Finite Group Databasebeta

← C47×#18962 #26058660

Subgroups — C47×#18962 #26058660

Order 12032.

964 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3546C211yesmaximal, characteristic, complemented
2C47×#3253C211yesmaximal, characteristic, complemented
3C47×#3247C211yesmaximal, characteristic, complemented
4C47×#3207C211yesmaximal, characteristic, complemented
5C47×#1638C211yesmaximal, characteristic, complemented
6C47×#1635C211yesmaximal, characteristic, complemented
7C47×#1631C211yesmaximal, characteristic, complemented
8C47×#1629C211yesmaximal, characteristic, complemented
9C47×#1628C211yesmaximal, characteristic, complemented
10C47×#1625C211yesmaximal, characteristic, complemented
11C47×#1621C211yesmaximal, characteristic, complemented
12C47×#1619C211yesmaximal, characteristic, complemented
13C47×#1547C211yesmaximal, characteristic, complemented
14C47×#1495C211yesmaximal, characteristic, complemented
15C47×#1480C211yesmaximal, 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×#493C2211yescharacteristic
35C47×#492C2211yescharacteristic
36C47×#487C2211yescharacteristic, complemented
37C47×#486C2211yescharacteristic, complemented
38C47×#478—21no—
39C47×#477C2211yescharacteristic, complemented
40C47×#476—21no—
41C47×#476C2211yescharacteristic
42C47×#476C2211yescharacteristic
43C47×#476C2211yescharacteristic, complemented
44C47×#469—21no—
45C47×#469—21no—
46C47×#466—21no—
47C47×#465—21no—
48C47×#463—21no—
49C47×#463—22no—
50C47×#460C2211yescharacteristic, complemented
51C47×#459—21no—
52C47×#459C2211yescharacteristic
53C47×#459C2211yescharacteristic
54C47×#459C2211yescharacteristic, complemented
55C47×#449—22no—
56C47×#431C2211yescharacteristic, complemented
57C47×#423C2211yescharacteristic, complemented
58C2×C4⋊C8×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×SD16×C47—21no—
79C2×SD16×C47—22no—
80C2×D8×C47—22no—
81C2×D8×C47—21no—
82C2×D8×C47—21no—
83C2×D8×C47—21no—
84C2×M16×C47—21no—
85C22×C8×C47—21no—
86C4⋊Q8×C47D411yescharacteristic
87C4⋊Q8×C47C2311yescharacteristic
88C4⋊Q8×C47C2311yescharacteristic
89#127×C47—22no—
90#127×C47—21no—
91#127×C47D411yescharacteristic
92#127×C47C2311yescharacteristic
93#127×C47C2311yescharacteristic
94#126×C47—22no—
95#126×C47—22no—
96#126×C47—21no—
97#125×C47D411yescharacteristic
98#124×C47—22no—
99#124×C47—21no—
100#124×C47—21no—
101#124×C47—21no—
102#124×C47—21no—
103#124×C47D411yescharacteristic
104#123×C47—22no—
105#123×C47—22no—
106#123×C47—21no—
107#123×C47—22no—
108C22⋊Q8×C47—22no—
109C22⋊Q8×C47—21no—
110C22⋊Q8×C47—21no—
111C22⋊Q8×C47D411yescharacteristic
112#121×C47—22no—
113#121×C47—22no—
114#121×C47—22no—
115#121×C47—22no—
116#121×C47—22no—
117#121×C47—21no—
118#121×C47—22no—
119#121×C47—21no—
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×C47D412yes—
127#121×C47D411yescharacteristic
128#121×C47D411yescharacteristic
129#121×C47D411yescharacteristic
130#120×C47—22no—
131#120×C47—22no—
132#120×C47—22no—
133#120×C47—22no—
134C4×Q8×C47—21no—
135C4×Q8×C47C2311yescharacteristic
