Finite Group Databasebeta

← C47×#18836 #26058534

Subgroups — C47×#18836 #26058534

Order 12032.

972 conjugacy classes of subgroups.

The subgroup lattice has 658 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3515C211yesmaximal, characteristic, complemented
2C47×#3217C211yesmaximal, characteristic, complemented
3C47×#3208C211yesmaximal, characteristic, complemented
4C47×#3038C211yesmaximal, characteristic, complemented
5C47×#1626C212yesmaximal, complemented
6C47×#1625C212yesmaximal, complemented
7C47×#1622C212yesmaximal, complemented
8C47×#1622C212yesmaximal, complemented
9C47×#1559C211yesmaximal, characteristic, complemented
10C47×#1495C211yesmaximal, characteristic, complemented
11C47×#1488C211yesmaximal, characteristic, complemented
12C2×AGL(1,ℤ/8)×C47—21no—
13C47×#557C2211yescharacteristic, complemented
14C47×#554C2211yescharacteristic, complemented
15C47×#554C2211yescharacteristic, complemented
16C47×#553—21no—
17C47×#552—21no—
18C47×#552—22no—
19C47×#552—21no—
20C47×#547—21no—
21C47×#547C2211yescharacteristic, complemented
22C47×#541—21no—
23C47×#539—22no—
24C47×#533C2211yescharacteristic
25C2×#127×C47C2211yescharacteristic
26C47×#529—21no—
27C47×#529C2211yescharacteristic
28C2×#125×C47—21no—
29C47×#520—21no—
30C4×#41×C47C2211yescharacteristic
31C47×#496—21no—
32C47×#492C2212yes—
33C47×#490—21no—
34C47×#486C2212yes—
35C47×#460—21no—
36C47×#460—22no—
37C47×#460C2212yes—
38C47×#460C2212yes—
39C47×#459—21no—
40C47×#459C2212yes—
41C47×#459C2212yes—
42C47×#450—22no—
43C47×#450—21no—
44C47×#447—21no—
45C47×#432C2211yescharacteristic
46C47×#431C2211yescharacteristic
47C47×#423C2211yescharacteristic
48C47×#418—21no—
49C47×#333C2212yescomplemented
50C47×#332C2212yescomplemented
51C47×Q8⋊C8C2212yescomplemented
52C47×Q8⋊C8C2212yescomplemented
53C47×D4⋊C8C2212yescomplemented
54C47×D4⋊C8C2212yescomplemented
55C2×#41×C47—21no—
56C2×#41×C47D411yescharacteristic
57C22×D4×C47—21no—
58C22×D4×C47—21no—
59C22×D4×C47—21no—
60AGL(1,ℤ/8)×C47—44no—
61C2×SD16×C47—22no—
62C2×SD16×C47—24no—
63C2×SD16×C47—22no—
64C2×D8×C47—22no—
65C2×D8×C47—22no—
66C2×M16×C47—21no—
67C4⋊Q8×C47—21no—
68C4⋊Q8×C47C2311yescharacteristic
69C4⋊Q8×C47C2311yescharacteristic
70#127×C47—21no—
71#127×C47—21no—
72#127×C47—21no—
73#127×C47C2312yes—
74#126×C47—22no—
75#126×C47—22no—
76#126×C47—22no—
77#126×C47—21no—
78#125×C47—22no—
79#125×C47—22no—
80#125×C47—22no—
81#125×C47—21no—
82#125×C47—21no—
83#125×C47—22no—
84#125×C47—21no—
85#125×C47—21no—
86#125×C47D411yescharacteristic
87#124×C47D411yescharacteristic
88#123×C47—22no—
89#123×C47—22no—
90#123×C47—22no—
