Finite Group Databasebeta

← D47×#2483 #26385198

Subgroups — D47×#2483 #26385198

Order 12032.

4382 conjugacy classes of subgroups.

The subgroup lattice has 544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C22⋊C4×D47C212yesmaximal
2#20247669C211yesmaximal, characteristic, complemented
3#20247668C214yesmaximal, complemented
4#20247667C214yesmaximal, complemented
5#20247666C212yesmaximal, complemented
6#20247665C214yesmaximal, complemented
7#397×D47C214yesmaximal, complemented
8#385×D47C214yesmaximal, complemented
9#381×D47C214yesmaximal, complemented
10#379×D47C211yesmaximal, characteristic
11C47×#2483C211yesmaximal, characteristic, complemented
12C25×D47C2211yescharacteristic
13C23×C4×D47C2212yes—
14C23×C4×D47C2212yes—
15C2×C4⋊C4×D47C2214yescomplemented
16C22×C22⋊Dic47C2212yes—
17C22×(C2×D47)⋊C4C2212yes—
18C22×(C2×D47)⋊C4C2212yes—
19C2×C22⋊C4×D47—216no—
20C2×C22⋊C4×D47C2214yes—
21C2×C22⋊C4×D47C2214yes—
22C2×C22⋊C4×D47C2214yes—
23C2×C22⋊C4×D47C2214yes—
24C2×C22⋊C4×D47C2214yes—
25C2×C22⋊C4×D47C2212yes—
26#15689052C2218yescomplemented
27#15689051C2218yescomplemented
28#15689050C2214yescomplemented
29#15689049C2214yescomplemented
30#15689048C2214yescomplemented
31#15688998C2214yescomplemented
32#15688997C2218yescomplemented
33#15688996C2214yescomplemented
34#15688995C2214yescomplemented
35#15688994C2218yescomplemented
36#15688986C2214yescomplemented
37#15688985C2218yescomplemented
38#15688985C2218yescomplemented
39#15688984C2214yescomplemented
40#15688984C2214yescomplemented
41#15688979C2211yescharacteristic
42#15688978C2212yes—
43#15688978C2214yes—
44#95×D47C2214yescomplemented
45#95×D47C2218yescomplemented
46C22×C22⋊C4×C47C2212yes—
47C47×#397C2214yescomplemented
48C47×#385C2214yescomplemented
49C47×#381C2214yescomplemented
50C47×#379C2211yescharacteristic
51C24×D47—216no—
52C24×D47—44no—
53C24×D47D418yes—
54C24×D47C2311yescharacteristic
55C24×D47C2311yescharacteristic
56C24×D47C2312yes—
57C24×D47C2312yes—
58C23×Dic47C2312yes—
59C23×Dic47C2312yes—
60C22×C4×D47—28no—
61C22×C4×D47—28no—
62C22×C4×D47—216no—
63C22×C4×D47—48no—
64C22×C4×D47C2314yes—
65C22×C4×D47C2314yes—
66C22×C4×D47C2314yes—
67C22×C4×D47C2314yes—
68C22×C4×D47C2314yes—
69C2×C4⋊Dic47C2314yescomplemented
70C2×Dic47⋊C4C2318yescomplemented
71C4⋊C4×D47—48no—
72C2×C22⋊Dic47—28no—
73C2×C22⋊Dic47C2314yes—
74C2×C22⋊Dic47C2314yes—
75C2×C22⋊Dic47C2314yes—
76C2×C22⋊Dic47C2312yes—
77C2×(C2×D47)⋊C4—28no—
78C2×(C2×D47)⋊C4—28no—
79C2×(C2×D47)⋊C4C2318yes—
80C2×(C2×D47)⋊C4C2314yes—
81C2×(C2×D47)⋊C4C2314yes—
82C2×(C2×D47)⋊C4C2314yes—
83C2×(C2×D47)⋊C4C2314yes—
84C2×(C2×D47)⋊C4C2314yes—
85C22⋊C4×D47—216no—
86C22⋊C4×D47—216no—
87C22⋊C4×D47—216no—
88C22⋊C4×D47—216no—
89C22⋊C4×D47—216no—
90C22⋊C4×D47—44no—
91C47⋊#95C2314yescomplemented
92C47⋊#95C2318yescomplemented
93C47⋊#95C2318yescomplemented
94C47⋊#95C2318yescomplemented
95C47⋊#95C2318yescomplemented
