Finite Group Databasebeta

← C47×#19042 #26058740

Subgroups — C47×#19042 #26058740

Order 12032.

1036 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3558C211yesmaximal, characteristic, complemented
2C47×#3213C211yesmaximal, characteristic, complemented
3C47×#3180C211yesmaximal, characteristic, complemented
4C47×#3150C211yesmaximal, characteristic, complemented
5C47×#1661C212yesmaximal, complemented
6C47×#1659C212yesmaximal, complemented
7C47×#1656C212yesmaximal, complemented
8C47×#1655C212yesmaximal, complemented
9C47×#1532C211yesmaximal, characteristic, complemented
10C47×#1530C211yesmaximal, characteristic, complemented
11C2×C47×#329C211yesmaximal, characteristic, complemented
12C2×#135×C47—22no—
13C47×#562C2212yes—
14C47×H(3,𝔽4)C2212yes—
15C47×#559—21no—
16C47×#548—21no—
17C47×#546—22no—
18C47×#546—21no—
19D42×C47—21no—
20C47×#542—21no—
21C47×#538—22no—
22C47×#538—21no—
23C47×#535—21no—
24C47×#534—21no—
25C47×#532C2211yescharacteristic
26C47×#532C2211yescharacteristic, complemented
27C47×#529C2211yescharacteristic
28C2×#124×C47C2211yescharacteristic
29C47×#501C2211yescharacteristic, complemented
30C47×#497—21no—
31C47×#497C2212yescomplemented
32C47×#496—21no—
33C47×#496C2212yescomplemented
34C47×#496C2211yescharacteristic, complemented
35C47×#496C2212yescomplemented
36C47×#490C2211yescharacteristic, complemented
37C47×#489C2211yescharacteristic, complemented
38C47×#489C2212yescomplemented
39C47×#466—21no—
40C47×#465—21no—
41C47×#463—22no—
42C47×#448—21no—
43C47×#447—21no—
44C47×#442—21no—
45C47×#440—21no—
46C47×#432C2211yescharacteristic, complemented
47C2×#97×C47C2211yescharacteristic, complemented
48C2×#97×C47C2211yescharacteristic, complemented
49C47×#330C2212yescomplemented
50C47×#329C2212yescomplemented
51C47×#329C2212yescomplemented
52C47×#329C2212yescomplemented
53C47×#329C2212yescomplemented
54C47×#329C2212yescomplemented
55C2×#41×C47—21no—
56C2×#41×C47—21no—
57C2×#41×C47D412yes—
58C22×Q8×C47D411yescharacteristic
59C22×D4×C47—22no—
60C22×D4×C47—21no—
61C22×D4×C47D411yescharacteristic
62#135×C47—48no—
63C2×Q16×C47—22no—
64C2×SD16×C47—21no—
65C2×SD16×C47—22no—
66C2×SD16×C47—22no—
67C2×SD16×C47—22no—
68C2×D8×C47—21no—
69C2×D8×C47—22no—
70C2×D8×C47—22no—
71C22×C8×C47—21no—
72C22×C8×C47—21no—
73C4⋊Q8×C47D411yescharacteristic
74C4⋊Q8×C47C2311yescharacteristic
75#127×C47—21no—
76#127×C47D411yescharacteristic
77#127×C47C2311yescharacteristic
78#126×C47—22no—
79#126×C47—21no—
80#125×C47C2311yescharacteristic
81#124×C47—21no—
82#124×C47—22no—
83#124×C47—22no—
84#124×C47—22no—
85#124×C47—21no—
86#124×C47—21no—
87#124×C47—21no—
88#124×C47D412yes—
89#124×C47C2312yes—
90#124×C47C2311yescharacteristic
91#124×C47C2312yes—
