Finite Group Databasebeta

← C47×#18930 #26058628

Subgroups — C47×#18930 #26058628

Order 12032.

1020 conjugacy classes of subgroups.

The subgroup lattice has 818 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3543C211yesmaximal, characteristic, complemented
2C47×#3251C211yesmaximal, characteristic, complemented
3C47×#3212C211yesmaximal, characteristic, complemented
4C47×#3205C211yesmaximal, characteristic, complemented
5C47×#1642C211yesmaximal, characteristic, complemented
6C47×#1641C211yesmaximal, characteristic, complemented
7C47×#1640C211yesmaximal, characteristic, complemented
8C47×#1639C211yesmaximal, characteristic, complemented
9C47×#1621C211yesmaximal, characteristic, complemented
10C47×#1621C211yesmaximal, characteristic, complemented
11C47×#1620C211yesmaximal, characteristic, complemented
12C47×#1619C211yesmaximal, characteristic, complemented
13C47×#1545C211yesmaximal, characteristic, complemented
14C47×#1495C211yesmaximal, characteristic, complemented
15C47×#1482C211yesmaximal, characteristic, complemented
16C47×#560—22no—
17C47×#559C2211yescharacteristic
18C47×#550C2211yescharacteristic
19C47×#550C2211yescharacteristic
20C47×#546—21no—
21C47×#546—21no—
22D42×C47—21no—
23D42×C47—21no—
24D42×C47C2211yescharacteristic
25C47×#540—21no—
26C47×#540—21no—
27C47×#535—21no—
28C47×#535—21no—
29C47×#534—22no—
30C47×#532C2211yescharacteristic, complemented
31C2×#127×C47C2211yescharacteristic
32C47×#529C2211yescharacteristic
33C47×#529C2211yescharacteristic
34C47×#495—21no—
35C47×#493C2211yescharacteristic
36C47×#493C2211yescharacteristic, complemented
37C47×#488—21no—
38C47×#486C2211yescharacteristic
39C47×#486C2211yescharacteristic, complemented
40C47×#478—21no—
41C47×#475C2211yescharacteristic, complemented
42C47×#474C2211yescharacteristic, complemented
43C47×#469—21no—
44C47×#468—21no—
45C47×#463—21no—
46C47×#462C2211yescharacteristic, complemented
47C47×#461C2211yescharacteristic, complemented
48C47×#460C2211yescharacteristic, complemented
49C47×#460C2211yescharacteristic, complemented
50C47×#459—22no—
51C47×#459C2211yescharacteristic, complemented
52C47×#459C2211yescharacteristic, complemented
53C47×#452—21no—
54C47×#449—21no—
55C47×#447—22no—
56C47×#431C2211yescharacteristic, complemented
57C47×#431C2211yescharacteristic, complemented
58C47×#423C2211yescharacteristic, complemented
59C47×#331C2211yescharacteristic
60C47×#331C2211yescharacteristic
61C47×#331C2211yescharacteristic, complemented
62C47×#331C2211yescharacteristic, complemented
63C47×Q8⋊C8C2211yescharacteristic, complemented
64C47×Q8⋊C8C2211yescharacteristic, complemented
65C47×Q8⋊C8C2211yescharacteristic, complemented
66C47×Q8⋊C8C2211yescharacteristic, complemented
67C47×D4⋊C8C2211yescharacteristic, complemented
68C47×D4⋊C8C2211yescharacteristic, complemented
69C47×D4⋊C8C2211yescharacteristic, complemented
70C47×D4⋊C8C2211yescharacteristic, complemented
