Finite Group Databasebeta

← C47×#25185 #26064883

Subgroups — C47×#25185 #26064883

Order 12032.

1016 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C47×#472C211yesmaximal, characteristic, complemented
2C47×#3041C211yesmaximal, characteristic, complemented
3C2×C47×#454C211yesmaximal, characteristic, complemented
4C47×#3010C211yesmaximal, characteristic, complemented
5C47×#2946C211yesmaximal, characteristic, complemented
6C47×#2898C211yesmaximal, characteristic, complemented
7C47×#2064C211yesmaximal, characteristic, complemented
8C47×#2051C211yesmaximal, characteristic, complemented
9C47×#2037C211yesmaximal, characteristic, complemented
10C47×#2012C211yesmaximal, characteristic, complemented
11C47×#1977C211yesmaximal, characteristic, complemented
12C47×#1929C211yesmaximal, characteristic, complemented
13C47×#1885C211yesmaximal, characteristic, complemented
14C47×#1883C211yesmaximal, characteristic, complemented
15C47×#1866C211yesmaximal, characteristic, complemented
16C2×2−1+4×C47C2211yescharacteristic
17C2×AGL(1,ℤ/8)×C47C2211yescharacteristic
18C2×AGL(1,ℤ/8)×C47C2211yescharacteristic
19C2×AGL(1,ℤ/8)×C47C2211yescharacteristic
20C22×SD16×C47C2211yescharacteristic
21C22×D8×C47C2211yescharacteristic
22C2×#131×C47C2211yescharacteristic
23C47×#535C2211yescharacteristic
24C2×#124×C47C2211yescharacteristic
25C47×#520C2211yescharacteristic
26C47×#518C2211yescharacteristic
27C47×#472—24no—
28C47×#463—21no—
29C47×#463—21no—
30C47×#459—21no—
31C47×#459—21no—
32C47×#454—24no—
33C47×#449—21no—
34C47×#449—21no—
35C47×#448—21no—
36C47×#448—21no—
37C47×#442—21no—
38C47×#440—21no—
39C4×SD16×C47—21no—
40C4×D8×C47—21no—
41C2×#108×C47C2211yescharacteristic
42C2×#108×C47C2211yescharacteristic
43C47×#428C2211yescharacteristic
44C47×#424C2211yescharacteristic
45C2×#104×C47C2211yescharacteristic
46C2×#104×C47C2211yescharacteristic
47C47×#419—21no—
48C47×#419C2211yescharacteristic
49C47×#419C2211yescharacteristic
50C47×#418C2211yescharacteristic
51C47×#417—21no—
52C47×#417C2211yescharacteristic
53C47×#416—21no—
54C47×#416C2211yescharacteristic
55C47×#416C2211yescharacteristic
56C2×#103×C47—21no—
57C2×#103×C47C2211yescharacteristic
58C2×#102×C47C2211yescharacteristic
59C2×#101×C47C2211yescharacteristic
60C2×#100×C47C2211yescharacteristic
61C2×#100×C47C2211yescharacteristic
62C47×#408C2211yescharacteristic
63C47×#405C2211yescharacteristic
64C47×#390C2211yescharacteristic
65C47×#343C2211yescharacteristic
66C47×#339C2211yescharacteristic
67C47×#339C2211yescharacteristic
68C47×#336C2211yescharacteristic
692−1+4×C47—22no—
702−1+4×C47—22no—
712−1+4×C47—22no—
722−1+4×C47—41no—
73C2×#41×C47—21no—
74C2×#41×C47—21no—
75C2×#41×C47—41no—
76C2×#41×C47C2311yescharacteristic
77C2×#41×C47C2311yescharacteristic
