Finite Group Databasebeta

← #26147507

Subgroups — #26147507

Order 12032.

2746 conjugacy classes of subgroups.

The subgroup lattice has 814 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C4×Dic47C211yesmaximal, characteristic, complemented
2C2×#15689011C212yesmaximal, complemented
3C2×#15689003C211yesmaximal, characteristic
4C2×#15689003C211yesmaximal, characteristic
5C2×#15688995C211yesmaximal, characteristic, complemented
6#20241625C212yesmaximal, complemented
7#20241619C212yesmaximal, complemented
8#20241612C212yesmaximal, complemented
9#20241611C211yesmaximal, characteristic, complemented
10#20241610C211yesmaximal, characteristic, complemented
11C2×C47×#386C211yesmaximal, characteristic
12C24×Dic47C2211yescharacteristic
13C24×Dic47C2211yescharacteristic
14C22×Dic47⋊C4C2212yes—
15C22×C22⋊Dic47C2212yes—
16C22×C22⋊Dic47C2211yescharacteristic
17C22×C22⋊Dic47C2211yescharacteristic
18C22×C22⋊Dic47C2212yes—
19C22×C4×Dic47—28no—
20C22×C4×Dic47—24no—
21C22×C4×Dic47C2212yes—
22C22×C4×Dic47C2212yes—
23#15689011—28no—
24#15689003—24no—
25#15689003C418yescomplemented
26#15688995—24no—
27C2×C47⋊#95C2212yes—
28C2×C47⋊#95C2212yes—
29C2×C47⋊#95C2212yes—
30C2×C47⋊#95C2212yes—
31C2×C47⋊#95C2212yes—
32C2×C47⋊#95C2212yes—
33C2×C47⋊#95C2212yes—
34C23×D4×C47C2211yescharacteristic
35C24×C4×C47C2211yescharacteristic
36C22×C22⋊C4×C47C2211yescharacteristic
37C22×C22⋊C4×C47C2211yescharacteristic
38C22×C22⋊C4×C47C2211yescharacteristic
39C47×#386—24no—
40C2×#95×C47C2211yescharacteristic
41C2×#95×C47C2211yescharacteristic
42C23×Dic47—22no—
43C23×Dic47—22no—
44C23×Dic47—22no—
45C23×Dic47—22no—
46C23×Dic47—24no—
47C23×Dic47—24no—
48C23×Dic47—24no—
49C23×Dic47—24no—
50C23×Dic47C2×C414yes—
51C23×Dic47D414yes—
52C23×Dic47C2312yes—
53C23×Dic47C2312yes—
54C23×Dic47C2312yes—
55C23×Dic47C2312yes—
56C2×Dic47⋊C4—24no—
57C2×Dic47⋊C4—24no—
58C2×Dic47⋊C4—24no—
59C2×C22⋊Dic47—22no—
60C2×C22⋊Dic47—22no—
61C2×C22⋊Dic47—24no—
62C2×C22⋊Dic47—24no—
63C2×C22⋊Dic47—22no—
64C2×C22⋊Dic47—22no—
65C2×C22⋊Dic47—22no—
66C2×C22⋊Dic47—24no—
67C2×C22⋊Dic47—24no—
68C2×C22⋊Dic47—24no—
69C2×C22⋊Dic47C2×C414yes—
70C2×C22⋊Dic47C2×C418yescomplemented
71C2×C4×Dic47—232no—
72C2×C4×Dic47—24no—
73C2×C4×Dic47—24no—
74C2×C4×Dic47—24no—
75C2×C4×Dic47—24no—
76C2×C4×Dic47—24no—
77C2×C4×Dic47D418yescomplemented
78C47⋊#95—24no—
79C47⋊#95—24no—
80C47⋊#95—24no—
81C47⋊#95—24no—
82C47⋊#95—24no—
83C47⋊#95—24no—
84C47⋊#95C2×C418yescomplemented
85C25×C47C2311yescharacteristic
86C25×C47C2311yescharacteristic
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×C414yes—
94C23×C4×C47—22no—
95C23×C4×C47—22no—
96C23×C4×C47—24no—
97C23×C4×C47—24no—
98C23×C4×C47D414yes—
99C23×C4×C47C2311yescharacteristic
100C23×C4×C47C2311yescharacteristic
101C23×C4×C47C2311yescharacteristic
102C23×C4×C47C2311yescharacteristic
103C23×C4×C47C2311yescharacteristic
104C2×C22⋊C4×C47—22no—
105C2×C22⋊C4×C47—22no—