91#123×C47—21no—
92#123×C47—22no—
93C22⋊Q8×C47—21no—
94C22⋊Q8×C47—22no—
95C22⋊Q8×C47—22no—
96C22⋊Q8×C47—21no—
97C22⋊Q8×C47—21no—
98C22⋊Q8×C47—21no—
99C22⋊Q8×C47D411yescharacteristic
100C22⋊Q8×C47D412yes—
101#121×C47—22no—
102#121×C47—21no—
103#121×C47D411yescharacteristic
104C4×Q8×C47—21no—
105C4×Q8×C47—21no—
106C4×Q8×C47—21no—
107C4×Q8×C47D411yescharacteristic
108C4×Q8×C47D412yes—
109C4×Q8×C47C2311yescharacteristic
110C4×Q8×C47C2311yescharacteristic
111C4×D4×C47—22no—
112C4×D4×C47—22no—
113C4×D4×C47—21no—
114C4×D4×C47—21no—
115C4×D4×C47—21no—
116C4×D4×C47—21no—
117C4×D4×C47—21no—
118C4×D4×C47D411yescharacteristic
119C4×D4×C47C2311yescharacteristic
120C4×D4×C47C2311yescharacteristic
121#117×C47—22no—
122#117×C47—22no—
123#117×C47—21no—
124#117×C47—21no—
125#117×C47—21no—
126#117×C47D411yescharacteristic
127C2×C4⋊C4×C47—22no—
128C2×C4⋊C4×C47—22no—
129C2×C4⋊C4×C47—21no—
130C2×C4⋊C4×C47—21no—
131C2×C4⋊C4×C47—21no—
132C2×C42×C47—21no—
133C2×C42×C47C2311yescharacteristic
134C4⋊C8×C47—21no—
135C4⋊C8×C47—21no—
136C4⋊C8×C47C2312yes—
137C4⋊C8×C47C2312yes—
138#102×C47—22no—
139#102×C47—24no—
140#102×C47—22no—
141#102×C47—22no—
142#102×C47—22no—
143C22⋊C8×C47—21no—
144C22⋊C8×C47—21no—
145#97×C47—21no—
146C4×C8×C47C2312yes—
147C24×C47—41no—
148#41×C47—22no—
149#41×C47—41no—
150#41×C47—42no—
151#41×C47—42no—
152C2×Q8×C47—21no—
153C2×Q8×C47C2×D411yescharacteristic
154C2×Q8×C47C2×D411yescharacteristic
155C2×Q8×C47C2×D412yes—
156C2×D4×C47—22no—
157C2×D4×C47—21no—
158C2×D4×C47—21no—
159C2×D4×C47—22no—
160C2×D4×C47—22no—
161C2×D4×C47—22no—
162C2×D4×C47—42no—
163C2×D4×C47—42no—
164C2×D4×C47—41no—
165C2×D4×C47—41no—
166C2×D4×C47—41no—
167C2×D4×C47—82no—
168C2×D4×C47—82no—
169C2×D4×C47C2×D411yescharacteristic
170C2×D4×C47C2×D411yescharacteristic
171C22×C4×C47—22no—
172C22×C4×C47—22no—
173C22×C4×C47—22no—
174C22×C4×C47—21no—
175C22×C4×C47—21no—
176C22×C4×C47—21no—
177C22×C4×C47—21no—
178C22×C4×C47C2×D411yescharacteristic
179C22×C4×C47C2×D411yescharacteristic
180C22×C4×C47C2×D411yescharacteristic
181SD16×C47—44no—
182SD16×C47—82no—
183SD16×C47—84no—
184D8×C47—44no—
185D8×C47—82no—
186M16×C47—42no—
187C2×C8×C47—22no—
188C2×C8×C47—22no—
189C2×C8×C47—22no—
190C4⋊C4×C47—22no—
191C4⋊C4×C47—22no—
192C4⋊C4×C47—22no—
193C4⋊C4×C47—22no—
194C4⋊C4×C47—22no—
195C4⋊C4×C47—22no—
196C4⋊C4×C47—22no—
197C4⋊C4×C47—22no—
198C4⋊C4×C47—21no—
199C4⋊C4×C47—21no—
200C4⋊C4×C47—22no—
201C4⋊C4×C47—22no—
202C4⋊C4×C47—21no—
203C4⋊C4×C47—21no—
204C4⋊C4×C47—21no—
205C4⋊C4×C47—21no—
206C4⋊C4×C47—21no—
207C4⋊C4×C47—21no—
208C4⋊C4×C47—21no—
209C4⋊C4×C47C2×D411yescharacteristic
