Finite Group Databasebeta

← #26153009

Subgroups — #26153009

Order 12032.

1294 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689065C211yesmaximal, characteristic
2C2×#15689062C211yesmaximal, characteristic
3C2×#15689020C211yesmaximal, characteristic
4C2×#15688992C211yesmaximal, characteristic
5#20241646C211yesmaximal, characteristic
6#20241646C211yesmaximal, characteristic
7#20241645C211yesmaximal, characteristic
8#20241642C211yesmaximal, characteristic
9#20241639C211yesmaximal, characteristic
10Dic47⋊#95C211yesmaximal, characteristic
11Dic47⋊#95C211yesmaximal, characteristic
12Dic47⋊#95C211yesmaximal, characteristic
13Dic47⋊#95C211yesmaximal, characteristic
14#95×Dic47C211yesmaximal, characteristic
15C47×#1442C211yesmaximal, characteristic
16C22×C4⋊Dic47C2211yescharacteristic
17C22×C4⋊Dic47C2211yescharacteristic
18C22×Dic47⋊C4C2211yescharacteristic
19C22×Dic47⋊C4C2211yescharacteristic
20C22×Dic47⋊C4C2211yescharacteristic
21C22×Dic47⋊C4C2211yescharacteristic
22C22×Dic47⋊C4C2211yescharacteristic
23C22×Dic47⋊C4C2211yescharacteristic
24C22×Dic47⋊C4C2211yescharacteristic
25C22×C4×Dic47C2211yescharacteristic
26C22×C4×Dic47C2211yescharacteristic
27C22×C4×Dic47C2211yescharacteristic
28#15689065—24no—
29#15689062—24no—
30#15689020—24no—
31#15688992—24no—
32C2×C47⋊#95C2211yescharacteristic
33C2×C47⋊#95C2211yescharacteristic
34C2×C47⋊#95C2211yescharacteristic
35C2×C47⋊#95C2211yescharacteristic
36C2×C47⋊#95C2211yescharacteristic
37C2×C47⋊#95C2211yescharacteristic
38C2×C47⋊#95C2211yescharacteristic
39C2×C47⋊#95C2211yescharacteristic
40C2×C47⋊#95C2211yescharacteristic
41C2×C47⋊#95C2211yescharacteristic
42C2×C47⋊#95C2211yescharacteristic
43C2×C47⋊#95C2211yescharacteristic
44C2×C47⋊#95C2211yescharacteristic
45C2×C47⋊#95C2211yescharacteristic
46C2×C47⋊#95C2211yescharacteristic
47C2×C47⋊#95C2211yescharacteristic
48C22×C4⋊C4×C47C2211yescharacteristic
49C2×#95×C47C2211yescharacteristic
50C2×#95×C47C2211yescharacteristic
51C2×#95×C47C2211yescharacteristic
52C2×#95×C47C2211yescharacteristic
53C2×#95×C47C2211yescharacteristic
54C2×#95×C47C2211yescharacteristic
55C23×Dic47C2311yescharacteristic
56C23×Dic47C2311yescharacteristic
57C23×Dic47C2311yescharacteristic
58C23×Dic47C2311yescharacteristic
59C23×Dic47C2311yescharacteristic
60C23×Dic47C2311yescharacteristic
61C23×Dic47C2311yescharacteristic
62C23×Dic47C2311yescharacteristic
63C2×C4⋊Dic47—22no—
64C2×C4⋊Dic47—22no—
65C2×C4⋊Dic47—22no—
66C2×C4⋊Dic47—22no—
67C2×C4⋊Dic47—41no—
68C2×C4⋊Dic47—41no—
69C2×Dic47⋊C4—22no—
70C2×Dic47⋊C4—22no—
71C2×Dic47⋊C4—22no—
72C2×Dic47⋊C4—22no—
73C2×Dic47⋊C4—22no—
74C2×Dic47⋊C4—22no—
75C2×Dic47⋊C4—22no—
76C2×Dic47⋊C4—22no—
77C2×Dic47⋊C4—22no—
