Finite Group Databasebeta

← #26138301

Subgroups — #26138301

Order 12032.

1486 conjugacy classes of subgroups.

The subgroup lattice has 682 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689009C212yesmaximal
2C2×#15688993C211yesmaximal, characteristic
3C2×C4×C4⋊Dic47C211yesmaximal, characteristic
4#20241645C212yesmaximal
5#20241641C212yesmaximal
6#20241622C212yesmaximal
7#20241618C211yesmaximal, characteristic
8#20241618C211yesmaximal, characteristic
9#20241618C211yesmaximal, characteristic
10#20241618C211yesmaximal, characteristic
11C2×C4×C4⋊C4×C47C211yesmaximal, characteristic
12C22×C4⋊Dic47C2211yescharacteristic
13C22×C4⋊Dic47C2211yescharacteristic
14C22×C4⋊Dic47C2212yes—
15C22×C4⋊Dic47C2212yes—
16C22×C4⋊Dic47C2211yescharacteristic
17C22×C4⋊Dic47C2211yescharacteristic
18C22×C4×Dic47C2212yes—
19#15689009—28no—
20#15688993—24no—
21C4×C4⋊Dic47—24no—
22C2×C47⋊#95C2212yes—
23C2×C47⋊#95C2212yes—
24C2×C47⋊#95C2212yes—
25C2×C47⋊#95C2212yes—
26C2×C47⋊#95C2212yes—
27C2×C47⋊#95C2212yes—
28C2×C47⋊#95C2212yes—
29C2×C47⋊#95C2212yes—
30C2×C47⋊#95C2212yes—
31C22×C4⋊C4×C47C2211yescharacteristic
32C22×C4⋊C4×C47C2211yescharacteristic
33C22×C42×C47C2211yescharacteristic
34C22×C42×C47C2211yescharacteristic
35C22×C42×C47C2211yescharacteristic
36C4×C4⋊C4×C47C418yescomplemented
37C2×#95×C47C2211yescharacteristic
38C2×#95×C47C2211yescharacteristic
39C23×Dic47C2312yes—
40C23×Dic47C2312yes—
41C23×Dic47C2312yes—
42C23×Dic47C2312yes—
43C2×C4⋊Dic47—22no—
44C2×C4⋊Dic47—22no—
45C2×C4⋊Dic47—22no—
46C2×C4⋊Dic47—22no—
47C2×C4⋊Dic47—22no—
48C2×C4⋊Dic47—24no—
49C2×C4⋊Dic47—24no—
50C2×C4⋊Dic47—22no—
51C2×C4⋊Dic47—22no—
52C2×C4⋊Dic47—22no—
53C2×C4⋊Dic47—22no—
54C2×C4⋊Dic47—22no—
55C2×C4⋊Dic47—24no—
56C2×C4⋊Dic47—24no—
57C2×C4⋊Dic47—42no—
58C2×C4⋊Dic47—42no—
59C2×C4⋊Dic47D414yes—
60C2×C4⋊Dic47Q814yes—
61C2×C4×Dic47—24no—
62C2×C4×Dic47—24no—
63C2×C4×Dic47—42no—
64C47⋊#95—24no—
65C47⋊#95—24no—
66C47⋊#95—24no—
67C47⋊#95—24no—
68C47⋊#95—24no—
69C47⋊#95—24no—
70C47⋊#95—42no—
71C47⋊#95—42no—
72C47⋊#95—42no—
73C23×C4×C47C2311yescharacteristic
74C23×C4×C47C2311yescharacteristic
75C23×C4×C47C2311yescharacteristic
76C23×C4×C47C2311yescharacteristic
77C23×C4×C47C2311yescharacteristic
78C23×C4×C47C2311yescharacteristic
79C23×C4×C47C2311yescharacteristic
80C2×C4⋊C4×C47—22no—
81C2×C4⋊C4×C47—22no—
82C2×C4⋊C4×C47C2×C414yes—
83C2×C4⋊C4×C47C2×C414yes—
84C2×C4⋊C4×C47D414yes—
85C2×C4⋊C4×C47Q814yes—
86C2×C42×C47—22no—
87C2×C42×C47—22no—
88C2×C42×C47—22no—
89C2×C42×C47—22no—
90C2×C42×C47—22no—
91C2×C42×C47—22no—
92C2×C42×C47C2×C414yes—
93C2×C42×C47C2×C414yes—
94C2×C42×C47C2×C414yes—
95#95×C47C2×C414yes—
96#95×C47C2×C414yes—
97C24×C47C2411yescharacteristic
98C22×C4×C47—21no—
99C22×C4×C47—21no—
100C22×C4×C47—21no—
