Finite Group Databasebeta

← D47×#1809 #26215847

Subgroups — D47×#1809 #26215847

Order 12032.

1662 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×M16×D47C211yesmaximal, characteristic
2C2×#107×D47C211yesmaximal, characteristic, complemented
3C2×#106×D47C211yesmaximal, characteristic, complemented
4#380×D47C212yesmaximal
5#20243422C211yesmaximal, characteristic, complemented
6#20243421C211yesmaximal, characteristic, complemented
7#20243420C212yesmaximal, complemented
8#20243419C212yesmaximal, complemented
9#20243418C211yesmaximal, characteristic, complemented
10#340×D47C212yesmaximal, complemented
11C47×#1809C211yesmaximal, characteristic, complemented
12C23×C4×D47C2211yescharacteristic
13C22×#10625329C2211yescharacteristic
14C22×#10625324C2211yescharacteristic
15C22×#10625324C2211yescharacteristic
16C2×M16×D47—24no—
17C2×M16×D47—24no—
18C2×M16×D47C418yescomplemented
19C22×C8×D47C2211yescharacteristic
20C22×C8×D47C2211yescharacteristic
21C2×C4⋊C4×D47C2212yes—
22C2×C4⋊C4×D47C2212yes—
23C2×C22⋊C4×D47—22no—
24C2×#13093958C2211yescharacteristic, complemented
25C2×#13093957C2212yescomplemented
26#107×D47—24no—
27C2×#13093956C2211yescharacteristic, complemented
28C2×#13093955C2212yescomplemented
29#106×D47—24no—
30#15688983C2212yes—
31#15688982—22no—
32#15688981—22no—
33#15688980C2212yes—
34#15688980C2212yes—
35#95×D47—22no—
36#15688886C2212yescomplemented
37#15688885C2212yescomplemented
38#15688885C2212yescomplemented
39C22×M16×C47C2211yescharacteristic
40C2×#107×C47C2211yescharacteristic, complemented
41C2×#106×C47C2211yescharacteristic, complemented
42C47×#380C2212yes—
43C47×#340C2212yescomplemented
44C24×D47D411yescharacteristic
45C23×Dic47D411yescharacteristic
46C22×C4×D47—22no—
47C22×C4×D47—22no—
48C22×C4×D47—22no—
49C22×C4×D47—22no—
50C22×C4×D47—22no—
51C22×C4×D47—22no—
52C22×C4×D47C2×C414yes—
53C22×C4×D47D411yescharacteristic
54C22×C4×D47D411yescharacteristic
55C22×C4×D47Q814yes—
56C22×C4×D47C2311yescharacteristic
57C22×C4×D47C2311yescharacteristic
58C2×#10625329—22no—
59C2×#10625329—22no—
60C2×#10625329C2×C414yescomplemented
61C2×#10625324—22no—
62C2×#10625324—22no—
63C2×#10625324—22no—
64C2×#10625324—22no—
65C2×#10625324C2×C414yescomplemented
66C2×#10625324C2×C414yescomplemented
67M16×D47—232no—
68C22×C47⋊C8C2311yescharacteristic
69C22×C47⋊C8C2311yescharacteristic
70C2×C8×D47—22no—
71C2×C8×D47—22no—
72C2×C8×D47C2×C414yes—
73C2×C8×D47C2×C414yes—
74C2×C8×D47D414yes—
75C2×C8×D47D414yes—
76C2×C4⋊Dic47C2312yes—
77C2×C4⋊Dic47C2312yes—
78C2×Dic47⋊C4—22no—
79C2×Dic47⋊C4—22no—
80C4⋊C4×D47—24no—
81C4⋊C4×D47—24no—
82C4⋊C4×D47—24no—
83C4⋊C4×D47—24no—
84C2×C22⋊Dic47—22no—
85C2×(C2×D47)⋊C4—22no—
86C2×(C2×D47)⋊C4—22no—
87C22⋊C4×D47—48no—
88#13093958—22no—
89#13093957—24no—
90#13093956—22no—
91#13093955—24no—
92C47⋊#95—22no—
93C47⋊#95—22no—
94C47⋊#95—22no—
95C23×C4×C47C2311yescharacteristic
96C2×M16×C47—22no—
97C2×M16×C47—22no—
