Finite Group Databasebeta

← D47×#2646 #26382719

Subgroups — D47×#2646 #26382719

Order 12032.

2374 conjugacy classes of subgroups.

The subgroup lattice has 538 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20249361C212yesmaximal, complemented
2#20249360C214yesmaximal, complemented
3#20249359C214yesmaximal, complemented
4#20249358C211yesmaximal, characteristic, complemented
5#20249357C214yesmaximal, complemented
6#400×D47C214yesmaximal, complemented
7#398×D47C214yesmaximal, complemented
8#385×D47C214yesmaximal
9#380×D47C212yesmaximal
10C2×#95×D47C211yesmaximal, characteristic
11C47×#2646C211yesmaximal, characteristic, complemented
12C23×C4×D47C2212yes—
13C23×C4×D47C2211yescharacteristic
14C2×C4⋊C4×D47C2214yes—
15C2×C4⋊C4×D47C2214yes—
16C2×C4⋊C4×D47C2212yes—
17C2×C4⋊C4×D47C2212yes—
18C2×C22⋊C4×D47C2214yes—
19#15689065C2214yescomplemented
20#15689065C2214yescomplemented
21#15689064C2214yescomplemented
22#15689064C2214yescomplemented
23#15689063C2214yescomplemented
24#15689062C2214yescomplemented
25#15689061C2214yescomplemented
26#15689057C2214yescomplemented
27#15689057C2214yescomplemented
28#15689056C2214yescomplemented
29#15689056C2214yescomplemented
30#15689055C2214yescomplemented
31#15689054C2214yescomplemented
32#15689053C2214yescomplemented
33#15688998C2214yes—
34#15688997C2214yes—
35#15688997C2214yes—
36#15688996C2214yes—
37#15688995C2214yes—
38#15688994C2214yes—
39#15688994C2214yes—
40#15688983C2212yes—
41#15688982C2214yes—
42#15688981C2214yes—
43#15688980C2212yes—
44#15688980C2212yes—
45C2×C47⋊#95C2212yes—
46C2×C47⋊#95C2211yescharacteristic
47#95×D47C2214yes—
48#95×D47C2214yes—
49#95×D47C2214yes—
50#95×D47C2214yes—
51#95×D47C2214yes—
52C47×#400C2214yescomplemented
53C47×#398C2214yescomplemented
54C47×#385C2214yes—
55C47×#380C2212yes—
56C2×#95×C47C2211yescharacteristic
57C24×D47C2311yescharacteristic
58C23×Dic47C2312yes—
59C23×Dic47C2311yescharacteristic
60C22×C4×D47—28no—
61C22×C4×D47—44no—
62C22×C4×D47—44no—
63C22×C4×D47—44no—
64C22×C4×D47Q818yes—
65C22×C4×D47C2314yes—
66C22×C4×D47C2314yes—
67C22×C4×D47C2314yes—
68C22×C4×D47C2312yes—
69C22×C4×D47C2314yes—
70C22×C4×D47C2312yes—
71C2×C4⋊Dic47C2312yes—
72C2×C4⋊Dic47C2312yes—
73C2×C4⋊Dic47C2314yes—
74C2×C4⋊Dic47C2314yes—
75C2×Dic47⋊C4C2314yes—
76C2×Dic47⋊C4C2314yes—
77C2×Dic47⋊C4C2314yes—
78C2×Dic47⋊C4C2314yes—
79C2×Dic47⋊C4C2314yes—
80C2×Dic47⋊C4C2314yes—
81C4⋊C4×D47—44no—
82C4⋊C4×D47—44no—
83C4⋊C4×D47—48no—
84C4⋊C4×D47—48no—
85C2×C22⋊Dic47C2314yes—