101C22×C4×C47—21no—
102C22×C4×C47—21no—
103C22×C4×C47—21no—
104C22×C4×C47—21no—
105C22×C4×C47—21no—
106C22×C4×C47—21no—
107C22×C4×C47—21no—
108C22×C4×C47—21no—
109C22×C4×C47—21no—
110C22×C4×C47—21no—
111C22×C4×C47—21no—
112C22×C4×C47—21no—
113C22×C4×C47—21no—
114C22×C4×C47—21no—
115C22×C4×C47—21no—
116C22×C4×C47—21no—
117C22×C4×C47—21no—
118C22×C4×C47—21no—
119C22×C4×C47—21no—
120C22×C4×C47—21no—
121C22×C4×C47—21no—
122C22×C4×C47—21no—
123C22×C4×C47—21no—
124C22×C4×C47—21no—
125C22×C4×C47—21no—
126C22×C4×C47C22×C412yes—
127C22×C4×C47C22×C412yes—
128C22×C4×C47C22×C412yes—
129C22×C4×C47C22×C412yes—
130C22×C4×C47C22×C412yes—
131C22×C4×C47C22×C412yes—
132C22×C4×C47C22×C412yes—
133C22×C4×C47C2×D412yes—
134C22×C4×C47C2×D412yes—
135C22×C4×C47C2×D412yes—
136C22×C4×C47C2×D412yes—
137C22×C4×C47C2×Q812yes—
138C22×C4×C47C2×Q812yes—
139C22×C4×C47C2×Q812yes—
140C22×C4×C47C2×Q812yes—
141C22×C4×C47#4112yes—
142C22×C4×C47#4112yes—
143C22×C4×C47#4112yes—
144C22×C4×C47#4112yes—
145C22×C4×C47#4112yes—
146C22×C4×C47#4112yes—
147C22×Dic47—22no—
148C22×Dic47—22no—
149C22×Dic47—22no—
150C22×Dic47—22no—
151C22×Dic47—22no—
152C22×Dic47—22no—
153C22×Dic47—22no—
154C22×Dic47—22no—
155C22×Dic47—22no—
156C22×Dic47—22no—
157C22×Dic47—22no—
158C22×Dic47—22no—
159C22×Dic47—22no—
160C22×Dic47—22no—
161C22×Dic47—22no—
162C22×Dic47—22no—
163C22×Dic47—22no—
164C22×Dic47—22no—
165C22×Dic47—22no—
166C22×Dic47—22no—
167C22×Dic47—22no—
168C22×Dic47—22no—
169C22×Dic47—22no—
170C22×Dic47—22no—
171C22×Dic47—22no—
172C22×Dic47—22no—
173C22×Dic47C2×D414yes—
174C22×Dic47C2×Q814yes—
175C4⋊C4×C47—28no—
176C4⋊C4×C47C4⋊C4116yescomplemented
177C42×C47—28no—
178C42×C47—28no—
179C42×C47—28no—
180C4⋊Dic47—28no—
181C4⋊Dic47—28no—
182C4⋊Dic47—48no—
183C4⋊Dic47—48no—
184C4⋊Dic47—44no—
185C4⋊Dic47—44no—
186C4×Dic47—48no—
187C23×C47C23×C411yescharacteristic
188C23×C47C22×D411yescharacteristic
189C23×C47C22×D411yescharacteristic
190C23×C47C22×Q811yescharacteristic
191C23×C47C22×Q811yescharacteristic
192C23×C47C2×#4111yescharacteristic
193C23×C47C2×#4111yescharacteristic
194C23×C47C2×#4111yescharacteristic
195C23×C47C2×#4111yescharacteristic
196C23×C47C2×#4111yescharacteristic
197C23×C47C2×#4111yescharacteristic
198C23×C47H(5,𝔽2)11yescharacteristic
199C23×C47H(5,𝔽2)11yescharacteristic
200C23×C472−1+411yescharacteristic
201C23×C472−1+411yescharacteristic
202C2×C4×C47—22no—
203C2×C4×C47—22no—
204C2×C4×C47—22no—
205C2×C4×C47—22no—
206C2×C4×C47—22no—
207C2×C4×C47—22no—
208C2×C4×C47—22no—
209C2×C4×C47—22no—
210C2×C4×C47—22no—
211C2×C4×C47—22no—
212C2×C4×C47—22no—
213C2×C4×C47—22no—
214C2×C4×C47—22no—
215C2×C4×C47—22no—
216C2×C4×C47—22no—
217C2×C4×C47—22no—
218C2×C4×C47—22no—
219C2×C4×C47—22no—
220C2×C4×C47—22no—
221C2×C4×C47—22no—
