Finite Group Databasebeta

← #26139998

Subgroups — #26139998

Order 12032.

1530 conjugacy classes of subgroups.

The subgroup lattice has 690 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689022C211yesmaximal, characteristic
2C2×#15689022C211yesmaximal, characteristic
3C2×#15689021C211yesmaximal, characteristic
4C2×C4×Dic47⋊C4C211yesmaximal, characteristic
5#20241652C212yesmaximal
6#20241640C212yesmaximal
7#20241621C212yesmaximal
8#20241618C212yesmaximal
9#20241617C211yesmaximal, characteristic
10#20241617C211yesmaximal, characteristic
11C2×C4×C4⋊C4×C47C211yesmaximal, characteristic
12C22×C4⋊Dic47C2211yescharacteristic
13C22×C4⋊Dic47C2212yes—
14C22×C4⋊Dic47C2211yescharacteristic
15C22×C4⋊Dic47C2212yes—
16C22×Dic47⋊C4C2211yescharacteristic
17C22×Dic47⋊C4C2211yescharacteristic
18C22×Dic47⋊C4C2212yes—
19C22×C4×Dic47C2211yescharacteristic
20C22×C4×Dic47C2211yescharacteristic
21#15689022—24no—
22#15689022C418yescomplemented
23#15689021—24no—
24C4×Dic47⋊C4—24no—
25C2×C47⋊#95C2212yes—
26C2×C47⋊#95C2212yes—
27C2×C47⋊#95C2212yes—
28C2×C47⋊#95C2211yescharacteristic
29C2×C47⋊#95C2211yescharacteristic
30C2×C47⋊#95C2212yes—
31C2×C47⋊#95C2212yes—
32C2×C47⋊#95C2212yes—
33C2×C47⋊#95C2212yes—
34C22×C4⋊C4×C47C2211yescharacteristic
35C22×C4⋊C4×C47C2211yescharacteristic
36C22×C42×C47C2212yes—
37C22×C42×C47C2211yescharacteristic
38C4×C4⋊C4×C47—24no—
39C2×#95×C47C2212yes—
40C23×Dic47C2312yes—
41C23×Dic47C2311yescharacteristic
42C23×Dic47C2312yes—
43C23×Dic47C2311yescharacteristic
44C23×Dic47C2311yescharacteristic
45C23×Dic47C2311yescharacteristic
46C2×C4⋊Dic47—22no—
47C2×C4⋊Dic47—22no—
48C2×C4⋊Dic47—22no—
49C2×C4⋊Dic47—24no—
50C2×C4⋊Dic47—22no—
51C2×C4⋊Dic47—22no—
52C2×C4⋊Dic47—24no—
53C2×C4⋊Dic47—42no—
54C2×C4⋊Dic47—42no—
55C2×C4⋊Dic47—42no—
56C2×C4⋊Dic47C2×C414yes—
57C2×C4⋊Dic47C2×C418yes—
58C2×Dic47⋊C4—22no—
59C2×Dic47⋊C4—22no—
60C2×Dic47⋊C4—22no—
61C2×Dic47⋊C4—22no—
62C2×Dic47⋊C4—22no—
63C2×Dic47⋊C4—24no—
64C2×Dic47⋊C4—42no—
65C2×Dic47⋊C4—42no—
66C2×Dic47⋊C4Q814yes—
67C2×C4×Dic47—22no—
68C2×C4×Dic47—22no—
69C2×C4×Dic47—22no—
70C2×C4×Dic47—22no—
71C2×C4×Dic47—22no—
72C2×C4×Dic47C2×C414yes—
73C47⋊#95—22no—
74C47⋊#95—22no—
75C47⋊#95—24no—
76C47⋊#95—24no—
77C47⋊#95—24no—
78C47⋊#95—42no—
79C47⋊#95—42no—
80C47⋊#95—42no—
81C47⋊#95C2×C418yes—
82C23×C4×C47C2311yescharacteristic
83C23×C4×C47C2312yes—
84C23×C4×C47C2312yes—
85C23×C4×C47C2311yescharacteristic
86C23×C4×C47C2311yescharacteristic
87C2×C4⋊C4×C47—22no—
88C2×C4⋊C4×C47—22no—
89C2×C4⋊C4×C47C2×C414yes—
90C2×C4⋊C4×C47D414yes—
91C2×C4⋊C4×C47Q814yes—
92C2×C4⋊C4×C47Q814yes—
93C2×C42×C47—22no—
94C2×C42×C47—22no—
95C2×C42×C47—24no—
96C2×C42×C47—24no—
97C2×C42×C47—42no—
98C2×C42×C47D414yes—
99#95×C47—24no—
100C24×C47C2411yescharacteristic
101C22×C4×C47—21no—
