Finite Group Databasebeta

← #26138367

Subgroups — #26138367

Order 12032.

2330 conjugacy classes of subgroups.

The subgroup lattice has 770 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689009C212yesmaximal, complemented
2C2×#15688983C211yesmaximal, characteristic, complemented
3C2×C4×C22⋊Dic47C211yesmaximal, characteristic, complemented
4#20241633C212yesmaximal, complemented
5#20241629C212yesmaximal
6#20241625C212yesmaximal, complemented
7#20241615C211yesmaximal, characteristic, complemented
8#20241615C211yesmaximal, characteristic, complemented
9#20241611C211yesmaximal, characteristic, complemented
10#20241611C211yesmaximal, characteristic, complemented
11C22×C4×D4×C47C211yesmaximal, characteristic
12C22×C4⋊Dic47C2212yes—
13C22×C22⋊Dic47C2212yes—
14C22×C22⋊Dic47C2212yes—
15C22×C22⋊Dic47C2212yes—
16C22×C22⋊Dic47C2212yes—
17C22×C4×Dic47C2212yes—
18#15689009—28no—
19#15688983—24no—
20C4×C22⋊Dic47—24no—
21C2×C47⋊#95C2211yescharacteristic
22C2×C47⋊#95C2212yes—
23C2×C47⋊#95C2212yes—
24C2×C47⋊#95C2212yes—
25C2×C47⋊#95C2212yes—
26C2×C47⋊#95C2211yescharacteristic
27C2×C47⋊#95C2211yescharacteristic
28C2×C47⋊#95C2212yes—
29C2×C47⋊#95C2212yes—
30C2×C47⋊#95C2211yescharacteristic
31C23×D4×C47C2211yescharacteristic
32C24×C4×C47C2211yescharacteristic
33C24×C4×C47C2211yescharacteristic
34C2×C4×D4×C47—28no—
35C2×C4×D4×C47C418yescomplemented
36C22×C4⋊C4×C47C2211yescharacteristic
37C22×C22⋊C4×C47C2211yescharacteristic
38C22×C22⋊C4×C47C2211yescharacteristic
39C22×C42×C47C2211yescharacteristic
40C23×Dic47C2312yes—
41C23×Dic47C2312yes—
42C23×Dic47C2312yes—
43C23×Dic47C2312yes—
44C2×C4⋊Dic47—24no—
45C2×C4⋊Dic47—24no—
46C2×C4⋊Dic47—42no—
47C2×C22⋊Dic47—24no—
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—24no—
55C2×C22⋊Dic47—42no—
56C2×C22⋊Dic47—42no—
57C2×C22⋊Dic47—42no—
58C2×C22⋊Dic47—42no—
59C2×C4×Dic47—24no—
60C2×C4×Dic47—24no—
61C2×C4×Dic47—42no—
62C47⋊#95—22no—
63C47⋊#95—22no—
64C47⋊#95—24no—
65C47⋊#95—24no—
66C47⋊#95—24no—
67C47⋊#95—24no—
68C47⋊#95—22no—
69C47⋊#95—24no—
70C47⋊#95—42no—
71C47⋊#95D414yescomplemented
72C25×C47C2311yescharacteristic
73C25×C47C2311yescharacteristic
74C22×D4×C47—24no—
75C22×D4×C47—22no—
76C22×D4×C47—22no—
77C22×D4×C47—24no—
78C22×D4×C47C2×C414yes—
79C23×C4×C47—22no—
80C23×C4×C47—22no—
81C23×C4×C47—24no—
82C23×C4×C47—24no—
83C23×C4×C47—22no—
84C23×C4×C47—22no—
85C23×C4×C47—42no—
86C23×C4×C47—42no—
87C23×C4×C47C2×C414yes—
88C23×C4×C47C2×C414yes—
89C23×C4×C47C2311yescharacteristic
90C23×C4×C47C2311yescharacteristic
91C23×C4×C47C2311yescharacteristic
92C23×C4×C47C2311yescharacteristic
93C23×C4×C47C2311yescharacteristic
94C4×D4×C47—232no—
95C2×C4⋊C4×C47C2×C414yes—
