Finite Group Databasebeta

← C47×#25566 #26065264

Subgroups — C47×#25566 #26065264

Order 12032.

1122 conjugacy classes of subgroups.

The subgroup lattice has 684 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3491C211yesmaximal, characteristic
2C47×#2484C211yesmaximal, characteristic, complemented
3C47×#2413C212yesmaximal, complemented
4C47×#2062C211yesmaximal, characteristic, complemented
5C47×#2044C211yesmaximal, characteristic
6C47×#2030C211yesmaximal, characteristic, complemented
7C47×#2022C211yesmaximal, characteristic
8C47×#1899C212yesmaximal, complemented
9C47×#1890C212yesmaximal, complemented
10C47×#1867C212yesmaximal, complemented
11C47×#1740C211yesmaximal, characteristic, complemented
12C47×#552—22no—
13C47×#552—22no—
14C47×#551—22no—
15C47×#551—22no—
16C47×#543C2211yescharacteristic
17C47×#539—21no—
18C47×#539—21no—
19C47×#534C2211yescharacteristic
20C47×#529—21no—
21C47×#529—21no—
22C2×#123×C47C2212yes—
23C2×#123×C47C2212yes—
24C47×#518C2212yes—
25C2×#117×C47C2212yes—
26C2×#117×C47C2211yescharacteristic
27C22×C4⋊C4×C47C2211yescharacteristic
28C2×#99×C47C2212yes—
29C2×#99×C47C2212yes—
30C47×#400—21no—
31C47×#398—22no—
32C47×#398—21no—
33C47×#396—22no—
34C47×#389—22no—
35C47×#388—22no—
36C47×#387—21no—
37C47×#387—21no—
38C47×#386C2212yes—
39C47×#385C2211yescharacteristic
40C47×#385C2212yes—
41C47×#385C2211yescharacteristic
42C47×#381C2211yescharacteristic
43C47×#381C2212yes—
44C47×#381C2211yescharacteristic
45C47×#381C2211yescharacteristic
46C47×#342C2211yescharacteristic
47C47×#342C2211yescharacteristic
48C47×#342C2212yes—
49C47×#342C2212yes—
50C47×#342C2212yes—
51C22×D4×C47C2312yes—
52C23×C4×C47C2311yescharacteristic
53C23×C4×C47C2311yescharacteristic
54C23×C4×C47C2311yescharacteristic
55#126×C47—22no—
56#126×C47—22no—
57#126×C47—22no—
58#126×C47—22no—
59#125×C47—21no—
60#125×C47—21no—
61#125×C47—22no—
62#125×C47—22no—
63#124×C47—21no—
64#124×C47—21no—
65#123×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—22no—
72#123×C47—24no—
73#123×C47—42no—
74C22⋊Q8×C47—22no—
75C22⋊Q8×C47—22no—
76C22⋊Q8×C47—21no—
77C22⋊Q8×C47—21no—
78C22⋊Q8×C47—22no—
79C22⋊Q8×C47—22no—
80#121×C47—21no—
81#121×C47—21no—
82#120×C47—22no—
83C4×Q8×C47—21no—
84C4×Q8×C47—21no—
85C4×D4×C47—21no—
86C4×D4×C47—21no—
87C4×D4×C47—22no—
88C4×D4×C47—22no—
89C4×D4×C47—22no—
90C4×D4×C47—22no—
91#117×C47—22no—
92#117×C47—22no—
93#117×C47—22no—
94#117×C47—22no—
95#117×C47—22no—
96#117×C47—24no—
97#117×C47—42no—
98C2×C4⋊C4×C47—21no—