78C22×Q8×C47—21no—
79C22×Q8×C47—21no—
80C22×Q8×C47C2311yescharacteristic
81C22×D4×C47C2311yescharacteristic
82C22×D4×C47C2311yescharacteristic
83AGL(1,ℤ/8)×C47—22no—
84AGL(1,ℤ/8)×C47—22no—
85AGL(1,ℤ/8)×C47—22no—
86AGL(1,ℤ/8)×C47—22no—
87AGL(1,ℤ/8)×C47—41no—
88AGL(1,ℤ/8)×C47D414yescomplemented
89C2×SD16×C47—21no—
90C2×SD16×C47—21no—
91C2×SD16×C47—21no—
92C2×SD16×C47—22no—
93C2×SD16×C47—21no—
94C2×SD16×C47—21no—
95C2×SD16×C47—41no—
96C2×D8×C47—21no—
97C2×D8×C47—21no—
98C2×D8×C47—21no—
99C2×D8×C47—22no—
100C2×D8×C47—21no—
101C2×D8×C47—21no—
102C2×D8×C47—41no—
103#131×C47—22no—
104#131×C47—41no—
105C2×M16×C47—21no—
106C2×M16×C47C2311yescharacteristic
107C2×M16×C47C2311yescharacteristic
108C2×M16×C47C2311yescharacteristic
109C2×M16×C47C2311yescharacteristic
110C22×C8×C47—21no—
111C22×C8×C47C2311yescharacteristic
112C22×C8×C47C2311yescharacteristic
113#127×C47—21no—
114#124×C47—21no—
115#124×C47—22no—
116#124×C47—22no—
117#121×C47—21no—
118#121×C47—21no—
119#120×C47—41no—
120C4×Q8×C47—21no—
121C4×D4×C47—21no—
122C4×D4×C47—21no—
123C4×D4×C47—21no—
124C4×D4×C47—21no—
125C4×D4×C47—21no—
126C4×D4×C47—41no—
127#117×C47—21no—
128#117×C47C2311yescharacteristic
129#117×C47C2311yescharacteristic
130C2×C4⋊C4×C47—21no—
131C2×C4⋊C4×C47C2311yescharacteristic
132C2×C22⋊C4×C47—41no—
133C2×C22⋊C4×C47—41no—
134C2×C22⋊C4×C47—41no—
135C2×C42×C47C2311yescharacteristic
136#108×C47—22no—
137#108×C47—41no—
138#107×C47—21no—
139#106×C47—21no—
140C4⋊C8×C47—21no—
141C4⋊C8×C47—21no—
142#104×C47—22no—
143#104×C47—22no—
144#103×C47—21no—
145#103×C47—21no—
146#103×C47—21no—
147#103×C47—21no—
148#103×C47—21no—
149#103×C47—21no—
150#103×C47—21no—
151#103×C47D411yescharacteristic
152#103×C47D411yescharacteristic
153#103×C47D411yescharacteristic
154#103×C47D411yescharacteristic
155#102×C47—21no—
156#102×C47—21no—
157#102×C47—21no—
158#102×C47—21no—
159#102×C47—21no—
160#102×C47D411yescharacteristic
161#102×C47D411yescharacteristic
162#102×C47D411yescharacteristic
163#102×C47D411yescharacteristic
164#101×C47—22no—
165#100×C47—22no—
166#100×C47—22no—
167C22⋊C8×C47—21no—
168C22⋊C8×C47—21no—
169#97×C47—21no—
170C4×C8×C47—21no—
171C24×C47—21no—
172C24×C47—21no—
173#41×C47—21no—
174#41×C47—21no—
175#41×C47—24no—
176#41×C47—21no—
177#41×C47—21no—
178#41×C47—21no—
179#41×C47—21no—
180#41×C47—42no—
181#41×C47—44no—
182#41×C47—42no—
183#41×C47—44no—
184#41×C47—42no—
185#41×C47C2×D412yes—
186#41×C47#4112yes—
187C2×Q8×C47—21no—
188C2×Q8×C47—24no—
189C2×Q8×C47—21no—
190C2×Q8×C47—21no—
191C2×Q8×C47—21no—
192C2×Q8×C47—21no—
193C2×Q8×C47—41no—
194C2×Q8×C47—42no—
195C2×Q8×C47—42no—
196C2×Q8×C47—42no—
197C2×Q8×C47C2×D411yescharacteristic
198C2×Q8×C47C2×D411yescharacteristic
199C2×Q8×C47#4112yes—
200C2×D4×C47—21no—
201C2×D4×C47—21no—
