Finite Group Databasebeta

← C47×#25565 #26065263

Subgroups — C47×#25565 #26065263

Order 12032.

1312 conjugacy classes of subgroups.

The subgroup lattice has 782 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3490C211yesmaximal, characteristic
2C47×#2483C211yesmaximal, characteristic, complemented
3C47×#2412C212yesmaximal, complemented
4C47×#2062C211yesmaximal, characteristic, complemented
5C47×#2044C211yesmaximal, characteristic, complemented
6C47×#2030C211yesmaximal, characteristic, complemented
7C47×#2022C211yesmaximal, characteristic, complemented
8C47×#1898C212yesmaximal, complemented
9C47×#1890C212yesmaximal, complemented
10C47×#1867C212yesmaximal, complemented
11C2×C47×#342C211yesmaximal, characteristic, complemented
12C47×#551—22no—
13C47×#551—22no—
14C47×#546—22no—
15C47×#546—22no—
16C47×#543C2211yescharacteristic
17C47×#538—21no—
18C47×#538—21no—
19C47×#534C2211yescharacteristic
20C47×#525—21no—
21C47×#525—21no—
22C2×#123×C47C2212yes—
23C2×#120×C47C2212yes—
24C47×#518C2212yes—
25C22×C22⋊C4×C47C2211yescharacteristic
26C22×C22⋊C4×C47C2211yescharacteristic
27C22×C22⋊C4×C47C2212yes—
28C2×#99×C47C2212yes—
29C2×#99×C47C2212yes—
30C47×#397—22no—
31C47×#397—21no—
32C47×#397—21no—
33C47×#394—22no—
34C47×#386—22no—
35C47×#386C2212yes—
36C47×#385—21no—
37C47×#385C2211yescharacteristic
38C47×#385C2212yes—
39C47×#385C2211yescharacteristic
40C47×#381—21no—
41C47×#381C2211yescharacteristic
42C47×#381C2212yes—
43C47×#381C2211yescharacteristic
44C47×#380—22no—
45C47×#379C2211yescharacteristic
46C47×#342C2211yescharacteristic
47C47×#342C2211yescharacteristic
48C47×#342C2212yes—
49C47×#342C2212yes—
50C47×#342C2212yes—
51C25×C47C2311yescharacteristic
52C2×#41×C47—21no—
53C2×#41×C47—21no—
54C22×D4×C47D412yes—
55C22×D4×C47D412yes—
56C22×D4×C47C2312yes—
57C23×C4×C47—22no—
58C23×C4×C47D411yescharacteristic
59C23×C4×C47D411yescharacteristic
60C23×C4×C47C2311yescharacteristic
61C23×C4×C47C2311yescharacteristic
62#126×C47—22no—
63#126×C47—22no—
64#124×C47—22no—
65#124×C47—22no—
66#123×C47—22no—
67#123×C47—22no—
68#123×C47—22no—
69#123×C47—22no—
70#123×C47—22no—
71#123×C47—24no—
72#123×C47—42no—
73C22⋊Q8×C47—21no—
74C22⋊Q8×C47—21no—
75C22⋊Q8×C47—21no—
76C22⋊Q8×C47—21no—
77C22⋊Q8×C47—22no—
78C22⋊Q8×C47—22no—
79#121×C47—21no—
80#121×C47—21no—
81#121×C47—22no—
82#121×C47—22no—
83#121×C47—21no—
84#121×C47—21no—
85#120×C47—22no—
86#120×C47—22no—
87#120×C47—22no—
88#120×C47—22no—
89#120×C47—22no—
90C4×D4×C47—22no—
91C4×D4×C47—22no—
92C4×D4×C47—22no—
93C4×D4×C47—22no—
94C4×D4×C47—22no—
95C4×D4×C47—22no—
96#117×C47—21no—
97#117×C47—21no—
98#117×C47—22no—
99C2×C4⋊C4×C47—22no—
100C2×C4⋊C4×C47—22no—
101C2×C4⋊C4×C47—21no—
102C2×C4⋊C4×C47—21no—
103C2×C22⋊C4×C47—22no—
104C2×C22⋊C4×C47—22no—