71C2×#41×C47—21no—
72C2×#41×C47—21no—
73C2×#41×C47—21no—
74C22×D4×C47—22no—
75C22×D4×C47—21no—
76C22×D4×C47—21no—
77C22×D4×C47—21no—
78C22×D4×C47—21no—
79C22×D4×C47D412yes—
80C2×Q16×C47—21no—
81C2×SD16×C47—21no—
82C2×SD16×C47—21no—
83C2×SD16×C47—21no—
84C2×D8×C47—21no—
85C2×D8×C47—22no—
86C2×D8×C47—22no—
87C2×D8×C47—21no—
88C2×M16×C47—21no—
89C4⋊Q8×C47C2311yescharacteristic
90#127×C47—21no—
91#127×C47—21no—
92#127×C47—21no—
93#127×C47—21no—
94#127×C47D412yes—
95#127×C47C2311yescharacteristic
96#127×C47C2311yescharacteristic
97#127×C47C2311yescharacteristic
98#126×C47—21no—
99#126×C47—21no—
100#125×C47D411yescharacteristic
101#125×C47D411yescharacteristic
102#124×C47—21no—
103#124×C47—21no—
104#124×C47—21no—
105#124×C47D411yescharacteristic
106#124×C47D411yescharacteristic
107#123×C47—22no—
108#123×C47—22no—
109#123×C47—22no—
110#123×C47—22no—
111#123×C47—21no—
112#123×C47—21no—
113C22⋊Q8×C47D411yescharacteristic
114C22⋊Q8×C47D411yescharacteristic
115#121×C47—22no—
116#121×C47—22no—
117#121×C47—22no—
118#121×C47—22no—
119#121×C47—22no—
120#121×C47—22no—
121#121×C47—22no—
122#121×C47—22no—
123#121×C47—21no—
124#121×C47—21no—
125#121×C47—21no—
126#121×C47—21no—
127#121×C47—21no—
128#121×C47—21no—
129#121×C47D411yescharacteristic
130#121×C47D411yescharacteristic
131#120×C47—22no—
132#120×C47—22no—
133#120×C47—22no—
134#120×C47—22no—
135#120×C47—22no—
136#120×C47—22no—
137C4×Q8×C47C2311yescharacteristic
138C4×Q8×C47C2311yescharacteristic
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×C47C2311yescharacteristic
148C4×D4×C47C2311yescharacteristic
149#117×C47—21no—
150#117×C47—21no—
151C2×C22⋊C4×C47—22no—
152C2×C42×C47C2311yescharacteristic
153#107×C47—21no—
154#106×C47—21no—
155C4⋊C8×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#102×C47—22no—
165#102×C47—22no—
166#102×C47—21no—
167#102×C47—21no—
168#102×C47—21no—
169#102×C47—21no—
170#102×C47—21no—
171C22⋊C8×C47—21no—
172C22⋊C8×C47—21no—
173C4×C8×C47—21no—
174C4×C8×C47C2311yescharacteristic
175C4×C8×C47C2311yescharacteristic
176C24×C47—22no—
177C24×C47—22no—
178#41×C47—81no—
179#41×C47—81no—
180#41×C47—81no—
181#41×C47—81no—
182#41×C47—81no—
183#41×C47—81no—
184C2×Q8×C47—21no—
185C2×Q8×C47C2×D411yescharacteristic
186C2×Q8×C47C2×D411yescharacteristic
187C2×D4×C47—21no—
188C2×D4×C47—21no—
189C2×D4×C47—22no—
190C2×D4×C47—22no—
191C2×D4×C47—22no—
192C2×D4×C47—22no—
193C2×D4×C47—22no—
194C2×D4×C47—22no—
195C2×D4×C47—22no—
196C2×D4×C47—22no—
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—21no—
204C2×D4×C47—21no—
205C2×D4×C47—41no—
206C2×D4×C47—81no—
207C2×D4×C47—81no—
208C2×D4×C47—81no—
209C2×D4×C47—81no—
210C2×D4×C47—81no—
211C2×D4×C47—81no—
212C2×D4×C47—81no—
213C2×D4×C47—81no—
214C2×D4×C47—82no—
215C2×D4×C47—84no—
216C2×D4×C47C2×D411yescharacteristic
217C2×D4×C47C2×D411yescharacteristic
218C2×D4×C47C2×D412yes—
219C2×D4×C47C2×D412yes—
