Finite Group Databasebeta

← D47×#2537 #26388013

Subgroups — D47×#2537 #26388013

Order 12032.

4782 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#121×D47C214yesmaximal, complemented
2C2×C4×D4×D47C212yesmaximal, complemented
3#20248304C211yesmaximal, characteristic, complemented
4#20248303C214yesmaximal, complemented
5#20248302C214yesmaximal, complemented
6#20248301C212yesmaximal, complemented
7#20248300C214yesmaximal, complemented
8#394×D47C214yesmaximal, complemented
9#384×D47C211yesmaximal, characteristic, complemented
10#380×D47C214yesmaximal, complemented
11C47×#2537C211yesmaximal, characteristic, complemented
12C22×D4×D47C2214yes—
13C22×D4×D47C2212yes—
14C23×C4×D47C2214yes—
15C2×#13093999C2214yescomplemented
16C2×#13093998C2214yescomplemented
17C2×#13093997C2218yescomplemented
18C2×#13093996C2218yescomplemented
19C2×#13093995C2214yescomplemented
20#121×D47—232no—
21C2×C4×D188C2212yescomplemented
22C2×D4×Dic47C2212yescomplemented
23C2×#13093986C2212yescomplemented
24C2×C4×C22⋊D47C2214yescomplemented
25C2×(C22⋊D47)⋊C4C2214yescomplemented
26C4×D4×D47—216no—
27C2×C4⋊C4×D47C2214yes—
28C2×C4⋊C4×D47C2212yes—
29C2×C4⋊C4×D47C2212yes—
30C2×C22⋊C4×D47C2214yes—
31C2×C22⋊C4×D47C2218yes—
32C2×C42×D47C2211yescharacteristic
33#15689041C2214yescomplemented
34#15689040C2214yescomplemented
35#15689039C2218yescomplemented
36#15689038C2218yescomplemented
37#15689037C2214yescomplemented
38#15688993C2211yescharacteristic, complemented
39#15688992C2212yescomplemented
40#15688992C2214yescomplemented
41#15688983C2214yescomplemented
42#15688982C2218yescomplemented
43#15688981C2218yescomplemented
44#15688980C2214yescomplemented
45#15688980C2214yescomplemented
46#95×D47C2214yes—
47C2×#121×C47C2214yescomplemented
48C2×C4×D4×C47C2212yescomplemented
49C47×#394C2214yescomplemented
50C47×#384C2211yescharacteristic, complemented
51C47×#380C2214yescomplemented
52C24×D47C2314yes—
53C22×D188C2314yes—
54C22×D188C2312yes—
55C22×C22⋊D47C2318yes—
56C22×C22⋊D47C2314yes—
57C2×D4×D47—232no—
58C2×D4×D47—28no—
59C2×D4×D47—28no—
60C2×D4×D47—48no—
61C2×D4×D47D4116yescomplemented
62C23×Dic47C2314yes—
63C22×C4×D47—216no—
64C22×C4×D47—216no—
65C22×C4×D47—216no—
66C22×C4×D47C2314yes—
67C22×C4×D47C2314yes—
68C22×C4×D47C2314yes—
69C22×C4×D47C2314yes—
70C22×C4×D47C2311yescharacteristic
71C22×C4×D47C2312yes—
72#13093999—216no—
73#13093998—216no—
74#13093997—232no—
75#13093996—232no—
76#13093995—216no—
77C4×D188—28no—
78D4×Dic47—28no—
79#13093986—28no—
