Finite Group Databasebeta

← C47×#18970 #26058668

Subgroups — C47×#18970 #26058668

Order 12032.

874 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3554C211yesmaximal, characteristic
2C47×#3239C211yesmaximal, characteristic, complemented
3C47×#3226C211yesmaximal, characteristic, complemented
4C47×#3209C211yesmaximal, characteristic, complemented
5C47×#1649C212yesmaximal, complemented
6C47×#1648C212yesmaximal, complemented
7C47×#1641C212yesmaximal, complemented
8C47×#1640C212yesmaximal, complemented
9C47×#1553C211yesmaximal, characteristic, complemented
10C47×#1497C211yesmaximal, characteristic, complemented
11C47×#1482C211yesmaximal, characteristic, complemented
12C47×#562—22no—
13C47×#559—21no—
14C47×#559C2211yescharacteristic
15C47×#557C2211yescharacteristic
16C47×#554—21no—
17C47×#550C2211yescharacteristic
18D4×Q8×C47C2211yescharacteristic
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×C4⋊Q8×C47C2211yescharacteristic
29C47×#529C2211yescharacteristic
30C47×#501—21no—
31C47×#500C2212yes—
32C47×#494—21no—
33C47×#489—21no—
34C47×#487—21no—
35C47×#486C2212yes—
36C47×#484—21no—
37C47×#481—21no—
38C47×#480—22no—
39C47×#475C2212yes—
40C47×#474—22no—
41C47×#474C2212yes—
42C47×#462C2212yes—
43C47×#462C2212yes—
44C47×#451—21no—
45C47×#451—21no—
46C47×#432C2211yescharacteristic
47C47×#431C2211yescharacteristic
48C47×#431C2211yescharacteristic
49C47×#332C2212yes—
50C47×#331C2212yes—
51C47×Q8⋊C8C2212yes—
52C47×Q8⋊C8C2212yes—
53C47×Q8⋊C8C2212yes—
54C47×D4⋊C8C2212yes—
55C2×#41×C47—21no—
56C2×#41×C47—21no—
57C22×Q8×C47—21no—
58C22×Q8×C47—21no—
59C2×Q16×C47—22no—
60C2×Q16×C47—22no—
61C4⋊Q8×C47—21no—
62C4⋊Q8×C47—21no—
63C4⋊Q8×C47—21no—
64C4⋊Q8×C47—21no—
65C4⋊Q8×C47—21no—
66C4⋊Q8×C47D411yescharacteristic
67C4⋊Q8×C47D411yescharacteristic
68C4⋊Q8×C47C2312yes—
69C4⋊Q8×C47C2311yescharacteristic
70#127×C47—21no—
71#127×C47C2311yescharacteristic
72#126×C47—22no—
73#126×C47—21no—
74#125×C47—22no—
75#125×C47—21no—
76#125×C47—21no—
77#125×C47D411yescharacteristic
78#124×C47—22no—
79#124×C47—22no—
80#124×C47—21no—
81#124×C47—21no—
82#124×C47—21no—
83#124×C47D411yescharacteristic
84#123×C47—22no—
85#123×C47—22no—
86#123×C47—22no—
87#123×C47—22no—
88#123×C47—22no—
89#123×C47—22no—
90#123×C47—21no—
91C22⋊Q8×C47—22no—
92C22⋊Q8×C47—22no—
93C22⋊Q8×C47—22no—
94C22⋊Q8×C47—22no—
95C22⋊Q8×C47—21no—
96C22⋊Q8×C47—22no—
97C22⋊Q8×C47—21no—
98C22⋊Q8×C47D411yescharacteristic
99C22⋊Q8×C47D411yescharacteristic
100C22⋊Q8×C47D411yescharacteristic
101#121×C47—22no—
102#121×C47—22no—
103#121×C47—22no—
104#121×C47—21no—
105#121×C47—21no—
106#121×C47D412yes—
107#121×C47D411yescharacteristic
