Finite Group Databasebeta

← #26139699

Subgroups — #26139699

Order 12032.

2178 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
1C2×#15689003C211yesmaximal, characteristic
2C2×#15689003C211yesmaximal, characteristic
3C2×C22⋊C4×Dic47C211yesmaximal, characteristic, complemented
4C22×C47⋊#95C211yesmaximal, characteristic, complemented
5#20241650C212yesmaximal, complemented
6#20241637C212yesmaximal, complemented
7#20241625C212yesmaximal, complemented
8#20241613C212yesmaximal, complemented
9#20241611C211yesmaximal, characteristic, complemented
10#20241610C211yesmaximal, characteristic, complemented
11C2×C47×#386C211yesmaximal, characteristic
12C24×Dic47C2211yescharacteristic
13C24×Dic47C2211yescharacteristic
14C22×C22⋊Dic47C2211yescharacteristic
15C22×C22⋊Dic47C2211yescharacteristic
16C22×C22⋊Dic47C2212yes—
17C22×C22⋊Dic47C2211yescharacteristic
18C22×C22⋊Dic47C2211yescharacteristic
19C22×C4×Dic47C2212yes—
20#15689003—24no—
21#15689003—24no—
22C22⋊C4×Dic47—24no—
23C2×C47⋊#95—24no—
24C2×C47⋊#95C2211yescharacteristic
25C2×C47⋊#95C2212yes—
26C2×C47⋊#95C2211yescharacteristic
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×C47C2212yes—
38C47×#386C418yescomplemented
39C2×#95×C47C2212yes—
40C23×Dic47—22no—
41C23×Dic47—22no—
42C23×Dic47—22no—
43C23×Dic47—24no—
44C23×Dic47—24no—
45C23×Dic47—22no—
46C23×Dic47—22no—
47C23×Dic47—42no—
48C23×Dic47—42no—
49C23×Dic47D414yes—
50C23×Dic47C2311yescharacteristic
51C23×Dic47C2311yescharacteristic
52C23×Dic47C2311yescharacteristic
53C23×Dic47C2312yes—
54C23×Dic47C2312yes—
55C23×Dic47C2311yescharacteristic
56C2×C22⋊Dic47—22no—
57C2×C22⋊Dic47—22no—
58C2×C22⋊Dic47—22no—
59C2×C22⋊Dic47—22no—
60C2×C22⋊Dic47—22no—
61C2×C22⋊Dic47—24no—
62C2×C22⋊Dic47—22no—
63C2×C22⋊Dic47—22no—
64C2×C22⋊Dic47—24no—
65C2×C22⋊Dic47—24no—
66C2×C22⋊Dic47—42no—
67C2×C22⋊Dic47—42no—
68C2×C22⋊Dic47D414yes—
69C2×C4×Dic47—24no—
70C2×C4×Dic47—24no—
71C2×C4×Dic47—42no—
72C47⋊#95—24no—
73C47⋊#95—24no—
74C47⋊#95—24no—
75C47⋊#95—24no—
76C47⋊#95—22no—
77C47⋊#95—22no—
78C47⋊#95—24no—
79C47⋊#95—42no—
80C47⋊#95—42no—
81C47⋊#95—42no—
82C25×C47C2311yescharacteristic
83C25×C47C2311yescharacteristic
84C22×D4×C47—22no—
85C22×D4×C47—22no—
86C22×D4×C47—22no—
87C22×D4×C47—22no—
88C22×D4×C47—22no—
89C22×D4×C47—22no—
90C22×D4×C47C2×C414yes—
91C23×C4×C47—22no—
92C23×C4×C47—22no—
93C23×C4×C47—42no—
94C23×C4×C47—42no—
95C23×C4×C47C2×C414yes—
96C23×C4×C47C2312yes—
97C23×C4×C47C2311yescharacteristic
98C23×C4×C47C2312yes—
99C2×C22⋊C4×C47—22no—
100C2×C22⋊C4×C47—22no—
101C2×C22⋊C4×C47—42no—
102C2×C22⋊C4×C47—42no—
103C2×C22⋊C4×C47C2×C414yes—
104C2×C22⋊C4×C47C2×C418yescomplemented
105#95×C47C2×C418yescomplemented
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—22no—
