Finite Group Databasebeta

← C47×#18739 #26058437

Subgroups — C47×#18739 #26058437

Order 12032.

938 conjugacy classes of subgroups.

The subgroup lattice has 776 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3546C211yesmaximal, characteristic
2C47×#3246C211yesmaximal, characteristic, complemented
3C47×#3233C211yesmaximal, characteristic, complemented
4C47×#3182C211yesmaximal, characteristic, complemented
5C47×#1650C211yesmaximal, characteristic, complemented
6C47×#1647C211yesmaximal, characteristic, complemented
7C47×#1642C211yesmaximal, characteristic, complemented
8C47×#1639C211yesmaximal, characteristic, complemented
9C47×#1638C211yesmaximal, characteristic, complemented
10C47×#1635C211yesmaximal, characteristic, complemented
11C47×#1631C211yesmaximal, characteristic, complemented
12C47×#1629C211yesmaximal, characteristic, complemented
13C47×#1540C211yesmaximal, characteristic, complemented
14C47×#1484C211yesmaximal, characteristic, complemented
15C47×#1483C211yesmaximal, characteristic, complemented
16C47×#560—22no—
17C47×#556C2211yescharacteristic
18C47×#553—21no—
19C47×#550—21no—
20C47×#550C2211yescharacteristic
21C47×#547C2211yescharacteristic
22C47×#546—21no—
23C47×#546—21no—
24D42×C47C2211yescharacteristic
25C47×#542—21no—
26C47×#538—22no—
27C47×#537—21no—
28C47×#535—21no—
29C47×#535—21no—
30C47×#533C2211yescharacteristic, complemented
31C47×#532C2211yescharacteristic
32C47×#532C2211yescharacteristic
33C47×#529C2211yescharacteristic
34C47×#500C2211yescharacteristic, complemented
35C47×#499—21no—
36C47×#492C2211yescharacteristic
37C47×#488—21no—
38C47×#487C2211yescharacteristic, complemented
39C47×#486C2211yescharacteristic
40C47×#485—21no—
41C47×#482—21no—
42C47×#477C2211yescharacteristic, complemented
43C47×#476C2211yescharacteristic
44C47×#476C2211yescharacteristic
45C47×#476C2211yescharacteristic, complemented
46C47×#475—21no—
47C47×#475C2211yescharacteristic, complemented
48C47×#474C2211yescharacteristic
49C47×#468—22no—
50C47×#465—21no—
51C47×#465—21no—
52C47×#461C2211yescharacteristic
53C47×#461C2211yescharacteristic, complemented
54C47×#460—21no—
55C47×#440—22no—
56C47×#431C2211yescharacteristic, complemented
57C2×C4⋊C8×C47C2211yescharacteristic, complemented
58C4×M16×C47C2211yescharacteristic, complemented
59C47×#332C2211yescharacteristic, complemented
60C47×#332C2211yescharacteristic, complemented
61C47×#331C2211yescharacteristic
62C47×#331C2211yescharacteristic
63C47×Q8⋊C8C2211yescharacteristic, complemented
64C47×Q8⋊C8C2211yescharacteristic, complemented
65C47×D4⋊C8C2211yescharacteristic
66C47×D4⋊C8C2211yescharacteristic
67C47×D4⋊C8C2211yescharacteristic
68C47×D4⋊C8C2211yescharacteristic