99C2×C4⋊C4×C47—22no—
100C2×C4⋊C4×C47—22no—
101C2×C4⋊C4×C47—21no—
102C2×C4⋊C4×C47—22no—
103C2×C4⋊C4×C47—22no—
104C2×C4⋊C4×C47—21no—
105C2×C4⋊C4×C47—21no—
106C2×C4⋊C4×C47—22no—
107C2×C4⋊C4×C47D411yescharacteristic
108C2×C4⋊C4×C47D411yescharacteristic
109C2×C4⋊C4×C47D412yes—
110C2×C4⋊C4×C47D412yes—
111C2×C22⋊C4×C47—22no—
112C2×C22⋊C4×C47—22no—
113C2×C22⋊C4×C47—22no—
114C2×C22⋊C4×C47D412yes—
115C2×C22⋊C4×C47D412yes—
116C2×C22⋊C4×C47C2312yes—
117C2×C22⋊C4×C47C2311yescharacteristic
118C2×C22⋊C4×C47C2311yescharacteristic
119C2×C22⋊C4×C47C2311yescharacteristic
120C2×C22⋊C4×C47C2311yescharacteristic
121C2×C22⋊C4×C47C2312yes—
122C2×C22⋊C4×C47C2312yes—
123C2×C42×C47—22no—
124C2×C42×C47D411yescharacteristic
125C2×C42×C47D411yescharacteristic
126#99×C47—24no—
127#99×C47—42no—
128#95×C47—21no—
129#95×C47—21no—
130#95×C47—21no—
131#95×C47—21no—
132#95×C47—21no—
133#95×C47—22no—
134#95×C47—22no—
135#95×C47—21no—
136#95×C47—21no—
137#95×C47—21no—
138#95×C47—22no—
139#95×C47—22no—
140C24×C47C2×D412yes—
141C24×C47C2411yescharacteristic
142C2×Q8×C47—21no—
143C2×Q8×C47—21no—
144C2×D4×C47—22no—
145C2×D4×C47—22no—
146C2×D4×C47—22no—
147C2×D4×C47—22no—
148C2×D4×C47—22no—
149C2×D4×C47—22no—
150C2×D4×C47—21no—
151C2×D4×C47—21no—
152C22×C4×C47—22no—
153C22×C4×C47—21no—
154C22×C4×C47—21no—
155C22×C4×C47—22no—
156C22×C4×C47—22no—
157C22×C4×C47—21no—
158C22×C4×C47—22no—
159C22×C4×C47—22no—
160C22×C4×C47—22no—
161C22×C4×C47—22no—
162C22×C4×C47—21no—
163C22×C4×C47—21no—
164C22×C4×C47—21no—
165C22×C4×C47—22no—
166C22×C4×C47—21no—
167C22×C4×C47—21no—
168C22×C4×C47—42no—
169C22×C4×C47C2×D412yes—
170C22×C4×C47C2×D412yes—
171C22×C4×C47C2×D411yescharacteristic
172C22×C4×C47C2×D412yes—
173C22×C4×C47C2×D411yescharacteristic
174C22×C4×C47C2×D411yescharacteristic
175C22×C4×C47C2×D411yescharacteristic
176C22×C4×C47C2×D411yescharacteristic
177C22×C4×C47C2×D411yescharacteristic
178C22×C4×C47C2×D412yes—
179C22×C4×C47C2×D412yes—
180C4⋊C4×C47—22no—
181C4⋊C4×C47—22no—
182C4⋊C4×C47—22no—
183C4⋊C4×C47—22no—
184C4⋊C4×C47—21no—
185C4⋊C4×C47—21no—
186C4⋊C4×C47—21no—
187C4⋊C4×C47—21no—
188C4⋊C4×C47—22no—
189C4⋊C4×C47—22no—
190C4⋊C4×C47—22no—
191C4⋊C4×C47—22no—
192C4⋊C4×C47—22no—
193C4⋊C4×C47—22no—
194C4⋊C4×C47—44no—
195C4⋊C4×C47—44no—
196C4⋊C4×C47—44no—
197C4⋊C4×C47—42no—
198C4⋊C4×C47—42no—
199C4⋊C4×C47—41no—
200C4⋊C4×C47—41no—
201C4⋊C4×C47—42no—
202C22⋊C4×C47—22no—
203C22⋊C4×C47—22no—
204C22⋊C4×C47—22no—
205C22⋊C4×C47—22no—
206C22⋊C4×C47—22no—
207C22⋊C4×C47—22no—
