Finite Group Databasebeta

← #26147525

Subgroups — #26147525

Order 12032.

3366 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13093995C211yesmaximal, characteristic
2C22×C42×D47C211yesmaximal, characteristic, complemented
3C2×#15689026C211yesmaximal, characteristic, complemented
4C2×#15688999C214yesmaximal, complemented
5C2×#15688980C211yesmaximal, characteristic, complemented
6#20241625C214yesmaximal, complemented
7#20241618C211yesmaximal, characteristic, complemented
8#20241617C211yesmaximal, characteristic, complemented
9C2×C47×#390C211yesmaximal, characteristic, complemented
10C23×C22⋊D47C2212yes—
11C23×C4×D47C2212yes—
12C23×C4×D47C2211yescharacteristic
13C2×#13093995—24no—
14C2×#13093995—24no—
15C2×#13093995C418yescomplemented
16C22×C4⋊Dic47C2211yescharacteristic
17C22×C4⋊Dic47C2211yescharacteristic
18C22×C22⋊Dic47C2214yes—
19C22×C22⋊Dic47C2212yes—
20C22×(C2×D47)⋊C4C2212yes—
21C22×C4×Dic47C2212yes—
22C22×C4×Dic47C2211yescharacteristic
23C2×C42×D47—24no—
24C2×C42×D47—24no—
25C2×C42×D47—24no—
26#15689026—24no—
27#15688999—216no—
28#15688980—24no—
29C2×C47⋊#95C2214yes—
30C2×C47⋊#95C2214yes—
31C2×C47⋊#95C2212yes—
32C23×D4×C47C2211yescharacteristic
33C22×C4⋊C4×C47C2211yescharacteristic
34C22×C22⋊C4×C47C2214yes—
35C22×C42×C47C2211yescharacteristic
36C47×#390—24no—
37C24×D47C2311yescharacteristic
38C22×C22⋊D47—28no—
39C22×C22⋊D47—24no—
40C22×C22⋊D47—24no—
41C22×C22⋊D47—28no—
42C22×C22⋊D47C2×C418yes—
43C23×Dic47C2312yes—
44C23×Dic47C2312yes—
45C23×Dic47C2311yescharacteristic
46C23×Dic47C2312yes—
47C22×C4×D47—24no—
48C22×C4×D47—24no—
49C22×C4×D47—24no—
50C22×C4×D47—22no—
51C22×C4×D47—22no—
52C22×C4×D47—24no—
53C22×C4×D47—22no—
54C22×C4×D47—22no—
55C22×C4×D47—24no—
56C22×C4×D47—24no—
57C22×C4×D47C2×C414yes—
58C22×C4×D47D414yes—
59C22×C4×D47D414yes—
60C22×C4×D47D418yescomplemented
61#13093995—232no—
62C2×C4⋊Dic47—22no—
63C2×C4⋊Dic47—22no—
64C2×C4⋊Dic47—22no—
65C2×C4⋊Dic47—22no—
66C2×C4⋊Dic47—22no—
67C2×C4⋊Dic47C2×C414yescomplemented
68C2×C22⋊Dic47—24no—
69C2×C22⋊Dic47—24no—
70C2×C22⋊Dic47—28no—
71C2×C22⋊Dic47—28no—
72C2×C22⋊Dic47—28no—
73C2×C22⋊Dic47C2×C418yescomplemented
74C2×(C2×D47)⋊C4—24no—
75C2×(C2×D47)⋊C4—28no—
76C2×C4×Dic47—24no—
77C2×C4×Dic47—22no—
78C2×C4×Dic47—22no—
79C2×C4×Dic47—24no—
80C2×C4×Dic47—24no—
81C2×C4×Dic47D414yescomplemented
82C42×D47—232no—
83C47⋊#95—28no—
84C47⋊#95—24no—
85C47⋊#95—28no—
86C25×C47C2312yes—
87C22×D4×C47—22no—
88C22×D4×C47—22no—
89C22×D4×C47—22no—
90C22×D4×C47—22no—
91C22×D4×C47—22no—
92C22×D4×C47—22no—
93C22×D4×C47C2×C414yescomplemented
94C23×C4×C47C2312yes—
95C23×C4×C47C2312yes—
96C23×C4×C47C2311yescharacteristic
97C2×C4⋊C4×C47—22no—
98C2×C4⋊C4×C47—22no—
99C2×C4⋊C4×C47—22no—
100C2×C22⋊C4×C47—28no—
101C2×C22⋊C4×C47—28no—
102C2×C22⋊C4×C47—28no—
103C2×C42×C47—22no—
104C2×C42×C47—22no—
105C2×C42×C47D414yescomplemented
