Finite Group Databasebeta

← #26147511

Subgroups — #26147511

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
1C2×#15689014C212yesmaximal, complemented
2C2×#15689002C211yesmaximal, characteristic
3C2×#15689002C211yesmaximal, characteristic
4C2×#15689002C211yesmaximal, characteristic
5C2×#15688996C211yesmaximal, characteristic, complemented
6#20241626C212yesmaximal, complemented
7#20241621C212yesmaximal, complemented
8#20241615C212yesmaximal, complemented
9#20241611C211yesmaximal, characteristic, complemented
10#20241611C211yesmaximal, characteristic, complemented
11C23×C42×C47C211yesmaximal, characteristic, complemented
12C23×C22⋊D47C2211yescharacteristic
13C22×Dic47⋊C4C2212yes—
14C22×C22⋊Dic47C2211yescharacteristic
15C22×C22⋊Dic47C2211yescharacteristic
16C22×C22⋊Dic47C2211yescharacteristic
17C22×(C2×D47)⋊C4C2211yescharacteristic
18C22×(C2×D47)⋊C4C2212yes—
19C22×(C2×D47)⋊C4C2211yescharacteristic
20C22×(C2×D47)⋊C4C2212yes—
21#15689014—28no—
22#15689002—24no—
23#15689002—24no—
24#15689002C418yescomplemented
25#15688996—24no—
26C2×C47⋊#95C2212yes—
27C2×C47⋊#95C2211yescharacteristic
28C2×C47⋊#95C2212yes—
29C2×C47⋊#95C2211yescharacteristic
30C2×C47⋊#95C2212yes—
31C2×C47⋊#95C2212yes—
32C2×C47⋊#95C2212yes—
33C2×C47⋊#95C2212yes—
34C2×C47⋊#95C2212yes—
35C24×C4×C47C2211yescharacteristic
36C24×C4×C47C2211yescharacteristic
37C24×C4×C47C2211yescharacteristic
38C22×C42×C47—24no—
39C22×C42×C47—28no—
40C22×C42×C47C2212yes—
41C22×C42×C47C2212yes—
42C24×D47C2311yescharacteristic
43C22×C22⋊D47—22no—
44C22×C22⋊D47—22no—
45C22×C22⋊D47—22no—
46C22×C22⋊D47—22no—
47C22×C22⋊D47—22no—
48C22×C22⋊D47—22no—
49C22×C22⋊D47C2×C414yes—
50C23×Dic47C2312yes—
51C23×Dic47C2311yescharacteristic
52C23×Dic47C2311yescharacteristic
53C23×Dic47C2311yescharacteristic
54C23×Dic47C2312yes—
55C2×Dic47⋊C4—24no—
56C2×Dic47⋊C4—24no—
57C2×Dic47⋊C4—24no—
58C2×C22⋊Dic47—22no—
59C2×C22⋊Dic47—22no—
60C2×C22⋊Dic47—22no—
61C2×C22⋊Dic47—22no—
62C2×C22⋊Dic47—22no—
63C2×C22⋊Dic47—22no—
64C2×C22⋊Dic47—22no—
65C2×C22⋊Dic47—22no—
66C2×C22⋊Dic47C2×C414yes—
67C2×(C2×D47)⋊C4—24no—
68C2×(C2×D47)⋊C4—24no—
69C2×(C2×D47)⋊C4—22no—
70C2×(C2×D47)⋊C4—24no—
71C2×(C2×D47)⋊C4—22no—
72C2×(C2×D47)⋊C4—24no—
73C2×(C2×D47)⋊C4—24no—
74C2×(C2×D47)⋊C4—24no—
75C2×(C2×D47)⋊C4—24no—
76C2×(C2×D47)⋊C4C2×C418yescomplemented
77C47⋊#95—24no—
78C47⋊#95—22no—
79C47⋊#95—24no—
80C47⋊#95—22no—
81C47⋊#95—24no—
82C47⋊#95—24no—
83C47⋊#95—24no—
84C47⋊#95—24no—
85C47⋊#95C2×C418yescomplemented
86C25×C47C2311yescharacteristic
87C23×C4×C47—22no—
88C23×C4×C47—22no—
89C23×C4×C47—22no—
90C23×C4×C47—22no—
91C23×C4×C47—22no—
92C23×C4×C47—22no—
93C23×C4×C47—24no—
94C23×C4×C47—24no—
95C23×C4×C47—24no—
96C23×C4×C47—24no—
97C23×C4×C47—24no—
98C23×C4×C47—24no—
99C23×C4×C47C2×C414yes—
100C23×C4×C47D414yes—
101C23×C4×C47D414yes—
102C23×C4×C47C2312yes—
103C23×C4×C47C2311yescharacteristic