105C2×C22⋊C4×C47—22no—
106C2×C22⋊C4×C47—24no—
107C2×C22⋊C4×C47—22no—
108C2×C22⋊C4×C47—21no—
109C2×C22⋊C4×C47—22no—
110C2×C22⋊C4×C47—22no—
111C2×C22⋊C4×C47—21no—
112C2×C22⋊C4×C47—22no—
113C2×C22⋊C4×C47—21no—
114C2×C22⋊C4×C47—21no—
115C2×C22⋊C4×C47—22no—
116C2×C22⋊C4×C47—42no—
117C2×C22⋊C4×C47D411yescharacteristic
118C2×C22⋊C4×C47D411yescharacteristic
119C2×C22⋊C4×C47D412yes—
120C2×C22⋊C4×C47D412yes—
121C2×C22⋊C4×C47C2312yes—
122C2×C22⋊C4×C47C2311yescharacteristic
123C2×C22⋊C4×C47C2311yescharacteristic
124C2×C22⋊C4×C47C2311yescharacteristic
125C2×C22⋊C4×C47C2311yescharacteristic
126C2×C22⋊C4×C47C2312yes—
127C2×C22⋊C4×C47C2312yes—
128#99×C47—24no—
129#99×C47—42no—
130#95×C47—22no—
131#95×C47—22no—
132#95×C47—21no—
133#95×C47—21no—
134#95×C47—21no—
135#95×C47—21no—
136#95×C47—21no—
137#95×C47—21no—
138#95×C47—22no—
139#95×C47—22no—
140C24×C47—22no—
141C24×C47—21no—
142C24×C47—21no—
143C24×C47—42no—
144C24×C47—81no—
145C24×C47C2×D412yes—
146C24×C47C2×D411yescharacteristic
147C24×C47C2×D412yes—
148C24×C47C2×D412yes—
149C24×C47C2×D411yescharacteristic
150C24×C47C2411yescharacteristic
151#41×C47—82no—
152#41×C47—82no—
153C2×Q8×C47—21no—
154C2×Q8×C47—21no—
155C2×D4×C47—22no—
156C2×D4×C47—22no—
157C2×D4×C47—22no—
158C2×D4×C47—22no—
159C2×D4×C47—22no—
160C2×D4×C47—22no—
161C2×D4×C47—22no—
162C2×D4×C47—22no—
163C2×D4×C47—21no—
164C2×D4×C47—21no—
165C2×D4×C47—22no—
166C2×D4×C47—22no—
167C2×D4×C47—44no—
168C2×D4×C47—82no—
169C22×C4×C47—21no—
170C22×C4×C47—21no—
171C22×C4×C47—22no—
172C22×C4×C47—22no—
173C22×C4×C47—22no—
174C22×C4×C47—21no—
175C22×C4×C47—21no—
176C22×C4×C47—22no—
177C22×C4×C47—22no—
178C22×C4×C47—21no—
179C22×C4×C47—21no—
180C22×C4×C47—22no—
181C22×C4×C47—21no—
182C22×C4×C47—21no—
183C22×C4×C47—22no—
184C22×C4×C47—21no—
185C22×C4×C47—21no—
186C22×C4×C47—44no—
187C22×C4×C47—42no—
188C22×C4×C47—44no—
189C22×C4×C47—81no—
190C22×C4×C47—81no—
191C22×C4×C47—82no—
192C22×C4×C47C2×D412yes—
193C22×C4×C47C2×D411yescharacteristic
194C22×C4×C47C2×D412yes—
195C22×C4×C47C2×D411yescharacteristic
196C22×C4×C47C2×D411yescharacteristic
197C22×C4×C47C2×D412yes—
198C22×C4×C47C2×D411yescharacteristic
199C4⋊C4×C47—22no—
200C4⋊C4×C47—22no—
201C4⋊C4×C47—21no—
202C4⋊C4×C47—21no—
203C4⋊C4×C47—21no—
204C4⋊C4×C47—21no—
205C4⋊C4×C47—22no—
206C4⋊C4×C47—22no—
207C4⋊C4×C47—44no—
208C4⋊C4×C47—82no—
209C4⋊C4×C47—81no—
210C4⋊C4×C47—81no—
211C22⋊C4×C47—22no—
212C22⋊C4×C47—22no—
213C22⋊C4×C47—22no—
214C22⋊C4×C47—22no—
215C22⋊C4×C47—22no—
216C22⋊C4×C47—22no—
217C22⋊C4×C47—22no—
218C22⋊C4×C47—22no—
219C22⋊C4×C47—22no—
220C22⋊C4×C47—22no—
221C22⋊C4×C47—22no—
222C22⋊C4×C47—22no—
223C22⋊C4×C47—22no—
224C22⋊C4×C47—22no—
225C22⋊C4×C47—22no—
226C22⋊C4×C47—22no—
227C22⋊C4×C47—22no—
228C22⋊C4×C47—22no—
229C22⋊C4×C47—21no—