69C47×D4⋊C8C2211yescharacteristic, complemented
70C47×D4⋊C8C2211yescharacteristic, complemented
71C2×#41×C47—21no—
72C2×#41×C47—21no—
73C2×#41×C47—21no—
74C2×#41×C47—21no—
75C22×D4×C47—21no—
76C22×D4×C47—21no—
77C2×SD16×C47—22no—
78C2×SD16×C47—21no—
79C2×SD16×C47—21no—
80C2×M16×C47—21no—
81C22×C8×C47—21no—
82C4⋊Q8×C47D411yescharacteristic
83C4⋊Q8×C47C2311yescharacteristic
84C4⋊Q8×C47C2311yescharacteristic
85C4⋊Q8×C47C2311yescharacteristic
86#127×C47—22no—
87#127×C47—21no—
88#127×C47D411yescharacteristic
89#127×C47C2311yescharacteristic
90#126×C47—22no—
91#126×C47—22no—
92#126×C47—21no—
93#125×C47—21no—
94#125×C47D411yescharacteristic
95#124×C47—22no—
96#124×C47—21no—
97#124×C47—21no—
98#124×C47—21no—
99#124×C47D411yescharacteristic
100#123×C47—22no—
101#123×C47—22no—
102#123×C47—21no—
103#123×C47—22no—
104C22⋊Q8×C47—22no—
105C22⋊Q8×C47—21no—
106C22⋊Q8×C47—21no—
107C22⋊Q8×C47—21no—
108C22⋊Q8×C47—21no—
109C22⋊Q8×C47D411yescharacteristic
110#121×C47—22no—
111#121×C47—22no—
112#121×C47—22no—
113#121×C47—22no—
114#121×C47—22no—
115#121×C47—21no—
116#121×C47—22no—
117#121×C47—21no—
118#121×C47—21no—
119#121×C47—21no—
120#121×C47—21no—
121#121×C47—21no—
122#121×C47D411yescharacteristic
123#121×C47D411yescharacteristic
124#121×C47D412yes—
125#121×C47D411yescharacteristic
126#120×C47—22no—
127#120×C47—22no—
128#120×C47—22no—
129#120×C47—22no—
130C4×Q8×C47—21no—
131C4×Q8×C47—21no—
132C4×Q8×C47—21no—
133C4×Q8×C47C2311yescharacteristic
134C4×D4×C47—22no—
135C4×D4×C47—21no—
136C4×D4×C47—21no—
137C4×D4×C47—21no—
138C4×D4×C47—21no—
139C4×D4×C47D412yes—
140C4×D4×C47C2311yescharacteristic
141C4×D4×C47C2311yescharacteristic
142C4×D4×C47C2311yescharacteristic
143#117×C47—21no—
144#117×C47—21no—
145#117×C47—21no—
146C2×C4⋊C4×C47—21no—
147C2×C22⋊C4×C47—22no—
148C2×C42×C47C2311yescharacteristic
149#107×C47—22no—
150#107×C47—21no—
151#107×C47—21no—
152#106×C47—21no—
153#106×C47—21no—
154#106×C47—21no—
155#106×C47—21no—
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#103×C47—22no—
166#102×C47—21no—
167#102×C47—21no—
168#102×C47—22no—
169#102×C47—21no—
170#102×C47—21no—
171C22⋊C8×C47—21no—
172#97×C47—21no—
173C4×C8×C47—21no—
174C4×C8×C47C2311yescharacteristic
175C4×C8×C47C2311yescharacteristic
176C24×C47—22no—
177#41×C47—81no—
178#41×C47—81no—
179#41×C47—81no—
180#41×C47—81no—
181#41×C47—81no—
182#41×C47—81no—
183#41×C47—81no—
184#41×C47—81no—
185C2×Q8×C47—21no—
186C2×Q8×C47—21no—
187C2×Q8×C47—21no—
188C2×Q8×C47—21no—
189C2×Q8×C47C2×D411yescharacteristic
190C2×D4×C47—22no—
191C2×D4×C47—22no—
192C2×D4×C47—22no—
193C2×D4×C47—22no—
194C2×D4×C47—22no—
195C2×D4×C47—21no—
196C2×D4×C47—21no—
197C2×D4×C47—22no—
198C2×D4×C47—21no—
199C2×D4×C47—21no—
200C2×D4×C47—21no—
201C2×D4×C47—21no—