136C4×D4×C47—22no—
137C4×D4×C47—21no—
138C4×D4×C47—21no—
139C4×D4×C47—21no—
140C4×D4×C47—21no—
141C4×D4×C47—21no—
142C4×D4×C47—21no—
143C4×D4×C47D412yes—
144C4×D4×C47C2311yescharacteristic
145C4×D4×C47C2311yescharacteristic
146C4×D4×C47C2311yescharacteristic
147#117×C47—21no—
148#117×C47—21no—
149C2×C4⋊C4×C47—21no—
150C2×C22⋊C4×C47—22no—
151C2×C42×C47C2311yescharacteristic
152#107×C47—21no—
153#106×C47—21no—
154#106×C47—21no—
155#106×C47—21no—
156C4⋊C8×C47—21no—
157C4⋊C8×C47—21no—
158C4⋊C8×C47—21no—
159C4⋊C8×C47C2311yescharacteristic
160C4⋊C8×C47C2311yescharacteristic
161C4⋊C8×C47C2311yescharacteristic
162C4⋊C8×C47C2311yescharacteristic
163#103×C47—21no—
164#103×C47—22no—
165#102×C47—21no—
166#102×C47—21no—
167#102×C47—21no—
168#102×C47—22no—
169#102×C47—21no—
170#102×C47—21no—
171#102×C47—21no—
172#102×C47—21no—
173C22⋊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—82no—
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—21no—
204C2×D4×C47—21no—
205C2×D4×C47—21no—
206C2×D4×C47—41no—
207C2×D4×C47—81no—
208C2×D4×C47—81no—
209C2×D4×C47—81no—
210C2×D4×C47—81no—
211C2×D4×C47C2×D411yescharacteristic
212C2×D4×C47C2×D411yescharacteristic
213C2×D4×C47C2×D411yescharacteristic
214C2×D4×C47C2×D412yes—
215C22×C4×C47—22no—
216C22×C4×C47—22no—
217C22×C4×C47—21no—
218C22×C4×C47—21no—
219C22×C4×C47—21no—
220C22×C4×C47—22no—
221C22×C4×C47—41no—
222C22×C4×C47C2×D411yescharacteristic
223C22×C4×C47C2×D411yescharacteristic
224C22×C4×C47C2×D411yescharacteristic
225SD16×C47—81no—
226SD16×C47—82no—
227D8×C47—81no—
228D8×C47—81no—
229D8×C47—81no—
230D8×C47—82no—
231M16×C47—81no—
232C2×C8×C47—21no—
233C2×C8×C47—21no—
234C2×C8×C47—21no—
235C2×C8×C47—21no—
236C2×C8×C47—21no—
237C2×C8×C47—21no—
238C2×C8×C47—81no—
239C4⋊C4×C47—22no—
240C4⋊C4×C47—22no—
241C4⋊C4×C47—21no—
242C4⋊C4×C47—21no—
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×C47C2×D412yes—
250C4⋊C4×C47C2×D411yescharacteristic
251C4⋊C4×C47C2×D411yescharacteristic
252C4⋊C4×C47C2×D411yescharacteristic
253C4⋊C4×C47C2×D411yescharacteristic
254C22⋊C4×C47—22no—
255C22⋊C4×C47—22no—
256C22⋊C4×C47—22no—
257C22⋊C4×C47—22no—
258C22⋊C4×C47—22no—
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—22no—
266C22⋊C4×C47—22no—
267C22⋊C4×C47—21no—
268C22⋊C4×C47—21no—
269C22⋊C4×C47—21no—
270C22⋊C4×C47—41no—
271C22⋊C4×C47—41no—
272C42×C47—22no—
273C42×C47—21no—
274C42×C47C2×D411yescharacteristic
275C42×C47C2×D411yescharacteristic
276C42×C47C2×D411yescharacteristic
277C42×C47C2411yescharacteristic
278C23×C47—21no—
279C23×C47—21no—
280C23×C47—22no—
281C23×C47—21no—
282C23×C47—41no—
283C23×C47—82no—
284C23×C47—82no—
285C23×C47—82no—
286C23×C47#12011yescharacteristic
287Q8×C47—21no—
288Q8×C47—21no—
289Q8×C47—42no—
290Q8×C47—41no—
291Q8×C47—41no—
292Q8×C47—81no—
293D4×C47—21no—
294D4×C47—21no—
295D4×C47—21no—
296D4×C47—21no—
297D4×C47—21no—
298D4×C47—21no—
299D4×C47—42no—
300D4×C47—42no—
301D4×C47—41no—
302D4×C47—41no—
303D4×C47—41no—
304D4×C47—41no—
305D4×C47—41no—
306D4×C47—41no—
