Finite Group Databasebeta

← C47×#18742 #26058440

Subgroups — C47×#18742 #26058440

Order 12032.

908 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3554C211yesmaximal, characteristic, complemented
2C47×#3246C211yesmaximal, characteristic, complemented
3C47×#3212C211yesmaximal, characteristic, complemented
4C47×#3184C211yesmaximal, characteristic, complemented
5C47×#1653C211yesmaximal, characteristic, complemented
6C47×#1651C211yesmaximal, characteristic, complemented
7C47×#1642C211yesmaximal, characteristic, complemented
8C47×#1640C211yesmaximal, characteristic, complemented
9C47×#1627C211yesmaximal, characteristic, complemented
10C47×#1626C211yesmaximal, characteristic, complemented
11C47×#1621C211yesmaximal, characteristic, complemented
12C47×#1620C211yesmaximal, characteristic, complemented
13C47×#1540C211yesmaximal, characteristic, complemented
14C47×#1485C211yesmaximal, characteristic, complemented
15C47×#1483C211yesmaximal, characteristic, complemented
16C47×#562—22no—
17C47×#559—21no—
18C47×#559C2211yescharacteristic
19C47×#557C2211yescharacteristic
20C47×#554—21no—
21C47×#550C2211yescharacteristic
22D4×Q8×C47C2211yescharacteristic
23C47×#548—21no—
24C47×#547—21no—
25C47×#542—21no—
26C47×#542—21no—
27C47×#540—21no—
28C47×#539—22no—
29C47×#536—21no—
30C47×#533C2211yescharacteristic
31C47×#532C2211yescharacteristic
32C47×#532C2211yescharacteristic
33C47×#529C2211yescharacteristic
34C47×#498C2211yescharacteristic
35C47×#495—21no—
36C47×#493C2211yescharacteristic
37C47×#488—21no—
38C47×#486C2211yescharacteristic
39C47×#486C2211yescharacteristic
40C47×#476—21no—
41C47×#475C2211yescharacteristic
42C47×#475C2211yescharacteristic
43C47×#469—22no—
44C47×#465—21no—
45C47×#465—21no—
46C47×#462C2211yescharacteristic
47C47×#461—21no—
48C47×#461C2211yescharacteristic
49C47×#460C2211yescharacteristic
50C47×#460C2211yescharacteristic
51C47×#460C2211yescharacteristic
52C47×#459C2211yescharacteristic
53C47×#452—21no—
54C47×#449—21no—
55C47×#442—22no—
56C47×#431C2211yescharacteristic
57C2×C4⋊C8×C47C2211yescharacteristic
58C4×M16×C47C2211yescharacteristic
59C47×#332C2211yescharacteristic
60C47×#332C2211yescharacteristic
61C47×#331C2211yescharacteristic
62C47×#331C2211yescharacteristic
63C47×Q8⋊C8C2211yescharacteristic
64C47×Q8⋊C8C2211yescharacteristic
65C47×Q8⋊C8C2211yescharacteristic
66C47×Q8⋊C8C2211yescharacteristic
67C47×Q8⋊C8C2211yescharacteristic
68C47×Q8⋊C8C2211yescharacteristic
69C47×D4⋊C8C2211yescharacteristic
70C47×D4⋊C8C2211yescharacteristic
71C2×#41×C47—21no—
72C2×#41×C47—21no—
73C2×#41×C47—21no—
74C22×Q8×C47—21no—