80C4×C22⋊D47—216no—
81(C22⋊D47)⋊C4—216no—
82C2×C4⋊Dic47C2312yes—
83C2×C4⋊Dic47C2314yes—
84C2×C4⋊Dic47C2312yes—
85C2×Dic47⋊C4C2314yes—
86C2×Dic47⋊C4C2318yes—
87C2×Dic47⋊C4C2314yes—
88C4⋊C4×D47—28no—
89C4⋊C4×D47—216no—
90C4⋊C4×D47—44no—
91C2×C22⋊Dic47C2318yes—
92C2×C22⋊Dic47C2314yes—
93C2×(C2×D47)⋊C4C2318yes—
94C2×(C2×D47)⋊C4C2318yes—
95C2×(C2×D47)⋊C4C2314yes—
96C2×(C2×D47)⋊C4C2314yes—
97C22⋊C4×D47—232no—
98C22⋊C4×D47—216no—
99C2×C4×Dic47C2311yescharacteristic
100C2×C4×Dic47C2312yes—
101C42×D47D418yescomplemented
102C47⋊#95C2314yes—
103C47⋊#95C2318yes—
104C22×D4×C47C2314yes—
105C22×D4×C47C2312yes—
106C23×C4×C47C2314yes—
107#121×C47—216no—
108C4×D4×C47—28no—
109C2×C4⋊C4×C47C2312yes—
110C2×C4⋊C4×C47C2314yes—
111C2×C4⋊C4×C47C2312yes—
112C2×C22⋊C4×C47C2318yes—
113C2×C22⋊C4×C47C2314yes—
114C2×C42×C47C2311yescharacteristic
115#95×C47C2314yes—
116C24×C47C2414yes—
117C23×D47—28no—
118C23×D47—28no—
119C23×D47—28no—
120C23×D47—28no—
121C23×D47—28no—
122C23×D47—28no—
123C23×D47C2×D4116yes—
124C23×D47C2414yes—
125C23×D47C2411yescharacteristic
126C2×D4×C47—216no—
127C2×D4×C47—24no—
128C2×D4×C47—24no—
129C2×D4×C47—44no—
130C2×D4×C47C2×D418yescomplemented
131C22×C4×C47—28no—
132C22×C4×C47—28no—
133C22×C4×C47—28no—
134C22×C4×C47C2414yes—
135C22×C4×C47C2414yes—
136C22×C4×C47C2411yescharacteristic
137C22×C4×C47C2412yes—
138C2×C22⋊D47—216no—
139C2×C22⋊D47—216no—
140C2×C22⋊D47—28no—
141C2×C22⋊D47—28no—
142C2×C22⋊D47—48no—
143C2×C22⋊D47C2×D4116yescomplemented
144C22×Dic47—28no—
145C22×Dic47—28no—
146C22×Dic47—28no—
147C22×Dic47C2414yes—
148C22×Dic47C2414yes—
149C22×Dic47C2411yescharacteristic
150C22×Dic47C2412yes—
151D4×D47—264no—
152D4×D47—464no—
153C2×D188—24no—
154C2×D188—24no—
155C2×D188—216no—
156C2×D188—44no—
157C2×D188C2×D418yescomplemented
158C2×C4×D47—22no—
159C2×C4×D47—22no—
160C2×C4×D47—28no—
161C2×C4×D47—28no—
162C2×C4×D47—216no—
163C2×C4×D47—28no—
164C2×C4×D47—28no—
165C2×C4×D47—28no—
166C2×C4×D47—28no—
167C2×C4×D47—28no—
168C2×C4×D47—28no—
169C2×C4×D47—28no—
170C2×C4×D47—28no—
171C2×C4×D47—464no—
172C2×C4×D47C2×D414yes—
173C2×C4×D47C2×D418yes—
174C2×C4×D47C2×D418yes—
175C2×C4×D47#4118yes—
176C4⋊C4×C47—24no—
177C4⋊C4×C47—28no—
178C4⋊C4×C47—42no—
179C22⋊C4×C47—216no—
180C22⋊C4×C47—28no—
181C42×C47C2×D414yescomplemented
182C22⋊Dic47—216no—
183C22⋊Dic47—28no—
184(C2×D47)⋊C4—216no—
185(C2×D47)⋊C4—216no—
186(C2×D47)⋊C4—28no—
187(C2×D47)⋊C4—28no—
188C4⋊Dic47—24no—
189C4⋊Dic47—28no—
190C4⋊Dic47—42no—
191Dic47⋊C4—28no—
192Dic47⋊C4—216no—
