Finite Group Databasebeta

← C47×#18595 #26058293

Subgroups — C47×#18595 #26058293

Order 12032.

940 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3514C211yesmaximal, characteristic
2C47×#3252C211yesmaximal, characteristic, complemented
3C47×#3182C211yesmaximal, characteristic, complemented
4C47×#3076C211yesmaximal, characteristic, complemented
5C47×#1650C211yesmaximal, characteristic, complemented
6C47×#1649C211yesmaximal, characteristic, complemented
7C47×#1640C211yesmaximal, characteristic, complemented
8C47×#1639C211yesmaximal, characteristic, complemented
9C47×#1638C211yesmaximal, characteristic, complemented
10C47×#1637C211yesmaximal, characteristic, complemented
11C47×#1630C211yesmaximal, characteristic, complemented
12C47×#1629C211yesmaximal, characteristic, complemented
13C47×#1547C211yesmaximal, characteristic, complemented
14C47×#1489C211yesmaximal, characteristic, complemented
15C47×#1483C211yesmaximal, characteristic, complemented
16C47×#559C2211yescharacteristic
17C47×#556C2211yescharacteristic
18C47×#555—21no—
19C47×#551—22no—
20D4×Q8×C47C2211yescharacteristic
21C47×#548—21no—
22C47×#546—21no—
23C47×#546—21no—
24D42×C47C2211yescharacteristic
25C47×#542—21no—
26C47×#538—22no—
27C47×#533C2211yescharacteristic, complemented
28C47×#532C2211yescharacteristic
29C47×#529—21no—
30C47×#529C2211yescharacteristic
31C2×#124×C47—21no—
32C47×#518—21no—
33C4×#41×C47C2211yescharacteristic
34C47×#500C2211yescharacteristic, complemented
35C47×#492C2211yescharacteristic
36C47×#487C2211yescharacteristic, complemented
37C47×#486C2211yescharacteristic
38C47×#479—21no—
39C47×#479—21no—
40C47×#478—21no—
41C47×#477C2211yescharacteristic, complemented
42C47×#477C2211yescharacteristic, complemented
43C47×#476C2211yescharacteristic
44C47×#476C2211yescharacteristic
45C47×#475C2211yescharacteristic, complemented
46C47×#474C2211yescharacteristic
47C47×#470—21no—
48C47×#468—22no—
49C47×#468—21no—
50C47×#464—21no—
51C47×#462C2211yescharacteristic, complemented
52C47×#461C2211yescharacteristic
53C47×#440—22no—
54C47×#427—21no—
55C47×#423C2211yescharacteristic, complemented
56C2×C4⋊C8×C47C2211yescharacteristic, complemented
57C47×#416—21no—
58C4×M16×C47C2211yescharacteristic, complemented
59C47×#332C2211yescharacteristic, complemented
60C47×#332C2211yescharacteristic, complemented
61C47×#331C2211yescharacteristic
62C47×#331C2211yescharacteristic
63C47×Q8⋊C8C2211yescharacteristic, complemented
64C47×Q8⋊C8C2211yescharacteristic, complemented
65C47×Q8⋊C8C2211yescharacteristic, complemented
66C47×Q8⋊C8C2211yescharacteristic, complemented
67C47×D4⋊C8C2211yescharacteristic
68C47×D4⋊C8C2211yescharacteristic
69C47×D4⋊C8C2211yescharacteristic