202C2×D4×C47—21no—
203C2×D4×C47—81no—
204C2×D4×C47—81no—
205C2×D4×C47—81no—
206C2×D4×C47—81no—
207C2×D4×C47C2×D411yescharacteristic
208C2×D4×C47C2×D411yescharacteristic
209C2×D4×C47C2×D411yescharacteristic
210C2×D4×C47C2×D412yes—
211C22×C4×C47—22no—
212C22×C4×C47—22no—
213C22×C4×C47—21no—
214C22×C4×C47—21no—
215C22×C4×C47—21no—
216C22×C4×C47—22no—
217C22×C4×C47C2×D411yescharacteristic
218C22×C4×C47C2×D411yescharacteristic
219C22×C4×C47C2×D411yescharacteristic
220SD16×C47—44no—
221SD16×C47—81no—
222SD16×C47—81no—
223M16×C47—42no—
224C2×C8×C47—21no—
225C2×C8×C47—21no—
226C2×C8×C47—21no—
227C2×C8×C47—21no—
228C2×C8×C47—21no—
229C2×C8×C47—21no—
230C2×C8×C47—81no—
231C4⋊C4×C47—22no—
232C4⋊C4×C47—22no—
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—41no—
244C4⋊C4×C47—41no—
245C4⋊C4×C47C2×D411yescharacteristic
246C4⋊C4×C47C2×D411yescharacteristic
247C4⋊C4×C47C2×D412yes—
248C4⋊C4×C47C2×D411yescharacteristic
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—21no—
265C22⋊C4×C47—21no—
266C22⋊C4×C47—41no—
267C42×C47—22no—
268C42×C47—21no—
269C42×C47—41no—
270C42×C47C2×D411yescharacteristic
271C42×C47C2×D411yescharacteristic
272C42×C47C2×D411yescharacteristic
273C42×C47C2411yescharacteristic
274C23×C47—21no—
275C23×C47—21no—
276C23×C47—22no—
277C23×C47—21no—
278C23×C47—82no—
279C23×C47—82no—
280C23×C47—82no—
281C23×C47#12011yescharacteristic
282Q8×C47—21no—
283Q8×C47—21no—
284Q8×C47—42no—
285Q8×C47—41no—
286Q8×C47—41no—
287Q8×C47—41no—
288Q8×C47—41no—
289Q8×C47—81no—
290D4×C47—21no—
291D4×C47—21no—
292D4×C47—21no—
293D4×C47—21no—
294D4×C47—21no—
295D4×C47—21no—
296D4×C47—42no—
297D4×C47—41no—
298D4×C47—41no—
299D4×C47—41no—
300D4×C47—41no—
301D4×C47—81no—
302D4×C47—81no—
303D4×C47—81no—
304D4×C47—81no—
305D4×C47—81no—
306D4×C47—82no—
307D4×C47—82no—
308D4×C47—82no—
309D4×C47—82no—
310D4×C47—82no—
311D4×C47—82no—
312C2×C4×C47—21no—
313C2×C4×C47—21no—
314C2×C4×C47—21no—
315C2×C4×C47—21no—
316C2×C4×C47—21no—
317C2×C4×C47—21no—
318C2×C4×C47—21no—
319C2×C4×C47—22no—
320C2×C4×C47—21no—
321C2×C4×C47—21no—
322C2×C4×C47—41no—
323C2×C4×C47—41no—
324C2×C4×C47—41no—
325C2×C4×C47—41no—
326C2×C4×C47—41no—
327C2×C4×C47—41no—
328C2×C4×C47—41no—
329C2×C4×C47—41no—
330C2×C4×C47—41no—
331C2×C4×C47—82no—
332C2×C4×C47—82no—
333C2×C4×C47—82no—
334C2×C4×C47#12011yescharacteristic
335C2×C4×C47#12011yescharacteristic
336C2×C4×C47#12011yescharacteristic
337C2×C4×C47C22×D411yescharacteristic
338C2×C4×C47C22×D411yescharacteristic
339C2×C4×C47C22×D411yescharacteristic
340C8×C47—22no—
341C8×C47—41no—
342C8×C47—41no—
343C8×C47—41no—
344C8×C47—41no—
345C8×C47—41no—
346#18739C4711yesmaximal, characteristic, direct product factor, Sylow
347C22×C47—21no—
348C22×C47—21no—
