Finite Group Databasebeta

← C47×#18966 #26058664

Subgroups — C47×#18966 #26058664

Order 12032.

938 conjugacy classes of subgroups.

The subgroup lattice has 652 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3546C211yesmaximal, characteristic
2C47×#3239C211yesmaximal, characteristic, complemented
3C47×#3226C211yesmaximal, characteristic, complemented
4C47×#3206C211yesmaximal, characteristic, complemented
5C47×#1650C212yesmaximal, complemented
6C47×#1647C212yesmaximal, complemented
7C47×#1642C212yesmaximal, complemented
8C47×#1639C212yesmaximal, complemented
9C47×#1553C211yesmaximal, characteristic, complemented
10C47×#1496C211yesmaximal, characteristic, complemented
11C47×#1482C211yesmaximal, characteristic, complemented
12C47×#560—22no—
13C47×#556C2211yescharacteristic
14C47×#553—21no—
15C47×#550—21no—
16C47×#550C2211yescharacteristic
17C47×#547C2211yescharacteristic
18C47×#546—21no—
19C47×#546—21no—
20D42×C47C2211yescharacteristic
21C47×#542—21no—
22C47×#538—22no—
23C47×#537—21no—
24C47×#535—21no—
25C47×#535—21no—
26C47×#532C2211yescharacteristic
27C47×#532C2211yescharacteristic
28C2×C4⋊Q8×C47C2211yescharacteristic, complemented
29C47×#529C2211yescharacteristic
30C47×#501—21no—
31C47×#500C2212yescomplemented
32C47×#492—21no—
33C47×#489—21no—
34C47×#487—21no—
35C47×#486C2212yes—
36C47×#484—21no—
37C47×#481—21no—
38C47×#480—22no—
39C47×#475C2212yescomplemented
40C47×#474—22no—
41C47×#474C2212yes—
42C47×#461C2212yes—
43C47×#461C2212yescomplemented
44C47×#448—21no—
45C47×#448—21no—
46C47×#432C2211yescharacteristic, complemented
47C47×#431C2211yescharacteristic, complemented
48C47×#431C2211yescharacteristic, complemented
49C47×#332C2212yescomplemented
50C47×#331C2212yes—
51C47×Q8⋊C8C2212yescomplemented
52C47×D4⋊C8C2212yes—
53C47×D4⋊C8C2212yes—
54C47×D4⋊C8C2212yescomplemented
55C2×#41×C47—21no—
56C2×#41×C47—21no—
57C2×#41×C47—21no—
58C2×#41×C47—21no—
59C22×Q8×C47—21no—
60C22×D4×C47—21no—
61C22×D4×C47—21no—
62C2×SD16×C47—22no—
63C2×SD16×C47—22no—
64C4⋊Q8×C47—21no—
65C4⋊Q8×C47—21no—
66C4⋊Q8×C47—21no—
67C4⋊Q8×C47D411yescharacteristic
68C4⋊Q8×C47C2312yes—
69C4⋊Q8×C47C2311yescharacteristic
70#127×C47—22no—
71#127×C47—21no—
72#127×C47D411yescharacteristic
73#127×C47C2311yescharacteristic
74#126×C47—22no—
75#126×C47—22no—
76#126×C47—21no—
77#125×C47D411yescharacteristic
78#124×C47—22no—
79#124×C47—21no—
80#124×C47—21no—
81#124×C47—21no—
82#124×C47D411yescharacteristic
83#123×C47—22no—
84#123×C47—22no—
85#123×C47—21no—
86#123×C47—22no—
87C22⋊Q8×C47—22no—
88C22⋊Q8×C47—21no—
89C22⋊Q8×C47—21no—