102C22×C4×C47—22no—
103C22×C4×C47—21no—
104C22×C4×C47—22no—
105C22×C4×C47—21no—
106C22×C4×C47—22no—
107C22×C4×C47—22no—
108C22×C4×C47—21no—
109C22×C4×C47—22no—
110C22×C4×C47—21no—
111C22×C4×C47—21no—
112C22×C4×C47—22no—
113C22×C4×C47—22no—
114C22×C4×C47—22no—
115C22×C4×C47—21no—
116C22×C4×C47—21no—
117C22×C4×C47—22no—
118C22×C4×C47—22no—
119C22×C4×C47—21no—
120C22×C4×C47—21no—
121C22×C4×C47C22×C414yes—
122C22×C4×C47C22×C412yes—
123C22×C4×C47C2×D412yes—
124C22×C4×C47C2×D414yes—
125C22×C4×C47C2×D412yes—
126C22×C4×C47C2×D412yes—
127C22×C4×C47C2×D412yes—
128C22×C4×C47C2×Q814yes—
129C22×C4×C47C2×Q814yes—
130C22×C4×C47C2×Q812yes—
131C22×C4×C47C2×Q812yes—
132C22×C4×C47C2×Q812yes—
133C22×C4×C47#4112yes—
134C22×C4×C47#4112yes—
135C22×C4×C47#4112yes—
136C22×Dic47—21no—
137C22×Dic47—21no—
138C22×Dic47—21no—
139C22×Dic47—21no—
140C22×Dic47—21no—
141C22×Dic47—21no—
142C22×Dic47—21no—
143C22×Dic47—21no—
144C22×Dic47—22no—
145C22×Dic47—21no—
146C22×Dic47—21no—
147C22×Dic47—21no—
148C22×Dic47—21no—
149C22×Dic47—21no—
150C22×Dic47—21no—
151C22×Dic47—22no—
152C22×Dic47—21no—
153C22×Dic47—21no—
154C22×Dic47—21no—
155C22×Dic47—22no—
156C22×Dic47—22no—
157C22×Dic47—22no—
158C22×Dic47—21no—
159C22×Dic47—21no—
160C22×Dic47—21no—
161C22×Dic47—21no—
162C22×Dic47—22no—
163C22×Dic47—21no—
164C22×Dic47—22no—
165C22×Dic47—22no—
166C22×Dic47—22no—
167C22×Dic47—22no—
168C22×Dic47—22no—
169C22×Dic47—22no—
170C22×Dic47—22no—
171C22×Dic47C22×C414yes—
172C22×Dic47C22×C412yes—
173C22×Dic47C22×C412yes—
174C22×Dic47C2×Q812yes—
175C22×Dic47C2×Q812yes—
176C22×Dic47#4112yes—
177C22×Dic47#4112yes—
178C4⋊C4×C47—28no—
179C4⋊C4×C47C4⋊C4116yescomplemented
180C42×C47—28no—
181C42×C47—48no—
182C4⋊Dic47—28no—
183C4⋊Dic47—48no—
184C4⋊Dic47—48no—
185C4⋊Dic47—44no—
186Dic47⋊C4—28no—
187Dic47⋊C4—28no—
188Dic47⋊C4—48no—
189C4×Dic47—28no—
190C4×Dic47—44no—
191C23×C47C23×C411yescharacteristic
192C23×C47C22×D411yescharacteristic
193C23×C47C22×D411yescharacteristic
194C23×C47C22×Q811yescharacteristic
195C23×C47C22×Q811yescharacteristic
196C23×C47C22×Q811yescharacteristic
197C23×C47C2×#4111yescharacteristic
198C23×C47C2×#4111yescharacteristic
199C23×C47C2×#4111yescharacteristic
200C23×C47C2×#4111yescharacteristic
201C23×C47C2×#4111yescharacteristic
202C23×C47H(5,𝔽2)11yescharacteristic
203C23×C47H(5,𝔽2)11yescharacteristic
204C23×C47H(5,𝔽2)11yescharacteristic
205C23×C472−1+411yescharacteristic
206C2×C4×C47—24no—
207C2×C4×C47—24no—
208C2×C4×C47—22no—
209C2×C4×C47—22no—
210C2×C4×C47—24no—
211C2×C4×C47—22no—
212C2×C4×C47—24no—
213C2×C4×C47—22no—
214C2×C4×C47—22no—
215C2×C4×C47—22no—
216C2×C4×C47—24no—
217C2×C4×C47—24no—
218C2×C4×C47—22no—
219C2×C4×C47—24no—
220C2×C4×C47—22no—
221C2×C4×C47—22no—
222C2×C4×C47—24no—
223C2×C4×C47—24no—
