Finite Group Databasebeta

← #26232575

Subgroups — #26232575

Order 12032.

1194 conjugacy classes of subgroups.

The subgroup lattice has 752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689838C211yesmaximal, characteristic
2C2×#15689195C211yesmaximal, characteristic, complemented
3#20244360C211yesmaximal, characteristic, complemented
4#20244340C211yesmaximal, characteristic, complemented
5#20243824C211yesmaximal, characteristic, complemented
6#20243814C211yesmaximal, characteristic, complemented
7#20243710C211yesmaximal, characteristic, complemented
8#20243705C211yesmaximal, characteristic, complemented
9#20243480C211yesmaximal, characteristic, complemented
10#20243480C211yesmaximal, characteristic, complemented
11#20243395C211yesmaximal, characteristic, complemented
12#20243216C211yesmaximal, characteristic, complemented
13#20243107C211yesmaximal, characteristic, complemented
14#20243104C211yesmaximal, characteristic, complemented
15C47×#2352C211yesmaximal, characteristic, complemented
16C22×#10625329C2211yescharacteristic
17C23×C47⋊C8C2211yescharacteristic
18#15689838—24no—
19#15689838C418yescomplemented
20C2×#13094024C2211yescharacteristic
21C2×#13094010—21no—
22C2×#13094010—21no—
23C2×#13093998C2211yescharacteristic
24C2×#13093998C2211yescharacteristic
25C2×#13093995—21no—
26C2×C4×D188C2211yescharacteristic
27C2×#13093983C2211yescharacteristic
28C2×#13093983C2211yescharacteristic
29C2×#13093982—21no—
30#15689195—24no—
31C2×C4⋊(C47⋊C8)C2211yescharacteristic
32C2×#13093944C2211yescharacteristic
33C2×#13093944C2211yescharacteristic
34C2×#13093944C2211yescharacteristic
35C2×#13093944C2211yescharacteristic
36C2×C22⋊(C47⋊C8)C2211yescharacteristic
37C2×C22⋊(C47⋊C8)C2211yescharacteristic
38C2×#13093935C2211yescharacteristic
39#15688885C2211yescharacteristic
40#15688885C2211yescharacteristic
41#15688885C2211yescharacteristic
42#15688885C2211yescharacteristic
43#15688885C2211yescharacteristic
44#15688885C2211yescharacteristic
45#15688885C2211yescharacteristic
46#15688885C2211yescharacteristic
47#15688885C2211yescharacteristic
48#15688885C2211yescharacteristic
49#15688885C2211yescharacteristic
50#15688885C2211yescharacteristic
51C2×C4×D4×C47C2211yescharacteristic
52C2×#117×C47C2211yescharacteristic
53C22×C4⋊C4×C47C2211yescharacteristic
54C47×#388—21no—
55C47×#387—21no—
56C47×#386—21no—
57C47×#382C2211yescharacteristic
58C47×#380C2211yescharacteristic
59C47×#380C2211yescharacteristic
60C4×C4⋊C4×C47C2211yescharacteristic
61C4×C22⋊C4×C47—21no—
62C22×Dic94—21no—
63C22×D188C2311yescharacteristic
64C22×C22⋊D47—21no—
65C22×C22⋊D47—21no—
66C22×C4×D47—21no—
67C2×#10625329—22no—
68C2×#10625329—22no—
69C2×#10625329—41no—
70C22×C47⋊C8—22no—
71C22×C47⋊C8—22no—
72C22×C47⋊C8—41no—
73C22×C47⋊C8C2311yescharacteristic
74C22×C47⋊C8C2311yescharacteristic