104C23×C4×C47C2312yes—
105C23×C4×C47C2311yescharacteristic
106C2×C42×C47—232no—
107C2×C42×C47—24no—
108C2×C42×C47—24no—
109C2×C42×C47—24no—
110C2×C42×C47—24no—
111C2×C42×C47—24no—
112C2×C42×C47D418yescomplemented
113C24×C47—22no—
114C24×C47—22no—
115C24×C47—22no—
116C24×C47—22no—
117C24×C47C22×C412yes—
118C24×C47C2×D412yes—
119C24×C47C2×D412yes—
120C24×C47#4112yes—
121C24×C47#4112yes—
122C24×C47#4112yes—
123C24×C47#4112yes—
124C24×C47C2411yescharacteristic
125C23×D47—22no—
126C23×D47—21no—
127C23×D47—21no—
128C23×D47—22no—
129C23×D47—22no—
130C23×D47—22no—
131C23×D47—21no—
132C23×D47—21no—
133C23×D47—21no—
134C23×D47—21no—
135C23×D47C22×C412yes—
136C22×C4×C47—28no—
137C22×C4×C47—28no—
138C22×C4×C47—216no—
139C22×C4×C47—216no—
140C22×C4×C47—216no—
141C22×C4×C47—216no—
142C22×C4×C47—28no—
143C22×C4×C47—28no—
144C22×C4×C47—28no—
145C22×C4×C47—28no—
146C22×C4×C47—28no—
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—22no—
156C22×C4×C47—21no—
157C22×C4×C47—21no—
158C22×C4×C47—22no—
159C22×C4×C47—21no—
160C22×C4×C47—21no—
161C22×C4×C47—216no—
162C22×C4×C47—28no—
163C22×C4×C47—216no—
164C22×C4×C47—28no—
165C22×C4×C47C22×C414yes—
166C22×C4×C47C2×D414yes—
167C22×C4×C47C2×D412yes—
168C22×C4×C47C2×D414yes—
169C22×C4×C47C2×D414yes—
170C22×C4×C47C2×D414yes—
171C22×C4×C47C2×D412yes—
172C22×C4×C47#4114yes—
173C22×C4×C47#4114yes—
174C22×C4×C47#4114yes—
175C2×C22⋊D47—28no—
176C2×C22⋊D47—28no—
177C2×C22⋊D47—28no—
178C2×C22⋊D47—44no—
179C2×C22⋊D47—44no—
180C2×C22⋊D47—44no—
181C2×C22⋊D47—44no—
182C22×Dic47—21no—
183C22×Dic47—21no—
184C22×Dic47—22no—
185C22×Dic47—22no—
186C22×Dic47—22no—
187C22×Dic47—22no—
188C22×Dic47—22no—
189C22×Dic47—22no—
190C22×Dic47—21no—
191C22×Dic47—21no—
192C22×Dic47—21no—
193C22×Dic47—21no—
194C22×Dic47—22no—
195C22×Dic47—21no—
196C22×Dic47—21no—
197C22×Dic47—22no—
198C22×Dic47—21no—
199C22×Dic47—22no—
200C22×Dic47—21no—
201C22×Dic47—22no—
202C22×Dic47—22no—
203C22×Dic47—22no—
204C22×Dic47—22no—
205C22×Dic47—22no—
206C22×Dic47—21no—
207C22×Dic47—21no—
208C22×Dic47—22no—
209C22×Dic47—22no—
210C22×Dic47—22no—
211C22×Dic47C22×C412yes—
212C22×Dic47C22×C414yes—
213C42×C47—216no—
214C42×C47—216no—
215C22⋊Dic47—28no—
216C22⋊Dic47—44no—
217C22⋊Dic47—44no—
218(C2×D47)⋊C4—216no—
219(C2×D47)⋊C4—44no—
220(C2×D47)⋊C4—48no—
221(C2×D47)⋊C4—44no—
222Dic47⋊C4—48no—
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#11714yes—
240C23×C47C4×D414yes—
241C23×C47C4×D414yes—
242C23×C47#12114yes—
243C23×C47#12314yes—
244C23×C47#12414yes—
245C23×C47#12614yes—
246C23×C47C23×C411yescharacteristic
247C23×C47C22×D411yescharacteristic
248C23×C47C22×D412yes—
249C23×C47C22×D411yescharacteristic
250C23×C47C2×#4111yescharacteristic
251C23×C47C2×#4111yescharacteristic
252C23×C47C2×#4111yescharacteristic
253C23×C47C2×#4111yescharacteristic
254C23×C47C2×#4112yes—
255C23×C47C2×#4112yes—
256C23×C47C2×#4112yes—