75C2×Q16×C47—21no—
76C2×SD16×C47—21no—
77C2×SD16×C47—21no—
78C2×SD16×C47—21no—
79C2×SD16×C47—21no—
80C2×D8×C47—22no—
81C2×D8×C47—21no—
82C2×M16×C47—21no—
83C22×C8×C47—21no—
84C4⋊Q8×C47—21no—
85C4⋊Q8×C47—21no—
86C4⋊Q8×C47D411yescharacteristic
87C4⋊Q8×C47D411yescharacteristic
88C4⋊Q8×C47C2311yescharacteristic
89C4⋊Q8×C47C2311yescharacteristic
90#127×C47—21no—
91#127×C47C2311yescharacteristic
92#127×C47C2311yescharacteristic
93#126×C47—22no—
94#126×C47—21no—
95#125×C47—22no—
96#125×C47—21no—
97#125×C47—21no—
98#125×C47D411yescharacteristic
99#124×C47—22no—
100#124×C47—22no—
101#124×C47—21no—
102#124×C47—21no—
103#124×C47—21no—
104#124×C47—21no—
105#124×C47D411yescharacteristic
106#123×C47—22no—
107#123×C47—22no—
108#123×C47—22no—
109#123×C47—22no—
110#123×C47—22no—
111#123×C47—22no—
112#123×C47—21no—
113C22⋊Q8×C47—22no—
114C22⋊Q8×C47—22no—
115C22⋊Q8×C47—22no—
116C22⋊Q8×C47—22no—
117C22⋊Q8×C47—21no—
118C22⋊Q8×C47—22no—
119C22⋊Q8×C47—21no—
120C22⋊Q8×C47D411yescharacteristic
121C22⋊Q8×C47D411yescharacteristic
122C22⋊Q8×C47D411yescharacteristic
123#121×C47—22no—
124#121×C47—22no—
125#121×C47—22no—
126#121×C47—21no—
127#121×C47—21no—
128#121×C47—21no—
129#121×C47—21no—
130#121×C47D411yescharacteristic
131#121×C47D412yes—
132C4×Q8×C47—21no—
133C4×Q8×C47—21no—
134C4×Q8×C47—21no—
135C4×Q8×C47C2311yescharacteristic
136C4×Q8×C47C2311yescharacteristic
137C4×Q8×C47C2311yescharacteristic
138C4×D4×C47—22no—
139C4×D4×C47—21no—
140C4×D4×C47—21no—
141C4×D4×C47—21no—
142C4×D4×C47—21no—
143C4×D4×C47—21no—
144C4×D4×C47—21no—
145C4×D4×C47—21no—
146C4×D4×C47—21no—
147C4×D4×C47D412yes—
148C4×D4×C47C2311yescharacteristic
149#117×C47—21no—
150#117×C47—21no—
151C2×C4⋊C4×C47—22no—
152C2×C42×C47C2311yescharacteristic
153#106×C47—21no—
154#106×C47—21no—
155#106×C47—22no—
156C4⋊C8×C47—21no—
157C4⋊C8×C47C2311yescharacteristic
158C4⋊C8×C47C2311yescharacteristic
159C4⋊C8×C47C2311yescharacteristic
160C4⋊C8×C47C2311yescharacteristic
161#103×C47—21no—
162#103×C47—21no—
163#103×C47—21no—
164#103×C47—21no—
165#102×C47—22no—
166#102×C47—21no—
167#102×C47—21no—
168#102×C47—21no—
169#102×C47—21no—
170#102×C47—22no—
171C22⋊C8×C47—21no—
172#97×C47—21no—
173C4×C8×C47—21no—
174C4×C8×C47C2311yescharacteristic
175C4×C8×C47C2311yescharacteristic
176#41×C47—81no—
177#41×C47—81no—
178#41×C47—81no—
179#41×C47—81no—
180#41×C47—81no—
181#41×C47—81no—
182C2×Q8×C47—22no—
183C2×Q8×C47—21no—
184C2×Q8×C47—21no—
185C2×Q8×C47—21no—
186C2×Q8×C47—81no—
187C2×Q8×C47—81no—
188C2×Q8×C47C2×D411yescharacteristic
189C2×Q8×C47C2×D411yescharacteristic
190C2×Q8×C47C2×D411yescharacteristic
