Finite Group Databasebeta

← C47×#18738 #26058436

Subgroups — C47×#18738 #26058436

Order 12032.

972 conjugacy classes of subgroups.

The subgroup lattice has 806 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3546C211yesmaximal, characteristic, complemented
2C47×#3245C211yesmaximal, characteristic, complemented
3C47×#3212C211yesmaximal, characteristic, complemented
4C47×#3184C211yesmaximal, characteristic, complemented
5C47×#1654C211yesmaximal, characteristic, complemented
6C47×#1652C211yesmaximal, characteristic, complemented
7C47×#1641C211yesmaximal, characteristic, complemented
8C47×#1639C211yesmaximal, characteristic, complemented
9C47×#1628C211yesmaximal, characteristic, complemented
10C47×#1625C211yesmaximal, characteristic, complemented
11C47×#1621C211yesmaximal, characteristic, complemented
12C47×#1619C211yesmaximal, 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×#532C2211yescharacteristic
31C47×#532C2211yescharacteristic
32C47×#532C2211yescharacteristic, complemented
33C47×#529C2211yescharacteristic
34C47×#498C2211yescharacteristic, complemented
35C47×#495—21no—
36C47×#493C2211yescharacteristic
37C47×#488—21no—
38C47×#486C2211yescharacteristic
39C47×#486C2211yescharacteristic, complemented
40C47×#474—21no—
41C47×#474C2211yescharacteristic
42C47×#474C2211yescharacteristic, complemented
43C47×#469—22no—
44C47×#466—21no—
45C47×#466—21no—
46C47×#462C2211yescharacteristic, complemented
47C47×#461C2211yescharacteristic
48C47×#460C2211yescharacteristic, complemented
49C47×#459—21no—
50C47×#459C2211yescharacteristic
51C47×#459C2211yescharacteristic
52C47×#459C2211yescharacteristic, complemented
53C47×#452—21no—
54C47×#449—21no—
55C47×#442—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—
75C2×#41×C47—21no—
76C22×D4×C47—21no—
77C22×D4×C47—21no—
78C2×Q16×C47—21no—
79C2×SD16×C47—21no—
80C2×SD16×C47—21no—
81C2×D8×C47—22no—
82C2×D8×C47—21no—
83C2×D8×C47—21no—
84C2×D8×C47—21no—
85C2×M16×C47—21no—
86C22×C8×C47—21no—
87C4⋊Q8×C47D411yescharacteristic
88C4⋊Q8×C47C2311yescharacteristic
89C4⋊Q8×C47C2311yescharacteristic
90#127×C47—22no—
91#127×C47—21no—
92#127×C47D411yescharacteristic
93#127×C47C2311yescharacteristic
94#127×C47C2311yescharacteristic
95#126×C47—22no—
96#126×C47—22no—
97#126×C47—21no—
98#125×C47D411yescharacteristic
99#124×C47—22no—
100#124×C47—21no—
101#124×C47—21no—
102#124×C47—21no—
103#124×C47—21no—
104#124×C47D411yescharacteristic
105#123×C47—22no—
106#123×C47—22no—
107#123×C47—21no—
108#123×C47—22no—
109C22⋊Q8×C47—22no—
110C22⋊Q8×C47—21no—
111C22⋊Q8×C47—21no—
112C22⋊Q8×C47D411yescharacteristic
113#121×C47—22no—
114#121×C47—22no—
115#121×C47—22no—
116#121×C47—22no—
117#121×C47—22no—
118#121×C47—21no—
119#121×C47—22no—
120#121×C47—21no—
121#121×C47—21no—
122#121×C47—21no—
123#121×C47—21no—
124#121×C47—21no—
125#121×C47—21no—
126#121×C47—21no—
127#121×C47D411yescharacteristic
128#121×C47D411yescharacteristic
129#121×C47D411yescharacteristic
130#121×C47D412yes—
131#120×C47—22no—