117C24×C47—22no—
118C24×C47—22no—
119C24×C47—22no—
120C24×C47C22×C412yes—
121C24×C47C22×C412yes—
122C24×C47C2×D412yes—
123C24×C47C2×D412yes—
124C24×C47#4112yes—
125C24×C47#4112yes—
126C24×C47#4112yes—
127C24×C47#4112yes—
128C24×C47C2411yescharacteristic
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—28no—
137C22×C4×C47—22no—
138C22×C4×C47—22no—
139C22×C4×C47—21no—
140C22×C4×C47—21no—
141C22×C4×C47—22no—
142C22×C4×C47—22no—
143C22×C4×C47—21no—
144C22×C4×C47—21no—
145C22×C4×C47—21no—
146C22×C4×C47—21no—
147C22×C4×C47—22no—
148C22×C4×C47—22no—
149C22×C4×C47—22no—
150C22×C4×C47—22no—
151C22×C4×C47—22no—
152C22×C4×C47—22no—
153C22×C4×C47—22no—
154C22×C4×C47—22no—
155C22×C4×C47—48no—
156C22×C4×C47—44no—
157C22×C4×C47—44no—
158C22×C4×C47—48no—
159C22×C4×C47C22×C414yes—
160C22×C4×C47C22×C414yes—
161C22×C4×C47C22×C412yes—
162C22×Dic47—21no—
163C22×Dic47—21no—
164C22×Dic47—22no—
165C22×Dic47—28no—
166C22×Dic47—28no—
167C22×Dic47—21no—
168C22×Dic47—22no—
169C22×Dic47—22no—
170C22×Dic47—22no—
171C22×Dic47—22no—
172C22×Dic47—22no—
173C22×Dic47—22no—
174C22×Dic47—21no—
175C22×Dic47—22no—
176C22×Dic47—22no—
177C22×Dic47—22no—
178C22×Dic47—22no—
179C22×Dic47—22no—
180C22×Dic47—22no—
181C22×Dic47—22no—
182C22×Dic47—22no—
183C22×Dic47—28no—
184C22×Dic47—21no—
185C22×Dic47—21no—
186C22×Dic47—22no—
187C22×Dic47—22no—
188C22×Dic47—21no—
189C22×Dic47—21no—
190C22×Dic47—21no—
191C22×Dic47—21no—
192C22×Dic47—22no—
193C22×Dic47—22no—
194C22×Dic47—44no—
195C22×Dic47—48no—
196C22×Dic47—48no—
197C22×Dic47—48no—
198C22×Dic47—48no—
199C22×Dic47—44no—
200C22×Dic47—44no—
201C22×Dic47C2×D412yes—
202C22×Dic47C2×D414yes—
203C22×Dic47C2×D412yes—
204C22×Dic47#4114yes—
205C22×Dic47#4114yes—
206C22⋊C4×C47—28no—
207C22⋊C4×C47—48no—
208C22⋊Dic47—28no—
209C22⋊Dic47—48no—
210C22⋊Dic47—44no—
211C22⋊Dic47—44no—
212C22⋊Dic47—44no—
213C4×Dic47—48no—
214C23×C47—24no—
215C23×C47—24no—
216C23×C47—22no—
217C23×C47—22no—
218C23×C47—24no—
219C23×C47—22no—
220C23×C47—22no—
221C23×C47—24no—
222C23×C47—24no—
223C23×C47—24no—
224C23×C47—24no—
225C23×C47—24no—
226C23×C47—24no—
227C23×C47—24no—
228C23×C47—24no—
229C23×C47—24no—
230C23×C47—22no—
231C23×C47—22no—
232C23×C47—22no—
233C23×C47—24no—
234C23×C47—24no—
235C23×C47—41no—
236C23×C47—41no—
237C23×C47—41no—
238C23×C47—41no—
239C23×C47—41no—
240C23×C47—41no—
241C23×C47—42no—
242C23×C47—41no—
243C23×C47—41no—
244C23×C47—42no—
245C23×C47—42no—
246C23×C47—42no—
247C23×C47—42no—
248C23×C47—42no—
249C23×C47—42no—
250C23×C47—42no—
251C23×C47—42no—
252C23×C47—42no—
253C23×C47#11714yes—
254C23×C47C4×D414yes—
255C23×C47C4×D414yes—
256C23×C47#12114yes—
257C23×C47#12314yes—
258C23×C47#12414yes—
259C23×C47#12614yes—
260C23×C47C23×C411yescharacteristic