108C4×Q8×C47—21no—
109C4×Q8×C47—21no—
110C4×Q8×C47—21no—
111C4×Q8×C47C2311yescharacteristic
112C4×Q8×C47C2311yescharacteristic
113C4×Q8×C47C2311yescharacteristic
114C4×D4×C47—22no—
115C4×D4×C47—21no—
116C4×D4×C47—21no—
117C4×D4×C47—21no—
118C4×D4×C47—21no—
119C4×D4×C47—21no—
120C4×D4×C47—21no—
121C4×D4×C47D412yes—
122C4×D4×C47C2311yescharacteristic
123#117×C47—21no—
124#117×C47—21no—
125C2×C4⋊C4×C47—22no—
126C2×C4⋊C4×C47—21no—
127C2×C4⋊C4×C47—21no—
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—
146#41×C47—82no—
147#41×C47—82no—
148C2×Q8×C47—22no—
149C2×Q8×C47—21no—
150C2×Q8×C47—21no—
151C2×Q8×C47—22no—
152C2×Q8×C47—41no—
153C2×Q8×C47—82no—
154C2×Q8×C47—82no—
155C2×Q8×C47C2×D411yescharacteristic
156C2×Q8×C47C2×D411yescharacteristic
157C2×Q8×C47C2×D411yescharacteristic
158C2×D4×C47—22no—
159C2×D4×C47—22no—
160C2×D4×C47—21no—
161C2×D4×C47—22no—
162C2×D4×C47—21no—
163C2×D4×C47—21no—
164C2×D4×C47C2×D411yescharacteristic
165C2×D4×C47C2×D412yes—
166C22×C4×C47—22no—
167C22×C4×C47—22no—
168C22×C4×C47—22no—
169C22×C4×C47—21no—
170C22×C4×C47—22no—
171C22×C4×C47—41no—
172C22×C4×C47C2×D411yescharacteristic
173C22×C4×C47C2×D411yescharacteristic
174C22×C4×C47C2×D411yescharacteristic
175Q16×C47—82no—
176Q16×C47—82no—
177C2×C8×C47—22no—
178C2×C8×C47—22no—
179C2×C8×C47—22no—
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—21no—
189C4⋊C4×C47—21no—
190C4⋊C4×C47—21no—
191C4⋊C4×C47—21no—
192C4⋊C4×C47—21no—
193C4⋊C4×C47—21no—
194C4⋊C4×C47—21no—
195C4⋊C4×C47—21no—
196C4⋊C4×C47—22no—
197C4⋊C4×C47—22no—
198C4⋊C4×C47—41no—
199C4⋊C4×C47—41no—
200C4⋊C4×C47C2×D411yescharacteristic
201C4⋊C4×C47C2×D411yescharacteristic
202C4⋊C4×C47C2×D411yescharacteristic
203C4⋊C4×C47C2×D411yescharacteristic
204C4⋊C4×C47C2×D412yes—
205C22⋊C4×C47—22no—
206C22⋊C4×C47—22no—
207C22⋊C4×C47—22no—
208C22⋊C4×C47—22no—
209C22⋊C4×C47—22no—
210C22⋊C4×C47—21no—
211C22⋊C4×C47—21no—
212C22⋊C4×C47—21no—
213C22⋊C4×C47—21no—
214C22⋊C4×C47—21no—
215C22⋊C4×C47—21no—
216C22⋊C4×C47—22no—
217C22⋊C4×C47—22no—
218C22⋊C4×C47—21no—
219C42×C47—22no—
220C42×C47—21no—
221C42×C47—21no—
222C42×C47—21no—
223C42×C47C2×D411yescharacteristic
224C42×C47C2×D411yescharacteristic
225C42×C47C2×D411yescharacteristic
226C42×C47C2411yescharacteristic
227C23×C47—21no—
228C23×C47—22no—
229C23×C47#12011yescharacteristic
230Q8×C47—22no—
231Q8×C47—22no—
232Q8×C47—22no—
233Q8×C47—42no—
234Q8×C47—42no—
235Q8×C47—42no—
236Q8×C47—81no—
237Q8×C47—82no—
238Q8×C47—82no—
239D4×C47—22no—
240D4×C47—42no—
241D4×C47—42no—
242D4×C47—42no—
243D4×C47—81no—
244D4×C47—82no—
245D4×C47—82no—
246D4×C47—82no—
247C2×C4×C47—22no—
248C2×C4×C47—22no—
249C2×C4×C47—21no—
