Finite Group Databasebeta

← #26138323

Subgroups — #26138323

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×#15689016C212yesmaximal, complemented
2C2×#15688986C211yesmaximal, characteristic, complemented
3C2×C4×C22⋊Dic47C211yesmaximal, characteristic, complemented
4#20241633C212yesmaximal, complemented
5#20241629C212yesmaximal
6#20241620C212yesmaximal, complemented
7#20241618C211yesmaximal, 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#15689016—28no—
19#15688986—24no—
20C4×C22⋊Dic47—24no—
21C2×C47⋊#95C2211yescharacteristic
22C2×C47⋊#95C2212yes—
23C2×C47⋊#95C2212yes—
24C2×C47⋊#95C2212yes—
25C2×C47⋊#95C2211yescharacteristic
26C2×C47⋊#95C2211yescharacteristic
27C2×C47⋊#95C2212yes—
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—24no—
76C22×D4×C47—22no—
77C22×D4×C47—22no—
78C22×D4×C47C2×C414yes—
79C23×C4×C47—24no—
80C23×C4×C47—22no—
81C23×C4×C47—22no—
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×C47—24no—
96C2×C4⋊C4×C47C2×C414yes—
97C2×C22⋊C4×C47—24no—
98C2×C22⋊C4×C47C2×C414yes—
99C2×C22⋊C4×C47C2×C414yes—
100C2×C22⋊C4×C47D418yes—
101C2×C42×C47—24no—
102C2×C42×C47C2×C414yes—
103C24×C47—22no—
104C24×C47—21no—
105C24×C47—21no—
106C24×C47—21no—
107C24×C47—21no—
108C24×C47—22no—
109C24×C47—21no—
110C24×C47—21no—
111C24×C47—21no—
112C24×C47—21no—
113C24×C47—22no—
114C24×C47—22no—
115C24×C47—22no—
116C24×C47—22no—
117C24×C47—21no—
118C24×C47—21no—
119C24×C47—21no—
120C24×C47—21no—
121C24×C47C22×C412yes—
122C24×C47C22×C412yes—
123C24×C47C2×D414yes—
124C24×C47#4114yes—
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—22no—
133C22×C4×C47—21no—
134C22×C4×C47—21no—
135C22×C4×C47—22no—
136C22×C4×C47—22no—
137C22×C4×C47—22no—
138C22×C4×C47—22no—
139C22×C4×C47—21no—
140C22×C4×C47—21no—
141C22×C4×C47—28no—
142C22×C4×C47—22no—
143C22×C4×C47—21no—
144C22×C4×C47—21no—
145C22×C4×C47—22no—
146C22×C4×C47—28no—
147C22×C4×C47—28no—
148C22×C4×C47—28no—
149C22×C4×C47—44no—
150C22×C4×C47—44no—
151C22×C4×C47—48no—
152C22×C4×C47—48no—
153C22×C4×C47—48no—
154C22×C4×C47—48no—
155C22×C4×C47C22×C412yes—
156C22×C4×C47C22×C412yes—
157C22×C4×C47C22×C412yes—
158C22×C4×C47C22×C412yes—
159C22×C4×C47C22×C412yes—
160C22×C4×C47C2×D414yes—
161C22×C4×C47C2×D414yes—
162C22×C4×C47C2×D412yes—
163C22×C4×C47#4112yes—
164C22×C4×C47#4112yes—
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×C47—28no—
195C22⋊C4×C47—28no—
196C22⋊C4×C47C22⋊C4116yescomplemented
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—24no—
225C23×C47—24no—
226C23×C47—24no—
227C23×C47—24no—
228C23×C47—42no—
229C23×C47—42no—
230C23×C47—42no—
231C23×C47—42no—
232C23×C47—42no—
233C23×C47—42no—
234C23×C47—42no—
235C23×C47—42no—
236C23×C47—41no—
237C23×C47—41no—
238C23×C47—41no—
239C23×C47—41no—
240C23×C47—42no—
241C23×C47—42no—
242C23×C47—41no—
243C23×C47—41no—
244C23×C47—41no—
245C23×C47—41no—
246C23×C47—42no—
247C23×C47—42no—
248C23×C47C2×C22⋊C414yes—
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×C47#11714yes—
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#13886—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#54612yes—
356C22×C47#54712yes—
357C22×C47#54711yescharacteristic
358C22×C47#55011yescharacteristic
359C22×C47#55312yes—
360C22×C47#55511yescharacteristic
361C22×C47#55611yescharacteristic
362C22×C47#55912yes—
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×#388—472no—
374C2×#381—471no—
375C2×C4×C22⋊C4—471no—
376#1439—472no—
377#1438—472no—
378#1436—472no—
379C4⋊#95—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#233911yescharacteristic
390C2×C47#235411yescharacteristic
391C2×C47#235711yescharacteristic
392C2×C47#245512yes—
393C2×C47#245612yes—
394C2×C47#245912yes—
395C2×C47#246612yes—
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#388—948no—
412#381—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#1388611yescharacteristic, complemented, Sylow
425C25C22×D4711yescharacteristic
426C25C22×D4711yescharacteristic
427C22×D4—24no—
428C22×D4—24no—
429C22×D4—22no—
430C22×D4—22no—
431C22×D4C2×Dic4714yes—
432C23×C4—24no—
433C23×C4—22no—
434C23×C4—22no—
435C23×C4—22no—
436C23×C4—22no—
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—24no—