191C2×D4×C47—22no—
192C2×D4×C47—22no—
193C2×D4×C47—21no—
194C2×D4×C47—22no—
195C2×D4×C47—21no—
196C2×D4×C47—21no—
197C2×D4×C47—21no—
198C2×D4×C47—21no—
199C2×D4×C47—21no—
200C2×D4×C47—41no—
201C2×D4×C47C2×D411yescharacteristic
202C2×D4×C47C2×D412yes—
203C22×C4×C47—22no—
204C22×C4×C47—22no—
205C22×C4×C47—22no—
206C22×C4×C47—21no—
207C22×C4×C47—22no—
208C22×C4×C47—41no—
209C22×C4×C47C2×D411yescharacteristic
210C22×C4×C47C2×D411yescharacteristic
211C22×C4×C47C2×D411yescharacteristic
212Q16×C47—81no—
213SD16×C47—81no—
214SD16×C47—81no—
215SD16×C47—81no—
216SD16×C47—81no—
217D8×C47—44no—
218D8×C47—81no—
219M16×C47—42no—
220C2×C8×C47—21no—
221C2×C8×C47—21no—
222C2×C8×C47—21no—
223C2×C8×C47—21no—
224C2×C8×C47—21no—
225C2×C8×C47—21no—
226C2×C8×C47—81no—
227C4⋊C4×C47—22no—
228C4⋊C4×C47—22no—
229C4⋊C4×C47—22no—
230C4⋊C4×C47—22no—
231C4⋊C4×C47—21no—
232C4⋊C4×C47—21no—
233C4⋊C4×C47—21no—
234C4⋊C4×C47—21no—
235C4⋊C4×C47—21no—
236C4⋊C4×C47—21no—
237C4⋊C4×C47—21no—
238C4⋊C4×C47—21no—
239C4⋊C4×C47—21no—
240C4⋊C4×C47—21no—
241C4⋊C4×C47—21no—
242C4⋊C4×C47—21no—
243C4⋊C4×C47—21no—
244C4⋊C4×C47—21no—
245C4⋊C4×C47C2×D411yescharacteristic
246C4⋊C4×C47C2×D411yescharacteristic
247C4⋊C4×C47C2×D411yescharacteristic
248C4⋊C4×C47C2×D412yes—
249C4⋊C4×C47C2×D411yescharacteristic
250C22⋊C4×C47—22no—
251C22⋊C4×C47—22no—
252C22⋊C4×C47—22no—
253C22⋊C4×C47—22no—
254C22⋊C4×C47—22no—
255C22⋊C4×C47—21no—
256C22⋊C4×C47—21no—
257C22⋊C4×C47—21no—
258C22⋊C4×C47—21no—
259C22⋊C4×C47—21no—
260C22⋊C4×C47—21no—
261C22⋊C4×C47—22no—
262C22⋊C4×C47—22no—
263C22⋊C4×C47—21no—
264C22⋊C4×C47—41no—
265C22⋊C4×C47—41no—
266C42×C47—22no—
267C42×C47—21no—
268C42×C47—21no—
269C42×C47—21no—
270C42×C47C2×D411yescharacteristic
271C42×C47C2×D411yescharacteristic
272C42×C47C2×D411yescharacteristic
273C42×C47C2411yescharacteristic
274C23×C47—21no—
275C23×C47—22no—
276C23×C47—41no—
277C23×C47#12011yescharacteristic
278Q8×C47—21no—
279Q8×C47—21no—
280Q8×C47—21no—
281Q8×C47—21no—
282Q8×C47—21no—
283Q8×C47—21no—
284Q8×C47—41no—
285Q8×C47—41no—
286Q8×C47—41no—
287Q8×C47—41no—
288Q8×C47—81no—
289Q8×C47—82no—
290D4×C47—21no—
291D4×C47—21no—
292D4×C47—42no—
293D4×C47—42no—
294D4×C47—41no—
295D4×C47—41no—
296D4×C47—41no—
297D4×C47—41no—
298D4×C47—41no—
299D4×C47—41no—
300D4×C47—41no—
301D4×C47—41no—
302D4×C47—81no—
303D4×C47—82no—
304D4×C47—82no—
305D4×C47—82no—
306D4×C47—82no—
307C2×C4×C47—21no—
308C2×C4×C47—21no—
309C2×C4×C47—21no—
310C2×C4×C47—21no—
311C2×C4×C47—21no—
312C2×C4×C47—21no—
313C2×C4×C47—21no—
314C2×C4×C47—21no—
315C2×C4×C47—21no—
316C2×C4×C47—22no—
317C2×C4×C47—21no—