261C23×C47C22×D411yescharacteristic
262C23×C47C22×D411yescharacteristic
263C23×C47C2×#4112yes—
264C23×C47C2×#4112yes—
265C23×C47C2×#4111yescharacteristic
266C23×C47C2×#4111yescharacteristic
267C23×C47C2×#4111yescharacteristic
268C23×C47C2×#4111yescharacteristic
269C23×C47H(5,𝔽2)12yes—
270C23×C47H(5,𝔽2)12yes—
271D4×C47—416no—
272C2×C4×C47—22no—
273C2×C4×C47—24no—
274C2×C4×C47—24no—
275C2×C4×C47—22no—
276C2×C4×C47—22no—
277C2×C4×C47—24no—
278C2×C4×C47—24no—
279C2×C4×C47—24no—
280C2×C4×C47—24no—
281C2×C4×C47—416no—
282C2×C4×C47—41no—
283C2×C4×C47—41no—
284C2×C4×C47—41no—
285C2×C4×C47—41no—
286C2×C4×C47—42no—
287C2×C4×C47—42no—
288C2×C4×C47—42no—
289C2×C4×C47—42no—
290C2×C4×C47—42no—
291C2×C4×C47—42no—
292C2×C4×C47—42no—
293C2×C4×C47—42no—
294C2×Dic47—22no—
295C2×Dic47—22no—
296C2×Dic47—24no—
297C2×Dic47—24no—
298C2×Dic47—22no—
299C2×Dic47—24no—
300C2×Dic47—22no—
301C2×Dic47—24no—
302C2×Dic47—22no—
303C2×Dic47—24no—
304C2×Dic47—24no—
305C2×Dic47—24no—
306C2×Dic47—24no—
307C2×Dic47—416no—
308C2×Dic47—416no—
309C2×Dic47—42no—
310C2×Dic47—42no—
311C2×Dic47—42no—
312C2×Dic47—42no—
313C2×Dic47—42no—
314C2×Dic47—42no—
315C2×Dic47—42no—
316C2×Dic47—42no—
317C2×Dic47—42no—
318C2×Dic47—42no—
319C2×Dic47—41no—
320C2×Dic47—41no—
321C2×Dic47—41no—
322C2×Dic47—41no—
323C2×Dic47—41no—
324C2×Dic47—41no—
325C2×Dic47—42no—
326C2×Dic47—42no—
327C2×Dic47—42no—
328C2×Dic47—42no—
329C2×Dic47#12314yes—
330#14020—471nomaximal, Sylow
331C22×C47—24no—
332C22×C47—24no—
333C22×C47—28no—
334C22×C47—28no—
335C22×C47—24no—
336C22×C47—24no—
337C22×C47—28no—
338C22×C47—24no—
339C22×C47—28no—
340C22×C47—24no—
341C22×C47—42no—
342C22×C47—44no—
343C22×C47—44no—
344C22×C47—42no—
345C22×C47—42no—
346C22×C47—81no—
347C22×C47—81no—
348C22×C47—81no—
349C22×C47—82no—
350C22×C47—81no—
351C22×C47—82no—
352C22×C47#38818yes—
353C22×C47C2×#11711yescharacteristic
354C22×C47C2×C4×D411yescharacteristic
355C22×C47C2×C4×D411yescharacteristic
356C22×C47C4×#4112yes—
357C22×C47#51812yes—
358C22×C47C2×#12111yescharacteristic
359C22×C47C2×#12311yescharacteristic
360C22×C47C2×#12311yescharacteristic
361C22×C47#52511yescharacteristic
362C22×C47C2×#12411yescharacteristic
363C22×C47C2×#12611yescharacteristic
364C22×C47#52912yes—
365C22×C47#53411yescharacteristic
366C22×C47#53511yescharacteristic
367C22×C47#53812yes—
368C22×C47#54612yes—
369C22×C47#54612yes—
370C22×C47#55112yes—
371C22×C47#55112yes—
372C22×C47#55312yes—
373C22×C47#55312yes—
374C22×C47#55312yes—
375C22×C47#55312yes—
376C4×C47—44no—
377C4×C47—44no—
378C4×C47—42no—
379Dic47—24no—
380Dic47—44no—
381Dic47—42no—
382Dic47—44no—
383Dic47—81no—
384Dic47—81no—
385C2×#386—471no—
386C2×#386—471no—
387C2×#386D4711yescharacteristic