193Dic47⋊C4—44no—
194C4×Dic47C2×D414yescomplemented
195C4×Dic47C2×D418yescomplemented
196C23×C47—24no—
197C23×C47—24no—
198C23×C47—24no—
199C23×C47—24no—
200C23×C47—24no—
201C23×C47—24no—
202C23×C47C22×D418yes—
203C23×C47C2511yescharacteristic
204C22×D47—24no—
205C22×D47—24no—
206C22×D47—24no—
207C22×D47—24no—
208C22×D47—24no—
209C22×D47—24no—
210C22×D47—232no—
211C22×D47—232no—
212C22×D47—232no—
213C22×D47—416no—
214C22×D47—416no—
215C22×D47—416no—
216C22×D47—416no—
217C22×D47C22×D418yes—
218C22×D47C22×D412yes—
219C22×D47C22×D414yes—
220C22×D47C2×#4114yes—
221C22×D47H(5,𝔽2)12yes—
222C22×D472−1+412yes—
223D4×C47—216no—
224D4×C47—416no—
225C2×C4×C47—21no—
226C2×C4×C47—21no—
227C2×C4×C47—24no—
228C2×C4×C47—28no—
229C2×C4×C47—24no—
230C2×C4×C47—24no—
231C2×C4×C47—24no—
232C2×C4×C47—416no—
233C2×C4×C47C22×D412yes—
234C2×C4×C47C22×D414yes—
235C2×C4×C47C22×D414yes—
236C2×C4×C47C2×#4114yes—
237C22⋊D47—232no—
238C22⋊D47—432no—
239C2×Dic47—21no—
240C2×Dic47—21no—
241C2×Dic47—24no—
242C2×Dic47—28no—
243C2×Dic47—24no—
244C2×Dic47—24no—
245C2×Dic47—24no—
246C2×Dic47—416no—
247C2×Dic47C22×D412yes—
248C2×Dic47C22×D414yes—
249C2×Dic47C22×D414yes—
250C2×Dic47C2×#4114yes—
251D188—216no—
252D188—416no—
253C4×D47—28no—
254C4×D47—416no—
255C4×D47—416no—
256C4×D47—416no—
257C4×D47—416no—
258C4×D47#121132yescomplemented
259C2×#2537—471nomaximal, Sylow
260C22×C47—28no—
261C22×C47—28no—
262C22×C47—28no—
263C22×C47—44no—
264C22×C47—44no—
265C22×C47—44no—
266C22×C47—44no—
267C22×C47C23×D411yescharacteristic
268C22×C47C23×D412yes—
269C22×C47C22×#4112yes—
270C22×C47C2×H(5,𝔽2)11yescharacteristic
271C22×C47C2×2−1+411yescharacteristic
272C2×D47—28no—
273C2×D47—28no—
274C2×D47—28no—
275C2×D47—44no—
276C2×D47—44no—
277C2×D47—44no—
278C2×D47—44no—
279C2×D47—464no—
280C2×D47C2×#12118yes—
281C2×D47#53714yes—
282C2×D47D4214yes—
283C2×D47#54718yes—
284C2×D47#55514yes—
285C4×C47—22no—
286C4×C47—44no—
287C4×C47—44no—
288C4×C47C2×#12118yescomplemented
289Dic47—22no—
290Dic47—44no—
291Dic47—44no—
292Dic47C2×#12118yescomplemented
293C22×#121—474no—
294C22×C4×D4—472no—
295#2537—474no—
296#2537—471no—
297#2537—474no—
298#2537—474no—
299#2537—472no—
300#2537D4711yescharacteristic, direct product factor
301C2×#394—474no—
302C2×#384—471no—
303C2×#380—474no—
304C2×C47—48no—
305C2×C47C22×#12112yes—
306C2×C47C2×#53711yescharacteristic
307C2×C47C2×D4211yescharacteristic
308C2×C47C2×#54712yes—
309C2×C47C2×#55511yescharacteristic
310D47—48no—