222C2×C4×C47—22no—
223C2×C4×C47—22no—
224C2×C4×C47—22no—
225C2×C4×C47—22no—
226C2×C4×C47—22no—
227C2×C4×C47—22no—
228C2×C4×C47—22no—
229C2×C4×C47—22no—
230C2×C4×C47—22no—
231C2×C4×C47—22no—
232C2×C4×C47—41no—
233C2×C4×C47—41no—
234C2×C4×C47—41no—
235C2×C4×C47—41no—
236C2×C4×C47—41no—
237C2×C4×C47—41no—
238C2×C4×C47—41no—
239C2×C4×C47—41no—
240C2×C4×C47C2×C4⋊C414yes—
241C2×C4×C47C2×C4⋊C414yes—
242C2×C4×C47C2×C4⋊C414yes—
243C2×C4×C47#11714yes—
244C2×C4×C47#11714yes—
245C2×C4×C47C4×D414yes—
246C2×C4×C47C4×Q814yes—
247C2×C4×C47C22⋊Q814yes—
248C2×C4×C47#12314yes—
249C2×C4×C47#12514yes—
250C2×C4×C47#12614yes—
251C2×Dic47—24no—
252C2×Dic47—24no—
253C2×Dic47—24no—
254C2×Dic47—24no—
255C2×Dic47—24no—
256C2×Dic47—24no—
257C2×Dic47—42no—
258C2×Dic47—42no—
259C2×Dic47—42no—
260C2×Dic47—42no—
261C2×Dic47—42no—
262C2×Dic47—42no—
263C2×Dic47—42no—
264C2×Dic47—42no—
265C2×Dic47—42no—
266C2×Dic47—42no—
267C2×Dic47—42no—
268C2×Dic47—42no—
269C2×Dic47—42no—
270C2×Dic47—42no—
271C2×Dic47—42no—
272C2×Dic47—42no—
273C2×Dic47—42no—
274C2×Dic47—42no—
275C2×Dic47—42no—
276C2×Dic47—42no—
277C2×Dic47—42no—
278C2×Dic47—42no—
279#13884—471nomaximal, Sylow
280C22×C47C22×C4⋊C411yescharacteristic
281C22×C47C2×#11711yescharacteristic
282C22×C47C2×#11711yescharacteristic
283C22×C47C2×C4×D411yescharacteristic
284C22×C47C2×C4×Q811yescharacteristic
285C22×C47#52011yescharacteristic
286C22×C47#52011yescharacteristic
287C22×C47C2×C22⋊Q811yescharacteristic
288C22×C47C2×#12311yescharacteristic
289C22×C47C2×#12511yescharacteristic
290C22×C47C2×#12611yescharacteristic
291C22×C47#53211yescharacteristic
292C22×C47#53211yescharacteristic
293C22×C47#53311yescharacteristic
294C22×C47#53311yescharacteristic
295C22×C47#54011yescharacteristic
296C22×C47#54111yescharacteristic
297C22×C47#54211yescharacteristic
298C22×C47#54211yescharacteristic
299C22×C47D4211yescharacteristic
300C22×C47#54611yescharacteristic
301C22×C47#54711yescharacteristic
302C22×C47#54811yescharacteristic
303C22×C47D4×Q811yescharacteristic
304C22×C47D4×Q811yescharacteristic
305C22×C47#55011yescharacteristic
306C22×C47#55211yescharacteristic
307C22×C47#55311yescharacteristic
308C22×C47#55411yescharacteristic
309C22×C47#55411yescharacteristic
310C22×C47#55611yescharacteristic
311C22×C47#55711yescharacteristic
312C22×C47#55711yescharacteristic
313C22×C47Q8211yescharacteristic
314C22×C47#55911yescharacteristic
315C4×C47—24no—
316C4×C47—24no—
317C4×C47—24no—
318C4×C47—24no—
319C4×C47—42no—
320C4×C47—42no—
321C4×C47#38718yescomplemented
322Dic47—44no—
323Dic47—44no—
324Dic47—82no—
325Dic47—82no—
326C2×#387—472no—
327C2×#384—471no—
328C2×C4×C4⋊C4—471no—
329C2×C4×C4⋊C4D4711yescharacteristic
330#1442—472no—
331#1441—472no—
332#1436—472no—
333C4⋊#95—471no—
