Finite Group Databasebeta

← C47×#18958 #26058656

Subgroups — C47×#18958 #26058656

Order 12032.

950 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3554C211yesmaximal, characteristic, complemented
2C47×#3217C211yesmaximal, characteristic, complemented
3C47×#3208C211yesmaximal, characteristic, complemented
4C47×#3205C211yesmaximal, characteristic, complemented
5C47×#1627C212yesmaximal, complemented
6C47×#1626C212yesmaximal, complemented
7C47×#1621C212yesmaximal, complemented
8C47×#1620C212yesmaximal, complemented
9C47×#1553C211yesmaximal, characteristic, complemented
10C47×#1497C211yesmaximal, characteristic, complemented
11C47×#1482C211yesmaximal, characteristic, complemented
12C47×#562—22no—
13C47×#559—21no—
14C47×#559C2211yescharacteristic, complemented
15C47×#557C2211yescharacteristic, complemented
16C47×#554—21no—
17C47×#550C2211yescharacteristic, complemented
18D4×Q8×C47C2211yescharacteristic, complemented
19C47×#548—21no—
20C47×#547—21no—
21C47×#542—21no—
22C47×#542—21no—
23C47×#540—21no—
24C47×#539—22no—
25C47×#536—21no—
26C47×#533C2211yescharacteristic
27C47×#532C2211yescharacteristic
28C2×#127×C47C2211yescharacteristic
29C47×#529C2211yescharacteristic
30C47×#496—21no—
31C47×#493C2212yes—
32C47×#492—21no—
33C47×#490—21no—
34C47×#486—21no—
35C47×#486C2212yes—
36C47×#460C2212yes—
37C47×#460C2212yes—
38C47×#460C2212yes—
39C47×#459—22no—
40C47×#459C2212yes—
41C47×#450—21no—
42C47×#450—21no—
43C47×#450—21no—
44C47×#447—22no—
45C47×#447—21no—
46C47×#432C2211yescharacteristic
47C47×#431C2211yescharacteristic
48C47×#431C2211yescharacteristic
49C47×#332C2212yescomplemented
50C47×#331C2212yescomplemented
51C47×Q8⋊C8C2212yescomplemented
52C47×Q8⋊C8C2212yescomplemented
53C47×Q8⋊C8C2212yescomplemented
54C47×D4⋊C8C2212yescomplemented
55C2×#41×C47—21no—
56C2×#41×C47—21no—
57C22×Q8×C47—21no—
58C22×D4×C47—21no—
59C22×D4×C47—21no—
60C22×D4×C47—21no—
61C2×SD16×C47—22no—
62C2×SD16×C47—22no—
63C2×SD16×C47—22no—
64C2×D8×C47—24no—
65C2×D8×C47—22no—
66C4⋊Q8×C47—21no—
67C4⋊Q8×C47—21no—
68C4⋊Q8×C47D411yescharacteristic
69C4⋊Q8×C47D411yescharacteristic
70C4⋊Q8×C47C2311yescharacteristic
71#127×C47—21no—
72#127×C47—21no—
73#127×C47—21no—
74#127×C47—21no—
75#127×C47C2312yes—
76#127×C47C2311yescharacteristic
77#126×C47—22no—
78#126×C47—21no—
79#125×C47—22no—
80#125×C47—21no—
81#125×C47—21no—
82#125×C47D411yescharacteristic
83#124×C47—22no—
84#124×C47—22no—
85#124×C47—21no—
86#124×C47—21no—
87#124×C47—21no—
88#124×C47D411yescharacteristic
89#123×C47—22no—
90#123×C47—22no—
91#123×C47—22no—
92#123×C47—22no—
93#123×C47—22no—
94#123×C47—22no—
95#123×C47—21no—
96C22⋊Q8×C47—22no—
97C22⋊Q8×C47—22no—
98C22⋊Q8×C47—22no—
99C22⋊Q8×C47—22no—
100C22⋊Q8×C47—21no—
101C22⋊Q8×C47—22no—
102C22⋊Q8×C47—21no—
103C22⋊Q8×C47D411yescharacteristic
104C22⋊Q8×C47D411yescharacteristic
105C22⋊Q8×C47D411yescharacteristic
106#121×C47—22no—
107#121×C47—22no—
108#121×C47—22no—
109#121×C47—21no—
110#121×C47—21no—
111#121×C47D411yescharacteristic