98C2×M16×C47C2×C414yescomplemented
99C22×C8×C47C2311yescharacteristic
100C22×C8×C47C2311yescharacteristic
101C2×C4⋊C4×C47C2312yes—
102C2×C4⋊C4×C47C2312yes—
103C2×C22⋊C4×C47—22no—
104#107×C47—22no—
105#106×C47—22no—
106#95×C47—22no—
107C24×C47C2×D411yescharacteristic
108C23×D47—22no—
109C23×D47—22no—
110C23×D47—24no—
111C23×D47—24no—
112C23×D47C4⋊C414yes—
113C23×D47C2×D411yescharacteristic
114C23×D47C2×D411yescharacteristic
115C22×C4×C47—21no—
116C22×C4×C47—21no—
117C22×C4×C47—21no—
118C22×C4×C47—21no—
119C22×C4×C47—22no—
120C22×C4×C47—22no—
121C22×C4×C47C22×C412yes—
122C22×C4×C47C2×D411yescharacteristic
123C22×C4×C47C2×Q812yes—
124C22×C4×C47C2411yescharacteristic
125C22×Dic47—22no—
126C22×Dic47—22no—
127C22×Dic47—22no—
128C22×Dic47—22no—
129C22×Dic47C4⋊C414yes—
130C22×Dic47C2×D411yescharacteristic
131C22×Dic47C2×D411yescharacteristic
132C2×C4×D47—22no—
133C2×C4×D47—22no—
134C2×C4×D47—21no—
135C2×C4×D47—21no—
136C2×C4×D47—21no—
137C2×C4×D47—21no—
138C2×C4×D47—22no—
139C2×C4×D47—22no—
140C2×C4×D47—28no—
141C2×C4×D47—28no—
142C2×C4×D47—28no—
143C2×C4×D47—28no—
144C2×C4×D47—44no—
145C2×C4×D47—44no—
146C2×C4×D47—44no—
147C2×C4×D47—44no—
148C2×C4×D47—44no—
149C2×C4×D47—44no—
150C2×C4×D47C4⋊C414yes—
151C2×C4×D47C4⋊C414yes—
152C2×C4×D47C22×C412yes—
153C2×C4×D47C22×C412yes—
154C2×C4×D47C2×D412yes—
155C2×C4×D47C2×D412yes—
156C2×C4×D47C2×Q812yes—
157C2×C4×D47C2×Q812yes—
158C2×C4×D47#4112yes—
159C2×C4×D47#4112yes—
160M16×C47—28no—
161C2×C8×C47—21no—
162C2×C8×C47—21no—
163C2×C8×C47C22×C412yes—
164C2×C8×C47C22×C412yes—
165C2×C8×C47C2×D412yes—
166C2×C8×C47C2×D412yes—
167C4⋊C4×C47—22no—
168C4⋊C4×C47—22no—
169C4⋊C4×C47—22no—
170C4⋊C4×C47—22no—
171C22⋊C4×C47—44no—
172C22⋊Dic47—44no—
173(C2×D47)⋊C4—44no—
174(C2×D47)⋊C4—44no—
175C4⋊Dic47—22no—
176C4⋊Dic47—22no—
177C4⋊Dic47—22no—
178C4⋊Dic47—22no—
179Dic47⋊C4—44no—
180Dic47⋊C4—44no—
181#10625329—28no—
182C2×C47⋊C8—21no—
183C2×C47⋊C8—21no—
184C2×C47⋊C8C22×C412yes—
185C2×C47⋊C8C22×C412yes—
186C2×C47⋊C8C2×D412yes—
187C2×C47⋊C8C2×D412yes—
188#10625324—28no—
189#10625324—28no—
190C8×D47—28no—
191C8×D47C22⋊C4116yescomplemented
192C23×C47—21no—
193C23×C47—21no—
194C23×C47—22no—
195C23×C47—22no—
196C23×C47C2×C4⋊C412yes—
197C23×C47C22×D411yescharacteristic
198C22×D47—21no—
199C22×D47—21no—
200C22×D47—22no—
201C22×D47—22no—
202C22×D47—28no—
203C22×D47—216no—
204C22×D47—48no—
205C22×D47—44no—
206C22×D47—44no—
207C22×D47C2×C4⋊C412yes—
208C22×D47C2×C4⋊C412yes—
209C22×D47#12112yes—
210C22×D47#12112yes—
211C22×D47AGL(1,ℤ/8)14yes—
212C22×D47#13714yes—
213C2×C4×C47—21no—
214C2×C4×C47—21no—
215C2×C4×C47—22no—
216C2×C4×C47—22no—
217C2×C4×C47—22no—
218C2×C4×C47—22no—
219C2×C4×C47—42no—
220C2×C4×C47—42no—
221C2×C4×C47—42no—
222C2×C4×C47—42no—
223C2×C4×C47—42no—
224C2×C4×C47—42no—
225C2×C4×C47C2×C4⋊C412yes—
226C2×C4×C47C23×C411yescharacteristic
227C2×C4×C47C22×D411yescharacteristic
228C2×C4×C47C22×D411yescharacteristic