334C4⋊#95—471no—
335C4⋊#95—471no—
336C4⋊#95—471no—
337C2×C47#228511yescharacteristic
338C2×C47C2×#38711yescharacteristic
339C2×C47#231411yescharacteristic
340C2×C47D4×C4⋊C411yescharacteristic
341C2×C47Q8×C4⋊C411yescharacteristic
342C2×C47#235211yescharacteristic
343C2×C47#235511yescharacteristic
344C2×C47#244511yescharacteristic
345C2×C47#244611yescharacteristic
346C2×C47#245111yescharacteristic
347C2×C47#245211yescharacteristic
348C2×C47#250611yescharacteristic
349C2×C47#250711yescharacteristic
350C2×C47#251111yescharacteristic
351C2×C47#251211yescharacteristic
352C22×C4⋊C4—471no—
353C22×C4⋊C4—471no—
354C22×C4⋊C4—471no—
355C22×C4⋊C4—471no—
356C22×C4⋊C4—472no—
357C22×C4⋊C4—472no—
358C22×C4⋊C4C2×D4711yescharacteristic
359C22×C4⋊C4C2×D4711yescharacteristic
360C22×C42—472no—
361C22×C42C2×D4711yescharacteristic
362C22×C42C2×D4711yescharacteristic
363C22×C42C2×D4711yescharacteristic
364#387—948no—
365#384—944no—
366C4×C4⋊C4—944no—
367C4×C4⋊C4Dic4718yescomplemented
368C2×#95—472no—
369C2×#95—472no—
370C2×#95—472no—
371C2×#95—472no—
372C2×#95—472no—
373C2×#95—472no—
374C2×#95—472no—
375C2×#95—472no—
376C2×#95—472no—
377C2×#95C2×D4711yescharacteristic
378C2×#95C2×D4711yescharacteristic
379C47#1388411yescharacteristic, complemented, Sylow
380C23×C4—472no—
381C23×C4—472no—
382C23×C4—472no—
383C23×C4—472no—
384C23×C4C22×D4711yescharacteristic
385C23×C4C22×D4711yescharacteristic
386C23×C4C22×D4711yescharacteristic
387C23×C4C22×D4711yescharacteristic
388C23×C4C22×D4711yescharacteristic
389C23×C4C22×D4711yescharacteristic
390C23×C4C22×D4711yescharacteristic
391C2×C4⋊C4—22no—
392C2×C4⋊C4—22no—
393C2×C4⋊C4—474no—
394C2×C4⋊C4—474no—
395C2×C4⋊C4—942no—
396C2×C4⋊C4—942no—
397C2×C4⋊C4—942no—
398C2×C4⋊C4—942no—
399C2×C4⋊C4—944no—
400C2×C4⋊C4—944no—
401C2×C4⋊C4—944no—
402C2×C4⋊C4—944no—
403C2×C4⋊C4—942no—
404C2×C4⋊C4—942no—
405C2×C4⋊C4—942no—
406C2×C4⋊C4—942no—
407C2×C4⋊C4—942no—
408C2×C4⋊C4—942no—
409C2×C4⋊C4—1882no—
410C2×C4⋊C4—1882no—
411C2×C4⋊C4Dic9414yes—
412C2×C4⋊C4D18814yes—
413C2×C4⋊C4C2×Dic4714yes—
414C2×C4⋊C4C2×Dic4714yes—
415C2×C42—22no—
416C2×C42—22no—
417C2×C42—22no—
418C2×C42—22no—
419C2×C42—22no—
420C2×C42—22no—
421C2×C42—944no—
422C2×C42—944no—
423C2×C42—1882no—
424C2×C42C2×Dic4714yes—
425C2×C42C2×Dic4714yes—
426C2×C42C2×Dic4714yes—
427#95—944no—
428#95—944no—
429#95—944no—
430#95—944no—
431#95—944no—
432#95—944no—
433#95—1882no—
434#95—1882no—
435#95—1882no—
436#95C2×Dic4714yes—
437#95C2×Dic4714yes—
438C24C23×D4711yescharacteristic
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—474no—
468C22×C4—474no—
469C22×C4—942no—
470C22×C4—942no—
471C22×C4—942no—
472C22×C4—942no—
473C22×C4—942no—
474C22×C4—942no—
475C22×C4—942no—
476C22×C4—942no—
477C22×C4—942no—
