Finite Group Databasebeta

← C47×#18463 #26058161

Subgroups — C47×#18463 #26058161

Order 12032.

930 conjugacy classes of subgroups.

The subgroup lattice has 786 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3560C211yesmaximal, characteristic
2C47×#3218C211yesmaximal, characteristic, complemented
3C47×#3206C211yesmaximal, characteristic, complemented
4C47×#2821C211yesmaximal, characteristic, complemented
5C47×#1606C212yesmaximal, complemented
6C47×#1604C212yesmaximal, complemented
7C47×#1603C212yesmaximal, complemented
8C47×#1601C212yesmaximal, complemented
9C47×#1521C211yesmaximal, characteristic, complemented
10C47×#1514C211yesmaximal, characteristic, complemented
11C47×#1473C211yesmaximal, characteristic, complemented
12C47×#563—21no—
13C47×#560—21no—
14C47×#553—21no—
15C47×#553—21no—
16C47×#551—21no—
17C47×#547—21no—
18C47×#546—21no—
19C47×#546—21no—
20C47×#542—21no—
21C47×#539—21no—
22C47×#539C2211yescharacteristic
23C47×#538—21no—
24C47×#538—21no—
25C47×#538C2211yescharacteristic
26C47×#537C2211yescharacteristic
27C47×#534C2211yescharacteristic
28C47×#532C2211yescharacteristic
29C2×C4⋊Q8×C47C2211yescharacteristic, complemented
30C47×#529C2211yescharacteristic
31C2×#126×C47C2211yescharacteristic
32C47×#497—21no—
33C47×#492—21no—
34C47×#491—21no—
35C47×#487—21no—
36C47×#462—21no—
37C47×#461—21no—
38C47×#461—21no—
39C47×#461—21no—
40C47×#451C2212yescomplemented
41C47×#448C2212yes—
42C47×#448C2212yes—
43C47×#448C2212yescomplemented
44C47×#432C2211yescharacteristic, complemented
45C47×#431C2211yescharacteristic, complemented
46C47×#400—21no—
47C47×#399—21no—
48C47×#398—21no—
49C47×#397—21no—
50C47×#395C2212yescomplemented
51C47×#393C2212yes—
52C47×#383C2211yescharacteristic, complemented
53C47×#328C2212yescomplemented
54C47×#327C2212yes—
55C47×#327C2212yes—
56C47×#327C2212yescomplemented
57C47×#324C2212yescomplemented
58C47×#323C2212yes—
59C2×#41×C47—21no—
60C2×#41×C47—21no—
61C22×Q8×C47C2312yes—
62C22×D4×C47—21no—
63C2×Q16×C47—22no—
64C2×SD16×C47—22no—
65C2×SD16×C47—22no—
66C2×SD16×C47—22no—
67C4⋊Q8×C47—21no—
68C4⋊Q8×C47—21no—
69C4⋊Q8×C47—21no—
70C4⋊Q8×C47—21no—
71C4⋊Q8×C47—21no—
72C4⋊Q8×C47D411yescharacteristic
73#127×C47D411yescharacteristic
74#126×C47—21no—
75#126×C47—21no—
76#126×C47—21no—
77#126×C47—21no—
78#126×C47—21no—
79#126×C47—21no—
80#126×C47—21no—
81#126×C47—21no—
82#126×C47—21no—
83#125×C47—21no—
84#125×C47—21no—
85#125×C47D411yescharacteristic
86#124×C47—21no—
87#124×C47—21no—
88#124×C47—21no—
89#124×C47—21no—
90#124×C47D411yescharacteristic
91#123×C47—21no—
92#123×C47—21no—
93#123×C47—21no—
94#123×C47—21no—
95#123×C47—21no—
96#123×C47—21no—
97#123×C47—21no—
98#123×C47—21no—
99#123×C47—21no—
100#123×C47—21no—
101#123×C47—21no—
102#123×C47—21no—
103C22⋊Q8×C47—21no—
104C22⋊Q8×C47—21no—
105C22⋊Q8×C47—21no—
106C22⋊Q8×C47—21no—
107C22⋊Q8×C47—21no—
108C22⋊Q8×C47—21no—
109C22⋊Q8×C47—21no—
110C22⋊Q8×C47C2311yescharacteristic