90C22⋊Q8×C47D411yescharacteristic
91#121×C47—22no—
92#121×C47—22no—
93#121×C47—22no—
94#121×C47—22no—
95#121×C47—22no—
96#121×C47—21no—
97#121×C47—22no—
98#121×C47—21no—
99#121×C47—21no—
100#121×C47—21no—
101#121×C47—21no—
102#121×C47—21no—
103#121×C47D412yes—
104#121×C47D411yescharacteristic
105#121×C47D411yescharacteristic
106#121×C47D411yescharacteristic
107#120×C47—22no—
108#120×C47—22no—
109#120×C47—22no—
110#120×C47—22no—
111C4×Q8×C47—21no—
112C4×Q8×C47C2311yescharacteristic
113C4×D4×C47—22no—
114C4×D4×C47—21no—
115C4×D4×C47—21no—
116C4×D4×C47—21no—
117C4×D4×C47—21no—
118C4×D4×C47D412yes—
119C4×D4×C47C2311yescharacteristic
120C4×D4×C47C2311yescharacteristic
121C4×D4×C47C2311yescharacteristic
122#117×C47—21no—
123#117×C47—21no—
124C2×C4⋊C4×C47—21no—
125C2×C4⋊C4×C47—21no—
126C2×C4⋊C4×C47—21no—
127C2×C22⋊C4×C47—22no—
128C2×C42×C47C2311yescharacteristic
129#107×C47—24no—
130#107×C47—22no—
131#106×C47—22no—
132C4⋊C8×C47—21no—
133C4⋊C8×C47C2312yes—
134C4⋊C8×C47C2312yes—
135#103×C47—22no—
136#103×C47—22no—
137#103×C47—22no—
138#102×C47—24no—
139#102×C47—22no—
140C22⋊C8×C47—21no—
141C22⋊C8×C47—21no—
142C22⋊C8×C47—21no—
143#97×C47—21no—
144C4×C8×C47—21no—
145C4×C8×C47C2312yes—
146C24×C47—22no—
147#41×C47—82no—
148#41×C47—82no—
149#41×C47—82no—
150#41×C47—82no—
151C2×Q8×C47—21no—
152C2×Q8×C47—21no—
153C2×Q8×C47—22no—
154C2×Q8×C47—41no—
155C2×Q8×C47—82no—
156C2×Q8×C47C2×D411yescharacteristic
157C2×D4×C47—22no—
158C2×D4×C47—22no—
159C2×D4×C47—22no—
160C2×D4×C47—22no—
161C2×D4×C47—22no—
162C2×D4×C47—21no—
163C2×D4×C47—21no—
164C2×D4×C47—22no—
165C2×D4×C47—21no—
166C2×D4×C47—21no—
167C2×D4×C47—21no—
168C2×D4×C47—21no—
169C2×D4×C47—21no—
170C2×D4×C47—82no—
171C2×D4×C47—82no—
172C2×D4×C47C2×D411yescharacteristic
173C2×D4×C47C2×D411yescharacteristic
174C2×D4×C47C2×D411yescharacteristic
175C2×D4×C47C2×D412yes—
176C22×C4×C47—22no—
177C22×C4×C47—22no—
178C22×C4×C47—21no—
179C22×C4×C47—21no—
180C22×C4×C47—21no—
181C22×C4×C47—22no—
182C22×C4×C47—41no—
183C22×C4×C47C2×D411yescharacteristic
184C22×C4×C47C2×D411yescharacteristic
185C22×C4×C47C2×D411yescharacteristic
186SD16×C47—82no—
187SD16×C47—82no—
188C2×C8×C47—22no—
189C2×C8×C47—22no—
190C2×C8×C47—22no—
191C4⋊C4×C47—22no—
192C4⋊C4×C47—22no—
193C4⋊C4×C47—21no—
194C4⋊C4×C47—21no—
195C4⋊C4×C47—21no—
196C4⋊C4×C47—21no—
197C4⋊C4×C47—21no—
198C4⋊C4×C47—21no—
199C4⋊C4×C47—22no—
200C4⋊C4×C47—22no—
201C4⋊C4×C47—41no—
202C4⋊C4×C47—41no—
203C4⋊C4×C47C2×D411yescharacteristic
204C4⋊C4×C47C2×D411yescharacteristic
205C4⋊C4×C47C2×D411yescharacteristic
206C4⋊C4×C47C2×D411yescharacteristic