210C4⋊C4×C47C2×D411yescharacteristic
211C4⋊C4×C47C2×D411yescharacteristic
212C4⋊C4×C47C2×D411yescharacteristic
213C4⋊C4×C47C2×D412yes—
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—21no—
221C22⋊C4×C47—21no—
222C22⋊C4×C47—21no—
223C22⋊C4×C47—21no—
224C22⋊C4×C47—21no—
225C22⋊C4×C47—21no—
226C42×C47—22no—
227C42×C47—21no—
228C42×C47—21no—
229C42×C47—22no—
230C42×C47—21no—
231C42×C47—21no—
232C42×C47C2×D411yescharacteristic
233C42×C47C2×D411yescharacteristic
234C42×C47C2×D411yescharacteristic
235C42×C47C2411yescharacteristic
236C23×C47—21no—
237C23×C47—21no—
238C23×C47—42no—
239C23×C47—82no—
240C23×C47—82no—
241C23×C47—82no—
242C23×C47#12011yescharacteristic
243Q8×C47—21no—
244Q8×C47—21no—
245Q8×C47—22no—
246Q8×C47—42no—
247Q8×C47—41no—
248Q8×C47—41no—
249D4×C47—21no—
250D4×C47—22no—
251D4×C47—44no—
252D4×C47—42no—
253D4×C47—44no—
254D4×C47—42no—
255D4×C47—42no—
256D4×C47—42no—
257D4×C47—42no—
258D4×C47—82no—
259D4×C47—82no—
260D4×C47—82no—
261D4×C47—81no—
262D4×C47AGL(1,ℤ/8)12yes—
263C2×C4×C47—21no—
264C2×C4×C47—21no—
265C2×C4×C47—22no—
266C2×C4×C47—21no—
267C2×C4×C47—21no—
268C2×C4×C47—21no—
269C2×C4×C47—21no—
270C2×C4×C47—22no—
271C2×C4×C47—22no—
272C2×C4×C47—21no—
273C2×C4×C47—21no—
274C2×C4×C47—41no—
275C2×C4×C47—42no—
276C2×C4×C47—44no—
277C2×C4×C47—41no—
278C2×C4×C47—41no—
279C2×C4×C47—42no—
280C2×C4×C47—81no—
281C2×C4×C47—82no—
282C2×C4×C47—82no—
283C2×C4×C47#12011yescharacteristic
284C2×C4×C47#12011yescharacteristic
285C2×C4×C47#12011yescharacteristic
286C2×C4×C47C22×D411yescharacteristic
287C2×C4×C47C22×D411yescharacteristic
288C2×C4×C47C22×D411yescharacteristic
289C8×C47—42no—
290C8×C47—42no—
291C8×C47—42no—
292#18836C4711yesmaximal, characteristic, direct product factor, Sylow
293C22×C47—21no—
294C22×C47—22no—
295C22×C47—21no—
296C22×C47—21no—
297C22×C47—41no—
298C22×C47—41no—
299C22×C47—41no—
300C22×C47—41no—
301C22×C47—41no—
302C22×C47—82no—
303C22×C47—82no—
304C22×C47—82no—
305C22×C47—164no—
306C22×C47C2×#12011yescharacteristic
307C4×C47—21no—
308C4×C47—21no—
309C4×C47—21no—
310C4×C47—21no—
311C4×C47—41no—
312C4×C47—41no—
313C4×C47—42no—
314C4×C47—41no—
315C4×C47—41no—
316C4×C47—41no—
317C4×C47—41no—
318C4×C47—42no—
319C4×C47C2×AGL(1,ℤ/8)11yescharacteristic
320C4×C47#57511yescharacteristic
321C4×C47#57712yes—
322#3515C2×C4711yescharacteristic, complemented
323#3217C2×C4711yescharacteristic, complemented
324#3208C2×C4711yescharacteristic, complemented
325#3038C2×C4711yescharacteristic, complemented
326#1626C2×C4712yescomplemented
327#1625C2×C4712yescomplemented
328#1622C2×C4712yescomplemented