349C22×C47—21no—
350C22×C47—41no—
351C22×C47—41no—
352C22×C47—42no—
353C22×C47—41no—
354C22×C47—41no—
355C22×C47—41no—
356C22×C47—42no—
357C22×C47—41no—
358C22×C47—42no—
359C22×C47—41no—
360C22×C47—41no—
361C22×C47—41no—
362C22×C47—164no—
363C22×C47C2×#12011yescharacteristic
364C4×C47—21no—
365C4×C47—21no—
366C4×C47—21no—
367C4×C47—21no—
368C4×C47—41no—
369C4×C47—41no—
370C4×C47—41no—
371C4×C47—41no—
372C4×C47—42no—
373C4×C47—41no—
374C4×C47—81no—
375C4×C47—81no—
376C4×C47#57611yescharacteristic
377C4×C47#57711yescharacteristic
378C4×C47#57711yescharacteristic
379C4×C47#57711yescharacteristic
380#3546C2×C4711yescharacteristic
381#3246C2×C4711yescharacteristic, complemented
382#3233C2×C4711yescharacteristic, complemented
383#3182C2×C4711yescharacteristic, complemented
384#1650C2×C4711yescharacteristic, complemented
385#1647C2×C4711yescharacteristic, complemented
386#1642C2×C4711yescharacteristic, complemented
387#1639C2×C4711yescharacteristic, complemented
388#1638C2×C4711yescharacteristic, complemented
389#1635C2×C4711yescharacteristic, complemented
390#1631C2×C4711yescharacteristic, complemented
391#1629C2×C4711yescharacteristic, complemented
392#1540C2×C4711yescharacteristic, complemented
393#1484C2×C4711yescharacteristic, complemented
394#1483C2×C4711yescharacteristic, complemented
395C2×C47—41no—
396C2×C47—81no—
397C2×C47—82no—
398C2×C47—81no—
399C2×C47—81no—
400C2×C47#300911yescharacteristic
401C2×C47#301211yescharacteristic
402C2×C47#301811yescharacteristic
403#560—22no—
404#556C22×C4711yescharacteristic
405#553—21no—
406#550—21no—
407#550C22×C4711yescharacteristic
408#547C22×C4711yescharacteristic
409#546—21no—
410#546—21no—
411D42C22×C4711yescharacteristic
412#542—21no—
413#538—22no—
414#537—21no—
415#535—21no—
416#535—21no—
417#533C22×C4711yescharacteristic, complemented
418#532C22×C4711yescharacteristic
419#532C22×C4711yescharacteristic
420#529C22×C4711yescharacteristic
421#500C22×C4711yescharacteristic, complemented
422#499—21no—
423#492C22×C4711yescharacteristic
424#488—21no—
425#487C22×C4711yescharacteristic, complemented
426#486C22×C4711yescharacteristic
427#485—21no—
428#482—21no—
429#477C22×C4711yescharacteristic, complemented
430#476C22×C4711yescharacteristic
431#476C22×C4711yescharacteristic
432#476C22×C4711yescharacteristic, complemented
433#475—21no—
434#475C22×C4711yescharacteristic, complemented
435#474C22×C4711yescharacteristic
436#468—22no—
437#465—21no—
438#465—21no—
439#461C22×C4711yescharacteristic
440#461C22×C4711yescharacteristic, complemented
441#460—21no—
442#440—22no—
443#431C22×C4711yescharacteristic, complemented
444C2×C4⋊C8C22×C4711yescharacteristic, complemented
445C4×M16C22×C4711yescharacteristic, complemented