207C4⋊C4×C47C2×D412yes—
208C22⋊C4×C47—22no—
209C22⋊C4×C47—22no—
210C22⋊C4×C47—22no—
211C22⋊C4×C47—22no—
212C22⋊C4×C47—22no—
213C22⋊C4×C47—21no—
214C22⋊C4×C47—21no—
215C22⋊C4×C47—21no—
216C22⋊C4×C47—21no—
217C22⋊C4×C47—21no—
218C22⋊C4×C47—21no—
219C22⋊C4×C47—22no—
220C22⋊C4×C47—22no—
221C22⋊C4×C47—21no—
222C22⋊C4×C47—21no—
223C22⋊C4×C47—21no—
224C42×C47—22no—
225C42×C47—21no—
226C42×C47C2×D411yescharacteristic
227C42×C47C2×D411yescharacteristic
228C42×C47C2×D411yescharacteristic
229C42×C47C2411yescharacteristic
230C23×C47—21no—
231C23×C47—21no—
232C23×C47—22no—
233C23×C47—21no—
234C23×C47—82no—
235C23×C47—82no—
236C23×C47—82no—
237C23×C47#12011yescharacteristic
238Q8×C47—22no—
239Q8×C47—42no—
240Q8×C47—42no—
241Q8×C47—42no—
242Q8×C47—81no—
243Q8×C47—82no—
244D4×C47—22no—
245D4×C47—22no—
246D4×C47—22no—
247D4×C47—42no—
248D4×C47—42no—
249D4×C47—42no—
250D4×C47—81no—
251D4×C47—81no—
252D4×C47—81no—
253D4×C47—82no—
254D4×C47—81no—
255D4×C47—81no—
256D4×C47—82no—
257D4×C47—82no—
258D4×C47—82no—
259D4×C47—82no—
260D4×C47—82no—
261C2×C4×C47—22no—
262C2×C4×C47—22no—
263C2×C4×C47—21no—
264C2×C4×C47—21no—
265C2×C4×C47—21no—
266C2×C4×C47—22no—
267C2×C4×C47—21no—
268C2×C4×C47—21no—
269C2×C4×C47—41no—
270C2×C4×C47—42no—
271C2×C4×C47—42no—
272C2×C4×C47—42no—
273C2×C4×C47—42no—
274C2×C4×C47—82no—
275C2×C4×C47—82no—
276C2×C4×C47—82no—
277C2×C4×C47—82no—
278C2×C4×C47#12011yescharacteristic
279C2×C4×C47#12011yescharacteristic
280C2×C4×C47#12011yescharacteristic
281C2×C4×C47C22×D411yescharacteristic
282C2×C4×C47C22×D411yescharacteristic
283C2×C4×C47C22×D411yescharacteristic
284C8×C47—42no—
285C8×C47—42no—
286C8×C47—42no—
287#18966C4711yesmaximal, characteristic, direct product factor, Sylow
288C22×C47—21no—
289C22×C47—21no—
290C22×C47—21no—
291C22×C47—41no—
292C22×C47—41no—
293C22×C47—42no—
294C22×C47—41no—
295C22×C47—41no—
296C22×C47—41no—
297C22×C47—42no—
298C22×C47—41no—
299C22×C47—42no—
300C22×C47—41no—
301C22×C47—41no—
302C22×C47—41no—
303C22×C47—164no—
304C22×C47C2×#12011yescharacteristic
305C4×C47—21no—
306C4×C47—21no—
307C4×C47—21no—
308C4×C47—21no—
309C4×C47—41no—
310C4×C47—42no—
311C4×C47—41no—
312C4×C47—41no—
313C4×C47—41no—
314C4×C47—41no—
315C4×C47—82no—
316C4×C47#57612yes—
317C4×C47#57712yes—
318#3546C2×C4711yescharacteristic
319#3239C2×C4711yescharacteristic, complemented
320#3226C2×C4711yescharacteristic, complemented
321#3206C2×C4711yescharacteristic, complemented
322#1650C2×C4712yescomplemented
323#1647C2×C4712yescomplemented
324#1642C2×C4712yescomplemented
325#1639C2×C4712yescomplemented
