Finite Group Databasebeta

← #26389469

Subgroups — #26389469

Order 12032.

2042 conjugacy classes of subgroups.

The subgroup lattice has 598 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20251698C211yesmaximal, characteristic, complemented
2#20251696C212yesmaximal, complemented
3#20249360C214yesmaximal, complemented
4#20248611C214yesmaximal, complemented
5#20248610C214yesmaximal, complemented
6#20247115C212yesmaximal, complemented
7#20247114C212yesmaximal, complemented
8#20247110C212yesmaximal, complemented
9#20247108C212yesmaximal, complemented
10#20245999C214yesmaximal
11#380×D47C212yesmaximal
12C2×C4×(C2×D47)⋊C4C211yesmaximal, characteristic
13C47×#2851C211yesmaximal, characteristic, complemented
14C23×C4×D47C2211yescharacteristic
15C2×#13094016C2211yescharacteristic, complemented
16C2×#13094015C2212yescomplemented
17C2×C4⋊C4×D47C2212yes—
18C2×C4⋊C4×D47C2212yes—
19C22×(C2×D47)⋊C4C2212yes—
20C2×C22⋊C4×D47C2214yes—
21C22×C4×Dic47C2211yescharacteristic
22#15689064C2214yescomplemented
23#15689064C2214yescomplemented
24#15689063C2214yescomplemented
25#15689061C2214yescomplemented
26#15689057C2214yescomplemented
27#15689056C2214yescomplemented
28#15689054C2214yescomplemented
29#15689053C2214yescomplemented
30#15689022C2212yescomplemented
31#15689021C2212yescomplemented
32#15689019C2212yescomplemented
33#15689010C2214yescomplemented
34#15689007C2214yescomplemented
35#15689006C2214yescomplemented
36#15688998C2214yes—
37#15688997C2214yes—
38#15688997C2214yes—
39#15688996C2214yes—
40#15688995C2214yes—
41#15688994C2214yes—
42#15688994C2214yes—
43#15688989C2211yescharacteristic, complemented
44#15688988C2212yescomplemented
45#15688983C2212yes—
46#15688982C2214yes—
47#15688982C2214yes—
48#15688982C2214yes—
49#15688981C2214yes—
50#15688980C2214yes—
51#15688980C2214yes—
52#15688980C2212yes—
53#15688980C2212yes—
54C4×(C2×D47)⋊C4C2212yes—
55C4×(C2×D47)⋊C4C2212yes—
56C4×(C2×D47)⋊C4C2212yes—
57C4×(C2×D47)⋊C4C2212yes—
58C2×C47⋊#95C2212yes—
59#95×D47C2214yes—
60C2×#125×C47C2211yescharacteristic, complemented
61C22×C42×C47C2211yescharacteristic
62C47×#389C2212yescomplemented
63C47×#387C2214yescomplemented
64C47×#385C2214yes—
65C47×#382C2211yescharacteristic, complemented
66C47×#380C2212yes—
67C24×D47C2311yescharacteristic
68C23×Dic47C2312yes—
69C23×Dic47C2311yescharacteristic
70C22×C4×D47—42no—
71C22×C4×D47—42no—
72C22×C4×D47Q818yes—
73C22×C4×D47C2312yes—
74C22×C4×D47C2314yes—
75C22×C4×D47C2314yes—
76C22×C4×D47C2312yes—
77#13094016—42no—
78#13094015—44no—
79C2×C4⋊Dic47C2312yes—
80C2×C4⋊Dic47C2312yes—
81C2×C4⋊Dic47C2314yes—
82C2×C4⋊Dic47C2314yes—
83C2×Dic47⋊C4C2314yes—
84C2×Dic47⋊C4C2314yes—
85C2×Dic47⋊C4C2314yes—
86C2×Dic47⋊C4C2314yes—
87C2×Dic47⋊C4C2314yes—
88C2×Dic47⋊C4C2314yes—
89C4⋊C4×D47—44no—
90C4⋊C4×D47—44no—
91C2×C22⋊Dic47C2314yes—
92C2×(C2×D47)⋊C4—28no—
93C2×(C2×D47)⋊C4C2312yes—
94C2×(C2×D47)⋊C4C2312yes—
95C2×(C2×D47)⋊C4C2312yes—
96C2×(C2×D47)⋊C4C2312yes—
97C2×(C2×D47)⋊C4C2314yes—
98C2×(C2×D47)⋊C4C2314yes—
99C22⋊C4×D47—216no—
100C2×C4×Dic47—42no—
101C2×C4×Dic47C2312yes—
102C2×C4×Dic47C2311yescharacteristic
103C2×C4×Dic47C2311yescharacteristic
104C47⋊#95C2314yes—
105C47⋊#95C2314yes—
106C47⋊#95C2314yes—
107C47⋊#95C2312yes—