446#332C22×C4711yescharacteristic, complemented
447#332C22×C4711yescharacteristic, complemented
448#331C22×C4711yescharacteristic
449#331C22×C4711yescharacteristic
450Q8⋊C8C22×C4711yescharacteristic, complemented
451Q8⋊C8C22×C4711yescharacteristic, complemented
452D4⋊C8C22×C4711yescharacteristic
453D4⋊C8C22×C4711yescharacteristic
454D4⋊C8C22×C4711yescharacteristic
455D4⋊C8C22×C4711yescharacteristic
456D4⋊C8C22×C4711yescharacteristic, complemented
457D4⋊C8C22×C4711yescharacteristic, complemented
458C47#1873911yescharacteristic, direct product factor, Sylow
459C2×#41—21no—
460C2×#41—21no—
461C2×#41—21no—
462C2×#41—21no—
463C22×D4—21no—
464C22×D4—21no—
465C2×SD16—22no—
466C2×SD16—21no—
467C2×SD16—21no—
468C2×M16—21no—
469C22×C8—21no—
470C4⋊Q8D4×C4711yescharacteristic
471C4⋊Q8C23×C4711yescharacteristic
472C4⋊Q8C23×C4711yescharacteristic
473C4⋊Q8C23×C4711yescharacteristic
474#127—22no—
475#127—21no—
476#127D4×C4711yescharacteristic
477#127C23×C4711yescharacteristic
478#126—22no—
479#126—22no—
480#126—21no—
481#125—21no—
482#125D4×C4711yescharacteristic
483#124—22no—
484#124—21no—
485#124—21no—
486#124—21no—
487#124D4×C4711yescharacteristic
488#123—22no—
489#123—22no—
490#123—21no—
491#123—22no—
492C22⋊Q8—22no—
493C22⋊Q8—21no—
494C22⋊Q8—21no—
495C22⋊Q8—21no—
496C22⋊Q8—21no—
497C22⋊Q8D4×C4711yescharacteristic
498#121—22no—
499#121—22no—
500#121—22no—
501#121—22no—
502#121—22no—
503#121—21no—
504#121—22no—
505#121—21no—
506#121—21no—
507#121—21no—
508#121—21no—
509#121—21no—
510#121D4×C4711yescharacteristic
511#121D4×C4711yescharacteristic
512#121D4×C4711yescharacteristic
513#121D4×C4712yes—
514#120—22no—
515#120—22no—
516#120—22no—
517#120—22no—
518C4×Q8—21no—
519C4×Q8—21no—
520C4×Q8—21no—
521C4×Q8C23×C4711yescharacteristic
522C4×D4—22no—
523C4×D4—21no—
524C4×D4—21no—
525C4×D4—21no—
526C4×D4—21no—
527C4×D4D4×C4712yes—
528C4×D4C23×C4711yescharacteristic
529C4×D4C23×C4711yescharacteristic
530C4×D4C23×C4711yescharacteristic
531#117—21no—
532#117—21no—
533#117—21no—
534C2×C4⋊C4—21no—
535C2×C22⋊C4—22no—
536C2×C42C23×C4711yescharacteristic
537#107—22no—
538#107—21no—
539#107—21no—
540#106—21no—
541#106—21no—
542#106—21no—
543#106—21no—
544C4⋊C8—21no—
545C4⋊C8C23×C4711yescharacteristic
546C4⋊C8C23×C4711yescharacteristic
547C4⋊C8C23×C4711yescharacteristic
548C4⋊C8C23×C4711yescharacteristic
549#103—21no—
550#103—21no—
551#103—22no—
552#103—21no—
553#103—21no—
554#102—22no—
555#102—21no—
556#102—21no—
557#102—21no—
558#102—21no—
559C22⋊C8—21no—
560#97—21no—
561C4×C8—21no—
562C4×C8C23×C4711yescharacteristic
563C4×C8C23×C4711yescharacteristic
564C24—22no—
565#41—81no—
566#41—81no—
567#41—81no—
568#41—81no—
569#41—81no—
570#41—81no—