307D4×C47—41no—
308D4×C47—41no—
309D4×C47—81no—
310D4×C47—81no—
311D4×C47—81no—
312D4×C47—81no—
313D4×C47—81no—
314D4×C47—82no—
315D4×C47—82no—
316D4×C47—82no—
317D4×C47—82no—
318D4×C47—82no—
319D4×C47—82no—
320D4×C47—82no—
321C2×C4×C47—21no—
322C2×C4×C47—21no—
323C2×C4×C47—21no—
324C2×C4×C47—21no—
325C2×C4×C47—21no—
326C2×C4×C47—21no—
327C2×C4×C47—21no—
328C2×C4×C47—22no—
329C2×C4×C47—21no—
330C2×C4×C47—21no—
331C2×C4×C47—41no—
332C2×C4×C47—41no—
333C2×C4×C47—41no—
334C2×C4×C47—41no—
335C2×C4×C47—41no—
336C2×C4×C47—41no—
337C2×C4×C47—41no—
338C2×C4×C47—41no—
339C2×C4×C47—82no—
340C2×C4×C47—82no—
341C2×C4×C47—82no—
342C2×C4×C47—82no—
343C2×C4×C47#12011yescharacteristic
344C2×C4×C47#12011yescharacteristic
345C2×C4×C47#12011yescharacteristic
346C2×C4×C47C22×D411yescharacteristic
347C2×C4×C47C22×D411yescharacteristic
348C2×C4×C47C22×D411yescharacteristic
349C8×C47—41no—
350C8×C47—41no—
351C8×C47—41no—
352C8×C47—41no—
353C8×C47—41no—
354C8×C47—41no—
355#18962C4711yesmaximal, characteristic, direct product factor, Sylow
356C22×C47—21no—
357C22×C47—21no—
358C22×C47—21no—
359C22×C47—41no—
360C22×C47—41no—
361C22×C47—41no—
362C22×C47—41no—
363C22×C47—42no—
364C22×C47—42no—
365C22×C47—41no—
366C22×C47—41no—
367C22×C47—42no—
368C22×C47—41no—
369C22×C47—41no—
370C22×C47—41no—
371C22×C47—81no—
372C22×C47—81no—
373C22×C47—81no—
374C22×C47—164no—
375C22×C47C2×#12011yescharacteristic
376C4×C47—21no—
377C4×C47—21no—
378C4×C47—21no—
379C4×C47—21no—
380C4×C47—41no—
381C4×C47—41no—
382C4×C47—41no—
383C4×C47—41no—
384C4×C47—42no—
385C4×C47—41no—
386C4×C47—81no—
387C4×C47#57611yescharacteristic
388C4×C47#57611yescharacteristic
389C4×C47#57711yescharacteristic
390C4×C47#57711yescharacteristic
391#3546C2×C4711yescharacteristic, complemented
392#3253C2×C4711yescharacteristic, complemented
393#3247C2×C4711yescharacteristic, complemented
394#3207C2×C4711yescharacteristic, complemented
395#1638C2×C4711yescharacteristic, complemented
396#1635C2×C4711yescharacteristic, complemented
397#1631C2×C4711yescharacteristic, complemented
398#1629C2×C4711yescharacteristic, complemented
399#1628C2×C4711yescharacteristic, complemented
400#1625C2×C4711yescharacteristic, complemented
401#1621C2×C4711yescharacteristic, complemented
402#1619C2×C4711yescharacteristic, complemented
403#1547C2×C4711yescharacteristic, complemented
404#1495C2×C4711yescharacteristic, complemented
405#1480C2×C4711yescharacteristic, complemented
406C2×C47—41no—
407C2×C47—81no—
408C2×C47—82no—
409C2×C47—81no—
410C2×C47—81no—
411C2×C47—161no—
412C2×C47#301211yescharacteristic
413C2×C47#301211yescharacteristic
414C2×C47#302111yescharacteristic
415#560—22no—
416#556C22×C4711yescharacteristic
417#553—21no—
418#550—21no—
419#550C22×C4711yescharacteristic
420#547C22×C4711yescharacteristic
421#546—21no—
422#546—21no—
423D42C22×C4711yescharacteristic
424#542—21no—
425#538—22no—
426#537—21no—
427#535—21no—
428#535—21no—
429#532C22×C4711yescharacteristic
430#532C22×C4711yescharacteristic