230C22⋊C4×C47—21no—
231C22⋊C4×C47—44no—
232C22⋊C4×C47—44no—
233C22⋊C4×C47—42no—
234C22⋊C4×C47—42no—
235C22⋊C4×C47—41no—
236C22⋊C4×C47—41no—
237C22⋊C4×C47—81no—
238C22⋊C4×C47—82no—
239C22⋊C4×C47#4114yescomplemented
240C42×C47—22no—
241C42×C47—22no—
242C23×C47—21no—
243C23×C47—21no—
244C23×C47—22no—
245C23×C47—22no—
246C23×C47—22no—
247C23×C47—24no—
248C23×C47—21no—
249C23×C47—21no—
250C23×C47—22no—
251C23×C47—22no—
252C23×C47—22no—
253C23×C47—22no—
254C23×C47—22no—
255C23×C47—41no—
256C23×C47—42no—
257C23×C47—41no—
258C23×C47—41no—
259C23×C47—41no—
260C23×C47—42no—
261C23×C47—41no—
262C23×C47—42no—
263C23×C47—42no—
264C23×C47—42no—
265C23×C47—84no—
266C23×C47—82no—
267C23×C47—82no—
268C23×C47#12012yes—
269C23×C47#12011yescharacteristic
270C23×C47#12011yescharacteristic
271C23×C47C22×D411yescharacteristic
272C23×C47C22×D412yes—
273C23×C47C2×#4112yes—
274C23×C47H(5,𝔽2)11yescharacteristic
275C23×C472−1+411yescharacteristic
276Q8×C47—81no—
277Q8×C47—81no—
278D4×C47—44no—
279D4×C47—42no—
280D4×C47—42no—
281D4×C47—42no—
282D4×C47—42no—
283D4×C47—44no—
284D4×C47—82no—
285D4×C47—82no—
286D4×C47—81no—
287D4×C47—81no—
288C2×C4×C47—22no—
289C2×C4×C47—21no—
290C2×C4×C47—21no—
291C2×C4×C47—22no—
292C2×C4×C47—22no—
293C2×C4×C47—21no—
294C2×C4×C47—21no—
295C2×C4×C47—24no—
296C2×C4×C47—22no—
297C2×C4×C47—22no—
298C2×C4×C47—42no—
299C2×C4×C47—42no—
300C2×C4×C47—42no—
301C2×C4×C47—42no—
302C2×C4×C47—41no—
303C2×C4×C47—41no—
304C2×C4×C47—42no—
305C2×C4×C47—41no—
306C2×C4×C47—41no—
307C2×C4×C47—42no—
308C2×C4×C47—41no—
309C2×C4×C47—41no—
310C2×C4×C47—41no—
311C2×C4×C47—41no—
312C2×C4×C47—42no—
313C2×C4×C47—42no—
314C2×C4×C47—41no—
315C2×C4×C47—41no—
316C2×C4×C47—42no—
317C2×C4×C47—42no—
318C2×C4×C47—41no—
319C2×C4×C47—41no—
320C2×C4×C47—41no—
321C2×C4×C47—41no—
322C2×C4×C47—41no—
323C2×C4×C47—41no—
324C2×C4×C47—42no—
325C2×C4×C47—42no—
326C2×C4×C47—42no—
327C2×C4×C47—81no—
328C2×C4×C47—81no—
329C2×C4×C47—82no—
330C2×C4×C47—82no—
331C2×C4×C47—88no—
332#25565C4711yesmaximal, characteristic, direct product factor, Sylow
333C22×C47—21no—
334C22×C47—21no—
335C22×C47—22no—
336C22×C47—21no—
337C22×C47—22no—
338C22×C47—21no—
339C22×C47—21no—
340C22×C47—22no—
341C22×C47—21no—
342C22×C47—22no—
343C22×C47—21no—
344C22×C47—22no—
345C22×C47—42no—
346C22×C47—41no—
347C22×C47—41no—
348C22×C47—44no—
349C22×C47—42no—
350C22×C47—42no—
351C22×C47—44no—
352C22×C47—42no—
353C22×C47—42no—
354C22×C47—42no—
355C22×C47—82no—
356C22×C47—81no—
357C22×C47—81no—
358C22×C47—82no—
359C22×C47—82no—
360C22×C47—82no—
361C22×C47#45812yes—
362C22×C47C2×#12011yescharacteristic
363C22×C47#53211yescharacteristic
364C22×C47#53711yescharacteristic
365C22×C47#54612yes—
366C22×C47#54712yes—
367C4×C47—44no—
368C4×C47—42no—
