Finite Group Databasebeta

← #26137652

Subgroups — #26137652

Order 12032.

1434 conjugacy classes of subgroups.

The subgroup lattice has 870 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689018C211yesmaximal, characteristic
2C2×#15689007C211yesmaximal, characteristic
3C2×#15689004C211yesmaximal, characteristic
4#20241623C211yesmaximal, characteristic
5#20241620C211yesmaximal, characteristic
6#20241620C211yesmaximal, characteristic
7#20241619C211yesmaximal, characteristic
8#20241619C211yesmaximal, characteristic
9#20241619C211yesmaximal, characteristic
10Dic47⋊#95C211yesmaximal, characteristic
11#20241612C211yesmaximal, characteristic
12C4×C47⋊#95C211yesmaximal, characteristic
13#95×Dic47C211yesmaximal, characteristic
14#95×Dic47C211yesmaximal, characteristic
15C47×C4⋊#95C211yesmaximal, characteristic
16C22×Dic47⋊C4C2211yescharacteristic
17C22×Dic47⋊C4C2211yescharacteristic
18C22×Dic47⋊C4C2211yescharacteristic
19C22×Dic47⋊C4C2211yescharacteristic
20C22×C4×Dic47C2211yescharacteristic
21C22×C4×Dic47C2211yescharacteristic
22C22×C4×Dic47C2211yescharacteristic
23C22×C4×Dic47C2211yescharacteristic
24C22×C4×Dic47C2211yescharacteristic
25C22×C4×Dic47C2211yescharacteristic
26#15689018C418yescomplemented
27#15689007C418yescomplemented
28#15689004C418yescomplemented
29C2×C47⋊#95C2211yescharacteristic
30C2×C47⋊#95C2211yescharacteristic
31C2×C47⋊#95C2211yescharacteristic
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
47C22×C4⋊C4×C47C2211yescharacteristic
48C22×C4⋊C4×C47C2211yescharacteristic
49C22×C42×C47C2211yescharacteristic
50C2×#95×C47C2211yescharacteristic
51C2×#95×C47C2211yescharacteristic
52C2×#95×C47C2211yescharacteristic
53C2×#95×C47C2211yescharacteristic
54C23×Dic47C2311yescharacteristic
55C23×Dic47C2311yescharacteristic
56C23×Dic47C2311yescharacteristic
57C23×Dic47C2311yescharacteristic
58C23×Dic47C2311yescharacteristic
59C23×Dic47C2311yescharacteristic
60C23×Dic47C2311yescharacteristic
61C23×Dic47C2311yescharacteristic
62C2×Dic47⋊C4—41no—
63C2×Dic47⋊C4—41no—
64C2×Dic47⋊C4—41no—
65C2×Dic47⋊C4—41no—
66C2×Dic47⋊C4—41no—
67C2×Dic47⋊C4—41no—
68C2×Dic47⋊C4C2×C414yes—
69C2×Dic47⋊C4C2×C414yes—
70C2×Dic47⋊C4C2×C414yes—
71C2×Dic47⋊C4C2×C414yes—
72C2×Dic47⋊C4C2×C414yes—
73C2×Dic47⋊C4C2×C414yes—
74C2×C4×Dic47—22no—
75C2×C4×Dic47—22no—
76C2×C4×Dic47—22no—
77C2×C4×Dic47—41no—
78C2×C4×Dic47—41no—
79C2×C4×Dic47—41no—
80C2×C4×Dic47—41no—
81C2×C4×Dic47—41no—
82C2×C4×Dic47—41no—
83C2×C4×Dic47—41no—
84C2×C4×Dic47—41no—
85C2×C4×Dic47—41no—
86C2×C4×Dic47—41no—
87C2×C4×Dic47—41no—
88C2×C4×Dic47—41no—
89C2×C4×Dic47C2×C414yes—
90C2×C4×Dic47C2×C414yes—
91C2×C4×Dic47Q814yes—
92C47⋊#95—22no—
93C47⋊#95—22no—
94C47⋊#95—22no—
95C47⋊#95—22no—
96C47⋊#95—41no—
97C47⋊#95—41no—
98C47⋊#95—41no—
99C47⋊#95—41no—
100C47⋊#95C2×C414yes—
101C47⋊#95C2×C414yes—
102C47⋊#95C2×C414yes—
103C47⋊#95C2×C414yes—
104C47⋊#95C2×C414yes—
105C47⋊#95C2×C414yes—
106C47⋊#95C2×C414yes—
107C47⋊#95C2×C414yes—
108C47⋊#95C2×C414yes—
109C47⋊#95C2×C414yes—
110C23×C4×C47C2311yescharacteristic