257C22×D47—22no—
258C22×D47—24no—
259C22×D47—22no—
260C22×D47—22no—
261C22×D47—24no—
262C22×D47—41no—
263C22×D47—42no—
264C22×D47—41no—
265C22×D47—41no—
266C22×D47—41no—
267C22×D47—42no—
268C22×D47—42no—
269C22×D47—42no—
270C22×D47—41no—
271C22×D47—42no—
272C22×D47—41no—
273C22×D47—41no—
274C22×D47—41no—
275C22×D47—42no—
276C22×D47—42no—
277C22×D47—42no—
278C22×D47—42no—
279C22×D47—42no—
280C2×C4×C47—232no—
281C2×C4×C47—232no—
282C2×C4×C47—232no—
283C2×C4×C47—24no—
284C2×C4×C47—24no—
285C2×C4×C47—24no—
286C2×C4×C47—22no—
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—24no—
294C2×C4×C47—24no—
295C2×C4×C47—24no—
296C2×C4×C47—24no—
297C2×C4×C47—24no—
298C2×C4×C47—24no—
299C2×C4×C47—24no—
300C2×C4×C47—24no—
301C2×C4×C47—24no—
302C2×C4×C47—24no—
303C2×C4×C47C4×D418yes—
304C2×C4×C47#12014yes—
305C2×C4×C47#12118yes—
306C2×C4×C47#12314yes—
307C22⋊D47—416no—
308C2×Dic47—22no—
309C2×Dic47—24no—
310C2×Dic47—24no—
311C2×Dic47—22no—
312C2×Dic47—22no—
313C2×Dic47—24no—
314C2×Dic47—42no—
315C2×Dic47—41no—
316C2×Dic47—41no—
317C2×Dic47—42no—
318C2×Dic47—41no—
319C2×Dic47—41no—
320C2×Dic47—42no—
321C2×Dic47—42no—
322C2×Dic47—41no—
323C2×Dic47—42no—
324C2×Dic47—42no—
325C2×Dic47—41no—
326C2×Dic47—41no—
327C2×Dic47—41no—
328C2×Dic47—42no—
329C2×Dic47—41no—
330C2×Dic47—42no—
331C2×Dic47—42no—
332C2×Dic47—41no—
333C2×Dic47—42no—
334C2×Dic47—42no—
335C2×Dic47—42no—
336C2×Dic47—42no—
337C2×Dic47—42no—
338C2×Dic47—42no—
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#38818yescomplemented
351C22×C47C2×#11711yescharacteristic
352C22×C47C2×C4×D411yescharacteristic
353C22×C47C2×C4×D412yes—
354C22×C47C2×C4×D411yescharacteristic
355C22×C47C4×#4112yes—
356C22×C47C2×#12011yescharacteristic
357C22×C47C2×#12112yes—
358C22×C47C2×#12111yescharacteristic
359C22×C47C2×#12311yescharacteristic
360C22×C47C2×#12311yescharacteristic
361C22×C47#52512yes—
362C22×C47#52511yescharacteristic
363C22×C47#52512yes—
364C22×C47#52512yes—
365C22×C47#52512yes—
366C22×C47#52511yescharacteristic
367C22×C47C2×#12411yescharacteristic
368C22×C47C2×#12611yescharacteristic
369C22×C47#52912yes—
370C22×C47#52912yes—
371C22×C47#52912yes—
372C22×C47#52912yes—
373C22×C47#53212yes—
374C2×D47—42no—
375C2×D47—44no—
376C2×D47—42no—
377C2×D47—44no—
378C2×D47—42no—
379C2×D47—81no—
380C2×D47—81no—
381C2×D47—82no—
382C2×D47—82no—
383C2×D47—81no—
384C2×D47—81no—
385C4×C47—28no—
386C4×C47—24no—
387C4×C47—24no—
388C4×C47—28no—
389Dic47—42no—
390Dic47—44no—
391Dic47—81no—
392Dic47—82no—
393Dic47—81no—
394C23×C42D4711yescharacteristic, complemented
395C2×#388—472no—
396C2×#386—471no—
397C2×#386—471no—
398C2×#386—471no—
399C2×#385—471no—
400#1437—472no—
401#1436—472no—
402#1434—472no—
403C22⋊#95—471no—
404C22⋊#95—471no—
405C2×C47—28no—
406C2×C47C2×#38811yescharacteristic
407C2×C47#229012yes—
408C2×C47C4×#12011yescharacteristic