220C22×C4×C47—22no—
221C22×C4×C47—22no—
222C22×C4×C47—22no—
223C22×C4×C47—21no—
224C22×C4×C47—21no—
225C22×C4×C47—41no—
226C22×C4×C47C2×D411yescharacteristic
227C22×C4×C47C2×D411yescharacteristic
228C22×C4×C47C2×D411yescharacteristic
229Q16×C47—81no—
230SD16×C47—81no—
231SD16×C47—81no—
232SD16×C47—81no—
233D8×C47—81no—
234D8×C47—81no—
235D8×C47—82no—
236D8×C47—82no—
237M16×C47—81no—
238C2×C8×C47—21no—
239C2×C8×C47—21no—
240C2×C8×C47—21no—
241C2×C8×C47—21no—
242C2×C8×C47—21no—
243C2×C8×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×C47—21no—
252C4⋊C4×C47—21no—
253C4⋊C4×C47—21no—
254C4⋊C4×C47C2×D411yescharacteristic
255C4⋊C4×C47C2×D411yescharacteristic
256C4⋊C4×C47C2×D411yescharacteristic
257C4⋊C4×C47C2×D411yescharacteristic
258C22⋊C4×C47—22no—
259C22⋊C4×C47—22no—
260C22⋊C4×C47—22no—
261C22⋊C4×C47—22no—
262C22⋊C4×C47—22no—
263C22⋊C4×C47—22no—
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—21no—
274C22⋊C4×C47—41no—
275C22⋊C4×C47—41no—
276C42×C47—21no—
277C42×C47—21no—
278C42×C47C2×D411yescharacteristic
279C42×C47C2×D411yescharacteristic
280C42×C47C2×D411yescharacteristic
281C42×C47C2411yescharacteristic
282C23×C47—21no—
283C23×C47—21no—
284C23×C47—22no—
285C23×C47—22no—
286C23×C47—44no—
287C23×C47—41no—
288C23×C47—82no—
289C23×C47—82no—
290C23×C47—82no—
291C23×C47—82no—
292C23×C47—82no—
293C23×C47#12011yescharacteristic
294Q8×C47—21no—
295Q8×C47—21no—
296Q8×C47—21no—
297Q8×C47—21no—
298Q8×C47—41no—
299Q8×C47—41no—
300D4×C47—21no—
301D4×C47—21no—
302D4×C47—21no—
303D4×C47—21no—
304D4×C47—42no—
305D4×C47—42no—
306D4×C47—42no—
307D4×C47—42no—
308D4×C47—42no—
309D4×C47—41no—
310D4×C47—41no—
311D4×C47—41no—
312D4×C47—41no—
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—82no—
322D4×C47—82no—
323D4×C47—82no—
324D4×C47—82no—
325D4×C47—82no—
326D4×C47—82no—
327D4×C47—82no—
328D4×C47—82no—
329D4×C47—82no—
330D4×C47—82no—
331C2×C4×C47—21no—
332C2×C4×C47—21no—
333C2×C4×C47—21no—
334C2×C4×C47—21no—
335C2×C4×C47—21no—
336C2×C4×C47—21no—
337C2×C4×C47—21no—
338C2×C4×C47—21no—
339C2×C4×C47—21no—
340C2×C4×C47—21no—
341C2×C4×C47—41no—
342C2×C4×C47—41no—
343C2×C4×C47—41no—
344C2×C4×C47—41no—
345C2×C4×C47—41no—
346C2×C4×C47—41no—
347C2×C4×C47—82no—
348C2×C4×C47—82no—
349C2×C4×C47—82no—
350C2×C4×C47—82no—
351C2×C4×C47#12011yescharacteristic
352C2×C4×C47#12011yescharacteristic
353C2×C4×C47#12011yescharacteristic
354C2×C4×C47C22×D411yescharacteristic
355C2×C4×C47C22×D411yescharacteristic
356C2×C4×C47C22×D411yescharacteristic
357C8×C47—41no—
358C8×C47—41no—
359C8×C47—41no—
360C8×C47—41no—
361C8×C47—41no—
362C8×C47—41no—
363#18930C4711yesmaximal, characteristic, direct product factor, Sylow
364C22×C47—21no—
365C22×C47—21no—
366C22×C47—21no—
367C22×C47—41no—
368C22×C47—42no—
369C22×C47—41no—
370C22×C47—42no—
371C22×C47—41no—
372C22×C47—42no—
373C22×C47—41no—
374C22×C47—42no—
375C22×C47—42no—
376C22×C47—41no—
377C22×C47—41no—
378C22×C47—42no—