106C2×C22⋊C4×C47—22no—
107C2×C22⋊C4×C47—24no—
108C2×C22⋊C4×C47—22no—
109C2×C22⋊C4×C47—22no—
110C2×C22⋊C4×C47—24no—
111#95×C47—22no—
112#95×C47—22no—
113C24×C47—22no—
114C24×C47—22no—
115C24×C47—22no—
116C24×C47—22no—
117C24×C47—21no—
118C24×C47—22no—
119C24×C47—21no—
120C24×C47—22no—
121C24×C47—21no—
122C24×C47—21no—
123C24×C47—21no—
124C24×C47—21no—
125C24×C47—22no—
126C24×C47—22no—
127C24×C47C22×C412yes—
128C24×C47C22×C412yes—
129C24×C47C2×D412yes—
130C24×C47C2×D412yes—
131C24×C47#4112yes—
132C24×C47#4112yes—
133C24×C47#4112yes—
134C24×C47#4112yes—
135C24×C47C2411yescharacteristic
136C2×D4×C47—28no—
137C2×D4×C47—28no—
138C2×D4×C47—28no—
139C2×D4×C47—44no—
140C2×D4×C47—44no—
141C2×D4×C47—44no—
142C2×D4×C47—44no—
143C22×C4×C47—216no—
144C22×C4×C47—216no—
145C22×C4×C47—28no—
146C22×C4×C47—22no—
147C22×C4×C47—21no—
148C22×C4×C47—21no—
149C22×C4×C47—22no—
150C22×C4×C47—21no—
151C22×C4×C47—21no—
152C22×C4×C47—28no—
153C22×C4×C47—28no—
154C22×C4×C47—21no—
155C22×C4×C47—21no—
156C22×C4×C47—21no—
157C22×C4×C47—21no—
158C22×C4×C47—21no—
159C22×C4×C47—21no—
160C22×C4×C47—21no—
161C22×C4×C47—21no—
162C22×C4×C47—21no—
163C22×C4×C47—22no—
164C22×C4×C47—21no—
165C22×C4×C47—21no—
166C22×C4×C47—21no—
167C22×C4×C47—22no—
168C22×C4×C47—22no—
169C22×C4×C47—22no—
170C22×C4×C47C22×C412yes—
171C22×C4×C47C2×D414yes—
172C22×C4×C47C2×D412yes—
173C22×C4×C47C2×D412yes—
174C22×C4×C47#4114yes—
175C22×Dic47—28no—
176C22×Dic47—28no—
177C22×Dic47—216no—
178C22×Dic47—216no—
179C22×Dic47—28no—
180C22×Dic47—28no—
181C22×Dic47—28no—
182C22×Dic47—28no—
183C22×Dic47—22no—
184C22×Dic47—22no—
185C22×Dic47—22no—
186C22×Dic47—22no—
187C22×Dic47—22no—
188C22×Dic47—22no—
189C22×Dic47—22no—
190C22×Dic47—22no—
191C22×Dic47—216no—
192C22×Dic47—216no—
193C22×Dic47—22no—
194C22×Dic47—22no—
195C22×Dic47—22no—
196C22×Dic47—22no—
197C22×Dic47—22no—
198C22×Dic47—22no—
199C22×Dic47—22no—
200C22×Dic47—22no—
201C22×Dic47—22no—
202C22×Dic47—22no—
203C22×Dic47—22no—
204C22×Dic47—22no—
205C22×Dic47—22no—
206C22×Dic47C22×C414yes—
207C22×Dic47C22×C414yes—
208C22×Dic47C2×D414yes—
209C22×Dic47C2×D414yes—
210C22×Dic47C2×D414yes—
211C22×Dic47#4114yes—
212C22×Dic47#4114yes—
213C22⋊C4×C47—44no—
214C22⋊C4×C47—44no—
215C22⋊C4×C47—44no—
216C22⋊Dic47—28no—
217C22⋊Dic47—216no—
218C22⋊Dic47—44no—
219C22⋊Dic47—48no—
220Dic47⋊C4—48no—
221C4×Dic47—216no—
222C4×Dic47—216no—
223C23×C47—24no—
224C23×C47—24no—
225C23×C47—22no—
226C23×C47—24no—
227C23×C47—22no—
228C23×C47—22no—
229C23×C47—22no—
230C23×C47—24no—
231C23×C47—24no—
232C23×C47—24no—
233C23×C47—24no—
234C23×C47—24no—
235C23×C47—24no—
236C23×C47—24no—
237C23×C47—24no—
238C23×C47—24no—
239C23×C47—22no—
240C23×C47—24no—
241C23×C47—22no—
242C23×C47—22no—
243C23×C47—24no—
244C23×C47—41no—
245C23×C47—42no—
246C23×C47—41no—
247C23×C47—41no—
248C23×C47—41no—
249C23×C47—42no—
250C23×C47—42no—
251C23×C47—41no—
252C23×C47—41no—
253C23×C47—42no—
254C23×C47—42no—