311D47#253718yesdirect product factor
312C23×D4—472no—
313C23×D4—474no—
314C24×C4—474no—
315C2×#121—474no—
316C2×#121—478no—
317C2×#121—474no—
318C2×#121—474no—
319C2×#121—478no—
320C2×#121—9432no—
321C2×#121C2×D4714yescomplemented
322C2×C4×D4—472no—
323C2×C4×D4—474no—
324C2×C4×D4—472no—
325C2×C4×D4—474no—
326C2×C4×D4—472no—
327C2×C4×D4—9416no—
328C2×C4×D4C2×D4712yescomplemented
329C22×C4⋊C4—472no—
330C22×C4⋊C4—474no—
331C22×C4⋊C4—472no—
332C22×C22⋊C4—474no—
333C22×C22⋊C4—478no—
334C22×C42—471no—
335#394—474no—
336#394—474no—
337#394—478no—
338#394—478no—
339#394—474no—
340#394C2×D4714yescomplemented
341#384—472no—
342#384—474no—
343#384—471no—
344#384C2×D4711yescharacteristic, complemented
345#380—474no—
346#380—474no—
347#380—474no—
348#380—478no—
349#380—478no—
350#380C2×D4714yescomplemented
351C2×#95—474no—
352C47C2×#253711yescharacteristic, complemented, Sylow
353C25—474no—
354C22×D4—474no—
355C22×D4—4716no—
356C22×D4—478no—
357C22×D4—472no—
358C22×D4—474no—
359C22×D4—948no—
360C22×D4—948no—
361C22×D4—9432no—
362C22×D4—1888no—
363C22×D4C22×D4714yes—
364C22×D4C22×D4712yes—
365C23×C4—472no—
366C23×C4—471no—
367C23×C4—474no—
368C23×C4—474no—
369C23×C4—474no—
370C23×C4—474no—
371C23×C4—474no—
372C23×C4—9416no—
373C23×C4—9416no—
374C23×C4—9416no—
375C23×C4C22×D4714yes—
376#121—216no—
377#121—9432no—
378#121—9416no—
379#121—9416no—
380#121—9432no—
381#121—9416no—
382C4×D4—28no—
383C4×D4—9416no—
384C4×D4—948no—
385C4×D4—9416no—
386C4×D4—948no—
387C4×D4—948no—
388C2×C4⋊C4—474no—
389C2×C4⋊C4—472no—
390C2×C4⋊C4—478no—
391C2×C4⋊C4—474no—
392C2×C4⋊C4—474no—
393C2×C4⋊C4—472no—
394C2×C4⋊C4—948no—
395C2×C4⋊C4—9416no—
396C2×C4⋊C4—1884no—
397C2×C4⋊C4C22×D4712yes—
398C2×C4⋊C4C22×D4714yes—
399C2×C4⋊C4C22×D4712yes—
400C2×C22⋊C4—474no—
401C2×C22⋊C4—478no—
402C2×C22⋊C4—474no—
403C2×C22⋊C4—474no—
404C2×C22⋊C4—478no—
405C2×C22⋊C4—478no—
406C2×C22⋊C4—9416no—
407C2×C22⋊C4—9432no—
408C2×C22⋊C4C22×D4714yes—
409C2×C22⋊C4C22×D4718yes—
410C2×C42—471no—
411C2×C42—472no—
412C2×C42—478no—
413C2×C42C22×D4711yescharacteristic
414#95—474no—
415#95—478no—
416#95C22×D4714yes—
417C24—471no—
418C24—4716no—
419C24—474no—
420C24—948no—
421C24—948no—
422C24—948no—
423C24—948no—
424C24—948no—
425C24—948no—
426C24C23×D4714yes—
427C2×D4—216no—
428C2×D4—24no—
429C2×D4—24no—
430C2×D4—44no—
431C2×D4—4716no—
432C2×D4—478no—
433C2×D4—9416no—
434C2×D4—9464no—
435C2×D4—948no—
436C2×D4—948no—
437C2×D4—9416no—
438C2×D4—9416no—
439C2×D4—944no—
440C2×D4—944no—
441C2×D4—1884no—