108C47⋊#95C2312yes—
109C47⋊#95C2312yes—
110C47⋊#95C2312yes—
111C47⋊#95C2314yes—
112C47⋊#95C2314yes—
113C47⋊#95C2314yes—
114C47⋊#95C2314yes—
115C47⋊#95C2314yes—
116C47⋊#95C2314yes—
117C23×C4×C47C2311yescharacteristic
118C23×C4×C47C2312yes—
119#125×C47—42no—
120C2×C4⋊C4×C47C2312yes—
121C2×C4⋊C4×C47C2312yes—
122C2×C4⋊C4×C47C2314yes—
123C2×C4⋊C4×C47C2314yes—
124C2×C22⋊C4×C47C2314yes—
125C2×C42×C47—42no—
126C2×C42×C47C2311yescharacteristic
127C2×C42×C47C2311yescharacteristic
128C2×C42×C47C2312yes—
129#95×C47C2314yes—
130#95×C47C2314yes—
131#95×C47C2314yes—
132C24×C47C2411yescharacteristic
133C23×D47—41no—
134C23×D47—41no—
135C23×D47—42no—
136C23×D47C2×Q814yes—
137C23×D47#4118yes—
138C23×D47C2412yes—
139C22×C4×C47—22no—
140C22×C4×C47—22no—
141C22×C4×C47—24no—
142C22×C4×C47—42no—
143C22×C4×C47—42no—
144C22×C4×C47C2×Q814yes—
145C22×C4×C47C2412yes—
146C22×C4×C47C2412yes—
147C22×C4×C47C2414yes—
148C22×C4×C47C2414yes—
149C22×C4×C47C2411yescharacteristic
150C22×C4×C47C2411yescharacteristic
151C22×Dic47—24no—
152C22×Dic47—42no—
153C22×Dic47—41no—
154C22×Dic47—41no—
155C22×Dic47—42no—
156C22×Dic47C2×Q814yes—
157C22×Dic47C2412yes—
158C22×Dic47C2412yes—
159C22×Dic47C2414yes—
160C22×Dic47C2414yes—
161C22×Dic47C2412yes—
162C2×C4×D47—24no—
163C2×C4×D47—24no—
164C2×C4×D47—28no—
165C2×C4×D47—28no—
166C2×C4×D47—416no—
167C2×C4×D47—42no—
168C2×C4×D47—42no—
169C2×C4×D47—44no—
170C2×C4×D47—44no—
171C2×C4×D47—44no—
172C2×C4×D47—44no—
173C2×C4×D47C2×Q818yes—
174C2×C4×D47C2×Q818yes—
175C4⋊C4×C47—24no—
176C4⋊C4×C47—24no—
177C4⋊C4×C47—44no—
178C4⋊C4×C47—44no—
179C22⋊C4×C47—28no—
180C42×C47—22no—
181C42×C47—22no—
182C42×C47—42no—
183C22⋊Dic47—28no—
184(C2×D47)⋊C4—28no—
185(C2×D47)⋊C4—28no—
186(C2×D47)⋊C4—24no—
187(C2×D47)⋊C4—24no—
188(C2×D47)⋊C4—24no—
189(C2×D47)⋊C4—24no—
190C4⋊Dic47—24no—
191C4⋊Dic47—24no—
192C4⋊Dic47—44no—
193C4⋊Dic47—44no—
194Dic47⋊C4—44no—
195Dic47⋊C4—44no—
196Dic47⋊C4—44no—
197Dic47⋊C4—44no—
198Dic47⋊C4—44no—
199Dic47⋊C4—44no—
200C4×Dic47—24no—
201C4×Dic47—41no—
202C4×Dic47—41no—
203C23×C47—21no—
204C23×C47—21no—
205C23×C47—22no—
206C23×C47C22×Q812yes—
207C23×C47C2×#4114yes—
208C23×C47C2511yescharacteristic
209C22×D47—22no—
210C22×D47—22no—
211C22×D47—22no—
212C22×D47—22no—
213C22×D47—44no—
214C22×D47—44no—
215C22×D47—48no—
216C22×D47—48no—
217C22×D47#125116yescomplemented
218C22×D47C22×Q814yes—
219C22×D47C2×#4114yes—
220C22×D47C2×#4114yes—
221C2×C4×C47—21no—
222C2×C4×C47—21no—
223C2×C4×C47—28no—
224C2×C4×C47—22no—
225C2×C4×C47—22no—
226C2×C4×C47—24no—
227C2×C4×C47—24no—
228C2×C4×C47—24no—
229C2×C4×C47—22no—
230C2×C4×C47—24no—
231C2×C4×C47—22no—
232C2×C4×C47—22no—
233C2×C4×C47—24no—
234C2×C4×C47—24no—
235C2×C4×C47—22no—
236C2×C4×C47—48no—
237C2×C4×C47C22×Q812yes—
238C2×C4×C47C22×Q812yes—
239C2×C4×C47H(5,𝔽2)12yes—
240C2×C4×C47H(5,𝔽2)12yes—
241C2×Dic47—22no—
242C2×Dic47—22no—
243C2×Dic47—22no—
244C2×Dic47—22no—
245C2×Dic47—24no—
246C2×Dic47—24no—
247C2×Dic47—22no—
248C2×Dic47—22no—
249C2×Dic47—24no—
250C2×Dic47—24no—
251C2×Dic47—24no—
252C2×Dic47—22no—
253C2×Dic47—24no—
254C2×Dic47—22no—
255C2×Dic47—44no—
256C2×Dic47—48no—
257C2×Dic47C22×Q814yes—
258C4×D47—216no—
259C4×D47—48no—
260C4×D47—88no—
261C4×D47—88no—
262#35020—471nomaximal, Sylow
263C22×C47—22no—