70C47×D4⋊C8C2211yescharacteristic
71C2×#41×C47—21no—
72C2×#41×C47D411yescharacteristic
73C22×Q8×C47—21no—
74C22×D4×C47—21no—
75C22×D4×C47—21no—
76C2×Q16×C47—21no—
77C2×SD16×C47—22no—
78C2×SD16×C47—21no—
79C2×M16×C47—21no—
80C2×M16×C47—21no—
81C22×C8×C47—21no—
82C4⋊Q8×C47—21no—
83C4⋊Q8×C47C2311yescharacteristic
84C4⋊Q8×C47C2311yescharacteristic
85C4⋊Q8×C47C2311yescharacteristic
86#127×C47C2311yescharacteristic
87#126×C47—22no—
88#126×C47—22no—
89#126×C47—21no—
90#125×C47—21no—
91#125×C47D411yescharacteristic
92#124×C47—22no—
93#124×C47—22no—
94#124×C47—22no—
95#124×C47—21no—
96#124×C47—21no—
97#124×C47—21no—
98#124×C47—21no—
99#124×C47D411yescharacteristic
100#123×C47—22no—
101#123×C47—22no—
102#123×C47—22no—
103#123×C47—21no—
104C22⋊Q8×C47—22no—
105C22⋊Q8×C47—21no—
106C22⋊Q8×C47—21no—
107C22⋊Q8×C47—22no—
108C22⋊Q8×C47—21no—
109C22⋊Q8×C47—21no—
110C22⋊Q8×C47D411yescharacteristic
111#121×C47—22no—
112#121×C47—22no—
113#121×C47—21no—
114#121×C47—21no—
115#121×C47—21no—
116#121×C47D411yescharacteristic
117#121×C47D412yes—
118#120×C47—22no—
119#120×C47—22no—
120C4×Q8×C47—21no—
121C4×Q8×C47—21no—
122C4×Q8×C47—21no—
123C4×Q8×C47D411yescharacteristic
124C4×Q8×C47C2311yescharacteristic
125C4×Q8×C47C2311yescharacteristic
126C4×D4×C47—22no—
127C4×D4×C47—22no—
128C4×D4×C47—21no—
129C4×D4×C47—21no—
130C4×D4×C47—21no—
131C4×D4×C47—21no—
132C4×D4×C47—21no—
133C4×D4×C47—21no—
134C4×D4×C47—21no—
135C4×D4×C47D411yescharacteristic
136C4×D4×C47D412yes—
137C4×D4×C47C2311yescharacteristic
138C4×D4×C47C2311yescharacteristic
139#117×C47—22no—
140#117×C47—21no—
141#117×C47—21no—
142#117×C47—21no—
143#117×C47—21no—
144#117×C47D411yescharacteristic
145C2×C22⋊C4×C47—22no—
146C2×C22⋊C4×C47—22no—
147C2×C22⋊C4×C47—22no—
148C2×C42×C47—21no—
149C2×C42×C47C2311yescharacteristic
150#107×C47—21no—
151#107×C47—22no—
152#107×C47—21no—
153#107×C47—21no—
154#106×C47—21no—
155#106×C47—21no—
156#106×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—21no—
165#103×C47—21no—
166#103×C47—21no—
167#103×C47—21no—
168#103×C47—22no—
169#102×C47—21no—
170#102×C47—22no—
171#102×C47—21no—
172#102×C47—21no—
173#97×C47—21no—
174C4×C8×C47C2311yescharacteristic
175C4×C8×C47C2311yescharacteristic
176C24×C47—22no—
177#41×C47—22no—
178#41×C47—41no—
179#41×C47—81no—
180#41×C47—81no—
181C2×Q8×C47—22no—
182C2×Q8×C47—21no—
183C2×Q8×C47—21no—
184C2×Q8×C47—21no—
185C2×Q8×C47—81no—
186C2×Q8×C47—81no—
187C2×Q8×C47C2×D411yescharacteristic
188C2×Q8×C47C2×D411yescharacteristic
189C2×D4×C47—22no—
190C2×D4×C47—21no—
191C2×D4×C47—22no—
192C2×D4×C47—21no—
193C2×D4×C47—22no—
194C2×D4×C47—21no—
195C2×D4×C47—21no—
196C2×D4×C47—42no—
197C2×D4×C47—42no—
198C2×D4×C47—81no—
199C2×D4×C47—81no—
