Finite Group Databasebeta

← C47×#18959 #26058657

Subgroups — C47×#18959 #26058657

Order 12032.

874 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3554C211yesmaximal, characteristic
2C47×#3238C211yesmaximal, characteristic, complemented
3C47×#3230C211yesmaximal, characteristic, complemented
4C47×#3206C211yesmaximal, characteristic, complemented
5C47×#1637C212yesmaximal, complemented
6C47×#1636C212yesmaximal, complemented
7C47×#1631C212yesmaximal, complemented
8C47×#1630C212yesmaximal, 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×#500—21no—
32C47×#492C2212yes—
33C47×#489—21no—
34C47×#487—21no—
35C47×#487C2212yes—
36C47×#484—21no—
37C47×#484—21no—
38C47×#483—21no—
39C47×#480—21no—
40C47×#477C2212yes—
41C47×#477C2212yes—
42C47×#477C2212yes—
43C47×#476C2212yes—
44C47×#461—22no—
45C47×#448—22no—
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×SD16×C47—24no—
60C4⋊Q8×C47—21no—
61C4⋊Q8×C47—21no—
62C4⋊Q8×C47—21no—
63C4⋊Q8×C47—21no—
64C4⋊Q8×C47—21no—
65C4⋊Q8×C47D411yescharacteristic
66C4⋊Q8×C47D411yescharacteristic
67C4⋊Q8×C47C2312yes—
68C4⋊Q8×C47C2311yescharacteristic
69#127×C47—21no—
70#127×C47C2311yescharacteristic
71#126×C47—22no—
72#126×C47—21no—
73#125×C47—22no—
74#125×C47—21no—
75#125×C47—21no—
76#125×C47D411yescharacteristic
77#124×C47—22no—
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—22no—
86#123×C47—22no—
87#123×C47—22no—
88#123×C47—22no—
89#123×C47—21no—
90C22⋊Q8×C47—22no—
91C22⋊Q8×C47—22no—
92C22⋊Q8×C47—22no—
93C22⋊Q8×C47—22no—
94C22⋊Q8×C47—21no—
95C22⋊Q8×C47—22no—
96C22⋊Q8×C47—21no—
97C22⋊Q8×C47D411yescharacteristic
98C22⋊Q8×C47D411yescharacteristic
99C22⋊Q8×C47D411yescharacteristic
100#121×C47—22no—
101#121×C47—22no—
102#121×C47—22no—
103#121×C47—21no—
104#121×C47—21no—
105#121×C47D411yescharacteristic
106#121×C47D412yes—
107C4×Q8×C47—21no—
108C4×Q8×C47—21no—
109C4×Q8×C47—21no—
110C4×Q8×C47C2311yescharacteristic
111C4×Q8×C47C2311yescharacteristic
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×C47—21no—
119C4×D4×C47—21no—
120C4×D4×C47D412yes—
121C4×D4×C47C2311yescharacteristic
122#117×C47—21no—
123#117×C47—21no—
124C2×C4⋊C4×C47—22no—
125C2×C4⋊C4×C47—21no—
126C2×C4⋊C4×C47—21no—
127C2×C42×C47C2311yescharacteristic
128#107×C47—22no—
129#107×C47—22no—
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#103×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
175SD16×C47—84no—
176C2×C8×C47—22no—
177C2×C8×C47—22no—
178C2×C8×C47—22no—
179C4⋊C4×C47—22no—
180C4⋊C4×C47—22no—
181C4⋊C4×C47—22no—
182C4⋊C4×C47—22no—
183C4⋊C4×C47—21no—
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—22no—
196C4⋊C4×C47—22no—
197C4⋊C4×C47—41no—
198C4⋊C4×C47—41no—
199C4⋊C4×C47C2×D412yes—
200C4⋊C4×C47C2×D411yescharacteristic
201C4⋊C4×C47C2×D411yescharacteristic
202C4⋊C4×C47C2×D411yescharacteristic
203C4⋊C4×C47C2×D411yescharacteristic
204C22⋊C4×C47—22no—
205C22⋊C4×C47—22no—
206C22⋊C4×C47—22no—
207C22⋊C4×C47—22no—