86C2×(C2×D47)⋊C4C2314yes—
87C2×(C2×D47)⋊C4C2314yes—
88C22⋊C4×D47—216no—
89C47⋊#95C2314yes—
90C47⋊#95C2314yes—
91C47⋊#95C2314yes—
92C47⋊#95C2314yes—
93C47⋊#95C2314yes—
94C47⋊#95C2314yes—
95C47⋊#95C2314yes—
96C47⋊#95C2314yes—
97C47⋊#95C2314yes—
98C47⋊#95C2314yes—
99C47⋊#95C2314yes—
100C47⋊#95C2314yes—
101C23×C4×C47C2312yes—
102C23×C4×C47C2311yescharacteristic
103C2×C4⋊C4×C47C2312yes—
104C2×C4⋊C4×C47C2312yes—
105C2×C4⋊C4×C47C2314yes—
106C2×C4⋊C4×C47C2314yes—
107C2×C22⋊C4×C47C2314yes—
108#95×C47C2314yes—
109#95×C47C2314yes—
110#95×C47C2314yes—
111#95×C47C2314yes—
112C24×C47C2411yescharacteristic
113C23×D47—22no—
114C23×D47—24no—
115C23×D47—22no—
116C23×D47C2×Q814yes—
117C23×D47#4118yes—
118C23×D47C2411yescharacteristic
119C23×D47C2411yescharacteristic
120C22×C4×C47—24no—
121C22×C4×C47—42no—
122C22×C4×C47—42no—
123C22×C4×C47—42no—
124C22×C4×C47C2×Q814yes—
125C22×C4×C47C2414yes—
126C22×C4×C47C2414yes—
127C22×C4×C47C2414yes—
128C22×C4×C47C2412yes—
129C22×Dic47—24no—
130C22×Dic47—42no—
131C22×Dic47—42no—
132C22×Dic47—42no—
133C22×Dic47C2×Q814yes—
134C22×Dic47C2414yes—
135C22×Dic47C2414yes—
136C22×Dic47C2414yes—
137C22×Dic47C2412yes—
138C2×C4×D47—24no—
139C2×C4×D47—24no—
140C2×C4×D47—28no—
141C2×C4×D47—28no—
142C2×C4×D47—28no—
143C2×C4×D47—28no—
144C2×C4×D47—28no—
145C2×C4×D47—28no—
146C2×C4×D47—28no—
147C2×C4×D47—28no—
148C2×C4×D47—28no—
149C2×C4×D47—28no—
150C2×C4×D47—416no—
151C2×C4×D47—42no—
152C2×C4×D47—42no—
153C2×C4×D47—44no—
154C2×C4×D47—44no—
155C2×C4×D47—432no—
156C2×C4×D47C2×Q818yes—
157C2×C4×D47C2×Q818yes—
158C4⋊C4×C47—42no—
159C4⋊C4×C47—42no—
160C4⋊C4×C47—44no—
161C4⋊C4×C47—44no—
162C22⋊C4×C47—28no—
163C22⋊Dic47—28no—
164(C2×D47)⋊C4—28no—
165(C2×D47)⋊C4—28no—
166C4⋊Dic47—42no—
167C4⋊Dic47—44no—
168C4⋊Dic47—42no—
169C4⋊Dic47—44no—
170Dic47⋊C4—44no—
171Dic47⋊C4—44no—
172Dic47⋊C4—44no—
173Dic47⋊C4—44no—
174Dic47⋊C4—44no—
175Dic47⋊C4—44no—
176C23×C47—21no—
177C23×C47—22no—
178C23×C47—21no—
179C23×C47C22×Q812yes—
180C23×C47C2×#4114yes—
181C23×C47C2511yescharacteristic
182C22×D47—21no—
183C22×D47—22no—
184C22×D47—21no—
185C22×D47—216no—
186C22×D47—216no—
187C22×D47—28no—
188C22×D47—28no—
189C22×D47#125116yes—
190C22×D47C22×Q812yes—
191C22×D47C22×Q812yes—
192C22×D47C2×#4114yes—
193C22×D47C2×#4114yes—
194C22×D47H(5,𝔽2)12yes—
195C22×D47H(5,𝔽2)14yes—
196C22×D472−1+412yes—
197C2×C4×C47—22no—
198C2×C4×C47—22no—
199C2×C4×C47—24no—
200C2×C4×C47—24no—
201C2×C4×C47—24no—
202C2×C4×C47—24no—
203C2×C4×C47—24no—