250C2×C4×C47—21no—
251C2×C4×C47—21no—
252C2×C4×C47—21no—
253C2×C4×C47—21no—
254C2×C4×C47—22no—
255C2×C4×C47—21no—
256C2×C4×C47—21no—
257C2×C4×C47—41no—
258C2×C4×C47—42no—
259C2×C4×C47—42no—
260C2×C4×C47—82no—
261C2×C4×C47—82no—
262C2×C4×C47—82no—
263C2×C4×C47—82no—
264C2×C4×C47—82no—
265C2×C4×C47#12011yescharacteristic
266C2×C4×C47#12011yescharacteristic
267C2×C4×C47#12011yescharacteristic
268C2×C4×C47C22×D411yescharacteristic
269C2×C4×C47C22×D411yescharacteristic
270C2×C4×C47C22×D411yescharacteristic
271C8×C47—42no—
272C8×C47—42no—
273C8×C47—42no—
274#18970C4711yesmaximal, characteristic, direct product factor, Sylow
275C22×C47—21no—
276C22×C47—21no—
277C22×C47—21no—
278C22×C47—41no—
279C22×C47—42no—
280C22×C47—41no—
281C22×C47—42no—
282C22×C47—42no—
283C22×C47—41no—
284C22×C47C2×#12011yescharacteristic
285C4×C47—21no—
286C4×C47—21no—
287C4×C47—21no—
288C4×C47—21no—
289C4×C47—41no—
290C4×C47—41no—
291C4×C47—42no—
292C4×C47—41no—
293C4×C47—41no—
294C4×C47—41no—
295C4×C47—41no—
296C4×C47—41no—
297C4×C47—82no—
298C4×C47#57612yes—
299C4×C47#57812yes—
300#3554C2×C4711yescharacteristic
301#3239C2×C4711yescharacteristic, complemented
302#3226C2×C4711yescharacteristic, complemented
303#3209C2×C4711yescharacteristic, complemented
304#1649C2×C4712yescomplemented
305#1648C2×C4712yescomplemented
306#1641C2×C4712yescomplemented
307#1640C2×C4712yescomplemented
308#1553C2×C4711yescharacteristic, complemented
309#1497C2×C4711yescharacteristic, complemented
310#1482C2×C4711yescharacteristic, complemented
311C2×C47—41no—
312C2×C47—81no—
313C2×C47—82no—
314C2×C47#300811yescharacteristic
315C2×C47#301111yescharacteristic
316C2×C47#302211yescharacteristic
317#562—22no—
318#559—21no—
319#559C22×C4711yescharacteristic
320#557C22×C4711yescharacteristic
321#554—21no—
322#550C22×C4711yescharacteristic
323D4×Q8C22×C4711yescharacteristic
324#548—21no—
325#547—21no—
326#542—21no—
327#542—21no—
328#540—21no—
329#539—22no—
330#536—21no—
331#533C22×C4711yescharacteristic
332#532C22×C4711yescharacteristic
333C2×C4⋊Q8C22×C4711yescharacteristic
334#529C22×C4711yescharacteristic
335#501—21no—
336#500C22×C4712yes—
337#494—21no—
338#489—21no—
339#487—21no—
340#486C22×C4712yes—
341#484—21no—
342#481—21no—
343#480—22no—
344#475C22×C4712yes—
345#474—22no—
346#474C22×C4712yes—
347#462C22×C4712yes—
348#462C22×C4712yes—
349#451—21no—
350#451—21no—
351#432C22×C4711yescharacteristic
352#431C22×C4711yescharacteristic
353#431C22×C4711yescharacteristic
354#332C22×C4712yes—
355#331C22×C4712yes—
356Q8⋊C8C22×C4712yes—
357Q8⋊C8C22×C4712yes—
358Q8⋊C8C22×C4712yes—
359D4⋊C8C22×C4712yes—