106C24×C47—22no—
107C24×C47—24no—
108C24×C47—22no—
109C24×C47—22no—
110C24×C47—22no—
111C24×C47—24no—
112C24×C47—22no—
113C24×C47—22no—
114C24×C47—24no—
115C24×C47—24no—
116C24×C47C22×C414yes—
117C24×C47C2411yescharacteristic
118C23×D47—21no—
119C23×D47—21no—
120C23×D47—21no—
121C23×D47—21no—
122C23×D47—22no—
123C23×D47—22no—
124C23×D47C22×C412yes—
125C23×D47C2×D412yes—
126C23×D47C2×D412yes—
127C23×D47C2×D414yes—
128C23×D47#4114yes—
129C2×D4×C47—28no—
130C2×D4×C47—28no—
131C2×D4×C47—28no—
132C2×D4×C47—44no—
133C2×D4×C47—44no—
134C2×D4×C47—44no—
135C2×D4×C47—44no—
136C22×C4×C47—22no—
137C22×C4×C47—22no—
138C22×C4×C47—22no—
139C22×C4×C47—22no—
140C22×C4×C47—22no—
141C22×C4×C47—24no—
142C22×C4×C47—22no—
143C22×C4×C47—24no—
144C22×C4×C47—22no—
145C22×C4×C47C22×C412yes—
146C22×C4×C47C2×D414yes—
147C22×C4×C47C2×D414yes—
148C22×C4×C47C2×D412yes—
149C22×C4×C47C2×D412yes—
150C22×C4×C47C2×D412yes—
151C22×C4×C47C2×D412yes—
152C22×C4×C47#4114yes—
153C22×C4×C47#4112yes—
154C22×C4×C47#4112yes—
155C2×C22⋊D47—216no—
156C2×C22⋊D47—232no—
157C2×C22⋊D47—416no—
158C2×C22⋊D47—48no—
159C2×C22⋊D47—48no—
160C22×Dic47—21no—
161C22×Dic47—21no—
162C22×Dic47—22no—
163C22×Dic47—22no—
164C22×Dic47—21no—
165C22×Dic47—21no—
166C22×Dic47—22no—
167C22×Dic47—22no—
168C22×Dic47—24no—
169C22×Dic47—22no—
170C22×Dic47—22no—
171C22×Dic47—24no—
172C22×Dic47—24no—
173C22×Dic47—22no—
174C22×Dic47—22no—
175C22×Dic47—24no—
176C22×Dic47—22no—
177C22×Dic47C22×C414yes—
178C22×Dic47C22×C412yes—
179C22×Dic47C2×D412yes—
180C22×Dic47C2×D412yes—
181C22×Dic47C2×D414yes—
182C22×Dic47C2×D414yes—
183C22×Dic47#4114yes—
184C2×C4×D47—216no—
185C2×C4×D47—216no—
186C2×C4×D47—216no—
187C2×C4×D47—216no—
188C2×C4×D47—216no—
189C2×C4×D47—28no—
190C2×C4×D47—28no—
191C2×C4×D47—28no—
192C2×C4×D47—28no—
193C2×C4×D47—28no—
194C2×C4×D47—216no—
195C2×C4×D47—28no—
196C2×C4×D47—216no—
197C2×C4×D47C22⋊C4116yescomplemented
198C4⋊C4×C47—44no—
199C22⋊C4×C47—416no—
200C42×C47—28no—
201C22⋊Dic47—216no—
202C22⋊Dic47—416no—
203(C2×D47)⋊C4—48no—
204C4⋊Dic47—28no—
205C4⋊Dic47—44no—
206C4×Dic47—216no—
207C4×Dic47—28no—
208C23×C47—24no—
209C23×C47—28no—
210C23×C47—24no—
211C23×C47—24no—
212C23×C47—28no—
213C23×C47—42no—
214C23×C47—44no—
215C23×C47—44no—
216C23×C47—44no—
217C23×C47—42no—
218C23×C47—42no—
219C23×C47—42no—
220C23×C47—44no—
221C23×C47—44no—
222C23×C47—44no—
223C23×C47—42no—
224C23×C47—44no—
225C23×C47—44no—
226C23×C47—42no—
227C23×C47—44no—
228C23×C47—42no—
229C23×C47—44no—
230C23×C47—42no—
231C23×C47C23×C411yescharacteristic
232C23×C47C22×D411yescharacteristic
233C23×C47C22×D411yescharacteristic
234C23×C47C22×D411yescharacteristic
235C23×C47C22×D412yes—
236C23×C47C22×D411yescharacteristic
237C23×C47C2×#4112yes—
238C23×C47C2×#4112yes—
239C23×C47C2×#4111yescharacteristic
240C23×C47C2×#4112yes—