96C25×C47C2311yescharacteristic
97C23×C4×C47C2312yes—
98C23×C4×C47C2312yes—
99C2×C4⋊C4×C47C2314yescomplemented
100C2×C22⋊C4×C47—28no—
101C2×C22⋊C4×C47C2314yes—
102C2×C22⋊C4×C47C2314yes—
103C2×C22⋊C4×C47C2314yes—
104C2×C22⋊C4×C47C2312yes—
105#95×C47C2314yescomplemented
106#95×C47C2318yescomplemented
107C24×C47—28no—
108C24×C47—42no—
109C24×C47C2×D414yes—
110C24×C47C2411yescharacteristic
111C24×C47C2412yes—
112C23×D47—28no—
113C23×D47—28no—
114C23×D47—28no—
115C23×D47—264no—
116C23×D47—28no—
117C23×D47—28no—
118C23×D47—28no—
119C23×D47—24no—
120C23×D47—416no—
121C23×D47—42no—
122C23×D47—44no—
123C23×D47—464no—
124C23×D47C2×D414yes—
125C23×D47C2×D414yes—
126C23×D47C2×D418yes—
127C23×D47C2×D418yes—
128C23×D47#41116yes—
129C23×D47C2411yescharacteristic
130C23×D47C2412yes—
131C23×D47C2411yescharacteristic
132C22×C4×C47—24no—
133C22×C4×C47—24no—
134C22×C4×C47—28no—
135C22×C4×C47—44no—
136C22×C4×C47C2414yes—
137C22×C4×C47C2414yes—
138C22×C4×C47C2414yes—
139C22×Dic47—24no—
140C22×Dic47—24no—
141C22×Dic47—28no—
142C22×Dic47—44no—
143C22×Dic47C2414yes—
144C22×Dic47C2414yes—
145C22×Dic47C2414yes—
146C2×C4×D47—28no—
147C2×C4×D47—28no—
148C2×C4×D47—28no—
149C2×C4×D47—28no—
150C2×C4×D47—216no—
151C2×C4×D47—216no—
152C2×C4×D47—216no—
153C2×C4×D47—28no—
154C2×C4×D47—216no—
155C2×C4×D47—48no—
156C2×C4×D47—432no—
157C2×C4×D47—432no—
158C4⋊C4×C47—44no—
159C22⋊C4×C47—28no—
160C22⋊C4×C47—28no—
161C22⋊C4×C47—28no—
162C22⋊C4×C47—42no—
163C22⋊Dic47—28no—
164C22⋊Dic47—28no—
165C22⋊Dic47—28no—
166C22⋊Dic47—42no—
167(C2×D47)⋊C4—28no—
168(C2×D47)⋊C4—28no—
169(C2×D47)⋊C4—28no—
170(C2×D47)⋊C4—28no—
171(C2×D47)⋊C4—216no—
172(C2×D47)⋊C4—44no—
173C4⋊Dic47—44no—
174Dic47⋊C4—48no—
175C23×C47—24no—
176C23×C47—24no—
177C23×C47—216no—
178C23×C47—24no—
179C23×C47—22no—
180C23×C47—44no—
181C23×C47—416no—
182C23×C47C22×D412yes—
183C23×C47C22×D414yes—
184C23×C47C2×#4118yes—
185C23×C47C2511yescharacteristic
186C22×D47—24no—
187C22×D47—24no—
188C22×D47—216no—
189C22×D47—216no—
190C22×D47—264no—
191C22×D47—216no—
192C22×D47—24no—
193C22×D47—22no—
194C22×D47—216no—
195C22×D47—216no—
196C22×D47—216no—
197C22×D47—28no—
198C22×D47—44no—
199C22×D47—48no—
200C22×D47—416no—
201C22×D47—4128no—
202C22×D47—432no—
203C22×D47—416no—
204C22×D47#123132yes—
205C22×D47C22×D412yes—
206C22×D47C22×D414yes—
207C22×D47C22×D412yes—
208C22×D47C2×#4118yes—
209C22×D47C2×#4118yes—
210C22×D47H(5,𝔽2)14yes—
211C2×C4×C47—24no—
212C2×C4×C47—24no—
213C2×C4×C47—28no—
214C2×C4×C47—28no—
215C2×C4×C47—28no—
216C2×C4×C47—24no—
217C2×C4×C47—48no—
218C2×C4×C47—48no—
219C2×Dic47—24no—
220C2×Dic47—24no—
221C2×Dic47—28no—
222C2×Dic47—28no—
223C2×Dic47—24no—
224C2×Dic47—28no—
225C2×Dic47—48no—
226C2×Dic47—48no—
227C4×D47—416no—
228C4×D47—416no—
229C4×D47—416no—
230C4×D47—416no—
231C4×D47—416no—
232C2×#2483—471nomaximal, Sylow
233C22×C47—24no—
234C22×C47—24no—
235C22×C47—216no—