453C2×C4⋊C4—944no—
454C2×C4⋊C4—944no—
455C2×C4⋊C4—1882no—
456C2×C4⋊C4C2×Dic4714yes—
457C2×C22⋊C4—24no—
458C2×C22⋊C4—944no—
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—1882no—
467C2×C22⋊C4—1882no—
468C2×C22⋊C4—1882no—
469C2×C22⋊C4—1882no—
470C2×C22⋊C4C2×Dic4714yes—
471C2×C22⋊C4C2×Dic4714yes—
472C2×C22⋊C4C22⋊D4718yes—
473C2×C42—24no—
474C2×C42—944no—
475C2×C42—944no—
476C2×C42—1882no—
477C2×C42C2×Dic4714yes—
478#95—474no—
479#95—944no—
480#95—944no—
481#95—944no—
482#95—942no—
483#95—942no—
484#95—942no—
485#95—944no—
486#95—944no—
487#95—1882no—
488C24—21no—
489C24—21no—
490C24—22no—
491C24—22no—
492C24—22no—
493C24—21no—
494C24—21no—
495C24—21no—
496C24—21no—
497C24—21no—
498C24—21no—
499C24—22no—
500C24—22no—
501C24—22no—
502C24—21no—
503C24—21no—
504C24—21no—
505C24—21no—
506C24#1062535014yes—
507C24C22×Dic4712yes—
508C24C22×Dic4712yes—
509C24C2×C22⋊D4714yes—
510C24C23×D4711yescharacteristic
511C2×D4—216no—
512C2×D4—216no—
513C2×D4—28no—
514C2×D4—28no—
515C2×D4—28no—
516C22×C4—21no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—21no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—28no—
527C22×C4—21no—
528C22×C4—22no—
529C22×C4—21no—
530C22×C4—22no—
531C22×C4—28no—
532C22×C4—28no—
533C22×C4—28no—
534C22×C4—44no—
535C22×C4—44no—
536C22×C4—48no—
537C22×C4—48no—
538C22×C4—48no—
539C22×C4—48no—
540C22×C4—474no—
541C22×C4—474no—
542C22×C4—942no—
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#1062535012yes—
569C22×C4#1062535012yes—
570C22×C4D4×D4712yes—
571C22×C4#1062535212yes—
572C22×C4C22×Dic4712yes—
573C22×C4C22×Dic4712yes—
574C22×C4C22×Dic4712yes—
575C22×C4C22×Dic4712yes—
576C22×C4C22×Dic4712yes—
577C22×C4C2×C22⋊D4714yes—
578C22×C4C2×C22⋊D4714yes—
579C4⋊C4—28no—
580C4⋊C4—1888no—
581C22⋊C4—28no—
582C22⋊C4—9416no—
583C22⋊C4—1888no—
584C22⋊C4—1888no—
585C22⋊C4—1888no—
586C22⋊C4C22⋊Dic47116yescomplemented
587C42—28no—
588C42—1888no—
589C23—24no—
590C23—24no—
591C23—24no—
592C23—24no—
593C23—22no—
594C23—22no—
595C23—22no—
596C23—22no—
597C23—22no—
598C23—22no—
599C23—22no—
600C23—22no—
601C23—22no—
602C23—22no—
603C23—22no—
604C23—22no—
605C23—24no—
606C23—24no—
607C23—24no—
608C23—24no—
609C23—24no—
610C23—24no—
611C23—24no—
612C23—24no—
613C23—42no—
614C23—42no—
615C23—42no—
616C23—42no—
617C23—41no—
618C23—41no—
619C23—41no—
620C23—41no—
621C23—42no—
622C23—42no—
623C23—41no—
624C23—41no—
625C23—41no—
626C23—41no—
627C23—42no—
628C23—42no—
629C23—42no—
630C23—42no—
631C23—42no—
632C23—42no—
633C23C2×C22⋊Dic4714yes—
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×C4#1309398314yes—
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—42no—
715C22—42no—
716C22—44no—
717C22—44no—
718C22—42no—
719C22—42no—
720C22—44no—
721C22—44no—
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#1568976112yes—
739C22#1568976712yes—
740C22#1568977212yes—
741C22#1568977811yescharacteristic
742C22#1568979411yescharacteristic
743C22#1568982312yes—
744C22#1568983811yescharacteristic
745C22#1568984311yescharacteristic
746C22#1568985612yes—
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#2024621811yescharacteristic
763C2#2024633711yescharacteristic
764C2#2024636111yescharacteristic
765C2#2024726512yes—
766C2#2024728012yes—
767C2#2024731912yes—
768C2#2024741812yes—
subgroupG/H
center, FrattiniC24C23×D47
commutatorC23×C47C23×C4
FittingC22×C4×D4×C47C2
socle, cosocleC24×C47C24
prime radicalC23×D4×C47C22
hypercenterC22×C4×D4D47
hypocenterC47#13886
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×#15689016C2semidirect
2. C2×#15688986C2semidirect
3. C2×C4×C22⋊Dic47C2semidirect
4. #20241633C2semidirect
6. #20241620C2semidirect
7. #20241618C2semidirect
8. #20241615C2semidirect
9. #20241611C2semidirect
10. #20241611C2semidirect
35. C2×C4×D4×C47C4semidirect
71. C47⋊#95D4semidirect
196. C22⋊C4×C47C22⋊C4semidirect
400. C2×C4×D4Dic47semidirect
424. C47#13886semidirect
586. C22⋊C4C22⋊Dic47semidirect

Maximal subgroups

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

subgroupindex
C2×#156890162
C2×#156889862
C2×C4×C22⋊Dic472
#202416332
#202416292
#202416202
#202416182
#202416152
#202416112
C22×C4×D4×C472
#1388647