369C4×C47—41no—
370C4×C47—41no—
371C4×C47—42no—
372C4×C47—41no—
373C4×C47—41no—
374C4×C47—42no—
375C4×C47—81no—
376C4×C47—81no—
377C4×C47—82no—
378C4×C47—81no—
379C4×C47—81no—
380#3490C2×C4711yescharacteristic
381#2483C2×C4711yescharacteristic, complemented
382#2412C2×C4712yescomplemented
383#2062C2×C4711yescharacteristic, complemented
384#2044C2×C4711yescharacteristic, complemented
385#2030C2×C4711yescharacteristic, complemented
386#2022C2×C4711yescharacteristic, complemented
387#1898C2×C4712yescomplemented
388#1890C2×C4712yescomplemented
389#1867C2×C4712yescomplemented
390C2×#342C2×C4711yescharacteristic, complemented
391C2×C47—22no—
392C2×C47—21no—
393C2×C47—21no—
394C2×C47—22no—
395C2×C47—22no—
396C2×C47—41no—
397C2×C47—42no—
398C2×C47—82no—
399C2×C47#243011yescharacteristic
400C2×C47C2×#45811yescharacteristic
401C2×C47#302611yescharacteristic
402#551—22no—
403#551—22no—
404#546—22no—
405#546—22no—
406#543C22×C4711yescharacteristic
407#538—21no—
408#538—21no—
409#534C22×C4711yescharacteristic
410#525—21no—
411#525—21no—
412C2×#123C22×C4712yes—
413C2×#120C22×C4712yes—
414#518C22×C4712yes—
415C22×C22⋊C4C22×C4711yescharacteristic
416C22×C22⋊C4C22×C4711yescharacteristic
417C22×C22⋊C4C22×C4712yes—
418C2×#99C22×C4712yes—
419C2×#99C22×C4712yes—
420#397—22no—
421#397—21no—
422#397—21no—
423#394—22no—
424#386—22no—
425#386C22×C4712yes—
426#385—21no—
427#385C22×C4712yes—
428#385C22×C4711yescharacteristic
429#385C22×C4711yescharacteristic
430#381—21no—
431#381C22×C4711yescharacteristic
432#381C22×C4712yes—
433#381C22×C4711yescharacteristic
434#380—22no—
435#379C22×C4711yescharacteristic
436#342C22×C4712yes—
437#342C22×C4711yescharacteristic
438#342C22×C4712yes—
439#342C22×C4712yes—
440#342C22×C4711yescharacteristic
441C47#2556511yescharacteristic, direct product factor, Sylow
442C25C23×C4711yescharacteristic
443C2×#41—21no—
444C2×#41—21no—
445C22×D4D4×C4712yes—
446C22×D4D4×C4712yes—
447C22×D4C23×C4712yes—
448C23×C4—22no—
449C23×C4D4×C4711yescharacteristic
450C23×C4D4×C4711yescharacteristic
451C23×C4C23×C4711yescharacteristic
452C23×C4C23×C4711yescharacteristic
453#126—22no—
454#126—22no—
455#124—22no—
456#124—22no—
457#123—22no—
458#123—22no—
459#123—22no—
460#123—22no—
461#123—22no—
462#123—24no—
463#123—42no—
464C22⋊Q8—21no—
465C22⋊Q8—21no—
466C22⋊Q8—21no—
467C22⋊Q8—21no—
468C22⋊Q8—22no—
469C22⋊Q8—22no—
470#121—21no—
471#121—21no—
472#121—22no—
473#121—22no—
474#121—21no—
475#121—21no—
476#120—22no—
477#120—22no—
478#120—22no—
479#120—22no—
480#120—22no—
481C4×D4—22no—
482C4×D4—22no—
483C4×D4—22no—
484C4×D4—22no—
485C4×D4—22no—
486C4×D4—22no—
487#117—21no—
488#117—21no—
489#117—22no—
490C2×C4⋊C4—22no—
491C2×C4⋊C4—22no—
492C2×C4⋊C4—21no—
493C2×C4⋊C4—21no—
494C2×C22⋊C4—22no—