255C23×C47—41no—
256C23×C47—41no—
257C23×C47—42no—
258C23×C47—42no—
259C23×C47—42no—
260C23×C47—42no—
261C23×C47—42no—
262C23×C47#11714yes—
263C23×C47C4×D414yes—
264C23×C47C4×D414yes—
265C23×C47#12114yes—
266C23×C47#12314yes—
267C23×C47#12414yes—
268C23×C47#12614yes—
269C23×C47C23×C411yescharacteristic
270C23×C47C22×D412yes—
271C23×C47C22×D411yescharacteristic
272C23×C47C22×D411yescharacteristic
273C23×C47C2×#4112yes—
274C23×C47C2×#4112yes—
275C23×C47C2×#4111yescharacteristic
276C23×C47C2×#4111yescharacteristic
277C23×C47C2×#4111yescharacteristic
278C23×C47C2×#4112yes—
279C23×C47C2×#4111yescharacteristic
280D4×C47—416no—
281C2×C4×C47—232no—
282C2×C4×C47—22no—
283C2×C4×C47—22no—
284C2×C4×C47—22no—
285C2×C4×C47—22no—
286C2×C4×C47—24no—
287C2×C4×C47—24no—
288C2×C4×C47—24no—
289C2×C4×C47—24no—
290C2×C4×C47—22no—
291C2×C4×C47—22no—
292C2×C4×C47—22no—
293C2×C4×C47—41no—
294C2×C4×C47—41no—
295C2×C4×C47—41no—
296C2×C4×C47—41no—
297C2×C4×C47—41no—
298C2×C4×C47—42no—
299C2×C4×C47—41no—
300C2×C4×C47—41no—
301C2×C4×C47—41no—
302C2×C4×C47—41no—
303C2×C4×C47—41no—
304C2×C4×C47—42no—
305C2×C4×C47—42no—
306C2×C4×C47—42no—
307C2×C4×C47#12014yes—
308C2×C4×C47#12314yes—
309C2×Dic47—232no—
310C2×Dic47—232no—
311C2×Dic47—24no—
312C2×Dic47—24no—
313C2×Dic47—24no—
314C2×Dic47—24no—
315C2×Dic47—24no—
316C2×Dic47—24no—
317C2×Dic47—24no—
318C2×Dic47—24no—
319C2×Dic47—24no—
320C2×Dic47—24no—
321C2×Dic47—24no—
322C2×Dic47—24no—
323C2×Dic47—24no—
324C2×Dic47—24no—
325C2×Dic47—24no—
326C2×Dic47—42no—
327C2×Dic47—42no—
328C2×Dic47—42no—
329C2×Dic47—42no—
330C2×Dic47—42no—
331C2×Dic47—42no—
332C2×Dic47—42no—
333C2×Dic47—42no—
334C2×Dic47—42no—
335C2×Dic47—42no—
336C2×Dic47—42no—
337C2×Dic47C4×D418yes—
338C2×Dic47#12118yes—
339#14696—471nomaximal, Sylow
340C22×C47—24no—
341C22×C47—24no—
342C22×C47—28no—
343C22×C47—28no—
344C22×C47—24no—
345C22×C47—24no—
346C22×C47—28no—
347C22×C47—24no—
348C22×C47—28no—
349C22×C47—24no—
350C22×C47—42no—
351C22×C47—44no—
352C22×C47—42no—
353C22×C47—44no—
354C22×C47—42no—
355C22×C47—81no—
356C22×C47—81no—
357C22×C47—82no—
358C22×C47—82no—
359C22×C47—81no—
360C22×C47—81no—
361C22×C47#38818yescomplemented
362C22×C47C2×#11711yescharacteristic
363C22×C47C2×C4×D412yes—
364C22×C47C2×C4×D411yescharacteristic
365C22×C47C2×C4×D411yescharacteristic
366C22×C47C4×#4112yes—
367C22×C47C2×#12011yescharacteristic
368C22×C47C2×#12112yes—
369C22×C47C2×#12111yescharacteristic
370C22×C47C2×#12311yescharacteristic
371C22×C47C2×#12311yescharacteristic
372C22×C47#52512yes—
373C22×C47#52512yes—
374C22×C47#52511yescharacteristic
375C22×C47#52511yescharacteristic
376C22×C47#52512yes—
377C22×C47#52512yes—
378C22×C47C2×#12411yescharacteristic
379C22×C47C2×#12611yescharacteristic
380C22×C47#52912yes—
381C22×C47#52912yes—
382C22×C47#52912yes—
383C22×C47#52912yes—
384C22×C47#53212yes—
385C4×C47—24no—
386C4×C47—24no—
387C4×C47—42no—
388C4×C47—81no—