388C2×C4×C22⋊C4—471no—
389C22×#95—471no—
390#1443—472no—
391#1440—472no—
392#1437—472no—
393#1434—472no—
394C22⋊#95—471no—
395C22⋊#95—471no—
396C2×C47—28no—
397C2×C47—82no—
398C2×C47C2×#38811yescharacteristic
399C2×C47C4×#12311yescharacteristic
400C2×C47#232111yescharacteristic
401C2×C47#235312yes—
402C2×C47#236412yes—
403C2×C47#241111yescharacteristic
404C2×C47#241211yescharacteristic
405C2×C47#244412yes—
406C2×C47#250411yescharacteristic
407C2×C47#251012yes—
408C2×C47#259111yescharacteristic
409C23×D4C2×D4711yescharacteristic
410C24×C4—471no—
411C24×C4—471no—
412C24×C4C2×D4711yescharacteristic
413C22×C22⋊C4—471no—
414C22×C22⋊C4—471no—
415C22×C22⋊C4—471no—
416C22×C22⋊C4—472no—
417C22×C22⋊C4—471no—
418C22×C22⋊C4C2×D4711yescharacteristic
419C22×C22⋊C4C2×D4712yes—
420C22×C42—472no—
421#386—944no—
422#386—944no—
423#386Dic4718yescomplemented
424C4×C22⋊C4—944no—
425C2×#95—472no—
426C2×#95—471no—
427C2×#95—472no—
428C2×#95—472no—
429C2×#95—472no—
430C2×#95—472no—
431C2×#95—471no—
432C2×#95—472no—
433C2×#95—472no—
434C2×#95—472no—
435C2×#95—944no—
436C2×#95C2×D4712yes—
437C47#1402011yescharacteristic, complemented, Sylow
438C25C22×D4711yescharacteristic
439C25C22×D4711yescharacteristic
440C22×D4—22no—
441C22×D4—22no—
442C22×D4—22no—
443C22×D4—22no—
444C22×D4—22no—
445C22×D4—22no—
446C22×D4C2×Dic4714yes—
447C23×C4—22no—
448C23×C4—22no—
449C23×C4—42no—
450C23×C4—42no—
451C23×C4—471no—
452C23×C4—472no—
453C23×C4—471no—
454C23×C4—472no—
455C23×C4—474no—
456C23×C4—471no—
457C23×C4—471no—
458C23×C4—944no—
459C23×C4—944no—
460C23×C4—942no—
461C23×C4—942no—
462C23×C4—942no—
463C23×C4—942no—
464C23×C4—942no—
465C23×C4—1882no—
466C23×C4—1882no—
467C23×C4C2×Dic4714yes—
468C23×C4C22×D4712yes—
469C23×C4C22×D4712yes—
470C23×C4C22×D4711yescharacteristic
471C2×C22⋊C4—22no—
472C2×C22⋊C4—22no—
473C2×C22⋊C4—42no—
474C2×C22⋊C4—42no—
475C2×C22⋊C4—474no—
476C2×C22⋊C4—942no—
477C2×C22⋊C4—942no—
478C2×C22⋊C4—944no—
479C2×C22⋊C4—944no—
480C2×C22⋊C4—942no—
481C2×C22⋊C4—944no—
482C2×C22⋊C4—942no—
483C2×C22⋊C4—942no—
484C2×C22⋊C4—942no—
485C2×C22⋊C4—942no—
486C2×C22⋊C4—1882no—
487C2×C22⋊C4—1882no—
488C2×C22⋊C4C2×Dic4714yes—
489C2×C22⋊C4C2×Dic4718yescomplemented
490C2×C42—944no—
491C2×C42—944no—
492C2×C42—1882no—
493#95—944no—
494#95—944no—
495#95—944no—
496#95—944no—
497#95—942no—
498#95—942no—
499#95—944no—
500#95—1882no—
501#95—1882no—
502#95—1882no—
503#95C2×Dic4718yescomplemented
504C24—22no—
505C24—22no—
506C24—22no—
507C24—22no—
508C24—21no—
509C24—21no—
510C24—22no—
511C24—22no—
512C24—21no—
513C24—21no—
514C24—21no—
515C24—21no—
516C24—22no—
517C24—22no—
518C24#1062535012yes—
519C24#1062535012yes—
520C24D4×D4712yes—
521C24D4×D4712yes—
522C24#1062535212yes—