204C2×C4×C47—24no—
205C2×C4×C47—24no—
206C2×C4×C47—24no—
207C2×C4×C47—24no—
208C2×C4×C47—44no—
209C2×C4×C47—48no—
210C2×C4×C47C22×Q814yes—
211C2×Dic47—22no—
212C2×Dic47—22no—
213C2×Dic47—24no—
214C2×Dic47—24no—
215C2×Dic47—24no—
216C2×Dic47—24no—
217C2×Dic47—24no—
218C2×Dic47—24no—
219C2×Dic47—24no—
220C2×Dic47—24no—
221C2×Dic47—24no—
222C2×Dic47—44no—
223C2×Dic47—48no—
224C2×Dic47C22×Q814yes—
225C4×D47—216no—
226C4×D47—48no—
227C4×D47—416no—
228C4×D47—416no—
229C4×D47—416no—
230C4×D47—416no—
231C2×#2646—471nomaximal, Sylow
232C22×C47—24no—
233C22×C47—24no—
234C22×C47—22no—
235C22×C47—22no—
236C22×C47C2×#12514yes—
237C22×C47C23×Q811yescharacteristic
238C22×C47C22×#4112yes—
239C22×C47C2×H(5,𝔽2)11yescharacteristic
240C22×C47C2×H(5,𝔽2)12yes—
241C22×C47C2×2−1+411yescharacteristic
242C2×D47—24no—
243C2×D47—24no—
244C2×D47—22no—
245C2×D47—22no—
246C2×D47—232no—
247C2×D47C2×#12514yes—
248C2×D47C2×#12514yes—
249C2×D47#53818yes—
250C2×D47#53918yes—
251C2×D47#54314yes—
252C2×D47#54414yes—
253C4×C47—24no—
254C4×C47—44no—
255C4×C47—44no—
256C4×C47—44no—
257Dic47—24no—
258Dic47—44no—
259Dic47—44no—
260Dic47—44no—
261#2646—474no—
262#2646—474no—
263#2646—474no—
264#2646—472no—
265#2646—471no—
266#2646D4711yescharacteristic, direct product factor
267C2×#400—474no—
268C2×#398—474no—
269C2×#385—474no—
270C2×#380—472no—
271C22×#95—471no—
272C2×C47—24no—
273C2×C47C22×#12511yescharacteristic
274C2×C47C2×#53812yes—
275C2×C47C2×#53912yes—
276C2×C47C2×#54311yescharacteristic
277C2×C47C2×#54411yescharacteristic
278D47—24no—
279D47#264618yesdirect product factor
280C24×C4—471no—
281C24×C4—472no—
282C22×C4⋊C4—472no—
283C22×C4⋊C4—474no—
284C22×C4⋊C4—474no—
285C22×C4⋊C4—472no—
286C22×C22⋊C4—474no—
287#400—474no—
288#400—474no—
289#400—474no—
290#400—474no—
291#400—474no—
292#400—474no—
293#400—474no—
294#400C2×D4714yescomplemented
295#398—474no—
296#398—474no—
297#398—474no—
298#398—474no—
299#398—474no—
300#398—474no—
301#398—474no—
302#398C2×D4714yescomplemented
303#385—474no—
304#385—474no—
305#385—474no—
306#385—474no—
307#385—474no—
308#385—474no—
309#385—474no—
310#385C2×D4714yes—
311#380—472no—
312#380—472no—
313#380—472no—
314#380—474no—
315#380—474no—
316#380C2×D4712yes—
317C2×#95—472no—
318C2×#95—471no—
319C2×#95—474no—
320C2×#95—474no—
321C2×#95—474no—
322C2×#95—474no—
323C2×#95—474no—
324C2×#95C2×D4711yescharacteristic
325C47C2×#264611yescharacteristic, complemented, Sylow
326C25—471no—
327C23×C4—471no—
328C23×C4—472no—