202C2×D4×C47—21no—
203C2×D4×C47—21no—
204C2×D4×C47—21no—
205C2×D4×C47—21no—
206C2×D4×C47—21no—
207C2×D4×C47—21no—
208C2×D4×C47—21no—
209C2×D4×C47—21no—
210C2×D4×C47—21no—
211C2×D4×C47—21no—
212C2×D4×C47—21no—
213C2×D4×C47—41no—
214C2×D4×C47—41no—
215C2×D4×C47—41no—
216C2×D4×C47C2×D412yes—
217C2×D4×C47C2×D411yescharacteristic
218C2×D4×C47C2×D411yescharacteristic
219C22×C4×C47—21no—
220C22×C4×C47—21no—
221C22×C4×C47—21no—
222C22×C4×C47—21no—
223C22×C4×C47—21no—
224C22×C4×C47—41no—
225C22×C4×C47—41no—
226C22×C4×C47—41no—
227C22×C4×C47—41no—
228C22×C4×C47—41no—
229C22×C4×C47C2411yescharacteristic
230SD16×C47—24no—
231SD16×C47—42no—
232SD16×C47—42no—
233SD16×C47—42no—
234SD16×C47—42no—
235D8×C47—24no—
236D8×C47—42no—
237D8×C47—42no—
238D8×C47—42no—
239D8×C47—42no—
240M16×C47—21no—
241M16×C47—21no—
242M16×C47—21no—
243M16×C47—21no—
244M16×C47—21no—
245M16×C47—21no—
246M16×C47—21no—
247M16×C47—42no—
248M16×C47C2×D412yes—
249C2×C8×C47—21no—
250C2×C8×C47—21no—
251C2×C8×C47—21no—
252C2×C8×C47—21no—
253C2×C8×C47—21no—
254C2×C8×C47—21no—
255C2×C8×C47—21no—
256C2×C8×C47—21no—
257C2×C8×C47—42no—
258C2×C8×C47C2×D411yescharacteristic
259C2×C8×C47C2×D411yescharacteristic
260C2×C8×C47C2×D411yescharacteristic
261C2×C8×C47C2×D411yescharacteristic
262C4⋊C4×C47—21no—
263C4⋊C4×C47—21no—
264C4⋊C4×C47—41no—
265C4⋊C4×C47C2×D411yescharacteristic
266C4⋊C4×C47C2×D411yescharacteristic
267C4⋊C4×C47C2×D411yescharacteristic
268C4⋊C4×C47C2×D411yescharacteristic
269C22⋊C4×C47—21no—
270C22⋊C4×C47—21no—
271C22⋊C4×C47—41no—
272C22⋊C4×C47—41no—
273C22⋊C4×C47—41no—
274C22⋊C4×C47—41no—
275C22⋊C4×C47—44no—
276C22⋊C4×C47—41no—
277C22⋊C4×C47—82no—
278C42×C47—21no—
279C42×C47—21no—
280C42×C47—21no—
281C42×C47—21no—
282C42×C47—41no—
283C23×C47—21no—
284C23×C47—21no—
285C23×C47—22no—
286C23×C47—41no—
287C23×C47—41no—
288C23×C47—41no—
289C23×C47—41no—
290C23×C47—41no—
291C23×C47—81no—
292C23×C47—81no—
293C23×C47—81no—
294C23×C47—81no—
295C23×C47H(5,𝔽2)11yescharacteristic
296Q8×C47—21no—
297Q8×C47—21no—
298Q8×C47—22no—
299Q8×C47—21no—
300Q8×C47—22no—
301Q8×C47—44no—
302Q8×C47—41no—
303Q8×C47—41no—
304Q8×C47#12112yes—
305D4×C47—22no—
306D4×C47—22no—
307D4×C47—22no—
308D4×C47—21no—
309D4×C47—22no—
310D4×C47—21no—
311D4×C47—21no—
312D4×C47—44no—
313D4×C47—41no—
314D4×C47—41no—
315D4×C47—41no—
316D4×C47—41no—
317D4×C47—41no—
318D4×C47—41no—
319D4×C47—41no—
320D4×C47—41no—
321D4×C47—161no—
322D4×C47—161no—
323D4×C47#12112yes—
324C2×C4×C47—21no—
325C2×C4×C47—22no—
326C2×C4×C47—22no—
327C2×C4×C47—21no—
328C2×C4×C47—21no—
329C2×C4×C47—21no—
330C2×C4×C47—21no—
331C2×C4×C47—21no—
332C2×C4×C47—22no—
333C2×C4×C47—44no—
334C2×C4×C47—44no—
335C2×C4×C47—41no—
336C2×C4×C47—41no—
337C2×C4×C47—41no—
338C2×C4×C47—41no—
339C2×C4×C47—41no—