224C2×C4×C47—42no—
225C2×C4×C47—42no—
226C2×C4×C47—42no—
227C2×C4×C47—41no—
228C2×C4×C47—41no—
229C2×C4×C47—42no—
230C2×C4×C47—41no—
231C2×C4×C47—41no—
232C2×C4×C47C2×C4⋊C418yes—
233C2×C4×C47C2×C4⋊C414yes—
234C2×C4×C47C4×D414yes—
235C2×C4×C47C4×Q814yes—
236C2×C4×C47#12114yes—
237C2×C4×C47C22⋊Q814yes—
238C2×C4×C47C22⋊Q814yes—
239C2×C4×C47#12514yes—
240C2×C4×C47C4⋊Q814yes—
241C2×Dic47—22no—
242C2×Dic47—22no—
243C2×Dic47—22no—
244C2×Dic47—22no—
245C2×Dic47—22no—
246C2×Dic47—22no—
247C2×Dic47—22no—
248C2×Dic47—24no—
249C2×Dic47—22no—
250C2×Dic47—24no—
251C2×Dic47—22no—
252C2×Dic47—24no—
253C2×Dic47—22no—
254C2×Dic47—22no—
255C2×Dic47—22no—
256C2×Dic47—22no—
257C2×Dic47—22no—
258C2×Dic47—22no—
259C2×Dic47—41no—
260C2×Dic47—41no—
261C2×Dic47—42no—
262C2×Dic47—41no—
263C2×Dic47—41no—
264C2×Dic47—41no—
265C2×Dic47—42no—
266C2×Dic47—41no—
267C2×Dic47—41no—
268C2×Dic47—42no—
269C2×Dic47—41no—
270C2×Dic47—42no—
271C2×Dic47—41no—
272C2×Dic47—41no—
273C2×Dic47—41no—
274C2×Dic47—41no—
275C2×Dic47—42no—
276C2×Dic47—42no—
277C2×Dic47—42no—
278C2×Dic47—42no—
279C2×Dic47—42no—
280C2×Dic47—42no—
281C2×Dic47—42no—
282C2×Dic47C4×Q814yes—
283#14045—471nomaximal, Sylow
284C22×C47C22×C4⋊C411yescharacteristic
285C22×C47C2×C4×D411yescharacteristic
286C22×C47C2×C4×Q811yescharacteristic
287C22×C47C2×C4×Q811yescharacteristic
288C22×C47C4×#4111yescharacteristic
289C22×C47#51811yescharacteristic
290C22×C47#52011yescharacteristic
291C22×C47C2×#12111yescharacteristic
292C22×C47C2×C22⋊Q811yescharacteristic
293C22×C47C2×C22⋊Q811yescharacteristic
294C22×C47#52511yescharacteristic
295C22×C47C2×#12511yescharacteristic
296C22×C47#52911yescharacteristic
297C22×C47C2×C4⋊Q811yescharacteristic
298C22×C47#53311yescharacteristic
299C22×C47#53511yescharacteristic
300C22×C47#53711yescharacteristic
301C22×C47#54011yescharacteristic
302C22×C47#54211yescharacteristic
303C22×C47#54611yescharacteristic
304C22×C47#54611yescharacteristic
305C22×C47D4×Q811yescharacteristic
306C22×C47#55011yescharacteristic
307C22×C47#55211yescharacteristic
308C22×C47#55311yescharacteristic
309C22×C47#55411yescharacteristic
310C22×C47#55411yescharacteristic
311C22×C47#55411yescharacteristic
312C22×C47#55411yescharacteristic
313C22×C47#55411yescharacteristic
314C22×C47#55511yescharacteristic
315C22×C47#55711yescharacteristic
316C22×C47#55711yescharacteristic
317C22×C47Q8211yescharacteristic
318C22×C47Q8211yescharacteristic
319C4×C47—28no—
320C4×C47—24no—
321C4×C47—42no—
322C4×C47—44no—
323C4×C47#38918yes—
324Dic47—24no—
325Dic47—42no—
326Dic47—44no—
327Dic47—42no—
328Dic47—42no—
329Dic47—82no—
330C2×#389—471no—
331C2×#389—471no—
332C2×#389—471no—
333C2×C4×C4⋊C4—471no—
334C2×C4×C4⋊C4D4711yescharacteristic
335#1444—472no—
336#1441—472no—
337#1436—472no—