78C2×Dic47⋊C4—22no—
79C2×Dic47⋊C4—22no—
80C2×Dic47⋊C4—22no—
81C2×Dic47⋊C4—22no—
82C2×Dic47⋊C4—22no—
83C2×Dic47⋊C4—22no—
84C2×Dic47⋊C4—22no—
85C2×Dic47⋊C4—22no—
86C2×Dic47⋊C4—41no—
87C2×Dic47⋊C4—41no—
88C2×Dic47⋊C4—41no—
89C2×Dic47⋊C4D414yes—
90C2×C4×Dic47—22no—
91C2×C4×Dic47—22no—
92C2×C4×Dic47—22no—
93C2×C4×Dic47—22no—
94C2×C4×Dic47—22no—
95C2×C4×Dic47—22no—
96C2×C4×Dic47—22no—
97C2×C4×Dic47—22no—
98C2×C4×Dic47Q814yes—
99C47⋊#95—22no—
100C47⋊#95—22no—
101C47⋊#95—22no—
102C47⋊#95—22no—
103C47⋊#95—22no—
104C47⋊#95—22no—
105C47⋊#95—22no—
106C47⋊#95—22no—
107C47⋊#95—22no—
108C47⋊#95—22no—
109C47⋊#95—22no—
110C47⋊#95—22no—
111C47⋊#95—41no—
112C47⋊#95—41no—
113C47⋊#95—41no—
114C47⋊#95D414yes—
115C23×C4×C47C2311yescharacteristic
116C23×C4×C47C2311yescharacteristic
117C23×C4×C47C2311yescharacteristic
118C23×C4×C47C2311yescharacteristic
119C23×C4×C47C2311yescharacteristic
120C23×C4×C47C2311yescharacteristic
121C23×C4×C47C2311yescharacteristic
122C2×C4⋊C4×C47—22no—
123C2×C4⋊C4×C47—22no—
124C2×C4⋊C4×C47—41no—
125#95×C47—22no—
126#95×C47—22no—
127#95×C47—41no—
128#95×C47—41no—
129#95×C47—41no—
130#95×C47Q814yes—
131C24×C47C2411yescharacteristic
132C22×C4×C47—21no—
133C22×C4×C47—21no—
134C22×C4×C47—21no—
135C22×C4×C47—21no—
136C22×C4×C47—21no—
137C22×C4×C47—21no—
138C22×C4×C47—21no—
139C22×C4×C47—21no—
140C22×C4×C47—21no—
141C22×C4×C47—21no—
142C22×C4×C47—21no—
143C22×C4×C47—21no—
144C22×C4×C47—21no—
145C22×C4×C47—21no—
146C22×C4×C47—21no—
147C22×C4×C47—21no—
148C22×C4×C47—21no—
149C22×C4×C47—21no—
150C22×C4×C47—21no—
151C22×C4×C47—21no—
152C22×C4×C47—21no—
153C22×C4×C47—21no—
154C22×C4×C47—21no—
155C22×C4×C47—21no—
156C22×C4×C47—21no—
157C22×C4×C47—21no—
158C22×C4×C47—21no—
159C22×C4×C47—21no—
160C22×C4×C47—21no—
161C22×C4×C47—21no—
162C22×C4×C47—21no—
163C22×C4×C47—21no—
164C22×C4×C47—21no—
165C22×C4×C47—21no—
166C22×C4×C47—21no—
167C22×C4×C47—21no—
168C22×C4×C47—21no—
169C22×C4×C47—21no—
170C22×C4×C47—21no—
171C22×C4×C47—21no—
172C22×C4×C47—21no—
173C22×C4×C47—21no—
174C22×C4×C47—21no—
175C22×C4×C47C2×D412yes—
176C22×C4×C47C2×D412yes—
177C22×C4×C47C2×Q812yes—
178C22×C4×C47C2×Q812yes—
179C22×C4×C47C2×Q812yes—
180C22×C4×C47C2×Q812yes—
181C22×Dic47—21no—
182C22×Dic47—21no—
183C22×Dic47—21no—
184C22×Dic47—21no—
185C22×Dic47—21no—
186C22×Dic47—21no—
187C22×Dic47—21no—
188C22×Dic47—21no—
189C22×Dic47—21no—
190C22×Dic47—21no—
191C22×Dic47—21no—
192C22×Dic47—21no—
193C22×Dic47—21no—
194C22×Dic47—21no—
195C22×Dic47—21no—
196C22×Dic47—21no—
197C22×Dic47—21no—
198C22×Dic47—21no—
199C22×Dic47—21no—
200C22×Dic47—21no—
201C22×Dic47—21no—
202C22×Dic47—21no—
203C22×Dic47—21no—
204C22×Dic47—21no—
205C22×Dic47—21no—
206C22×Dic47—21no—