340C2×C4×C47—41no—
341C2×C4×C47—41no—
342C2×C4×C47—41no—
343C2×C4×C47—81no—
344C2×C4×C47—161no—
345C2×C4×C47—161no—
346C2×C4×C47—161no—
347C2×C4×C47C22×D411yescharacteristic
348C2×C4×C47C22×D411yescharacteristic
349C2×C4×C47C22×D411yescharacteristic
350C2×C4×C47C2×#4111yescharacteristic
351C2×C4×C47C2×#4111yescharacteristic
352C2×C4×C47H(5,𝔽2)11yescharacteristic
353C8×C47—22no—
354C8×C47—21no—
355C8×C47—21no—
356C8×C47—21no—
357C8×C47—21no—
358C8×C47—41no—
359C8×C47—41no—
360C8×C47—41no—
361#25185C4711yesmaximal, characteristic, direct product factor, Sylow
362C22×C47—21no—
363C22×C47—21no—
364C22×C47—22no—
365C22×C47—41no—
366C22×C47—41no—
367C22×C47—41no—
368C22×C47—42no—
369C22×C47—41no—
370C22×C47—41no—
371C22×C47—82no—
372C22×C47—82no—
373C22×C47—81no—
374C22×C47—81no—
375C22×C47—81no—
376C22×C47—81no—
377C22×C47—81no—
378C22×C47—161no—
379C22×C47—161no—
380C22×C47#53811yescharacteristic
381C22×C47D4211yescharacteristic
382C22×C47#54611yescharacteristic
383C4×C47—22no—
384C4×C47—41no—
385C4×C47—42no—
386C4×C47—41no—
387C4×C47—41no—
388C4×C47—41no—
389C4×C47—41no—
390C4×C47—81no—
391C4×C47—81no—
392C4×C47C2×#12111yescharacteristic
393C4×C47#52511yescharacteristic
394C4×C47D4211yescharacteristic
395C4×C47#54611yescharacteristic
396C2×#472C2×C4711yescharacteristic, complemented
397#3041C2×C4711yescharacteristic, complemented
398C2×#454C2×C4711yescharacteristic, complemented
399#3010C2×C4711yescharacteristic, complemented
400#2946C2×C4711yescharacteristic, complemented
401#2898C2×C4711yescharacteristic, complemented
402#2064C2×C4711yescharacteristic, complemented
403#2051C2×C4711yescharacteristic, complemented
404#2037C2×C4711yescharacteristic, complemented
405#2012C2×C4711yescharacteristic, complemented
406#1977C2×C4711yescharacteristic, complemented
407#1929C2×C4711yescharacteristic, complemented
408#1885C2×C4711yescharacteristic, complemented
409#1883C2×C4711yescharacteristic, complemented
410#1866C2×C4711yescharacteristic, complemented
411C2×C47—21no—
412C2×C47—21no—
413C2×C47—42no—
414C2×C47—81no—
415C2×C47—82no—
416C2×C47—161no—
417C2×C47#242411yescharacteristic
418C2×C47#328811yescharacteristic
419C2×C47#329011yescharacteristic
420C2×2−1+4C22×C4711yescharacteristic
421C2×AGL(1,ℤ/8)C22×C4711yescharacteristic
422C2×AGL(1,ℤ/8)C22×C4711yescharacteristic
423C2×AGL(1,ℤ/8)C22×C4711yescharacteristic
424C22×SD16C22×C4711yescharacteristic
425C22×D8C22×C4711yescharacteristic
426C2×#131C22×C4711yescharacteristic
427#535C22×C4711yescharacteristic
428C2×#124C22×C4711yescharacteristic
429#520C22×C4711yescharacteristic
430#518C22×C4711yescharacteristic
431#472—24no—
432#463—21no—
433#463—21no—
434#459—21no—
435#459—21no—
436#454—24no—
437#449—21no—
438#449—21no—
439#448—21no—
440#448—21no—