132#120×C47—22no—
133#120×C47—22no—
134#120×C47—22no—
135C4×Q8×C47—21no—
136C4×Q8×C47C2311yescharacteristic
137C4×D4×C47—22no—
138C4×D4×C47—21no—
139C4×D4×C47—21no—
140C4×D4×C47—21no—
141C4×D4×C47—21no—
142C4×D4×C47—21no—
143C4×D4×C47—21no—
144C4×D4×C47D412yes—
145C4×D4×C47C2311yescharacteristic
146C4×D4×C47C2311yescharacteristic
147C4×D4×C47C2311yescharacteristic
148#117×C47—21no—
149#117×C47—21no—
150C2×C4⋊C4×C47—21no—
151C2×C22⋊C4×C47—22no—
152C2×C42×C47C2311yescharacteristic
153#107×C47—21no—
154#107×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#102×C47—21no—
164#102×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
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—
185#41×C47—81no—
186#41×C47—81no—
187C2×Q8×C47—21no—
188C2×Q8×C47—21no—
189C2×Q8×C47—21no—
190C2×Q8×C47C2×D411yescharacteristic
191C2×D4×C47—22no—
192C2×D4×C47—22no—
193C2×D4×C47—22no—
194C2×D4×C47—22no—
195C2×D4×C47—22no—
196C2×D4×C47—21no—
197C2×D4×C47—21no—
198C2×D4×C47—22no—
199C2×D4×C47—21no—
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—41no—
208C2×D4×C47—81no—
209C2×D4×C47—81no—
210C2×D4×C47—81no—
211C2×D4×C47—81no—
212C2×D4×C47C2×D411yescharacteristic
213C2×D4×C47C2×D411yescharacteristic
214C2×D4×C47C2×D411yescharacteristic
215C2×D4×C47C2×D412yes—
216C22×C4×C47—22no—
217C22×C4×C47—22no—
218C22×C4×C47—21no—
219C22×C4×C47—21no—
220C22×C4×C47—21no—
221C22×C4×C47—22no—
222C22×C4×C47—41no—
223C22×C4×C47C2×D411yescharacteristic
224C22×C4×C47C2×D411yescharacteristic
225C22×C4×C47C2×D411yescharacteristic
226Q16×C47—81no—
227SD16×C47—81no—
228SD16×C47—81no—
229D8×C47—44no—
230D8×C47—81no—
231D8×C47—81no—
232D8×C47—81no—
233M16×C47—42no—
234C2×C8×C47—21no—
235C2×C8×C47—21no—
236C2×C8×C47—21no—
237C2×C8×C47—21no—
238C2×C8×C47—21no—
239C2×C8×C47—21no—
240C2×C8×C47—81no—
241C4⋊C4×C47—22no—
242C4⋊C4×C47—22no—
243C4⋊C4×C47—21no—
244C4⋊C4×C47—21no—
245C4⋊C4×C47—21no—
246C4⋊C4×C47—21no—
247C4⋊C4×C47—21no—
248C4⋊C4×C47—21no—
249C4⋊C4×C47—21no—
250C4⋊C4×C47—21no—
251C4⋊C4×C47C2×D411yescharacteristic
252C4⋊C4×C47C2×D411yescharacteristic
253C4⋊C4×C47C2×D412yes—
254C4⋊C4×C47C2×D411yescharacteristic
255C4⋊C4×C47C2×D411yescharacteristic
256C22⋊C4×C47—22no—
257C22⋊C4×C47—22no—
258C22⋊C4×C47—22no—
259C22⋊C4×C47—22no—
260C22⋊C4×C47—22no—
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—22no—
268C22⋊C4×C47—22no—
269C22⋊C4×C47—21no—
270C22⋊C4×C47—21no—
271C22⋊C4×C47—21no—
272C22⋊C4×C47—41no—
273C22⋊C4×C47—41no—
274C42×C47—22no—
275C42×C47—21no—
276C42×C47C2×D411yescharacteristic
277C42×C47C2×D411yescharacteristic
278C42×C47C2×D411yescharacteristic
279C42×C47C2411yescharacteristic
280C23×C47—21no—
281C23×C47—21no—
282C23×C47—22no—
283C23×C47—21no—
284C23×C47—41no—
285C23×C47—82no—
286C23×C47—82no—
287C23×C47—82no—
288C23×C47#12011yescharacteristic
289Q8×C47—21no—
290Q8×C47—21no—
291Q8×C47—41no—
292Q8×C47—41no—
293Q8×C47—41no—
294Q8×C47—41no—
295Q8×C47—81no—
296D4×C47—21no—
297D4×C47—21no—
298D4×C47—21no—
299D4×C47—21no—