208C22⋊C4×C47—22no—
209C22⋊C4×C47—22no—
210C22⋊C4×C47—22no—
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—21no—
219C22⋊C4×C47—21no—
220C22⋊C4×C47—44no—
221C22⋊C4×C47—44no—
222C22⋊C4×C47#4114yes—
223C42×C47—22no—
224C42×C47—22no—
225C42×C47—21no—
226C42×C47—21no—
227C42×C47—21no—
228C42×C47—21no—
229C42×C47—44no—
230C23×C47—22no—
231C23×C47—22no—
232C23×C47—22no—
233C23×C47—41no—
234C23×C47—41no—
235C23×C47—42no—
236C23×C47—42no—
237C23×C47C22×D411yescharacteristic
238C23×C47C22×D412yes—
239C23×C47C2×#4112yes—
240C23×C47H(5,𝔽2)11yescharacteristic
241C23×C472−1+411yescharacteristic
242Q8×C47—81no—
243Q8×C47—81no—
244D4×C47—42no—
245D4×C47—42no—
246D4×C47—42no—
247D4×C47—42no—
248D4×C47—81no—
249D4×C47—81no—
250C2×C4×C47—21no—
251C2×C4×C47—21no—
252C2×C4×C47—21no—
253C2×C4×C47—21no—
254C2×C4×C47—22no—
255C2×C4×C47—22no—
256C2×C4×C47—22no—
257C2×C4×C47—22no—
258C2×C4×C47—24no—
259C2×C4×C47—22no—
260C2×C4×C47—21no—
261C2×C4×C47—21no—
262C2×C4×C47—21no—
263C2×C4×C47—21no—
264C2×C4×C47—22no—
265C2×C4×C47—22no—
266C2×C4×C47—22no—
267C2×C4×C47—24no—
268C2×C4×C47—22no—
269C2×C4×C47—22no—
270C2×C4×C47—42no—
271C2×C4×C47—42no—
272C2×C4×C47—41no—
273C2×C4×C47—42no—
274C2×C4×C47—41no—
275C2×C4×C47—41no—
276C2×C4×C47—42no—
277C2×C4×C47—41no—
278C2×C4×C47—41no—
279C2×C4×C47—42no—
280C2×C4×C47—41no—
281C2×C4×C47—42no—
282C2×C4×C47—41no—
283C2×C4×C47—41no—
284C2×C4×C47—41no—
285C2×C4×C47—41no—
286C2×C4×C47—42no—
287C2×C4×C47—41no—
288C2×C4×C47—41no—
289C2×C4×C47—41no—
290C2×C4×C47—41no—
291C2×C4×C47—41no—
292C2×C4×C47—42no—
293C2×C4×C47—42no—
294C2×C4×C47—42no—
295C2×C4×C47—82no—
296C2×C4×C47—82no—
297C2×C4×C47#12011yescharacteristic
298C2×C4×C47#12011yescharacteristic
299C2×C4×C47#12012yes—
300#25566C4711yesmaximal, characteristic, direct product factor, Sylow
301C22×C47—21no—
302C22×C47—22no—
303C22×C47—21no—
304C22×C47—22no—
305C22×C47—42no—
306C22×C47—41no—
307C22×C47—41no—
308C22×C47—42no—
309C22×C47—42no—
310C22×C47—42no—
311C22×C47—82no—
312C22×C47—82no—
313C22×C47C2×#12011yescharacteristic
314C22×C47#53211yescharacteristic
315C22×C47#53711yescharacteristic
316C22×C47#54612yes—
317C22×C47#54712yes—
318C4×C47—21no—
319C4×C47—22no—
320C4×C47—21no—
321C4×C47—44no—
322C4×C47—42no—
323C4×C47—42no—
324C4×C47—41no—
325C4×C47—42no—
326C4×C47—41no—
327C4×C47—41no—
328C4×C47—42no—
329C4×C47—41no—
330C4×C47—82no—
331C4×C47—81no—
332C4×C47—81no—
333C4×C47—81no—
334#3491C2×C4711yescharacteristic