75C22×C47⋊C8C2311yescharacteristic
76C22×C47⋊C8C2311yescharacteristic
77#13094024—22no—
78#13094024C2×C414yescomplemented
79#13094010—28no—
80#13094010—28no—
81#13093998—22no—
82#13093998—22no—
83#13093998C2×C414yes—
84#13093998C2×C414yescomplemented
85#13093995—28no—
86C4×D188—22no—
87C4×D188C2×C414yescomplemented
88#13093983—22no—
89#13093983—22no—
90#13093983C2×C414yes—
91#13093983C2×C414yescomplemented
92#13093982—28no—
93C2×C4⋊Dic47—21no—
94C2×C4⋊Dic47C2311yescharacteristic
95C2×C4⋊Dic47C2311yescharacteristic
96C2×C4⋊Dic47C2311yescharacteristic
97C2×C22⋊Dic47—21no—
98C2×C22⋊Dic47—21no—
99C2×(C2×D47)⋊C4—21no—
100C2×(C2×D47)⋊C4—21no—
101C2×(C2×D47)⋊C4—21no—
102C2×C4×Dic47—21no—
103C2×C4×Dic47—21no—
104C4⋊(C47⋊C8)—22no—
105#13093944—22no—
106#13093944—22no—
107#13093944—41no—
108#13093944—41no—
109C22⋊(C47⋊C8)—22no—
110C22⋊(C47⋊C8)—22no—
111#13093935—22no—
112C22×D4×C47D411yescharacteristic
113C23×C4×C47—21no—
114C23×C4×C47C2311yescharacteristic
115C23×C4×C47C2311yescharacteristic
116C4×D4×C47C2×C414yes—
117C4×D4×C47D414yes—
118#117×C47—22no—
119#117×C47—41no—
120C2×C4⋊C4×C47—22no—
121C2×C4⋊C4×C47—21no—
122C2×C4⋊C4×C47—41no—
123C2×C4⋊C4×C47D411yescharacteristic
124C2×C4⋊C4×C47C2311yescharacteristic
125C2×C4⋊C4×C47C2311yescharacteristic
126C2×C4⋊C4×C47C2311yescharacteristic
127C2×C4⋊C4×C47C2311yescharacteristic
128C2×C22⋊C4×C47—21no—
129C2×C22⋊C4×C47—21no—
130C2×C22⋊C4×C47—21no—
131C2×C22⋊C4×C47D411yescharacteristic
132C2×C22⋊C4×C47D411yescharacteristic
133C2×C42×C47—21no—
134C2×C42×C47—21no—
135C2×C42×C47C2311yescharacteristic
136#95×C47—21no—
137#95×C47—21no—
138#95×C47—21no—
139#95×C47—21no—
140#95×C47—21no—
141C24×C47C2×D411yescharacteristic
142C24×C47C2×D411yescharacteristic
143C23×D47—21no—
144C2×D4×C47—41no—
145C2×D4×C47—41no—
146C2×D4×C47C22⋊C414yes—
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—42no—
160C22×C4×C47—42no—
161C22×C4×C47—81no—
162C22×C4×C47C22×C412yes—
163C22×C4×C47C22×C412yes—
164C22×C4×C47C2×D411yescharacteristic
165C22×C4×C47C2×D411yescharacteristic
166C22×C4×C47C2×D411yescharacteristic
167C22×C4×C47C2×D411yescharacteristic
168C22×C4×C47C2×D412yes—
169C22×C4×C47C2×D412yes—
170C22×C4×C47C2411yescharacteristic
171C2×C22⋊D47—24no—
172C2×C22⋊D47—24no—
173C2×C22⋊D47—81no—
174C2×C22⋊D47—81no—
175C2×C22⋊D47—81no—
176C2×C22⋊D47—81no—
177C22×Dic47—21no—
178C22×Dic47—21no—
179C22×Dic47—21no—
180C2×D188—21no—
181C2×D188—21no—
182C2×D188—21no—
183C2×D188—21no—
184C2×D188—21no—
185C2×D188C22×C412yes—
186C2×C4×D47—24no—
187C2×C4×D47—42no—
188C2×C4×D47—42no—
189C2×Dic94—24no—
190C2×Dic94—81no—
191C2×Dic94—81no—
192C4⋊C4×C47—21no—
193C4⋊C4×C47—21no—
194C4⋊C4×C47—21no—
195C4⋊C4×C47—21no—
196C4⋊C4×C47—21no—
197C4⋊C4×C47—21no—
198C4⋊C4×C47—21no—
199C4⋊C4×C47—42no—
200C4⋊C4×C47C22⋊C414yes—