241C23×C47C2×#4111yescharacteristic
242C22×D47—22no—
243C22×D47—22no—
244C22×D47—24no—
245C22×D47—22no—
246C22×D47—24no—
247C22×D47—24no—
248C22×D47—22no—
249C22×D47—22no—
250C22×D47—22no—
251C22×D47—24no—
252C22×D47—24no—
253C22×D47—24no—
254C22×D47—24no—
255C22×D47—24no—
256C22×D47—24no—
257C22×D47—22no—
258C22×D47—24no—
259C22×D47—22no—
260C22×D47C2×C22⋊C414yes—
261C22×D47C4×D418yes—
262C22×D47#12118yes—
263C22×D47#12414yes—
264C22×D47#12714yes—
265D4×C47—416no—
266C2×C4×C47—24no—
267C2×C4×C47—24no—
268C2×C4×C47—24no—
269C2×C4×C47—24no—
270C2×C4×C47—24no—
271C2×C4×C47—24no—
272C2×C4×C47—44no—
273C2×C4×C47—42no—
274C2×C4×C47—42no—
275C2×C4×C47—42no—
276C2×C4×C47—44no—
277C2×C4×C47C2×C22⋊C414yes—
278C2×C4×C47C4×D414yes—
279C2×C4×C47C4×D414yes—
280C2×C4×C47#12014yes—
281C2×C4×C47#12114yes—
282C2×C4×C47#12114yes—
283C2×C4×C47#12118yescomplemented
284C2×C4×C47#12314yes—
285C22⋊D47—432no—
286C2×Dic47—22no—
287C2×Dic47—22no—
288C2×Dic47—24no—
289C2×Dic47—22no—
290C2×Dic47—24no—
291C2×Dic47—24no—
292C2×Dic47—22no—
293C2×Dic47—22no—
294C2×Dic47—22no—
295C2×Dic47—24no—
296C2×Dic47—24no—
297C2×Dic47—24no—
298C2×Dic47—24no—
299C2×Dic47—28no—
300C2×Dic47—44no—
301C2×Dic47—42no—
302C2×Dic47—42no—
303C2×Dic47—42no—
304C2×Dic47—44no—
305C2×Dic47—42no—
306C2×Dic47—44no—
307C2×Dic47—42no—
308C2×Dic47C2×C22⋊C414yes—
309C2×Dic47#12118yescomplemented
310C4×D47—264no—
311C4×D47—232no—
312#14698—471nomaximal, Sylow
313C22×C47—44no—
314C22×C47—44no—
315C22×C47—44no—
316C22×C47—48no—
317C22×C47—48no—
318C22×C47—84no—
319C22×C47—82no—
320C22×C47—82no—
321C22×C47—84no—
322C22×C47—82no—
323C22×C47—82no—
324C22×C47C22×C22⋊C411yescharacteristic
325C22×C47C2×C4×D412yes—
326C22×C47C2×C4×D411yescharacteristic
327C22×C47C2×C4×D411yescharacteristic
328C22×C47C4×#4112yes—
329C22×C47C2×#12011yescharacteristic
330C22×C47C2×#12112yes—
331C22×C47C2×#12112yes—
332C22×C47C2×#12112yes—
333C22×C47C2×#12111yescharacteristic
334C22×C47C2×#12111yescharacteristic
335C22×C47C2×#12311yescharacteristic
336C22×C47#52512yes—
337C22×C47#52512yes—
338C22×C47#52512yes—
339C22×C47C2×#12411yescharacteristic
340C22×C47#52912yes—
341C22×C47#52912yes—
342C22×C47C2×#12711yescharacteristic
343C22×C47#53212yes—
344C22×C47#53211yescharacteristic
345C22×C47#53212yes—
346C22×C47#53211yescharacteristic
347C2×D47—28no—
348C2×D47—24no—
349C2×D47—24no—
350C2×D47—28no—
351C2×D47—24no—
352C2×D47—24no—
353C2×D47—24no—
354C2×D47—24no—
355C2×D47—28no—
356C2×D47—28no—
357C2×D47#39018yescomplemented
358C4×C47—28no—
359C4×C47—82no—
360C4×C47#38618yescomplemented
361Dic47—28no—
362Dic47—24no—
363Dic47—44no—
364Dic47—82no—
365C22×#121—471no—
366C23×C42—471no—
367C2×#390—471no—
368C2×#390D4711yescharacteristic, complemented
369C2×#386—474no—
370C2×#380—471no—
371#1437—474no—
372C4⋊#95—471no—
373C4⋊#95—471no—
374C2×C47—84no—
375C2×C47C2×#38611yescharacteristic