389C4×C47—81no—
390Dic47—28no—
391Dic47—28no—
392Dic47—44no—
393Dic47—82no—
394C23×C42—471no—
395C2×#388—472no—
396C2×#386—471no—
397C2×#386—471no—
398C2×#386D4711yescharacteristic
399C2×#385—471no—
400#1437—472no—
401#1436—472no—
402#1434—472no—
403C22⋊#95—471no—
404C22⋊#95—471no—
405C2×C47—28no—
406C2×C47—82no—
407C2×C47C2×#38811yescharacteristic
408C2×C47#229012yes—
409C2×C47C4×#12011yescharacteristic
410C2×C47C4×#12112yes—
411C2×C47C4×#12311yescharacteristic
412C2×C47#284711yescharacteristic
413C2×C47#284911yescharacteristic
414C2×C47#285012yes—
415C2×C47#285212yes—
416C2×C47#285311yescharacteristic
417C2×C47#285411yescharacteristic
418C23×D4C2×D4711yescharacteristic
419C24×C4—471no—
420C24×C4—471no—
421C24×C4C2×D4711yescharacteristic
422C22×C4⋊C4—472no—
423C22×C22⋊C4—471no—
424C22×C22⋊C4—472no—
425C22×C22⋊C4—471no—
426C22×C22⋊C4—472no—
427C22×C22⋊C4C2×D4711yescharacteristic
428C22×C22⋊C4C2×D4711yescharacteristic
429C22×C22⋊C4C2×D4711yescharacteristic
430C22×C42—472no—
431C22×C42—472no—
432C22×C42—948no—
433C22×C42—944no—
434#388—948no—
435#386—24no—
436#386—478no—
437#386—944no—
438#385—944no—
439C2×#95—472no—
440C2×#95—472no—
441C2×#95—472no—
442C2×#95—472no—
443C2×#95—472no—
444C2×#95—472no—
445C2×#95—472no—
446C2×#95C2×D4711yescharacteristic
447C2×#95C2×D4711yescharacteristic
448C47#1469611yescharacteristic, complemented, Sylow
449C25C22×D4711yescharacteristic
450C25C22×D4711yescharacteristic
451C22×D4—22no—
452C22×D4—22no—
453C22×D4—22no—
454C22×D4—22no—
455C22×D4—22no—
456C22×D4—22no—
457C22×D4C4×D4714yes—
458C23×C4—22no—
459C23×C4—22no—
460C23×C4—24no—
461C23×C4—24no—
462C23×C4—472no—
463C23×C4—472no—
464C23×C4—474no—
465C23×C4—474no—
466C23×C4—472no—
467C23×C4—472no—
468C23×C4—944no—
469C23×C4—944no—
470C23×C4—944no—
471C23×C4—944no—
472C23×C4—942no—
473C23×C4—942no—
474C23×C4—942no—
475C23×C4—942no—
476C23×C4C22⋊D4714yes—
477C23×C4C22×D4711yescharacteristic
478C23×C4C22×D4711yescharacteristic
479C23×C4C22×D4711yescharacteristic
480C23×C4C22×D4711yescharacteristic
481C23×C4C22×D4711yescharacteristic
482C2×C4⋊C4—944no—
483C2×C4⋊C4—944no—
484C2×C4⋊C4—944no—
485C2×C22⋊C4—22no—
486C2×C22⋊C4—22no—
487C2×C22⋊C4—22no—
488C2×C22⋊C4—24no—
489C2×C22⋊C4—24no—
490C2×C22⋊C4—22no—
491C2×C22⋊C4—22no—
492C2×C22⋊C4—474no—
493C2×C22⋊C4—478no—
494C2×C22⋊C4—944no—
495C2×C22⋊C4—944no—
496C2×C22⋊C4—942no—
497C2×C22⋊C4—942no—
498C2×C22⋊C4—944no—
499C2×C22⋊C4—944no—
500C2×C22⋊C4—944no—
501C2×C22⋊C4—942no—
502C2×C22⋊C4—942no—
503C2×C22⋊C4—942no—
504C2×C42—478no—
505C2×C42—944no—
506C2×C42—944no—
507C2×C42—9432no—
508C2×C42—944no—
509C2×C42—944no—
510C2×C42—944no—
511#95—22no—
512#95—22no—
513#95—478no—
514#95—944no—
515#95—944no—
516#95—944no—
517#95—944no—
518#95—944no—
519#95—944no—
520C24—22no—
521C24—22no—
522C24—22no—
523C24—22no—
524C24—22no—
525C24—21no—
526C24—21no—
527C24—22no—
528C24—22no—
529C24—22no—
530C24—21no—
531C24—21no—