208C22⋊C4×C47—22no—
209C22⋊C4×C47—21no—
210C22⋊C4×C47—21no—
211C22⋊C4×C47—21no—
212C22⋊C4×C47—21no—
213C22⋊C4×C47—21no—
214C22⋊C4×C47—21no—
215C22⋊C4×C47—22no—
216C22⋊C4×C47—22no—
217C22⋊C4×C47—21no—
218C42×C47—22no—
219C42×C47—21no—
220C42×C47—21no—
221C42×C47—21no—
222C42×C47C2×D411yescharacteristic
223C42×C47C2×D411yescharacteristic
224C42×C47C2×D411yescharacteristic
225C42×C47C2411yescharacteristic
226C23×C47—21no—
227C23×C47—22no—
228C23×C47#12011yescharacteristic
229Q8×C47—22no—
230Q8×C47—22no—
231Q8×C47—22no—
232Q8×C47—44no—
233Q8×C47—42no—
234Q8×C47—81no—
235Q8×C47—82no—
236Q8×C47—82no—
237D4×C47—22no—
238D4×C47—42no—
239D4×C47—42no—
240D4×C47—42no—
241D4×C47—81no—
242D4×C47—82no—
243D4×C47—82no—
244D4×C47—82no—
245C2×C4×C47—22no—
246C2×C4×C47—22no—
247C2×C4×C47—21no—
248C2×C4×C47—21no—
249C2×C4×C47—21no—
250C2×C4×C47—21no—
251C2×C4×C47—21no—
252C2×C4×C47—22no—
253C2×C4×C47—21no—
254C2×C4×C47—21no—
255C2×C4×C47—41no—
256C2×C4×C47—42no—
257C2×C4×C47—42no—
258C2×C4×C47—82no—
259C2×C4×C47—82no—
260C2×C4×C47—82no—
261C2×C4×C47—82no—
262C2×C4×C47—82no—
263C2×C4×C47#12011yescharacteristic
264C2×C4×C47#12011yescharacteristic
265C2×C4×C47#12011yescharacteristic
266C2×C4×C47C22×D411yescharacteristic
267C2×C4×C47C22×D411yescharacteristic
268C2×C4×C47C22×D411yescharacteristic
269C8×C47—42no—
270C8×C47—42no—
271C8×C47—42no—
272#18959C4711yesmaximal, characteristic, direct product factor, Sylow
273C22×C47—21no—
274C22×C47—21no—
275C22×C47—21no—
276C22×C47—41no—
277C22×C47—42no—
278C22×C47—41no—
279C22×C47—42no—
280C22×C47—42no—
281C22×C47—41no—
282C22×C47C2×#12011yescharacteristic
283C4×C47—21no—
284C4×C47—21no—
285C4×C47—21no—
286C4×C47—21no—
287C4×C47—41no—
288C4×C47—41no—
289C4×C47—42no—
290C4×C47—41no—
291C4×C47—41no—
292C4×C47—41no—
293C4×C47—41no—
294C4×C47—41no—
295C4×C47—82no—
296C4×C47#57712yes—
297C4×C47#57812yes—
298#3554C2×C4711yescharacteristic
299#3238C2×C4711yescharacteristic, complemented
300#3230C2×C4711yescharacteristic, complemented
301#3206C2×C4711yescharacteristic, complemented
302#1637C2×C4712yescomplemented
303#1636C2×C4712yescomplemented
304#1631C2×C4712yescomplemented
305#1630C2×C4712yescomplemented
306#1553C2×C4711yescharacteristic, complemented
307#1497C2×C4711yescharacteristic, complemented
308#1482C2×C4711yescharacteristic, complemented
309C2×C47—41no—
310C2×C47—81no—
311C2×C47—82no—
312C2×C47#300911yescharacteristic
313C2×C47#301111yescharacteristic
314C2×C47#302111yescharacteristic
315#562—22no—
316#559—21no—
317#559C22×C4711yescharacteristic
318#557C22×C4711yescharacteristic
319#554—21no—
320#550C22×C4711yescharacteristic
321D4×Q8C22×C4711yescharacteristic
322#548—21no—
323#547—21no—
324#542—21no—
325#542—21no—
326#540—21no—
327#539—22no—
328#536—21no—
329#533C22×C4711yescharacteristic
330#532C22×C4711yescharacteristic
331C2×C4⋊Q8C22×C4711yescharacteristic
332#529C22×C4711yescharacteristic