376C2×C47C2×#39011yescharacteristic
377C2×C47#229711yescharacteristic
378C2×C47C4×#12112yes—
379C2×C47C4×#12112yes—
380C2×C47#284712yes—
381C2×C47#285011yescharacteristic
382C2×C47#285011yescharacteristic
383C2×C47#285412yes—
384C2×C47#285611yescharacteristic
385C2×C47#285611yescharacteristic
386D47—28no—
387C23×D4—472no—
388C23×D4C2×D4711yescharacteristic
389C24×C4—471no—
390C24×C4—472no—
391C2×#121—478no—
392C2×#121—944no—
393C2×#121—944no—
394C22×C4⋊C4—471no—
395C22×C4⋊C4—471no—
396C22×C4⋊C4C2×D4711yescharacteristic
397C22×C22⋊C4—472no—
398C22×C22⋊C4—474no—
399C22×C22⋊C4—472no—
400C22×C22⋊C4C2×D4714yes—
401C22×C42—471no—
402C22×C42—472no—
403C22×C42—944no—
404C22×C42—944no—
405C22×C42—944no—
406C22×C42C2×D4711yescharacteristic
407#390—24no—
408#390—944no—
409#386—9416no—
410#380—944no—
411C2×#95—474no—
412C2×#95—474no—
413C2×#95—472no—
414C47#1469811yescharacteristic, complemented, Sylow
415C25—471no—
416C25C22×D4712yes—
417C22×D4—22no—
418C22×D4—22no—
419C22×D4—22no—
420C22×D4—22no—
421C22×D4—22no—
422C22×D4—22no—
423C22×D4—478no—
424C22×D4—944no—
425C22×D4—944no—
426C22×D4—948no—
427C22×D4—948no—
428C22×D4C4×D4714yescomplemented
429C23×C4—471no—
430C23×C4—472no—
431C23×C4—474no—
432C23×C4—474no—
433C23×C4—474no—
434C23×C4—472no—
435C23×C4—478no—
436C23×C4—472no—
437C23×C4—944no—
438C23×C4—944no—
439C23×C4—944no—
440C23×C4—944no—
441C23×C4—942no—
442C23×C4—942no—
443C23×C4—944no—
444C23×C4—942no—
445C23×C4—944no—
446C23×C4—942no—
447C23×C4C22×D4712yes—
448C23×C4C22×D4712yes—
449C23×C4C22×D4711yescharacteristic
450#121—9432no—
451C2×C4⋊C4—22no—
452C2×C4⋊C4—22no—
453C2×C4⋊C4—22no—
454C2×C4⋊C4—474no—
455C2×C4⋊C4—942no—
456C2×C4⋊C4—942no—
457C2×C4⋊C4—942no—
458C2×C4⋊C4—942no—
459C2×C4⋊C4—942no—
460C2×C22⋊C4—28no—
461C2×C22⋊C4—28no—
462C2×C22⋊C4—28no—
463C2×C22⋊C4—478no—
464C2×C22⋊C4—944no—
465C2×C22⋊C4—944no—
466C2×C22⋊C4—944no—
467C2×C22⋊C4—948no—
468C2×C22⋊C4—948no—
469C2×C22⋊C4—948no—
470C2×C22⋊C4—948no—
471C2×C42—22no—
472C2×C42—22no—
473C2×C42—474no—
474C2×C42—9432no—
475C2×C42—944no—
476C2×C42—944no—
477C2×C42—942no—
478C2×C42—944no—
479C2×C42—942no—
480C2×C42C22⋊D4714yescomplemented
481#95—944no—
482#95—948no—
483#95—948no—
484C24—24no—
485C24—22no—
486C24—22no—
487C24—22no—
488C24—22no—
489C24—24no—
490C24—24no—
491C24—24no—
492C24—22no—
493C24—22no—
494C24—472no—
495C24—472no—
496C24—474no—
497C24—472no—
498C24—474no—
499C24—941no—
500C24—941no—
501C24—942no—
502C24—941no—
503C24—942no—
504C24—941no—
505C24C2×C4×D4714yes—
506C24C23×D4711yescharacteristic
507C2×D4—28no—
508C2×D4—28no—
509C2×D4—28no—
510C2×D4—44no—
511C2×D4—44no—
512C2×D4—44no—
513C2×D4—44no—
514C2×D4—9416no—
515C2×D4—9432no—
516C2×D4—18816no—
517C2×D4—1888no—
518C2×D4—1888no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—24no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—24no—
