Finite Group Databasebeta

← D47×#2608 #26387705

Subgroups — D47×#2608 #26387705

Order 12032.

2270 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20249058C211yesmaximal, characteristic, complemented
2#20249057C214yesmaximal, complemented
3#20249056C214yesmaximal, complemented
4#20249055C212yesmaximal, complemented
5#20249054C214yesmaximal, complemented
6#396×D47C214yesmaximal
7#389×D47C214yesmaximal, complemented
8#387×D47C214yesmaximal, complemented
9#381×D47C211yesmaximal, characteristic
10C4×C22⋊C4×D47C212yesmaximal
11C47×#2608C211yesmaximal, characteristic, complemented
12C23×C4×D47C2211yescharacteristic
13C2×C4⋊C4×D47C2214yes—
14C2×C4⋊C4×D47C2214yes—
15C2×C4⋊C4×D47C2214yes—
16C2×C22⋊C4×D47C2214yes—
17C2×C22⋊C4×D47C2212yes—
18C2×C42×D47C2212yes—
19C2×C42×D47C2212yes—
20#15689047C2214yes—
21#15689046C2214yes—
22#15689046C2214yes—
23#15689046C2214yes—
24#15689045C2214yes—
25#15689045C2214yes—
26#15689045C2214yes—
27#15689022C2214yescomplemented
28#15689021C2214yescomplemented
29#15689020C2214yescomplemented
30#15689020C2214yescomplemented
31#15689019C2214yescomplemented
32#15689018C2214yescomplemented
33#15689018C2214yescomplemented
34#15689010C2214yescomplemented
35#15689009C2214yescomplemented
36#15689008C2214yescomplemented
37#15689007C2214yescomplemented
38#15689006C2214yescomplemented
39#15689005C2214yescomplemented
40#15689004C2214yescomplemented
41#15688986C2211yescharacteristic
42#15688985C2214yes—
43#15688984C2212yes—
44C22⋊C4×Dic47C2214yes—
45C4×(C2×D47)⋊C4C2212yes—
46C4×(C2×D47)⋊C4C2212yes—
47C4×C22⋊Dic47C2212yes—
48#15688970C2214yes—
49#95×D47C2214yes—
50#95×D47C2214yes—
51#95×D47C2214yes—
52C47×#396C2214yes—
53C47×#389C2214yescomplemented
54C47×#387C2214yescomplemented
55C47×#381C2211yescharacteristic
56C4×C22⋊C4×C47C2212yes—
57C24×D47C2311yescharacteristic
58C23×Dic47C2311yescharacteristic
59C22×C4×D47—44no—
60C22×C4×D47Q818yes—
61C22×C4×D47C2314yes—
62C22×C4×D47C2314yes—
63C22×C4×D47C2312yes—
64C22×C4×D47C2314yes—
65C22×C4×D47C2312yes—
66C2×C4⋊Dic47C2314yes—
67C2×C4⋊Dic47C2314yes—
68C2×C4⋊Dic47C2314yes—
69C2×Dic47⋊C4C2314yes—
70C2×Dic47⋊C4C2314yes—
71C2×Dic47⋊C4C2314yes—
72C2×Dic47⋊C4C2314yes—
73C2×Dic47⋊C4C2314yes—
74C2×Dic47⋊C4C2314yes—
75C4⋊C4×D47—216no—
76C4⋊C4×D47—216no—
77C4⋊C4×D47—48no—
78C2×C22⋊Dic47C2314yes—
79C2×C22⋊Dic47C2312yes—
80C2×(C2×D47)⋊C4C2314yes—
81C2×(C2×D47)⋊C4C2314yes—
82C2×(C2×D47)⋊C4C2314yes—
83C22⋊C4×D47—216no—
84C22⋊C4×D47—44no—
85C2×C4×Dic47C2314yes—
86C2×C4×Dic47C2314yes—
87C2×C4×Dic47C2312yes—
88C2×C4×Dic47C2312yes—
89C42×D47—44no—
90C42×D47—44no—
91C47⋊#95C2314yes—
92C47⋊#95C2314yes—
93C47⋊#95C2314yes—
94C47⋊#95C2314yes—
95C47⋊#95C2314yes—
96C47⋊#95C2314yes—
97C47⋊#95C2314yes—
98C47⋊#95C2314yes—
99C47⋊#95C2314yes—
100C23×C4×C47C2311yescharacteristic
101C2×C4⋊C4×C47C2314yes—
102C2×C4⋊C4×C47C2314yes—