326#1553C2×C4711yescharacteristic, complemented
327#1496C2×C4711yescharacteristic, complemented
328#1482C2×C4711yescharacteristic, complemented
329C2×C47—41no—
330C2×C47—81no—
331C2×C47—82no—
332C2×C47—81no—
333C2×C47—81no—
334C2×C47#300811yescharacteristic
335C2×C47#300911yescharacteristic
336C2×C47#302211yescharacteristic
337#560—22no—
338#556C22×C4711yescharacteristic
339#553—21no—
340#550—21no—
341#550C22×C4711yescharacteristic
342#547C22×C4711yescharacteristic
343#546—21no—
344#546—21no—
345D42C22×C4711yescharacteristic
346#542—21no—
347#538—22no—
348#537—21no—
349#535—21no—
350#535—21no—
351#532C22×C4711yescharacteristic
352#532C22×C4711yescharacteristic
353C2×C4⋊Q8C22×C4711yescharacteristic, complemented
354#529C22×C4711yescharacteristic
355#501—21no—
356#500C22×C4712yescomplemented
357#492—21no—
358#489—21no—
359#487—21no—
360#486C22×C4712yes—
361#484—21no—
362#481—21no—
363#480—22no—
364#475C22×C4712yescomplemented
365#474—22no—
366#474C22×C4712yes—
367#461C22×C4712yes—
368#461C22×C4712yescomplemented
369#448—21no—
370#448—21no—
371#432C22×C4711yescharacteristic, complemented
372#431C22×C4711yescharacteristic, complemented
373#431C22×C4711yescharacteristic, complemented
374#332C22×C4712yescomplemented
375#331C22×C4712yes—
376Q8⋊C8C22×C4712yescomplemented
377D4⋊C8C22×C4712yes—
378D4⋊C8C22×C4712yes—
379D4⋊C8C22×C4712yescomplemented
380C47#1896611yescharacteristic, direct product factor, Sylow
381C2×#41—21no—
382C2×#41—21no—
383C2×#41—21no—
384C2×#41—21no—
385C22×Q8—21no—
386C22×D4—21no—
387C22×D4—21no—
388C2×SD16—22no—
389C2×SD16—22no—
390C4⋊Q8—21no—
391C4⋊Q8—21no—
392C4⋊Q8—21no—
393C4⋊Q8D4×C4711yescharacteristic
394C4⋊Q8C23×C4712yes—
395C4⋊Q8C23×C4711yescharacteristic
396#127—22no—
397#127—21no—
398#127D4×C4711yescharacteristic
399#127C23×C4711yescharacteristic
400#126—22no—
401#126—22no—
402#126—21no—
403#125D4×C4711yescharacteristic
404#124—22no—
405#124—21no—
406#124—21no—
407#124—21no—
408#124D4×C4711yescharacteristic
409#123—22no—
410#123—22no—
411#123—21no—
412#123—22no—
413C22⋊Q8—22no—
414C22⋊Q8—21no—
415C22⋊Q8—21no—
416C22⋊Q8D4×C4711yescharacteristic
417#121—22no—
418#121—22no—
419#121—22no—
420#121—22no—
421#121—22no—
422#121—21no—
423#121—22no—
424#121—21no—
425#121—21no—
426#121—21no—
427#121—21no—
428#121—21no—
429#121D4×C4711yescharacteristic
430#121D4×C4711yescharacteristic
431#121D4×C4711yescharacteristic
432#121D4×C4712yes—
433#120—22no—
434#120—22no—
435#120—22no—
436#120—22no—
437C4×Q8—21no—
438C4×Q8C23×C4711yescharacteristic
439C4×D4—22no—
440C4×D4—21no—
441C4×D4—21no—
