Finite Group Databasebeta

← D47×#2834 #26422490

Subgroups — D47×#2834 #26422490

Order 12032.

1958 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20251574C211yesmaximal, characteristic, complemented
2#20251573C213yesmaximal, complemented
3#20251572C212yesmaximal, complemented
4#20251571C213yesmaximal, complemented
5#20251570C216yesmaximal, complemented
6#401×D47C212yesmaximal, complemented
7#399×D47C211yesmaximal, characteristic
8#398×D47C216yesmaximal, complemented
9#397×D47C213yesmaximal
10#385×D47C213yesmaximal
11C47×#2834C211yesmaximal, characteristic, complemented
12C23×C4×D47C2211yescharacteristic
13C2×C4⋊C4×D47C2216yes—
14C2×C4⋊C4×D47C2213yes—
15C2×C4⋊C4×D47C2213yes—
16C2×C22⋊C4×D47C2213yes—
17C2×C22⋊C4×D47C2213yes—
18C47⋊#401C2216yescomplemented
19C47⋊#401C2216yescomplemented
20C47⋊#401C2212yescomplemented
21#15689060C2211yescharacteristic
22#15689059C2213yes—
23#15689058C2213yes—
24#15689057C2216yescomplemented
25#15689057C2216yescomplemented
26#15689056C2216yescomplemented
27#15689056C2216yescomplemented
28#15689055C2216yescomplemented
29#15689054C2216yescomplemented
30#15689053C2216yescomplemented
31#15689052C2216yes—
32#15689051C2216yes—
33#15689050C2213yes—
34#15689049C2213yes—
35#15689048C2213yes—
36#15688998C2213yes—
37#15688997C2216yes—
38#15688996C2213yes—
39#15688995C2213yes—
40#15688994C2216yes—
41#95×D47C2216yes—
42#95×D47C2213yes—
43#95×D47C2216yes—
44#95×D47C2211yescharacteristic
45C47×#401C2212yescomplemented
46C47×#399C2211yescharacteristic
47C47×#398C2216yescomplemented
48C47×#397C2213yes—
49C47×#385C2213yes—
50C24×D47C2311yescharacteristic
51C23×Dic47C2311yescharacteristic
52C22×C4×D47—46no—
53C22×C4×D47C2313yes—
54C22×C4×D47C2316yes—
55C22×C4×D47C2312yes—
56C22×C4×D47C2313yes—
57C22×C4×D47C2312yes—
58C2×C4⋊Dic47C2316yes—
59C2×C4⋊Dic47C2313yes—
60C2×C4⋊Dic47C2313yes—
61C2×Dic47⋊C4C2316yes—
62C2×Dic47⋊C4C2316yes—
63C2×Dic47⋊C4C2316yes—
64C2×Dic47⋊C4C2316yes—
65C4⋊C4×D47—46no—
66C4⋊C4×D47—46no—
67C4⋊C4×D47—412no—
68C2×C22⋊Dic47C2313yes—
69C2×C22⋊Dic47C2313yes—
70C2×(C2×D47)⋊C4C2316yes—
71C2×(C2×D47)⋊C4C2313yes—
72C2×(C2×D47)⋊C4C2313yes—
73C22⋊C4×D47—212no—
74C22⋊C4×D47—46no—
75C47⋊#95C2316yes—
76C47⋊#95C2316yes—
77C47⋊#95C2316yes—
78C47⋊#95C2313yes—
79C47⋊#95C2316yes—
80C47⋊#95C2316yes—
81C47⋊#95C2316yes—
82C47⋊#95C2316yes—
83C47⋊#95C2313yes—
84C23×C4×C47C2311yescharacteristic
85C2×C4⋊C4×C47C2316yes—
86C2×C4⋊C4×C47C2313yes—
87C2×C4⋊C4×C47C2313yes—
88C2×C22⋊C4×C47C2313yes—
89C2×C22⋊C4×C47C2313yes—
90#95×C47C2316yes—
91#95×C47C2313yes—
92#95×C47C2316yes—
93#95×C47C2311yescharacteristic
94C24×C47C2411yescharacteristic
95C23×D47—26no—
96C23×D47—26no—
97C23×D47#4114yes—
98C23×D47C2411yescharacteristic
99C23×D47C2411yescharacteristic
100C22×C4×C47—43no—
101C22×C4×C47C2413yes—
102C22×C4×C47C2416yes—
103C22×C4×C47C2413yes—
104C22×C4×C47C2412yes—
105C22×Dic47—43no—
106C22×Dic47C2413yes—
107C22×Dic47C2416yes—
108C22×Dic47C2412yes—
109C22×Dic47C2413yes—
110C2×C4×D47—212no—
111C2×C4×D47—26no—
112C2×C4×D47—26no—
113C2×C4×D47—212no—
114C2×C4×D47—212no—
115C2×C4×D47—212no—
116C2×C4×D47—212no—
117C2×C4×D47—212no—
118C2×C4×D47—46no—
119C2×C4×D47—416no—
120C4⋊C4×C47—43no—