318C2×C4×C47—21no—
319C2×C4×C47—41no—
320C2×C4×C47—41no—
321C2×C4×C47—41no—
322C2×C4×C47—41no—
323C2×C4×C47—82no—
324C2×C4×C47—82no—
325C2×C4×C47—82no—
326C2×C4×C47—82no—
327C2×C4×C47—82no—
328C2×C4×C47#12011yescharacteristic
329C2×C4×C47#12011yescharacteristic
330C2×C4×C47#12011yescharacteristic
331C2×C4×C47C22×D411yescharacteristic
332C2×C4×C47C22×D411yescharacteristic
333C2×C4×C47C22×D411yescharacteristic
334C8×C47—22no—
335C8×C47—41no—
336C8×C47—41no—
337C8×C47—41no—
338C8×C47—41no—
339C8×C47—41no—
340#18742C4711yesmaximal, characteristic, direct product factor, Sylow
341C22×C47—21no—
342C22×C47—21no—
343C22×C47—21no—
344C22×C47—41no—
345C22×C47—42no—
346C22×C47—41no—
347C22×C47—42no—
348C22×C47—42no—
349C22×C47—41no—
350C22×C47—81no—
351C22×C47—81no—
352C22×C47—81no—
353C22×C47C2×#12011yescharacteristic
354C4×C47—21no—
355C4×C47—21no—
356C4×C47—21no—
357C4×C47—21no—
358C4×C47—41no—
359C4×C47—41no—
360C4×C47—41no—
361C4×C47—42no—
362C4×C47—41no—
363C4×C47—41no—
364C4×C47—41no—
365C4×C47—41no—
366C4×C47—81no—
367C4×C47#57611yescharacteristic
368C4×C47#57711yescharacteristic
369C4×C47#57711yescharacteristic
370C4×C47#57711yescharacteristic
371#3554C2×C4711yescharacteristic, complemented
372#3246C2×C4711yescharacteristic, complemented
373#3212C2×C4711yescharacteristic, complemented
374#3184C2×C4711yescharacteristic, complemented
375#1653C2×C4711yescharacteristic, complemented
376#1651C2×C4711yescharacteristic, complemented
377#1642C2×C4711yescharacteristic, complemented
378#1640C2×C4711yescharacteristic, complemented
379#1627C2×C4711yescharacteristic, complemented
380#1626C2×C4711yescharacteristic, complemented
381#1621C2×C4711yescharacteristic, complemented
382#1620C2×C4711yescharacteristic, complemented
383#1540C2×C4711yescharacteristic, complemented
384#1485C2×C4711yescharacteristic, complemented
385#1483C2×C4711yescharacteristic, complemented
386C2×C47—41no—
387C2×C47—81no—
388C2×C47—82no—
389C2×C47—161no—
390C2×C47#301011yescharacteristic
391C2×C47#301211yescharacteristic
392C2×C47#301811yescharacteristic
393#562—22no—
394#559—21no—
395#559C22×C4711yescharacteristic
396#557C22×C4711yescharacteristic
397#554—21no—
398#550C22×C4711yescharacteristic
399D4×Q8C22×C4711yescharacteristic
400#548—21no—
401#547—21no—
402#542—21no—
403#542—21no—
404#540—21no—
405#539—22no—
406#536—21no—
407#533C22×C4711yescharacteristic
408#532C22×C4711yescharacteristic
409#532C22×C4711yescharacteristic
410#529C22×C4711yescharacteristic
411#498C22×C4711yescharacteristic
412#495—21no—
413#493C22×C4711yescharacteristic
414#488—21no—