207C22×Dic47—21no—
208C22×Dic47—21no—
209C22×Dic47—21no—
210C22×Dic47—21no—
211C22×Dic47—21no—
212C22×Dic47—21no—
213C22×Dic47—21no—
214C22×Dic47—21no—
215C22×Dic47—21no—
216C22×Dic47—21no—
217C22×Dic47—21no—
218C22×Dic47—21no—
219C22×Dic47—21no—
220C22×Dic47—21no—
221C22×Dic47—21no—
222C22×Dic47—21no—
223C22×Dic47—21no—
224C22×Dic47C2×D412yes—
225C22×Dic47C2×D412yes—
226C22×Dic47C2×D412yes—
227C22×Dic47C2×D412yes—
228C22×Dic47C2×Q812yes—
229C22×Dic47C2×Q812yes—
230C22×Dic47#4112yes—
231C22×Dic47#4112yes—
232C22×Dic47#4112yes—
233C22×Dic47#4112yes—
234C22×Dic47#4112yes—
235C22×Dic47#4112yes—
236C22×Dic47#4112yes—
237C4⋊C4×C47—44no—
238C4⋊Dic47—44no—
239C4⋊Dic47—44no—
240Dic47⋊C4—28no—
241Dic47⋊C4—44no—
242Dic47⋊C4—44no—
243Dic47⋊C4—44no—
244Dic47⋊C4—44no—
245Dic47⋊C4—44no—
246Dic47⋊C4—44no—
247C4×Dic47—28no—
248C4×Dic47—44no—
249C4×Dic47—44no—
250C23×C47C22×D411yescharacteristic
251C23×C47C22×D411yescharacteristic
252C23×C47C22×Q811yescharacteristic
253C23×C47C22×Q811yescharacteristic
254C23×C47C2×#4111yescharacteristic
255C23×C47C2×#4111yescharacteristic
256C23×C47C2×#4111yescharacteristic
257C23×C47C2×#4111yescharacteristic
258C23×C47C2×#4111yescharacteristic
259C23×C47C2×#4111yescharacteristic
260C23×C47C2×#4111yescharacteristic
261C23×C47H(5,𝔽2)11yescharacteristic
262C23×C47H(5,𝔽2)11yescharacteristic
263C23×C472−1+411yescharacteristic
264C23×C472−1+411yescharacteristic
265C2×C4×C47—22no—
266C2×C4×C47—22no—
267C2×C4×C47—22no—
268C2×C4×C47—22no—
269C2×C4×C47—22no—
270C2×C4×C47—22no—
271C2×C4×C47—22no—
272C2×C4×C47—22no—
273C2×C4×C47—22no—
274C2×C4×C47—22no—
275C2×C4×C47—22no—
276C2×C4×C47—22no—
277C2×C4×C47—22no—
278C2×C4×C47—22no—
279C2×C4×C47—22no—
280C2×C4×C47—41no—
281C2×C4×C47—41no—
282C2×C4×C47—41no—
283C2×C4×C47—41no—
284C2×C4×C47—41no—
285C2×C4×C47—41no—
286C2×C4×C47—41no—
287C2×C4×C47—41no—
288C2×C4×C47—41no—
289C2×C4×C47—41no—
290C2×C4×C47—41no—
291C2×C4×C47—41no—
292C2×C4×C47—41no—
293C2×C4×C47—41no—
294C2×C4×C47—41no—
295C2×C4×C47—41no—
296C2×C4×C47—41no—
297C2×C4×C47—41no—
298C2×C4×C47—41no—
299C2×C4×C47—41no—
300C2×C4×C47—41no—
301C2×C4×C47—41no—
302C2×C4×C47—41no—
303C2×C4×C47—41no—
304C2×C4×C47—41no—
305C2×C4×C47—41no—
306C2×C4×C47—41no—
307C2×C4×C47—41no—
308C2×C4×C47—41no—
309C2×C4×C47—41no—
310C2×C4×C47—41no—
311C2×C4×C47—41no—
312C2×C4×C47—41no—
313C2×C4×C47C4⋊Q814yes—
314C2×Dic47—22no—
315C2×Dic47—22no—
316C2×Dic47—22no—
317C2×Dic47—22no—
318C2×Dic47—22no—
319C2×Dic47—22no—
320C2×Dic47—22no—
321C2×Dic47—22no—
322C2×Dic47—22no—
323C2×Dic47—22no—
324C2×Dic47—22no—
325C2×Dic47—22no—
326C2×Dic47—22no—
327C2×Dic47—22no—
328C2×Dic47—22no—
329C2×Dic47—41no—
330C2×Dic47—41no—
331C2×Dic47—41no—
332C2×Dic47—41no—