200C2×D4×C47C2×D411yescharacteristic
201C2×D4×C47C2×D411yescharacteristic
202C2×D4×C47C2×D412yes—
203C22×C4×C47—22no—
204C22×C4×C47—22no—
205C22×C4×C47—21no—
206C22×C4×C47—21no—
207C22×C4×C47—21no—
208C22×C4×C47—21no—
209C22×C4×C47—22no—
210C22×C4×C47C2×D411yescharacteristic
211C22×C4×C47C2×D411yescharacteristic
212C22×C4×C47C2×D411yescharacteristic
213Q16×C47—81no—
214SD16×C47—44no—
215SD16×C47—81no—
216M16×C47—42no—
217M16×C47—81no—
218C2×C8×C47—21no—
219C2×C8×C47—21no—
220C2×C8×C47—21no—
221C2×C8×C47—21no—
222C2×C8×C47—21no—
223C2×C8×C47—21no—
224C2×C8×C47—42no—
225C4⋊C4×C47—22no—
226C4⋊C4×C47—22no—
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—41no—
239C4⋊C4×C47—41no—
240C4⋊C4×C47C2×D411yescharacteristic
241C4⋊C4×C47C2×D411yescharacteristic
242C4⋊C4×C47C2×D412yes—
243C4⋊C4×C47C2×D411yescharacteristic
244C4⋊C4×C47C2×D411yescharacteristic
245C22⋊C4×C47—22no—
246C22⋊C4×C47—22no—
247C22⋊C4×C47—22no—
248C22⋊C4×C47—22no—
249C22⋊C4×C47—22no—
250C22⋊C4×C47—22no—
251C22⋊C4×C47—22no—
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—22no—
259C22⋊C4×C47—22no—
260C22⋊C4×C47—21no—
261C22⋊C4×C47—21no—
262C22⋊C4×C47—41no—
263C42×C47—22no—
264C42×C47—21no—
265C42×C47—21no—
266C42×C47—21no—
267C42×C47—21no—
268C42×C47—41no—
269C42×C47C2×D411yescharacteristic
270C42×C47C2×D411yescharacteristic
271C42×C47C2×D411yescharacteristic
272C42×C47C2411yescharacteristic
273C23×C47—21no—
274C23×C47—21no—
275C23×C47—22no—
276C23×C47—44no—
277C23×C47—82no—
278C23×C47—82no—
279C23×C47#12011yescharacteristic
280Q8×C47—21no—
281Q8×C47—21no—
282Q8×C47—21no—
283Q8×C47—21no—
284Q8×C47—42no—
285Q8×C47—41no—
286Q8×C47—41no—
287Q8×C47—41no—
288Q8×C47—41no—
289Q8×C47—82no—
290D4×C47—21no—
291D4×C47—21no—
292D4×C47—21no—
293D4×C47—42no—
294D4×C47—42no—
295D4×C47—44no—
296D4×C47—41no—
297D4×C47—41no—
298D4×C47—41no—
299D4×C47—41no—
300D4×C47—81no—
301D4×C47—82no—
302D4×C47—82no—
303D4×C47#13712yes—
304C2×C4×C47—21no—
305C2×C4×C47—21no—
306C2×C4×C47—21no—
307C2×C4×C47—21no—
308C2×C4×C47—21no—
309C2×C4×C47—21no—
310C2×C4×C47—21no—
311C2×C4×C47—21no—
312C2×C4×C47—21no—
313C2×C4×C47—21no—
314C2×C4×C47—22no—
315C2×C4×C47—41no—
316C2×C4×C47—42no—
317C2×C4×C47—41no—
318C2×C4×C47—41no—
319C2×C4×C47—41no—
320C2×C4×C47—41no—
321C2×C4×C47—41no—
322C2×C4×C47—41no—
323C2×C4×C47—81no—
324C2×C4×C47—82no—
325C2×C4×C47—82no—
326C2×C4×C47—82no—
327C2×C4×C47#12011yescharacteristic
328C2×C4×C47#12011yescharacteristic
329C2×C4×C47#12011yescharacteristic
330C2×C4×C47C22×D411yescharacteristic
331C2×C4×C47C22×D411yescharacteristic
332C2×C4×C47C22×D411yescharacteristic
333C8×C47—22no—
334C8×C47—41no—
335C8×C47—41no—
336C8×C47—41no—
337C8×C47—41no—
338C8×C47—41no—