96C2×C4⋊C4×C47D418yes—
97C2×C22⋊C4×C47—24no—
98C2×C22⋊C4×C47—24no—
99C2×C22⋊C4×C47C2×C414yes—
100C2×C22⋊C4×C47C2×C414yes—
101C2×C42×C47—24no—
102C2×C42×C47C2×C414yes—
103C24×C47—22no—
104C24×C47—22no—
105C24×C47—21no—
106C24×C47—21no—
107C24×C47—21no—
108C24×C47—21no—
109C24×C47—22no—
110C24×C47—21no—
111C24×C47—21no—
112C24×C47—22no—
113C24×C47—22no—
114C24×C47—22no—
115C24×C47—22no—
116C24×C47—21no—
117C24×C47—21no—
118C24×C47—21no—
119C24×C47—21no—
120C24×C47C22×C412yes—
121C24×C47C22×C412yes—
122C24×C47#4114yes—
123C24×C47#4112yes—
124C24×C47#4112yes—
125C24×C47C2411yescharacteristic
126C2×D4×C47—216no—
127C2×D4×C47—216no—
128C2×D4×C47—28no—
129C2×D4×C47—28no—
130C2×D4×C47—28no—
131C22×C4×C47—22no—
132C22×C4×C47—21no—
133C22×C4×C47—21no—
134C22×C4×C47—21no—
135C22×C4×C47—21no—
136C22×C4×C47—22no—
137C22×C4×C47—21no—
138C22×C4×C47—21no—
139C22×C4×C47—22no—
140C22×C4×C47—22no—
141C22×C4×C47—22no—
142C22×C4×C47—22no—
143C22×C4×C47—22no—
144C22×C4×C47—21no—
145C22×C4×C47—21no—
146C22×C4×C47—28no—
147C22×C4×C47—28no—
148C22×C4×C47—28no—
149C22×C4×C47—28no—
150C22×C4×C47—44no—
151C22×C4×C47—44no—
152C22×C4×C47—48no—
153C22×C4×C47—48no—
154C22×C4×C47—48no—
155C22×C4×C47—48no—
156C22×C4×C47C22×C412yes—
157C22×C4×C47C22×C412yes—
158C22×C4×C47C22×C412yes—
159C22×C4×C47C22×C412yes—
160C22×C4×C47C22×C412yes—
161C22×C4×C47C2×D414yes—
162C22×C4×C47C2×D414yes—
163C22×C4×C47C2×D414yes—
164C22×C4×C47C2×D412yes—
165C22×C4×C47#4112yes—
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—22no—
179C22×Dic47—22no—
180C22×Dic47—22no—
181C22×Dic47—22no—
182C22×Dic47—22no—
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—22no—
192C22×Dic47C2×D414yes—
193C22×Dic47#4114yes—
194C4⋊C4×C47C22⋊C4116yescomplemented
195C22⋊C4×C47—28no—
196C22⋊C4×C47—28no—
197C42×C47—28no—
198C22⋊Dic47—216no—
199C22⋊Dic47—48no—
200C22⋊Dic47—48no—
201C22⋊Dic47—48no—
202C4⋊Dic47—48no—
203C4×Dic47—48no—
204C23×C47—22no—
205C23×C47—22no—
206C23×C47—22no—
207C23×C47—22no—
208C23×C47—22no—
209C23×C47—22no—
210C23×C47—22no—
211C23×C47—22no—
212C23×C47—22no—
213C23×C47—22no—
214C23×C47—22no—
215C23×C47—22no—
216C23×C47—24no—
217C23×C47—24no—
218C23×C47—24no—
219C23×C47—24no—
220C23×C47—24no—
221C23×C47—24no—
222C23×C47—24no—
223C23×C47—24no—
224C23×C47—22no—
225C23×C47—22no—
226C23×C47—24no—
227C23×C47—22no—
228C23×C47—22no—
229C23×C47—24no—
230C23×C47—42no—
231C23×C47—42no—
232C23×C47—42no—
233C23×C47—42no—
234C23×C47—42no—
235C23×C47—42no—
236C23×C47—42no—
237C23×C47—42no—
238C23×C47—41no—
239C23×C47—42no—
240C23×C47—42no—
241C23×C47—41no—
242C23×C47—42no—
243C23×C47—42no—
244C23×C47—42no—
245C23×C47—41no—
246C23×C47—41no—
247C23×C47—42no—
248C23×C47#11714yes—