379C22×C47—81no—
380C22×C47—81no—
381C22×C47—81no—
382C22×C47—164no—
383C22×C47—164no—
384C22×C47C2×#12011yescharacteristic
385C4×C47—21no—
386C4×C47—21no—
387C4×C47—21no—
388C4×C47—21no—
389C4×C47—41no—
390C4×C47—41no—
391C4×C47—41no—
392C4×C47—41no—
393C4×C47—41no—
394C4×C47—41no—
395C4×C47—81no—
396C4×C47#57611yescharacteristic
397C4×C47#57611yescharacteristic
398C4×C47#57611yescharacteristic
399C4×C47#57711yescharacteristic
400#3543C2×C4711yescharacteristic, complemented
401#3251C2×C4711yescharacteristic, complemented
402#3212C2×C4711yescharacteristic, complemented
403#3205C2×C4711yescharacteristic, complemented
404#1642C2×C4711yescharacteristic, complemented
405#1641C2×C4711yescharacteristic, complemented
406#1640C2×C4711yescharacteristic, complemented
407#1639C2×C4711yescharacteristic, complemented
408#1621C2×C4711yescharacteristic, complemented
409#1621C2×C4711yescharacteristic, complemented
410#1620C2×C4711yescharacteristic, complemented
411#1619C2×C4711yescharacteristic, complemented
412#1545C2×C4711yescharacteristic, complemented
413#1495C2×C4711yescharacteristic, complemented
414#1482C2×C4711yescharacteristic, complemented
415C2×C47—41no—
416C2×C47—82no—
417C2×C47—81no—
418C2×C47—81no—
419C2×C47—82no—
420C2×C47—161no—
421C2×C47#300811yescharacteristic
422C2×C47#301211yescharacteristic
423C2×C47#301911yescharacteristic
424#560—22no—
425#559C22×C4711yescharacteristic
426#550C22×C4711yescharacteristic
427#550C22×C4711yescharacteristic
428#546—21no—
429#546—21no—
430D42—21no—
431D42—21no—
432D42C22×C4711yescharacteristic
433#540—21no—
434#540—21no—
435#535—21no—
436#535—21no—
437#534—22no—
438#532C22×C4711yescharacteristic, complemented
439C2×#127C22×C4711yescharacteristic
440#529C22×C4711yescharacteristic
441#529C22×C4711yescharacteristic
442#495—21no—
443#493C22×C4711yescharacteristic
444#493C22×C4711yescharacteristic, complemented
445#488—21no—
446#486C22×C4711yescharacteristic
447#486C22×C4711yescharacteristic, complemented
448#478—21no—
449#475C22×C4711yescharacteristic, complemented
450#474C22×C4711yescharacteristic, complemented
451#469—21no—
452#468—21no—
453#463—21no—
454#462C22×C4711yescharacteristic, complemented
455#461C22×C4711yescharacteristic, complemented
456#460C22×C4711yescharacteristic, complemented
457#460C22×C4711yescharacteristic, complemented
458#459—22no—
459#459C22×C4711yescharacteristic, complemented
460#459C22×C4711yescharacteristic, complemented
461#452—21no—
462#449—21no—
463#447—22no—
464#431C22×C4711yescharacteristic, complemented
465#431C22×C4711yescharacteristic, complemented
466#423C22×C4711yescharacteristic, complemented
467#331C22×C4711yescharacteristic
468#331C22×C4711yescharacteristic
469#331C22×C4711yescharacteristic, complemented
470#331C22×C4711yescharacteristic, complemented
471Q8⋊C8C22×C4711yescharacteristic, complemented
472Q8⋊C8C22×C4711yescharacteristic, complemented