571#41—81no—
572#41—81no—
573C2×Q8—21no—
574C2×Q8—21no—
575C2×Q8—21no—
576C2×Q8—21no—
577C2×Q8C2×D4×C4711yescharacteristic
578C2×D4—22no—
579C2×D4—22no—
580C2×D4—22no—
581C2×D4—22no—
582C2×D4—22no—
583C2×D4—21no—
584C2×D4—21no—
585C2×D4—22no—
586C2×D4—21no—
587C2×D4—21no—
588C2×D4—21no—
589C2×D4—21no—
590C2×D4—21no—
591C2×D4—81no—
592C2×D4—81no—
593C2×D4—81no—
594C2×D4—81no—
595C2×D4C2×D4×C4711yescharacteristic
596C2×D4C2×D4×C4711yescharacteristic
597C2×D4C2×D4×C4711yescharacteristic
598C2×D4C2×D4×C4712yes—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—22no—
605C22×C4C2×D4×C4711yescharacteristic
606C22×C4C2×D4×C4711yescharacteristic
607C22×C4C2×D4×C4711yescharacteristic
608SD16—44no—
609SD16—81no—
610SD16—81no—
611M16—42no—
612C2×C8—21no—
613C2×C8—21no—
614C2×C8—21no—
615C2×C8—21no—
616C2×C8—21no—
617C2×C8—21no—
618C2×C8—81no—
619C4⋊C4—22no—
620C4⋊C4—22no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4—21no—
625C4⋊C4—21no—
626C4⋊C4—21no—
627C4⋊C4—21no—
628C4⋊C4—21no—
629C4⋊C4—21no—
630C4⋊C4—21no—
631C4⋊C4—41no—
632C4⋊C4—41no—
633C4⋊C4C2×D4×C4711yescharacteristic
634C4⋊C4C2×D4×C4711yescharacteristic
635C4⋊C4C2×D4×C4712yes—
636C4⋊C4C2×D4×C4711yescharacteristic
637C4⋊C4C2×D4×C4711yescharacteristic
638C22⋊C4—22no—
639C22⋊C4—22no—
640C22⋊C4—22no—
641C22⋊C4—22no—
642C22⋊C4—22no—
643C22⋊C4—21no—
644C22⋊C4—21no—
645C22⋊C4—21no—
646C22⋊C4—21no—
647C22⋊C4—21no—
648C22⋊C4—21no—
649C22⋊C4—22no—
650C22⋊C4—22no—
651C22⋊C4—21no—
652C22⋊C4—21no—
653C22⋊C4—21no—
654C22⋊C4—41no—
655C42—22no—
656C42—21no—
657C42—41no—
658C42C2×D4×C4711yescharacteristic
659C42C2×D4×C4711yescharacteristic
660C42C2×D4×C4711yescharacteristic
661C42C24×C4711yescharacteristic
662C23—21no—
663C23—21no—
664C23—22no—
665C23—21no—
666C23—82no—
667C23—82no—
668C23—82no—
669C23#120×C4711yescharacteristic
670Q8—21no—
671Q8—21no—
672Q8—42no—
673Q8—41no—
674Q8—41no—
675Q8—41no—
676Q8—41no—
677Q8—81no—
678D4—21no—
679D4—21no—
680D4—21no—
681D4—21no—
682D4—21no—
683D4—21no—
684D4—42no—
685D4—41no—
686D4—41no—
687D4—41no—
688D4—41no—
689D4—81no—
690D4—81no—
691D4—81no—
692D4—81no—
693D4—81no—
694D4—82no—
695D4—82no—
696D4—82no—
697D4—82no—
698D4—82no—
699D4—82no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—22no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—82no—
720C2×C4—82no—
721C2×C4—82no—
722C2×C4#120×C4711yescharacteristic
723C2×C4#120×C4711yescharacteristic
724C2×C4#120×C4711yescharacteristic
725C2×C4C22×D4×C4711yescharacteristic
726C2×C4C22×D4×C4711yescharacteristic
727C2×C4C22×D4×C4711yescharacteristic
728C8—22no—
729C8—41no—
730C8—41no—
731C8—41no—
732C8—41no—
733C8—41no—
734C22—21no—
735C22—21no—
736C22—21no—
737C22—41no—
738C22—41no—
739C22—42no—