111C23×C4×C47C2311yescharacteristic
112C23×C4×C47C2311yescharacteristic
113C23×C4×C47C2311yescharacteristic
114C23×C4×C47C2311yescharacteristic
115C23×C4×C47C2311yescharacteristic
116C23×C4×C47C2311yescharacteristic
117C2×C4⋊C4×C47—41no—
118C2×C4⋊C4×C47—41no—
119C2×C4⋊C4×C47—41no—
120C2×C4⋊C4×C47—41no—
121C2×C4⋊C4×C47C2×C414yes—
122C2×C4⋊C4×C47C2×C414yes—
123C2×C42×C47—41no—
124C2×C42×C47—41no—
125C2×C42×C47C2×C414yes—
126#95×C47—22no—
127#95×C47—22no—
128#95×C47—41no—
129#95×C47—41no—
130C24×C47C2411yescharacteristic
131C22×C4×C47—21no—
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×C47C22×C412yes—
170C22×C4×C47C22×C412yes—
171C22×C4×C47C22×C412yes—
172C22×C4×C47C22×C412yes—
173C22×C4×C47C22×C412yes—
174C22×C4×C47C22×C412yes—
175C22×C4×C47C22×C412yes—
176C22×C4×C47C22×C412yes—
177C22×C4×C47C22×C412yes—
178C22×C4×C47C2×Q812yes—
179C22×C4×C47#4112yes—
180C22×Dic47—21no—
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×Dic47C22×C412yes—
221C22×Dic47C22×C412yes—
222C22×Dic47C22×C412yes—
223C22×Dic47C22×C412yes—
224C22×Dic47C22×C412yes—
225C22×Dic47C22×C412yes—
226C22×Dic47C22×C412yes—
227C22×Dic47C22×C412yes—
228C22×Dic47C22×C412yes—
229C22×Dic47C22×C412yes—
230C22×Dic47C22×C412yes—
231C22×Dic47C22×C412yes—
232C22×Dic47C2×Q812yes—
233C22×Dic47C2×Q812yes—
234C22×Dic47#4112yes—
235C22×Dic47#4112yes—
236C4⋊C4×C47—44no—
237C4⋊C4×C47—44no—
238C42×C47—44no—
239Dic47⋊C4—44no—
240Dic47⋊C4—44no—
241Dic47⋊C4—44no—
242Dic47⋊C4C42116yescomplemented
243C4×Dic47—44no—
244C4×Dic47—44no—
245C4×Dic47—44no—
246C4×Dic47—44no—
247C4×Dic47—44no—
248C4×Dic47—44no—
249C23×C47C23×C411yescharacteristic
250C23×C47C23×C411yescharacteristic
251C23×C47C23×C411yescharacteristic
252C23×C47C22×Q811yescharacteristic
253C23×C47C2×#4111yescharacteristic
254C23×C47C2×#4111yescharacteristic
255C23×C47C2×#4111yescharacteristic
256C23×C47H(5,𝔽2)11yescharacteristic
257C23×C47H(5,𝔽2)11yescharacteristic
258C23×C47H(5,𝔽2)11yescharacteristic
259C23×C47H(5,𝔽2)11yescharacteristic
260C23×C47H(5,𝔽2)11yescharacteristic
261C23×C472−1+411yescharacteristic
262C23×C472−1+411yescharacteristic
263C23×C472−1+411yescharacteristic
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—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—22no—
281C2×C4×C47—22no—
282C2×C4×C47—22no—
283C2×C4×C47—22no—
284C2×C4×C47—22no—
285C2×C4×C47—22no—
286C2×C4×C47—22no—
287C2×C4×C47—22no—
288C2×C4×C47—22no—
289C2×C4×C47—22no—
290C2×C4×C47—22no—
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×C47C2×C4214yes—
312C2×C4×C47C4×Q814yes—
313C2×Dic47—22no—
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—22no—
330C2×Dic47—22no—
331C2×Dic47—22no—
332C2×Dic47—22no—
333C2×Dic47—22no—
334C2×Dic47—22no—
335C2×Dic47—22no—
336C2×Dic47—22no—
337C2×Dic47—22no—
338C2×Dic47—22no—
339C2×Dic47—22no—
340C2×Dic47—22no—
341C2×Dic47—22no—
342C2×Dic47—22no—
343C2×Dic47—22no—
344C2×Dic47—22no—
345C2×Dic47—22no—
346C2×Dic47—22no—
347C2×Dic47—22no—
348C2×Dic47—22no—
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×Dic47—41no—