333#501—21no—
334#500—21no—
335#492C22×C4712yes—
336#489—21no—
337#487—21no—
338#487C22×C4712yes—
339#484—21no—
340#484—21no—
341#483—21no—
342#480—21no—
343#477C22×C4712yes—
344#477C22×C4712yes—
345#477C22×C4712yes—
346#476C22×C4712yes—
347#461—22no—
348#448—22no—
349#432C22×C4711yescharacteristic
350#431C22×C4711yescharacteristic
351#431C22×C4711yescharacteristic
352#332C22×C4712yes—
353#331C22×C4712yes—
354Q8⋊C8C22×C4712yes—
355Q8⋊C8C22×C4712yes—
356Q8⋊C8C22×C4712yes—
357D4⋊C8C22×C4712yes—
358C47#1895911yescharacteristic, direct product factor, Sylow
359C2×#41—21no—
360C2×#41—21no—
361C22×Q8—21no—
362C22×Q8—21no—
363C2×SD16—24no—
364C4⋊Q8—21no—
365C4⋊Q8—21no—
366C4⋊Q8—21no—
367C4⋊Q8—21no—
368C4⋊Q8—21no—
369C4⋊Q8D4×C4711yescharacteristic
370C4⋊Q8D4×C4711yescharacteristic
371C4⋊Q8C23×C4712yes—
372C4⋊Q8C23×C4711yescharacteristic
373#127—21no—
374#127C23×C4711yescharacteristic
375#126—22no—
376#126—21no—
377#125—22no—
378#125—21no—
379#125—21no—
380#125D4×C4711yescharacteristic
381#124—22no—
382#124—22no—
383#124—21no—
384#124—21no—
385#124—21no—
386#124D4×C4711yescharacteristic
387#123—22no—
388#123—22no—
389#123—22no—
390#123—22no—
391#123—22no—
392#123—22no—
393#123—21no—
394C22⋊Q8—22no—
395C22⋊Q8—22no—
396C22⋊Q8—22no—
397C22⋊Q8—22no—
398C22⋊Q8—21no—
399C22⋊Q8—22no—
400C22⋊Q8—21no—
401C22⋊Q8D4×C4711yescharacteristic
402C22⋊Q8D4×C4711yescharacteristic
403C22⋊Q8D4×C4711yescharacteristic
404#121—22no—
405#121—22no—
406#121—22no—
407#121—21no—
408#121—21no—
409#121D4×C4711yescharacteristic
410#121D4×C4712yes—
411C4×Q8—21no—
412C4×Q8—21no—
413C4×Q8—21no—
414C4×Q8C23×C4711yescharacteristic
415C4×Q8C23×C4711yescharacteristic
416C4×Q8C23×C4711yescharacteristic
417C4×D4—22no—
418C4×D4—21no—
419C4×D4—21no—
420C4×D4—21no—
421C4×D4—21no—
422C4×D4—21no—
423C4×D4—21no—
424C4×D4D4×C4712yes—
425C4×D4C23×C4711yescharacteristic
426#117—21no—
427#117—21no—
428C2×C4⋊C4—22no—
429C2×C4⋊C4—21no—
430C2×C4⋊C4—21no—
431C2×C42C23×C4711yescharacteristic
432#107—22no—
433#107—22no—
434#107—22no—
435#106—22no—
436C4⋊C8—21no—
437C4⋊C8C23×C4712yes—
438C4⋊C8C23×C4712yes—
439#103—22no—
440#103—22no—
441#103—22no—
442#103—24no—
443#102—22no—
444C22⋊C8—21no—
445C22⋊C8—21no—
446C22⋊C8—21no—
447#97—21no—
448C4×C8—21no—
449C4×C8C23×C4712yes—
450#41—82no—
451#41—82no—
452C2×Q8—22no—
453C2×Q8—21no—
454C2×Q8—21no—
455C2×Q8—22no—
456C2×Q8—41no—
457C2×Q8—82no—
458C2×Q8—82no—
459C2×Q8C2×D4×C4711yescharacteristic
460C2×Q8C2×D4×C4711yescharacteristic
461C2×Q8C2×D4×C4711yescharacteristic
462C2×D4—22no—
463C2×D4—22no—
464C2×D4—21no—
465C2×D4—22no—
466C2×D4—21no—
467C2×D4—21no—
468C2×D4C2×D4×C4711yescharacteristic
469C2×D4C2×D4×C4712yes—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—21no—
474C22×C4—22no—
475C22×C4—41no—
476C22×C4C2×D4×C4711yescharacteristic
477C22×C4C2×D4×C4711yescharacteristic
478C22×C4C2×D4×C4711yescharacteristic
479SD16—84no—
480C2×C8—22no—