236C22×C47—24no—
237C22×C47—22no—
238C22×C47—416no—
239C22×C47—44no—
240C22×C47C2×#12318yes—
241C22×C47C23×D411yescharacteristic
242C22×C47C22×#4114yes—
243C22×C47C2×H(5,𝔽2)12yes—
244C2×D47—24no—
245C2×D47—24no—
246C2×D47—216no—
247C2×D47—264no—
248C2×D47—24no—
249C2×D47—22no—
250C2×D47—416no—
251C2×D47—432no—
252C2×D47—44no—
253C2×D47—416no—
254C2×D47C2×#12318yes—
255C2×D47C2×#12318yes—
256C2×D47#53414yes—
257C2×D47#551116yes—
258C4×C47—44no—
259C4×C47—44no—
260C4×C47—44no—
261Dic47—44no—
262Dic47—44no—
263Dic47—44no—
264C23×C22⋊C4—472no—
265#2483—474no—
266#2483—474no—
267#2483—474no—
268#2483—471no—
269#2483—472no—
270#2483D4711yescharacteristic, direct product factor
271C2×#397—474no—
272C2×#385—474no—
273C2×#381—474no—
274C2×#379—471no—
275C2×C47—28no—
276C2×C47—42no—
277C2×C47C22×#12312yes—
278C2×C47C2×#53411yescharacteristic
279C2×C47C2×#55114yes—
280D47—28no—
281D47—42no—
282D47#248318yesdirect product factor
283C26—471no—
284C24×C4—472no—
285C24×C4—472no—
286C22×C4⋊C4—474no—
287C22×C22⋊C4—472no—
288C22×C22⋊C4—472no—
289C22×C22⋊C4—472no—
290C22×C22⋊C4—474no—
291C22×C22⋊C4—474no—
292C22×C22⋊C4—474no—
293C22×C22⋊C4—474no—
294C22×C22⋊C4—474no—
295C22×C22⋊C4—472no—
296C22×C22⋊C4—9416no—
297C22×C22⋊C4C2×D4712yes—
298#397—474no—
299#397—474no—
300#397—478no—
301#397—474no—
302#397—478no—
303#397C2×D4714yescomplemented
304#385—474no—
305#385—478no—
306#385—474no—
307#385—474no—
308#385—478no—
309#385C2×D4714yescomplemented
310#381—474no—
311#381—474no—
312#381—474no—
313#381—478no—
314#381—478no—
315#381C2×D4714yescomplemented
316#379—471no—
317#379—474no—
318#379—472no—
319#379C2×D4711yescharacteristic
320C2×#95—474no—
321C2×#95—478no—
322C47C2×#248311yescharacteristic, complemented, Sylow
323C25—472no—
324C25—471no—
325C25—478no—
326C25—471no—
327C25—472no—
328C25—9416no—
329C25—1884no—
330C25C22×D4711yescharacteristic
331C23×C4—472no—
332C23×C4—472no—
333C23×C4—474no—
334C23×C4—474no—
335C23×C4—474no—
336C23×C4—474no—
337C23×C4—474no—
338C23×C4—948no—
339C23×C4—948no—
340C23×C4—9416no—
341C23×C4—1888no—
342C23×C4C22×D4712yes—
343C23×C4C22×D4712yes—
344C2×C4⋊C4—478no—
345C2×C4⋊C4—474no—
346C2×C4⋊C4—1888no—
347C2×C4⋊C4C22×D4714yescomplemented
348C2×C22⋊C4—28no—
349C2×C22⋊C4—474no—
350C2×C22⋊C4—474no—
351C2×C22⋊C4—474no—
352C2×C22⋊C4—474no—
353C2×C22⋊C4—474no—
354C2×C22⋊C4—474no—
355C2×C22⋊C4—474no—
356C2×C22⋊C4—478no—
357C2×C22⋊C4—472no—
358C2×C22⋊C4—474no—
359C2×C22⋊C4—9416no—
360C2×C22⋊C4—9416no—
361C2×C22⋊C4—9416no—
362C2×C22⋊C4—9416no—
363C2×C22⋊C4—9416no—
364C2×C22⋊C4—948no—
365C2×C22⋊C4—948no—
366C2×C22⋊C4—948no—
367C2×C22⋊C4—1884no—
368C2×C22⋊C4C22×D4714yes—
369C2×C22⋊C4C22×D4714yes—
370C2×C22⋊C4C22×D4714yes—
371C2×C22⋊C4C22×D4712yes—
372#95—474no—
373#95—478no—
374#95—478no—
375#95—478no—
376#95—478no—
377#95C22×D4714yescomplemented
378#95C22×D4718yescomplemented
379C24—28no—
380C24—42no—