92#123×C47—22no—
93#123×C47—22no—
94#123×C47—21no—
95#123×C47—22no—
96#123×C47—22no—
97C22⋊Q8×C47—21no—
98C22⋊Q8×C47—22no—
99C22⋊Q8×C47—22no—
100C22⋊Q8×C47D411yescharacteristic
101#121×C47—22no—
102#121×C47—22no—
103#121×C47—22no—
104#121×C47—21no—
105#121×C47—22no—
106#121×C47—22no—
107#121×C47—21no—
108#121×C47—21no—
109#121×C47—21no—
110#121×C47—21no—
111#121×C47D411yescharacteristic
112#120×C47—22no—
113#120×C47—22no—
114#120×C47—22no—
115#120×C47—22no—
116#120×C47—22no—
117C4×Q8×C47—21no—
118C4×Q8×C47D411yescharacteristic
119C4×D4×C47—22no—
120C4×D4×C47—22no—
121C4×D4×C47—21no—
122C4×D4×C47—21no—
123C4×D4×C47—21no—
124C4×D4×C47—21no—
125C4×D4×C47—21no—
126C4×D4×C47—21no—
127C4×D4×C47D411yescharacteristic
128#117×C47—21no—
129C2×C22⋊C4×C47—22no—
130C2×C22⋊C4×C47—21no—
131C2×C22⋊C4×C47—21no—
132C2×C42×C47C2311yescharacteristic
133#107×C47—21no—
134#106×C47—21no—
135C4⋊C8×C47—21no—
136#103×C47—22no—
137#103×C47—21no—
138#102×C47—22no—
139#102×C47—21no—
140#102×C47—21no—
141#102×C47—21no—
142C22⋊C8×C47—21no—
143#97×C47—21no—
144#97×C47—21no—
145#97×C47C2311yescharacteristic
146#97×C47C2312yes—
147#97×C47C2312yes—
148#97×C47C2311yescharacteristic
149C24×C47—22no—
150C24×C47—21no—
151#41×C47—44no—
152#41×C47—44no—
153#41×C47—82no—
154C2×Q8×C47—21no—
155C2×Q8×C47—21no—
156C2×Q8×C47—81no—
157C2×Q8×C47C2×D411yescharacteristic
158C2×Q8×C47C2×D412yes—
159C2×Q8×C47C2×D412yes—
160C2×D4×C47—22no—
161C2×D4×C47—21no—
162C2×D4×C47—22no—
163C2×D4×C47—22no—
164C2×D4×C47—22no—
165C2×D4×C47—22no—
166C2×D4×C47—22no—
167C2×D4×C47—21no—
168C2×D4×C47—21no—
169C2×D4×C47—21no—
170C2×D4×C47—21no—
171C2×D4×C47—21no—
172C2×D4×C47—21no—
173C2×D4×C47—41no—
174C2×D4×C47—81no—
175C2×D4×C47—82no—
176C2×D4×C47—84no—
177C2×D4×C47C2×D411yescharacteristic
178C2×D4×C47C2×D412yes—
179C2×D4×C47C2×D412yes—
180C22×C4×C47—22no—
181C22×C4×C47—22no—
182C22×C4×C47—21no—
183C22×C4×C47—21no—
184C22×C4×C47—22no—
185C22×C4×C47—41no—
186C22×C4×C47C2×D411yescharacteristic
187C22×C4×C47C2×D411yescharacteristic
188C22×C4×C47C2×D411yescharacteristic
189Q16×C47—44no—
190SD16×C47—42no—
191SD16×C47—44no—
192SD16×C47—44no—
193SD16×C47—82no—
194D8×C47—42no—
195D8×C47—44no—
196D8×C47—82no—
197C2×C8×C47—24no—
198C2×C8×C47—21no—
199C2×C8×C47—22no—
200C2×C8×C47—22no—
201C2×C8×C47—21no—
202C2×C8×C47—42no—
203C4⋊C4×C47—22no—
204C4⋊C4×C47—22no—
205C4⋊C4×C47—21no—
206C4⋊C4×C47—21no—
207C4⋊C4×C47—21no—
208C4⋊C4×C47—21no—
209C4⋊C4×C47—21no—
210C4⋊C4×C47—21no—
211C4⋊C4×C47—21no—
212C4⋊C4×C47—21no—
213C4⋊C4×C47C2×D411yescharacteristic
214C4⋊C4×C47C2×D411yescharacteristic
215C22⋊C4×C47—22no—
216C22⋊C4×C47—22no—
217C22⋊C4×C47—22no—
218C22⋊C4×C47—22no—
219C22⋊C4×C47—22no—
220C22⋊C4×C47—21no—