441#442—21no—
442#440—21no—
443C4×SD16—21no—
444C4×D8—21no—
445C2×#108C22×C4711yescharacteristic
446C2×#108C22×C4711yescharacteristic
447#428C22×C4711yescharacteristic
448#424C22×C4711yescharacteristic
449C2×#104C22×C4711yescharacteristic
450C2×#104C22×C4711yescharacteristic
451#419—21no—
452#419C22×C4711yescharacteristic
453#419C22×C4711yescharacteristic
454#418C22×C4711yescharacteristic
455#417—21no—
456#417C22×C4711yescharacteristic
457#416—21no—
458#416C22×C4711yescharacteristic
459#416C22×C4711yescharacteristic
460C2×#103—21no—
461C2×#103C22×C4711yescharacteristic
462C2×#102C22×C4711yescharacteristic
463C2×#101C22×C4711yescharacteristic
464C2×#100C22×C4711yescharacteristic
465C2×#100C22×C4711yescharacteristic
466#408C22×C4711yescharacteristic
467#405C22×C4711yescharacteristic
468#390C22×C4711yescharacteristic
469#343C22×C4711yescharacteristic
470#339C22×C4711yescharacteristic
471#339C22×C4711yescharacteristic
472#336C22×C4711yescharacteristic
473C47#2518511yescharacteristic, direct product factor, Sylow
4742−1+4—22no—
4752−1+4—22no—
4762−1+4—22no—
4772−1+4—41no—
478C2×#41—21no—
479C2×#41—21no—
480C2×#41—41no—
481C2×#41C23×C4711yescharacteristic
482C2×#41C23×C4711yescharacteristic
483C22×Q8—21no—
484C22×Q8—21no—
485C22×Q8C23×C4711yescharacteristic
486C22×D4C23×C4711yescharacteristic
487C22×D4C23×C4711yescharacteristic
488AGL(1,ℤ/8)—22no—
489AGL(1,ℤ/8)—22no—
490AGL(1,ℤ/8)—22no—
491AGL(1,ℤ/8)—22no—
492AGL(1,ℤ/8)—41no—
493AGL(1,ℤ/8)D4×C4714yescomplemented
494C2×SD16—21no—
495C2×SD16—21no—
496C2×SD16—21no—
497C2×SD16—22no—
498C2×SD16—21no—
499C2×SD16—21no—
500C2×SD16—41no—
501C2×D8—21no—
502C2×D8—22no—
503C2×D8—21no—
504C2×D8—21no—
505C2×D8—21no—
506C2×D8—21no—
507C2×D8—41no—
508#131—22no—
509#131—41no—
510C2×M16—21no—
511C2×M16C23×C4711yescharacteristic
512C2×M16C23×C4711yescharacteristic
513C2×M16C23×C4711yescharacteristic
514C2×M16C23×C4711yescharacteristic
515C22×C8—21no—
516C22×C8C23×C4711yescharacteristic
517C22×C8C23×C4711yescharacteristic
518#127—21no—
519#124—21no—
520#124—22no—
521#124—22no—
522#121—21no—
523#121—21no—
524#120—41no—
525C4×Q8—21no—
526C4×D4—21no—
527C4×D4—21no—
528C4×D4—21no—
529C4×D4—21no—
530C4×D4—21no—
531C4×D4—41no—
532#117—21no—
533#117C23×C4711yescharacteristic
534#117C23×C4711yescharacteristic
535C2×C4⋊C4—21no—
536C2×C4⋊C4C23×C4711yescharacteristic
537C2×C22⋊C4—41no—
538C2×C22⋊C4—41no—
539C2×C22⋊C4—41no—
540C2×C42C23×C4711yescharacteristic
541#108—22no—
542#108—41no—
543#107—21no—
544#106—21no—
545C4⋊C8—21no—
546C4⋊C8—21no—
547#104—22no—
548#104—22no—
549#103—21no—
550#103—21no—
551#103—21no—
552#103—21no—
553#103—21no—
554#103—21no—
555#103—21no—
556#103D4×C4711yescharacteristic
557#103D4×C4711yescharacteristic
558#103D4×C4711yescharacteristic