523C24#1062535212yes—
524C24C22×Dic4712yes—
525C24C22×Dic4712yes—
526C24C23×D4711yescharacteristic
527C2×D4—28no—
528C2×D4—28no—
529C2×D4—28no—
530C2×D4—44no—
531C2×D4—44no—
532C2×D4—44no—
533C2×D4—44no—
534C22×C4—28no—
535C22×C4—22no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—48no—
554C22×C4—44no—
555C22×C4—44no—
556C22×C4—48no—
557C22×C4—472no—
558C22×C4—474no—
559C22×C4—472no—
560C22×C4—474no—
561C22×C4—474no—
562C22×C4—948no—
563C22×C4—941no—
564C22×C4—941no—
565C22×C4—942no—
566C22×C4—948no—
567C22×C4—948no—
568C22×C4—941no—
569C22×C4—942no—
570C22×C4—942no—
571C22×C4—942no—
572C22×C4—942no—
573C22×C4—942no—
574C22×C4—942no—
575C22×C4—942no—
576C22×C4—942no—
577C22×C4—942no—
578C22×C4—941no—
579C22×C4—942no—
580C22×C4—942no—
581C22×C4—942no—
582C22×C4—942no—
583C22×C4—942no—
584C22×C4—941no—
585C22×C4—941no—
586C22×C4—942no—
587C22×C4—942no—
588C22×C4—941no—
589C22×C4—941no—
590C22×C4—941no—
591C22×C4—941no—
592C22×C4—942no—
593C22×C4—942no—
594C22×C4—1884no—
595C22×C4—1888no—
596C22×C4—1888no—
597C22×C4—1888no—
598C22×C4—1888no—
599C22×C4—1884no—
600C22×C4—1884no—
601C22×C4C22×Dic4712yes—
602C22×C4C22×Dic4714yes—
603C22×C4C22×Dic4714yes—
604C22⋊C4—28no—
605C22⋊C4—48no—
606C22⋊C4—948no—
607C22⋊C4—1884no—
608C22⋊C4—1888no—
609C22⋊C4—1884no—
610C22⋊C4—1884no—
611C42—1888no—
612C23—24no—
613C23—24no—
614C23—24no—
615C23—24no—
616C23—24no—
617C23—24no—
618C23—24no—
619C23—24no—
620C23—24no—
621C23—24no—
622C23—22no—
623C23—22no—
624C23—24no—
625C23—22no—
626C23—22no—
627C23—24no—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—24no—
632C23—24no—
633C23—42no—
634C23—42no—
635C23—42no—
636C23—42no—
637C23—42no—
638C23—42no—
639C23—42no—
640C23—42no—
641C23—41no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—42no—
648C23—41no—
649C23—41no—
650C23—42no—
651C23#1309398314yes—
652C23D4×Dic4714yes—
653C23D4×Dic4714yes—
654C23#1309399714yes—
655C23#1309400614yes—
656C23#1309401014yes—
657C23#1309401714yes—
658C23C23×Dic4711yescharacteristic
659C23C2×D4×D4711yescharacteristic
660C23C2×D4×D4711yescharacteristic
661C23#41×D4712yes—
662C23#41×D4712yes—
663C23C2×#1062535211yescharacteristic
664C23C2×#1062535211yescharacteristic
665C23C2×#1062535011yescharacteristic
666C23C2×#1062535011yescharacteristic
667C23#1309406912yes—
668C23#1309406912yes—
669D4—416no—
670C2×C4—22no—
671C2×C4—24no—
672C2×C4—24no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—24no—
676C2×C4—24no—
677C2×C4—24no—
678C2×C4—24no—
679C2×C4—416no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—474no—
693C2×C4—944no—
694C2×C4—944no—
695C2×C4—942no—
696C2×C4—942no—
697C2×C4—944no—
698C2×C4—944no—
699C2×C4—944no—
700C2×C4—944no—
701C2×C4—942no—
702C2×C4—942no—