201C4⋊C4×C47#4112yes—
202C22⋊C4×C47—42no—
203C22⋊C4×C47—42no—
204C22⋊C4×C47—81no—
205C22⋊C4×C47C22⋊C414yes—
206C22⋊C4×C47C22⋊C414yes—
207C42×C47—42no—
208C42×C47—81no—
209C42×C47C22×C412yes—
210C42×C47C2×D412yes—
211C22⋊Dic47—24no—
212C22⋊Dic47—24no—
213(C2×D47)⋊C4—24no—
214(C2×D47)⋊C4—24no—
215(C2×D47)⋊C4—24no—
216C4⋊Dic47—24no—
217C4⋊Dic47—21no—
218C4⋊Dic47—21no—
219C4⋊Dic47—21no—
220C4⋊Dic47C22×C412yes—
221C4⋊Dic47C22×C412yes—
222C4⋊Dic47C22×C412yes—
223C4×Dic47—24no—
224C4×Dic47—24no—
225#10625329—44no—
226C2×C47⋊C8—21no—
227C2×C47⋊C8—21no—
228C2×C47⋊C8—21no—
229C2×C47⋊C8—21no—
230C2×C47⋊C8—21no—
231C2×C47⋊C8—21no—
232C2×C47⋊C8—21no—
233C2×C47⋊C8—21no—
234C2×C47⋊C8—21no—
235C2×C47⋊C8—21no—
236C2×C47⋊C8—21no—
237C2×C47⋊C8—44no—
238C2×C47⋊C8#4112yes—
239C23×C47—21no—
240C23×C47—21no—
241C23×C47—21no—
242C23×C47—21no—
243C23×C47—21no—
244C23×C47—21no—
245C23×C47—21no—
246C23×C47—21no—
247C23×C47—21no—
248C23×C47—21no—
249C23×C47—21no—
250C23×C47—21no—
251C23×C47C2×C22⋊C412yes—
252C23×C47C2×C22⋊C412yes—
253C23×C47C22×D411yescharacteristic
254C22×D47—22no—
255C22×D47—41no—
256C22×D47—41no—
257C22×D47—41no—
258C22×D47—41no—
259C22×D47—41no—
260C22×D47—41no—
261D4×C47—44no—
262C2×C4×C47—21no—
263C2×C4×C47—21no—
264C2×C4×C47—21no—
265C2×C4×C47—21no—
266C2×C4×C47—21no—
267C2×C4×C47—21no—
268C2×C4×C47—21no—
269C2×C4×C47—21no—
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—41no—
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—84no—
291C2×C4×C47C2×C22⋊C412yes—
292C2×C4×C47C2×C22⋊C412yes—
293C2×C4×C47C2×C22⋊C412yes—
294C2×C4×C47C2×C22⋊C412yes—
295C2×C4×C47C23×C411yescharacteristic
296C2×C4×C47C22×D411yescharacteristic
297C2×C4×C47C2×#4111yescharacteristic
298C2×C4×C47C2×#4111yescharacteristic
299C2×C4×C47H(5,𝔽2)11yescharacteristic
300C2×C4×C472−1+411yescharacteristic
301C22⋊D47—84no—
302C22⋊D47—84no—
303C2×Dic47—22no—
304C2×Dic47—22no—
305C2×Dic47—22no—
306C2×Dic47—41no—
307C2×Dic47—41no—
308C2×Dic47—41no—
309C2×Dic47—41no—
310C2×Dic47—41no—
311C2×Dic47—41no—
312D188—22no—
313D188—22no—
314D188—41no—
315D188—41no—
316C4×D47—48no—
317Dic94—84no—
318C47⋊C8—22no—
319C47⋊C8—41no—
320C47⋊C8—41no—
321C47⋊C8—41no—
322#22492—471nomaximal, Sylow
323C22×C47—22no—
324C22×C47—22no—
325C22×C47—22no—
326C22×C47—22no—
327C22×C47—22no—
328C22×C47—22no—
329C22×C47—41no—
330C22×C47—41no—
331C22×C47—41no—
332C22×C47—41no—
333C22×C47—41no—
334C22×C47—41no—
335C22×C47—41no—
336C22×C47—41no—
337C22×C47C22×C22⋊C411yescharacteristic
338C22×C47#54611yescharacteristic
339C22×C47#54711yescharacteristic
340C22×C47#57511yescharacteristic
341C22×C47#57511yescharacteristic
342C22×C47#57611yescharacteristic
343C22×C47#57711yescharacteristic
344C2×D47—42no—
345C2×D47—42no—
346C2×D47—42no—
347C2×D47—81no—
348C2×D47—81no—
349C2×D47—81no—
350C2×D47—81no—