360C47#1897011yescharacteristic, direct product factor, Sylow
361C2×#41—21no—
362C2×#41—21no—
363C22×Q8—21no—
364C22×Q8—21no—
365C2×Q16—22no—
366C2×Q16—22no—
367C4⋊Q8—21no—
368C4⋊Q8—21no—
369C4⋊Q8—21no—
370C4⋊Q8—21no—
371C4⋊Q8—21no—
372C4⋊Q8D4×C4711yescharacteristic
373C4⋊Q8D4×C4711yescharacteristic
374C4⋊Q8C23×C4712yes—
375C4⋊Q8C23×C4711yescharacteristic
376#127—21no—
377#127C23×C4711yescharacteristic
378#126—22no—
379#126—21no—
380#125—22no—
381#125—21no—
382#125—21no—
383#125D4×C4711yescharacteristic
384#124—22no—
385#124—22no—
386#124—21no—
387#124—21no—
388#124—21no—
389#124D4×C4711yescharacteristic
390#123—22no—
391#123—22no—
392#123—22no—
393#123—22no—
394#123—22no—
395#123—22no—
396#123—21no—
397C22⋊Q8—22no—
398C22⋊Q8—22no—
399C22⋊Q8—22no—
400C22⋊Q8—22no—
401C22⋊Q8—21no—
402C22⋊Q8—22no—
403C22⋊Q8—21no—
404C22⋊Q8D4×C4711yescharacteristic
405C22⋊Q8D4×C4711yescharacteristic
406C22⋊Q8D4×C4711yescharacteristic
407#121—22no—
408#121—22no—
409#121—22no—
410#121—21no—
411#121—21no—
412#121D4×C4711yescharacteristic
413#121D4×C4712yes—
414C4×Q8—21no—
415C4×Q8—21no—
416C4×Q8—21no—
417C4×Q8C23×C4711yescharacteristic
418C4×Q8C23×C4711yescharacteristic
419C4×Q8C23×C4711yescharacteristic
420C4×D4—22no—
421C4×D4—21no—
422C4×D4—21no—
423C4×D4—21no—
424C4×D4—21no—
425C4×D4—21no—
426C4×D4—21no—
427C4×D4D4×C4712yes—
428C4×D4C23×C4711yescharacteristic
429#117—21no—
430#117—21no—
431C2×C4⋊C4—22no—
432C2×C4⋊C4—21no—
433C2×C4⋊C4—21no—
434C2×C42C23×C4711yescharacteristic
435#107—24no—
436#107—22no—
437#106—22no—
438C4⋊C8—21no—
439C4⋊C8C23×C4712yes—
440C4⋊C8C23×C4712yes—
441#103—22no—
442#103—22no—
443#103—22no—
444#102—24no—
445#102—22no—
446C22⋊C8—21no—
447C22⋊C8—21no—
448C22⋊C8—21no—
449#97—21no—
450C4×C8—21no—
451C4×C8C23×C4712yes—
452#41—82no—
453#41—82no—
454C2×Q8—22no—
455C2×Q8—21no—
456C2×Q8—21no—
457C2×Q8—22no—
458C2×Q8—41no—
459C2×Q8—82no—
460C2×Q8—82no—
461C2×Q8C2×D4×C4711yescharacteristic
462C2×Q8C2×D4×C4711yescharacteristic
463C2×Q8C2×D4×C4711yescharacteristic
464C2×D4—22no—
465C2×D4—22no—
466C2×D4—21no—
467C2×D4—22no—
468C2×D4—21no—
469C2×D4—21no—
470C2×D4C2×D4×C4711yescharacteristic
471C2×D4C2×D4×C4712yes—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—21no—
476C22×C4—22no—
477C22×C4—41no—
478C22×C4C2×D4×C4711yescharacteristic
479C22×C4C2×D4×C4711yescharacteristic
480C22×C4C2×D4×C4711yescharacteristic
481Q16—82no—
482Q16—82no—
483C2×C8—22no—
484C2×C8—22no—
485C2×C8—22no—
486C4⋊C4—22no—
487C4⋊C4—22no—
488C4⋊C4—22no—
489C4⋊C4—22no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—22no—
503C4⋊C4—22no—
504C4⋊C4—41no—
505C4⋊C4—41no—
506C4⋊C4C2×D4×C4711yescharacteristic