442C4×D4—21no—
443C4×D4—21no—
444C4×D4D4×C4712yes—
445C4×D4C23×C4711yescharacteristic
446C4×D4C23×C4711yescharacteristic
447C4×D4C23×C4711yescharacteristic
448#117—21no—
449#117—21no—
450C2×C4⋊C4—21no—
451C2×C4⋊C4—21no—
452C2×C4⋊C4—21no—
453C2×C22⋊C4—22no—
454C2×C42C23×C4711yescharacteristic
455#107—24no—
456#107—22no—
457#106—22no—
458C4⋊C8—21no—
459C4⋊C8C23×C4712yes—
460C4⋊C8C23×C4712yes—
461#103—22no—
462#103—22no—
463#103—22no—
464#102—24no—
465#102—22no—
466C22⋊C8—21no—
467C22⋊C8—21no—
468C22⋊C8—21no—
469#97—21no—
470C4×C8—21no—
471C4×C8C23×C4712yes—
472C24—22no—
473#41—82no—
474#41—82no—
475#41—82no—
476#41—82no—
477C2×Q8—21no—
478C2×Q8—21no—
479C2×Q8—22no—
480C2×Q8—41no—
481C2×Q8—82no—
482C2×Q8C2×D4×C4711yescharacteristic
483C2×D4—22no—
484C2×D4—22no—
485C2×D4—22no—
486C2×D4—22no—
487C2×D4—22no—
488C2×D4—21no—
489C2×D4—21no—
490C2×D4—22no—
491C2×D4—21no—
492C2×D4—21no—
493C2×D4—21no—
494C2×D4—21no—
495C2×D4—21no—
496C2×D4—82no—
497C2×D4—82no—
498C2×D4C2×D4×C4711yescharacteristic
499C2×D4C2×D4×C4711yescharacteristic
500C2×D4C2×D4×C4711yescharacteristic
501C2×D4C2×D4×C4712yes—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—22no—
508C22×C4—41no—
509C22×C4C2×D4×C4711yescharacteristic
510C22×C4C2×D4×C4711yescharacteristic
511C22×C4C2×D4×C4711yescharacteristic
512SD16—82no—
513SD16—82no—
514C2×C8—22no—
515C2×C8—22no—
516C2×C8—22no—
517C4⋊C4—22no—
518C4⋊C4—22no—
519C4⋊C4—21no—
520C4⋊C4—21no—
521C4⋊C4—21no—
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—22no—
526C4⋊C4—22no—
527C4⋊C4—41no—
528C4⋊C4—41no—
529C4⋊C4C2×D4×C4711yescharacteristic
530C4⋊C4C2×D4×C4711yescharacteristic
531C4⋊C4C2×D4×C4711yescharacteristic
532C4⋊C4C2×D4×C4711yescharacteristic
533C4⋊C4C2×D4×C4712yes—
534C22⋊C4—22no—
535C22⋊C4—22no—
536C22⋊C4—22no—
537C22⋊C4—22no—
538C22⋊C4—22no—
539C22⋊C4—21no—
540C22⋊C4—21no—
541C22⋊C4—21no—
542C22⋊C4—21no—
543C22⋊C4—21no—
544C22⋊C4—21no—
545C22⋊C4—22no—
546C22⋊C4—22no—
547C22⋊C4—21no—
548C22⋊C4—21no—
549C22⋊C4—21no—
550C42—22no—
551C42—21no—
552C42C2×D4×C4711yescharacteristic
553C42C2×D4×C4711yescharacteristic
554C42C2×D4×C4711yescharacteristic
555C42C24×C4711yescharacteristic
556C23—21no—
557C23—21no—
558C23—22no—
559C23—21no—
560C23—82no—
561C23—82no—
562C23—82no—
563C23#120×C4711yescharacteristic
564Q8—22no—
565Q8—42no—
566Q8—42no—
567Q8—42no—
568Q8—81no—
569Q8—82no—
570D4—22no—
571D4—22no—
572D4—22no—
573D4—42no—
574D4—42no—
575D4—42no—
576D4—81no—
577D4—81no—
578D4—81no—
579D4—82no—
580D4—81no—
581D4—81no—
582D4—82no—
583D4—82no—
584D4—82no—
585D4—82no—
586D4—82no—