103C2×C4⋊C4×C47C2314yes—
104C2×C22⋊C4×C47C2314yes—
105C2×C22⋊C4×C47C2312yes—
106C2×C42×C47C2312yes—
107C2×C42×C47C2312yes—
108#95×C47C2314yes—
109#95×C47C2314yes—
110#95×C47C2314yes—
111C24×C47C2411yescharacteristic
112C23×D47—28no—
113C23×D47—24no—
114C23×D47C2×Q814yes—
115C23×D47C2411yescharacteristic
116C23×D47C2411yescharacteristic
117C22×C4×C47—42no—
118C22×C4×C47C2×Q814yes—
119C22×C4×C47C2414yes—
120C22×C4×C47C2414yes—
121C22×C4×C47C2412yes—
122C22×C4×C47C2414yes—
123C22×Dic47—42no—
124C22×Dic47C2×Q814yes—
125C22×Dic47C2414yes—
126C22×Dic47C2414yes—
127C22×Dic47C2412yes—
128C22×Dic47C2414yes—
129C2×C4×D47—28no—
130C2×C4×D47—28no—
131C2×C4×D47—24no—
132C2×C4×D47—24no—
133C2×C4×D47—28no—
134C2×C4×D47—28no—
135C2×C4×D47—28no—
136C2×C4×D47—28no—
137C2×C4×D47—28no—
138C2×C4×D47—28no—
139C2×C4×D47—416no—
140C2×C4×D47—42no—
141C2×C4×D47—42no—
142C2×C4×D47C2×Q818yes—
143C2×C4×D47C2×Q818yes—
144C2×C4×D47#41116yes—
145C4⋊C4×C47—28no—
146C4⋊C4×C47—28no—
147C4⋊C4×C47—44no—
148C22⋊C4×C47—28no—
149C22⋊C4×C47—42no—
150C42×C47—42no—
151C42×C47—42no—
152C22⋊Dic47—28no—
153C22⋊Dic47—42no—
154(C2×D47)⋊C4—28no—
155(C2×D47)⋊C4—28no—
156(C2×D47)⋊C4—44no—
157C4⋊Dic47—28no—
158C4⋊Dic47—28no—
159C4⋊Dic47—44no—
160Dic47⋊C4—28no—
161Dic47⋊C4—28no—
162Dic47⋊C4—28no—
163Dic47⋊C4—28no—
164Dic47⋊C4—44no—
165Dic47⋊C4—44no—
166C4×Dic47—42no—
167C4×Dic47—44no—
168C4×Dic47—44no—
169C4×Dic47—42no—
170C23×C47—24no—
171C23×C47—22no—
172C23×C47C22×Q812yes—
173C23×C47C2511yescharacteristic
174C22×D47—24no—
175C22×D47—22no—
176C22×D47—216no—
177C22×D47—28no—
178C22×D47—416no—
179C22×D47C22×Q812yes—
180C22×D47C22×Q812yes—
181C22×D47C2×#4118yes—
182C22×D47H(5,𝔽2)14yes—
183C2×C4×C47—24no—
184C2×C4×C47—24no—
185C2×C4×C47—22no—
186C2×C4×C47—22no—
187C2×C4×C47—24no—
188C2×C4×C47—24no—
189C2×C4×C47—24no—
190C2×C4×C47—24no—
191C2×C4×C47—24no—
192C2×C4×C47—24no—
193C2×C4×C47—44no—
194C2×C4×C47C22×Q814yes—
195C2×C4×C47C2×#4118yes—
196C2×Dic47—24no—
197C2×Dic47—24no—
198C2×Dic47—22no—
199C2×Dic47—22no—
200C2×Dic47—24no—
201C2×Dic47—24no—
202C2×Dic47—24no—
203C2×Dic47—24no—
204C2×Dic47—24no—
205C2×Dic47—24no—
206C2×Dic47—44no—
207C2×Dic47C22×Q814yes—
208C2×Dic47C2×#4118yes—
209C4×D47—216no—
210C4×D47—232no—
211C4×D47—48no—
212C4×D47—416no—
213C4×D47—416no—
214C2×#2608—471nomaximal, Sylow
215C22×C47—24no—
216C22×C47—22no—
217C22×C47—44no—
218C22×C47C23×Q811yescharacteristic
219C22×C47C22×#4114yes—
220C22×C47C2×H(5,𝔽2)12yes—
221C2×D47—24no—
222C2×D47—22no—
223C2×D47—44no—
224C2×D47—416no—
225C2×D47#53318yes—
226C2×D47#54314yes—
227C2×D47#553116yes—
228C4×C47—24no—
229C4×C47—28no—
230C4×C47—44no—
231C4×C47—44no—
232Dic47—24no—
233Dic47—28no—
234Dic47—44no—
235Dic47—44no—
236#2608—474no—
237#2608—474no—
238#2608—474no—
239#2608—471no—
240#2608—472no—
241#2608D4711yescharacteristic, direct product factor