431#532C22×C4711yescharacteristic, complemented
432#529C22×C4711yescharacteristic
433#493C22×C4711yescharacteristic
434#492C22×C4711yescharacteristic
435#487C22×C4711yescharacteristic, complemented
436#486C22×C4711yescharacteristic, complemented
437#478—21no—
438#477C22×C4711yescharacteristic, complemented
439#476—21no—
440#476C22×C4711yescharacteristic
441#476C22×C4711yescharacteristic
442#476C22×C4711yescharacteristic, complemented
443#469—21no—
444#469—21no—
445#466—21no—
446#465—21no—
447#463—21no—
448#463—22no—
449#460C22×C4711yescharacteristic, complemented
450#459—21no—
451#459C22×C4711yescharacteristic
452#459C22×C4711yescharacteristic
453#459C22×C4711yescharacteristic, complemented
454#449—22no—
455#431C22×C4711yescharacteristic, complemented
456#423C22×C4711yescharacteristic, complemented
457C2×C4⋊C8C22×C4711yescharacteristic, complemented
458#332C22×C4711yescharacteristic, complemented
459#332C22×C4711yescharacteristic, complemented
460#331C22×C4711yescharacteristic
461#331C22×C4711yescharacteristic
462Q8⋊C8C22×C4711yescharacteristic, complemented
463Q8⋊C8C22×C4711yescharacteristic, complemented
464D4⋊C8C22×C4711yescharacteristic
465D4⋊C8C22×C4711yescharacteristic
466D4⋊C8C22×C4711yescharacteristic
467D4⋊C8C22×C4711yescharacteristic
468D4⋊C8C22×C4711yescharacteristic, complemented
469D4⋊C8C22×C4711yescharacteristic, complemented
470C47#1896211yescharacteristic, direct product factor, Sylow
471C2×#41—21no—
472C2×#41—21no—
473C2×#41—21no—
474C2×#41—21no—
475C2×#41—21no—
476C22×D4—21no—
477C22×D4—21no—
478C2×SD16—21no—
479C2×SD16—22no—
480C2×D8—22no—
481C2×D8—21no—
482C2×D8—21no—
483C2×D8—21no—
484C2×M16—21no—
485C22×C8—21no—
486C4⋊Q8D4×C4711yescharacteristic
487C4⋊Q8C23×C4711yescharacteristic
488C4⋊Q8C23×C4711yescharacteristic
489#127—22no—
490#127—21no—
491#127D4×C4711yescharacteristic
492#127C23×C4711yescharacteristic
493#127C23×C4711yescharacteristic
494#126—22no—
495#126—22no—
496#126—21no—
497#125D4×C4711yescharacteristic
498#124—22no—
499#124—21no—
500#124—21no—
501#124—21no—
502#124—21no—
503#124D4×C4711yescharacteristic
504#123—22no—
505#123—22no—
506#123—21no—
507#123—22no—
508C22⋊Q8—22no—
509C22⋊Q8—21no—
510C22⋊Q8—21no—
511C22⋊Q8D4×C4711yescharacteristic
512#121—22no—
513#121—22no—
514#121—22no—
515#121—22no—
516#121—22no—
517#121—21no—
518#121—22no—
519#121—21no—
520#121—21no—
521#121—21no—
522#121—21no—
523#121—21no—
524#121—21no—
525#121—21no—
526#121D4×C4711yescharacteristic
527#121D4×C4711yescharacteristic
528#121D4×C4711yescharacteristic
529#121D4×C4712yes—
530#120—22no—
531#120—22no—
532#120—22no—
533#120—22no—
534C4×Q8—21no—
535C4×Q8C23×C4711yescharacteristic
536C4×D4—22no—
537C4×D4—21no—
538C4×D4—21no—
539C4×D4—21no—
540C4×D4—21no—
541C4×D4—21no—
542C4×D4—21no—
543C4×D4D4×C4712yes—
544C4×D4C23×C4711yescharacteristic
545C4×D4C23×C4711yescharacteristic
546C4×D4C23×C4711yescharacteristic
547#117—21no—
548#117—21no—
549C2×C4⋊C4—21no—
550C2×C22⋊C4—22no—
551C2×C42C23×C4711yescharacteristic
552#107—21no—
553#106—21no—
554#106—21no—