111#121×C47—21no—
112#121×C47—21no—
113#121×C47—21no—
114#121×C47—21no—
115#121×C47—21no—
116#121×C47—21no—
117#121×C47—21no—
118#121×C47—21no—
119#121×C47—21no—
120#121×C47—21no—
121#121×C47—21no—
122#121×C47—21no—
123#121×C47C2311yescharacteristic
124#121×C47C2311yescharacteristic
125#121×C47C2311yescharacteristic
126#120×C47—21no—
127#120×C47—21no—
128#120×C47—21no—
129#120×C47—21no—
130#120×C47—21no—
131C4×Q8×C47D411yescharacteristic
132C4×D4×C47—21no—
133C4×D4×C47—21no—
134C4×D4×C47—21no—
135C4×D4×C47—21no—
136C4×D4×C47—21no—
137C4×D4×C47—21no—
138C4×D4×C47—21no—
139C4×D4×C47—21no—
140C4×D4×C47D411yescharacteristic
141C4×D4×C47D411yescharacteristic
142C4×D4×C47D411yescharacteristic
143#117×C47—21no—
144#117×C47—21no—
145C2×C4⋊C4×C47—21no—
146C2×C4⋊C4×C47—21no—
147C2×C4⋊C4×C47—21no—
148C2×C4⋊C4×C47—22no—
149C2×C4⋊C4×C47D411yescharacteristic
150C2×C4⋊C4×C47D411yescharacteristic
151C2×C4⋊C4×C47C2311yescharacteristic
152C2×C22⋊C4×C47—21no—
153C2×C22⋊C4×C47—21no—
154C2×C22⋊C4×C47—22no—
155C2×C22⋊C4×C47D411yescharacteristic
156C2×C22⋊C4×C47D411yescharacteristic
157C2×C22⋊C4×C47C2311yescharacteristic
158C2×C42×C47C2311yescharacteristic
159C4⋊C8×C47—21no—
160C4⋊C8×C47—21no—
161#103×C47—22no—
162#103×C47—22no—
163#103×C47—22no—
164#103×C47—22no—
165C22⋊C8×C47C2312yes—
166C22⋊C8×C47C2312yes—
167#97×C47—21no—
168C4×C8×C47—21no—
169#95×C47—21no—
170#95×C47—21no—
171#95×C47—22no—
172#95×C47—22no—
173#95×C47C2312yes—
174C24×C47—21no—
175C24×C47C2×D411yescharacteristic
176#41×C47—82no—
177#41×C47—82no—
178C2×Q8×C47—21no—
179C2×Q8×C47—21no—
180C2×Q8×C47—22no—
181C2×Q8×C47—22no—
182C2×Q8×C47—82no—
183C2×Q8×C47C2×D411yescharacteristic
184C2×D4×C47—21no—
185C2×D4×C47—21no—
186C2×D4×C47—21no—
187C2×D4×C47—21no—
188C2×D4×C47—21no—
189C2×D4×C47—21no—
190C2×D4×C47—21no—
191C2×D4×C47—21no—
192C2×D4×C47—21no—
193C2×D4×C47—21no—
194C2×D4×C47—21no—
195C2×D4×C47—21no—
196C2×D4×C47—82no—
197C2×D4×C47C2×D411yescharacteristic
198C2×D4×C47C2×D411yescharacteristic
199C2×D4×C47C2×D411yescharacteristic
200C22×C4×C47—21no—
201C22×C4×C47—21no—
202C22×C4×C47—21no—
203C22×C4×C47—21no—
204C22×C4×C47—21no—
205C22×C4×C47—21no—
206C22×C4×C47—21no—
207C22×C4×C47—21no—
208C22×C4×C47—22no—
209C22×C4×C47—22no—
210C22×C4×C47C2×D411yescharacteristic
211C22×C4×C47C2×D411yescharacteristic
212C22×C4×C47C2×D411yescharacteristic
213C22×C4×C47C2×D411yescharacteristic
214C22×C4×C47C2×D411yescharacteristic
215C22×C4×C47C2411yescharacteristic
216Q16×C47—82no—
217SD16×C47—82no—
218SD16×C47—82no—
219SD16×C47—82no—
220C2×C8×C47—22no—
221C2×C8×C47—22no—
222C4⋊C4×C47—21no—
223C4⋊C4×C47—21no—
224C4⋊C4×C47—21no—
225C4⋊C4×C47—21no—
226C4⋊C4×C47—21no—
227C4⋊C4×C47—21no—
228C4⋊C4×C47—21no—
229C4⋊C4×C47—21no—
230C4⋊C4×C47—21no—
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—41no—
240C4⋊C4×C47—41no—
241C4⋊C4×C47—41no—
242C4⋊C4×C47—41no—
243C4⋊C4×C47—82no—
244C4⋊C4×C47C2×D411yescharacteristic