249C23×C47#11714yes—
250C23×C47C23×C411yescharacteristic
251C23×C47C22×D411yescharacteristic
252C23×C47C22×D412yes—
253C23×C47C2×#4112yes—
254C23×C47C2×#4111yescharacteristic
255C23×C47C2×#4112yes—
256C23×C47C2×#4111yescharacteristic
257C23×C47C2×#4111yescharacteristic
258C23×C47H(5,𝔽2)12yes—
259C23×C47H(5,𝔽2)11yescharacteristic
260C23×C472−1+411yescharacteristic
261D4×C47—232no—
262C2×C4×C47—22no—
263C2×C4×C47—22no—
264C2×C4×C47—22no—
265C2×C4×C47—22no—
266C2×C4×C47—22no—
267C2×C4×C47—22no—
268C2×C4×C47—22no—
269C2×C4×C47—22no—
270C2×C4×C47—24no—
271C2×C4×C47—24no—
272C2×C4×C47—24no—
273C2×C4×C47—24no—
274C2×C4×C47—24no—
275C2×C4×C47—24no—
276C2×C4×C47—24no—
277C2×C4×C47—24no—
278C2×C4×C47—22no—
279C2×C4×C47—22no—
280C2×C4×C47—22no—
281C2×C4×C47—416no—
282C2×C4×C47—416no—
283C2×C4×C47—42no—
284C2×C4×C47—42no—
285C2×C4×C47C2×C22⋊C414yes—
286C2×C4×C47C2×C22⋊C414yes—
287C2×C4×C47C2×C22⋊C414yes—
288C2×C4×C47C4×D414yes—
289C2×Dic47—24no—
290C2×Dic47—24no—
291C2×Dic47—24no—
292C2×Dic47—24no—
293C2×Dic47—24no—
294C2×Dic47—24no—
295C2×Dic47—42no—
296C2×Dic47—42no—
297C2×Dic47—42no—
298C2×Dic47—42no—
299C2×Dic47—42no—
300C2×Dic47—42no—
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×Dic47—42no—
310C2×Dic47—42no—
311C2×Dic47—42no—
312C2×Dic47—42no—
313C2×Dic47—42no—
314C2×Dic47—42no—
315C2×Dic47—42no—
316C2×Dic47—42no—
317#13890—471nomaximal, Sylow
318C22×C47—24no—
319C22×C47—24no—
320C22×C47—24no—
321C22×C47—24no—
322C22×C47—24no—
323C22×C47—24no—
324C22×C47—42no—
325C22×C47—42no—
326C22×C47—42no—
327C22×C47—42no—
328C22×C47—42no—
329C22×C47—42no—
330C22×C47—42no—
331C22×C47—44no—
332C22×C47—44no—
333C22×C47—44no—
334C22×C47—44no—
335C22×C47—44no—
336C22×C47—44no—
337C22×C47—44no—
338C22×C47—44no—
339C22×C47—42no—
340C22×C47C22×C22⋊C411yescharacteristic
341C22×C47C2×#11711yescharacteristic
342C22×C47C2×#11711yescharacteristic
343C22×C47C2×C4×D411yescharacteristic
344C22×C47C4×#4111yescharacteristic
345C22×C47#51811yescharacteristic
346C22×C47#52011yescharacteristic
347C22×C47#52512yes—
348C22×C47#52512yes—
349C22×C47#52512yes—
350C22×C47#52912yes—
351C22×C47#53812yes—
352C22×C47#53912yes—
353C22×C47D4212yes—
354C22×C47#54612yes—
355C22×C47#54611yescharacteristic
356C22×C47#54812yes—
357C22×C47#54811yescharacteristic
358C22×C47#55012yes—
359C22×C47#55112yes—
360C22×C47#55211yescharacteristic
361C22×C47#55311yescharacteristic
362C22×C47#55312yes—
363C4×C47—24no—
364C4×C47—24no—
365C4×C47—24no—
366C4×C47—24no—
367C4×C47—42no—
368Dic47—44no—
369Dic47—44no—
370Dic47—82no—
371Dic47—82no—
372C22×C4×D4D4711yescharacteristic
373C2×#387—472no—
374C2×#380—471no—
375C2×C4×C22⋊C4—471no—
376#1439—472no—
