2×C42—944no—
467C2×C42—1881no—
468C2×C42—1881no—
469C2×C42—1882no—
470C2×C42—1882no—
471C2×C42—1882no—
472#95—478no—
473#95—478no—
474#95—944no—
475#95—944no—
476#95—944no—
477#95—1882no—
478#95C2×Dic4718yescomplemented
479C24—22no—
480C24—22no—
481C24—22no—
482C24—22no—
483C24—22no—
484C24—22no—
485C24—22no—
486C24—22no—
487C24—21no—
488C24—21no—
489C24—21no—
490C24—21no—
491C24—21no—
492C24—21no—
493C24—21no—
494C24—21no—
495C24C2×C4×D4712yes—
496C24C2×C4×D4712yes—
497C24C2×C4×D4712yes—
498C24C2×C4×D4712yes—
499C24C22×Dic4712yes—
500C24C22×Dic4712yes—
501C24C23×D4711yescharacteristic
502C2×D4—44no—
503C2×D4—44no—
504C2×D4—44no—
505C2×D4—44no—
506C2×D4—44no—
507C2×D4—44no—
508C2×D4C4×Dic47116yescomplemented
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—216no—
524C22×C4—44no—
525C22×C4—44no—
526C22×C4—48no—
527C22×C4—44no—
528C22×C4—474no—
529C22×C4—474no—
530C22×C4—474no—
531C22×C4—474no—
532C22×C4—474no—
533C22×C4—474no—
534C22×C4—474no—
535C22×C4—474no—
536C22×C4—9416no—
537C22×C4—942no—
538C22×C4—942no—
539C22×C4—942no—
540C22×C4—942no—
541C22×C4—942no—
542C22×C4—942no—
543C22×C4—942no—
544C22×C4—942no—
545C22×C4—942no—
546C22×C4—942no—
547C22×C4—942no—
548C22×C4—942no—
549C22×C4—942no—
550C22×C4—942no—
551C22×C4—942no—
552C22×C4—942no—
553C22×C4—942no—
554C22×C4—942no—
555C22×C4—942no—
556C22×C4—942no—
557C22×C4—1884no—
558C22×C4—1884no—
559C22×C4—1888no—
560C22×C4—1884no—
561C22×C4C2×C4×D4712yes—
562C22×C4C2×C4×D4712yes—
563C22×C4D4×D4714yes—
564C22×C4#1062535214yes—
565C22×C4C22×Dic4714yes—
566C22×C4C22×Dic4712yes—
567C22×C4C22×Dic4714yes—
568C4⋊C4—1884no—
569C22⋊C4—216no—
570C22⋊C4—44no—
571C22⋊C4—9416no—
572C22⋊C4—9416no—
573C22⋊C4—9416no—
574C22⋊C4—1884no—
575C42—1884no—
576C42—1888no—
577C42—1888no—
578C42—1888no—
579C23—24no—
580C23—24no—
581C23—24no—
582C23—24no—
583C23—24no—
584C23—24no—
585C23—24no—
586C23—24no—
587C23—24no—
588C23—24no—
589C23—24no—
590C23—24no—
591C23—22no—
592C23—22no—
593C23—22no—
594C23—22no—
595C23—22no—
596C23—22no—
597C23—22no—
598C23—22no—
599C23—22no—
600C23—22no—
601C23—22no—
602C23—22no—
603C23—41no—
604C23—41no—
605C23—42no—
606C23—42no—
607C23—42no—
608C23—42no—
609C23—42no—
610C23—42no—
611C23—41no—
612C23—41no—
613C23—41no—
614C23—41no—
615C23—42no—
616C23—42no—
617C23—42no—
618C23—42no—
619C23—42no—
620C23—42no—
621C23—41no—
622C23—41no—
623C23C2×C4×Dic4714yes—
624C23C2×C4×Dic4714yes—
625C23C22×C4×D4711yescharacteristic
626C23C22×C4×D4711yescharacteristic
627C23C23×Dic4711yescharacteristic
628C23C2×D4×D4712yes—
629C23#41×D4712yes—
630C23#41×D4712yes—
631C23C2×#1062535212yes—
632C23#1309406911yescharacteristic
633C23#1309406911yescharacteristic
634C23#1309406911yescharacteristic
635C23#1309406911yescharacteristic
636D4—416no—
637C2×C4—24no—
638C2×C4—24no—
639C2×C4—24no—
640C2×C4—24no—
641C2×C4—24no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—24no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—24no—
650C2×C4—24no—
651C2×C4—24no—
652C2×C4—416no—
653C2×C4—42no—
654C2×C4—42no—
655C2×C4—42no—
656C2×C4—42no—
657C2×C4—478no—
658C2×C4—478no—
659C2×C4—944no—
660C2×C4—944no—