363C2×Dic47—41no—
364C2×Dic47—41no—
365C2×Dic47C2×C4214yes—
366C2×Dic47C2×C4214yes—
367C2×Dic47C4×Q814yes—
368C2×Dic47C4×Q814yes—
369#13792—471nomaximal, Sylow
370C22×C47C22×C4211yescharacteristic
371C22×C47C2×C4×Q811yescharacteristic
372C22×C47C2×C4×Q811yescharacteristic
373C22×C47C2×C4×Q811yescharacteristic
374C22×C47C4×#4111yescharacteristic
375C22×C47C4×#4111yescharacteristic
376C22×C47C4×#4111yescharacteristic
377C22×C47#51811yescharacteristic
378C22×C47#51811yescharacteristic
379C22×C47#51811yescharacteristic
380C22×C47#51811yescharacteristic
381C22×C47#51911yescharacteristic
382C22×C47#52011yescharacteristic
383C22×C47#52011yescharacteristic
384C22×C47#52011yescharacteristic
385C22×C47#52011yescharacteristic
386C22×C47#52011yescharacteristic
387C22×C47#52011yescharacteristic
388C22×C47#52011yescharacteristic
389C22×C47#53811yescharacteristic
390C22×C47#53811yescharacteristic
391C22×C47#53811yescharacteristic
392C22×C47#53911yescharacteristic
393C22×C47#53911yescharacteristic
394C22×C47#53911yescharacteristic
395C22×C47#54011yescharacteristic
396C22×C47#54011yescharacteristic
397C22×C47#54111yescharacteristic
398C22×C47#54111yescharacteristic
399C22×C47#54211yescharacteristic
400C22×C47#54211yescharacteristic
401C22×C47#54311yescharacteristic
402C22×C47#54411yescharacteristic
403C22×C47#54411yescharacteristic
404C22×C47#54411yescharacteristic
405C4×C47—24no—
406C4×C47—24no—
407C4×C47—42no—
408C4×C47—42no—
409C4×C47—42no—
410C4×C47—42no—
411C4×C47—42no—
412Dic47—24no—
413Dic47—24no—
414Dic47—24no—
415Dic47—24no—
416Dic47—42no—
417Dic47—42no—
418Dic47—42no—
419Dic47—42no—
420C2×#389—471no—
421C2×#387—471no—
422C2×#387—471no—
423#1436—471no—
424#1436—471no—
425#1436—471no—
426#1436—471no—
427#1436—471no—
428#1436—471no—
429C4⋊#95—471no—
430C4⋊#95D4711yescharacteristic
431#1434—471no—
432C4×#95—471no—
433C4×#95—471no—
434C4×#95—471no—
435C2×C47C42×Q811yescharacteristic
436C2×C47#227411yescharacteristic
437C2×C47#227511yescharacteristic
438C2×C47#232911yescharacteristic
439C2×C47#232911yescharacteristic
440C2×C47#232911yescharacteristic
441C2×C47#233011yescharacteristic
442C2×C47#233011yescharacteristic
443C2×C47#233111yescharacteristic
444C2×C47#233311yescharacteristic
445C2×C47#233411yescharacteristic
446C2×C47#233411yescharacteristic
447C2×C47#233511yescharacteristic
448C2×C47#233511yescharacteristic
449C2×C47#233611yescharacteristic
450C22×C4⋊C4—471no—
451C22×C4⋊C4—471no—
452C22×C4⋊C4—471no—
453C22×C4⋊C4—471no—
454C22×C4⋊C4C2×D4711yescharacteristic
455C22×C4⋊C4C2×D4711yescharacteristic
456C22×C42—471no—
457C22×C42—471no—
458C22×C42—471no—
459C22×C42—471no—
460C22×C42—471no—
461C22×C42—471no—
462C22×C42C2×D4711yescharacteristic
463#389—478no—
464#387—478no—
465#387—478no—
466C2×#95—471no—
467C2×#95—471no—
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
488C47#1379211yescharacteristic, complemented, Sylow
489C23×C4—471no—
490C23×C4—471no—
491C23×C4—471no—
492C23×C4—471no—
493C23×C4—471no—
494C23×C4—471no—
495C23×C4—471no—