381C24—471no—
382C24—478no—
383C24—4716no—
384C24—472no—
385C24—474no—
386C24—471no—
387C24—474no—
388C24—478no—
389C24—948no—
390C24—948no—
391C24—944no—
392C24—948no—
393C24—9464no—
394C24—948no—
395C24—948no—
396C24—948no—
397C24—1884no—
398C24—1882no—
399C24—18816no—
400C24—18864no—
401C24D4×D4714yes—
402C24C23×D4711yescharacteristic
403C24C23×D4712yes—
404C22×C4—24no—
405C22×C4—24no—
406C22×C4—28no—
407C22×C4—44no—
408C22×C4—474no—
409C22×C4—474no—
410C22×C4—474no—
411C22×C4—948no—
412C22×C4—948no—
413C22×C4—948no—
414C22×C4—948no—
415C22×C4—9416no—
416C22×C4—948no—
417C22×C4—9416no—
418C22×C4—9416no—
419C22×C4—9416no—
420C22×C4—944no—
421C22×C4—944no—
422C22×C4—948no—
423C22×C4—1888no—
424C22×C4—18832no—
425C22×C4—18832no—
426C22×C4—1884no—
427C22×C4C23×D4714yes—
428C22×C4C23×D4714yes—
429C22×C4C23×D4714yes—
430C4⋊C4—44no—
431C4⋊C4—1888no—
432C4⋊C4—1884no—
433C22⋊C4—28no—
434C22⋊C4—28no—
435C22⋊C4—28no—
436C22⋊C4—42no—
437C22⋊C4—9416no—
438C22⋊C4—948no—
439C22⋊C4—948no—
440C22⋊C4—948no—
441C22⋊C4—948no—
442C22⋊C4—948no—
443C22⋊C4—948no—
444C22⋊C4—948no—
445C22⋊C4—1884no—
446C22⋊C4—1882no—
447C23—24no—
448C23—24no—
449C23—216no—
450C23—24no—
451C23—22no—
452C23—44no—
453C23—416no—
454C23—472no—
455C23—478no—
456C23—474no—
457C23—4732no—
458C23—474no—
459C23—478no—
460C23—472no—
461C23—9416no—
462C23—9416no—
463C23—9464no—
464C23—9416no—
465C23—9416no—
466C23—9416no—
467C23—948no—
468C23—944no—
469C23—944no—
470C23—9416no—
471C23—944no—
472C23—942no—
473C23—1888no—
474C23—1884no—
475C23—18832no—
476C23—18816no—
477C23—188128no—
478C23—18816no—
479C23C2×D4×D4712yes—
480C23C2×D4×D4714yes—
481C23#41×D4718yes—
482C23C24×D4711yescharacteristic
483C2×C4—24no—
484C2×C4—24no—
485C2×C4—28no—
486C2×C4—28no—
487C2×C4—24no—
488C2×C4—28no—
489C2×C4—48no—
490C2×C4—48no—
491C2×C4—944no—
492C2×C4—944no—
493C2×C4—948no—
494C2×C4—948no—
495C2×C4—944no—
496C2×C4—948no—
497C2×C4—18816no—
498C2×C4—18816no—
499C2×C4—18816no—
500C2×C4—18816no—
501C2×C4—18816no—
502C2×C4—1888no—
503C2×C4—1888no—
504C22—24no—
505C22—216no—
506C22—24no—
507C22—24no—
508C22—22no—
509C22—416no—
510C22—44no—
511C22—478no—
512C22—4716no—
513C22—474no—
514C22—478no—
515C22—9464no—
516C22—944no—
517C22—9416no—
518C22—944no—
519C22—944no—
520C22—942no—
521C22—18832no—
522C22—18816no—
523C22—18816no—
524C22—1884no—
525C22#123×D4718yes—
526C22C22×D4×D4711yescharacteristic
527C22C2×#41×D4714yes—
528C22H(5,𝔽2)×D4712yes—
529C4—44no—
530C4—44no—
531C4—44no—
532C4—1884no—
533C4—1884no—
534C4—1884no—
535C2—28no—
536C2—42no—
537C2—478no—
538C2—948no—
539C2—1882no—
540C2C2×#123×D4712yes—
541C2#534×D4711yescharacteristic
542C2#551×D4714yes—
subgroupG/H
center, FrattiniC23C24×D47
commutator, socle, cosocleC23×C47C25
FittingC47×#2483C2
prime radicalC25×D47C22
hypercenter#2483D47
hypocenterC47C2×#2483
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #2483