112#121×C47D412yes—
113C4×Q8×C47—21no—
114C4×Q8×C47—21no—
115C4×Q8×C47—21no—
116C4×Q8×C47C2311yescharacteristic
117C4×Q8×C47C2311yescharacteristic
118C4×Q8×C47C2311yescharacteristic
119C4×D4×C47—22no—
120C4×D4×C47—21no—
121C4×D4×C47—21no—
122C4×D4×C47—21no—
123C4×D4×C47—21no—
124C4×D4×C47—21no—
125C4×D4×C47—21no—
126C4×D4×C47D412yes—
127C4×D4×C47C2311yescharacteristic
128#117×C47—21no—
129#117×C47—21no—
130C2×C4⋊C4×C47—22no—
131C2×C42×C47C2311yescharacteristic
132C4⋊C8×C47—21no—
133C4⋊C8×C47C2312yes—
134C4⋊C8×C47C2312yes—
135#102×C47—22no—
136#102×C47—22no—
137#102×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—41no—
147#41×C47—82no—
148#41×C47—82no—
149C2×Q8×C47—22no—
150C2×Q8×C47—21no—
151C2×Q8×C47—21no—
152C2×Q8×C47—82no—
153C2×Q8×C47C2×D411yescharacteristic
154C2×Q8×C47C2×D411yescharacteristic
155C2×Q8×C47C2×D411yescharacteristic
156C2×D4×C47—22no—
157C2×D4×C47—22no—
158C2×D4×C47—21no—
159C2×D4×C47—22no—
160C2×D4×C47—21no—
161C2×D4×C47—21no—
162C2×D4×C47—22no—
163C2×D4×C47—22no—
164C2×D4×C47—22no—
165C2×D4×C47—41no—
166C2×D4×C47—41no—
167C2×D4×C47—41no—
168C2×D4×C47—82no—
169C2×D4×C47—82no—
170C2×D4×C47—82no—
171C2×D4×C47C2×D411yescharacteristic
172C2×D4×C47C2×D412yes—
173C22×C4×C47—22no—
174C22×C4×C47—22no—
175C22×C4×C47—22no—
176C22×C4×C47—21no—
177C22×C4×C47—22no—
178C22×C4×C47C2×D411yescharacteristic
179C22×C4×C47C2×D411yescharacteristic
180C22×C4×C47C2×D411yescharacteristic
181SD16×C47—82no—
182SD16×C47—82no—
183SD16×C47—82no—
184D8×C47—82no—
185D8×C47—84no—
186C2×C8×C47—22no—
187C2×C8×C47—22no—
188C2×C8×C47—22no—
189C4⋊C4×C47—22no—
190C4⋊C4×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—21no—
200C4⋊C4×C47—21no—
201C4⋊C4×C47—21no—
202C4⋊C4×C47—21no—
203C4⋊C4×C47—21no—
204C4⋊C4×C47—21no—
205C4⋊C4×C47C2×D411yescharacteristic
206C4⋊C4×C47C2×D411yescharacteristic
207C4⋊C4×C47C2×D411yescharacteristic
208C4⋊C4×C47C2×D412yes—
209C4⋊C4×C47C2×D411yescharacteristic
210C22⋊C4×C47—22no—
211C22⋊C4×C47—22no—
212C22⋊C4×C47—22no—
213C22⋊C4×C47—22no—
214C22⋊C4×C47—22no—
215C22⋊C4×C47—21no—
216C22⋊C4×C47—21no—
217C22⋊C4×C47—21no—
218C22⋊C4×C47—21no—
219C22⋊C4×C47—21no—
220C22⋊C4×C47—21no—
221C22⋊C4×C47—22no—
222C22⋊C4×C47—22no—
223C22⋊C4×C47—21no—
224C42×C47—22no—
225C42×C47—21no—
226C42×C47—21no—
227C42×C47—21no—
228C42×C47C2×D411yescharacteristic
229C42×C47C2×D411yescharacteristic
230C42×C47C2×D411yescharacteristic
231C42×C47C2411yescharacteristic
232C23×C47—21no—
233C23×C47—22no—
234C23×C47—42no—
235C23×C47—82no—
236C23×C47—82no—
237C23×C47—82no—
238C23×C47#12011yescharacteristic
239Q8×C47—22no—
240Q8×C47—22no—
241Q8×C47—22no—
242Q8×C47—42no—
243Q8×C47—81no—
244Q8×C47—82no—
245D4×C47—22no—
246D4×C47—42no—
247D4×C47—44no—
248D4×C47—42no—
249D4×C47—42no—
250D4×C47—42no—
251D4×C47—42no—
252D4×C47—42no—
253D4×C47—42no—
254D4×C47—82no—
255D4×C47—82no—
256D4×C47—82no—
257D4×C47—81no—
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—21no—
267C2×C4×C47—21no—