333C2×Dic47—41no—
334C2×Dic47—41no—
335C2×Dic47—41no—
336C2×Dic47—41no—
337C2×Dic47—41no—
338C2×Dic47—41no—
339C2×Dic47—41no—
340C2×Dic47—41no—
341C2×Dic47—41no—
342C2×Dic47—41no—
343C2×Dic47—41no—
344C2×Dic47—41no—
345C2×Dic47—41no—
346C2×Dic47—41no—
347C2×Dic47—41no—
348C2×Dic47—41no—
349C2×Dic47—41no—
350C2×Dic47—41no—
351C2×Dic47—41no—
352C2×Dic47—41no—
353C2×Dic47—41no—
354C2×Dic47—41no—
355C2×Dic47—41no—
356C2×Dic47—41no—
357C2×Dic47—41no—
358C2×Dic47—41no—
359C2×Dic47—41no—
360C2×Dic47—41no—
361C2×Dic47—41no—
362C2×Dic47C22⋊Q814yes—
363C2×Dic47#12314yes—
364C2×Dic47#12414yes—
365C2×Dic47#12514yes—
366C2×Dic47#12514yes—
367C2×Dic47#12514yes—
368C2×Dic47#12614yes—
369C2×Dic47#12614yes—
370#15146—471nomaximal, Sylow
371C22×C47C2×C22⋊Q811yescharacteristic
372C22×C47C2×#12311yescharacteristic
373C22×C47C2×#12411yescharacteristic
374C22×C47C2×#12511yescharacteristic
375C22×C47C2×#12511yescharacteristic
376C22×C47C2×#12511yescharacteristic
377C22×C47C2×#12611yescharacteristic
378C22×C47C2×#12611yescharacteristic
379C22×C47C2×C4⋊Q811yescharacteristic
380C22×C47#53211yescharacteristic
381C22×C47#53211yescharacteristic
382C22×C47#53311yescharacteristic
383C22×C47#53311yescharacteristic
384C22×C47#54011yescharacteristic
385C22×C47#54111yescharacteristic
386C22×C47#54211yescharacteristic
387C22×C47#54211yescharacteristic
388C22×C47#54411yescharacteristic
389C22×C47#54411yescharacteristic
390C22×C47D4211yescharacteristic
391C22×C47#54611yescharacteristic
392C22×C47#54711yescharacteristic
393C22×C47#54711yescharacteristic
394C22×C47#54811yescharacteristic
395C22×C47D4×Q811yescharacteristic
396C22×C47#55011yescharacteristic
397C22×C47#55211yescharacteristic
398C22×C47#55311yescharacteristic
399C22×C47#55411yescharacteristic
400C22×C47#55411yescharacteristic
401C22×C47#55511yescharacteristic
402C22×C47#55611yescharacteristic
403C22×C47#55611yescharacteristic
404C22×C47#55711yescharacteristic
405C22×C47#55911yescharacteristic
406C4×C47—24no—
407C4×C47—42no—
408C4×C47—42no—
409C4×C47—42no—
410C4×C47—81no—
411C4×C47—81no—
412C4×C47—81no—
413Dic47—24no—
414Dic47—42no—
415Dic47—42no—
416Dic47—42no—
417Dic47—81no—
418Dic47—81no—
419Dic47—81no—
420Dic47#40018yescomplemented
421C2×#400—471no—
422C2×#400—471no—
423C2×#389—471no—
424C2×#384—471no—
425#1442—471no—
426#1442—471no—
427#1442—471no—
428#1442D4711yescharacteristic
429#1441—471no—
430#1441—471no—
431C4⋊#95—471no—
432C4⋊#95—471no—
433C4⋊#95—471no—
434C4⋊#95—471no—
435C4×#95—471no—
436C2×C47C2×#40011yescharacteristic
437C2×C47#244011yescharacteristic
438C2×C47#244211yescharacteristic
439C2×C47#244511yescharacteristic
440C2×C47#244611yescharacteristic