264C22×C47—22no—
265C22×C47—24no—
266C22×C47—24no—
267C22×C47C2×#12514yes—
268C22×C47C23×Q811yescharacteristic
269C22×C47C22×#4112yes—
270C22×C47C2×H(5,𝔽2)11yescharacteristic
271C22×C47C2×H(5,𝔽2)11yescharacteristic
272C22×C47#58512yes—
273C2×D47—24no—
274C2×D47—24no—
275C2×D47—24no—
276C2×D47—24no—
277C2×D47—24no—
278C2×D47—24no—
279C2×D47—416no—
280C2×D47C2×#12518yes—
281C4×C47—22no—
282C4×C47—44no—
283C4×C47—44no—
284C4×C47—42no—
285C4×C47—42no—
286C4×C47#54314yes—
287Dic47—24no—
288Dic47—44no—
289Dic47—44no—
290Dic47—42no—
291Dic47—42no—
292#2851—471no—
293#2851—472no—
294#2851D4711yescharacteristic, complemented
295#2646—474no—
296#2569—474no—
297#2569—474no—
298#2442—472no—
299#2442—472no—
300#2442—472no—
301#2442—472no—
302#2315—474no—
303C2×#380—472no—
304C2×C4×C22⋊C4—471no—
305C2×C47—24no—
306C2×C47C22×#12511yescharacteristic
307C2×C47C2×#54311yescharacteristic
308C2×C47#345811yescharacteristic
309C2×C47#350512yes—
310C2×C47#350512yes—
311D47—28no—
312C24×C4—471no—
313C2×#125—472no—
314C2×#125—471no—
315C2×#125C2×D4711yescharacteristic, complemented
316C22×C4⋊C4—472no—
317C22×C4⋊C4—472no—
318C22×C22⋊C4—472no—
319C22×C22⋊C4—474no—
320C22×C42—471no—
321C22×C42C2×D4711yescharacteristic
322#400—474no—
323#400—474no—
324#400—474no—
325#400—474no—
326#398—474no—
327#398—474no—
328#398—474no—
329#398—474no—
330#389—472no—
331#389—472no—
332#389—472no—
333#389C2×D4712yescomplemented
334#387—474no—
335#387—474no—
336#387—474no—
337#387C2×D4714yescomplemented
338#385—474no—
339#385—474no—
340#385—474no—
341#385—474no—
342#385—474no—
343#385—474no—
344#385—474no—
345#385C2×D4714yes—
346#382—472no—
347#382—471no—
348#382C2×D4711yescharacteristic, complemented
349#380—472no—
350#380—474no—
351#380—474no—
352#380—472no—
353#380—472no—
354#380—474no—
355#380—474no—
356#380—474no—
357#380—474no—
358#380C2×D4712yes—
359C4×C22⋊C4—472no—
360C4×C22⋊C4—472no—
361C4×C22⋊C4—472no—
362C4×C22⋊C4—472no—
363C2×#95—472no—
364C2×#95—474no—
365C47#3502011yescharacteristic, complemented, Sylow
366C25—471no—
367C23×C4—471no—
368C23×C4—472no—
369C23×C4—478no—
370C23×C4—472no—
371C23×C4—472no—
372C23×C4—474no—
373C23×C4—474no—
374C23×C4—1882no—
375C23×C4—1882no—
376C23×C4C22×D4711yescharacteristic
377C23×C4C22×D4712yes—
378#125—42no—
379#125—1882no—
380#125—1884no—
381C2×C4⋊C4—472no—
382C2×C4⋊C4—472no—
383C2×C4⋊C4—474no—
384C2×C4⋊C4—474no—
385C2×C4⋊C4—474no—
386C2×C4⋊C4—474no—
387C2×C4⋊C4—474no—
388C2×C4⋊C4—474no—
389C2×C4⋊C4—474no—
390C2×C4⋊C4—474no—
391C2×C4⋊C4—1884no—
392C2×C4⋊C4—1884no—
393C2×C4⋊C4C22×D4712yes—
394C2×C4⋊C4C22×D4712yes—
395C2×C4⋊C4C22×D4714yes—
396C2×C4⋊C4C22×D4714yes—
397C2×C22⋊C4—474no—
398C2×C22⋊C4—472no—
399C2×C22⋊C4—472no—
400C2×C22⋊C4—472no—
401C2×C22⋊C4—472no—
402C2×C22⋊C4—474no—
403C2×C22⋊C4—474no—
404C2×C22⋊C4—9416no—
405C2×C22⋊C4—948no—
406C2×C22⋊C4C22×D4714yes—
407C2×C42—42no—
408C2×C42—472no—
409C2×C42—471no—
410C2×C42—471no—
411C2×C42—1882no—
412C2×C42C22×D4711yescharacteristic
413C2×C42C22×D4711yescharacteristic
414C2×C42C22×D4712yes—
415#95—472no—
416#95—472no—
417#95—472no—
418#95—472no—
419#95—474no—
420#95—474no—
421#95—474no—
422#95—474no—
423#95—474no—
424#95—474no—
425#95—474no—
426#95—474no—
427#95—474no—