229C2×C4×C47C22×Q811yescharacteristic
230C2×C4×C47C2×#4111yescharacteristic
231C2×C4×C47C2×#4111yescharacteristic
232C2×Dic47—21no—
233C2×Dic47—21no—
234C2×Dic47—28no—
235C2×Dic47—42no—
236C2×Dic47—42no—
237C2×Dic47—42no—
238C2×Dic47—42no—
239C2×Dic47—42no—
240C2×Dic47—42no—
241C2×Dic47C2×C4⋊C412yes—
242C2×Dic47C2×C4⋊C412yes—
243C2×Dic47#12112yes—
244C2×Dic47#12112yes—
245C4×D47—28no—
246C4×D47—22no—
247C4×D47—22no—
248C4×D47—22no—
249C4×D47—22no—
250C4×D47—28no—
251C4×D47—88no—
252C4×D47—88no—
253C4×D47C2×C22⋊C414yes—
254C4×D47#11714yes—
255C4×D47C22⋊Q814yes—
256C4×D47C22⋊Q814yes—
257C8×C47—22no—
258C8×C47C2×C22⋊C414yescomplemented
259C47⋊C8—22no—
260C47⋊C8C2×C22⋊C414yescomplemented
261C2×#1809—471nomaximal, Sylow
262C22×C47—24no—
263C22×C47—22no—
264C22×C47—42no—
265C22×C47—41no—
266C22×C47—41no—
267C22×C47C22×C4⋊C411yescharacteristic
268C22×C47C2×#12111yescharacteristic
269C22×C47C2×#12111yescharacteristic
270C22×C47C2×AGL(1,ℤ/8)12yes—
271C22×C47C2×#13712yes—
272C2×D47—24no—
273C2×D47—22no—
274C2×D47—42no—
275C2×D47—41no—
276C2×D47—41no—
277C2×D47—416no—
278C2×D47#38014yes—
279C2×D47#42818yes—
280C2×D47#46818yes—
281C2×D47#46914yes—
282C2×D47#47014yes—
283C4×C47—22no—
284C4×C47—82no—
285C4×C47—82no—
286C4×C47C22×C22⋊C411yescharacteristic
287C4×C47C2×#11711yescharacteristic
288C4×C47C2×C22⋊Q811yescharacteristic
289C4×C47C2×C22⋊Q811yescharacteristic
290Dic47—22no—
291Dic47—82no—
292Dic47—82no—
293Dic47#38014yes—
294C23×M16—471no—
295C22×#107—471no—
296C22×#106—471no—
297C2×#380—472no—
298#1809—471no—
299#1809—471no—
300#1809—472no—
301#1809—472no—
302#1809—471no—
303#1809D4711yescharacteristic, direct product factor
304C2×#340—472no—
305C2×C47—42no—
306C2×C47C2×#38011yescharacteristic
307C2×C47C2×#42812yes—
308C2×C47C2×#46812yes—
309C2×C47C2×#46911yescharacteristic
310C2×C47C2×#47011yescharacteristic
311D47—42no—
312D47#180918yesdirect product factor
313C24×C4—471no—
314C22×M16—471no—
315C22×M16—478no—
316C22×M16—471no—
317C22×M16—471no—
318C22×M16—944no—
319C22×M16—944no—
320C22×M16C2×D4711yescharacteristic
321C23×C8—471no—
322C23×C8—471no—
323C22×C4⋊C4—472no—
324C22×C4⋊C4—472no—
325C22×C22⋊C4—942no—
326C2×#107—471no—
327C2×#107—472no—
328C2×#107—944no—
329C2×#107C2×D4711yescharacteristic, complemented
330C2×#106—471no—
331C2×#106—472no—
332C2×#106—944no—
333C2×#106C2×D4711yescharacteristic, complemented
334#380—472no—
335#380—472no—
336#380—472no—
337#380—942no—
338#380—942no—
339#380C2×D4712yes—
340C2×#95—942no—
341#340—472no—
342#340—472no—
343#340—472no—
344#340C2×D4712yescomplemented
345C47C2×#180911yescharacteristic, complemented, Sylow
346C25—471no—
347C23×C4—471no—
348C23×C4—471no—
349C23×C4—474no—
350C23×C4—471no—
351C23×C4—471no—
352C23×C4—474no—
353C23×C4—471no—
354C23×C4—942no—
355C23×C4—942no—
356C23×C4—942no—
357C23×C4—942no—
358C23×C4—942no—
359C23×C4—942no—
360C23×C4C22×D4711yescharacteristic
361C2×M16—22no—
362C2×M16—22no—
363C2×M16—474no—