495C2×C22⋊C4—22no—
496C2×C22⋊C4—22no—
497C2×C22⋊C4—24no—
498C2×C22⋊C4—22no—
499C2×C22⋊C4—21no—
500C2×C22⋊C4—22no—
501C2×C22⋊C4—22no—
502C2×C22⋊C4—21no—
503C2×C22⋊C4—22no—
504C2×C22⋊C4—21no—
505C2×C22⋊C4—21no—
506C2×C22⋊C4—22no—
507C2×C22⋊C4—42no—
508C2×C22⋊C4D4×C4711yescharacteristic
509C2×C22⋊C4D4×C4711yescharacteristic
510C2×C22⋊C4D4×C4712yes—
511C2×C22⋊C4D4×C4712yes—
512C2×C22⋊C4C23×C4712yes—
513C2×C22⋊C4C23×C4711yescharacteristic
514C2×C22⋊C4C23×C4711yescharacteristic
515C2×C22⋊C4C23×C4711yescharacteristic
516C2×C22⋊C4C23×C4711yescharacteristic
517C2×C22⋊C4C23×C4712yes—
518C2×C22⋊C4C23×C4712yes—
519#99—24no—
520#99—42no—
521#95—22no—
522#95—22no—
523#95—21no—
524#95—21no—
525#95—21no—
526#95—21no—
527#95—21no—
528#95—21no—
529#95—22no—
530#95—22no—
531C24—22no—
532C24—21no—
533C24—21no—
534C24—42no—
535C24—81no—
536C24C2×D4×C4712yes—
537C24C2×D4×C4711yescharacteristic
538C24C2×D4×C4712yes—
539C24C2×D4×C4712yes—
540C24C2×D4×C4711yescharacteristic
541C24C24×C4711yescharacteristic
542#41—82no—
543#41—82no—
544C2×Q8—21no—
545C2×Q8—21no—
546C2×D4—22no—
547C2×D4—22no—
548C2×D4—22no—
549C2×D4—22no—
550C2×D4—22no—
551C2×D4—22no—
552C2×D4—22no—
553C2×D4—22no—
554C2×D4—21no—
555C2×D4—21no—
556C2×D4—22no—
557C2×D4—22no—
558C2×D4—44no—
559C2×D4—82no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—21no—
574C22×C4—22no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—44no—
578C22×C4—42no—
579C22×C4—44no—
580C22×C4—81no—
581C22×C4—81no—
582C22×C4—82no—
583C22×C4C2×D4×C4712yes—
584C22×C4C2×D4×C4711yescharacteristic
585C22×C4C2×D4×C4712yes—
586C22×C4C2×D4×C4711yescharacteristic
587C22×C4C2×D4×C4711yescharacteristic
588C22×C4C2×D4×C4712yes—
589C22×C4C2×D4×C4711yescharacteristic
590C4⋊C4—22no—
591C4⋊C4—22no—
592C4⋊C4—21no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—21no—
596C4⋊C4—22no—
597C4⋊C4—22no—
598C4⋊C4—44no—
599C4⋊C4—82no—
600C4⋊C4—81no—
601C4⋊C4—81no—
602C22⋊C4—22no—
603C22⋊C4—22no—
604C22⋊C4—22no—
605C22⋊C4—22no—
606C22⋊C4—22no—
607C22⋊C4—22no—
608C22⋊C4—22no—
609C22⋊C4—22no—
610C22⋊C4—22no—
611C22⋊C4—22no—
612C22⋊C4—22no—
613C22⋊C4—22no—
614C22⋊C4—22no—
615C22⋊C4—22no—
616C22⋊C4—22no—
617C22⋊C4—22no—
618C22⋊C4—22no—
619C22⋊C4—21no—
620C22⋊C4—22no—
621C22⋊C4—21no—
622C22⋊C4—44no—
623C22⋊C4—44no—
624C22⋊C4—42no—
625C22⋊C4—42no—
626C22⋊C4—41no—
627C22⋊C4—41no—
628C22⋊C4—81no—
629C22⋊C4—82no—
630C22⋊C4#41×C4714yescomplemented
631C42—22no—
632C42—22no—
633C23—22no—
634C23—24no—
635C23—21no—
636C23—21no—
637C23—22no—
638C23—22no—
639C23—21no—
640C23—21no—
641C23—22no—
642C23—22no—
643C23—22no—
644C23—22no—
645C23—22no—
646C23—41no—
647C23—42no—
648C23—41no—
649C23—41no—
650C23—41no—
651C23—42no—
652C23—41no—
653C23—42no—
654C23—42no—
655C23—42no—
656C23—84no—
657C23—82no—