329#1622C2×C4712yescomplemented
330#1559C2×C4711yescharacteristic, complemented
331#1495C2×C4711yescharacteristic, complemented
332#1488C2×C4711yescharacteristic, complemented
333C2×C47—41no—
334C2×C47—42no—
335C2×C47—81no—
336C2×C47—162no—
337C2×C47#300611yescharacteristic
338C2×C47#301011yescharacteristic
339C2×C47#302111yescharacteristic
340C2×AGL(1,ℤ/8)—21no—
341#557C22×C4711yescharacteristic, complemented
342#554C22×C4711yescharacteristic, complemented
343#554C22×C4711yescharacteristic, complemented
344#553—21no—
345#552—21no—
346#552—22no—
347#552—21no—
348#547—21no—
349#547C22×C4711yescharacteristic, complemented
350#541—21no—
351#539—22no—
352#533C22×C4711yescharacteristic
353C2×#127C22×C4711yescharacteristic
354#529—21no—
355#529C22×C4711yescharacteristic
356C2×#125—21no—
357#520—21no—
358C4×#41C22×C4711yescharacteristic
359#496—21no—
360#492C22×C4712yes—
361#490—21no—
362#486C22×C4712yes—
363#460—22no—
364#460—21no—
365#460C22×C4712yes—
366#460C22×C4712yes—
367#459—21no—
368#459C22×C4712yes—
369#459C22×C4712yes—
370#450—22no—
371#450—21no—
372#447—21no—
373#432C22×C4711yescharacteristic
374#431C22×C4711yescharacteristic
375#423C22×C4711yescharacteristic
376#418—21no—
377#333C22×C4712yescomplemented
378#332C22×C4712yescomplemented
379Q8⋊C8C22×C4712yescomplemented
380Q8⋊C8C22×C4712yescomplemented
381D4⋊C8C22×C4712yescomplemented
382D4⋊C8C22×C4712yescomplemented
383C47#1883611yescharacteristic, direct product factor, Sylow
384C2×#41—21no—
385C2×#41D4×C4711yescharacteristic
386C22×D4—21no—
387C22×D4—21no—
388C22×D4—21no—
389AGL(1,ℤ/8)—44no—
390C2×SD16—22no—
391C2×SD16—24no—
392C2×SD16—22no—
393C2×D8—22no—
394C2×D8—22no—
395C2×M16—21no—
396C4⋊Q8—21no—
397C4⋊Q8C23×C4711yescharacteristic
398C4⋊Q8C23×C4711yescharacteristic
399#127—21no—
400#127—21no—
401#127—21no—
402#127C23×C4712yes—
403#126—22no—
404#126—22no—
405#126—22no—
406#126—21no—
407#125—22no—
408#125—22no—
409#125—22no—
410#125—21no—
411#125—21no—
412#125—22no—
413#125—21no—
414#125—21no—
415#125D4×C4711yescharacteristic
416#124D4×C4711yescharacteristic
417#123—22no—
418#123—22no—
419#123—22no—
420#123—21no—
421#123—22no—
422C22⋊Q8—21no—
423C22⋊Q8—22no—
424C22⋊Q8—22no—
425C22⋊Q8—21no—
426C22⋊Q8—21no—
427C22⋊Q8—21no—
428C22⋊Q8D4×C4711yescharacteristic
429C22⋊Q8D4×C4712yes—
430#121—22no—
431#121—21no—
432#121D4×C4711yescharacteristic
433C4×Q8—21no—
434C4×Q8—21no—
435C4×Q8—21no—
436C4×Q8D4×C4711yescharacteristic
437C4×Q8D4×C4712yes—
438C4×Q8C23×C4711yescharacteristic
439C4×Q8C23×C4711yescharacteristic
440C4×D4—22no—
441C4×D4—22no—
442C4×D4—21no—
443C4×D4—21no—