473Q8⋊C8C22×C4711yescharacteristic, complemented
474Q8⋊C8C22×C4711yescharacteristic, complemented
475D4⋊C8C22×C4711yescharacteristic, complemented
476D4⋊C8C22×C4711yescharacteristic, complemented
477D4⋊C8C22×C4711yescharacteristic, complemented
478D4⋊C8C22×C4711yescharacteristic, complemented
479C47#1893011yescharacteristic, direct product factor, Sylow
480C2×#41—21no—
481C2×#41—21no—
482C2×#41—21no—
483C22×D4—22no—
484C22×D4—21no—
485C22×D4—21no—
486C22×D4—21no—
487C22×D4—21no—
488C22×D4D4×C4712yes—
489C2×Q16—21no—
490C2×SD16—21no—
491C2×SD16—21no—
492C2×SD16—21no—
493C2×D8—22no—
494C2×D8—22no—
495C2×D8—21no—
496C2×D8—21no—
497C2×M16—21no—
498C4⋊Q8C23×C4711yescharacteristic
499#127—21no—
500#127—21no—
501#127—21no—
502#127—21no—
503#127D4×C4712yes—
504#127C23×C4711yescharacteristic
505#127C23×C4711yescharacteristic
506#127C23×C4711yescharacteristic
507#126—21no—
508#126—21no—
509#125D4×C4711yescharacteristic
510#125D4×C4711yescharacteristic
511#124—21no—
512#124—21no—
513#124—21no—
514#124D4×C4711yescharacteristic
515#124D4×C4711yescharacteristic
516#123—22no—
517#123—22no—
518#123—22no—
519#123—22no—
520#123—21no—
521#123—21no—
522C22⋊Q8D4×C4711yescharacteristic
523C22⋊Q8D4×C4711yescharacteristic
524#121—22no—
525#121—22no—
526#121—22no—
527#121—22no—
528#121—22no—
529#121—22no—
530#121—22no—
531#121—22no—
532#121—21no—
533#121—21no—
534#121—21no—
535#121—21no—
536#121—21no—
537#121—21no—
538#121D4×C4711yescharacteristic
539#121D4×C4711yescharacteristic
540#120—22no—
541#120—22no—
542#120—22no—
543#120—22no—
544#120—22no—
545#120—22no—
546C4×Q8C23×C4711yescharacteristic
547C4×Q8C23×C4711yescharacteristic
548C4×D4—21no—
549C4×D4—21no—
550C4×D4—21no—
551C4×D4—21no—
552C4×D4—21no—
553C4×D4—21no—
554C4×D4—21no—
555C4×D4—21no—
556C4×D4C23×C4711yescharacteristic
557C4×D4C23×C4711yescharacteristic
558#117—21no—
559#117—21no—
560C2×C22⋊C4—22no—
561C2×C42C23×C4711yescharacteristic
562#107—21no—
563#106—21no—
564C4⋊C8—21no—
565C4⋊C8—21no—
566C4⋊C8C23×C4711yescharacteristic
567C4⋊C8C23×C4711yescharacteristic
568C4⋊C8C23×C4711yescharacteristic
569C4⋊C8C23×C4711yescharacteristic
570#103—21no—
571#103—21no—
572#103—21no—
573#102—22no—
574#102—22no—
575#102—21no—
576#102—21no—
577#102—21no—
578#102—21no—
579#102—21no—
580C22⋊C8—21no—
581C22⋊C8—21no—
582C4×C8—21no—
583C4×C8C23×C4711yescharacteristic
584C4×C8C23×C4711yescharacteristic
585C24—22no—
586C24—22no—
587#41—81no—
588#41—81no—
589#41—81no—
590#41—81no—
591#41—81no—
592#41—81no—
593C2×Q8—21no—
594C2×Q8C2×D4×C4711yescharacteristic
595C2×Q8C2×D4×C4711yescharacteristic
596C2×D4—21no—
597C2×D4—21no—
598C2×D4—22no—
599C2×D4—22no—
600C2×D4—22no—
601C2×D4—22no—
602C2×D4—22no—
603C2×D4—22no—
604C2×D4—22no—
605C2×D4—22no—
606C2×D4—22no—
607C2×D4—21no—
608C2×D4—21no—
609C2×D4—21no—
610C2×D4—21no—
611C2×D4—21no—
612C2×D4—21no—
613C2×D4—21no—
614C2×D4—41no—
615C2×D4—81no—