335#2484C2×C4711yescharacteristic, complemented
336#2413C2×C4712yescomplemented
337#2062C2×C4711yescharacteristic, complemented
338#2044C2×C4711yescharacteristic
339#2030C2×C4711yescharacteristic, complemented
340#2022C2×C4711yescharacteristic
341#1899C2×C4712yescomplemented
342#1890C2×C4712yescomplemented
343#1867C2×C4712yescomplemented
344#1740C2×C4711yescharacteristic, complemented
345C2×C47—22no—
346C2×C47—21no—
347C2×C47—21no—
348C2×C47—22no—
349C2×C47—82no—
350C2×C47#243011yescharacteristic
351C2×C47#302511yescharacteristic
352C2×C47#302811yescharacteristic
353#552—22no—
354#552—22no—
355#551—22no—
356#551—22no—
357#543C22×C4711yescharacteristic
358#539—21no—
359#539—21no—
360#534C22×C4711yescharacteristic
361#529—21no—
362#529—21no—
363C2×#123C22×C4712yes—
364C2×#123C22×C4712yes—
365#518C22×C4712yes—
366C2×#117C22×C4712yes—
367C2×#117C22×C4711yescharacteristic
368C22×C4⋊C4C22×C4711yescharacteristic
369C2×#99C22×C4712yes—
370C2×#99C22×C4712yes—
371#400—21no—
372#398—22no—
373#398—21no—
374#396—22no—
375#389—22no—
376#388—22no—
377#387—21no—
378#387—21no—
379#386C22×C4712yes—
380#385C22×C4712yes—
381#385C22×C4711yescharacteristic
382#385C22×C4711yescharacteristic
383#381C22×C4711yescharacteristic
384#381C22×C4712yes—
385#381C22×C4711yescharacteristic
386#381C22×C4711yescharacteristic
387#342C22×C4712yes—
388#342C22×C4711yescharacteristic
389#342C22×C4712yes—
390#342C22×C4712yes—
391#342C22×C4711yescharacteristic
392C47#2556611yescharacteristic, direct product factor, Sylow
393C22×D4C23×C4712yes—
394C23×C4C23×C4711yescharacteristic
395C23×C4C23×C4711yescharacteristic
396C23×C4C23×C4711yescharacteristic
397#126—22no—
398#126—22no—
399#126—22no—
400#126—22no—
401#125—21no—
402#125—21no—
403#125—22no—
404#125—22no—
405#124—21no—
406#124—21no—
407#123—22no—
408#123—22no—
409#123—22no—
410#123—22no—
411#123—22no—
412#123—22no—
413#123—22no—
414#123—24no—
415#123—42no—
416C22⋊Q8—22no—
417C22⋊Q8—22no—
418C22⋊Q8—21no—
419C22⋊Q8—21no—
420C22⋊Q8—22no—
421C22⋊Q8—22no—
422#121—21no—
423#121—21no—
424#120—22no—
425C4×Q8—21no—
426C4×Q8—21no—
427C4×D4—21no—
428C4×D4—21no—
429C4×D4—22no—
430C4×D4—22no—
431C4×D4—22no—
432C4×D4—22no—
433#117—22no—
434#117—22no—
435#117—22no—
436#117—22no—
437#117—22no—
438#117—24no—
439#117—42no—
440C2×C4⋊C4—21no—
441C2×C4⋊C4—22no—
442C2×C4⋊C4—22no—
443C2×C4⋊C4—21no—
444C2×C4⋊C4—22no—
445C2×C4⋊C4—22no—
446C2×C4⋊C4—21no—
447C2×C4⋊C4—21no—
448C2×C4⋊C4—22no—
449C2×C4⋊C4D4×C4711yescharacteristic