587C2×C4—22no—
588C2×C4—22no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—22no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—41no—
596C2×C4—42no—
597C2×C4—42no—
598C2×C4—42no—
599C2×C4—42no—
600C2×C4—82no—
601C2×C4—82no—
602C2×C4—82no—
603C2×C4—82no—
604C2×C4#120×C4711yescharacteristic
605C2×C4#120×C4711yescharacteristic
606C2×C4#120×C4711yescharacteristic
607C2×C4C22×D4×C4711yescharacteristic
608C2×C4C22×D4×C4711yescharacteristic
609C2×C4C22×D4×C4711yescharacteristic
610C8—42no—
611C8—42no—
612C8—42no—
613C22—21no—
614C22—21no—
615C22—21no—
616C22—41no—
617C22—41no—
618C22—42no—
619C22—41no—
620C22—41no—
621C22—41no—
622C22—42no—
623C22—41no—
624C22—42no—
625C22—41no—
626C22—41no—
627C22—41no—
628C22—164no—
629C22C2×#120×C4711yescharacteristic
630C4—21no—
631C4—21no—
632C4—21no—
633C4—21no—
634C4—41no—
635C4—42no—
636C4—41no—
637C4—41no—
638C4—41no—
639C4—41no—
640C4—82no—
641C4C47×#57612yes—
642C4C47×#57712yes—
643C2—41no—
644C2—81no—
645C2—81no—
646C2—82no—
647C2—81no—
648C2C47×#300811yescharacteristic
649C2C47×#300911yescharacteristic
650C2C47×#302211yescharacteristic
subgroupG/H
center, socleC22×C47C2×#120
commutator, Frattini, cosocleC42C24×C47
prime radicalC47×#3546C2
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×#3239C2semidirect
3. C47×#3226C2semidirect
4. C47×#3206C2semidirect
5. C47×#1650C2semidirect
6. C47×#1647C2semidirect
7. C47×#1642C2semidirect
8. C47×#1639C2semidirect
9. C47×#1553C2semidirect
10. C47×#1496C2semidirect
11. C47×#1482C2semidirect
28. C2×C4⋊Q8×C47C22semidirect
31. C47×#500C22semidirect
39. C47×#475C22semidirect
43. C47×#461C22semidirect
46. C47×#432C22semidirect
47. C47×#431C22semidirect
48. C47×#431C22semidirect
49. C47×#332C22semidirect
51. C47×Q8⋊C8C22semidirect
54. C47×D4⋊C8C22semidirect
287. #18966C47direct (N × H)
319. #3239C2×C47semidirect
320. #3226C2×C47semidirect
321. #3206C2×C47semidirect
322. #1650C2×C47semidirect
323. #1647C2×C47semidirect
324. #1642C2×C47semidirect
325. #1639C2×C47semidirect
326. #1553C2×C47semidirect
327. #1496C2×C47semidirect
328. #1482C2×C47semidirect
353. C2×C4⋊Q8C22×C47semidirect
356. #500C22×C47semidirect
364. #475C22×C47semidirect
368. #461C22×C47semidirect
371. #432C22×C47semidirect
372. #431C22×C47semidirect
373. #431C22×C47semidirect
374. #332C22×C47semidirect
376. Q8⋊C8C22×C47semidirect
379. D4⋊C8C22×C47semidirect
380. C47#18966direct (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×#32392
C47×#32262
C47×#32062
C47×#16502
C47×#16472
C47×#16422
C47×#16392
C47×#15532
C47×#14962
C47×#14822
#1896647