339#18595C4711yesmaximal, characteristic, direct product factor, Sylow
340C22×C47—21no—
341C22×C47—22no—
342C22×C47—21no—
343C22×C47—21no—
344C22×C47—41no—
345C22×C47—41no—
346C22×C47—41no—
347C22×C47—42no—
348C22×C47—42no—
349C22×C47—41no—
350C22×C47—42no—
351C22×C47—41no—
352C22×C47—164no—
353C22×C47C2×#12011yescharacteristic
354C4×C47—21no—
355C4×C47—21no—
356C4×C47—21no—
357C4×C47—21no—
358C4×C47—41no—
359C4×C47—41no—
360C4×C47—41no—
361C4×C47—42no—
362C4×C47—41no—
363C4×C47—41no—
364C4×C47—41no—
365C4×C47—81no—
366C4×C47—81no—
367C4×C47C2×#13711yescharacteristic
368C4×C47#57511yescharacteristic
369C4×C47#57611yescharacteristic
370C4×C47#57711yescharacteristic
371#3514C2×C4711yescharacteristic
372#3252C2×C4711yescharacteristic, complemented
373#3182C2×C4711yescharacteristic, complemented
374#3076C2×C4711yescharacteristic, complemented
375#1650C2×C4711yescharacteristic, complemented
376#1649C2×C4711yescharacteristic, complemented
377#1640C2×C4711yescharacteristic, complemented
378#1639C2×C4711yescharacteristic, complemented
379#1638C2×C4711yescharacteristic, complemented
380#1637C2×C4711yescharacteristic, complemented
381#1630C2×C4711yescharacteristic, complemented
382#1629C2×C4711yescharacteristic, complemented
383#1547C2×C4711yescharacteristic, complemented
384#1489C2×C4711yescharacteristic, complemented
385#1483C2×C4711yescharacteristic, complemented
386C2×C47—41no—
387C2×C47—42no—
388C2×C47—82no—
389C2×C47—81no—
390C2×C47#300711yescharacteristic
391C2×C47#301211yescharacteristic
392C2×C47#301811yescharacteristic
393#559C22×C4711yescharacteristic
394#556C22×C4711yescharacteristic
395#555—21no—
396#551—22no—
397D4×Q8C22×C4711yescharacteristic
398#548—21no—
399#546—21no—
400#546—21no—
401D42C22×C4711yescharacteristic
402#542—21no—
403#538—22no—
404#533C22×C4711yescharacteristic, complemented
405#532C22×C4711yescharacteristic
406#529—21no—
407#529C22×C4711yescharacteristic
408C2×#124—21no—
409#518—21no—
410C4×#41C22×C4711yescharacteristic
411#500C22×C4711yescharacteristic, complemented
412#492C22×C4711yescharacteristic
413#487C22×C4711yescharacteristic, complemented
414#486C22×C4711yescharacteristic
415#479—21no—
416#479—21no—
417#478—21no—
418#477C22×C4711yescharacteristic, complemented
419#477C22×C4711yescharacteristic, complemented
420#476C22×C4711yescharacteristic
421#476C22×C4711yescharacteristic
422#475C22×C4711yescharacteristic, complemented
423#474C22×C4711yescharacteristic
424#470—21no—
425#468—22no—
426#468—21no—
427#464—21no—
428#462C22×C4711yescharacteristic, complemented
429#461C22×C4711yescharacteristic
430#440—22no—
431#427—21no—
432#423C22×C4711yescharacteristic, complemented
433C2×C4⋊C8C22×C4711yescharacteristic, complemented