616C2×D4—81no—
617C2×D4—81no—
618C2×D4—81no—
619C2×D4—81no—
620C2×D4—81no—
621C2×D4—81no—
622C2×D4—81no—
623C2×D4—82no—
624C2×D4—84no—
625C2×D4C2×D4×C4711yescharacteristic
626C2×D4C2×D4×C4711yescharacteristic
627C2×D4C2×D4×C4712yes—
628C2×D4C2×D4×C4712yes—
629C22×C4—22no—
630C22×C4—22no—
631C22×C4—22no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—41no—
635C22×C4C2×D4×C4711yescharacteristic
636C22×C4C2×D4×C4711yescharacteristic
637C22×C4C2×D4×C4711yescharacteristic
638Q16—81no—
639SD16—81no—
640SD16—81no—
641SD16—81no—
642D8—81no—
643D8—81no—
644D8—82no—
645D8—82no—
646M16—81no—
647C2×C8—21no—
648C2×C8—21no—
649C2×C8—21no—
650C2×C8—21no—
651C2×C8—21no—
652C2×C8—21no—
653C4⋊C4—21no—
654C4⋊C4—21no—
655C4⋊C4—21no—
656C4⋊C4—21no—
657C4⋊C4—21no—
658C4⋊C4—21no—
659C4⋊C4—21no—
660C4⋊C4—21no—
661C4⋊C4—21no—
662C4⋊C4—21no—
663C4⋊C4C2×D4×C4711yescharacteristic
664C4⋊C4C2×D4×C4711yescharacteristic
665C4⋊C4C2×D4×C4711yescharacteristic
666C4⋊C4C2×D4×C4711yescharacteristic
667C22⋊C4—22no—
668C22⋊C4—22no—
669C22⋊C4—22no—
670C22⋊C4—22no—
671C22⋊C4—22no—
672C22⋊C4—22no—
673C22⋊C4—21no—
674C22⋊C4—21no—
675C22⋊C4—21no—
676C22⋊C4—21no—
677C22⋊C4—21no—
678C22⋊C4—21no—
679C22⋊C4—21no—
680C22⋊C4—21no—
681C22⋊C4—21no—
682C22⋊C4—21no—
683C22⋊C4—41no—
684C22⋊C4—41no—
685C42—21no—
686C42—21no—
687C42C2×D4×C4711yescharacteristic
688C42C2×D4×C4711yescharacteristic
689C42C2×D4×C4711yescharacteristic
690C42C24×C4711yescharacteristic
691C23—21no—
692C23—21no—
693C23—22no—
694C23—22no—
695C23—44no—
696C23—41no—
697C23—82no—
698C23—82no—
699C23—82no—
700C23—82no—
701C23—82no—
702C23#120×C4711yescharacteristic
703Q8—21no—
704Q8—21no—
705Q8—21no—
706Q8—21no—
707Q8—41no—
708Q8—41no—
709D4—21no—
710D4—21no—
711D4—21no—
712D4—21no—
713D4—42no—
714D4—42no—
715D4—42no—
716D4—42no—
717D4—42no—
718D4—41no—
719D4—41no—
720D4—41no—
721D4—41no—
722D4—41no—
723D4—41no—
724D4—41no—
725D4—41no—
726D4—41no—
727D4—41no—
728D4—41no—
729D4—41no—
730D4—82no—
731D4—82no—
732D4—82no—
733D4—82no—
734D4—82no—
735D4—82no—
736D4—82no—
737D4—82no—
738D4—82no—
739D4—82no—
740C2×C4—21no—
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—21no—
744C2×C4—21no—
745C2×C4—21no—
746C2×C4—21no—
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—82no—
757C2×C4—82no—
758C2×C4—82no—
759C2×C4—82no—
760C2×C4#120×C4711yescharacteristic
761C2×C4#120×C4711yescharacteristic
762C2×C4#120×C4711yescharacteristic
763C2×C4C22×D4×C4711yescharacteristic
764C2×C4C22×D4×C4711yescharacteristic
765C2×C4C22×D4×C4711yescharacteristic
766C8—41no—
767C8—41no—
768C8—41no—
769C8—41no—
770C8—41no—
771C8—41no—
772C22—21no—
773C22—21no—
774C22—21no—
775C22—41no—
776C22—42no—
777C22—41no—
778C22—42no—
779C22—41no—
780C22—42no—
781C22—41no—
782C22—42no—
783C22—42no—
784C22—41no—
785C22—41no—
786C22—42no—
787C22—81no—
788C22—81no—
789C22—81no—
790C22—164no—
791C22—164no—
792C22C2×#120×C4711yescharacteristic