441C2×C47#249111yescharacteristic
442C2×C47#249211yescharacteristic
443C2×C47#249611yescharacteristic
444C2×C47#249711yescharacteristic
445C2×C47#251111yescharacteristic
446C2×C47#251211yescharacteristic
447C2×C47#255211yescharacteristic
448C2×C47#257111yescharacteristic
449C2×C47#264711yescharacteristic
450C2×C47#285911yescharacteristic
451C22×C4⋊C4—471no—
452C22×C4⋊C4—471no—
453C22×C4⋊C4—471no—
454C22×C4⋊C4—471no—
455C22×C4⋊C4—471no—
456C22×C4⋊C4—471no—
457C22×C4⋊C4—471no—
458C22×C4⋊C4—471no—
459C22×C4⋊C4—471no—
460C22×C4⋊C4C2×D4711yescharacteristic
461C22×C42—471no—
462C22×C42—471no—
463C22×C42—471no—
464#400—944no—
465#400—944no—
466#389—944no—
467#384—944no—
468C2×#95—471no—
469C2×#95—471no—
470C2×#95—471no—
471C2×#95—471no—
472C2×#95—471no—
473C2×#95—471no—
474C2×#95—471no—
475C2×#95—471no—
476C2×#95—471no—
477C2×#95—471no—
478C2×#95—471no—
479C2×#95—471no—
480C2×#95—471no—
481C2×#95—471no—
482C2×#95—471no—
483C2×#95—471no—
484C2×#95C2×D4711yescharacteristic
485C2×#95C2×D4711yescharacteristic
486C2×#95C2×D4711yescharacteristic
487C2×#95C2×D4711yescharacteristic
488C2×#95C2×D4711yescharacteristic
489C2×#95C2×D4711yescharacteristic
490C47#1514611yescharacteristic, complemented, Sylow
491C23×C4—471no—
492C23×C4—471no—
493C23×C4—471no—
494C23×C4—471no—
495C23×C4—471no—
496C23×C4—471no—
497C23×C4—471no—
498C23×C4—471no—
499C23×C4C22×D4711yescharacteristic
500C23×C4C22×D4711yescharacteristic
501C23×C4C22×D4711yescharacteristic
502C23×C4C22×D4711yescharacteristic
503C23×C4C22×D4711yescharacteristic
504C23×C4C22×D4711yescharacteristic
505C23×C4C22×D4711yescharacteristic
506C2×C4⋊C4—22no—
507C2×C4⋊C4—22no—
508C2×C4⋊C4—41no—
509C2×C4⋊C4—474no—
510C2×C4⋊C4—942no—
511C2×C4⋊C4—942no—
512C2×C4⋊C4—942no—
513C2×C4⋊C4—942no—
514C2×C4⋊C4—942no—
515C2×C4⋊C4—942no—
516C2×C4⋊C4—942no—
517C2×C4⋊C4—942no—
518C2×C4⋊C4—942no—
519C2×C4⋊C4—942no—
520C2×C4⋊C4—942no—
521C2×C4⋊C4—942no—
522C2×C4⋊C4—942no—
523C2×C4⋊C4—942no—
524C2×C4⋊C4—942no—
525C2×C4⋊C4—942no—
526C2×C4⋊C4—942no—
527C2×C4⋊C4—942no—
528C2×C4⋊C4—942no—
529C2×C4⋊C4—942no—
530C2×C4⋊C4—942no—
531C2×C4⋊C4—1881no—
532C2×C4⋊C4—1881no—
533C2×C4⋊C4—1881no—
534C2×C4⋊C4—1881no—
535C2×C4⋊C4—1881no—
536C2×C42—474no—
537C2×C42—942no—
538C2×C42—942no—
539C2×C42—942no—
540C2×C42—942no—
541C2×C42—942no—
542C2×C42—942no—
543C2×C42—942no—
544C2×C42—942no—
545#95—22no—
546#95—22no—
547#95—41no—
548#95—41no—
549#95—41no—
550#95—474no—
551#95—942no—
552#95—942no—
553#95—942no—
554#95—942no—
555#95—942no—
556#95—942no—
557#95—942no—
558#95—942no—
559#95—942no—
560#95—942no—
561#95—942no—
562#95—942no—
563#95—1881no—
564#95—1881no—
565#95—1881no—
566#95Dic9414yes—
567C24C23×D4711yescharacteristic