428#95C22×D4714yes—
429#95C22×D4714yes—
430#95C22×D4714yes—
431C24—472no—
432C24—474no—
433C24—478no—
434C24—1881no—
435C24—1881no—
436C24—1882no—
437C24C23×D4711yescharacteristic
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—24no—
441C22×C4—42no—
442C22×C4—42no—
443C22×C4—472no—
444C22×C4—474no—
445C22×C4—478no—
446C22×C4—478no—
447C22×C4—472no—
448C22×C4—472no—
449C22×C4—474no—
450C22×C4—474no—
451C22×C4—948no—
452C22×C4—948no—
453C22×C4—944no—
454C22×C4—944no—
455C22×C4—944no—
456C22×C4—18816no—
457C22×C4—1884no—
458C22×C4—1884no—
459C22×C4—1884no—
460C22×C4—1884no—
461C22×C4—1882no—
462C22×C4—1882no—
463C22×C4—1882no—
464C22×C4—1882no—
465C22×C4—1881no—
466C22×C4—1881no—
467C22×C4Q8×D4714yes—
468C22×C4C23×D4712yes—
469C22×C4C23×D4712yes—
470C22×C4C23×D4714yes—
471C22×C4C23×D4714yes—
472C22×C4C23×D4711yescharacteristic
473C22×C4C23×D4711yescharacteristic
474C4⋊C4—24no—
475C4⋊C4—24no—
476C4⋊C4—44no—
477C4⋊C4—44no—
478C4⋊C4—944no—
479C4⋊C4—944no—
480C4⋊C4—1884no—
481C4⋊C4—1884no—
482C4⋊C4—1884no—
483C4⋊C4—1884no—
484C4⋊C4—1884no—
485C4⋊C4—1884no—
486C4⋊C4—1884no—
487C4⋊C4—1884no—
488C22⋊C4—28no—
489C22⋊C4—948no—
490C22⋊C4—948no—
491C22⋊C4—944no—
492C22⋊C4—944no—
493C22⋊C4—944no—
494C22⋊C4—944no—
495C22⋊C4—948no—
496C42—22no—
497C42—22no—
498C42—42no—
499C42—944no—
500C42—1881no—
501C42—1881no—
502C23—21no—
503C23—21no—
504C23—22no—
505C23—474no—
506C23—474no—
507C23—474no—
508C23—4716no—
509C23—942no—
510C23—942no—
511C23—942no—
512C23—942no—
513C23—1884no—
514C23—1884no—
515C23—1888no—
516C23—1888no—
517C23C2×Q8×D4712yes—
518C23#41×D4714yes—
519C23C24×D4711yescharacteristic
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—28no—
523C2×C4—24no—
524C2×C4—24no—
525C2×C4—22no—
526C2×C4—22no—
527C2×C4—22no—
528C2×C4—22no—
529C2×C4—24no—
530C2×C4—24no—
531C2×C4—22no—
532C2×C4—24no—
533C2×C4—24no—
534C2×C4—22no—
535C2×C4—48no—
536C2×C4—474no—
537C2×C4—942no—
538C2×C4—942no—
539C2×C4—9416no—
540C2×C4—944no—
541C2×C4—944no—
542C2×C4—942no—
543C2×C4—942no—
544C2×C4—944no—
545C2×C4—942no—
546C2×C4—942no—
547C2×C4—944no—
548C2×C4—944no—
549C2×C4—944no—
550C2×C4—942no—
551C2×C4—942no—
552C2×C4—3768no—
553C2×C4—3768no—
554C2×C4—1888no—
555C2×C4—1884no—
556C2×C4—1888no—
557C2×C4C2×Q8×D4712yes—
558C2×C4C2×Q8×D4712yes—
559C2×C4#1309406912yes—
560C2×C4#1309407012yes—
561C22—22no—
562C22—22no—
563C22—24no—
564C22—24no—
565C22—478no—
566C22—944no—
567C22—944no—
568C22—944no—
569C22—944no—
570C22—944no—
571C22—944no—
572C22—18816no—
573C22#125×D4714yes—
574C22C22×Q8×D4711yescharacteristic
575C22C2×#41×D4712yes—
576C22C2×#1309406911yescharacteristic
577C22C2×#1309407011yescharacteristic
578C22#1568995912yes—
579C4—22no—
580C4—42no—
581C4—42no—
582C4—44no—
583C4—44no—
584C4—944no—
585C4—1884no—
586C4—1884no—
587C4—1882no—
588C4—1882no—
589C4#1568974814yes—
590C2—24no—
591C2—948no—
592C2C2×#125×D4711yescharacteristic
593C2C2×#1568974811yescharacteristic
594C2#2025679111yescharacteristic
595C2#2025721612yes—
596C2#2025722312yes—
subgroupG/H
center, FrattiniC23C24×D47
commutator, socle, cosocleC23×C47C25
FittingC47×#2851C2
prime radicalC24×D47C23
hypercenter#2851D47
hypocenterC47#35020
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #2851