496C23×C4—471no—
497C23×C4C22×D4711yescharacteristic
498C23×C4C22×D4711yescharacteristic
499C23×C4C22×D4711yescharacteristic
500C23×C4C22×D4711yescharacteristic
501C23×C4C22×D4711yescharacteristic
502C23×C4C22×D4711yescharacteristic
503C23×C4C22×D4711yescharacteristic
504C2×C4⋊C4—41no—
505C2×C4⋊C4—41no—
506C2×C4⋊C4—41no—
507C2×C4⋊C4—41no—
508C2×C4⋊C4—474no—
509C2×C4⋊C4—474no—
510C2×C4⋊C4—474no—
511C2×C4⋊C4—474no—
512C2×C4⋊C4—474no—
513C2×C4⋊C4—474no—
514C2×C4⋊C4—1881no—
515C2×C4⋊C4—1881no—
516C2×C4⋊C4—1881no—
517C2×C4⋊C4—1881no—
518C2×C4⋊C4—1881no—
519C2×C4⋊C4—1881no—
520C2×C4⋊C4C4×D4714yes—
521C2×C4⋊C4C4×D4714yes—
522C2×C42—41no—
523C2×C42—41no—
524C2×C42—474no—
525C2×C42—474no—
526C2×C42—474no—
527C2×C42—942no—
528C2×C42—942no—
529C2×C42—942no—
530C2×C42—1881no—
531C2×C42—1881no—
532C2×C42—1881no—
533C2×C42—1881no—
534C2×C42—1881no—
535C2×C42—1881no—
536C2×C42—1881no—
537C2×C42—1881no—
538C2×C42—1881no—
539C2×C42—1881no—
540C2×C42—1881no—
541C2×C42—1881no—
542C2×C42C4×D4714yes—
543#95—22no—
544#95—22no—
545#95—41no—
546#95—41no—
547#95—474no—
548#95—474no—
549#95—474no—
550#95—474no—
551#95—474no—
552#95—474no—
553#95—474no—
554#95—474no—
555#95—474no—
556#95—474no—
557#95—942no—
558#95—942no—
559#95—942no—
560#95—942no—
561#95—1881no—
562#95—1881no—
563#95—1881no—
564#95—1881no—
565C24C23×D4711yescharacteristic
566C22×C4—21no—
567C22×C4—21no—
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—472no—
605C22×C4—472no—
606C22×C4—472no—
607C22×C4—472no—
608C22×C4—472no—
609C22×C4—472no—
610C22×C4—472no—
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—941no—
621C22×C4—941no—
622C22×C4—941no—
623C22×C4—941no—
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×C4C2×C4×D4712yes—
661C22×C4C2×C4×D4712yes—
662C22×C4C2×C4×D4712yes—
663C22×C4C2×C4×D4712yes—
664C22×C4C2×C4×D4712yes—
665C22×C4C2×C4×D4712yes—
666C22×C4C2×C4×D4712yes—
667C22×C4C2×C4×D4712yes—
668C22×C4C2×C4×D4712yes—
669C22×C4#1062535212yes—
670C22×C4Q8×D4712yes—
671C4⋊C4—44no—
672C4⋊C4—44no—
673C4⋊C4—4716no—
674C4⋊C4—1884no—
675C4⋊C4—1884no—
676C4⋊C4—1884no—
677C42—44no—
678C42—1884no—
679C42—1884no—
680C42—1884no—
681C42—1884no—
682C42—1884no—
683C42—1884no—
684C23C22×C4×D4711yescharacteristic
685C23C22×C4×D4711yescharacteristic
686C23C22×C4×D4711yescharacteristic
687C23C2×Q8×D4711yescharacteristic
688C23#41×D4711yescharacteristic
689C23#41×D4711yescharacteristic
690C23C2×#1062535211yescharacteristic
691C23#1309406911yescharacteristic
692C23#1309406911yescharacteristic
693C23#1309406911yescharacteristic
694C23#1309406911yescharacteristic
695C23#1309407011yescharacteristic
696C23#1309407111yescharacteristic
697C23#1309407211yescharacteristic
698C23#1309407211yescharacteristic
699C2×C4—22no—
700C2×C4—22no—
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—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
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—474no—
747C2×C4—474no—
748C2×C4—474no—
749C2×C4—474no—
750C2×C4—942no—
751C2×C4—942no—
752C2×C4—942no—