245C4⋊C4×C47C2×D411yescharacteristic
246C4⋊C4×C47C2×D411yescharacteristic
247C4⋊C4×C47C2×D411yescharacteristic
248C22⋊C4×C47—21no—
249C22⋊C4×C47—21no—
250C22⋊C4×C47—21no—
251C22⋊C4×C47—21no—
252C22⋊C4×C47—21no—
253C22⋊C4×C47—21no—
254C22⋊C4×C47—21no—
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—21no—
262C22⋊C4×C47—21no—
263C22⋊C4×C47—21no—
264C22⋊C4×C47—21no—
265C22⋊C4×C47—21no—
266C22⋊C4×C47—21no—
267C22⋊C4×C47—21no—
268C22⋊C4×C47—21no—
269C22⋊C4×C47—21no—
270C22⋊C4×C47—21no—
271C22⋊C4×C47—21no—
272C22⋊C4×C47—21no—
273C22⋊C4×C47—82no—
274C42×C47—21no—
275C42×C47—21no—
276C42×C47—21no—
277C42×C47C2×D411yescharacteristic
278C42×C47C2×D411yescharacteristic
279C42×C47C2×D411yescharacteristic
280C42×C47C2×D411yescharacteristic
281C23×C47—21no—
282C23×C47—21no—
283C23×C47—21no—
284C23×C47—21no—
285C23×C47—22no—
286C23×C47—41no—
287C23×C47—41no—
288C23×C47—81no—
289C23×C47—81no—
290C23×C47—81no—
291C23×C47C22×D411yescharacteristic
292Q8×C47—41no—
293Q8×C47—42no—
294Q8×C47—42no—
295Q8×C47—42no—
296Q8×C47—42no—
297Q8×C47—81no—
298Q8×C47—81no—
299D4×C47—41no—
300D4×C47—41no—
301D4×C47—41no—
302D4×C47—42no—
303D4×C47—42no—
304D4×C47—42no—
305D4×C47—81no—
306D4×C47—81no—
307D4×C47—81no—
308D4×C47—81no—
309D4×C47—81no—
310D4×C47—81no—
311D4×C47—81no—
312D4×C47—81no—
313D4×C47—81no—
314C2×C4×C47—22no—
315C2×C4×C47—21no—
316C2×C4×C47—21no—
317C2×C4×C47—21no—
318C2×C4×C47—21no—
319C2×C4×C47—21no—
320C2×C4×C47—21no—
321C2×C4×C47—21no—
322C2×C4×C47—21no—
323C2×C4×C47—22no—
324C2×C4×C47—41no—
325C2×C4×C47—41no—
326C2×C4×C47—41no—
327C2×C4×C47—41no—
328C2×C4×C47—42no—
329C2×C4×C47—42no—
330C2×C4×C47—42no—
331C2×C4×C47—42no—
332C2×C4×C47—42no—
333C2×C4×C47—42no—
334C2×C4×C47—81no—
335C2×C4×C47—81no—
336C2×C4×C47—81no—
337C2×C4×C47—81no—
338C2×C4×C47—81no—
339C2×C4×C47—81no—
340C2×C4×C47—81no—
341C2×C4×C47—81no—
342C2×C4×C47#12011yescharacteristic
343C2×C4×C47#12011yescharacteristic
344C2×C4×C47#12011yescharacteristic
345C2×C4×C47#12011yescharacteristic
346C2×C4×C47C22×D411yescharacteristic
347C2×C4×C47C22×D411yescharacteristic
348C8×C47—42no—
349C8×C47—42no—
350#18463C4711yesmaximal, characteristic, direct product factor, Sylow
351C22×C47—21no—
352C22×C47—21no—
353C22×C47—41no—
354C22×C47—41no—
355C22×C47—41no—
356C22×C47—41no—
357C22×C47—41no—
358C22×C47—41no—
359C22×C47—41no—
360C22×C47—41no—
361C22×C47—41no—
362C22×C47—41no—
363C22×C47—41no—
364C22×C47—41no—
365C22×C47—82no—
366C22×C47—162no—
367C22×C47C2×#12011yescharacteristic
368C22×C47#57712yes—
369C4×C47—21no—
370C4×C47—21no—
371C4×C47—21no—
372C4×C47—21no—
373C4×C47—21no—
374C4×C47—21no—
375C4×C47—41no—
376C4×C47—41no—
377C4×C47—41no—
378C4×C47—41no—
379C4×C47—41no—
380C4×C47—41no—
381C4×C47—41no—
382C4×C47—41no—
383C4×C47—82no—
384C4×C47—82no—
385#3560C2×C4711yescharacteristic
386#3218C2×C4711yescharacteristic, complemented
387#3206C2×C4711yescharacteristic, complemented