532C24—21no—
533C24—21no—
534C24C2×C4×D4712yes—
535C24C2×C4×D4712yes—
536C24#1062535012yes—
537C24D4×D4712yes—
538C24#1062535212yes—
539C24#1062535212yes—
540C24#1062535212yes—
541C24C2×C22⋊D4712yes—
542C24C23×D4711yescharacteristic
543C2×D4—28no—
544C2×D4—28no—
545C2×D4—28no—
546C2×D4—44no—
547C2×D4—44no—
548C2×D4—44no—
549C2×D4—44no—
550C22×C4—216no—
551C22×C4—216no—
552C22×C4—28no—
553C22×C4—22no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—22no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—28no—
560C22×C4—28no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—22no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—22no—
577C22×C4—474no—
578C22×C4—474no—
579C22×C4—474no—
580C22×C4—474no—
581C22×C4—474no—
582C22×C4—474no—
583C22×C4—474no—
584C22×C4—9416no—
585C22×C4—9416no—
586C22×C4—948no—
587C22×C4—948no—
588C22×C4—948no—
589C22×C4—948no—
590C22×C4—9416no—
591C22×C4—9416no—
592C22×C4—948no—
593C22×C4—948no—
594C22×C4—942no—
595C22×C4—942no—
596C22×C4—942no—
597C22×C4—942no—
598C22×C4—942no—
599C22×C4—942no—
600C22×C4—942no—
601C22×C4—942no—
602C22×C4—942no—
603C22×C4—942no—
604C22×C4—942no—
605C22×C4—942no—
606C22×C4—942no—
607C22×C4—942no—
608C22×C4—942no—
609C22×C4—942no—
610C22×C4—942no—
611C22×C4—942no—
612C22×C4—942no—
613C22×C4—942no—
614C22×C4—942no—
615C22×C4C2×C4×D4712yes—
616C22×C4D4×D4714yes—
617C22×C4#1062535214yes—
618C22×C4C2×C22⋊D4712yes—
619C22×C4C2×C22⋊D4712yes—
620C4⋊C4—1888no—
621C22⋊C4—44no—
622C22⋊C4—44no—
623C22⋊C4—44no—
624C22⋊C4—9416no—
625C22⋊C4—948no—
626C22⋊C4—1888no—
627C22⋊C4—1884no—
628C42—9416no—
629C42—9416no—
630C23—24no—
631C23—24no—
632C23—22no—
633C23—24no—
634C23—22no—
635C23—24no—
636C23—24no—
637C23—22no—
638C23—22no—
639C23—24no—
640C23—24no—
641C23—24no—
642C23—24no—
643C23—24no—
644C23—24no—
645C23—24no—
646C23—22no—
647C23—24no—
648C23—22no—
649C23—22no—
650C23—24no—
651C23—41no—
652C23—42no—
653C23—41no—
654C23—41no—
655C23—41no—
656C23—42no—
657C23—42no—
658C23—41no—
659C23—41no—
660C23—42no—
661C23—42no—
662C23—41no—
663C23—41no—
664C23—42no—
665C23—42no—
666C23—42no—
667C23—42no—
668C23—42no—
669C23#1309398014yes—
670C23(C22⋊D47)⋊C414yes—
671C23C4×C22⋊D4714yes—
672C23#1309399514yes—
673C23#1309400514yes—
674C23#1309401014yes—
675C23#1309401714yes—
676C23C22×C4×D4711yescharacteristic
677C23C2×D4×D4712yes—
678C23C2×D4×D4711yescharacteristic
679C23C22×C22⋊D4711yescharacteristic
680C23#41×D4712yes—
681C23#41×D4712yes—
682C23C2×#1062535211yescharacteristic
683C23C2×#1062535211yescharacteristic
684C23C2×#1062535211yescharacteristic
685C23C2×#1062535212yes—
686C23C2×#1062535011yescharacteristic
687D4—416no—
688C2×C4—232no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—24no—
694C2×C4—24no—
695C2×C4—24no—
696C2×C4—24no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—42no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—478no—
715C2×C4—478no—