434#416—21no—
435C4×M16C22×C4711yescharacteristic, complemented
436#332C22×C4711yescharacteristic, complemented
437#332C22×C4711yescharacteristic, complemented
438#331C22×C4711yescharacteristic
439#331C22×C4711yescharacteristic
440Q8⋊C8C22×C4711yescharacteristic, complemented
441Q8⋊C8C22×C4711yescharacteristic, complemented
442Q8⋊C8C22×C4711yescharacteristic, complemented
443Q8⋊C8C22×C4711yescharacteristic, complemented
444D4⋊C8C22×C4711yescharacteristic
445D4⋊C8C22×C4711yescharacteristic
446D4⋊C8C22×C4711yescharacteristic
447D4⋊C8C22×C4711yescharacteristic
448C47#1859511yescharacteristic, direct product factor, Sylow
449C2×#41—21no—
450C2×#41D4×C4711yescharacteristic
451C22×Q8—21no—
452C22×D4—21no—
453C22×D4—21no—
454C2×Q16—21no—
455C2×SD16—22no—
456C2×SD16—21no—
457C2×M16—21no—
458C2×M16—21no—
459C22×C8—21no—
460C4⋊Q8—21no—
461C4⋊Q8C23×C4711yescharacteristic
462C4⋊Q8C23×C4711yescharacteristic
463C4⋊Q8C23×C4711yescharacteristic
464#127C23×C4711yescharacteristic
465#126—22no—
466#126—22no—
467#126—21no—
468#125—21no—
469#125D4×C4711yescharacteristic
470#124—22no—
471#124—22no—
472#124—22no—
473#124—21no—
474#124—21no—
475#124—21no—
476#124—21no—
477#124D4×C4711yescharacteristic
478#123—22no—
479#123—22no—
480#123—22no—
481#123—21no—
482C22⋊Q8—22no—
483C22⋊Q8—21no—
484C22⋊Q8—21no—
485C22⋊Q8—22no—
486C22⋊Q8—21no—
487C22⋊Q8—21no—
488C22⋊Q8D4×C4711yescharacteristic
489#121—22no—
490#121—22no—
491#121—21no—
492#121—21no—
493#121—21no—
494#121D4×C4711yescharacteristic
495#121D4×C4712yes—
496#120—22no—
497#120—22no—
498C4×Q8—21no—
499C4×Q8—21no—
500C4×Q8—21no—
501C4×Q8D4×C4711yescharacteristic
502C4×Q8C23×C4711yescharacteristic
503C4×Q8C23×C4711yescharacteristic
504C4×D4—22no—
505C4×D4—22no—
506C4×D4—21no—
507C4×D4—21no—
508C4×D4—21no—
509C4×D4—21no—
510C4×D4—21no—
511C4×D4—21no—
512C4×D4—21no—
513C4×D4D4×C4711yescharacteristic
514C4×D4D4×C4712yes—
515C4×D4C23×C4711yescharacteristic
516C4×D4C23×C4711yescharacteristic
517#117—22no—
518#117—21no—
519#117—21no—
520#117—21no—
521#117—21no—
522#117D4×C4711yescharacteristic
523C2×C22⋊C4—22no—
524C2×C22⋊C4—22no—
525C2×C22⋊C4—22no—
526C2×C42—21no—
527C2×C42C23×C4711yescharacteristic
528#107—21no—
529#107—21no—
530#107—22no—
531#107—21no—
532#106—21no—
533#106—21no—
534#106—21no—
535C4⋊C8—21no—
536C4⋊C8—21no—
537C4⋊C8C23×C4711yescharacteristic
538C4⋊C8C23×C4711yescharacteristic
539C4⋊C8C23×C4711yescharacteristic
540C4⋊C8C23×C4711yescharacteristic
541#103—21no—
542#103—21no—
543#103—21no—
544#103—22no—
545#103—21no—
546#103—21no—
547#102—21no—
548#102—21no—
549#102—22no—
550#102—21no—
551#97—21no—
552C4×C8C23×C4711yescharacteristic
553C4×C8C23×C4711yescharacteristic
554C24—22no—