450C2×C4⋊C4D4×C4711yescharacteristic
451C2×C4⋊C4D4×C4712yes—
452C2×C4⋊C4D4×C4712yes—
453C2×C22⋊C4—22no—
454C2×C22⋊C4—22no—
455C2×C22⋊C4—22no—
456C2×C22⋊C4D4×C4712yes—
457C2×C22⋊C4D4×C4712yes—
458C2×C22⋊C4C23×C4712yes—
459C2×C22⋊C4C23×C4711yescharacteristic
460C2×C22⋊C4C23×C4711yescharacteristic
461C2×C22⋊C4C23×C4711yescharacteristic
462C2×C22⋊C4C23×C4711yescharacteristic
463C2×C22⋊C4C23×C4712yes—
464C2×C22⋊C4C23×C4712yes—
465C2×C42—22no—
466C2×C42D4×C4711yescharacteristic
467C2×C42D4×C4711yescharacteristic
468#99—24no—
469#99—42no—
470#95—21no—
471#95—21no—
472#95—21no—
473#95—21no—
474#95—21no—
475#95—22no—
476#95—22no—
477#95—21no—
478#95—21no—
479#95—21no—
480#95—22no—
481#95—22no—
482C24C2×D4×C4712yes—
483C24C24×C4711yescharacteristic
484C2×Q8—21no—
485C2×Q8—21no—
486C2×D4—22no—
487C2×D4—22no—
488C2×D4—22no—
489C2×D4—22no—
490C2×D4—22no—
491C2×D4—22no—
492C2×D4—21no—
493C2×D4—21no—
494C22×C4—22no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—22no—
498C22×C4—21no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—42no—
511C22×C4C2×D4×C4712yes—
512C22×C4C2×D4×C4711yescharacteristic
513C22×C4C2×D4×C4711yescharacteristic
514C22×C4C2×D4×C4712yes—
515C22×C4C2×D4×C4712yes—
516C22×C4C2×D4×C4711yescharacteristic
517C22×C4C2×D4×C4711yescharacteristic
518C22×C4C2×D4×C4712yes—
519C22×C4C2×D4×C4711yescharacteristic
520C22×C4C2×D4×C4711yescharacteristic
521C22×C4C2×D4×C4712yes—
522C4⋊C4—22no—
523C4⋊C4—22no—
524C4⋊C4—22no—
525C4⋊C4—22no—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—21no—
529C4⋊C4—21no—
530C4⋊C4—22no—
531C4⋊C4—22no—
532C4⋊C4—22no—
533C4⋊C4—22no—
534C4⋊C4—22no—
535C4⋊C4—22no—
536C4⋊C4—44no—
537C4⋊C4—44no—
538C4⋊C4—44no—
539C4⋊C4—42no—
540C4⋊C4—42no—
541C4⋊C4—41no—
542C4⋊C4—41no—
543C4⋊C4—42no—
544C22⋊C4—22no—
545C22⋊C4—22no—
546C22⋊C4—22no—
547C22⋊C4—22no—
548C22⋊C4—22no—
549C22⋊C4—22no—
550C22⋊C4—22no—
551C22⋊C4—22no—
552C22⋊C4—22no—
553C22⋊C4—22no—
554C22⋊C4—22no—
555C22⋊C4—22no—
556C22⋊C4—22no—
557C22⋊C4—22no—
558C22⋊C4—22no—
559C22⋊C4—21no—
560C22⋊C4—22no—
561C22⋊C4—21no—
562C22⋊C4—44no—
563C22⋊C4—44no—
564C22⋊C4#41×C4714yes—
565C42—22no—
566C42—22no—
567C42—21no—
568C42—21no—
569C42—21no—
570C42—21no—
571C42—44no—
572C23—22no—
573C23—22no—
574C23—22no—
575C23—41no—
576C23—41no—
577C23—42no—
578C23—42no—
579C23C22×D4×C4711yescharacteristic
580C23C22×D4×C4712yes—
581C23C2×#41×C4712yes—
582C23H(5,𝔽2)×C4711yescharacteristic
583C232−1+4×C4711yescharacteristic
584Q8—81no—
585Q8—81no—
586D4—42no—
587D4—42no—