351C4×C47—22no—
352C4×C47—22no—
353C4×C47—22no—
354C4×C47—22no—
355C4×C47—42no—
356C4×C47—81no—
357C4×C47—81no—
358C4×C47—81no—
359C4×C47C4×#4111yescharacteristic
360C4×C47#52011yescharacteristic
361C4×C47#54611yescharacteristic
362C4×C47#54711yescharacteristic
363Dic47—42no—
364Dic47—42no—
365Dic47—42no—
366C2×#555—471no—
367C2×#435—471no—
368#2352D4711yescharacteristic, complemented
369#1993—471no—
370#1988—471no—
371#1895—471no—
372#1893—471no—
373#1875—471no—
374#1874—471no—
375#1825—471no—
376#1825—471no—
377#1804—471no—
378#1762—471no—
379#1736—471no—
380#1735—471no—
381C2×C47—42no—
382C2×C47—42no—
383C2×C47#233911yescharacteristic
384C2×C47#289611yescharacteristic
385C2×C47#289711yescharacteristic
386C2×C47#331911yescharacteristic
387C2×C47#332111yescharacteristic
388C2×C47#334711yescharacteristic
389C2×C47#334811yescharacteristic
390D47—82no—
391C22×M16—471no—
392C23×C8—471no—
393#555—478no—
394#555—944no—
395C2×C4⋊Q8—471no—
396C2×#124—941no—
397C2×#124—941no—
398C2×#121—471no—
399C2×#121—471no—
400C2×#121—941no—
401C2×C4×D4—471no—
402C2×C4×D4C2×D4711yescharacteristic
403C2×#117—471no—
404C2×#117—471no—
405C2×#117—941no—
406C2×#117C2×D4711yescharacteristic
407C22×C4⋊C4C2×D4711yescharacteristic
408#435—944no—
409C2×C4⋊C8—471no—
410C2×#102—471no—
411C2×#102—471no—
412C2×#102—471no—
413C2×#102—471no—
414C2×C22⋊C8—471no—
415C2×C22⋊C8—471no—
416C2×#97—471no—
417#388—21no—
418#387—21no—
419#386—21no—
420#382C2×D4711yescharacteristic
421#380C2×D4711yescharacteristic
422#380C2×D4711yescharacteristic
423C4×C4⋊C4C2×D4711yescharacteristic
424C4×C22⋊C4—21no—
425#340—471no—
426#340—471no—
427#340—471no—
428#340—471no—
429#340—471no—
430#340—471no—
431#340—471no—
432#340—471no—
433#340—471no—
434#340—471no—
435#340—471no—
436#340—471no—
437C47#2249211yescharacteristic, complemented, Sylow
438C22×Q8—941no—
439C22×D4—471no—
440C22×D4—941no—
441C22×D4—941no—
442C22×D4C22⋊D4711yescharacteristic
443C23×C4—21no—
444C23×C4—941no—
445C23×C4C22×D4711yescharacteristic
446C23×C4C22×D4711yescharacteristic
447C2×M16—942no—
448C2×M16—942no—
449C2×M16—1881no—
450C22×C8—471no—
451C22×C8—471no—
452C22×C8—471no—
453C22×C8—471no—
454C22×C8—942no—
455C22×C8—942no—
456C22×C8—1881no—
457C4⋊Q8—474no—
458C4⋊Q8—942no—
459#124—948no—
460#124—948no—
461#121—474no—
462#121—474no—
463#121—948no—
464#121—942no—
465#121—942no—
466C4×D4—474no—
467C4×D4—942no—
468C4×D4C4×D4714yes—
469C4×D4D18814yes—
470#117—22no—
471#117—41no—
472#117—474no—
473#117—474no—
474#117—942no—
475#117—942no—
476#117—948no—
477C2×C4⋊C4—22no—
478C2×C4⋊C4—21no—
479C2×C4⋊C4—41no—
480C2×C4⋊C4—471no—
481C2×C4⋊C4—471no—
482C2×C4⋊C4—471no—
483C2×C4⋊C4—941no—
484C2×C4⋊C4C22⋊D4711yescharacteristic
485C2×C4⋊C4C22×D4711yescharacteristic
486C2×C4⋊C4C22×D4711yescharacteristic
487C2×C4⋊C4C22×D4711yescharacteristic