338C4⋊#95—472no—
339C4⋊#95—471no—
340C4⋊#95—471no—
341C2×C47C2×#38911yescharacteristic
342C2×C47C4×C22⋊Q811yescharacteristic
343C2×C47#232411yescharacteristic
344C2×C47#234911yescharacteristic
345C2×C47Q8×C4⋊C411yescharacteristic
346C2×C47#236911yescharacteristic
347C2×C47#237011yescharacteristic
348C2×C47#241411yescharacteristic
349C2×C47#241711yescharacteristic
350C2×C47#245111yescharacteristic
351C2×C47#245411yescharacteristic
352C2×C47#250711yescharacteristic
353C2×C47#250811yescharacteristic
354C2×C47#256711yescharacteristic
355C2×C47#258411yescharacteristic
356C22×C4⋊C4—471no—
357C22×C4⋊C4—471no—
358C22×C4⋊C4—472no—
359C22×C4⋊C4—471no—
360C22×C4⋊C4—471no—
361C22×C4⋊C4—472no—
362C22×C4⋊C4—472no—
363C22×C4⋊C4C2×D4711yescharacteristic
364C22×C4⋊C4C2×D4711yescharacteristic
365C22×C42—471no—
366C22×C42—471no—
367C22×C42C2×D4712yes—
368C22×C42C2×D4711yescharacteristic
369#389—478no—
370#389—944no—
371#389—944no—
372C4×C4⋊C4—24no—
373C4×C4⋊C4—944no—
374C2×#95—472no—
375C2×#95—471no—
376C2×#95—472no—
377C2×#95—472no—
378C2×#95—472no—
379C2×#95—471no—
380C2×#95—472no—
381C2×#95—472no—
382C2×#95—472no—
383C2×#95C2×D4712yes—
384C47#1404511yescharacteristic, complemented, Sylow
385C23×C4—471no—
386C23×C4—472no—
387C23×C4—471no—
388C23×C4—471no—
389C23×C4—471no—
390C23×C4—472no—
391C23×C4C22×D4712yes—
392C23×C4C22×D4711yescharacteristic
393C23×C4C22×D4712yes—
394C23×C4C22×D4711yescharacteristic
395C23×C4C22×D4711yescharacteristic
396C2×C4⋊C4—22no—
397C2×C4⋊C4—22no—
398C2×C4⋊C4—474no—
399C2×C4⋊C4—474no—
400C2×C4⋊C4—478no—
401C2×C4⋊C4—942no—
402C2×C4⋊C4—942no—
403C2×C4⋊C4—942no—
404C2×C4⋊C4—942no—
405C2×C4⋊C4—942no—
406C2×C4⋊C4—942no—
407C2×C4⋊C4—942no—
408C2×C4⋊C4—944no—
409C2×C4⋊C4—944no—
410C2×C4⋊C4—942no—
411C2×C4⋊C4—942no—
412C2×C4⋊C4—944no—
413C2×C4⋊C4—942no—
414C2×C4⋊C4—1882no—
415C2×C4⋊C4—1882no—
416C2×C4⋊C4—1882no—
417C2×C4⋊C4—1882no—
418C2×C4⋊C4—1882no—
419C2×C4⋊C4Dic9414yes—
420C2×C4⋊C4Dic9414yes—
421C2×C4⋊C4C4×D4714yes—
422C2×C4⋊C4C22⋊D4714yes—
423C2×C42—22no—
424C2×C42—22no—
425C2×C42—24no—
426C2×C42—24no—
427C2×C42—42no—
428C2×C42—474no—
429C2×C42—942no—
430C2×C42—942no—
431C2×C42—942no—
432C2×C42—942no—
433C2×C42—942no—
434C2×C42D18814yes—
435#95—24no—
436#95—478no—
437#95—944no—
438#95—942no—
439#95—942no—
440#95—944no—
441#95—944no—
442#95—1882no—
443#95—1882no—
444#95—1882no—
445C24C23×D4711yescharacteristic
446C22×C4—21no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—22no—
460C22×C4—21no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—472no—
467C22×C4—472no—
468C22×C4—472no—
469C22×C4—474no—
470C22×C4—472no—
471C22×C4—472no—
472C22×C4—472no—
473C22×C4—941no—
474C22×C4—941no—
475C22×C4—941no—
476C22×C4—941no—
477C22×C4—941no—
478C22×C4—941no—
479C22×C4—941no—