507C4⋊C4C2×D4×C4711yescharacteristic
508C4⋊C4C2×D4×C4711yescharacteristic
509C4⋊C4C2×D4×C4711yescharacteristic
510C4⋊C4C2×D4×C4712yes—
511C22⋊C4—22no—
512C22⋊C4—22no—
513C22⋊C4—22no—
514C22⋊C4—22no—
515C22⋊C4—22no—
516C22⋊C4—21no—
517C22⋊C4—21no—
518C22⋊C4—21no—
519C22⋊C4—21no—
520C22⋊C4—21no—
521C22⋊C4—21no—
522C22⋊C4—22no—
523C22⋊C4—22no—
524C22⋊C4—21no—
525C42—22no—
526C42—21no—
527C42—21no—
528C42—21no—
529C42C2×D4×C4711yescharacteristic
530C42C2×D4×C4711yescharacteristic
531C42C2×D4×C4711yescharacteristic
532C42C24×C4711yescharacteristic
533C23—21no—
534C23—22no—
535C23#120×C4711yescharacteristic
536Q8—22no—
537Q8—22no—
538Q8—22no—
539Q8—42no—
540Q8—42no—
541Q8—42no—
542Q8—81no—
543Q8—82no—
544Q8—82no—
545D4—22no—
546D4—42no—
547D4—42no—
548D4—42no—
549D4—81no—
550D4—82no—
551D4—82no—
552D4—82no—
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—22no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—41no—
564C2×C4—42no—
565C2×C4—42no—
566C2×C4—82no—
567C2×C4—82no—
568C2×C4—82no—
569C2×C4—82no—
570C2×C4—82no—
571C2×C4#120×C4711yescharacteristic
572C2×C4#120×C4711yescharacteristic
573C2×C4#120×C4711yescharacteristic
574C2×C4C22×D4×C4711yescharacteristic
575C2×C4C22×D4×C4711yescharacteristic
576C2×C4C22×D4×C4711yescharacteristic
577C8—42no—
578C8—42no—
579C8—42no—
580C22—21no—
581C22—21no—
582C22—21no—
583C22—41no—
584C22—42no—
585C22—41no—
586C22—42no—
587C22—42no—
588C22—41no—
589C22C2×#120×C4711yescharacteristic
590C4—21no—
591C4—21no—
592C4—21no—
593C4—21no—
594C4—41no—
595C4—41no—
596C4—42no—
597C4—41no—
598C4—41no—
599C4—41no—
600C4—41no—
601C4—41no—
602C4—82no—
603C4C47×#57612yes—
604C4C47×#57812yes—
605C2—41no—
606C2—81no—
607C2—82no—
608C2C47×#300811yescharacteristic
609C2C47×#301111yescharacteristic
610C2C47×#302211yescharacteristic
subgroupG/H
center, socleC22×C47C2×#120
commutator, Frattini, cosocleC42C24×C47
prime radicalC47×#3554C2
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×#3209C2semidirect
5. C47×#1649C2semidirect
6. C47×#1648C2semidirect
7. C47×#1641C2semidirect
8. C47×#1640C2semidirect
9. C47×#1553C2semidirect
10. C47×#1497C2semidirect
11. C47×#1482C2semidirect
274. #18970C47direct (N × H)
301. #3239C2×C47semidirect
302. #3226C2×C47semidirect
303. #3209C2×C47semidirect
304. #1649C2×C47semidirect
305. #1648C2×C47semidirect
306. #1641C2×C47semidirect
307. #1640C2×C47semidirect
308. #1553C2×C47semidirect
309. #1497C2×C47semidirect
310. #1482C2×C47semidirect
360. C47#18970direct (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×#32392
C47×#32262
C47×#32092
C47×#16492
C47×#16482
C47×#16412
C47×#16402
C47×#15532
C47×#14972
C47×#14822
#1897047