559#103D4×C4711yescharacteristic
560#102—21no—
561#102—21no—
562#102—21no—
563#102—21no—
564#102—21no—
565#102D4×C4711yescharacteristic
566#102D4×C4711yescharacteristic
567#102D4×C4711yescharacteristic
568#102D4×C4711yescharacteristic
569#101—22no—
570#100—22no—
571#100—22no—
572C22⋊C8—21no—
573C22⋊C8—21no—
574#97—21no—
575C4×C8—21no—
576C24—21no—
577C24—21no—
578#41—21no—
579#41—21no—
580#41—24no—
581#41—21no—
582#41—21no—
583#41—21no—
584#41—21no—
585#41—42no—
586#41—44no—
587#41—42no—
588#41—44no—
589#41—42no—
590#41C2×D4×C4712yes—
591#41#41×C4712yes—
592C2×Q8—21no—
593C2×Q8—24no—
594C2×Q8—21no—
595C2×Q8—21no—
596C2×Q8—21no—
597C2×Q8—21no—
598C2×Q8—41no—
599C2×Q8—42no—
600C2×Q8—42no—
601C2×Q8—42no—
602C2×Q8C2×D4×C4711yescharacteristic
603C2×Q8C2×D4×C4711yescharacteristic
604C2×Q8#41×C4712yes—
605C2×D4—21no—
606C2×D4—21no—
607C2×D4—21no—
608C2×D4—21no—
609C2×D4—21no—
610C2×D4—21no—
611C2×D4—21no—
612C2×D4—21no—
613C2×D4—21no—
614C2×D4—21no—
615C2×D4—21no—
616C2×D4—21no—
617C2×D4—21no—
618C2×D4—41no—
619C2×D4—41no—
620C2×D4—41no—
621C2×D4C2×D4×C4712yes—
622C2×D4C2×D4×C4711yescharacteristic
623C2×D4C2×D4×C4711yescharacteristic
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—41no—
630C22×C4—41no—
631C22×C4—41no—
632C22×C4—41no—
633C22×C4—41no—
634C22×C4C24×C4711yescharacteristic
635SD16—24no—
636SD16—42no—
637SD16—42no—
638SD16—42no—
639SD16—42no—
640D8—24no—
641D8—42no—
642D8—42no—
643D8—42no—
644D8—42no—
645M16—21no—
646M16—21no—
647M16—21no—
648M16—21no—
649M16—21no—
650M16—21no—
651M16—21no—
652M16—42no—
653M16C2×D4×C4712yes—
654C2×C8—21no—
655C2×C8—21no—
656C2×C8—21no—
657C2×C8—21no—
658C2×C8—21no—
659C2×C8—21no—
660C2×C8—21no—
661C2×C8—21no—
662C2×C8—42no—
663C2×C8C2×D4×C4711yescharacteristic
664C2×C8C2×D4×C4711yescharacteristic
665C2×C8C2×D4×C4711yescharacteristic
666C2×C8C2×D4×C4711yescharacteristic
667C4⋊C4—21no—
668C4⋊C4—21no—
669C4⋊C4—41no—
670C4⋊C4C2×D4×C4711yescharacteristic
671C4⋊C4C2×D4×C4711yescharacteristic
672C4⋊C4C2×D4×C4711yescharacteristic
673C4⋊C4C2×D4×C4711yescharacteristic
674C22⋊C4—21no—
675C22⋊C4—21no—
676C22⋊C4—41no—
677C22⋊C4—41no—
678C22⋊C4—41no—
679C22⋊C4—41no—
680C22⋊C4—44no—
681C22⋊C4—41no—
682C22⋊C4—82no—
683C42—21no—
684C42—21no—
685C42—21no—
686C42—21no—
687C42—41no—
688C23—21no—
689C23—21no—
690C23—22no—
691C23—41no—
692C23—41no—
693C23—41no—
694C23—41no—
695C23—41no—
696C23—81no—
697C23—81no—
698C23—81no—
699C23—81no—
700C23H(5,𝔽2)×C4711yescharacteristic
701Q8—21no—
702Q8—21no—
703Q8—22no—
704Q8—21no—
705Q8—22no—
706Q8—44no—
707Q8—41no—
708Q8—41no—
709Q8#121×C4712yes—
710D4—22no—
711D4—22no—
712D4—22no—
713D4—21no—
714D4—22no—
715D4—21no—
716D4—21no—
717D4—44no—
718D4—41no—
719D4—41no—
720D4—41no—
721D4—41no—
722D4—41no—
723D4—41no—
724D4—41no—