478C22×C4—942no—
479C22×C4—942no—
480C22×C4—942no—
481C22×C4—942no—
482C22×C4—942no—
483C22×C4—942no—
484C22×C4—942no—
485C22×C4—942no—
486C22×C4—942no—
487C22×C4—942no—
488C22×C4—942no—
489C22×C4—942no—
490C22×C4—942no—
491C22×C4—942no—
492C22×C4—942no—
493C22×C4—942no—
494C22×C4—942no—
495C22×C4C2×Dic9412yes—
496C22×C4C2×Dic9412yes—
497C22×C4C2×Dic9412yes—
498C22×C4C2×D18812yes—
499C22×C4C2×D18812yes—
500C22×C4C2×D18812yes—
501C22×C4#1062535012yes—
502C22×C4#1062535012yes—
503C22×C4#1062535012yes—
504C22×C4#1062535012yes—
505C22×C4D4×D4712yes—
506C22×C4#1062535212yes—
507C22×C4Q8×D4712yes—
508C22×C4#1062535412yes—
509C22×C4C22×Dic4712yes—
510C22×C4C22×Dic4712yes—
511C22×C4C22×Dic4712yes—
512C22×C4C22×Dic4712yes—
513C22×C4C22×Dic4712yes—
514C22×C4C22×Dic4712yes—
515C22×C4C22×Dic4712yes—
516C4⋊C4—28no—
517C4⋊C4—948no—
518C4⋊C4—948no—
519C4⋊C4—1888no—
520C4⋊C4—1888no—
521C4⋊C4—1884no—
522C4⋊C4—1884no—
523C4⋊C4C4⋊Dic47116yescomplemented
524C42—28no—
525C42—28no—
526C42—28no—
527C42—1888no—
528C23C23×Dic4711yescharacteristic
529C23C2×D4×D4711yescharacteristic
530C23C22×D18811yescharacteristic
531C23C2×Q8×D4711yescharacteristic
532C23C22×Dic9411yescharacteristic
533C23C2×#1062535211yescharacteristic
534C23C2×#1062535011yescharacteristic
535C23C2×#1062535011yescharacteristic
536C23C2×#1062535011yescharacteristic
537C23C2×#1062535011yescharacteristic
538C23C2×#1062535411yescharacteristic
539C23#1309407011yescharacteristic
540C23#1309407011yescharacteristic
541C23#1309407111yescharacteristic
542C23#1309407111yescharacteristic
543C2×C4—22no—
544C2×C4—22no—
545C2×C4—22no—
546C2×C4—22no—
547C2×C4—22no—
548C2×C4—22no—
549C2×C4—22no—
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—22no—
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—22no—
556C2×C4—22no—
557C2×C4—22no—
558C2×C4—22no—
559C2×C4—22no—
560C2×C4—22no—
561C2×C4—22no—
562C2×C4—22no—
563C2×C4—22no—
564C2×C4—22no—
565C2×C4—22no—
566C2×C4—22no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—22no—
570C2×C4—22no—
571C2×C4—22no—
572C2×C4—22no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—944no—
582C2×C4—944no—
583C2×C4—944no—
584C2×C4—944no—
585C2×C4—944no—
586C2×C4—944no—
587C2×C4—1882no—
588C2×C4—1882no—
589C2×C4—1882no—
590C2×C4—1882no—
591C2×C4—1882no—
592C2×C4—1882no—
593C2×C4—1882no—
594C2×C4—1882no—
595C2×C4—1882no—
596C2×C4—1882no—
597C2×C4—1882no—
598C2×C4—1882no—
599C2×C4—1882no—
600C2×C4—1882no—
601C2×C4—1882no—
602C2×C4—1882no—
603C2×C4—1882no—
604C2×C4—1882no—
605C2×C4—1882no—
606C2×C4—1882no—
607C2×C4—1882no—
608C2×C4—1882no—
609C2×C4C2×C4⋊Dic4714yes—
610C2×C4C2×C4⋊Dic4714yes—
611C2×C4C2×C4⋊Dic4714yes—
612C2×C4#1309398314yes—
613C2×C4#1309398314yes—
614C2×C4D4×Dic4714yes—
615C2×C4Q8×Dic4714yes—