703C2×C4—944no—
704C2×C4—944no—
705C2×C4—942no—
706C2×C4—18816no—
707C2×C4—1882no—
708C2×C4—1882no—
709C2×C4—1882no—
710C2×C4—1882no—
711C2×C4—1881no—
712C2×C4—1881no—
713C2×C4—1881no—
714C2×C4—1881no—
715C2×C4—1881no—
716C2×C4—1881no—
717C2×C4—18816no—
718C2×C4—1882no—
719C2×C4—1882no—
720C2×C4—1882no—
721C2×C4—1882no—
722C2×C4—1882no—
723C2×C4—1882no—
724C2×C4—1882no—
725C2×C4—1882no—
726C2×C4—1882no—
727C2×C4—1882no—
728C22—24no—
729C22—24no—
730C22—24no—
731C22—28no—
732C22—24no—
733C22—28no—
734C22—28no—
735C22—24no—
736C22—28no—
737C22—24no—
738C22—42no—
739C22—44no—
740C22—42no—
741C22—42no—
742C22—44no—
743C22—81no—
744C22—81no—
745C22—81no—
746C22—82no—
747C22—82no—
748C22—81no—
749C22#1568901618yes—
750C22C2×#1309398311yescharacteristic
751C22C2×D4×Dic4711yescharacteristic
752C22C2×D4×Dic4711yescharacteristic
753C22#41×Dic4712yes—
754C22#1568959812yes—
755C22C2×#1309399711yescharacteristic
756C22#123×D4711yescharacteristic
757C22C2×#1309400611yescharacteristic
758C22#1568963111yescharacteristic
759C22C2×#1309401011yescharacteristic
760C22C2×#1309401711yescharacteristic
761C22#1568965012yes—
762C22#1568968311yescharacteristic
763C22#1568968811yescharacteristic
764C22#1568970812yes—
765C22#1568976212yes—
766C22#1568976212yes—
767C22#1568980212yes—
768C22#1568980212yes—
769C22#1568981612yes—
770C22#1568981612yes—
771C22#1568982212yes—
772C22#1568982212yes—
773C4—44no—
774C4—42no—
775C4—44no—
776C4—944no—
777C4—3761no—
778C4—3761no—
779C4—1882no—
780C4—1884no—
781C4—1884no—
782C2—28no—
783C2—82no—
784C2C2×#1568901611yescharacteristic
785C2#123×Dic4711yescharacteristic
786C2#2024604911yescharacteristic
787C2#2024632812yes—
788C2#2024644012yes—
789C2#2024677611yescharacteristic
790C2#2024678711yescharacteristic
791C2#2024714412yes—
792C2#2024787811yescharacteristic
793C2#2024794612yes—
794C2#2024886711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D47
commutatorC23×C47C23×C4
FittingC2×C47×#386C2
socle, cosocleC24×C47C24
prime radicalC23×D4×C47C22
hypercenterC2×#386D47
hypocenterC47#14020
LCSG ▷ C23×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. C22×C47⋊#95C2semidirect
5. #20241650C2semidirect
6. #20241637C2semidirect
7. #20241625C2semidirect
8. #20241613C2semidirect
9. #20241611C2semidirect
10. #20241610C2semidirect
38. C47×#386C4semidirect
104. C2×C22⋊C4×C47C2×C4semidirect
105. #95×C47C2×C4semidirect
423. #386Dic47semidirect
437. C47#14020semidirect
489. C2×C22⋊C4C2×Dic47semidirect
503. #95C2×Dic47semidirect

Maximal subgroups

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

subgroupindex
C2×#156890032
C2×C22⋊C4×Dic472
C22×C47⋊#952
#202416502
#202416372
#202416252
#202416132
#202416112
#202416102
C2×C47×#3862
#1402047