300D4×C47—21no—
301D4×C47—21no—
302D4×C47—42no—
303D4×C47—42no—
304D4×C47—41no—
305D4×C47—41no—
306D4×C47—41no—
307D4×C47—41no—
308D4×C47—41no—
309D4×C47—41no—
310D4×C47—41no—
311D4×C47—41no—
312D4×C47—81no—
313D4×C47—81no—
314D4×C47—81no—
315D4×C47—81no—
316D4×C47—81no—
317D4×C47—82no—
318D4×C47—82no—
319D4×C47—82no—
320D4×C47—82no—
321D4×C47—82no—
322D4×C47—82no—
323D4×C47—82no—
324C2×C4×C47—21no—
325C2×C4×C47—21no—
326C2×C4×C47—21no—
327C2×C4×C47—21no—
328C2×C4×C47—21no—
329C2×C4×C47—21no—
330C2×C4×C47—21no—
331C2×C4×C47—22no—
332C2×C4×C47—21no—
333C2×C4×C47—21no—
334C2×C4×C47—41no—
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—82no—
343C2×C4×C47—82no—
344C2×C4×C47—82no—
345C2×C4×C47—82no—
346C2×C4×C47#12011yescharacteristic
347C2×C4×C47#12011yescharacteristic
348C2×C4×C47#12011yescharacteristic
349C2×C4×C47C22×D411yescharacteristic
350C2×C4×C47C22×D411yescharacteristic
351C2×C4×C47C22×D411yescharacteristic
352C8×C47—22no—
353C8×C47—41no—
354C8×C47—41no—
355C8×C47—41no—
356C8×C47—41no—
357C8×C47—41no—
358#18738C4711yesmaximal, characteristic, direct product factor, Sylow
359C22×C47—21no—
360C22×C47—21no—
361C22×C47—21no—
362C22×C47—41no—
363C22×C47—41no—
364C22×C47—42no—
365C22×C47—41no—
366C22×C47—41no—
367C22×C47—41no—
368C22×C47—42no—
369C22×C47—41no—
370C22×C47—42no—
371C22×C47—41no—
372C22×C47—41no—
373C22×C47—41no—
374C22×C47—81no—
375C22×C47—81no—
376C22×C47—81no—
377C22×C47—164no—
378C22×C47C2×#12011yescharacteristic
379C4×C47—21no—
380C4×C47—21no—
381C4×C47—21no—
382C4×C47—21no—
383C4×C47—41no—
384C4×C47—41no—
385C4×C47—41no—
386C4×C47—41no—
387C4×C47—42no—
388C4×C47—41no—
389C4×C47—81no—
390C4×C47#57611yescharacteristic
391C4×C47#57611yescharacteristic
392C4×C47#57611yescharacteristic
393C4×C47#57711yescharacteristic
394#3546C2×C4711yescharacteristic, complemented
395#3245C2×C4711yescharacteristic, complemented
396#3212C2×C4711yescharacteristic, complemented
397#3184C2×C4711yescharacteristic, complemented
398#1654C2×C4711yescharacteristic, complemented
399#1652C2×C4711yescharacteristic, complemented
400#1641C2×C4711yescharacteristic, complemented
401#1639C2×C4711yescharacteristic, complemented
402#1628C2×C4711yescharacteristic, complemented
403#1625C2×C4711yescharacteristic, complemented
404#1621C2×C4711yescharacteristic, complemented
405#1619C2×C4711yescharacteristic, complemented
406#1540C2×C4711yescharacteristic, complemented
407#1484C2×C4711yescharacteristic, complemented
408#1483C2×C4711yescharacteristic, complemented
409C2×C47—41no—
410C2×C47—81no—
411C2×C47—82no—
412C2×C47—81no—
413C2×C47—81no—
414C2×C47—161no—
415C2×C47#300811yescharacteristic
416C2×C47#301211yescharacteristic
417C2×C47#301811yescharacteristic
418#560—22no—
419#556C22×C4711yescharacteristic
420#553—21no—
421#550—21no—
422#550C22×C4711yescharacteristic
423#547C22×C4711yescharacteristic
424#546—21no—
425#546—21no—
426D42C22×C4711yescharacteristic
427#542—21no—
428#538—22no—
429#537—21no—
430#535—21no—
431#535—21no—