793C4—21no—
794C4—21no—
795C4—21no—
796C4—21no—
797C4—41no—
798C4—41no—
799C4—41no—
800C4—41no—
801C4—41no—
802C4—41no—
803C4—81no—
804C4C47×#57611yescharacteristic
805C4C47×#57611yescharacteristic
806C4C47×#57611yescharacteristic
807C4C47×#57711yescharacteristic
808C2—41no—
809C2—81no—
810C2—81no—
811C2—82no—
812C2—82no—
813C2—161no—
814C2C47×#300811yescharacteristic
815C2C47×#301211yescharacteristic
816C2C47×#301911yescharacteristic
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×#3543C2semidirect
2. C47×#3251C2semidirect
3. C47×#3212C2semidirect
4. C47×#3205C2semidirect
5. C47×#1642C2semidirect
6. C47×#1641C2semidirect
7. C47×#1640C2semidirect
8. C47×#1639C2semidirect
9. C47×#1621C2semidirect
10. C47×#1621C2semidirect
11. C47×#1620C2semidirect
12. C47×#1619C2semidirect
13. C47×#1545C2semidirect
14. C47×#1495C2semidirect
15. C47×#1482C2semidirect
30. C47×#532C22semidirect
36. C47×#493C22semidirect
39. C47×#486C22semidirect
41. C47×#475C22semidirect
42. C47×#474C22semidirect
46. C47×#462C22semidirect
47. C47×#461C22semidirect
48. C47×#460C22semidirect
49. C47×#460C22semidirect
51. C47×#459C22semidirect
52. C47×#459C22semidirect
56. C47×#431C22semidirect
57. C47×#431C22semidirect
58. C47×#423C22semidirect
61. C47×#331C22semidirect
62. C47×#331C22semidirect
63. C47×Q8⋊C8C22semidirect
64. C47×Q8⋊C8C22semidirect
65. C47×Q8⋊C8C22semidirect
66. C47×Q8⋊C8C22semidirect
67. C47×D4⋊C8C22semidirect
68. C47×D4⋊C8C22semidirect
69. C47×D4⋊C8C22semidirect
70. C47×D4⋊C8C22semidirect
363. #18930C47direct (N × H)
400. #3543C2×C47semidirect
401. #3251C2×C47semidirect
402. #3212C2×C47semidirect
403. #3205C2×C47semidirect
404. #1642C2×C47semidirect
405. #1641C2×C47semidirect
406. #1640C2×C47semidirect
407. #1639C2×C47semidirect
408. #1621C2×C47semidirect
409. #1621C2×C47semidirect
410. #1620C2×C47semidirect
411. #1619C2×C47semidirect
412. #1545C2×C47semidirect
413. #1495C2×C47semidirect
414. #1482C2×C47semidirect
438. #532C22×C47semidirect
444. #493C22×C47semidirect
447. #486C22×C47semidirect
449. #475C22×C47semidirect
450. #474C22×C47semidirect
454. #462C22×C47semidirect
455. #461C22×C47semidirect
456. #460C22×C47semidirect
457. #460C22×C47semidirect
459. #459C22×C47semidirect
460. #459C22×C47semidirect
464. #431C22×C47semidirect
465. #431C22×C47semidirect
466. #423C22×C47semidirect
469. #331C22×C47semidirect
470. #331C22×C47semidirect
471. Q8⋊C8C22×C47semidirect
472. Q8⋊C8C22×C47semidirect
473. Q8⋊C8C22×C47semidirect
474. Q8⋊C8C22×C47semidirect
475. D4⋊C8C22×C47semidirect
476. D4⋊C8C22×C47semidirect
477. D4⋊C8C22×C47semidirect
478. D4⋊C8C22×C47semidirect
479. C47#18930direct (N × H)

Maximal subgroups

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

subgroupindex
C47×#35432
C47×#32512
C47×#32122
C47×#32052
C47×#16422
C47×#16412
C47×#16402
C47×#16392
C47×#16212
C47×#16202
C47×#16192
C47×#15452
C47×#14952
C47×#14822
#1893047