588D4—42no—
589D4—42no—
590D4—81no—
591D4—81no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—22no—
597C2×C4—22no—
598C2×C4—22no—
599C2×C4—22no—
600C2×C4—24no—
601C2×C4—22no—
602C2×C4—21no—
603C2×C4—21no—
604C2×C4—21no—
605C2×C4—21no—
606C2×C4—22no—
607C2×C4—22no—
608C2×C4—22no—
609C2×C4—24no—
610C2×C4—22no—
611C2×C4—22no—
612C2×C4—42no—
613C2×C4—42no—
614C2×C4—41no—
615C2×C4—42no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—42no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—42no—
622C2×C4—41no—
623C2×C4—42no—
624C2×C4—41no—
625C2×C4—41no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—42no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—42no—
635C2×C4—42no—
636C2×C4—42no—
637C2×C4—82no—
638C2×C4—82no—
639C2×C4#120×C4711yescharacteristic
640C2×C4#120×C4711yescharacteristic
641C2×C4#120×C4712yes—
642C22—21no—
643C22—22no—
644C22—21no—
645C22—22no—
646C22—42no—
647C22—41no—
648C22—41no—
649C22—42no—
650C22—42no—
651C22—42no—
652C22—82no—
653C22—82no—
654C22C2×#120×C4711yescharacteristic
655C22C47×#53211yescharacteristic
656C22C47×#53711yescharacteristic
657C22C47×#54612yes—
658C22C47×#54712yes—
659C4—21no—
660C4—22no—
661C4—21no—
662C4—44no—
663C4—42no—
664C4—42no—
665C4—41no—
666C4—42no—
667C4—41no—
668C4—41no—
669C4—42no—
670C4—41no—
671C4—82no—
672C4—81no—
673C4—81no—
674C4—81no—
675C2—22no—
676C2—21no—
677C2—21no—
678C2—22no—
679C2—82no—
680C2C47×#243011yescharacteristic
681C2C47×#302511yescharacteristic
682C2C47×#302811yescharacteristic
subgroupG/H
center, socleC22×C47C2×#120
commutator, Frattini, cosocleC24C24×C47
prime radicalC47×#534C22
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C47 ◁ C23×C4×C47 ◁ G

Complements

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

NH ≅ G/Ntype
2. C47×#2484C2semidirect
3. C47×#2413C2semidirect
4. C47×#2062C2semidirect
6. C47×#2030C2semidirect
8. C47×#1899C2semidirect
9. C47×#1890C2semidirect
10. C47×#1867C2semidirect
11. C47×#1740C2semidirect
300. #25566C47direct (N × H)
335. #2484C2×C47semidirect
336. #2413C2×C47semidirect
337. #2062C2×C47semidirect
339. #2030C2×C47semidirect
341. #1899C2×C47semidirect
342. #1890C2×C47semidirect
343. #1867C2×C47semidirect
344. #1740C2×C47semidirect
392. C47#25566direct (N × H)

Maximal subgroups

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

subgroupindex
C47×#34912
C47×#24842
C47×#24132
C47×#20622
C47×#20442
C47×#20302
C47×#20222
C47×#18992
C47×#18902
C47×#18672
C47×#17402
#2556647