432#532C22×C4711yescharacteristic
433#532C22×C4711yescharacteristic
434#532C22×C4711yescharacteristic, complemented
435#529C22×C4711yescharacteristic
436#498C22×C4711yescharacteristic, complemented
437#495—21no—
438#493C22×C4711yescharacteristic
439#488—21no—
440#486C22×C4711yescharacteristic
441#486C22×C4711yescharacteristic, complemented
442#474—21no—
443#474C22×C4711yescharacteristic
444#474C22×C4711yescharacteristic, complemented
445#469—22no—
446#466—21no—
447#466—21no—
448#462C22×C4711yescharacteristic, complemented
449#461C22×C4711yescharacteristic
450#460C22×C4711yescharacteristic, complemented
451#459—21no—
452#459C22×C4711yescharacteristic
453#459C22×C4711yescharacteristic
454#459C22×C4711yescharacteristic, complemented
455#452—21no—
456#449—21no—
457#442—22no—
458#431C22×C4711yescharacteristic, complemented
459C2×C4⋊C8C22×C4711yescharacteristic, complemented
460C4×M16C22×C4711yescharacteristic, complemented
461#332C22×C4711yescharacteristic, complemented
462#332C22×C4711yescharacteristic, complemented
463#331C22×C4711yescharacteristic
464#331C22×C4711yescharacteristic
465Q8⋊C8C22×C4711yescharacteristic, complemented
466Q8⋊C8C22×C4711yescharacteristic, complemented
467D4⋊C8C22×C4711yescharacteristic
468D4⋊C8C22×C4711yescharacteristic
469D4⋊C8C22×C4711yescharacteristic
470D4⋊C8C22×C4711yescharacteristic
471D4⋊C8C22×C4711yescharacteristic, complemented
472D4⋊C8C22×C4711yescharacteristic, complemented
473C47#1873811yescharacteristic, direct product factor, Sylow
474C2×#41—21no—
475C2×#41—21no—
476C2×#41—21no—
477C2×#41—21no—
478C2×#41—21no—
479C22×D4—21no—
480C22×D4—21no—
481C2×Q16—21no—
482C2×SD16—21no—
483C2×SD16—21no—
484C2×D8—22no—
485C2×D8—21no—
486C2×D8—21no—
487C2×D8—21no—
488C2×M16—21no—
489C22×C8—21no—
490C4⋊Q8D4×C4711yescharacteristic
491C4⋊Q8C23×C4711yescharacteristic
492C4⋊Q8C23×C4711yescharacteristic
493#127—22no—
494#127—21no—
495#127D4×C4711yescharacteristic
496#127C23×C4711yescharacteristic
497#127C23×C4711yescharacteristic
498#126—22no—
499#126—22no—
500#126—21no—
501#125D4×C4711yescharacteristic
502#124—22no—
503#124—21no—
504#124—21no—
505#124—21no—
506#124—21no—
507#124D4×C4711yescharacteristic
508#123—22no—
509#123—22no—
510#123—21no—
511#123—22no—
512C22⋊Q8—22no—
513C22⋊Q8—21no—
514C22⋊Q8—21no—
515C22⋊Q8D4×C4711yescharacteristic
516#121—22no—
517#121—22no—
518#121—22no—
519#121—22no—
520#121—22no—
521#121—21no—
522#121—22no—
523#121—21no—
524#121—21no—
525#121—21no—
526#121—21no—
527#121—21no—
528#121—21no—
529#121—21no—
530#121D4×C4711yescharacteristic
531#121D4×C4711yescharacteristic
532#121D4×C4711yescharacteristic
533#121D4×C4712yes—
534#120—22no—
535#120—22no—
536#120—22no—
537#120—22no—
538C4×Q8—21no—
539C4×Q8C23×C4711yescharacteristic
540C4×D4—22no—
541C4×D4—21no—
542C4×D4—21no—
543C4×D4—21no—
544C4×D4—21no—
545C4×D4—21no—
546C4×D4—21no—
547C4×D4D4×C4712yes—
548C4×D4C23×C4711yescharacteristic
549C4×D4C23×C4711yescharacteristic
550C4×D4C23×C4711yescharacteristic