442C2×D4—1888no—
443C2×D4—18864no—
444C2×D4D4×D4718yescomplemented
445C22×C4—28no—
446C22×C4—28no—
447C22×C4—28no—
448C22×C4—472no—
449C22×C4—478no—
450C22×C4—478no—
451C22×C4—478no—
452C22×C4—471no—
453C22×C4—474no—
454C22×C4—474no—
455C22×C4—474no—
456C22×C4—948no—
457C22×C4—948no—
458C22×C4—948no—
459C22×C4—942no—
460C22×C4—942no—
461C22×C4—948no—
462C22×C4—948no—
463C22×C4—9416no—
464C22×C4—948no—
465C22×C4—948no—
466C22×C4—948no—
467C22×C4—948no—
468C22×C4—948no—
469C22×C4—948no—
470C22×C4—948no—
471C22×C4—948no—
472C22×C4—18864no—
473C22×C4C23×D4714yes—
474C22×C4C23×D4714yes—
475C22×C4C23×D4711yescharacteristic
476C22×C4C23×D4712yes—
477C4⋊C4—24no—
478C4⋊C4—28no—
479C4⋊C4—42no—
480C4⋊C4—948no—
481C4⋊C4—9416no—
482C4⋊C4—944no—
483C4⋊C4—948no—
484C4⋊C4—1884no—
485C4⋊C4—1882no—
486C22⋊C4—216no—
487C22⋊C4—28no—
488C22⋊C4—948no—
489C22⋊C4—9416no—
490C22⋊C4—9416no—
491C22⋊C4—948no—
492C22⋊C4—9416no—
493C22⋊C4—948no—
494C42—474no—
495C42—478no—
496C42D4×D4714yescomplemented
497C23—24no—
498C23—24no—
499C23—24no—
500C23—24no—
501C23—24no—
502C23—24no—
503C23—472no—
504C23—474no—
505C23—474no—
506C23—472no—
507C23—472no—
508C23—478no—
509C23—9432no—
510C23—9432no—
511C23—9432no—
512C23—944no—
513C23—944no—
514C23—944no—
515C23—944no—
516C23—944no—
517C23—944no—
518C23—18816no—
519C23—18816no—
520C23—18816no—
521C23—18816no—
522C23C2×D4×D4718yes—
523C23C24×D4711yescharacteristic
524D4—216no—
525D4—416no—
526D4—9432no—
527D4—9416no—
528D4—18816no—
529D4—18832no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—24no—
533C2×C4—24no—
534C2×C4—28no—
535C2×C4—24no—
536C2×C4—24no—
537C2×C4—416no—
538C2×C4—474no—
539C2×C4—474no—
540C2×C4—474no—
541C2×C4—4732no—
542C2×C4—472no—
543C2×C4—948no—
544C2×C4—941no—
545C2×C4—941no—
546C2×C4—944no—
547C2×C4—944no—
548C2×C4—948no—
549C2×C4—944no—
550C2×C4—944no—
551C2×C4—18816no—
552C2×C4—18816no—
553C2×C4—18816no—
554C2×C4—18816no—
555C2×C4—18816no—
556C2×C4C2×D4×D4712yes—
557C2×C4C2×D4×D4714yes—
558C2×C4C2×D4×D4714yes—
559C2×C4#41×D4714yes—
560C22—28no—
561C22—28no—
562C22—28no—
563C22—44no—
564C22—44no—
565C22—44no—
566C22—44no—
567C22—474no—
568C22—478no—
569C22—478no—
570C22—474no—
571C22—474no—
572C22—948no—
573C22—948no—
574C22—948no—
575C22—18864no—
576C22—1884no—
577C22—1884no—
578C22—1884no—
579C22—1884no—
580C22C22×D4×D4712yes—
581C22C22×D4×D4711yescharacteristic
582C22C2×#41×D4712yes—
583C22H(5,𝔽2)×D4711yescharacteristic
584C222−1+4×D4711yescharacteristic
585C4—22no—
586C4—44no—