364C2×M16—474no—
365C2×M16—474no—
366C2×M16—942no—
367C2×M16—942no—
368C2×M16—9432no—
369C2×M16—942no—
370C2×M16—942no—
371C2×M16—942no—
372C2×M16—942no—
373C2×M16C4×D4714yescomplemented
374C22×C8—471no—
375C22×C8—474no—
376C22×C8—474no—
377C22×C8—474no—
378C22×C8—471no—
379C22×C8—474no—
380C22×C8—942no—
381C22×C8—942no—
382C22×C8C22×D4711yescharacteristic
383C22×C8C22×D4711yescharacteristic
384C2×C4⋊C4—472no—
385C2×C4⋊C4—472no—
386C2×C4⋊C4—944no—
387C2×C4⋊C4—944no—
388C2×C4⋊C4—944no—
389C2×C4⋊C4—944no—
390C2×C4⋊C4—942no—
391C2×C4⋊C4—942no—
392C2×C4⋊C4C22×D4712yes—
393C2×C4⋊C4C22×D4712yes—
394C2×C22⋊C4—22no—
395C2×C22⋊C4—942no—
396C2×C22⋊C4—942no—
397C2×C22⋊C4—942no—
398C2×C22⋊C4—1888no—
399#107—22no—
400#107—944no—
401#107—942no—
402#106—22no—
403#106—944no—
404#106—942no—
405#95—22no—
406#95—942no—
407#95—942no—
408#95—942no—
409C24—471no—
410C24—474no—
411C24—471no—
412C24—944no—
413C24—942no—
414C24—942no—
415C24—944no—
416C24D4×D4711yescharacteristic
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—471no—
424C22×C4—472no—
425C22×C4—472no—
426C22×C4—472no—
427C22×C4—472no—
428C22×C4—472no—
429C22×C4—472no—
430C22×C4—474no—
431C22×C4—471no—
432C22×C4—474no—
433C22×C4—474no—
434C22×C4—472no—
435C22×C4—472no—
436C22×C4—948no—
437C22×C4—942no—
438C22×C4—942no—
439C22×C4—948no—
440C22×C4—948no—
441C22×C4—948no—
442C22×C4—942no—
443C22×C4—942no—
444C22×C4—942no—
445C22×C4—942no—
446C22×C4—941no—
447C22×C4—941no—
448C22×C4—941no—
449C22×C4—941no—
450C22×C4—942no—
451C22×C4—942no—
452C22×C4—1884no—
453C22×C4—1884no—
454C22×C4—1884no—
455C22×C4—1884no—
456C22×C4—1884no—
457C22×C4—1884no—
458C22×C4C2×C4×D4712yes—
459C22×C4D4×D4711yescharacteristic
460C22×C4Q8×D4712yes—
461C22×C4C23×D4711yescharacteristic
462M16—28no—
463M16—948no—
464M16—948no—
465M16—948no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—472no—
469C2×C8—472no—
470C2×C8—472no—
471C2×C8—4716no—
472C2×C8—472no—
473C2×C8—948no—
474C2×C8—941no—
475C2×C8—941no—
476C2×C8C2×C4×D4712yes—
477C2×C8C2×C4×D4712yes—
478C2×C8D4×D4712yes—
479C2×C8D4×D4712yes—
480C4⋊C4—22no—
481C4⋊C4—22no—
482C4⋊C4—22no—
483C4⋊C4—22no—
484C4⋊C4—942no—
485C4⋊C4—942no—
486C4⋊C4—942no—
487C4⋊C4—942no—
488C4⋊C4—1884no—
489C4⋊C4—1884no—
490C22⋊C4—44no—
491C22⋊C4—1884no—
492C22⋊C4—1884no—
493C22⋊C4—1884no—
494C23—21no—
495C23—21no—
496C23—22no—
497C23—22no—
498C23—472no—
499C23—472no—
500C23—472no—
501C23—474no—
502C23—474no—
503C23—472no—
504C23—948no—
505C23—9416no—
506C23—941no—
507C23—941no—
508C23—942no—
509C23—942no—
510C23—1888no—
511C23—1884no—
512C23—1884no—
513C23C4⋊C4×D4712yes—
514C23C2×D4×D4711yescharacteristic
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—22no—
518C2×C4—22no—
519C2×C4—22no—
520C2×C4—22no—
521C2×C4—42no—
522C2×C4—42no—
523C2×C4—42no—
524C2×C4—42no—
525C2×C4—42no—
526C2×C4—42no—
527C2×C4—472no—
528C2×C4—472no—
529C2×C4—472no—
530C2×C4—474no—
531C2×C4—474no—