121C4⋊C4×C47—46no—
122C4⋊C4×C47—43no—
123C22⋊C4×C47—26no—
124C22⋊C4×C47—43no—
125C22⋊Dic47—26no—
126C22⋊Dic47—43no—
127(C2×D47)⋊C4—212no—
128(C2×D47)⋊C4—43no—
129(C2×D47)⋊C4—43no—
130C4⋊Dic47—43no—
131C4⋊Dic47—43no—
132C4⋊Dic47—46no—
133Dic47⋊C4—46no—
134Dic47⋊C4—46no—
135Dic47⋊C4—46no—
136Dic47⋊C4—46no—
137C23×C47—23no—
138C23×C47—23no—
139C23×C47C2×#4112yes—
140C23×C47C2511yescharacteristic
141C22×D47—23no—
142C22×D47—23no—
143C22×D47—224no—
144C22×D47—44no—
145C22×D47—412no—
146C22×D47C2×#4112yes—
147C22×D47C2×#4112yes—
148C22×D47H(5,𝔽2)16yes—
149C22×D472−1+416yes—
150C2×C4×C47—26no—
151C2×C4×C47—26no—
152C2×C4×C47—26no—
153C2×C4×C47—26no—
154C2×C4×C47—23no—
155C2×C4×C47—23no—
156C2×C4×C47—26no—
157C2×C4×C47—26no—
158C2×C4×C47—44no—
159C2×Dic47—26no—
160C2×Dic47—26no—
161C2×Dic47—26no—
162C2×Dic47—23no—
163C2×Dic47—23no—
164C2×Dic47—26no—
165C2×Dic47—26no—
166C2×Dic47—26no—
167C2×Dic47—44no—
168C4×D47—48no—
169C4×D47—424no—
170C4×D47—412no—
171C4×D47—48no—
172C4×D47—412no—
173C2×#2834—471nomaximal, Sylow
174C22×C47—26no—
175C22×C47—41no—
176C22×C47—43no—
177C22×C47C22×#4111yescharacteristic
178C22×C47C2×H(5,𝔽2)13yes—
179C22×C47C2×2−1+413yes—
180C2×D47—26no—
181C2×D47—41no—
182C2×D47—43no—
183C2×D47—416no—
184C2×D47#539112yes—
185C2×D47#56014yes—
186C2×D47#563112yes—
187C4×C47—46no—
188C4×C47—42no—
189C4×C47—43no—
190C4×C47—43no—
191Dic47—46no—
192Dic47—42no—
193Dic47—43no—
194Dic47—43no—
195#2834—472no—
196#2834—471no—
197#2834—476no—
198#2834—473no—
199#2834—473no—
200#2834D4711yescharacteristic, direct product factor
201C2×#401—472no—
202C2×#399—471no—
203C2×#398—476no—
204C2×#397—473no—
205C2×#385—473no—
206C2×C47—42no—
207C2×C47C2×#53913yes—
208C2×C47C2×#56011yescharacteristic
209C2×C47C2×#56313yes—
210D47—42no—
211D47#283418yesdirect product factor
212C24×C4—471no—
213C22×C4⋊C4—473no—
214C22×C4⋊C4—473no—
215C22×C4⋊C4—476no—
216C22×C22⋊C4—473no—
217C22×C22⋊C4—473no—
218#401—472no—
219#401—476no—
220#401—476no—
221#401C2×D4712yescomplemented
222#399—473no—
223#399—473no—
224#399—471no—
225#399C2×D4711yescharacteristic
226#398—476no—
227#398—476no—
228#398—476no—
229#398—476no—
230#398—476no—
231#398—476no—
232#398—476no—
233#398C2×D4716yescomplemented
234#397—473no—
235#397—473no—
236#397—476no—
237#397—473no—
238#397—476no—
239#397C2×D4713yes—
240#385—473no—
241#385—476no—
242#385—473no—
243#385—473no—
244#385—476no—
245#385C2×D4713yes—
246C2×#95—473no—
247C2×#95—476no—
248C2×#95—476no—
249C2×#95—471no—
250C47C2×#283411yescharacteristic, complemented, Sylow
251C25—471no—
252C23×C4—471no—
253C23×C4—473no—
254C23×C4—476no—
255C23×C4—473no—
256C23×C4—472no—
257C23×C4—472no—
258C23×C4—1886no—
259C23×C4C22×D4711yescharacteristic
260C2×C4⋊C4—476no—
261C2×C4⋊C4—476no—
262C2×C4⋊C4—476no—
263C2×C4⋊C4—476no—
264C2×C4⋊C4—476no—
265C2×C4⋊C4—473no—
266C2×C4⋊C4—473no—
267C2×C4⋊C4—1886no—
268C2×C4⋊C4—1886no—
269C2×C4⋊C4—18812no—
270C2×C4⋊C4C22×D4716yes—
271C2×C4⋊C4C22×D4713yes—
272C2×C4⋊C4C22×D4713yes—
273C2×C22⋊C4—473no—
274C2×C22⋊C4—476no—
275C2×C22⋊C4—473no—
276C2×C22⋊C4—473no—
277C2×C22⋊C4—473no—
278C2×C22⋊C4—9412no—
279C2×C22⋊C4—1886no—
280C2×C22⋊C4C22×D4713yes—
281C2×C22⋊C4C22×D4713yes—
282#95—476no—