616C2×C4#1309400214yes—
617C2×C4#1309400914yes—
618C2×C4#1309401414yes—
619C2×C4#1309401914yes—
620C22C22×C4⋊Dic4711yescharacteristic
621C22C2×#1309398311yescharacteristic
622C22C2×#1309398311yescharacteristic
623C22C2×D4×Dic4711yescharacteristic
624C22C2×Q8×Dic4711yescharacteristic
625C22#1568960611yescharacteristic
626C22#1568960611yescharacteristic
627C22C2×#1309400211yescharacteristic
628C22C2×#1309400911yescharacteristic
629C22C2×#1309401411yescharacteristic
630C22C2×#1309401911yescharacteristic
631C22#1568967311yescharacteristic
632C22#1568967311yescharacteristic
633C22#1568968011yescharacteristic
634C22#1568968011yescharacteristic
635C22#1568972811yescharacteristic
636C22#1568973511yescharacteristic
637C22#1568974411yescharacteristic
638C22#1568974411yescharacteristic
639C22D4×D18811yescharacteristic
640C22#1568976911yescharacteristic
641C22#1568977711yescharacteristic
642C22#1568978211yescharacteristic
643C22D4×Dic9411yescharacteristic
644C22Q8×D18811yescharacteristic
645C22#1568979511yescharacteristic
646C22#1568981311yescharacteristic
647C22#1568981911yescharacteristic
648C22#1568983011yescharacteristic
649C22#1568983311yescharacteristic
650C22#1568984611yescharacteristic
651C22#1568985111yescharacteristic
652C22#1568985211yescharacteristic
653C22Q8×Dic9411yescharacteristic
654C22#1568985811yescharacteristic
655C4—24no—
656C4—24no—
657C4—24no—
658C4—24no—
659C4—42no—
660C4—42no—
661C4—3762no—
662C4—3762no—
663C4—1884no—
664C4—1884no—
665C4#1568900918yescomplemented
666C2#2024579511yescharacteristic
667C2C2×#1568900911yescharacteristic
668C2#2024599711yescharacteristic
669C2D4×C4⋊Dic4711yescharacteristic
670C2Q8×C4⋊Dic4711yescharacteristic
671C2#2024631711yescharacteristic
672C2#2024634511yescharacteristic
673C2#2024715311yescharacteristic
674C2#2024716411yescharacteristic
675C2#2024722711yescharacteristic
676C2#2024723811yescharacteristic
677C2#2024790411yescharacteristic
678C2#2024791511yescharacteristic
679C2#2024796311yescharacteristic
680C2#2024797411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D47
commutatorC23×C47C23×C4
FittingC2×C4×C4⋊C4×C47C2
socle, prime radical, cosocleC24×C47C24
hypercenterC2×C4×C4⋊C4D47
hypocenterC47#13884
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C24 ◁ C2×C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
36. C4×C4⋊C4×C47C4semidirect
176. C4⋊C4×C47C4⋊C4semidirect
321. C4×C47#387semidirect
367. C4×C4⋊C4Dic47semidirect
379. C47#13884semidirect
523. C4⋊C4C4⋊Dic47semidirect
665. C4#15689009semidirect

Maximal subgroups

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

subgroupindex
C2×#156890092
C2×#156889932
C2×C4×C4⋊Dic472
#202416452
#202416412
#202416222
#202416182
C2×C4×C4⋊C4×C472
#1388447