377#1438—472no—
378#1437—472no—
379#1434—471no—
380#1434—471no—
381C22⋊#95—471no—
382C22⋊#95—471no—
383C2×C47—44no—
384C2×C47—44no—
385C2×C47#228011yescharacteristic
386C2×C47#229011yescharacteristic
387C2×C47#231811yescharacteristic
388C2×C47D4×C22⋊C411yescharacteristic
389C2×C47#234111yescharacteristic
390C2×C47#235211yescharacteristic
391C2×C47#235311yescharacteristic
392C2×C47#245612yes—
393C2×C47#246012yes—
394C2×C47#246312yes—
395C2×C47#246712yes—
396C23×D4C2×D4711yescharacteristic
397C24×C4C2×D4711yescharacteristic
398C24×C4C2×D4711yescharacteristic
399C2×C4×D4—28no—
400C2×C4×D4Dic4718yescomplemented
401C22×C4⋊C4—472no—
402C22×C4⋊C4C2×D4711yescharacteristic
403C22×C22⋊C4—472no—
404C22×C22⋊C4—472no—
405C22×C22⋊C4—472no—
406C22×C22⋊C4—472no—
407C22×C22⋊C4C2×D4711yescharacteristic
408C22×C22⋊C4C2×D4711yescharacteristic
409C22×C42—472no—
410C22×C42C2×D4711yescharacteristic
411#387—948no—
412#380—944no—
413C4×C22⋊C4—944no—
414C2×#95—471no—
415C2×#95—471no—
416C2×#95—471no—
417C2×#95—471no—
418C2×#95—472no—
419C2×#95—472no—
420C2×#95—472no—
421C2×#95—472no—
422C2×#95—472no—
423C2×#95—472no—
424C47#1389011yescharacteristic, complemented, Sylow
425C25C22×D4711yescharacteristic
426C25C22×D4711yescharacteristic
427C22×D4—22no—
428C22×D4—22no—
429C22×D4—24no—
430C22×D4—24no—
431C22×D4C2×Dic4714yes—
432C23×C4—22no—
433C23×C4—22no—
434C23×C4—22no—
435C23×C4—22no—
436C23×C4—24no—
437C23×C4—24no—
438C23×C4—42no—
439C23×C4—42no—
440C23×C4—472no—
441C23×C4—472no—
442C23×C4—472no—
443C23×C4—472no—
444C23×C4C2×Dic4714yes—
445C23×C4C2×Dic4714yes—
446C23×C4C22×D4711yescharacteristic
447C23×C4C22×D4711yescharacteristic
448C23×C4C22×D4711yescharacteristic
449C23×C4C22×D4711yescharacteristic
450C23×C4C22×D4711yescharacteristic
451C4×D4—232no—
452C2×C4⋊C4—944no—
453C2×C4⋊C4—944no—
454C2×C4⋊C4—1882no—
455C2×C4⋊C4C2×Dic4714yes—
456C2×C4⋊C4C22⋊D4718yes—
457C2×C22⋊C4—24no—
458C2×C22⋊C4—24no—
459C2×C22⋊C4—944no—
460C2×C22⋊C4—944no—
461C2×C22⋊C4—944no—
462C2×C22⋊C4—944no—
463C2×C22⋊C4—944no—
464C2×C22⋊C4—944no—
465C2×C22⋊C4—944no—
466C2×C22⋊C4—944no—
467C2×C22⋊C4—1882no—
468C2×C22⋊C4—1882no—
469C2×C22⋊C4—1882no—
470C2×C22⋊C4—1882no—
471C2×C22⋊C4C2×Dic4714yes—
472C2×C22⋊C4C2×Dic4714yes—
473C2×C42—24no—
474C2×C42—944no—
475C2×C42—944no—
476C2×C42—1882no—
477C2×C42C2×Dic4714yes—
478#95—474no—
479#95—944no—
480#95—942no—
481#95—942no—
482#95—942no—
483#95—944no—
484#95—944no—
485#95—944no—
486#95—944no—
487#95—1882no—
488C24—21no—
489C24—21no—
490C24—22no—
491C24—22no—
492C24—22no—
493C24—22no—
494C24—21no—
495C24—21no—
496C24—21no—
497C24—21no—
498C24—22no—
499C24—22no—
500C24—22no—
501C24—21no—
502C24—21no—
503C24—21no—
504C24—21no—