221C22⋊C4×C47—22no—
222C22⋊C4×C47—21no—
223C22⋊C4×C47—22no—
224C22⋊C4×C47—21no—
225C22⋊C4×C47—22no—
226C22⋊C4×C47—22no—
227C22⋊C4×C47—21no—
228C22⋊C4×C47—21no—
229C22⋊C4×C47—22no—
230C22⋊C4×C47—22no—
231C22⋊C4×C47—41no—
232C22⋊C4×C47—41no—
233C42×C47—22no—
234C42×C47—21no—
235C42×C47C2×D411yescharacteristic
236C42×C47C2×D411yescharacteristic
237C42×C47C2×D411yescharacteristic
238C42×C47C2411yescharacteristic
239C23×C47—22no—
240C23×C47—21no—
241C23×C47—22no—
242C23×C47—42no—
243C23×C47—41no—
244C23×C47—81no—
245C23×C47—81no—
246C23×C47—82no—
247C23×C47—82no—
248C23×C47—82no—
249C23×C47#12011yescharacteristic
250Q8×C47—42no—
251Q8×C47—41no—
252Q8×C47—42no—
253Q8×C47—42no—
254Q8×C47—42no—
255D4×C47—42no—
256D4×C47—41no—
257D4×C47—42no—
258D4×C47—42no—
259D4×C47—42no—
260D4×C47—42no—
261D4×C47—41no—
262D4×C47—42no—
263D4×C47—41no—
264D4×C47—42no—
265D4×C47—44no—
266D4×C47—81no—
267D4×C47—82no—
268D4×C47—82no—
269D4×C47—82no—
270D4×C47—82no—
271D4×C47—82no—
272D4×C47—82no—
273C2×C4×C47—22no—
274C2×C4×C47—21no—
275C2×C4×C47—22no—
276C2×C4×C47—22no—
277C2×C4×C47—21no—
278C2×C4×C47—21no—
279C2×C4×C47—41no—
280C2×C4×C47—41no—
281C2×C4×C47—42no—
282C2×C4×C47—41no—
283C2×C4×C47—82no—
284C2×C4×C47—82no—
285C2×C4×C47—81no—
286C2×C4×C47—82no—
287C2×C4×C47—82no—
288C2×C4×C47#12011yescharacteristic
289C2×C4×C47#12011yescharacteristic
290C2×C4×C47#12011yescharacteristic
291C2×C4×C47C22×D411yescharacteristic
292C2×C4×C47C22×D411yescharacteristic
293C2×C4×C47C22×D411yescharacteristic
294C8×C47—24no—
295C8×C47—22no—
296C8×C47—41no—
297C8×C47—42no—
298#19042C4711yesmaximal, characteristic, direct product factor, Sylow
299C22×C47—21no—
300C22×C47—21no—
301C22×C47—42no—
302C22×C47—42no—
303C22×C47—41no—
304C22×C47—41no—
305C22×C47—42no—
306C22×C47—42no—
307C22×C47—41no—
308C22×C47—42no—
309C22×C47—42no—
310C22×C47—81no—
311C22×C47—81no—
312C22×C47—81no—
313C22×C47—162no—
314C22×C47—164no—
315C22×C47#45312yes—
316C22×C47C2×#12011yescharacteristic
317C4×C47—21no—
318C4×C47—21no—
319C4×C47—21no—
320C4×C47—21no—
321C4×C47—21no—
322C4×C47—21no—
323C4×C47—41no—
324C4×C47—42no—
325C4×C47—41no—
326C4×C47—41no—
327C4×C47—42no—
328C4×C47—81no—
329#3558C2×C4711yescharacteristic, complemented
330#3213C2×C4711yescharacteristic, complemented
331#3180C2×C4711yescharacteristic, complemented
332#3150C2×C4711yescharacteristic, complemented
333#1661C2×C4712yescomplemented
334#1659C2×C4712yescomplemented
335#1656C2×C4712yescomplemented
336#1655C2×C4712yescomplemented
337#1532C2×C4711yescharacteristic, complemented
338#1530C2×C4711yescharacteristic, complemented
339C2×#329C2×C4711yescharacteristic, complemented
340C2×C47—22no—
341C2×C47—82no—
342C2×C47—82no—