716C2×C4—9432no—
717C2×C4—9432no—
718C2×C4—944no—
719C2×C4—944no—
720C2×C4—944no—
721C2×C4—944no—
722C2×C4—944no—
723C2×C4—944no—
724C2×C4—944no—
725C2×C4—944no—
726C2×C4—944no—
727C2×C4—944no—
728C2×C4—944no—
729C2×C4—944no—
730C2×C4—944no—
731C2×C4—944no—
732C2×C4—944no—
733C2×C4—1882no—
734C2×C4—1882no—
735C2×C4—1882no—
736C2×C4—1882no—
737C2×C4—1882no—
738C2×C4—1882no—
739C2×C4—1882no—
740C2×C4—1882no—
741C2×C4—1882no—
742C2×C4—1882no—
743C2×C4—1882no—
744C2×C4#1309399214yes—
745C2×C4#1309400514yes—
746C22—24no—
747C22—24no—
748C22—28no—
749C22—28no—
750C22—24no—
751C22—24no—
752C22—28no—
753C22—24no—
754C22—28no—
755C22—24no—
756C22—42no—
757C22—44no—
758C22—42no—
759C22—44no—
760C22—42no—
761C22—81no—
762C22—81no—
763C22—82no—
764C22—82no—
765C22—81no—
766C22—81no—
767C22#1568901118yescomplemented
768C22C2×#1309398011yescharacteristic
769C22C4×D4×D4712yes—
770C22C2×(C22⋊D47)⋊C411yescharacteristic
771C22C2×C4×C22⋊D4711yescharacteristic
772C22C4×#1062535212yes—
773C22C2×#1309399211yescharacteristic
774C22#121×D4712yes—
775C22C2×#1309399511yescharacteristic
776C22C2×#1309400511yescharacteristic
777C22C2×#1309400511yescharacteristic
778C22#1568962912yes—
779C22#1568962912yes—
780C22#1568963011yescharacteristic
781C22#1568963011yescharacteristic
782C22#1568963212yes—
783C22#1568963312yes—
784C22C2×#1309401011yescharacteristic
785C22C2×#1309401711yescharacteristic
786C22#1568965012yes—
787C22#1568965012yes—
788C22#1568965312yes—
789C22#1568965412yes—
790C22#1568966812yes—
791C4—24no—
792C4—24no—
793C4—42no—
794C4—81no—
795C4—81no—
796C4—948no—
797C4—948no—
798C4—3762no—
799C4—1884no—
800C2—28no—
801C2—82no—
802C2C2×#1568901111yescharacteristic
803C2#2024582812yes—
804C2C4×#1309399211yescharacteristic
805C2#2024589812yes—
806C2C4×#1309400511yescharacteristic
807C2#2025166711yescharacteristic
808C2#2025167811yescharacteristic
809C2#2025168512yes—
810C2#2025170112yes—
811C2#2025170711yescharacteristic
812C2#2025171411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D47
commutatorC23×C47C23×C4
FittingC2×C47×#386C2
socle, cosocleC24×C47C24
prime radicalC23×D4×C47C22
hypercenterC2×#386D47
hypocenterC47#14696
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C24 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
1. C23×C4×Dic47C2semidirect
2. C2×#15689011C2semidirect
5. C2×#15688995C2semidirect
6. #20241625C2semidirect
7. #20241619C2semidirect
8. #20241612C2semidirect
9. #20241611C2semidirect
10. #20241610C2semidirect
25. #15689003C4semidirect
70. C2×C22⋊Dic47C2×C4semidirect
77. C2×C4×Dic47D4semidirect
84. C47⋊#95C2×C4semidirect
361. C22×C47#388semidirect
448. C47#14696semidirect
767. C22#15689011semidirect

Maximal subgroups

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

subgroupindex
C23×C4×Dic472
C2×#156890112
C2×#156890032
C2×#156889952
#202416252
#202416192
#202416122
#202416112
#202416102
C2×C47×#3862
#1469647