415#486C22×C4711yescharacteristic
416#486C22×C4711yescharacteristic
417#476—21no—
418#475C22×C4711yescharacteristic
419#475C22×C4711yescharacteristic
420#469—22no—
421#465—21no—
422#465—21no—
423#462C22×C4711yescharacteristic
424#461—21no—
425#461C22×C4711yescharacteristic
426#460C22×C4711yescharacteristic
427#460C22×C4711yescharacteristic
428#460C22×C4711yescharacteristic
429#459C22×C4711yescharacteristic
430#452—21no—
431#449—21no—
432#442—22no—
433#431C22×C4711yescharacteristic
434C2×C4⋊C8C22×C4711yescharacteristic
435C4×M16C22×C4711yescharacteristic
436#332C22×C4711yescharacteristic
437#332C22×C4711yescharacteristic
438#331C22×C4711yescharacteristic
439#331C22×C4711yescharacteristic
440Q8⋊C8C22×C4711yescharacteristic
441Q8⋊C8C22×C4711yescharacteristic
442Q8⋊C8C22×C4711yescharacteristic
443Q8⋊C8C22×C4711yescharacteristic
444Q8⋊C8C22×C4711yescharacteristic
445Q8⋊C8C22×C4711yescharacteristic
446D4⋊C8C22×C4711yescharacteristic
447D4⋊C8C22×C4711yescharacteristic
448C47#1874211yescharacteristic, direct product factor, Sylow
449C2×#41—21no—
450C2×#41—21no—
451C2×#41—21no—
452C22×Q8—21no—
453C2×Q16—21no—
454C2×SD16—21no—
455C2×SD16—21no—
456C2×SD16—21no—
457C2×SD16—21no—
458C2×D8—22no—
459C2×D8—21no—
460C2×M16—21no—
461C22×C8—21no—
462C4⋊Q8—21no—
463C4⋊Q8—21no—
464C4⋊Q8D4×C4711yescharacteristic
465C4⋊Q8D4×C4711yescharacteristic
466C4⋊Q8C23×C4711yescharacteristic
467C4⋊Q8C23×C4711yescharacteristic
468#127—21no—
469#127C23×C4711yescharacteristic
470#127C23×C4711yescharacteristic
471#126—22no—
472#126—21no—
473#125—22no—
474#125—21no—
475#125—21no—
476#125D4×C4711yescharacteristic
477#124—22no—
478#124—22no—
479#124—21no—
480#124—21no—
481#124—21no—
482#124—21no—
483#124D4×C4711yescharacteristic
484#123—22no—
485#123—22no—
486#123—22no—
487#123—22no—
488#123—22no—
489#123—22no—
490#123—21no—
491C22⋊Q8—22no—
492C22⋊Q8—22no—
493C22⋊Q8—22no—
494C22⋊Q8—22no—
495C22⋊Q8—21no—
496C22⋊Q8—22no—
497C22⋊Q8—21no—
498C22⋊Q8D4×C4711yescharacteristic
499C22⋊Q8D4×C4711yescharacteristic
500C22⋊Q8D4×C4711yescharacteristic
501#121—22no—
502#121—22no—
503#121—22no—
504#121—21no—
505#121—21no—
506#121—21no—
507#121—21no—
508#121D4×C4711yescharacteristic
509#121D4×C4712yes—
510C4×Q8—21no—
511C4×Q8—21no—
512C4×Q8—21no—
513C4×Q8C23×C4711yescharacteristic
514C4×Q8C23×C4711yescharacteristic
515C4×Q8C23×C4711yescharacteristic
516C4×D4—22no—
517C4×D4—21no—
518C4×D4—21no—
519C4×D4—21no—
520C4×D4—21no—
521C4×D4—21no—
522C4×D4—21no—
523C4×D4—21no—
524C4×D4—21no—
525C4×D4D4×C4712yes—
526C4×D4C23×C4711yescharacteristic
527#117—21no—
528#117—21no—
529C2×C4⋊C4—22no—