555#106—21no—
556C4⋊C8—21no—
557C4⋊C8—21no—
558C4⋊C8—21no—
559C4⋊C8C23×C4711yescharacteristic
560C4⋊C8C23×C4711yescharacteristic
561C4⋊C8C23×C4711yescharacteristic
562C4⋊C8C23×C4711yescharacteristic
563#103—21no—
564#103—22no—
565#102—21no—
566#102—21no—
567#102—21no—
568#102—22no—
569#102—21no—
570#102—21no—
571#102—21no—
572#102—21no—
573C22⋊C8—21no—
574C4×C8C23×C4711yescharacteristic
575C4×C8C23×C4711yescharacteristic
576C24—22no—
577#41—81no—
578#41—81no—
579#41—81no—
580#41—81no—
581#41—81no—
582#41—81no—
583#41—81no—
584#41—81no—
585#41—82no—
586C2×Q8—21no—
587C2×Q8—21no—
588C2×Q8—21no—
589C2×Q8C2×D4×C4711yescharacteristic
590C2×D4—22no—
591C2×D4—22no—
592C2×D4—22no—
593C2×D4—22no—
594C2×D4—22no—
595C2×D4—21no—
596C2×D4—21no—
597C2×D4—22no—
598C2×D4—21no—
599C2×D4—21no—
600C2×D4—21no—
601C2×D4—21no—
602C2×D4—21no—
603C2×D4—21no—
604C2×D4—21no—
605C2×D4—21no—
606C2×D4—41no—
607C2×D4—81no—
608C2×D4—81no—
609C2×D4—81no—
610C2×D4—81no—
611C2×D4C2×D4×C4711yescharacteristic
612C2×D4C2×D4×C4711yescharacteristic
613C2×D4C2×D4×C4711yescharacteristic
614C2×D4C2×D4×C4712yes—
615C22×C4—22no—
616C22×C4—22no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—22no—
621C22×C4—41no—
622C22×C4C2×D4×C4711yescharacteristic
623C22×C4C2×D4×C4711yescharacteristic
624C22×C4C2×D4×C4711yescharacteristic
625SD16—81no—
626SD16—82no—
627D8—81no—
628D8—81no—
629D8—81no—
630D8—82no—
631M16—81no—
632C2×C8—21no—
633C2×C8—21no—
634C2×C8—21no—
635C2×C8—21no—
636C2×C8—21no—
637C2×C8—21no—
638C2×C8—81no—
639C4⋊C4—22no—
640C4⋊C4—22no—
641C4⋊C4—21no—
642C4⋊C4—21no—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—21no—
646C4⋊C4—21no—
647C4⋊C4—21no—
648C4⋊C4—21no—
649C4⋊C4C2×D4×C4712yes—
650C4⋊C4C2×D4×C4711yescharacteristic
651C4⋊C4C2×D4×C4711yescharacteristic
652C4⋊C4C2×D4×C4711yescharacteristic
653C4⋊C4C2×D4×C4711yescharacteristic
654C22⋊C4—22no—
655C22⋊C4—22no—
656C22⋊C4—22no—
657C22⋊C4—22no—
658C22⋊C4—22no—
659C22⋊C4—21no—
660C22⋊C4—21no—
661C22⋊C4—21no—
662C22⋊C4—21no—
663C22⋊C4—21no—
664C22⋊C4—21no—
665C22⋊C4—22no—
666C22⋊C4—22no—
667C22⋊C4—21no—
668C22⋊C4—21no—
669C22⋊C4—21no—
670C22⋊C4—41no—
671C22⋊C4—41no—
672C42—22no—
673C42—21no—
674C42C2×D4×C4711yescharacteristic
675C42C2×D4×C4711yescharacteristic
676C42C2×D4×C4711yescharacteristic
677C42C24×C4711yescharacteristic
678C23—21no—
679C23—21no—
680C23—22no—
681C23—21no—
682C23—41no—
683C23—82no—
684C23—82no—
685C23—82no—
686C23#120×C4711yescharacteristic
687Q8—21no—
688Q8—21no—
689Q8—42no—
690Q8—41no—
691Q8—41no—
692Q8—81no—
693D4—21no—
694D4—21no—
695D4—21no—
696D4—21no—
697D4—21no—
698D4—21no—
699D4—42no—
700D4—42no—
701D4—41no—
702D4—41no—
703D4—41no—
704D4—41no—
705D4—41no—
706D4—41no—
707D4—41no—
708D4—41no—
709D4—81no—
710D4—81no—
711D4—81no—
712D4—81no—
713D4—81no—
714D4—82no—
715D4—82no—
716D4—82no—
717D4—82no—
718D4—82no—
719D4—82no—
720D4—82no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—22no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—82no—
740C2×C4—82no—
741C2×C4—82no—