505C24#1062535012yes—
506C24#1062535012yes—
507C24#1062535014yes—
508C24C22×Dic4712yes—
509C24C22×Dic4712yes—
510C24C23×D4711yescharacteristic
511C2×D4—216no—
512C2×D4—216no—
513C2×D4—28no—
514C2×D4—28no—
515C2×D4—28no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—22no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—28no—
532C22×C4—28no—
533C22×C4—28no—
534C22×C4—28no—
535C22×C4—44no—
536C22×C4—44no—
537C22×C4—48no—
538C22×C4—48no—
539C22×C4—48no—
540C22×C4—48no—
541C22×C4—474no—
542C22×C4—474no—
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—942no—
558C22×C4—942no—
559C22×C4—942no—
560C22×C4—942no—
561C22×C4—942no—
562C22×C4—942no—
563C22×C4—942no—
564C22×C4—942no—
565C22×C4—942no—
566C22×C4—942no—
567C22×C4—942no—
568C22×C4—942no—
569C22×C4D4×D4712yes—
570C22×C4#1062535212yes—
571C22×C4C22×Dic4712yes—
572C22×C4C22×Dic4712yes—
573C22×C4C22×Dic4712yes—
574C22×C4C22×Dic4712yes—
575C22×C4C22×Dic4712yes—
576C22×C4C2×C22⋊D4714yes—
577C22×C4C2×C22⋊D4714yes—
578C22×C4C2×C22⋊D4714yes—
579C4⋊C4—1888no—
580C4⋊C4C22⋊Dic47116yescomplemented
581C22⋊C4—28no—
582C22⋊C4—28no—
583C22⋊C4—9416no—
584C22⋊C4—1888no—
585C22⋊C4—1888no—
586C22⋊C4—1888no—
587C42—28no—
588C42—1888no—
589C23—22no—
590C23—22no—
591C23—24no—
592C23—22no—
593C23—22no—
594C23—24no—
595C23—22no—
596C23—22no—
597C23—22no—
598C23—22no—
599C23—22no—
600C23—22no—
601C23—22no—
602C23—22no—
603C23—22no—
604C23—22no—
605C23—22no—
606C23—22no—
607C23—24no—
608C23—24no—
609C23—24no—
610C23—24no—
611C23—24no—
612C23—24no—
613C23—24no—
614C23—24no—
615C23—42no—
616C23—42no—
617C23—42no—
618C23—42no—
619C23—41no—
620C23—42no—
621C23—42no—
622C23—41no—
623C23—42no—
624C23—42no—
625C23—42no—
626C23—41no—
627C23—41no—
628C23—42no—
629C23—42no—
630C23—42no—
631C23—42no—
632C23—42no—
633C23#1309398314yes—
634C23#1309398314yes—
635C23C23×Dic4711yescharacteristic
636C23C2×D4×D4711yescharacteristic
637C23C22×C22⋊D4712yes—
638C23#41×D4712yes—
639C23C2×#1062535211yescharacteristic
640C23C2×#1062535011yescharacteristic
641C23C2×#1062535011yescharacteristic
642C23C2×#1062535012yes—
643C23#1309406912yes—
644C23#1309407011yescharacteristic
645C23#1309407111yescharacteristic
646D4—232no—
647C2×C4—24no—
648C2×C4—24no—
649C2×C4—24no—
650C2×C4—24no—
651C2×C4—24no—
652C2×C4—24no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—24no—
662C2×C4—24no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—416no—
667C2×C4—416no—
668C2×C4—42no—
669C2×C4—42no—
670C2×C4—944no—
671C2×C4—944no—
672C2×C4—944no—
673C2×C4—944no—
674C2×C4—944no—
675C2×C4—944no—
676C2×C4—1882no—
677C2×C4—1882no—
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×C4—1882no—
687C2×C4—1882no—