530C2×C42C23×C4711yescharacteristic
531#106—22no—
532#106—21no—
533#106—21no—
534C4⋊C8—21no—
535C4⋊C8C23×C4711yescharacteristic
536C4⋊C8C23×C4711yescharacteristic
537C4⋊C8C23×C4711yescharacteristic
538C4⋊C8C23×C4711yescharacteristic
539#103—21no—
540#103—21no—
541#103—21no—
542#103—21no—
543#102—22no—
544#102—22no—
545#102—21no—
546#102—21no—
547#102—21no—
548#102—21no—
549C22⋊C8—21no—
550#97—21no—
551C4×C8—21no—
552C4×C8C23×C4711yescharacteristic
553C4×C8C23×C4711yescharacteristic
554#41—81no—
555#41—81no—
556#41—81no—
557#41—81no—
558#41—81no—
559#41—81no—
560C2×Q8—22no—
561C2×Q8—21no—
562C2×Q8—21no—
563C2×Q8—21no—
564C2×Q8—81no—
565C2×Q8—81no—
566C2×Q8C2×D4×C4711yescharacteristic
567C2×Q8C2×D4×C4711yescharacteristic
568C2×Q8C2×D4×C4711yescharacteristic
569C2×D4—22no—
570C2×D4—22no—
571C2×D4—21no—
572C2×D4—22no—
573C2×D4—21no—
574C2×D4—21no—
575C2×D4—21no—
576C2×D4—21no—
577C2×D4—21no—
578C2×D4—41no—
579C2×D4C2×D4×C4711yescharacteristic
580C2×D4C2×D4×C4712yes—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—21no—
585C22×C4—22no—
586C22×C4—41no—
587C22×C4C2×D4×C4711yescharacteristic
588C22×C4C2×D4×C4711yescharacteristic
589C22×C4C2×D4×C4711yescharacteristic
590Q16—81no—
591SD16—81no—
592SD16—81no—
593SD16—81no—
594SD16—81no—
595D8—44no—
596D8—81no—
597M16—42no—
598C2×C8—21no—
599C2×C8—21no—
600C2×C8—21no—
601C2×C8—21no—
602C2×C8—21no—
603C2×C8—21no—
604C2×C8—81no—
605C4⋊C4—22no—
606C4⋊C4—22no—
607C4⋊C4—22no—
608C4⋊C4—22no—
609C4⋊C4—21no—
610C4⋊C4—21no—
611C4⋊C4—21no—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—21no—
617C4⋊C4—21no—
618C4⋊C4—21no—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4C2×D4×C4711yescharacteristic
624C4⋊C4C2×D4×C4711yescharacteristic
625C4⋊C4C2×D4×C4711yescharacteristic
626C4⋊C4C2×D4×C4712yes—
627C4⋊C4C2×D4×C4711yescharacteristic
628C22⋊C4—22no—
629C22⋊C4—22no—
630C22⋊C4—22no—
631C22⋊C4—22no—
632C22⋊C4—22no—
633C22⋊C4—21no—
634C22⋊C4—21no—
635C22⋊C4—21no—
636C22⋊C4—21no—
637C22⋊C4—21no—
638C22⋊C4—21no—
639C22⋊C4—22no—
640C22⋊C4—22no—
641C22⋊C4—21no—
642C22⋊C4—41no—
643C22⋊C4—41no—
644C42—22no—
645C42—21no—
646C42—21no—
647C42—21no—
648C42C2×D4×C4711yescharacteristic
649C42C2×D4×C4711yescharacteristic
650C42C2×D4×C4711yescharacteristic
651C42C24×C4711yescharacteristic
652C23—21no—
653C23—22no—
654C23—41no—
655C23#120×C4711yescharacteristic
656Q8—21no—
657Q8—21no—
658Q8—21no—
659Q8—21no—
660Q8—21no—
661Q8—21no—
662Q8—41no—
663Q8—41no—
664Q8—41no—
665Q8—41no—
666Q8—81no—
667Q8—82no—
668D4—21no—
669D4—21no—
670D4—42no—
671D4—42no—
672D4—41no—
673D4—41no—
674D4—41no—