444C4×D4—21no—
445C4×D4—21no—
446C4×D4—21no—
447C4×D4D4×C4711yescharacteristic
448C4×D4C23×C4711yescharacteristic
449C4×D4C23×C4711yescharacteristic
450#117—22no—
451#117—22no—
452#117—21no—
453#117—21no—
454#117—21no—
455#117D4×C4711yescharacteristic
456C2×C4⋊C4—22no—
457C2×C4⋊C4—22no—
458C2×C4⋊C4—21no—
459C2×C4⋊C4—21no—
460C2×C4⋊C4—21no—
461C2×C42—21no—
462C2×C42C23×C4711yescharacteristic
463C4⋊C8—21no—
464C4⋊C8—21no—
465C4⋊C8C23×C4712yes—
466C4⋊C8C23×C4712yes—
467#102—22no—
468#102—22no—
469#102—22no—
470#102—22no—
471#102—24no—
472C22⋊C8—21no—
473C22⋊C8—21no—
474#97—21no—
475C4×C8C23×C4712yes—
476C24—41no—
477#41—22no—
478#41—41no—
479#41—42no—
480#41—42no—
481C2×Q8—21no—
482C2×Q8C2×D4×C4711yescharacteristic
483C2×Q8C2×D4×C4711yescharacteristic
484C2×Q8C2×D4×C4712yes—
485C2×D4—22no—
486C2×D4—21no—
487C2×D4—21no—
488C2×D4—22no—
489C2×D4—22no—
490C2×D4—22no—
491C2×D4—42no—
492C2×D4—42no—
493C2×D4—41no—
494C2×D4—41no—
495C2×D4—41no—
496C2×D4—82no—
497C2×D4—82no—
498C2×D4C2×D4×C4711yescharacteristic
499C2×D4C2×D4×C4711yescharacteristic
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4C2×D4×C4711yescharacteristic
508C22×C4C2×D4×C4711yescharacteristic
509C22×C4C2×D4×C4711yescharacteristic
510SD16—44no—
511SD16—82no—
512SD16—84no—
513D8—44no—
514D8—82no—
515M16—42no—
516C2×C8—22no—
517C2×C8—22no—
518C2×C8—22no—
519C4⋊C4—22no—
520C4⋊C4—22no—
521C4⋊C4—22no—
522C4⋊C4—22no—
523C4⋊C4—22no—
524C4⋊C4—22no—
525C4⋊C4—22no—
526C4⋊C4—22no—
527C4⋊C4—21no—
528C4⋊C4—21no—
529C4⋊C4—22no—
530C4⋊C4—22no—
531C4⋊C4—21no—
532C4⋊C4—21no—
533C4⋊C4—21no—
534C4⋊C4—21no—
535C4⋊C4—21no—
536C4⋊C4—21no—
537C4⋊C4—21no—
538C4⋊C4C2×D4×C4711yescharacteristic
539C4⋊C4C2×D4×C4711yescharacteristic
540C4⋊C4C2×D4×C4711yescharacteristic
541C4⋊C4C2×D4×C4711yescharacteristic
542C4⋊C4C2×D4×C4712yes—
543C22⋊C4—22no—
544C22⋊C4—22no—
545C22⋊C4—22no—
546C22⋊C4—22no—
547C22⋊C4—21no—
548C22⋊C4—21no—
549C22⋊C4—21no—
550C22⋊C4—21no—
551C22⋊C4—21no—
552C22⋊C4—21no—
553C22⋊C4—21no—
554C22⋊C4—21no—
555C42—22no—
556C42—21no—
557C42—21no—
558C42—22no—
559C42—21no—
560C42—21no—
561C42C2×D4×C4711yescharacteristic
562C42C2×D4×C4711yescharacteristic
563C42C2×D4×C4711yescharacteristic
564C42C24×C4711yescharacteristic
565C23—21no—
566C23—21no—
567C23—42no—
568C23—82no—
569C23—82no—
570C23—82no—
571C23#120×C4711yescharacteristic
572Q8—21no—
573Q8—21no—
574Q8—22no—
575Q8—42no—
576Q8—41no—
577Q8—41no—
578D4—21no—
579D4—22no—
580D4—44no—
581D4—42no—
582D4—44no—
583D4—42no—
584D4—42no—
585D4—42no—
586D4—42no—
587D4—82no—
588D4—82no—
589D4—82no—
590D4—81no—