725D4—41no—
726D4—161no—
727D4—161no—
728D4#121×C4712yes—
729C2×C4—21no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—22no—
738C2×C4—44no—
739C2×C4—44no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—81no—
749C2×C4—161no—
750C2×C4—161no—
751C2×C4—161no—
752C2×C4C22×D4×C4711yescharacteristic
753C2×C4C22×D4×C4711yescharacteristic
754C2×C4C22×D4×C4711yescharacteristic
755C2×C4C2×#41×C4711yescharacteristic
756C2×C4C2×#41×C4711yescharacteristic
757C2×C4H(5,𝔽2)×C4711yescharacteristic
758C8—22no—
759C8—21no—
760C8—21no—
761C8—21no—
762C8—21no—
763C8—41no—
764C8—41no—
765C8—41no—
766C22—21no—
767C22—21no—
768C22—22no—
769C22—41no—
770C22—41no—
771C22—41no—
772C22—41no—
773C22—41no—
774C22—42no—
775C22—82no—
776C22—82no—
777C22—81no—
778C22—81no—
779C22—81no—
780C22—81no—
781C22—81no—
782C22—161no—
783C22—161no—
784C22C47×#53811yescharacteristic
785C22D42×C4711yescharacteristic
786C22C47×#54611yescharacteristic
787C4—22no—
788C4—41no—
789C4—41no—
790C4—41no—
791C4—41no—
792C4—41no—
793C4—42no—
794C4—81no—
795C4—81no—
796C4C2×#121×C4711yescharacteristic
797C4C47×#52511yescharacteristic
798C4D42×C4711yescharacteristic
799C4C47×#54611yescharacteristic
800C2—21no—
801C2—21no—
802C2—42no—
803C2—81no—
804C2—82no—
805C2—161no—
806C2C47×#242411yescharacteristic
807C2C47×#328811yescharacteristic
808C2C47×#329011yescharacteristic
subgroupG/H
center, socleC22×C47D42
commutator, Frattini, cosocleC22×C4C24×C47
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C47 ◁ C22×C4×C47 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C47×#472C2semidirect
2. C47×#3041C2semidirect
3. C2×C47×#454C2semidirect
4. C47×#3010C2semidirect
5. C47×#2946C2semidirect
6. C47×#2898C2semidirect
7. C47×#2064C2semidirect
8. C47×#2051C2semidirect
9. C47×#2037C2semidirect
10. C47×#2012C2semidirect
11. C47×#1977C2semidirect
12. C47×#1929C2semidirect
13. C47×#1885C2semidirect
14. C47×#1883C2semidirect
15. C47×#1866C2semidirect
88. AGL(1,ℤ/8)×C47D4semidirect
361. #25185C47direct (N × H)
396. C2×#472C2×C47semidirect
397. #3041C2×C47semidirect
398. C2×#454C2×C47semidirect
399. #3010C2×C47semidirect
400. #2946C2×C47semidirect
401. #2898C2×C47semidirect
402. #2064C2×C47semidirect
403. #2051C2×C47semidirect
404. #2037C2×C47semidirect
405. #2012C2×C47semidirect
406. #1977C2×C47semidirect
407. #1929C2×C47semidirect
408. #1885C2×C47semidirect
409. #1883C2×C47semidirect
410. #1866C2×C47semidirect
473. C47#25185direct (N × H)
493. AGL(1,ℤ/8)D4×C47semidirect

Maximal subgroups

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

subgroupindex
C2×C47×#4722
C47×#30412
C2×C47×#4542
C47×#30102
C47×#29462
C47×#28982
C47×#20642
C47×#20512
C47×#20372
C47×#20122
C47×#19772
C47×#19292
C47×#18852
C47×#18832
C47×#18662
#2518547