753C2×C4—942no—
754C2×C4—942no—
755C2×C4—942no—
756C2×C4—942no—
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—942no—
773C2×C4—942no—
774C2×C4—942no—
775C2×C4—942no—
776C2×C4—942no—
777C2×C4—942no—
778C2×C4—942no—
779C2×C4—942no—
780C2×C4—942no—
781C2×C4—942no—
782C2×C4—942no—
783C2×C4—942no—
784C2×C4—942no—
785C2×C4—942no—
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×C4C42×D4714yes—
803C2×C4#1309398914yes—
804C22C2×C42×D4711yescharacteristic
805C22C4×Q8×D4711yescharacteristic
806C22C4×Q8×D4711yescharacteristic
807C22C2×#1309398911yescharacteristic
808C22C4×#1062535211yescharacteristic
809C22C4×#1062535211yescharacteristic
810C22#1568959111yescharacteristic
811C22#1568959511yescharacteristic
812C22#1568959611yescharacteristic
813C22#1568959611yescharacteristic
814C22#1568959611yescharacteristic
815C22#1568959911yescharacteristic
816C22#1568960211yescharacteristic
817C22#1568960311yescharacteristic
818C22#1568960411yescharacteristic
819C22#1568960411yescharacteristic
820C22#1568960411yescharacteristic
821C22#1568960411yescharacteristic
822C22#1568960511yescharacteristic
823C22#1568970511yescharacteristic
824C22#1568970711yescharacteristic
825C22#1568971011yescharacteristic
826C22#1568971811yescharacteristic
827C22#1568971911yescharacteristic
828C22#1568972111yescharacteristic
829C22#1568972311yescharacteristic
830C22#1568972711yescharacteristic
831C22#1568973211yescharacteristic
832C22#1568973411yescharacteristic
833C22#1568973711yescharacteristic
834C22#1568974311yescharacteristic
835C22#1568974811yescharacteristic
836C22#1568975011yescharacteristic
837C22#1568975011yescharacteristic
838C22#1568975211yescharacteristic
839C4—24no—
840C4—24no—
841C4—42no—
842C4—42no—
843C4—42no—
844C4—42no—
845C4—42no—
846C4—944no—
847C4—944no—
848C4—944no—
849C4—944no—
850C4—1882no—
851C4—1882no—
852C4—1882no—
853C4—1882no—
854C2C4×#1309398911yescharacteristic
855C2#2024574211yescharacteristic
856C2#2024574611yescharacteristic
857C2#2024611811yescharacteristic
858C2#2024612011yescharacteristic
859C2#2024612211yescharacteristic
860C2#2024612611yescharacteristic
861C2#2024612711yescharacteristic
862C2#2024613111yescharacteristic
863C2#2024614711yescharacteristic
864C2#2024615611yescharacteristic
865C2#2024615911yescharacteristic
866C2#2024617411yescharacteristic
867C2#2024617511yescharacteristic
868C2#2024618611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D47
commutatorC22×C47C22×C42
FittingC47×C4⋊#95C2
socle, prime radical, cosocleC24×C47C24
hypercenterC4⋊#95D47
hypocenterC47#13792
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C24 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
26. #15689018C4semidirect
27. #15689007C4semidirect
28. #15689004C4semidirect
242. Dic47⋊C4C42semidirect
488. C47#13792semidirect

Maximal subgroups

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

subgroupindex
C2×#156890182
C2×#156890072
C2×#156890042
#202416232
#202416202
#202416192
Dic47⋊#952
#202416122
C4×C47⋊#952
#95×Dic472
C47×C4⋊#952
#1379247