481C2×C8—22no—
482C2×C8—22no—
483C4⋊C4—22no—
484C4⋊C4—22no—
485C4⋊C4—22no—
486C4⋊C4—22no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—21no—
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—22no—
500C4⋊C4—22no—
501C4⋊C4—41no—
502C4⋊C4—41no—
503C4⋊C4C2×D4×C4712yes—
504C4⋊C4C2×D4×C4711yescharacteristic
505C4⋊C4C2×D4×C4711yescharacteristic
506C4⋊C4C2×D4×C4711yescharacteristic
507C4⋊C4C2×D4×C4711yescharacteristic
508C22⋊C4—22no—
509C22⋊C4—22no—
510C22⋊C4—22no—
511C22⋊C4—22no—
512C22⋊C4—22no—
513C22⋊C4—21no—
514C22⋊C4—21no—
515C22⋊C4—21no—
516C22⋊C4—21no—
517C22⋊C4—21no—
518C22⋊C4—21no—
519C22⋊C4—22no—
520C22⋊C4—22no—
521C22⋊C4—21no—
522C42—22no—
523C42—21no—
524C42—21no—
525C42—21no—
526C42C2×D4×C4711yescharacteristic
527C42C2×D4×C4711yescharacteristic
528C42C2×D4×C4711yescharacteristic
529C42C24×C4711yescharacteristic
530C23—21no—
531C23—22no—
532C23#120×C4711yescharacteristic
533Q8—22no—
534Q8—22no—
535Q8—22no—
536Q8—44no—
537Q8—42no—
538Q8—81no—
539Q8—82no—
540Q8—82no—
541D4—22no—
542D4—42no—
543D4—42no—
544D4—42no—
545D4—81no—
546D4—82no—
547D4—82no—
548D4—82no—
549C2×C4—22no—
550C2×C4—22no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—22no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—41no—
560C2×C4—42no—
561C2×C4—42no—
562C2×C4—82no—
563C2×C4—82no—
564C2×C4—82no—
565C2×C4—82no—
566C2×C4—82no—
567C2×C4#120×C4711yescharacteristic
568C2×C4#120×C4711yescharacteristic
569C2×C4#120×C4711yescharacteristic
570C2×C4C22×D4×C4711yescharacteristic
571C2×C4C22×D4×C4711yescharacteristic
572C2×C4C22×D4×C4711yescharacteristic
573C8—42no—
574C8—42no—
575C8—42no—
576C22—21no—
577C22—21no—
578C22—21no—
579C22—41no—
580C22—42no—
581C22—41no—
582C22—42no—
583C22—42no—
584C22—41no—
585C22C2×#120×C4711yescharacteristic
586C4—21no—
587C4—21no—
588C4—21no—
589C4—21no—
590C4—41no—
591C4—41no—
592C4—42no—
593C4—41no—
594C4—41no—
595C4—41no—
596C4—41no—
597C4—41no—
598C4—82no—
599C4C47×#57712yes—
600C4C47×#57812yes—
601C2—41no—
602C2—81no—
603C2—82no—
604C2C47×#300911yescharacteristic
605C2C47×#301111yescharacteristic
606C2C47×#302111yescharacteristic
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×#3238C2semidirect
3. C47×#3230C2semidirect
4. C47×#3206C2semidirect
5. C47×#1637C2semidirect
6. C47×#1636C2semidirect
7. C47×#1631C2semidirect
8. C47×#1630C2semidirect
9. C47×#1553C2semidirect
10. C47×#1497C2semidirect
11. C47×#1482C2semidirect
272. #18959C47direct (N × H)
299. #3238C2×C47semidirect
300. #3230C2×C47semidirect
301. #3206C2×C47semidirect
302. #1637C2×C47semidirect
303. #1636C2×C47semidirect
304. #1631C2×C47semidirect
305. #1630C2×C47semidirect
306. #1553C2×C47semidirect
307. #1497C2×C47semidirect
308. #1482C2×C47semidirect
358. C47#18959direct (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×#32382
C47×#32302
C47×#32062
C47×#16372
C47×#16362
C47×#16312
C47×#16302
C47×#15532
C47×#14972
C47×#14822
#1895947