388#2821C2×C4711yescharacteristic, complemented
389#1606C2×C4712yescomplemented
390#1604C2×C4712yescomplemented
391#1603C2×C4712yescomplemented
392#1601C2×C4712yescomplemented
393#1521C2×C4711yescharacteristic, complemented
394#1514C2×C4711yescharacteristic, complemented
395#1473C2×C4711yescharacteristic, complemented
396C2×C47—22no—
397C2×C47—81no—
398C2×C47—81no—
399C2×C47—81no—
400C2×C47—81no—
401C2×C47#300911yescharacteristic
402C2×C47#302211yescharacteristic
403C2×C47#302711yescharacteristic
404#563—21no—
405#560—21no—
406#553—21no—
407#553—21no—
408#551—21no—
409#547—21no—
410#546—21no—
411#546—21no—
412#542—21no—
413#539—21no—
414#539C22×C4711yescharacteristic
415#538—21no—
416#538—21no—
417#538C22×C4711yescharacteristic
418#537C22×C4711yescharacteristic
419#534C22×C4711yescharacteristic
420#532C22×C4711yescharacteristic
421C2×C4⋊Q8C22×C4711yescharacteristic, complemented
422#529C22×C4711yescharacteristic
423C2×#126C22×C4711yescharacteristic
424#497—21no—
425#492—21no—
426#491—21no—
427#487—21no—
428#462—21no—
429#461—21no—
430#461—21no—
431#461—21no—
432#451C22×C4712yescomplemented
433#448C22×C4712yes—
434#448C22×C4712yes—
435#448C22×C4712yescomplemented
436#432C22×C4711yescharacteristic, complemented
437#431C22×C4711yescharacteristic, complemented
438#400—21no—
439#399—21no—
440#398—21no—
441#397—21no—
442#395C22×C4712yescomplemented
443#393C22×C4712yes—
444#383C22×C4711yescharacteristic, complemented
445#328C22×C4712yescomplemented
446#327C22×C4712yes—
447#327C22×C4712yes—
448#327C22×C4712yescomplemented
449#324C22×C4712yescomplemented
450#323C22×C4712yes—
451C47#1846311yescharacteristic, direct product factor, Sylow
452C2×#41—21no—
453C2×#41—21no—
454C22×Q8C23×C4712yes—
455C22×D4—21no—
456C2×Q16—22no—
457C2×SD16—22no—
458C2×SD16—22no—
459C2×SD16—22no—
460C4⋊Q8—21no—
461C4⋊Q8—21no—
462C4⋊Q8—21no—
463C4⋊Q8—21no—
464C4⋊Q8—21no—
465C4⋊Q8D4×C4711yescharacteristic
466#127D4×C4711yescharacteristic
467#126—21no—
468#126—21no—
469#126—21no—
470#126—21no—
471#126—21no—
472#126—21no—
473#126—21no—
474#126—21no—
475#126—21no—
476#125—21no—
477#125—21no—
478#125D4×C4711yescharacteristic
479#124—21no—
480#124—21no—
481#124—21no—
482#124—21no—
483#124D4×C4711yescharacteristic
484#123—21no—
485#123—21no—
486#123—21no—
487#123—21no—
488#123—21no—
489#123—21no—
490#123—21no—
491#123—21no—
492#123—21no—
493#123—21no—
494#123—21no—
495#123—21no—
496C22⋊Q8—21no—
497C22⋊Q8—21no—
498C22⋊Q8—21no—
499C22⋊Q8—21no—
500C22⋊Q8—21no—
501C22⋊Q8—21no—
502C22⋊Q8—21no—
503C22⋊Q8C23×C4711yescharacteristic
504#121—21no—
505#121—21no—
506#121—21no—
507#121—21no—
508#121—21no—
509#121—21no—
510#121—21no—
511#121—21no—
512#121—21no—
513#121—21no—
514#121—21no—
515#121—21no—
516#121C23×C4711yescharacteristic
517#121C23×C4711yescharacteristic
518#121C23×C4711yescharacteristic
519#120—21no—
520#120—21no—
521#120—21no—
522#120—21no—
523#120—21no—