488C2×C4⋊C4C22×D4711yescharacteristic
489C2×C22⋊C4—21no—
490C2×C22⋊C4—21no—
491C2×C22⋊C4—21no—
492C2×C22⋊C4—941no—
493C2×C22⋊C4—941no—
494C2×C22⋊C4—941no—
495C2×C22⋊C4—941no—
496C2×C22⋊C4—941no—
497C2×C22⋊C4C22⋊D4711yescharacteristic
498C2×C22⋊C4C22⋊D4711yescharacteristic
499C2×C42—21no—
500C2×C42—21no—
501C2×C42—941no—
502C2×C42—941no—
503C2×C42C22×D4711yescharacteristic
504C4⋊C8—942no—
505#102—942no—
506#102—942no—
507#102—1881no—
508#102—1881no—
509C22⋊C8—942no—
510C22⋊C8—942no—
511#97—942no—
512#95—21no—
513#95—21no—
514#95—21no—
515#95—21no—
516#95—21no—
517C24—941no—
518C24C2×C22⋊D4711yescharacteristic
519C24C2×C22⋊D4711yescharacteristic
520C2×Q8—944no—
521C2×Q8—3761no—
522C2×Q8—3761no—
523C2×D4—41no—
524C2×D4—41no—
525C2×D4—472no—
526C2×D4—944no—
527C2×D4—944no—
528C2×D4—941no—
529C2×D4—941no—
530C2×D4—941no—
531C2×D4—941no—
532C2×D4—941no—
533C2×D4—3761no—
534C2×D4—3761no—
535C2×D4—3761no—
536C2×D4—3761no—
537C2×D4(C2×D47)⋊C414yes—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—42no—
551C22×C4—42no—
552C22×C4—81no—
553C22×C4—941no—
554C22×C4—941no—
555C22×C4—941no—
556C22×C4—944no—
557C22×C4—1882no—
558C22×C4—1882no—
559C22×C4C2×C4×D4712yes—
560C22×C4C2×C4×D4712yes—
561C22×C4C2×D18812yes—
562C22×C4C2×D18812yes—
563C22×C4C2×C22⋊D4711yescharacteristic
564C22×C4C2×C22⋊D4711yescharacteristic
565C22×C4C2×C22⋊D4711yescharacteristic
566C22×C4C2×C22⋊D4711yescharacteristic
567C22×C4C23×D4711yescharacteristic
568M16—1884no—
569C2×C8—472no—
570C2×C8—941no—
571C2×C8—941no—
572C2×C8—941no—
573C2×C8—941no—
574C2×C8—941no—
575C2×C8—941no—
576C2×C8—941no—
577C2×C8—941no—
578C2×C8—941no—
579C2×C8—941no—
580C2×C8—941no—
581C2×C8—1884no—
582C4⋊C4—21no—
583C4⋊C4—21no—
584C4⋊C4—21no—
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—42no—
590C4⋊C4—472no—
591C4⋊C4—472no—
592C4⋊C4—472no—
593C4⋊C4—944no—
594C4⋊C4—941no—
595C4⋊C4—941no—
596C4⋊C4—941no—
597C4⋊C4(C2×D47)⋊C414yes—
598C4⋊C4#1062535212yes—
599C22⋊C4—42no—
600C22⋊C4—42no—
601C22⋊C4—81no—
602C22⋊C4—944no—
603C22⋊C4—944no—
604C22⋊C4—944no—
605C22⋊C4—944no—
606C22⋊C4—944no—
607C22⋊C4(C2×D47)⋊C414yes—
608C22⋊C4(C2×D47)⋊C414yes—
609C42—42no—
610C42—81no—
611C42—944no—
612C42—944no—
613C42C2×C4×D4712yes—
614C42C2×D18812yes—
615C23—21no—
616C23—21no—
617C23—21no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—21no—
627C23—942no—
628C23—1881no—
629C23—1881no—
630C23—1881no—
631C23—1881no—
632C23—1881no—
633C23—1881no—
634C23C2×(C2×D47)⋊C412yes—
635C23C2×(C2×D47)⋊C412yes—
636C23C22×C22⋊D4711yescharacteristic
637Q8—3764no—
638D4—44no—
639D4—942no—
640D4—942no—
641D4—3764no—
642D4—3764no—
643D4—1881no—
644D4—1881no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
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—22no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—84no—