343C2×C47—81no—
344C2×C47—161no—
345C2×C47C2×#45311yescharacteristic
346C2×C47#301811yescharacteristic
347C2×C47#301911yescharacteristic
348C2×#135—22no—
349#562C22×C4712yes—
350H(3,𝔽4)C22×C4712yes—
351#559—21no—
352#548—21no—
353#546—22no—
354#546—21no—
355D42—21no—
356#542—21no—
357#538—22no—
358#538—21no—
359#535—21no—
360#534—21no—
361#532C22×C4711yescharacteristic
362#532C22×C4711yescharacteristic, complemented
363#529C22×C4711yescharacteristic
364C2×#124C22×C4711yescharacteristic
365#501C22×C4711yescharacteristic, complemented
366#497—21no—
367#497C22×C4712yescomplemented
368#496—21no—
369#496C22×C4712yescomplemented
370#496C22×C4711yescharacteristic, complemented
371#496C22×C4712yescomplemented
372#490C22×C4711yescharacteristic, complemented
373#489C22×C4711yescharacteristic, complemented
374#489C22×C4712yescomplemented
375#466—21no—
376#465—21no—
377#463—22no—
378#448—21no—
379#447—21no—
380#442—21no—
381#440—21no—
382#432C22×C4711yescharacteristic, complemented
383C2×#97C22×C4711yescharacteristic, complemented
384C2×#97C22×C4711yescharacteristic, complemented
385#330C22×C4712yescomplemented
386#329C22×C4712yescomplemented
387#329C22×C4712yescomplemented
388#329C22×C4712yescomplemented
389#329C22×C4712yescomplemented
390#329C22×C4712yescomplemented
391C47#1904211yescharacteristic, direct product factor, Sylow
392C2×#41—21no—
393C2×#41—21no—
394C2×#41D4×C4712yes—
395C22×Q8D4×C4711yescharacteristic
396C22×D4—22no—
397C22×D4—21no—
398C22×D4D4×C4711yescharacteristic
399#135—48no—
400C2×Q16—22no—
401C2×SD16—22no—
402C2×SD16—21no—
403C2×SD16—22no—
404C2×SD16—22no—
405C2×D8—22no—
406C2×D8—21no—
407C2×D8—22no—
408C22×C8—21no—
409C22×C8—21no—
410C4⋊Q8D4×C4711yescharacteristic
411C4⋊Q8C23×C4711yescharacteristic
412#127—21no—
413#127D4×C4711yescharacteristic
414#127C23×C4711yescharacteristic
415#126—22no—
416#126—21no—
417#125C23×C4711yescharacteristic
418#124—21no—
419#124—22no—
420#124—22no—
421#124—22no—
422#124—21no—
423#124—21no—
424#124—21no—
425#124D4×C4712yes—
426#124C23×C4712yes—
427#124C23×C4711yescharacteristic
428#124C23×C4712yes—
429#123—22no—
430#123—22no—
431#123—21no—
432#123—22no—
433#123—22no—
434C22⋊Q8—21no—
435C22⋊Q8—22no—
436C22⋊Q8—22no—
437C22⋊Q8D4×C4711yescharacteristic
438#121—22no—
439#121—22no—
440#121—22no—
441#121—21no—
442#121—22no—
443#121—22no—
444#121—21no—
445#121—21no—
446#121—21no—
447#121—21no—
448#121D4×C4711yescharacteristic
449#120—22no—
450#120—22no—
451#120—22no—
452#120—22no—
453#120—22no—
454C4×Q8—21no—
455C4×Q8D4×C4711yescharacteristic
456C4×D4—22no—
457C4×D4—22no—
458C4×D4—21no—
459C4×D4—21no—
460C4×D4—21no—
461C4×D4—21no—
462C4×D4—21no—
463C4×D4—21no—
464C4×D4D4×C4711yescharacteristic