740C22—41no—
741C22—41no—
742C22—41no—
743C22—42no—
744C22—41no—
745C22—42no—
746C22—41no—
747C22—41no—
748C22—41no—
749C22—164no—
750C22C2×#120×C4711yescharacteristic
751C4—21no—
752C4—21no—
753C4—21no—
754C4—21no—
755C4—41no—
756C4—41no—
757C4—41no—
758C4—41no—
759C4—42no—
760C4—41no—
761C4—81no—
762C4—81no—
763C4C47×#57611yescharacteristic
764C4C47×#57711yescharacteristic
765C4C47×#57711yescharacteristic
766C4C47×#57711yescharacteristic
767C2—41no—
768C2—81no—
769C2—81no—
770C2—82no—
771C2—81no—
772C2C47×#300911yescharacteristic
773C2C47×#301211yescharacteristic
774C2C47×#301811yescharacteristic
subgroupG/H
center, socleC22×C47C2×#120
commutator, Frattini, cosocleC42C24×C47
prime radicalC47×#3546C2
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
2. C47×#3246C2semidirect
3. C47×#3233C2semidirect
4. C47×#3182C2semidirect
5. C47×#1650C2semidirect
6. C47×#1647C2semidirect
7. C47×#1642C2semidirect
8. C47×#1639C2semidirect
9. C47×#1638C2semidirect
10. C47×#1635C2semidirect
11. C47×#1631C2semidirect
12. C47×#1629C2semidirect
13. C47×#1540C2semidirect
14. C47×#1484C2semidirect
15. C47×#1483C2semidirect
30. C47×#533C22semidirect
34. C47×#500C22semidirect
38. C47×#487C22semidirect
42. C47×#477C22semidirect
45. C47×#476C22semidirect
47. C47×#475C22semidirect
53. C47×#461C22semidirect
56. C47×#431C22semidirect
57. C2×C4⋊C8×C47C22semidirect
58. C4×M16×C47C22semidirect
59. C47×#332C22semidirect
60. C47×#332C22semidirect
63. C47×Q8⋊C8C22semidirect
64. C47×Q8⋊C8C22semidirect
69. C47×D4⋊C8C22semidirect
70. C47×D4⋊C8C22semidirect
346. #18739C47direct (N × H)
381. #3246C2×C47semidirect
382. #3233C2×C47semidirect
383. #3182C2×C47semidirect
384. #1650C2×C47semidirect
385. #1647C2×C47semidirect
386. #1642C2×C47semidirect
387. #1639C2×C47semidirect
388. #1638C2×C47semidirect
389. #1635C2×C47semidirect
390. #1631C2×C47semidirect
391. #1629C2×C47semidirect
392. #1540C2×C47semidirect
393. #1484C2×C47semidirect
394. #1483C2×C47semidirect
417. #533C22×C47semidirect
421. #500C22×C47semidirect
425. #487C22×C47semidirect
429. #477C22×C47semidirect
432. #476C22×C47semidirect
434. #475C22×C47semidirect
440. #461C22×C47semidirect
443. #431C22×C47semidirect
444. C2×C4⋊C8C22×C47semidirect
445. C4×M16C22×C47semidirect
446. #332C22×C47semidirect
447. #332C22×C47semidirect
450. Q8⋊C8C22×C47semidirect
451. Q8⋊C8C22×C47semidirect
456. D4⋊C8C22×C47semidirect
457. D4⋊C8C22×C47semidirect
458. C47#18739direct (N × H)

Maximal subgroups

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

subgroupindex
C47×#35462
C47×#32462
C47×#32332
C47×#31822
C47×#16502
C47×#16472
C47×#16422
C47×#16392
C47×#16382
C47×#16352
C47×#16312
C47×#16292
C47×#15402
C47×#14842
C47×#14832
#1873947