661C2×C4—944no—
662C2×C4—944no—
663C2×C4—944no—
664C2×C4—944no—
665C2×C4—944no—
666C2×C4—944no—
667C2×C4—944no—
668C2×C4—944no—
669C2×C4—944no—
670C2×C4—944no—
671C2×C4—944no—
672C2×C4—944no—
673C2×C4—944no—
674C2×C4—944no—
675C2×C4—944no—
676C2×C4—944no—
677C2×C4—18816no—
678C2×C4—1882no—
679C2×C4—1882no—
680C2×C4—1882no—
681C2×C4—1882no—
682C2×C4—1882no—
683C2×C4—1882no—
684C2×C4—1882no—
685C2×C4—1882no—
686C2×C4C2×C4×Dic4714yes—
687C2×C4D4×Dic4718yes—
688C22—28no—
689C22—28no—
690C22—24no—
691C22—24no—
692C22—42no—
693C22—42no—
694C22—42no—
695C22—42no—
696C22—44no—
697C22—44no—
698C22—44no—
699C22—44no—
700C22—44no—
701C22—44no—
702C22—42no—
703C22—42no—
704C22—42no—
705C22—42no—
706C22—42no—
707C22—42no—
708C22—42no—
709C22—42no—
710C22C22×C4×Dic4711yescharacteristic
711C22C4×D4×D4712yes—
712C22C4×D4×D4712yes—
713C22C2×D4×Dic4712yes—
714C22C4×#1062535212yes—
715C22C4×#1062535212yes—
716C22#41×Dic4712yes—
717C22#1568959611yescharacteristic
718C22#1568959611yescharacteristic
719C22#1568959611yescharacteristic
720C22#1568959611yescharacteristic
721C22#1568959811yescharacteristic
722C22#1568959811yescharacteristic
723C22#1568975511yescharacteristic
724C22#1568976012yes—
725C22#1568977012yes—
726C22#1568979112yes—
727C22#1568980111yescharacteristic
728C22#1568980411yescharacteristic
729C22#1568981812yes—
730C22#1568982012yes—
731C22#1568983712yes—
732C22#1568985711yescharacteristic
733C4—28no—
734C4—24no—
735C4—44no—
736C4—948no—
737C4—948no—
738C4—1884no—
739C4—1884no—
740C2—44no—
741C2—44no—
742C2C4×D4×Dic4712yes—
743C2#2024574111yescharacteristic
744C2#2024637111yescharacteristic
745C2#2024637211yescharacteristic
746C2#2024642912yes—
747C2#2024643012yes—
748C2#2024643712yes—
749C2#2024645111yescharacteristic
750C2#2024649711yescharacteristic
751C2#2024652111yescharacteristic
752C2#2024652411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D47
commutatorC22×C47C22×C42
FittingC2×C47×#386C2
socle, cosocleC24×C47C24
prime radicalC23×D4×C47C22
hypercenterC2×#386D47
hypocenterC47#13824
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C24 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
3. C2×C22⋊C4×Dic47C2semidirect
4. C2×C4×C22⋊Dic47C2semidirect
5. #20241625C2semidirect
6. #20241625C2semidirect
7. #20241622C2semidirect
8. #95×Dic47C2semidirect
20. #15689026C4semidirect
21. #15689003C4semidirect
34. C47×#386C4semidirect
40. C23×Dic47C2×C4semidirect
47. C2×C4⋊Dic47C2×C4semidirect
57. C2×C22⋊Dic47C2×C4semidirect
58. C2×C22⋊Dic47C2×C4semidirect
59. C2×C22⋊Dic47C2×C4semidirect
71. C2×C4×Dic47C2×C4semidirect
76. C47⋊#95C2×C4semidirect
77. C47⋊#95D4semidirect
91. C23×C4×C47C2×C4semidirect
100. C2×C22⋊C4×C47C2×C4semidirect
101. #95×C47C2×C4semidirect
131. C2×D4×C47C42semidirect
402. #386Dic47semidirect
412. C47#13824semidirect
435. C23×C4C2×Dic47semidirect
459. C2×C22⋊C4C2×Dic47semidirect
478. #95C2×Dic47semidirect
508. C2×D4C4×Dic47semidirect

Maximal subgroups

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

subgroupindex
C2×#156890262
C2×#156890032
C2×C22⋊C4×Dic472
C2×C4×C22⋊Dic472
#202416252
#202416222
#95×Dic472
C2×C47×#3862
#1382447