658C23—82no—
659C23#120×C4712yes—
660C23#120×C4711yescharacteristic
661C23#120×C4711yescharacteristic
662C23C22×D4×C4711yescharacteristic
663C23C22×D4×C4712yes—
664C23C2×#41×C4712yes—
665C23H(5,𝔽2)×C4711yescharacteristic
666C232−1+4×C4711yescharacteristic
667Q8—81no—
668Q8—81no—
669D4—44no—
670D4—44no—
671D4—42no—
672D4—42no—
673D4—42no—
674D4—42no—
675D4—82no—
676D4—82no—
677D4—81no—
678D4—81no—
679C2×C4—22no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—24no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—42no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—42no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—81no—
719C2×C4—81no—
720C2×C4—82no—
721C2×C4—82no—
722C2×C4—88no—
723C22—21no—
724C22—21no—
725C22—22no—
726C22—21no—
727C22—22no—
728C22—21no—
729C22—21no—
730C22—22no—
731C22—21no—
732C22—22no—
733C22—21no—
734C22—22no—
735C22—42no—
736C22—41no—
737C22—41no—
738C22—44no—
739C22—42no—
740C22—42no—
741C22—44no—
742C22—42no—
743C22—42no—
744C22—42no—
745C22—82no—
746C22—81no—
747C22—81no—
748C22—82no—
749C22—82no—
750C22—82no—
751C22C47×#45812yes—
752C22C2×#120×C4711yescharacteristic
753C22C47×#53211yescharacteristic
754C22C47×#53711yescharacteristic
755C22C47×#54612yes—
756C22C47×#54712yes—
757C4—44no—
758C4—42no—
759C4—41no—
760C4—41no—
761C4—42no—
762C4—41no—
763C4—41no—
764C4—42no—
765C4—82no—
766C4—81no—
767C4—81no—
768C4—81no—
769C4—81no—
770C2—22no—
771C2—21no—
772C2—21no—
773C2—22no—
774C2—22no—
775C2—41no—
776C2—42no—
777C2—82no—
778C2C47×#243011yescharacteristic
779C2C2×C47×#45811yescharacteristic
780C2C47×#302611yescharacteristic
subgroupG/H
center, socleC22×C47C2×#120
commutator, Frattini, cosocleC24C24×C47
prime radicalC47×#3490C2
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C47 ◁ C25×C47 ◁ G

Complements

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

NH ≅ G/Ntype
2. C47×#2483C2semidirect
3. C47×#2412C2semidirect
4. C47×#2062C2semidirect
5. C47×#2044C2semidirect
6. C47×#2030C2semidirect
7. C47×#2022C2semidirect
8. C47×#1898C2semidirect
9. C47×#1890C2semidirect
10. C47×#1867C2semidirect
11. C2×C47×#342C2semidirect
239. C22⋊C4×C47#41semidirect
332. #25565C47direct (N × H)
381. #2483C2×C47semidirect
382. #2412C2×C47semidirect
383. #2062C2×C47semidirect
384. #2044C2×C47semidirect
385. #2030C2×C47semidirect
386. #2022C2×C47semidirect
387. #1898C2×C47semidirect
388. #1890C2×C47semidirect
389. #1867C2×C47semidirect
390. C2×#342C2×C47semidirect
441. C47#25565direct (N × H)
630. C22⋊C4#41×C47semidirect

Maximal subgroups

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

subgroupindex
C47×#34902
C47×#24832
C47×#24122
C47×#20622
C47×#20442
C47×#20302
C47×#20222
C47×#18982
C47×#18902
C47×#18672
C2×C47×#3422
#2556547