532C2×C4—474no—
533C2×C4—474no—
534C2×C4—472no—
535C2×C4—948no—
536C2×C4—948no—
537C2×C4—948no—
538C2×C4—941no—
539C2×C4—941no—
540C2×C4—942no—
541C2×C4—942no—
542C2×C4—942no—
543C2×C4—942no—
544C2×C4—3768no—
545C2×C4—3768no—
546C2×C4—1882no—
547C2×C4—1882no—
548C2×C4—1882no—
549C2×C4—1882no—
550C2×C4—1882no—
551C2×C4—1882no—
552C2×C4C4⋊C4×D4712yes—
553C2×C4C22×C4×D4711yescharacteristic
554C2×C4C2×D4×D4711yescharacteristic
555C2×C4C2×D4×D4711yescharacteristic
556C2×C4C2×Q8×D4711yescharacteristic
557C2×C4#41×D4711yescharacteristic
558C2×C4#41×D4711yescharacteristic
559C8—22no—
560C8—474no—
561C8—942no—
562C8C22⋊C4×D4714yescomplemented
563C22—24no—
564C22—22no—
565C22—42no—
566C22—41no—
567C22—41no—
568C22—478no—
569C22—474no—
570C22—474no—
571C22—478no—
572C22—474no—
573C22—944no—
574C22—942no—
575C22—18816no—
576C22—1882no—
577C22—1881no—
578C22—1881no—
579C22C2×C4⋊C4×D4711yescharacteristic
580C22#121×D4711yescharacteristic
581C22#121×D4711yescharacteristic
582C22AGL(1,ℤ/8)×D4712yes—
583C22#137×D4712yes—
584C4—22no—
585C4—82no—
586C4—82no—
587C4—474no—
588C4—942no—
589C4—3762no—
590C4—3762no—
591C4C2×C22⋊C4×D4711yescharacteristic
592C4#117×D4711yescharacteristic
593C4C22⋊Q8×D4711yescharacteristic
594C4C22⋊Q8×D4711yescharacteristic
595C2—42no—
596C2—478no—
597C2—1882no—
598C2#380×D4711yescharacteristic
599C2#428×D4712yes—
600C2#468×D4712yes—
601C2#469×D4711yescharacteristic
602C2#470×D4711yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC47×#1809C2
socleC23×C47C22×D4
prime radicalC24×D47D4
cosocleC22×C4×C47C24
hypercenter#1809D47
hypocenterC47C2×#1809
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1809

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×#107×D47C2semidirect
3. C2×#106×D47C2semidirect
5. #20243422C2semidirect
6. #20243421C2semidirect
7. #20243420C2semidirect
8. #20243419C2semidirect
9. #20243418C2semidirect
10. #340×D47C2semidirect
11. C47×#1809C2semidirect
18. C2×M16×D47C4semidirect
24. C2×#13093958C22semidirect
25. C2×#13093957C22semidirect
27. C2×#13093956C22semidirect
28. C2×#13093955C22semidirect
36. #15688886C22semidirect
37. #15688885C22semidirect
38. #15688885C22semidirect
40. C2×#107×C47C22semidirect
41. C2×#106×C47C22semidirect
43. C47×#340C22semidirect
60. C2×#10625329C2×C4semidirect
65. C2×#10625324C2×C4semidirect
66. C2×#10625324C2×C4semidirect
98. C2×M16×C47C2×C4semidirect
191. C8×D47C22⋊C4semidirect
258. C8×C47C2×C22⋊C4semidirect
260. C47⋊C8C2×C22⋊C4semidirect
303. #1809D47direct (N × H)
312. D47#1809direct (N × H)
329. C2×#107C2×D47semidirect
333. C2×#106C2×D47semidirect
344. #340C2×D47semidirect
345. C47C2×#1809semidirect
373. C2×M16C4×D47semidirect
562. C8C22⋊C4×D47semidirect

Maximal subgroups

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

subgroupindex
C22×M16×D472
C2×#107×D472
C2×#106×D472
#380×D472
#202434222
#202434212
#202434202
#202434192
#202434182
#340×D472
C47×#18092
C2×#180947