524C4×Q8D4×C4711yescharacteristic
525C4×D4—21no—
526C4×D4—21no—
527C4×D4—21no—
528C4×D4—21no—
529C4×D4—21no—
530C4×D4—21no—
531C4×D4—21no—
532C4×D4—21no—
533C4×D4D4×C4711yescharacteristic
534C4×D4D4×C4711yescharacteristic
535C4×D4D4×C4711yescharacteristic
536#117—21no—
537#117—21no—
538C2×C4⋊C4—21no—
539C2×C4⋊C4—21no—
540C2×C4⋊C4—21no—
541C2×C4⋊C4—22no—
542C2×C4⋊C4D4×C4711yescharacteristic
543C2×C4⋊C4D4×C4711yescharacteristic
544C2×C4⋊C4C23×C4711yescharacteristic
545C2×C22⋊C4—21no—
546C2×C22⋊C4—21no—
547C2×C22⋊C4—22no—
548C2×C22⋊C4D4×C4711yescharacteristic
549C2×C22⋊C4D4×C4711yescharacteristic
550C2×C22⋊C4C23×C4711yescharacteristic
551C2×C42C23×C4711yescharacteristic
552C4⋊C8—21no—
553C4⋊C8—21no—
554#103—22no—
555#103—22no—
556#103—22no—
557#103—22no—
558C22⋊C8C23×C4712yes—
559C22⋊C8C23×C4712yes—
560#97—21no—
561C4×C8—21no—
562#95—21no—
563#95—21no—
564#95—22no—
565#95—22no—
566#95C23×C4712yes—
567C24—21no—
568C24C2×D4×C4711yescharacteristic
569#41—82no—
570#41—82no—
571C2×Q8—21no—
572C2×Q8—21no—
573C2×Q8—22no—
574C2×Q8—22no—
575C2×Q8—82no—
576C2×Q8C2×D4×C4711yescharacteristic
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—21no—
580C2×D4—21no—
581C2×D4—21no—
582C2×D4—21no—
583C2×D4—21no—
584C2×D4—21no—
585C2×D4—21no—
586C2×D4—21no—
587C2×D4—21no—
588C2×D4—21no—
589C2×D4—82no—
590C2×D4C2×D4×C4711yescharacteristic
591C2×D4C2×D4×C4711yescharacteristic
592C2×D4C2×D4×C4711yescharacteristic
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—22no—
602C22×C4—22no—
603C22×C4C2×D4×C4711yescharacteristic
604C22×C4C2×D4×C4711yescharacteristic
605C22×C4C2×D4×C4711yescharacteristic
606C22×C4C2×D4×C4711yescharacteristic
607C22×C4C2×D4×C4711yescharacteristic
608C22×C4C24×C4711yescharacteristic
609Q16—82no—
610SD16—82no—
611SD16—82no—
612SD16—82no—
613C2×C8—22no—
614C2×C8—22no—
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⋊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—21no—
632C4⋊C4—41no—
633C4⋊C4—41no—
634C4⋊C4—41no—
635C4⋊C4—41no—
636C4⋊C4—82no—
637C4⋊C4C2×D4×C4711yescharacteristic
638C4⋊C4C2×D4×C4711yescharacteristic
639C4⋊C4C2×D4×C4711yescharacteristic
640C4⋊C4C2×D4×C4711yescharacteristic
641C22⋊C4—21no—
642C22⋊C4—21no—
643C22⋊C4—21no—
644C22⋊C4—21no—
645C22⋊C4—21no—
646C22⋊C4—21no—
647C22⋊C4—21no—
648C22⋊C4—21no—
649C22⋊C4—21no—
650C22⋊C4—21no—
651C22⋊C4—21no—
652C22⋊C4—21no—
653C22⋊C4—21no—
654C22⋊C4—21no—
655C22⋊C4—21no—
656C22⋊C4—21no—
657C22⋊C4—21no—
658C22⋊C4—21no—
659C22⋊C4—21no—
660C22⋊C4—21no—
661C22⋊C4—21no—
662C22⋊C4—21no—
663C22⋊C4—21no—
664C22⋊C4—21no—
665C22⋊C4—21no—
666C22⋊C4—82no—
667C42—21no—
668C42—21no—
669C42—21no—
670C42C2×D4×C4711yescharacteristic
671C42C2×D4×C4711yescharacteristic
672C42C2×D4×C4711yescharacteristic
673C42C2×D4×C4711yescharacteristic
674C23—21no—
675C23—21no—
676C23—21no—
677C23—21no—
678C23—22no—
679C23—41no—
680C23—41no—
681C23—81no—
682C23—81no—
683C23—81no—
684C23C22×D4×C4711yescharacteristic