409C2×C47C4×#12112yes—
410C2×C47C4×#12311yescharacteristic
411C2×C47#284711yescharacteristic
412C2×C47#284911yescharacteristic
413C2×C47#285012yes—
414C2×C47#285212yes—
415C2×C47#285311yescharacteristic
416C2×C47#285411yescharacteristic
417D47—82no—
418C23×D4—471no—
419C24×C4C2×D4711yescharacteristic
420C24×C4C2×D4711yescharacteristic
421C24×C4C2×D4711yescharacteristic
422C22×C4⋊C4—472no—
423C22×C22⋊C4—471no—
424C22×C22⋊C4—472no—
425C22×C22⋊C4—471no—
426C22×C22⋊C4—471no—
427C22×C22⋊C4—471no—
428C22×C22⋊C4—472no—
429C22×C22⋊C4—471no—
430C22×C42—24no—
431C22×C42—28no—
432C22×C42C2×D4712yes—
433C22×C42C2×D4712yes—
434#388—948no—
435#386—478no—
436#386—944no—
437#386—944no—
438#385—944no—
439C2×#95—472no—
440C2×#95—472no—
441C2×#95—472no—
442C2×#95—472no—
443C2×#95—472no—
444C2×#95—471no—
445C2×#95—472no—
446C2×#95—472no—
447C2×#95—471no—
448C47#1469611yescharacteristic, complemented, Sylow
449C25—471no—
450C25C22×D4711yescharacteristic
451C22×D4—474no—
452C22×D4—942no—
453C22×D4—942no—
454C22×D4—942no—
455C22×D4—942no—
456C22×D4—942no—
457C22×D4—942no—
458C23×C4—22no—
459C23×C4—22no—
460C23×C4—22no—
461C23×C4—22no—
462C23×C4—22no—
463C23×C4—22no—
464C23×C4—24no—
465C23×C4—24no—
466C23×C4—24no—
467C23×C4—24no—
468C23×C4—24no—
469C23×C4—24no—
470C23×C4—472no—
471C23×C4—471no—
472C23×C4—471no—
473C23×C4—472no—
474C23×C4—471no—
475C23×C4C4×D4714yes—
476C23×C4D18814yes—
477C23×C4C22⋊D4714yes—
478C23×C4C22×D4712yes—
479C23×C4C22×D4712yes—
480C23×C4C22×D4711yescharacteristic
481C23×C4C22×D4711yescharacteristic
482C2×C4⋊C4—944no—
483C2×C4⋊C4—944no—
484C2×C4⋊C4—944no—
485C2×C22⋊C4—474no—
486C2×C22⋊C4—478no—
487C2×C22⋊C4—942no—
488C2×C22⋊C4—942no—
489C2×C22⋊C4—944no—
490C2×C22⋊C4—944no—
491C2×C22⋊C4—942no—
492C2×C22⋊C4—942no—
493C2×C22⋊C4—942no—
494C2×C22⋊C4—942no—
495C2×C22⋊C4—942no—
496C2×C22⋊C4—942no—
497C2×C22⋊C4—944no—
498C2×C22⋊C4—944no—
499C2×C22⋊C4—944no—
500C2×C22⋊C4—942no—
501C2×C22⋊C4—942no—
502C2×C22⋊C4—944no—
503C2×C22⋊C4—944no—
504C2×C42—232no—
505C2×C42—24no—
506C2×C42—24no—
507C2×C42—24no—
508C2×C42—24no—
509C2×C42—24no—
510C2×C42C22⋊D4718yescomplemented
511#95—478no—
512#95—944no—
513#95—944no—
514#95—944no—
515#95—944no—
516#95—942no—
517#95—942no—
518#95—944no—
519#95—944no—
520C24—22no—
521C24—22no—
522C24—22no—
523C24—22no—
524C24—472no—
525C24—942no—
526C24—941no—
527C24—941no—
528C24—942no—
529C24—942no—
530C24—942no—
531C24—941no—
532C24—941no—
533C24—941no—
534C24—941no—
535C24C2×C4×D4712yes—
536C24C2×D18812yes—
537C24#1062535012yes—
538C24#1062535012yes—
539C24#1062535012yes—
540C24#1062535012yes—
541C24C2×C22⋊D4712yes—
542C24C23×D4711yescharacteristic
543C2×D4—948no—
544C2×D4—948no—
545C2×D4—948no—
546C2×D4—1884no—
547C2×D4—1884no—
548C2×D4—1884no—
549C2×D4—1884no—
550C22×C4—28no—
551C22×C4—28no—
552C22×C4—28no—
553C22×C4—28no—
554C22×C4—216no—
555C22×C4—216no—
556C22×C4—216no—