674C2×C4—942no—
675C2×C4—942no—
676C2×C4—942no—
677C2×C4—1888no—
678C2×C4—1881no—
679C2×C4—1881no—
680C2×C4—1881no—
681C2×C4—1881no—
682C2×C4—1881no—
683C2×C4—1881no—
684C2×C4C2×(C2×D47)⋊C412yes—
685C2×C4C2×(C2×D47)⋊C412yes—
686C2×C4C2×(C2×D47)⋊C412yes—
687C2×C4C2×(C2×D47)⋊C412yes—
688C2×C4C22×C4×D4711yescharacteristic
689C2×C4C22×D18811yescharacteristic
690C2×C4#41×D4711yescharacteristic
691C2×C4C2×#1062535211yescharacteristic
692C2×C4#1309406911yescharacteristic
693C2×C4#1309407111yescharacteristic
694C8—942no—
695C8—1881no—
696C8—1881no—
697C8—1881no—
698C22—22no—
699C22—22no—
700C22—22no—
701C22—22no—
702C22—22no—
703C22—22no—
704C22—41no—
705C22—41no—
706C22—41no—
707C22—41no—
708C22—41no—
709C22—41no—
710C22—41no—
711C22—41no—
712C22—3761no—
713C22—3761no—
714C22—3761no—
715C22—3761no—
716C22—1882no—
717C22—1882no—
718C22—1882no—
719C22C22×(C2×D47)⋊C411yescharacteristic
720C22#1568976711yescharacteristic
721C22#1568977211yescharacteristic
722C22#1568992111yescharacteristic
723C22#1568992111yescharacteristic
724C22#1568992611yescharacteristic
725C22#1568993111yescharacteristic
726C4—22no—
727C4—22no—
728C4—22no—
729C4—22no—
730C4—42no—
731C4—81no—
732C4—81no—
733C4—81no—
734C4—1882no—
735C4—1882no—
736C4—1882no—
737C4C4×#1062535211yescharacteristic
738C4#1568960211yescharacteristic
739C4#1568976811yescharacteristic
740C4#1568977711yescharacteristic
741C2—42no—
742C2—42no—
743C2—3762no—
744C2#2024621311yescharacteristic
745C2#2025190511yescharacteristic
746C2#2025191111yescharacteristic
747C2#2025554411yescharacteristic
748C2#2025557411yescharacteristic
749C2#2025588211yescharacteristic
750C2#2025589711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC47×#2352C2
socleC23×C47C22×D4
prime radicalC2×#15689838C2
cosocleC22×C4×C47C24
hypercenter#2352D47
hypocenterC47#22492
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2352

Complements

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

NH ≅ G/Ntype
2. C2×#15689195C2semidirect
3. #20244360C2semidirect
4. #20244340C2semidirect
5. #20243824C2semidirect
6. #20243814C2semidirect
7. #20243710C2semidirect
8. #20243705C2semidirect
9. #20243480C2semidirect
10. #20243480C2semidirect
11. #20243395C2semidirect
12. #20243216C2semidirect
13. #20243107C2semidirect
14. #20243104C2semidirect
15. C47×#2352C2semidirect
19. #15689838C4semidirect
78. #13094024C2×C4semidirect
84. #13093998C2×C4semidirect
87. C4×D188C2×C4semidirect
91. #13093983C2×C4semidirect
368. #2352D47semidirect
437. C47#22492semidirect

Maximal subgroups

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

subgroupindex
C2×#156898382
C2×#156891952
#202443602
#202443402
#202438242
#202438142
#202437102
#202437052
#202434802
#202433952
#202432162
#202431072
#202431042
C47×#23522
#2249247