527C22×C4—22no—
528C22×C4—472no—
529C22×C4—472no—
530C22×C4—474no—
531C22×C4—474no—
532C22×C4—472no—
533C22×C4—474no—
534C22×C4—4716no—
535C22×C4—474no—
536C22×C4—9416no—
537C22×C4—9416no—
538C22×C4—9416no—
539C22×C4—9416no—
540C22×C4—9416no—
541C22×C4—9416no—
542C22×C4—941no—
543C22×C4—942no—
544C22×C4—941no—
545C22×C4—942no—
546C22×C4—942no—
547C22×C4—941no—
548C22×C4—942no—
549C22×C4—941no—
550C22×C4—948no—
551C22×C4—948no—
552C22×C4—948no—
553C22×C4—948no—
554C22×C4—9416no—
555C22×C4—948no—
556C22×C4—948no—
557C22×C4—944no—
558C22×C4—942no—
559C22×C4—942no—
560C22×C4—944no—
561C22×C4—944no—
562C22×C4—942no—
563C22×C4—942no—
564C22×C4—944no—
565C22×C4—942no—
566C22×C4C2×C4×D4712yes—
567C22×C4#1062535012yes—
568C22×C4D4×D4714yes—
569C22×C4D4×D4712yes—
570C22×C4D4×D4712yes—
571C22×C4D4×D4712yes—
572C22×C4#1062535214yes—
573C22×C4#1062535212yes—
574C22×C4C2×C22⋊D4714yes—
575C22×C4C2×C22⋊D4712yes—
576C4⋊C4—44no—
577C4⋊C4—948no—
578C4⋊C4—1884no—
579C22⋊C4—416no—
580C22⋊C4—9416no—
581C22⋊C4—1888no—
582C22⋊C4—18816no—
583C42—28no—
584C42—9416no—
585C42—948no—
586C23—24no—
587C23—28no—
588C23—24no—
589C23—24no—
590C23—28no—
591C23—42no—
592C23—44no—
593C23—44no—
594C23—44no—
595C23—42no—
596C23—42no—
597C23—42no—
598C23—44no—
599C23—44no—
600C23—44no—
601C23—42no—
602C23—44no—
603C23—44no—
604C23—42no—
605C23—44no—
606C23—42no—
607C23—44no—
608C23—42no—
609C23—474no—
610C23—478no—
611C23—478no—
612C23—474no—
613C23—474no—
614C23—942no—
615C23—942no—
616C23—944no—
617C23—942no—
618C23—944no—
619C23—944no—
620C23—942no—
621C23—942no—
622C23—942no—
623C23—944no—
624C23—944no—
625C23—944no—
626C23—944no—
627C23—944no—
628C23—944no—
629C23—942no—
630C23—944no—
631C23—942no—
632C23C22×C4×D4711yescharacteristic
633C23C2×D4×D4711yescharacteristic
634C23C2×D4×D4711yescharacteristic
635C23C2×D4×D4712yes—
636C23C2×D4×D4711yescharacteristic
637C23C22×C22⋊D4711yescharacteristic
638C23#41×D4712yes—
639C23#41×D4712yes—
640C23C2×#1062535211yescharacteristic
641C23C2×#1062535212yes—
642C23C2×#1062535011yescharacteristic
643D4—416no—
644D4—18832no—
645C2×C4—24no—
646C2×C4—24no—
647C2×C4—24no—
648C2×C4—24no—
649C2×C4—24no—
650C2×C4—24no—
651C2×C4—44no—
652C2×C4—42no—
653C2×C4—42no—
654C2×C4—42no—
655C2×C4—44no—
656C2×C4—474no—
657C2×C4—478no—
658C2×C4—9464no—
659C2×C4—942no—
660C2×C4—942no—
661C2×C4—944no—
662C2×C4—942no—
663C2×C4—944no—
664C2×C4—944no—
665C2×C4—942no—
666C2×C4—942no—
667C2×C4—942no—
668C2×C4—944no—
669C2×C4—944no—
670C2×C4—944no—
671C2×C4—9432no—
672C2×C4—944no—
673C2×C4—948no—
674C2×C4—1884no—
675C2×C4—1882no—
676C2×C4—1882no—
677C2×C4—1884no—
678C2×C4—1882no—
679C2×C4—1884no—
680C2×C4—1882no—
681C2×C4—1882no—
682C2×C4C22⋊C4×D4714yes—
683C2×C4(C22⋊D47)⋊C414yes—
684C2×C4C4×C22⋊D4714yes—
685C2×C4#1309399214yes—