283#95—476no—
284#95—476no—
285#95—473no—
286#95—476no—
287#95—476no—
288#95—476no—
289#95—476no—
290#95—473no—
291#95C22×D4716yes—
292#95C22×D4713yes—
293#95C22×D4716yes—
294#95C22×D4711yescharacteristic
295C24—471no—
296C24—474no—
297C24—471no—
298C24—946no—
299C24—946no—
300C24C23×D4711yescharacteristic
301C22×C4—43no—
302C22×C4—473no—
303C22×C4—476no—
304C22×C4—472no—
305C22×C4—473no—
306C22×C4—9412no—
307C22×C4—946no—
308C22×C4—946no—
309C22×C4—9412no—
310C22×C4—9412no—
311C22×C4—9412no—
312C22×C4—9412no—
313C22×C4—9412no—
314C22×C4—1886no—
315C22×C4—18816no—
316C22×C4—1883no—
317C22×C4C23×D4713yes—
318C22×C4C23×D4716yes—
319C22×C4C23×D4712yes—
320C22×C4C23×D4713yes—
321C4⋊C4—43no—
322C4⋊C4—43no—
323C4⋊C4—46no—
324C4⋊C4—1886no—
325C4⋊C4—1886no—
326C4⋊C4—1886no—
327C4⋊C4—1886no—
328C4⋊C4—1883no—
329C4⋊C4—1883no—
330C4⋊C4—1886no—
331C22⋊C4—26no—
332C22⋊C4—43no—
333C22⋊C4—9412no—
334C22⋊C4—946no—
335C22⋊C4—1883no—
336C22⋊C4—1883no—
337C22⋊C4—1883no—
338C23—23no—
339C23—23no—
340C23—472no—
341C23—476no—
342C23—476no—
343C23—472no—
344C23—9424no—
345C23—943no—
346C23—943no—
347C23—1884no—
348C23—18812no—
349C23#41×D4712yes—
350C23C24×D4711yescharacteristic
351C2×C4—26no—
352C2×C4—23no—
353C2×C4—23no—
354C2×C4—26no—
355C2×C4—26no—
356C2×C4—26no—
357C2×C4—26no—
358C2×C4—26no—
359C2×C4—44no—
360C2×C4—946no—
361C2×C4—943no—
362C2×C4—943no—
363C2×C4—946no—
364C2×C4—946no—
365C2×C4—946no—
366C2×C4—946no—
367C2×C4—946no—
368C2×C4—18824no—
369C2×C4—18812no—
370C2×C4—18812no—
371C2×C4—1888no—
372C2×C4—1888no—
373C2×C4—1884no—
374C22—26no—
375C22—41no—
376C22—43no—
377C22—4712no—
378C22—474no—
379C22—4712no—
380C22—946no—
381C22—18816no—
382C22—1881no—
383C22—1883no—
384C22C2×#41×D4711yescharacteristic
385C22H(5,𝔽2)×D4713yes—
386C222−1+4×D4713yes—
387C4—46no—
388C4—42no—
389C4—43no—
390C4—43no—
391C4—1886no—
392C4—1882no—
393C4—1883no—
394C4—1883no—
395C2—42no—
396C2—478no—
397C2—1882no—
398C2#539×D4713yes—
399C2#560×D4711yescharacteristic
400C2#563×D4713yes—
subgroupG/H
center, FrattiniC23C24×D47
commutator, socle, cosocleC23×C47C25
FittingC47×#2834C2
prime radicalC24×D47C23
hypercenter#2834D47
hypocenterC47C2×#2834
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #2834

Complements

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

NH ≅ G/Ntype
1. #20251574C2semidirect
2. #20251573C2semidirect
3. #20251572C2semidirect
4. #20251571C2semidirect
5. #20251570C2semidirect
6. #401×D47C2semidirect
8. #398×D47C2semidirect
11. C47×#2834C2semidirect
18. C47⋊#401C22semidirect
19. C47⋊#401C22semidirect
20. C47⋊#401C22semidirect
24. #15689057C22semidirect
25. #15689057C22semidirect
26. #15689056C22semidirect
27. #15689056C22semidirect
28. #15689055C22semidirect
29. #15689054C22semidirect
30. #15689053C22semidirect
45. C47×#401C22semidirect
47. C47×#398C22semidirect
200. #2834D47direct (N × H)
211. D47#2834direct (N × H)
221. #401C2×D47semidirect
233. #398C2×D47semidirect
250. C47C2×#2834semidirect

Maximal subgroups

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

subgroupindex
#202515742
#202515732
#202515722
#202515712
#202515702
#401×D472
#399×D472
#398×D472
#397×D472
#385×D472
C47×#28342
C2×#283447