465#117—21no—
466C2×C22⋊C4—22no—
467C2×C22⋊C4—21no—
468C2×C22⋊C4—21no—
469C2×C42C23×C4711yescharacteristic
470#107—21no—
471#106—21no—
472C4⋊C8—21no—
473#103—21no—
474#103—22no—
475#102—21no—
476#102—22no—
477#102—21no—
478#102—21no—
479C22⋊C8—21no—
480#97—21no—
481#97—21no—
482#97C23×C4711yescharacteristic
483#97C23×C4711yescharacteristic
484#97C23×C4712yes—
485#97C23×C4712yes—
486C24—22no—
487C24—21no—
488#41—44no—
489#41—44no—
490#41—82no—
491C2×Q8—21no—
492C2×Q8—21no—
493C2×Q8—81no—
494C2×Q8C2×D4×C4711yescharacteristic
495C2×Q8C2×D4×C4712yes—
496C2×Q8C2×D4×C4712yes—
497C2×D4—22no—
498C2×D4—21no—
499C2×D4—22no—
500C2×D4—22no—
501C2×D4—22no—
502C2×D4—22no—
503C2×D4—22no—
504C2×D4—21no—
505C2×D4—21no—
506C2×D4—21no—
507C2×D4—21no—
508C2×D4—21no—
509C2×D4—21no—
510C2×D4—41no—
511C2×D4—81no—
512C2×D4—82no—
513C2×D4—84no—
514C2×D4C2×D4×C4711yescharacteristic
515C2×D4C2×D4×C4712yes—
516C2×D4C2×D4×C4712yes—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—22no—
522C22×C4—41no—
523C22×C4C2×D4×C4711yescharacteristic
524C22×C4C2×D4×C4711yescharacteristic
525C22×C4C2×D4×C4711yescharacteristic
526Q16—44no—
527SD16—42no—
528SD16—44no—
529SD16—44no—
530SD16—82no—
531D8—42no—
532D8—44no—
533D8—82no—
534C2×C8—24no—
535C2×C8—21no—
536C2×C8—22no—
537C2×C8—21no—
538C2×C8—22no—
539C2×C8—42no—
540C4⋊C4—22no—
541C4⋊C4—22no—
542C4⋊C4—21no—
543C4⋊C4—21no—
544C4⋊C4—21no—
545C4⋊C4—21no—
546C4⋊C4—21no—
547C4⋊C4—21no—
548C4⋊C4—21no—
549C4⋊C4—21no—
550C4⋊C4C2×D4×C4711yescharacteristic
551C4⋊C4C2×D4×C4711yescharacteristic
552C22⋊C4—22no—
553C22⋊C4—22no—
554C22⋊C4—22no—
555C22⋊C4—22no—
556C22⋊C4—22no—
557C22⋊C4—21no—
558C22⋊C4—22no—
559C22⋊C4—21no—
560C22⋊C4—22no—
561C22⋊C4—21no—
562C22⋊C4—22no—
563C22⋊C4—22no—
564C22⋊C4—21no—
565C22⋊C4—21no—
566C22⋊C4—22no—
567C22⋊C4—22no—
568C22⋊C4—41no—
569C22⋊C4—41no—
570C42—22no—
571C42—21no—
572C42C2×D4×C4711yescharacteristic
573C42C2×D4×C4711yescharacteristic
574C42C2×D4×C4711yescharacteristic
575C42C24×C4711yescharacteristic
576C23—22no—
577C23—21no—
578C23—22no—
579C23—42no—
580C23—41no—
581C23—81no—
582C23—81no—
583C23—82no—
584C23—82no—
585C23—82no—
586C23#120×C4711yescharacteristic
587Q8—42no—
588Q8—41no—
589Q8—42no—
590Q8—42no—
591Q8—42no—
592D4—42no—
593D4—41no—
594D4—42no—
595D4—42no—
596D4—42no—
597D4—42no—
598D4—41no—
599D4—42no—
600D4—41no—
601D4—42no—
602D4—44no—
603D4—81no—
604D4—82no—
605D4—82no—
606D4—82no—
607D4—82no—
608D4—82no—
609D4—82no—
610C2×C4—22no—
611C2×C4—21no—
612C2×C4—22no—
613C2×C4—22no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—42no—
619C2×C4—41no—
620C2×C4—82no—
621C2×C4—82no—
622C2×C4—81no—
623C2×C4—82no—
624C2×C4—82no—
625C2×C4#120×C4711yescharacteristic