557C22×C4—216no—
558C22×C4—28no—
559C22×C4—28no—
560C22×C4—28no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—22no—
575C22×C4—216no—
576C22×C4—28no—
577C22×C4—216no—
578C22×C4—28no—
579C22×C4—472no—
580C22×C4—474no—
581C22×C4—941no—
582C22×C4—942no—
583C22×C4—941no—
584C22×C4—942no—
585C22×C4—942no—
586C22×C4—942no—
587C22×C4—942no—
588C22×C4—942no—
589C22×C4—941no—
590C22×C4—941no—
591C22×C4—941no—
592C22×C4—941no—
593C22×C4—942no—
594C22×C4—941no—
595C22×C4—941no—
596C22×C4—942no—
597C22×C4—941no—
598C22×C4—942no—
599C22×C4—941no—
600C22×C4—942no—
601C22×C4—942no—
602C22×C4—942no—
603C22×C4—941no—
604C22×C4—941no—
605C22×C4—942no—
606C22×C4—942no—
607C22×C4—942no—
608C22×C4—942no—
609C22×C4—942no—
610C22×C4C2×C4×D4714yes—
611C22×C4C2×D18814yes—
612C22×C4#1062535014yes—
613C22×C4#1062535014yes—
614C22×C4#1062535014yes—
615C22×C4C2×C22⋊D4714yes—
616C22×C4C2×C22⋊D4712yes—
617C22×C4C2×C22⋊D4714yes—
618C22×C4C2×C22⋊D4714yes—
619C22×C4C2×C22⋊D4712yes—
620C4⋊C4—1888no—
621C22⋊C4—948no—
622C22⋊C4—9416no—
623C22⋊C4—1884no—
624C22⋊C4—1884no—
625C22⋊C4—1884no—
626C22⋊C4—1888no—
627C22⋊C4—1884no—
628C42—216no—
629C42—216no—
630C23—24no—
631C23—24no—
632C23—22no—
633C23—24no—
634C23—22no—
635C23—24no—
636C23—24no—
637C23—24no—
638C23—24no—
639C23—22no—
640C23—22no—
641C23—24no—
642C23—24no—
643C23—24no—
644C23—24no—
645C23—24no—
646C23—942no—
647C23—944no—
648C23—942no—
649C23—942no—
650C23—944no—
651C23—1881no—
652C23—1882no—
653C23—1881no—
654C23—1881no—
655C23—1881no—
656C23—1882no—
657C23—1881no—
658C23—1882no—
659C23—1882no—
660C23—1882no—
661C23—1881no—
662C23—1881no—
663C23—1881no—
664C23—1882no—
665C23—1882no—
666C23—1882no—
667C23—1882no—
668C23—1882no—
669C23#1309398114yes—
670C23C4×C22⋊D4714yes—
671C23C4×D18814yes—
672C23#1309399814yes—
673C23#1309400714yes—
674C23#1309401214yes—
675C23#1309401814yes—
676C23C22×C4×D4711yescharacteristic
677C23C22×C22⋊D4711yescharacteristic
678C23C22×C22⋊D4712yes—
679C23C22×D18811yescharacteristic
680C23C2×#1062535011yescharacteristic
681C23C2×#1062535011yescharacteristic
682C23C2×#1062535011yescharacteristic
683C23C2×#1062535012yes—
684C23C2×#1062535011yescharacteristic
685C23C2×#1062535012yes—
686C23C2×#1062535012yes—
687D4—18816no—
688C2×C4—232no—
689C2×C4—232no—
690C2×C4—232no—
691C2×C4—24no—
692C2×C4—24no—
693C2×C4—24no—
694C2×C4—22no—
695C2×C4—24no—
696C2×C4—24no—
697C2×C4—24no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—24no—
702C2×C4—24no—
703C2×C4—24no—
704C2×C4—24no—
705C2×C4—24no—
706C2×C4—24no—
707C2×C4—24no—
708C2×C4—24no—
709C2×C4—24no—
710C2×C4—24no—
711C2×C4—942no—
712C2×C4—944no—
713C2×C4—942no—
714C2×C4—944no—
715C2×C4—942no—
716C2×C4—944no—
717C2×C4—1881no—
718C2×C4—1881no—
719C2×C4—1882no—
720C2×C4—1881no—
721C2×C4—1882no—
722C2×C4—1881no—
723C2×C4—1882no—
724C2×C4—1881no—
725C2×C4—1882no—
726C2×C4—1882no—