675D4—41no—
676D4—41no—
677D4—41no—
678D4—41no—
679D4—41no—
680D4—81no—
681D4—82no—
682D4—82no—
683D4—82no—
684D4—82no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—22no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—82no—
702C2×C4—82no—
703C2×C4—82no—
704C2×C4—82no—
705C2×C4—82no—
706C2×C4#120×C4711yescharacteristic
707C2×C4#120×C4711yescharacteristic
708C2×C4#120×C4711yescharacteristic
709C2×C4C22×D4×C4711yescharacteristic
710C2×C4C22×D4×C4711yescharacteristic
711C2×C4C22×D4×C4711yescharacteristic
712C8—22no—
713C8—41no—
714C8—41no—
715C8—41no—
716C8—41no—
717C8—41no—
718C22—21no—
719C22—21no—
720C22—21no—
721C22—41no—
722C22—42no—
723C22—41no—
724C22—42no—
725C22—42no—
726C22—41no—
727C22—81no—
728C22—81no—
729C22—81no—
730C22C2×#120×C4711yescharacteristic
731C4—21no—
732C4—21no—
733C4—21no—
734C4—21no—
735C4—41no—
736C4—41no—
737C4—41no—
738C4—42no—
739C4—41no—
740C4—41no—
741C4—41no—
742C4—41no—
743C4—81no—
744C4C47×#57611yescharacteristic
745C4C47×#57711yescharacteristic
746C4C47×#57711yescharacteristic
747C4C47×#57711yescharacteristic
748C2—41no—
749C2—81no—
750C2—82no—
751C2—161no—
752C2C47×#301011yescharacteristic
753C2C47×#301211yescharacteristic
754C2C47×#301811yescharacteristic
subgroupG/H
center, socleC22×C47C2×#120
commutator, Frattini, cosocleC42C24×C47
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C47 ◁ C2×C42×C47 ◁ G

Complements

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

NH ≅ G/Ntype
1. C47×#3554C2semidirect
2. C47×#3246C2semidirect
3. C47×#3212C2semidirect
4. C47×#3184C2semidirect
5. C47×#1653C2semidirect
6. C47×#1651C2semidirect
7. C47×#1642C2semidirect
8. C47×#1640C2semidirect
9. C47×#1627C2semidirect
10. C47×#1626C2semidirect
11. C47×#1621C2semidirect
12. C47×#1620C2semidirect
13. C47×#1540C2semidirect
14. C47×#1485C2semidirect
15. C47×#1483C2semidirect
340. #18742C47direct (N × H)
371. #3554C2×C47semidirect
372. #3246C2×C47semidirect
373. #3212C2×C47semidirect
374. #3184C2×C47semidirect
375. #1653C2×C47semidirect
376. #1651C2×C47semidirect
377. #1642C2×C47semidirect
378. #1640C2×C47semidirect
379. #1627C2×C47semidirect
380. #1626C2×C47semidirect
381. #1621C2×C47semidirect
382. #1620C2×C47semidirect
383. #1540C2×C47semidirect
384. #1485C2×C47semidirect
385. #1483C2×C47semidirect
448. C47#18742direct (N × H)

Maximal subgroups

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

subgroupindex
C47×#35542
C47×#32462
C47×#32122
C47×#31842
C47×#16532
C47×#16512
C47×#16422
C47×#16402
C47×#16272
C47×#16262
C47×#16212
C47×#16202
C47×#15402
C47×#14852
C47×#14832
#1874247