685Q8—41no—
686Q8—42no—
687Q8—42no—
688Q8—42no—
689Q8—42no—
690Q8—81no—
691Q8—81no—
692D4—41no—
693D4—41no—
694D4—41no—
695D4—42no—
696D4—42no—
697D4—42no—
698D4—81no—
699D4—81no—
700D4—81no—
701D4—81no—
702D4—81no—
703D4—81no—
704D4—81no—
705D4—81no—
706D4—81no—
707C2×C4—22no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—22no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—81no—
728C2×C4—81no—
729C2×C4—81no—
730C2×C4—81no—
731C2×C4—81no—
732C2×C4—81no—
733C2×C4—81no—
734C2×C4—81no—
735C2×C4#120×C4711yescharacteristic
736C2×C4#120×C4711yescharacteristic
737C2×C4#120×C4711yescharacteristic
738C2×C4#120×C4711yescharacteristic
739C2×C4C22×D4×C4711yescharacteristic
740C2×C4C22×D4×C4711yescharacteristic
741C8—42no—
742C8—42no—
743C22—21no—
744C22—21no—
745C22—41no—
746C22—41no—
747C22—41no—
748C22—41no—
749C22—41no—
750C22—41no—
751C22—41no—
752C22—41no—
753C22—41no—
754C22—41no—
755C22—41no—
756C22—41no—
757C22—82no—
758C22—162no—
759C22C2×#120×C4711yescharacteristic
760C22C47×#57712yes—
761C4—21no—
762C4—21no—
763C4—21no—
764C4—21no—
765C4—21no—
766C4—21no—
767C4—41no—
768C4—41no—
769C4—41no—
770C4—41no—
771C4—41no—
772C4—41no—
773C4—41no—
774C4—41no—
775C4—82no—
776C4—82no—
777C2—22no—
778C2—81no—
779C2—81no—
780C2—81no—
781C2—81no—
782C2C47×#300911yescharacteristic
783C2C47×#302211yescharacteristic
784C2C47×#302711yescharacteristic
subgroupG/H
center, socleC22×C47C2×#120
commutator, Frattini, cosocleC22×C4C24×C47
prime radicalC47×#3560C2
LCSG ▷ C22×C4 ▷ 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×#3218C2semidirect
3. C47×#3206C2semidirect
4. C47×#2821C2semidirect
5. C47×#1606C2semidirect
6. C47×#1604C2semidirect
7. C47×#1603C2semidirect
8. C47×#1601C2semidirect
9. C47×#1521C2semidirect
10. C47×#1514C2semidirect
11. C47×#1473C2semidirect
29. C2×C4⋊Q8×C47C22semidirect
40. C47×#451C22semidirect
43. C47×#448C22semidirect
44. C47×#432C22semidirect
45. C47×#431C22semidirect
50. C47×#395C22semidirect
52. C47×#383C22semidirect
53. C47×#328C22semidirect
56. C47×#327C22semidirect
57. C47×#324C22semidirect
350. #18463C47direct (N × H)
386. #3218C2×C47semidirect
387. #3206C2×C47semidirect
388. #2821C2×C47semidirect
389. #1606C2×C47semidirect
390. #1604C2×C47semidirect
391. #1603C2×C47semidirect
392. #1601C2×C47semidirect
393. #1521C2×C47semidirect
394. #1514C2×C47semidirect
395. #1473C2×C47semidirect
421. C2×C4⋊Q8C22×C47semidirect
432. #451C22×C47semidirect
435. #448C22×C47semidirect
436. #432C22×C47semidirect
437. #431C22×C47semidirect
442. #395C22×C47semidirect
444. #383C22×C47semidirect
445. #328C22×C47semidirect
448. #327C22×C47semidirect
449. #324C22×C47semidirect
451. C47#18463direct (N × H)

Maximal subgroups

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

subgroupindex
C47×#35602
C47×#32182
C47×#32062
C47×#28212
C47×#16062
C47×#16042
C47×#16032
C47×#16012
C47×#15212
C47×#15142
C47×#14732
#1846347