329C23×C4—478no—
330C23×C4—472no—
331C23×C4—472no—
332C23×C4—474no—
333C23×C4—474no—
334C23×C4—474no—
335C23×C4—474no—
336C23×C4—948no—
337C23×C4—1884no—
338C23×C4—1884no—
339C23×C4—1884no—
340C23×C4C22×D4712yes—
341C23×C4C22×D4711yescharacteristic
342C2×C4⋊C4—474no—
343C2×C4⋊C4—474no—
344C2×C4⋊C4—474no—
345C2×C4⋊C4—474no—
346C2×C4⋊C4—474no—
347C2×C4⋊C4—474no—
348C2×C4⋊C4—472no—
349C2×C4⋊C4—472no—
350C2×C4⋊C4—474no—
351C2×C4⋊C4—474no—
352C2×C4⋊C4—1884no—
353C2×C4⋊C4—1884no—
354C2×C4⋊C4—1888no—
355C2×C4⋊C4—1888no—
356C2×C4⋊C4C22×D4712yes—
357C2×C4⋊C4C22×D4712yes—
358C2×C4⋊C4C22×D4714yes—
359C2×C4⋊C4C22×D4714yes—
360C2×C22⋊C4—474no—
361C2×C22⋊C4—474no—
362C2×C22⋊C4—474no—
363C2×C22⋊C4—9416no—
364C2×C22⋊C4C22×D4714yes—
365#95—474no—
366#95—474no—
367#95—474no—
368#95—474no—
369#95—474no—
370#95—474no—
371#95—474no—
372#95—474no—
373#95—474no—
374#95—474no—
375#95—474no—
376#95—474no—
377#95C22×D4714yes—
378#95C22×D4714yes—
379#95C22×D4714yes—
380#95C22×D4714yes—
381C24—471no—
382C24—474no—
383C24—478no—
384C24—471no—
385C24—944no—
386C24—942no—
387C24—942no—
388C24C23×D4711yescharacteristic
389C22×C4—24no—
390C22×C4—42no—
391C22×C4—42no—
392C22×C4—42no—
393C22×C4—472no—
394C22×C4—474no—
395C22×C4—478no—
396C22×C4—478no—
397C22×C4—474no—
398C22×C4—474no—
399C22×C4—474no—
400C22×C4—944no—
401C22×C4—944no—
402C22×C4—948no—
403C22×C4—948no—
404C22×C4—948no—
405C22×C4—948no—
406C22×C4—948no—
407C22×C4—948no—
408C22×C4—948no—
409C22×C4—948no—
410C22×C4—948no—
411C22×C4—948no—
412C22×C4—944no—
413C22×C4—1882no—
414C22×C4—1882no—
415C22×C4—1884no—
416C22×C4—1884no—
417C22×C4—18816no—
418C22×C4—18832no—
419C22×C4—1882no—
420C22×C4—1882no—
421C22×C4—1882no—
422C22×C4Q8×D4714yes—
423C22×C4C23×D4714yes—
424C22×C4C23×D4714yes—
425C22×C4C23×D4714yes—
426C22×C4C23×D4712yes—
427C4⋊C4—42no—
428C4⋊C4—42no—
429C4⋊C4—44no—
430C4⋊C4—44no—
431C4⋊C4—1884no—
432C4⋊C4—1884no—
433C4⋊C4—1884no—
434C4⋊C4—1884no—
435C4⋊C4—1884no—
436C4⋊C4—1884no—
437C4⋊C4—1882no—
438C4⋊C4—1882no—
439C4⋊C4—1884no—
440C4⋊C4—1884no—
441C22⋊C4—28no—
442C22⋊C4—948no—
443C22⋊C4—948no—
444C22⋊C4—948no—
445C23—22no—
446C23—21no—
447C23—21no—
448C23—472no—
449C23—474no—
450C23—474no—
451C23—472no—
452C23—472no—
453C23—4716no—
454C23—472no—
455C23—474no—
456C23—948no—
457C23—9416no—
458C23—948no—
459C23—9416no—
460C23—942no—
461C23—941no—
462C23—941no—
463C23C2×Q8×D4712yes—
464C23#41×D4714yes—
465C23C24×D4711yescharacteristic
466C2×C4—22no—
467C2×C4—22no—
468C2×C4—24no—