555#41—22no—
556#41—41no—
557#41—81no—
558#41—81no—
559C2×Q8—22no—
560C2×Q8—21no—
561C2×Q8—21no—
562C2×Q8—21no—
563C2×Q8—81no—
564C2×Q8—81no—
565C2×Q8C2×D4×C4711yescharacteristic
566C2×Q8C2×D4×C4711yescharacteristic
567C2×D4—22no—
568C2×D4—21no—
569C2×D4—22no—
570C2×D4—21no—
571C2×D4—22no—
572C2×D4—21no—
573C2×D4—21no—
574C2×D4—42no—
575C2×D4—42no—
576C2×D4—81no—
577C2×D4—81no—
578C2×D4C2×D4×C4711yescharacteristic
579C2×D4C2×D4×C4711yescharacteristic
580C2×D4C2×D4×C4712yes—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—22no—
588C22×C4C2×D4×C4711yescharacteristic
589C22×C4C2×D4×C4711yescharacteristic
590C22×C4C2×D4×C4711yescharacteristic
591Q16—81no—
592SD16—44no—
593SD16—81no—
594M16—42no—
595M16—81no—
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—21no—
600C2×C8—21no—
601C2×C8—21no—
602C2×C8—42no—
603C4⋊C4—22no—
604C4⋊C4—22no—
605C4⋊C4—21no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—21no—
609C4⋊C4—21no—
610C4⋊C4—21no—
611C4⋊C4—21no—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—41no—
617C4⋊C4—41no—
618C4⋊C4C2×D4×C4711yescharacteristic
619C4⋊C4C2×D4×C4711yescharacteristic
620C4⋊C4C2×D4×C4712yes—
621C4⋊C4C2×D4×C4711yescharacteristic
622C4⋊C4C2×D4×C4711yescharacteristic
623C22⋊C4—22no—
624C22⋊C4—22no—
625C22⋊C4—22no—
626C22⋊C4—22no—
627C22⋊C4—22no—
628C22⋊C4—22no—
629C22⋊C4—22no—
630C22⋊C4—21no—
631C22⋊C4—21no—
632C22⋊C4—21no—
633C22⋊C4—21no—
634C22⋊C4—21no—
635C22⋊C4—21no—
636C22⋊C4—22no—
637C22⋊C4—22no—
638C22⋊C4—21no—
639C22⋊C4—21no—
640C22⋊C4—41no—
641C42—22no—
642C42—21no—
643C42—21no—
644C42—21no—
645C42—21no—
646C42—41no—
647C42C2×D4×C4711yescharacteristic
648C42C2×D4×C4711yescharacteristic
649C42C2×D4×C4711yescharacteristic
650C42C24×C4711yescharacteristic
651C23—21no—
652C23—21no—
653C23—22no—
654C23—44no—
655C23—82no—
656C23—82no—
657C23#120×C4711yescharacteristic
658Q8—21no—
659Q8—21no—
660Q8—21no—
661Q8—21no—
662Q8—42no—
663Q8—41no—
664Q8—41no—
665Q8—41no—
666Q8—41no—
667Q8—82no—
668D4—21no—
669D4—21no—
670D4—21no—
671D4—42no—
672D4—42no—
673D4—44no—
674D4—41no—
675D4—41no—
676D4—41no—
677D4—41no—
678D4—81no—
679D4—82no—
680D4—82no—
681D4#137×C4712yes—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—22no—
693C2×C4—41no—
694C2×C4—42no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—81no—
702C2×C4—82no—
703C2×C4—82no—
704C2×C4—82no—
705C2×C4#120×C4711yescharacteristic
706C2×C4#120×C4711yescharacteristic
707C2×C4#120×C4711yescharacteristic
708C2×C4C22×D4×C4711yescharacteristic
709C2×C4C22×D4×C4711yescharacteristic
710C2×C4C22×D4×C4711yescharacteristic
711C8—22no—
712C8—41no—
713C8—41no—
714C8—41no—
715C8—41no—
716C8—41no—
717C22—21no—
718C22—22no—
719C22—21no—
720C22—21no—