591D4AGL(1,ℤ/8)×C4712yes—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—22no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—22no—
600C2×C4—22no—
601C2×C4—21no—
602C2×C4—21no—
603C2×C4—41no—
604C2×C4—42no—
605C2×C4—44no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—42no—
609C2×C4—81no—
610C2×C4—82no—
611C2×C4—82no—
612C2×C4#120×C4711yescharacteristic
613C2×C4#120×C4711yescharacteristic
614C2×C4#120×C4711yescharacteristic
615C2×C4C22×D4×C4711yescharacteristic
616C2×C4C22×D4×C4711yescharacteristic
617C2×C4C22×D4×C4711yescharacteristic
618C8—42no—
619C8—42no—
620C8—42no—
621C22—21no—
622C22—22no—
623C22—21no—
624C22—21no—
625C22—41no—
626C22—41no—
627C22—41no—
628C22—41no—
629C22—41no—
630C22—82no—
631C22—82no—
632C22—82no—
633C22—164no—
634C22C2×#120×C4711yescharacteristic
635C4—21no—
636C4—21no—
637C4—21no—
638C4—21no—
639C4—41no—
640C4—41no—
641C4—42no—
642C4—41no—
643C4—41no—
644C4—41no—
645C4—41no—
646C4—42no—
647C4C2×AGL(1,ℤ/8)×C4711yescharacteristic
648C4C47×#57511yescharacteristic
649C4C47×#57712yes—
650C2—41no—
651C2—42no—
652C2—81no—
653C2—162no—
654C2C47×#300611yescharacteristic
655C2C47×#301011yescharacteristic
656C2C47×#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×#3515C2semidirect
2. C47×#3217C2semidirect
3. C47×#3208C2semidirect
4. C47×#3038C2semidirect
5. C47×#1626C2semidirect
6. C47×#1625C2semidirect
7. C47×#1622C2semidirect
8. C47×#1622C2semidirect
9. C47×#1559C2semidirect
10. C47×#1495C2semidirect
11. C47×#1488C2semidirect
13. C47×#557C22semidirect
14. C47×#554C22semidirect
15. C47×#554C22semidirect
21. C47×#547C22semidirect
49. C47×#333C22semidirect
50. C47×#332C22semidirect
51. C47×Q8⋊C8C22semidirect
52. C47×Q8⋊C8C22semidirect
53. C47×D4⋊C8C22semidirect
54. C47×D4⋊C8C22semidirect
292. #18836C47direct (N × H)
322. #3515C2×C47semidirect
323. #3217C2×C47semidirect
324. #3208C2×C47semidirect
325. #3038C2×C47semidirect
326. #1626C2×C47semidirect
327. #1625C2×C47semidirect
328. #1622C2×C47semidirect
329. #1622C2×C47semidirect
330. #1559C2×C47semidirect
331. #1495C2×C47semidirect
332. #1488C2×C47semidirect
341. #557C22×C47semidirect
342. #554C22×C47semidirect
343. #554C22×C47semidirect
349. #547C22×C47semidirect
377. #333C22×C47semidirect
378. #332C22×C47semidirect
379. Q8⋊C8C22×C47semidirect
380. Q8⋊C8C22×C47semidirect
381. D4⋊C8C22×C47semidirect
382. D4⋊C8C22×C47semidirect
383. C47#18836direct (N × H)

Maximal subgroups

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

subgroupindex
C47×#35152
C47×#32172
C47×#32082
C47×#30382
C47×#16262
C47×#16252
C47×#16222
C47×#15592
C47×#14952
C47×#14882
#1883647