268C2×C4×C47—22no—
269C2×C4×C47—21no—
270C2×C4×C47—21no—
271C2×C4×C47—41no—
272C2×C4×C47—42no—
273C2×C4×C47—82no—
274C2×C4×C47—82no—
275C2×C4×C47—82no—
276C2×C4×C47—82no—
277C2×C4×C47#12011yescharacteristic
278C2×C4×C47#12011yescharacteristic
279C2×C4×C47#12011yescharacteristic
280C2×C4×C47C22×D411yescharacteristic
281C2×C4×C47C22×D411yescharacteristic
282C2×C4×C47C22×D411yescharacteristic
283C8×C47—42no—
284C8×C47—42no—
285C8×C47—42no—
286#18958C4711yesmaximal, characteristic, direct product factor, Sylow
287C22×C47—21no—
288C22×C47—21no—
289C22×C47—21no—
290C22×C47—41no—
291C22×C47—42no—
292C22×C47—41no—
293C22×C47—42no—
294C22×C47—42no—
295C22×C47—41no—
296C22×C47—82no—
297C22×C47—82no—
298C22×C47—82no—
299C22×C47—164no—
300C22×C47C2×#12011yescharacteristic
301C4×C47—21no—
302C4×C47—21no—
303C4×C47—21no—
304C4×C47—21no—
305C4×C47—41no—
306C4×C47—41no—
307C4×C47—42no—
308C4×C47—41no—
309C4×C47—41no—
310C4×C47—41no—
311C4×C47—41no—
312C4×C47—41no—
313C4×C47#57612yes—
314C4×C47#57712yes—
315#3554C2×C4711yescharacteristic, complemented
316#3217C2×C4711yescharacteristic, complemented
317#3208C2×C4711yescharacteristic, complemented
318#3205C2×C4711yescharacteristic, complemented
319#1627C2×C4712yescomplemented
320#1626C2×C4712yescomplemented
321#1621C2×C4712yescomplemented
322#1620C2×C4712yescomplemented
323#1553C2×C4711yescharacteristic, complemented
324#1497C2×C4711yescharacteristic, complemented
325#1482C2×C4711yescharacteristic, complemented
326C2×C47—41no—
327C2×C47—81no—
328C2×C47—82no—
329C2×C47—162no—
330C2×C47#300811yescharacteristic
331C2×C47#301011yescharacteristic
332C2×C47#302111yescharacteristic
333#562—22no—
334#559—21no—
335#559C22×C4711yescharacteristic, complemented
336#557C22×C4711yescharacteristic, complemented
337#554—21no—
338#550C22×C4711yescharacteristic, complemented
339D4×Q8C22×C4711yescharacteristic, complemented
340#548—21no—
341#547—21no—
342#542—21no—
343#542—21no—
344#540—21no—
345#539—22no—
346#536—21no—
347#533C22×C4711yescharacteristic
348#532C22×C4711yescharacteristic
349C2×#127C22×C4711yescharacteristic
350#529C22×C4711yescharacteristic
351#496—21no—
352#493C22×C4712yes—
353#492—21no—
354#490—21no—
355#486—21no—
356#486C22×C4712yes—
357#460C22×C4712yes—
358#460C22×C4712yes—
359#460C22×C4712yes—
360#459—22no—
361#459C22×C4712yes—
362#450—21no—
363#450—21no—
364#450—21no—
365#447—22no—
366#447—21no—
367#432C22×C4711yescharacteristic
368#431C22×C4711yescharacteristic
369#431C22×C4711yescharacteristic
370#332C22×C4712yescomplemented
371#331C22×C4712yescomplemented
372Q8⋊C8C22×C4712yescomplemented
373Q8⋊C8C22×C4712yescomplemented
374Q8⋊C8C22×C4712yescomplemented
375D4⋊C8C22×C4712yescomplemented
376C47#1895811yescharacteristic, direct product factor, Sylow
377C2×#41—21no—
378C2×#41—21no—
379C22×Q8—21no—
380C22×D4—21no—
381C22×D4—21no—
382C22×D4—21no—
383C2×SD16—22no—
384C2×SD16—22no—
385C2×SD16—22no—
386C2×D8—24no—
387C2×D8—22no—
388C4⋊Q8—21no—
389C4⋊Q8—21no—