551#117—21no—
552#117—21no—
553C2×C4⋊C4—21no—
554C2×C22⋊C4—22no—
555C2×C42C23×C4711yescharacteristic
556#107—21no—
557#107—21no—
558#106—22no—
559C4⋊C8—21no—
560C4⋊C8C23×C4711yescharacteristic
561C4⋊C8C23×C4711yescharacteristic
562C4⋊C8C23×C4711yescharacteristic
563C4⋊C8C23×C4711yescharacteristic
564#103—21no—
565#103—21no—
566#102—22no—
567#102—21no—
568#102—21no—
569#102—22no—
570#102—21no—
571#102—21no—
572#102—21no—
573#102—21no—
574C22⋊C8—21no—
575#97—21no—
576C4×C8—21no—
577C4×C8C23×C4711yescharacteristic
578C4×C8C23×C4711yescharacteristic
579C24—22no—
580#41—81no—
581#41—81no—
582#41—81no—
583#41—81no—
584#41—81no—
585#41—81no—
586#41—81no—
587#41—81no—
588#41—81no—
589#41—81no—
590C2×Q8—21no—
591C2×Q8—21no—
592C2×Q8—21no—
593C2×Q8C2×D4×C4711yescharacteristic
594C2×D4—22no—
595C2×D4—22no—
596C2×D4—22no—
597C2×D4—22no—
598C2×D4—22no—
599C2×D4—21no—
600C2×D4—21no—
601C2×D4—22no—
602C2×D4—21no—
603C2×D4—21no—
604C2×D4—21no—
605C2×D4—21no—
606C2×D4—21no—
607C2×D4—21no—
608C2×D4—21no—
609C2×D4—21no—
610C2×D4—41no—
611C2×D4—81no—
612C2×D4—81no—
613C2×D4—81no—
614C2×D4—81no—
615C2×D4C2×D4×C4711yescharacteristic
616C2×D4C2×D4×C4711yescharacteristic
617C2×D4C2×D4×C4711yescharacteristic
618C2×D4C2×D4×C4712yes—
619C22×C4—22no—
620C22×C4—22no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—22no—
625C22×C4—41no—
626C22×C4C2×D4×C4711yescharacteristic
627C22×C4C2×D4×C4711yescharacteristic
628C22×C4C2×D4×C4711yescharacteristic
629Q16—81no—
630SD16—81no—
631SD16—81no—
632D8—44no—
633D8—81no—
634D8—81no—
635D8—81no—
636M16—42no—
637C2×C8—21no—
638C2×C8—21no—
639C2×C8—21no—
640C2×C8—21no—
641C2×C8—21no—
642C2×C8—21no—
643C2×C8—81no—
644C4⋊C4—22no—
645C4⋊C4—22no—
646C4⋊C4—21no—
647C4⋊C4—21no—
648C4⋊C4—21no—
649C4⋊C4—21no—
650C4⋊C4—21no—
651C4⋊C4—21no—
652C4⋊C4—21no—
653C4⋊C4—21no—
654C4⋊C4C2×D4×C4711yescharacteristic
655C4⋊C4C2×D4×C4711yescharacteristic
656C4⋊C4C2×D4×C4712yes—
657C4⋊C4C2×D4×C4711yescharacteristic
658C4⋊C4C2×D4×C4711yescharacteristic
659C22⋊C4—22no—
660C22⋊C4—22no—
661C22⋊C4—22no—
662C22⋊C4—22no—
663C22⋊C4—22no—
664C22⋊C4—21no—
665C22⋊C4—21no—
666C22⋊C4—21no—
667C22⋊C4—21no—
668C22⋊C4—21no—
669C22⋊C4—21no—
670C22⋊C4—22no—
671C22⋊C4—22no—
672C22⋊C4—21no—
673C22⋊C4—21no—
674C22⋊C4—21no—
675C22⋊C4—41no—
676C22⋊C4—41no—
677C42—22no—
678C42—21no—
679C42C2×D4×C4711yescharacteristic
680C42C2×D4×C4711yescharacteristic
681C42C2×D4×C4711yescharacteristic
682C42C24×C4711yescharacteristic
683C23—21no—
684C23—21no—
685C23—22no—
686C23—21no—
687C23—41no—
688C23—82no—
689C23—82no—
690C23—82no—
691C23#120×C4711yescharacteristic
692Q8—21no—
693Q8—21no—
694Q8—41no—
695Q8—41no—
696Q8—41no—
697Q8—41no—
698Q8—81no—
699D4—21no—
700D4—21no—
701D4—21no—
702D4—21no—
703D4—21no—
704D4—21no—
705D4—42no—
706D4—42no—
707D4—41no—
708D4—41no—
709D4—41no—
710D4—41no—
711D4—41no—
712D4—41no—
713D4—41no—
714D4—41no—
715D4—81no—
716D4—81no—
717D4—81no—
718D4—81no—
719D4—81no—
720D4—82no—
721D4—82no—
722D4—82no—
723D4—82no—
724D4—82no—