Complements

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

NH ≅ G/Ntype
1. #20251698C2semidirect
2. #20251696C2semidirect
3. #20249360C2semidirect
4. #20248611C2semidirect
5. #20248610C2semidirect
6. #20247115C2semidirect
7. #20247114C2semidirect
8. #20247110C2semidirect
9. #20247108C2semidirect
13. C47×#2851C2semidirect
15. C2×#13094016C22semidirect
16. C2×#13094015C22semidirect
22. #15689064C22semidirect
23. #15689064C22semidirect
24. #15689063C22semidirect
25. #15689061C22semidirect
26. #15689057C22semidirect
27. #15689056C22semidirect
28. #15689054C22semidirect
29. #15689053C22semidirect
30. #15689022C22semidirect
31. #15689021C22semidirect
32. #15689019C22semidirect
33. #15689010C22semidirect
34. #15689007C22semidirect
35. #15689006C22semidirect
43. #15688989C22semidirect
44. #15688988C22semidirect
60. C2×#125×C47C22semidirect
62. C47×#389C22semidirect
63. C47×#387C22semidirect
65. C47×#382C22semidirect
217. C22×D47#125semidirect
294. #2851D47semidirect
315. C2×#125C2×D47semidirect
333. #389C2×D47semidirect
337. #387C2×D47semidirect
348. #382C2×D47semidirect
365. C47#35020semidirect

Maximal subgroups

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

subgroupindex
#202516982
#202516962
#202493602
#202486112
#202486102
#202471152
#202471142
#202471102
#202471082
#202459992
#380×D472
C2×C4×(C2×D47)⋊C42
C47×#28512
#3502047