390C4⋊Q8D4×C4711yescharacteristic
391C4⋊Q8D4×C4711yescharacteristic
392C4⋊Q8C23×C4711yescharacteristic
393#127—21no—
394#127—21no—
395#127—21no—
396#127—21no—
397#127C23×C4712yes—
398#127C23×C4711yescharacteristic
399#126—22no—
400#126—21no—
401#125—22no—
402#125—21no—
403#125—21no—
404#125D4×C4711yescharacteristic
405#124—22no—
406#124—22no—
407#124—21no—
408#124—21no—
409#124—21no—
410#124D4×C4711yescharacteristic
411#123—22no—
412#123—22no—
413#123—22no—
414#123—22no—
415#123—22no—
416#123—22no—
417#123—21no—
418C22⋊Q8—22no—
419C22⋊Q8—22no—
420C22⋊Q8—22no—
421C22⋊Q8—22no—
422C22⋊Q8—21no—
423C22⋊Q8—22no—
424C22⋊Q8—21no—
425C22⋊Q8D4×C4711yescharacteristic
426C22⋊Q8D4×C4711yescharacteristic
427C22⋊Q8D4×C4711yescharacteristic
428#121—22no—
429#121—22no—
430#121—22no—
431#121—21no—
432#121—21no—
433#121D4×C4711yescharacteristic
434#121D4×C4712yes—
435C4×Q8—21no—
436C4×Q8—21no—
437C4×Q8—21no—
438C4×Q8C23×C4711yescharacteristic
439C4×Q8C23×C4711yescharacteristic
440C4×Q8C23×C4711yescharacteristic
441C4×D4—22no—
442C4×D4—21no—
443C4×D4—21no—
444C4×D4—21no—
445C4×D4—21no—
446C4×D4—21no—
447C4×D4—21no—
448C4×D4D4×C4712yes—
449C4×D4C23×C4711yescharacteristic
450#117—21no—
451#117—21no—
452C2×C4⋊C4—22no—
453C2×C42C23×C4711yescharacteristic
454C4⋊C8—21no—
455C4⋊C8C23×C4712yes—
456C4⋊C8C23×C4712yes—
457#102—24no—
458#102—22no—
459#102—22no—
460#102—22no—
461#102—22no—
462C22⋊C8—21no—
463C22⋊C8—21no—
464C22⋊C8—21no—
465#97—21no—
466C4×C8—21no—
467C4×C8C23×C4712yes—
468C24—41no—
469#41—82no—
470#41—82no—
471C2×Q8—22no—
472C2×Q8—21no—
473C2×Q8—21no—
474C2×Q8—82no—
475C2×Q8C2×D4×C4711yescharacteristic
476C2×Q8C2×D4×C4711yescharacteristic
477C2×Q8C2×D4×C4711yescharacteristic
478C2×D4—22no—
479C2×D4—22no—
480C2×D4—21no—
481C2×D4—22no—
482C2×D4—21no—
483C2×D4—21no—
484C2×D4—22no—
485C2×D4—22no—
486C2×D4—22no—
487C2×D4—41no—
488C2×D4—41no—
489C2×D4—41no—
490C2×D4—82no—
491C2×D4—82no—
492C2×D4—82no—
493C2×D4C2×D4×C4711yescharacteristic
494C2×D4C2×D4×C4712yes—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—21no—
499C22×C4—22no—
500C22×C4C2×D4×C4711yescharacteristic
501C22×C4C2×D4×C4711yescharacteristic
502C22×C4C2×D4×C4711yescharacteristic
503SD16—82no—
504SD16—82no—
505SD16—82no—
506D8—82no—
507D8—84no—
508C2×C8—22no—
509C2×C8—22no—
510C2×C8—22no—
511C4⋊C4—22no—
512C4⋊C4—22no—
513C4⋊C4—22no—
514C4⋊C4—22no—
515C4⋊C4—21no—
516C4⋊C4—21no—
517C4⋊C4—21no—
518C4⋊C4—21no—
519C4⋊C4—21no—
520C4⋊C4—21no—
521C4⋊C4—21no—
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4C2×D4×C4711yescharacteristic
528C4⋊C4C2×D4×C4711yescharacteristic
529C4⋊C4C2×D4×C4711yescharacteristic
530C4⋊C4C2×D4×C4712yes—
531C4⋊C4C2×D4×C4711yescharacteristic
532C22⋊C4—22no—
533C22⋊C4—22no—
534C22⋊C4—22no—
535C22⋊C4—22no—
536C22⋊C4—22no—
537C22⋊C4—21no—
538C22⋊C4—21no—
539C22⋊C4—21no—
540C22⋊C4—21no—
541C22⋊C4—21no—
542C22⋊C4—21no—
543C22⋊C4—22no—
544C22⋊C4—22no—
545C22⋊C4—21no—
546C42—22no—
547C42—21no—
548C42—21no—
549C42—21no—