721C22—41no—
722C22—41no—
723C22—41no—
724C22—42no—
725C22—42no—
726C22—41no—
727C22—42no—
728C22—41no—
729C22—164no—
730C22C2×#120×C4711yescharacteristic
731C4—21no—
732C4—21no—
733C4—21no—
734C4—21no—
735C4—41no—
736C4—41no—
737C4—41no—
738C4—42no—
739C4—41no—
740C4—41no—
741C4—41no—
742C4—81no—
743C4—81no—
744C4C2×#137×C4711yescharacteristic
745C4C47×#57511yescharacteristic
746C4C47×#57611yescharacteristic
747C4C47×#57711yescharacteristic
748C2—41no—
749C2—42no—
750C2—81no—
751C2—82no—
752C2C47×#300711yescharacteristic
753C2C47×#301211yescharacteristic
754C2C47×#301811yescharacteristic
subgroupG/H
center, socleC22×C47C2×#120
commutator, Frattini, cosocleC42C24×C47
prime radicalC47×#3514C2
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
2. C47×#3252C2semidirect
3. C47×#3182C2semidirect
4. C47×#3076C2semidirect
5. C47×#1650C2semidirect
6. C47×#1649C2semidirect
7. C47×#1640C2semidirect
8. C47×#1639C2semidirect
9. C47×#1638C2semidirect
10. C47×#1637C2semidirect
11. C47×#1630C2semidirect
12. C47×#1629C2semidirect
13. C47×#1547C2semidirect
14. C47×#1489C2semidirect
15. C47×#1483C2semidirect
27. C47×#533C22semidirect
34. C47×#500C22semidirect
36. C47×#487C22semidirect
41. C47×#477C22semidirect
42. C47×#477C22semidirect
45. C47×#475C22semidirect
51. C47×#462C22semidirect
55. C47×#423C22semidirect
56. C2×C4⋊C8×C47C22semidirect
58. C4×M16×C47C22semidirect
59. C47×#332C22semidirect
60. C47×#332C22semidirect
63. C47×Q8⋊C8C22semidirect
64. C47×Q8⋊C8C22semidirect
65. C47×Q8⋊C8C22semidirect
66. C47×Q8⋊C8C22semidirect
339. #18595C47direct (N × H)
372. #3252C2×C47semidirect
373. #3182C2×C47semidirect
374. #3076C2×C47semidirect
375. #1650C2×C47semidirect
376. #1649C2×C47semidirect
377. #1640C2×C47semidirect
378. #1639C2×C47semidirect
379. #1638C2×C47semidirect
380. #1637C2×C47semidirect
381. #1630C2×C47semidirect
382. #1629C2×C47semidirect
383. #1547C2×C47semidirect
384. #1489C2×C47semidirect
385. #1483C2×C47semidirect
404. #533C22×C47semidirect
411. #500C22×C47semidirect
413. #487C22×C47semidirect
418. #477C22×C47semidirect
419. #477C22×C47semidirect
422. #475C22×C47semidirect
428. #462C22×C47semidirect
432. #423C22×C47semidirect
433. C2×C4⋊C8C22×C47semidirect
435. C4×M16C22×C47semidirect
436. #332C22×C47semidirect
437. #332C22×C47semidirect
440. Q8⋊C8C22×C47semidirect
441. Q8⋊C8C22×C47semidirect
442. Q8⋊C8C22×C47semidirect
443. Q8⋊C8C22×C47semidirect
448. C47#18595direct (N × H)

Maximal subgroups

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

subgroupindex
C47×#35142
C47×#32522
C47×#31822
C47×#30762
C47×#16502
C47×#16492
C47×#16402
C47×#16392
C47×#16382
C47×#16372
C47×#16302
C47×#16292
C47×#15472
C47×#14892
C47×#14832
#1859547