688C2×C4—1882no—
689C2×C4—1882no—
690C2×C4—1882no—
691C2×C4—1882no—
692C2×C4—1882no—
693C2×C4—1882no—
694C2×C4—1882no—
695C2×C4—1882no—
696C2×C4—1882no—
697C2×C4—1882no—
698C2×C4C2×C22⋊Dic4714yes—
699C2×C4C2×C22⋊Dic4714yes—
700C2×C4C2×C22⋊Dic4714yes—
701C2×C4D4×Dic4714yes—
702C22—24no—
703C22—24no—
704C22—24no—
705C22—24no—
706C22—24no—
707C22—24no—
708C22—42no—
709C22—44no—
710C22—44no—
711C22—42no—
712C22—42no—
713C22—42no—
714C22—44no—
715C22—44no—
716C22—44no—
717C22—44no—
718C22—42no—
719C22—42no—
720C22—42no—
721C22—42no—
722C22—44no—
723C22—44no—
724C22C22×C22⋊Dic4711yescharacteristic
725C22C2×#1309398311yescharacteristic
726C22C2×#1309398311yescharacteristic
727C22C2×D4×Dic4711yescharacteristic
728C22#41×Dic4711yescharacteristic
729C22#1568959811yescharacteristic
730C22#1568960611yescharacteristic
731C22#1568963212yes—
732C22#1568963412yes—
733C22#1568963412yes—
734C22#1568965312yes—
735C22#1568970612yes—
736C22#1568971512yes—
737C22D4×C22⋊D4712yes—
738C22#1568976712yes—
739C22#1568976911yescharacteristic
740C22#1568978012yes—
741C22#1568978211yescharacteristic
742C22#1568979212yes—
743C22#1568980212yes—
744C22#1568981311yescharacteristic
745C22#1568981911yescharacteristic
746C22#1568982212yes—
747C4—24no—
748C4—24no—
749C4—24no—
750C4—24no—
751C4—42no—
752C4—3762no—
753C4—3762no—
754C4—1884no—
755C4—1884no—
756C2—44no—
757C2—44no—
758C2#2024577111yescharacteristic
759C2#2024583311yescharacteristic
760C2#2024602111yescharacteristic
761C2D4×C22⋊Dic4711yescharacteristic
762C2#2024622911yescharacteristic
763C2#2024631711yescharacteristic
764C2#2024632811yescharacteristic
765C2#2024727412yes—
766C2#2024733412yes—
767C2#2024737912yes—
768C2#2024743312yes—
subgroupG/H
center, FrattiniC24C23×D47
commutatorC23×C47C23×C4
FittingC22×C4×D4×C47C2
socle, cosocleC24×C47C24
prime radicalC23×D4×C47C22
hypercenterC22×C4×D4D47
hypocenterC47#13890
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C24 ◁ C22×C4×D4

Complements

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

NH ≅ G/Ntype
1. C2×#15689009C2semidirect
2. C2×#15688983C2semidirect
3. C2×C4×C22⋊Dic47C2semidirect
4. #20241633C2semidirect
6. #20241625C2semidirect
7. #20241615C2semidirect
8. #20241615C2semidirect
9. #20241611C2semidirect
10. #20241611C2semidirect
35. C2×C4×D4×C47C4semidirect
71. C47⋊#95D4semidirect
194. C4⋊C4×C47C22⋊C4semidirect
400. C2×C4×D4Dic47semidirect
424. C47#13890semidirect
580. C4⋊C4C22⋊Dic47semidirect

Maximal subgroups

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

subgroupindex
C2×#156890092
C2×#156889832
C2×C4×C22⋊Dic472
#202416332
#202416292
#202416252
#202416152
#202416112
C22×C4×D4×C472
#1389047