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—472no—
612C22×C4—472no—
613C22×C4—472no—
614C22×C4—472no—
615C22×C4—472no—
616C22×C4—472no—
617C22×C4—472no—
618C22×C4—472no—
619C22×C4—472no—
620C22×C4—472no—
621C22×C4—472no—
622C22×C4—472no—
623C22×C4—472no—
624C22×C4—941no—
625C22×C4—941no—
626C22×C4—941no—
627C22×C4—941no—
628C22×C4—941no—
629C22×C4—941no—
630C22×C4—941no—
631C22×C4—941no—
632C22×C4—941no—
633C22×C4—941no—
634C22×C4—941no—
635C22×C4—941no—
636C22×C4—941no—
637C22×C4—941no—
638C22×C4—941no—
639C22×C4—941no—
640C22×C4—941no—
641C22×C4—941no—
642C22×C4—941no—
643C22×C4—941no—
644C22×C4—941no—
645C22×C4—941no—
646C22×C4—941no—
647C22×C4—941no—
648C22×C4—941no—
649C22×C4—941no—
650C22×C4—941no—
651C22×C4—941no—
652C22×C4—941no—
653C22×C4—941no—
654C22×C4—941no—
655C22×C4—941no—
656C22×C4—941no—
657C22×C4—941no—
658C22×C4—941no—
659C22×C4—941no—
660C22×C4—941no—
661C22×C4—941no—
662C22×C4—941no—
663C22×C4—941no—
664C22×C4—941no—
665C22×C4—941no—
666C22×C4—941no—
667C22×C4C2×Dic9412yes—
668C22×C4C2×Dic9412yes—
669C22×C4C2×Dic9412yes—
670C22×C4D4×D4712yes—
671C22×C4D4×D4712yes—
672C22×C4Q8×D4712yes—
673C4⋊C4—44no—
674C4⋊C4—948no—
675C4⋊C4—1884no—
676C4⋊C4—1884no—
677C4⋊C4—1884no—
678C4⋊C4—1884no—
679C4⋊C4—1884no—
680C4⋊C4—1884no—
681C4⋊C4—1884no—
682C4⋊C4—1884no—
683C42—948no—
684C42—1884no—
685C42—1884no—
686C23C2×D4×D4711yescharacteristic
687C23C2×D4×D4711yescharacteristic
688C23C2×Q8×D4711yescharacteristic
689C23C22×Dic9411yescharacteristic
690C23#41×D4711yescharacteristic
691C23#41×D4711yescharacteristic
692C23#41×D4711yescharacteristic
693C23#41×D4711yescharacteristic
694C23#41×D4711yescharacteristic
695C23#41×D4711yescharacteristic
696C23#41×D4711yescharacteristic
697C23#1309406911yescharacteristic
698C23#1309406911yescharacteristic
699C23#1309407111yescharacteristic
700C23#1309407211yescharacteristic
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—474no—
750C2×C4—474no—
751C2×C4—474no—
752C2×C4—474no—
753C2×C4—474no—
754C2×C4—474no—
755C2×C4—474no—
756C2×C4—474no—
757C2×C4—942no—
758C2×C4—942no—
759C2×C4—942no—
760C2×C4—942no—
761C2×C4—942no—
762C2×C4—942no—
763C2×C4—942no—
764C2×C4—942no—
765C2×C4—942no—
766C2×C4—942no—
767C2×C4—942no—
768C2×C4—942no—
769C2×C4—942no—
770C2×C4—942no—
771C2×C4—942no—
772C2×C4—1881no—
773C2×C4—1881no—
774C2×C4—1881no—
775C2×C4—1881no—
776C2×C4—1881no—
777C2×C4—1881no—
778C2×C4—1881no—
779C2×C4—1881no—
780C2×C4—1881no—
781C2×C4—1881no—
782C2×C4—1881no—
783C2×C4—1881no—
784C2×C4—1881no—
785C2×C4—1881no—
786C2×C4—1881no—
787C2×C4—1881no—
788C2×C4—1881no—
789C2×C4—1881no—
790C2×C4—1881no—
791C2×C4—1881no—
792C2×C4—1881no—
793C2×C4—1881no—
794C2×C4—1881no—
795C2×C4—1881no—