480C22×C4—941no—
481C22×C4—941no—
482C22×C4—942no—
483C22×C4—941no—
484C22×C4—941no—
485C22×C4—941no—
486C22×C4—941no—
487C22×C4—941no—
488C22×C4—942no—
489C22×C4—941no—
490C22×C4—942no—
491C22×C4—941no—
492C22×C4—941no—
493C22×C4—941no—
494C22×C4—942no—
495C22×C4—941no—
496C22×C4—941no—
497C22×C4—942no—
498C22×C4—941no—
499C22×C4—942no—
500C22×C4—941no—
501C22×C4—942no—
502C22×C4—942no—
503C22×C4—942no—
504C22×C4—942no—
505C22×C4—942no—
506C22×C4—942no—
507C22×C4—942no—
508C22×C4C2×Dic9414yes—
509C22×C4C2×Dic9414yes—
510C22×C4C2×Dic9412yes—
511C22×C4C2×Dic9412yes—
512C22×C4C2×C4×D4714yes—
513C22×C4C2×C4×D4712yes—
514C22×C4C2×D18812yes—
515C22×C4C2×D18812yes—
516C22×C4C2×D18812yes—
517C22×C4#1062535012yes—
518C22×C4#1062535012yes—
519C22×C4#1062535212yes—
520C22×C4Q8×D4712yes—
521C22×C4C2×C22⋊D4714yes—
522C22×C4C2×C22⋊D4712yes—
523C4⋊C4—28no—
524C4⋊C4—948no—
525C4⋊C4—948no—
526C4⋊C4—948no—
527C4⋊C4—1888no—
528C4⋊C4—1888no—
529C4⋊C4—1888no—
530C4⋊C4—1884no—
531C4⋊C4Dic47⋊C4116yescomplemented
532C42—28no—
533C42—48no—
534C42—948no—
535C42—1884no—
536C23C22×C4×D4711yescharacteristic
537C23C22×C22⋊D4711yescharacteristic
538C23C22×D18811yescharacteristic
539C23C2×Q8×D4711yescharacteristic
540C23C22×Dic9411yescharacteristic
541C23C22×Dic9411yescharacteristic
542C23#41×D4711yescharacteristic
543C23#41×D4711yescharacteristic
544C23C2×#1062535211yescharacteristic
545C23C2×#1062535011yescharacteristic
546C23C2×#1062535011yescharacteristic
547C23#1309406911yescharacteristic
548C23#1309407011yescharacteristic
549C23#1309407011yescharacteristic
550C23#1309407211yescharacteristic
551C2×C4—24no—
552C2×C4—22no—
553C2×C4—24no—
554C2×C4—22no—
555C2×C4—22no—
556C2×C4—22no—
557C2×C4—24no—
558C2×C4—24no—
559C2×C4—24no—
560C2×C4—24no—
561C2×C4—22no—
562C2×C4—22no—
563C2×C4—24no—
564C2×C4—24no—
565C2×C4—22no—
566C2×C4—24no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—41no—
570C2×C4—42no—
571C2×C4—41no—
572C2×C4—42no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—42no—
576C2×C4—42no—
577C2×C4—474no—
578C2×C4—942no—
579C2×C4—942no—
580C2×C4—942no—
581C2×C4—942no—
582C2×C4—942no—
583C2×C4—942no—
584C2×C4—942no—
585C2×C4—942no—
586C2×C4—942no—
587C2×C4—942no—
588C2×C4—942no—
589C2×C4—944no—
590C2×C4—942no—
591C2×C4—944no—
592C2×C4—944no—
593C2×C4—942no—
594C2×C4—942no—
595C2×C4—942no—
596C2×C4—1882no—
597C2×C4—1882no—
598C2×C4—1882no—
599C2×C4—1882no—
600C2×C4—1882no—
601C2×C4—1882no—
602C2×C4—1882no—
603C2×C4—1881no—
604C2×C4—1882no—
605C2×C4—1881no—
606C2×C4—1881no—
607C2×C4—1881no—
608C2×C4—1881no—
609C2×C4—1881no—
610C2×C4—1881no—
611C2×C4—1882no—
612C2×C4—1881no—
613C2×C4—1881no—
614C2×C4—1881no—
615C2×C4—1881no—
616C2×C4—1882no—
617C2×C4—1881no—
618C2×C4—1882no—
619C2×C4C2×Dic47⋊C418yes—