725D4—82no—
726D4—82no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—22no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—82no—
746C2×C4—82no—
747C2×C4—82no—
748C2×C4—82no—
749C2×C4#120×C4711yescharacteristic
750C2×C4#120×C4711yescharacteristic
751C2×C4#120×C4711yescharacteristic
752C2×C4C22×D4×C4711yescharacteristic
753C2×C4C22×D4×C4711yescharacteristic
754C2×C4C22×D4×C4711yescharacteristic
755C8—22no—
756C8—41no—
757C8—41no—
758C8—41no—
759C8—41no—
760C8—41no—
761C22—21no—
762C22—21no—
763C22—21no—
764C22—41no—
765C22—41no—
766C22—42no—
767C22—41no—
768C22—41no—
769C22—41no—
770C22—42no—
771C22—41no—
772C22—42no—
773C22—41no—
774C22—41no—
775C22—41no—
776C22—81no—
777C22—81no—
778C22—81no—
779C22—164no—
780C22C2×#120×C4711yescharacteristic
781C4—21no—
782C4—21no—
783C4—21no—
784C4—21no—
785C4—41no—
786C4—41no—
787C4—41no—
788C4—41no—
789C4—42no—
790C4—41no—
791C4—81no—
792C4C47×#57611yescharacteristic
793C4C47×#57611yescharacteristic
794C4C47×#57611yescharacteristic
795C4C47×#57711yescharacteristic
796C2—41no—
797C2—81no—
798C2—81no—
799C2—82no—
800C2—81no—
801C2—161no—
802C2C47×#300811yescharacteristic
803C2C47×#301211yescharacteristic
804C2C47×#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×#3546C2semidirect
2. C47×#3245C2semidirect
3. C47×#3212C2semidirect
4. C47×#3184C2semidirect
5. C47×#1654C2semidirect
6. C47×#1652C2semidirect
7. C47×#1641C2semidirect
8. C47×#1639C2semidirect
9. C47×#1628C2semidirect
10. C47×#1625C2semidirect
11. C47×#1621C2semidirect
12. C47×#1619C2semidirect
13. C47×#1540C2semidirect
14. C47×#1484C2semidirect
15. C47×#1483C2semidirect
32. C47×#532C22semidirect
34. C47×#498C22semidirect
39. C47×#486C22semidirect
42. C47×#474C22semidirect
46. C47×#462C22semidirect
48. C47×#460C22semidirect
52. C47×#459C22semidirect
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
358. #18738C47direct (N × H)
394. #3546C2×C47semidirect
395. #3245C2×C47semidirect
396. #3212C2×C47semidirect
397. #3184C2×C47semidirect
398. #1654C2×C47semidirect
399. #1652C2×C47semidirect
400. #1641C2×C47semidirect
401. #1639C2×C47semidirect
402. #1628C2×C47semidirect
403. #1625C2×C47semidirect
404. #1621C2×C47semidirect
405. #1619C2×C47semidirect
406. #1540C2×C47semidirect
407. #1484C2×C47semidirect
408. #1483C2×C47semidirect
434. #532C22×C47semidirect
436. #498C22×C47semidirect
441. #486C22×C47semidirect
444. #474C22×C47semidirect
448. #462C22×C47semidirect
450. #460C22×C47semidirect
454. #459C22×C47semidirect
458. #431C22×C47semidirect
459. C2×C4⋊C8C22×C47semidirect
460. C4×M16C22×C47semidirect
461. #332C22×C47semidirect
462. #332C22×C47semidirect
465. Q8⋊C8C22×C47semidirect
466. Q8⋊C8C22×C47semidirect
471. D4⋊C8C22×C47semidirect
472. D4⋊C8C22×C47semidirect
473. C47#18738direct (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×#32452
C47×#32122
C47×#31842
C47×#16542
C47×#16522
C47×#16412
C47×#16392
C47×#16282
C47×#16252
C47×#16212
C47×#16192
C47×#15402
C47×#14842
C47×#14832
#1873847