626C2×C4#120×C4711yescharacteristic
627C2×C4#120×C4711yescharacteristic
628C2×C4C22×D4×C4711yescharacteristic
629C2×C4C22×D4×C4711yescharacteristic
630C2×C4C22×D4×C4711yescharacteristic
631C8—24no—
632C8—22no—
633C8—41no—
634C8—42no—
635C22—21no—
636C22—21no—
637C22—42no—
638C22—42no—
639C22—41no—
640C22—41no—
641C22—42no—
642C22—42no—
643C22—41no—
644C22—42no—
645C22—42no—
646C22—81no—
647C22—81no—
648C22—81no—
649C22—162no—
650C22—164no—
651C22C47×#45312yes—
652C22C2×#120×C4711yescharacteristic
653C4—21no—
654C4—21no—
655C4—21no—
656C4—21no—
657C4—21no—
658C4—21no—
659C4—41no—
660C4—42no—
661C4—41no—
662C4—41no—
663C4—42no—
664C4—81no—
665C2—22no—
666C2—82no—
667C2—81no—
668C2—82no—
669C2—161no—
670C2C2×C47×#45311yescharacteristic
671C2C47×#301811yescharacteristic
672C2C47×#301911yescharacteristic
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×#3558C2semidirect
2. C47×#3213C2semidirect
3. C47×#3180C2semidirect
4. C47×#3150C2semidirect
5. C47×#1661C2semidirect
6. C47×#1659C2semidirect
7. C47×#1656C2semidirect
8. C47×#1655C2semidirect
9. C47×#1532C2semidirect
10. C47×#1530C2semidirect
11. C2×C47×#329C2semidirect
26. C47×#532C22semidirect
29. C47×#501C22semidirect
31. C47×#497C22semidirect
33. C47×#496C22semidirect
34. C47×#496C22semidirect
35. C47×#496C22semidirect
36. C47×#490C22semidirect
37. C47×#489C22semidirect
38. C47×#489C22semidirect
46. C47×#432C22semidirect
47. C2×#97×C47C22semidirect
48. C2×#97×C47C22semidirect
49. C47×#330C22semidirect
50. C47×#329C22semidirect
51. C47×#329C22semidirect
52. C47×#329C22semidirect
53. C47×#329C22semidirect
54. C47×#329C22semidirect
298. #19042C47direct (N × H)
329. #3558C2×C47semidirect
330. #3213C2×C47semidirect
331. #3180C2×C47semidirect
332. #3150C2×C47semidirect
333. #1661C2×C47semidirect
334. #1659C2×C47semidirect
335. #1656C2×C47semidirect
336. #1655C2×C47semidirect
337. #1532C2×C47semidirect
338. #1530C2×C47semidirect
339. C2×#329C2×C47semidirect
362. #532C22×C47semidirect
365. #501C22×C47semidirect
367. #497C22×C47semidirect
369. #496C22×C47semidirect
370. #496C22×C47semidirect
371. #496C22×C47semidirect
372. #490C22×C47semidirect
373. #489C22×C47semidirect
374. #489C22×C47semidirect
382. #432C22×C47semidirect
383. C2×#97C22×C47semidirect
384. C2×#97C22×C47semidirect
385. #330C22×C47semidirect
386. #329C22×C47semidirect
387. #329C22×C47semidirect
388. #329C22×C47semidirect
389. #329C22×C47semidirect
390. #329C22×C47semidirect
391. C47#19042direct (N × H)

Maximal subgroups

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

subgroupindex
C47×#35582
C47×#32132
C47×#31802
C47×#31502
C47×#16612
C47×#16592
C47×#16562
C47×#16552
C47×#15322
C47×#15302
C2×C47×#3292
#1904247