620C2×C4C2×Dic47⋊C414yes—
621C2×C4C4×D18814yes—
622C2×C4C4×Dic9414yes—
623C2×C4#1309399814yes—
624C2×C4#1309400314yes—
625C2×C4#1309400414yes—
626C2×C4#1309401614yes—
627C2×C4#1309402414yes—
628C22C22×Dic47⋊C411yescharacteristic
629C22C2×C4×D18811yescharacteristic
630C22C4×Q8×D4711yescharacteristic
631C22C2×C4×Dic9411yescharacteristic
632C22C4×#1062535211yescharacteristic
633C22#1568959511yescharacteristic
634C22#1568960511yescharacteristic
635C22C2×#1309399811yescharacteristic
636C22C2×#1309400311yescharacteristic
637C22C2×#1309400411yescharacteristic
638C22#1568963511yescharacteristic
639C22C2×#1309401611yescharacteristic
640C22#1568965511yescharacteristic
641C22C2×#1309402411yescharacteristic
642C22#1568967711yescharacteristic
643C22#1568969211yescharacteristic
644C22#1568970411yescharacteristic
645C22#1568972411yescharacteristic
646C22#1568974511yescharacteristic
647C22#1568976111yescharacteristic
648C22#1568976711yescharacteristic
649C22Q8×C22⋊D4711yescharacteristic
650C22#1568979211yescharacteristic
651C22#1568980811yescharacteristic
652C22#1568981711yescharacteristic
653C22#1568982811yescharacteristic
654C22#1568983011yescharacteristic
655C22#1568983011yescharacteristic
656C22#1568983211yescharacteristic
657C22#1568983211yescharacteristic
658C22#1568983611yescharacteristic
659C22#1568984911yescharacteristic
660C22#1568984911yescharacteristic
661C22Q8×Dic9411yescharacteristic
662C22Q8×Dic9411yescharacteristic
663C4—28no—
664C4—24no—
665C4—42no—
666C4—44no—
667C4—944no—
668C4—3762no—
669C4—1882no—
670C4—1882no—
671C4—1882no—
672C4—1884no—
673C4#1568902118yes—
674C2C2×#1568902111yescharacteristic
675C2C4×#1309400411yescharacteristic
676C2#2024608211yescharacteristic
677C2#2024629311yescharacteristic
678C2Q8×Dic47⋊C411yescharacteristic
679C2#2024647511yescharacteristic
680C2#2024648611yescharacteristic
681C2#2024680011yescharacteristic
682C2#2024683311yescharacteristic
683C2#2024722111yescharacteristic
684C2#2024725411yescharacteristic
685C2#2024790911yescharacteristic
686C2#2024792011yescharacteristic
687C2#2024859611yescharacteristic
688C2#2024877111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D47
commutatorC23×C47C23×C4
FittingC2×C4×C4⋊C4×C47C2
socle, prime radical, cosocleC24×C47C24
hypercenterC2×C4×C4⋊C4D47
hypocenterC47#14045
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C24 ◁ C2×C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
22. #15689022C4semidirect
179. C4⋊C4×C47C4⋊C4semidirect
384. C47#14045semidirect
531. C4⋊C4Dic47⋊C4semidirect

Maximal subgroups

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

subgroupindex
C2×#156890222
C2×#156890212
C2×C4×Dic47⋊C42
#202416522
#202416402
#202416212
#202416182
#202416172
C2×C4×C4⋊C4×C472
#1404547