796C2×C4—1881no—
797C2×C4—1881no—
798C2×C4—1881no—
799C2×C4—1881no—
800C2×C4—1881no—
801C2×C4—1881no—
802C2×C4—1881no—
803C2×C4—1881no—
804C2×C4—1881no—
805C2×C4#1309402314yes—
806C22C22⋊Q8×D4711yescharacteristic
807C22#123×D4711yescharacteristic
808C22#124×D4711yescharacteristic
809C22#125×D4711yescharacteristic
810C22#125×D4711yescharacteristic
811C22#125×D4711yescharacteristic
812C22#126×D4711yescharacteristic
813C22#126×D4711yescharacteristic
814C22C2×#1309402311yescharacteristic
815C22#1568967211yescharacteristic
816C22#1568967211yescharacteristic
817C22#1568967611yescharacteristic
818C22#1568967611yescharacteristic
819C22#1568972311yescharacteristic
820C22#1568973211yescharacteristic
821C22#1568974111yescharacteristic
822C22#1568974311yescharacteristic
823C22#1568975011yescharacteristic
824C22#1568975211yescharacteristic
825C22#1568975511yescharacteristic
826C22#1568976211yescharacteristic
827C22#1568977111yescharacteristic
828C22#1568977511yescharacteristic
829C22#1568978311yescharacteristic
830C22D4×Dic9411yescharacteristic
831C22#1568979111yescharacteristic
832C22#1568980511yescharacteristic
833C22#1568981811yescharacteristic
834C22#1568983211yescharacteristic
835C22#1568983211yescharacteristic
836C22#1568983511yescharacteristic
837C22#1568984011yescharacteristic
838C22#1568984011yescharacteristic
839C22#1568984911yescharacteristic
840C22#1568985711yescharacteristic
841C4—24no—
842C4—42no—
843C4—42no—
844C4—42no—
845C4—81no—
846C4—81no—
847C4—81no—
848C4—478no—
849C4—944no—
850C4—3761no—
851C4—3761no—
852C4—3761no—
853C4—1882no—
854C4—1882no—
855C4—1882no—
856C2#400×D4711yescharacteristic
857C2#2024708911yescharacteristic
858C2#2024710711yescharacteristic
859C2#2024714811yescharacteristic
860C2#2024716311yescharacteristic
861C2#2024774611yescharacteristic
862C2#2024775911yescharacteristic
863C2#2024780511yescharacteristic
864C2#2024781811yescharacteristic
865C2#2024796211yescharacteristic
866C2#2024796911yescharacteristic
867C2#2024842511yescharacteristic
868C2#2024862611yescharacteristic
869C2#2024936211yescharacteristic
870C2#2025175011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D47
commutator, socle, prime radical, cosocleC24×C47C24
FittingC47×#1442C2
hypercenter#1442D47
hypocenterC47#15146
LCSG ▷ C24×C47 ▷ C47
UCSC1 ◁ C24 ◁ #1442

Complements

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

NH ≅ G/Ntype
420. Dic47#400semidirect
490. C47#15146semidirect

Maximal subgroups

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

subgroupindex
C2×#156890652
C2×#156890622
C2×#156890202
C2×#156889922
#202416462
#202416452
#202416422
#202416392
Dic47⋊#952
#95×Dic472
C47×#14422
#1514647