469C2×C4—24no—
470C2×C4—24no—
471C2×C4—24no—
472C2×C4—24no—
473C2×C4—24no—
474C2×C4—24no—
475C2×C4—24no—
476C2×C4—24no—
477C2×C4—44no—
478C2×C4—48no—
479C2×C4—474no—
480C2×C4—9416no—
481C2×C4—942no—
482C2×C4—942no—
483C2×C4—944no—
484C2×C4—944no—
485C2×C4—944no—
486C2×C4—944no—
487C2×C4—944no—
488C2×C4—944no—
489C2×C4—944no—
490C2×C4—944no—
491C2×C4—944no—
492C2×C4—1888no—
493C2×C4—18816no—
494C2×C4—18816no—
495C2×C4—18816no—
496C2×C4—18816no—
497C2×C4—1884no—
498C2×C4—1888no—
499C2×C4C2×Q8×D4714yes—
500C22—22no—
501C22—22no—
502C22—24no—
503C22—24no—
504C22—474no—
505C22—474no—
506C22—474no—
507C22—478no—
508C22—478no—
509C22—474no—
510C22—9432no—
511C22—942no—
512C22—942no—
513C22—944no—
514C22—944no—
515C22#125×D4714yes—
516C22C22×Q8×D4711yescharacteristic
517C22C2×#41×D4712yes—
518C22H(5,𝔽2)×D4712yes—
519C22H(5,𝔽2)×D4711yescharacteristic
520C222−1+4×D4711yescharacteristic
521C4—24no—
522C4—44no—
523C4—44no—
524C4—44no—
525C4—944no—
526C4—1884no—
527C4—1884no—
528C4—1884no—
529C2—24no—
530C2—478no—
531C2—944no—
532C2C2×#125×D4711yescharacteristic
533C2#538×D4712yes—
534C2#539×D4712yes—
535C2#543×D4711yescharacteristic
536C2#544×D4711yescharacteristic
subgroupG/H
center, FrattiniC23C24×D47
commutator, socle, cosocleC23×C47C25
FittingC47×#2646C2
prime radicalC24×D47C23
hypercenter#2646D47
hypocenterC47C2×#2646
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #2646

Complements

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

NH ≅ G/Ntype
1. #20249361C2semidirect
2. #20249360C2semidirect
3. #20249359C2semidirect
4. #20249358C2semidirect
5. #20249357C2semidirect
6. #400×D47C2semidirect
7. #398×D47C2semidirect
11. C47×#2646C2semidirect
19. #15689065C22semidirect
20. #15689065C22semidirect
21. #15689064C22semidirect
22. #15689064C22semidirect
23. #15689063C22semidirect
24. #15689062C22semidirect
25. #15689061C22semidirect
26. #15689057C22semidirect
27. #15689057C22semidirect
28. #15689056C22semidirect
29. #15689056C22semidirect
30. #15689055C22semidirect
31. #15689054C22semidirect
32. #15689053C22semidirect
52. C47×#400C22semidirect
53. C47×#398C22semidirect
266. #2646D47direct (N × H)
279. D47#2646direct (N × H)
294. #400C2×D47semidirect
302. #398C2×D47semidirect
325. C47C2×#2646semidirect

Maximal subgroups

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

subgroupindex
#202493612
#202493602
#202493592
#202493582
#202493572
#400×D472
#398×D472
#385×D472
#380×D472
C2×#95×D472
C47×#26462
C2×#264647