242C2×#396—474no—
243C2×#389—474no—
244C2×#387—474no—
245C2×#381—471no—
246C2×C4×C22⋊C4—472no—
247C2×C47—42no—
248C2×C47C2×#53312yes—
249C2×C47C2×#54311yescharacteristic
250C2×C47C2×#55314yes—
251D47—42no—
252D47#260818yesdirect product factor
253C24×C4—471no—
254C22×C4⋊C4—474no—
255C22×C4⋊C4—474no—
256C22×C4⋊C4—474no—
257C22×C22⋊C4—474no—
258C22×C22⋊C4—472no—
259C22×C42—472no—
260C22×C42—472no—
261#396—474no—
262#396—474no—
263#396—474no—
264#396—474no—
265#396—474no—
266#396—474no—
267#396—474no—
268#396C2×D4714yes—
269#389—474no—
270#389—474no—
271#389—474no—
272#389—474no—
273#389—474no—
274#389—474no—
275#389—474no—
276#389C2×D4714yescomplemented
277#387—474no—
278#387—474no—
279#387—474no—
280#387—474no—
281#387—474no—
282#387—474no—
283#387—474no—
284#387C2×D4714yescomplemented
285#381—471no—
286#381—472no—
287#381—474no—
288#381C2×D4711yescharacteristic
289C4×C22⋊C4—472no—
290C4×C22⋊C4—474no—
291C4×C22⋊C4—472no—
292C4×C22⋊C4—472no—
293C4×C22⋊C4—474no—
294C4×C22⋊C4C2×D4712yes—
295C2×#95—474no—
296C2×#95—474no—
297C2×#95—474no—
298C47C2×#260811yescharacteristic, complemented, Sylow
299C25—471no—
300C23×C4—471no—
301C23×C4—474no—
302C23×C4—472no—
303C23×C4—478no—
304C23×C4—472no—
305C23×C4—474no—
306C23×C4—474no—
307C23×C4—1884no—
308C23×C4C22×D4711yescharacteristic
309C2×C4⋊C4—474no—
310C2×C4⋊C4—474no—
311C2×C4⋊C4—474no—
312C2×C4⋊C4—474no—
313C2×C4⋊C4—474no—
314C2×C4⋊C4—474no—
315C2×C4⋊C4—474no—
316C2×C4⋊C4—474no—
317C2×C4⋊C4—474no—
318C2×C4⋊C4—9416no—
319C2×C4⋊C4—9416no—
320C2×C4⋊C4—1888no—
321C2×C4⋊C4C22×D4714yes—
322C2×C4⋊C4C22×D4714yes—
323C2×C4⋊C4C22×D4714yes—
324C2×C22⋊C4—474no—
325C2×C22⋊C4—474no—
326C2×C22⋊C4—474no—
327C2×C22⋊C4—472no—
328C2×C22⋊C4—474no—
329C2×C22⋊C4—9416no—
330C2×C22⋊C4—1884no—
331C2×C22⋊C4C22×D4714yes—
332C2×C22⋊C4C22×D4712yes—
333C2×C42—474no—
334C2×C42—472no—
335C2×C42—474no—
336C2×C42—472no—
337C2×C42—1884no—
338C2×C42—1884no—
339C2×C42C22×D4712yes—
340C2×C42C22×D4712yes—
341#95—474no—
342#95—474no—
343#95—474no—
344#95—474no—
345#95—474no—
346#95—474no—
347#95—474no—
348#95—474no—
349#95—474no—
350#95C22×D4714yes—
351#95C22×D4714yes—
352#95C22×D4714yes—
353C24—471no—
354C24—474no—
355C24—471no—
356C24—948no—
357C24—944no—
358C24C23×D4711yescharacteristic
359C22×C4—42no—
360C22×C4—472no—
361C22×C4—474no—
362C22×C4—474no—
363C22×C4—478no—
364C22×C4—4716no—
365C22×C4—478no—
366C22×C4—474no—
367C22×C4—474no—
368C22×C4—948no—
369C22×C4—944no—
370C22×C4—944no—
371C22×C4—948no—
372C22×C4—948no—
373C22×C4—948no—
374C22×C4—948no—
375C22×C4—948no—
376C22×C4—948no—
377C22×C4—948no—
378C22×C4—1882no—
379C22×C4—1882no—
380C22×C4—18816no—
381C22×C4—1882no—
382C22×C4Q8×D4714yes—
383C22×C4C23×D4714yes—
384C22×C4C23×D4714yes—
385C22×C4C23×D4712yes—
386C22×C4C23×D4714yes—
387C4⋊C4—28no—
388C4⋊C4—28no—
389C4⋊C4—44no—