550C42C2×D4×C4711yescharacteristic
551C42C2×D4×C4711yescharacteristic
552C42C2×D4×C4711yescharacteristic
553C42C24×C4711yescharacteristic
554C23—21no—
555C23—22no—
556C23—42no—
557C23—82no—
558C23—82no—
559C23—82no—
560C23#120×C4711yescharacteristic
561Q8—22no—
562Q8—22no—
563Q8—22no—
564Q8—42no—
565Q8—81no—
566Q8—82no—
567D4—22no—
568D4—42no—
569D4—44no—
570D4—42no—
571D4—42no—
572D4—42no—
573D4—42no—
574D4—42no—
575D4—42no—
576D4—82no—
577D4—82no—
578D4—82no—
579D4—81no—
580D4—82no—
581D4—82no—
582D4—82no—
583C2×C4—22no—
584C2×C4—22no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—22no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—41no—
594C2×C4—42no—
595C2×C4—82no—
596C2×C4—82no—
597C2×C4—82no—
598C2×C4—82no—
599C2×C4#120×C4711yescharacteristic
600C2×C4#120×C4711yescharacteristic
601C2×C4#120×C4711yescharacteristic
602C2×C4C22×D4×C4711yescharacteristic
603C2×C4C22×D4×C4711yescharacteristic
604C2×C4C22×D4×C4711yescharacteristic
605C8—42no—
606C8—42no—
607C8—42no—
608C22—21no—
609C22—21no—
610C22—21no—
611C22—41no—
612C22—42no—
613C22—41no—
614C22—42no—
615C22—42no—
616C22—41no—
617C22—82no—
618C22—82no—
619C22—82no—
620C22—164no—
621C22C2×#120×C4711yescharacteristic
622C4—21no—
623C4—21no—
624C4—21no—
625C4—21no—
626C4—41no—
627C4—41no—
628C4—42no—
629C4—41no—
630C4—41no—
631C4—41no—
632C4—41no—
633C4—41no—
634C4C47×#57612yes—
635C4C47×#57712yes—
636C2—41no—
637C2—81no—
638C2—82no—
639C2—162no—
640C2C47×#300811yescharacteristic
641C2C47×#301011yescharacteristic
642C2C47×#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×#3554C2semidirect
2. C47×#3217C2semidirect
3. C47×#3208C2semidirect
4. C47×#3205C2semidirect
5. C47×#1627C2semidirect
6. C47×#1626C2semidirect
7. C47×#1621C2semidirect
8. C47×#1620C2semidirect
9. C47×#1553C2semidirect
10. C47×#1497C2semidirect
11. C47×#1482C2semidirect
14. C47×#559C22semidirect
15. C47×#557C22semidirect
17. C47×#550C22semidirect
18. D4×Q8×C47C22semidirect
49. C47×#332C22semidirect
50. C47×#331C22semidirect
51. C47×Q8⋊C8C22semidirect
52. C47×Q8⋊C8C22semidirect
53. C47×Q8⋊C8C22semidirect
54. C47×D4⋊C8C22semidirect
286. #18958C47direct (N × H)
315. #3554C2×C47semidirect
316. #3217C2×C47semidirect
317. #3208C2×C47semidirect
318. #3205C2×C47semidirect
319. #1627C2×C47semidirect
320. #1626C2×C47semidirect
321. #1621C2×C47semidirect
322. #1620C2×C47semidirect
323. #1553C2×C47semidirect
324. #1497C2×C47semidirect
325. #1482C2×C47semidirect
335. #559C22×C47semidirect
336. #557C22×C47semidirect
338. #550C22×C47semidirect
339. D4×Q8C22×C47semidirect
370. #332C22×C47semidirect
371. #331C22×C47semidirect
372. Q8⋊C8C22×C47semidirect
373. Q8⋊C8C22×C47semidirect
374. Q8⋊C8C22×C47semidirect
375. D4⋊C8C22×C47semidirect
376. C47#18958direct (N × H)

Maximal subgroups

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

subgroupindex
C47×#35542
C47×#32172
C47×#32082
C47×#32052
C47×#16272
C47×#16262
C47×#16212
C47×#16202
C47×#15532
C47×#14972
C47×#14822
#1895847