742C2×C4—82no—
743C2×C4#120×C4711yescharacteristic
744C2×C4#120×C4711yescharacteristic
745C2×C4#120×C4711yescharacteristic
746C2×C4C22×D4×C4711yescharacteristic
747C2×C4C22×D4×C4711yescharacteristic
748C2×C4C22×D4×C4711yescharacteristic
749C8—41no—
750C8—41no—
751C8—41no—
752C8—41no—
753C8—41no—
754C8—41no—
755C22—21no—
756C22—21no—
757C22—21no—
758C22—41no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—42no—
763C22—42no—
764C22—41no—
765C22—41no—
766C22—42no—
767C22—41no—
768C22—41no—
769C22—41no—
770C22—81no—
771C22—81no—
772C22—81no—
773C22—164no—
774C22C2×#120×C4711yescharacteristic
775C4—21no—
776C4—21no—
777C4—21no—
778C4—21no—
779C4—41no—
780C4—41no—
781C4—41no—
782C4—41no—
783C4—42no—
784C4—41no—
785C4—81no—
786C4C47×#57611yescharacteristic
787C4C47×#57611yescharacteristic
788C4C47×#57711yescharacteristic
789C4C47×#57711yescharacteristic
790C2—41no—
791C2—81no—
792C2—81no—
793C2—82no—
794C2—81no—
795C2—161no—
796C2C47×#301211yescharacteristic
797C2C47×#301211yescharacteristic
798C2C47×#302111yescharacteristic
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×#3253C2semidirect
3. C47×#3247C2semidirect
4. C47×#3207C2semidirect
5. C47×#1638C2semidirect
6. C47×#1635C2semidirect
7. C47×#1631C2semidirect
8. C47×#1629C2semidirect
9. C47×#1628C2semidirect
10. C47×#1625C2semidirect
11. C47×#1621C2semidirect
12. C47×#1619C2semidirect
13. C47×#1547C2semidirect
14. C47×#1495C2semidirect
15. C47×#1480C2semidirect
32. C47×#532C22semidirect
36. C47×#487C22semidirect
37. C47×#486C22semidirect
39. C47×#477C22semidirect
43. C47×#476C22semidirect
50. C47×#460C22semidirect
54. C47×#459C22semidirect
56. C47×#431C22semidirect
57. C47×#423C22semidirect
58. C2×C4⋊C8×C47C22semidirect
59. C47×#332C22semidirect
60. C47×#332C22semidirect
63. C47×Q8⋊C8C22semidirect
64. C47×Q8⋊C8C22semidirect
69. C47×D4⋊C8C22semidirect
70. C47×D4⋊C8C22semidirect
355. #18962C47direct (N × H)
391. #3546C2×C47semidirect
392. #3253C2×C47semidirect
393. #3247C2×C47semidirect
394. #3207C2×C47semidirect
395. #1638C2×C47semidirect
396. #1635C2×C47semidirect
397. #1631C2×C47semidirect
398. #1629C2×C47semidirect
399. #1628C2×C47semidirect
400. #1625C2×C47semidirect
401. #1621C2×C47semidirect
402. #1619C2×C47semidirect
403. #1547C2×C47semidirect
404. #1495C2×C47semidirect
405. #1480C2×C47semidirect
431. #532C22×C47semidirect
435. #487C22×C47semidirect
436. #486C22×C47semidirect
438. #477C22×C47semidirect
442. #476C22×C47semidirect
449. #460C22×C47semidirect
453. #459C22×C47semidirect
455. #431C22×C47semidirect
456. #423C22×C47semidirect
457. C2×C4⋊C8C22×C47semidirect
458. #332C22×C47semidirect
459. #332C22×C47semidirect
462. Q8⋊C8C22×C47semidirect
463. Q8⋊C8C22×C47semidirect
468. D4⋊C8C22×C47semidirect
469. D4⋊C8C22×C47semidirect
470. C47#18962direct (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×#32532
C47×#32472
C47×#32072
C47×#16382
C47×#16352
C47×#16312
C47×#16292
C47×#16282
C47×#16252
C47×#16212
C47×#16192
C47×#15472
C47×#14952
C47×#14802
#1896247