390C4⋊C4—948no—
391C4⋊C4—948no—
392C4⋊C4—948no—
393C4⋊C4—948no—
394C4⋊C4—948no—
395C4⋊C4—948no—
396C4⋊C4—1884no—
397C4⋊C4—1884no—
398C4⋊C4—1884no—
399C22⋊C4—28no—
400C22⋊C4—42no—
401C22⋊C4—948no—
402C22⋊C4—948no—
403C22⋊C4—948no—
404C22⋊C4—1884no—
405C22⋊C4—1882no—
406C42—42no—
407C42—42no—
408C42—1884no—
409C42—1882no—
410C42—1882no—
411C42—1884no—
412C23—24no—
413C23—22no—
414C23—472no—
415C23—478no—
416C23—474no—
417C23—472no—
418C23—948no—
419C23—9416no—
420C23—944no—
421C23—942no—
422C23—18816no—
423C23C2×Q8×D4712yes—
424C23C24×D4711yescharacteristic
425C2×C4—24no—
426C2×C4—24no—
427C2×C4—22no—
428C2×C4—22no—
429C2×C4—24no—
430C2×C4—24no—
431C2×C4—24no—
432C2×C4—24no—
433C2×C4—24no—
434C2×C4—24no—
435C2×C4—44no—
436C2×C4—474no—
437C2×C4—478no—
438C2×C4—9432no—
439C2×C4—9416no—
440C2×C4—944no—
441C2×C4—944no—
442C2×C4—942no—
443C2×C4—942no—
444C2×C4—944no—
445C2×C4—944no—
446C2×C4—944no—
447C2×C4—944no—
448C2×C4—944no—
449C2×C4—944no—
450C2×C4—1888no—
451C2×C4—18816no—
452C2×C4—18816no—
453C2×C4—1884no—
454C2×C4C2×Q8×D4714yes—
455C2×C4#41×D4718yes—
456C22—22no—
457C22—24no—
458C22—44no—
459C22—474no—
460C22—4716no—
461C22—478no—
462C22—942no—
463C22—944no—
464C22—18816no—
465C22—1884no—
466C22C22×Q8×D4711yescharacteristic
467C22C2×#41×D4714yes—
468C22H(5,𝔽2)×D4712yes—
469C4—24no—
470C4—28no—
471C4—44no—
472C4—44no—
473C4—944no—
474C4—948no—
475C4—1884no—
476C4—1884no—
477C2—42no—
478C2—478no—
479C2—1882no—
480C2#533×D4712yes—
481C2#543×D4711yescharacteristic
482C2#553×D4714yes—
subgroupG/H
center, FrattiniC23C24×D47
commutator, socle, cosocleC23×C47C25
FittingC47×#2608C2
prime radicalC24×D47C23
hypercenter#2608D47
hypocenterC47C2×#2608
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #2608

Complements

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

NH ≅ G/Ntype
1. #20249058C2semidirect
2. #20249057C2semidirect
3. #20249056C2semidirect
4. #20249055C2semidirect
5. #20249054C2semidirect
7. #389×D47C2semidirect
8. #387×D47C2semidirect
11. C47×#2608C2semidirect
27. #15689022C22semidirect
28. #15689021C22semidirect
29. #15689020C22semidirect
30. #15689020C22semidirect
31. #15689019C22semidirect
32. #15689018C22semidirect
33. #15689018C22semidirect
34. #15689010C22semidirect
35. #15689009C22semidirect
36. #15689008C22semidirect
37. #15689007C22semidirect
38. #15689006C22semidirect
39. #15689005C22semidirect
40. #15689004C22semidirect
53. C47×#389C22semidirect
54. C47×#387C22semidirect
241. #2608D47direct (N × H)
252. D47#2608direct (N × H)
276. #389C2×D47semidirect
284. #387C2×D47semidirect
298. C47C2×#2608semidirect

Maximal subgroups

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

subgroupindex
#202490582
#202490572
#202490562
#202490552
#202490542
#396×D472
#389×D472
#387×D472
#381×D472
C4×C22⋊C4×D472
C47×#26082
C2×#260847