Complements

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

NH ≅ G/Ntype
2. #20247669C2semidirect
3. #20247668C2semidirect
4. #20247667C2semidirect
5. #20247666C2semidirect
6. #20247665C2semidirect
7. #397×D47C2semidirect
8. #385×D47C2semidirect
9. #381×D47C2semidirect
11. C47×#2483C2semidirect
15. C2×C4⋊C4×D47C22semidirect
26. #15689052C22semidirect
27. #15689051C22semidirect
28. #15689050C22semidirect
29. #15689049C22semidirect
30. #15689048C22semidirect
31. #15688998C22semidirect
32. #15688997C22semidirect
33. #15688996C22semidirect
34. #15688995C22semidirect
35. #15688994C22semidirect
36. #15688986C22semidirect
37. #15688985C22semidirect
38. #15688985C22semidirect
39. #15688984C22semidirect
40. #15688984C22semidirect
44. #95×D47C22semidirect
45. #95×D47C22semidirect
47. C47×#397C22semidirect
48. C47×#385C22semidirect
49. C47×#381C22semidirect
69. C2×C4⋊Dic47C23semidirect
70. C2×Dic47⋊C4C23semidirect
91. C47⋊#95C23semidirect
92. C47⋊#95C23semidirect
93. C47⋊#95C23semidirect
94. C47⋊#95C23semidirect
95. C47⋊#95C23semidirect
99. C2×C4⋊C4×C47C23semidirect
105. #95×C47C23semidirect
106. #95×C47C23semidirect
270. #2483D47direct (N × H)
282. D47#2483direct (N × H)
303. #397C2×D47semidirect
309. #385C2×D47semidirect
315. #381C2×D47semidirect
322. C47C2×#2483semidirect
347. C2×C4⋊C4C22×D47semidirect
377. #95C22×D47semidirect
378. #95C22×D47semidirect

Maximal subgroups

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

subgroupindex
C22×C22⋊C4×D472
#202476692
#202476682
#202476672
#202476662
#202476652
#397×D472
#385×D472
#381×D472
#379×D472
C47×#24832
C2×#248347