587C4—44no—
588C4—478no—
589C4—942no—
590C4—1884no—
591C4—1884no—
592C4#121×D4718yescomplemented
593C2—48no—
594C2—478no—
595C2—1888no—
596C2C2×#121×D4712yes—
597C2#537×D4711yescharacteristic
598C2D42×D4711yescharacteristic
599C2#547×D4712yes—
600C2#555×D4711yescharacteristic
subgroupG/H
center, FrattiniC23C24×D47
commutator, socle, cosocleC23×C47C25
FittingC47×#2537C2
hypercenter#2537D47
hypocenterC47C2×#2537
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #2537

Complements

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

NH ≅ G/Ntype
1. C2×#121×D47C2semidirect
2. C2×C4×D4×D47C2semidirect
3. #20248304C2semidirect
4. #20248303C2semidirect
5. #20248302C2semidirect
6. #20248301C2semidirect
7. #20248300C2semidirect
8. #394×D47C2semidirect
9. #384×D47C2semidirect
10. #380×D47C2semidirect
11. C47×#2537C2semidirect
15. C2×#13093999C22semidirect
16. C2×#13093998C22semidirect
17. C2×#13093997C22semidirect
18. C2×#13093996C22semidirect
19. C2×#13093995C22semidirect
21. C2×C4×D188C22semidirect
22. C2×D4×Dic47C22semidirect
23. C2×#13093986C22semidirect
24. C2×C4×C22⋊D47C22semidirect
25. C2×(C22⋊D47)⋊C4C22semidirect
33. #15689041C22semidirect
34. #15689040C22semidirect
35. #15689039C22semidirect
36. #15689038C22semidirect
37. #15689037C22semidirect
38. #15688993C22semidirect
39. #15688992C22semidirect
40. #15688992C22semidirect
41. #15688983C22semidirect
42. #15688982C22semidirect
43. #15688981C22semidirect
44. #15688980C22semidirect
45. #15688980C22semidirect
47. C2×#121×C47C22semidirect
48. C2×C4×D4×C47C22semidirect
49. C47×#394C22semidirect
50. C47×#384C22semidirect
51. C47×#380C22semidirect
61. C2×D4×D47D4semidirect
101. C42×D47D4semidirect
130. C2×D4×C47C2×D4semidirect
143. C2×C22⋊D47C2×D4semidirect
157. C2×D188C2×D4semidirect
181. C42×C47C2×D4semidirect
194. C4×Dic47C2×D4semidirect
195. C4×Dic47C2×D4semidirect
258. C4×D47#121semidirect
288. C4×C47C2×#121semidirect
292. Dic47C2×#121semidirect
300. #2537D47direct (N × H)
311. D47#2537direct (N × H)
321. C2×#121C2×D47semidirect
328. C2×C4×D4C2×D47semidirect
340. #394C2×D47semidirect
344. #384C2×D47semidirect
350. #380C2×D47semidirect
352. C47C2×#2537semidirect
444. C2×D4D4×D47semidirect
496. C42D4×D47semidirect
592. C4#121×D47semidirect

Maximal subgroups

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

subgroupindex
C2×#121×D472
C2×C4×D4×D472
#202483042
#202483032
#202483022
#202483012
#202483002
#394×D472
#384×D472
#380×D472
C47×#25372
C2×#253747