727C2×C4—1881no—
728C2×C4—1882no—
729C2×C4—1882no—
730C2×C4—1882no—
731C2×C4—1882no—
732C2×C4—1882no—
733C2×C4—1882no—
734C2×C4—1882no—
735C2×C4—1881no—
736C2×C4—1881no—
737C2×C4—1882no—
738C2×C4—1881no—
739C2×C4—1881no—
740C2×C4—1882no—
741C2×C4—1882no—
742C2×C4C4×C22⋊D4718yes—
743C2×C4#1309399314yes—
744C2×C4#1309399818yes—
745C2×C4#1309400714yes—
746C22—24no—
747C22—24no—
748C22—28no—
749C22—28no—
750C22—24no—
751C22—24no—
752C22—28no—
753C22—24no—
754C22—28no—
755C22—24no—
756C22—3761no—
757C22—3761no—
758C22—3762no—
759C22—3762no—
760C22—3761no—
761C22—3761no—
762C22—1882no—
763C22—1884no—
764C22—1882no—
765C22—1884no—
766C22—1882no—
767C22#1568901418yescomplemented
768C22C2×#1309398111yescharacteristic
769C22C2×C4×C22⋊D4711yescharacteristic
770C22C2×C4×C22⋊D4712yes—
771C22C2×C4×D18811yescharacteristic
772C22C4×#1062535012yes—
773C22C2×#1309399311yescharacteristic
774C22C2×#1309399812yes—
775C22C2×#1309399811yescharacteristic
776C22C2×#1309400711yescharacteristic
777C22C2×#1309400711yescharacteristic
778C22#1568963412yes—
779C22#1568963411yescharacteristic
780C22#1568963412yes—
781C22#1568963412yes—
782C22#1568963412yes—
783C22#1568963411yescharacteristic
784C22C2×#1309401211yescharacteristic
785C22C2×#1309401811yescharacteristic
786C22#1568965712yes—
787C22#1568965712yes—
788C22#1568965712yes—
789C22#1568965712yes—
790C22#1568967312yes—
791C4—28no—
792C4—24no—
793C4—24no—
794C4—28no—
795C4—3761no—
796C4—3762no—
797C4—3761no—
798C4—1882no—
799C4—1884no—
800C2—28no—
801C2—3762no—
802C2C2×#1568901411yescharacteristic
803C2#2024583112yes—
804C2C4×#1309399311yescharacteristic
805C2C4×#1309399812yes—
806C2C4×#1309400711yescharacteristic
807C2#2025167011yescharacteristic
808C2#2025168011yescharacteristic
809C2#2025168912yes—
810C2#2025170312yes—
811C2#2025171011yescharacteristic
812C2#2025171911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D47
commutatorC23×C47C23×C4
FittingC23×C42×C47C2
socle, cosocleC24×C47C24
prime radicalC23×C22⋊D47C22
hypercenterC23×C42D47
hypocenterC47#14696
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C24 ◁ C23×C42

Complements

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

NH ≅ G/Ntype
1. C2×#15689014C2semidirect
5. C2×#15688996C2semidirect
6. #20241626C2semidirect
7. #20241621C2semidirect
8. #20241615C2semidirect
9. #20241611C2semidirect
10. #20241611C2semidirect
11. C23×C42×C47C2semidirect
24. #15689002C4semidirect
76. C2×(C2×D47)⋊C4C2×C4semidirect
85. C47⋊#95C2×C4semidirect
112. C2×C42×C47D4semidirect
350. C22×C47#388semidirect
394. C23×C42D47semidirect
448. C47#14696semidirect
510. C2×C42C22⋊D47semidirect
767. C22#15689014semidirect

Maximal subgroups

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

subgroupindex
C2×#156890142
C2×#156890022
C2×#156889962
#202416262
#202416212
#202416152
#202416112
C23×C42×C472
#1469647