686C2×C4#1309399514yes—
687C2×C4#1309399518yescomplemented
688C2×C4#1309399714yes—
689C2×C4#1309400614yes—
690C22—44no—
691C22—44no—
692C22—44no—
693C22—48no—
694C22—48no—
695C22—84no—
696C22—82no—
697C22—82no—
698C22—84no—
699C22—82no—
700C22—82no—
701C22—478no—
702C22—948no—
703C22—944no—
704C22—944no—
705C22—944no—
706C22—948no—
707C22—944no—
708C22—944no—
709C22—944no—
710C22—948no—
711C22—948no—
712C22C2×C22⋊C4×D4711yescharacteristic
713C22C4×D4×D4712yes—
714C22C2×(C22⋊D47)⋊C411yescharacteristic
715C22C2×C4×C22⋊D4711yescharacteristic
716C22C4×#1062535212yes—
717C22C2×#1309399211yescharacteristic
718C22#121×D4712yes—
719C22#121×D4712yes—
720C22C2×#1309399512yes—
721C22C2×#1309399511yescharacteristic
722C22C2×#1309399711yescharacteristic
723C22C2×#1309400611yescharacteristic
724C22#1568963012yes—
725C22#1568963312yes—
726C22#1568963312yes—
727C22#124×D4711yescharacteristic
728C22#1568965212yes—
729C22#1568965512yes—
730C22#127×D4711yescharacteristic
731C22#1568967012yes—
732C22#1568967111yescharacteristic
733C22#1568967112yes—
734C22#1568967211yescharacteristic
735C4—28no—
736C4—82no—
737C4—948no—
738C4—944no—
739C4—3762no—
740C4—1884no—
741C4#1568899918yescomplemented
742C2—84no—
743C2—948no—
744C2C2×#1568899911yescharacteristic
745C2#390×D4711yescharacteristic
746C2#2024587511yescharacteristic
747C2C4×#1309399512yes—
748C2#2024590412yes—
749C2#2025166712yes—
750C2#2025168411yescharacteristic
751C2#2025168811yescharacteristic
752C2#2025171812yes—
753C2#2025173011yescharacteristic
754C2#2025173211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D47
commutatorC23×C47C23×C4
FittingC2×C47×#390C2
socle, cosocleC24×C47C24
prime radicalC22×#13093995C2
hypercenterC2×#390D47
hypocenterC47#14698
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C24 ◁ C2×#390

Complements

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

NH ≅ G/Ntype
2. C22×C42×D47C2semidirect
3. C2×#15689026C2semidirect
4. C2×#15688999C2semidirect
5. C2×#15688980C2semidirect
6. #20241625C2semidirect
7. #20241618C2semidirect
8. #20241617C2semidirect
9. C2×C47×#390C2semidirect
15. C2×#13093995C4semidirect
60. C22×C4×D47D4semidirect
67. C2×C4⋊Dic47C2×C4semidirect
73. C2×C22⋊Dic47C2×C4semidirect
81. C2×C4×Dic47D4semidirect
93. C22×D4×C47C2×C4semidirect
105. C2×C42×C47D4semidirect
197. C2×C4×D47C22⋊C4semidirect
283. C2×C4×C47#121semidirect
309. C2×Dic47#121semidirect
357. C2×D47#390semidirect
360. C4×C47#386semidirect
368. C2×#390D47semidirect
414. C47#14698semidirect
428. C22×D4C4×D47semidirect
480. C2×C42C22⋊D47semidirect
687. C2×C4#13093995semidirect
741. C4#15688999semidirect

Maximal subgroups

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

subgroupindex
C22×#130939952
C22×C42×D472
C2×#156890262
C2×#156889992
C2×#156889802
#202416252
#202416182
#202416172
C2×C47×#3902
#1469847