Finite Group Databasebeta

← D47×#1386 #26131191

Subgroups — D47×#1386 #26131191

Order 12032.

630 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×M32×D47C211yesmaximal, characteristic
2#427×D47C211yesmaximal, characteristic
3C2×#106×D47C211yesmaximal, characteristic
4#20241495C211yesmaximal, characteristic, complemented
5#20241494C211yesmaximal, characteristic, complemented
6#20241493C211yesmaximal, characteristic, complemented
7C47×#1386C211yesmaximal, characteristic, complemented
8C22×C8×D47C2211yescharacteristic
9#117×D47—21no—
10C2×C4⋊C4×D47—21no—
11C2×#13093964C2211yescharacteristic
12C2×#13093963—21no—
13M32×D47—22no—
14M32×D47C414yescomplemented
15C2×C16×D47—21no—
16#15689161C2211yescharacteristic
17#15689160C412yescomplemented
18#15689159—21no—
19#15689158—21no—
20#107×D47C412yescomplemented
21C2×#13093956C2211yescharacteristic
22C2×#13093955—21no—
23#106×D47—22no—
24#106×D47—21no—
25#106×D47C414yescomplemented
26C2×M32×C47C2211yescharacteristic
27C47×#427C2211yescharacteristic
28C2×#106×C47C2211yescharacteristic
29C22×C4×D47—41no—
30C22×C4×D47D411yescharacteristic
31C22×C47⋊C8D411yescharacteristic
32C2×C8×D47C2×C412yes—
33C2×C8×D47C2×C412yes—
34C2×C8×D47C2×C411yescharacteristic
35C2×C8×D47C2×C411yescharacteristic
36C2×C8×D47D411yescharacteristic
37C2×C8×D47D412yes—
38C2×C8×D47D411yescharacteristic
39C2×C8×D47Q812yes—
40#13093983—21no—
41#13093982—22no—
42#13093981—41no—
43#13093980—41no—
44C2×C4⋊Dic47—21no—
45C2×Dic47⋊C4—41no—
46C4⋊C4×D47—24no—
47C4⋊C4×D47—22no—
48C4⋊C4×D47—42no—
49C22⋊C4×D47—41no—
50C42×D47—41no—
51#13093964—21no—
52#13093964C2×C412yescomplemented
53#13093963—24no—
54C2×C47⋊C16—21no—
55C16×D47—24no—
56#13093958C2×C412yescomplemented
57#13093957—22no—
58#13093956—21no—
59#13093956—21no—
60#13093956C2×C412yescomplemented
61#13093955—24no—
62#13093955—22no—
63C22×C8×C47C2311yescharacteristic
64#117×C47—21no—
65C2×C4⋊C4×C47—21no—
66M32×C47—21no—
67M32×C47C2×C412yescomplemented
68C2×C16×C47—21no—
69#107×C47C2×C412yescomplemented
70#106×C47—21no—
71#106×C47—21no—
72#106×C47C2×C412yescomplemented
73C23×D47D811yescharacteristic
74C22×C4×C47—41no—
75C22×C4×C47C2×D411yescharacteristic
76C22×Dic47—41no—
77C22×Dic47D811yescharacteristic
78C2×C4×D47—42no—
79C2×C4×D47—44no—
80C2×C4×D47—84no—
81C2×C4×D47C22⋊C412yes—
82C2×C4×D47C22⋊C411yescharacteristic
83C2×C4×D47C22⋊C411yescharacteristic
84C2×C4×D47C4⋊C412yes—
85C2×C4×D47SD1611yescharacteristic
86C2×C4×D47SD1612yes—
87C2×C4×D47SD1611yescharacteristic
88C2×C4×D47Q1612yes—
89C2×C8×C47C22×C411yescharacteristic
90C2×C8×C47C22×C411yescharacteristic
91C2×C8×C47C22×C411yescharacteristic
92C2×C8×C47C2×D411yescharacteristic
93C2×C8×C47C2×D411yescharacteristic
94C2×C8×C47C2×Q811yescharacteristic
95C4⋊C4×C47—22no—
96C4⋊C4×C47—22no—
97C4⋊C4×C47—41no—
98C22⋊C4×C47—41no—
99C42×C47—41no—
100C22⋊Dic47—41no—
101(C2×D47)⋊C4—42no—
102C4⋊Dic47—22no—
103C4⋊Dic47—22no—
104C4⋊Dic47—41no—
105Dic47⋊C4—44no—
106Dic47⋊C4—42no—
107C4×Dic47—41no—
108C4×Dic47—42no—
109C2×C47⋊C8C22⋊C412yes—
110C2×C47⋊C8C22⋊C411yescharacteristic
111C2×C47⋊C8C22⋊C411yescharacteristic
112C2×C47⋊C8C4⋊C412yes—
113C8×D47C4212yes—
114C8×D47C4212yes—
115C8×D47C22⋊C412yes—
116C8×D47C22⋊C412yes—
117C8×D47C4⋊C412yes—
118C8×D47C4⋊C412yes—
119C8×D47C4⋊C412yes—
120C8×D47C4⋊C412yes—
121C16×C47—22no—
122C47⋊C16—22no—
123C23×C47C2×D811yescharacteristic
124C22×D47—24no—
125C22×D47#10211yescharacteristic
126C22×D47#10212yes—
127C22×D47#10211yescharacteristic
128C22×D47#10712yes—
129C2×C4×C47—42no—
130C2×C4×C47—42no—
131C2×C4×C47—82no—
132C2×C4×C47C2×C22⋊C411yescharacteristic
133C2×C4×C47C2×C22⋊C411yescharacteristic
134C2×C4×C47C2×C4⋊C411yescharacteristic
135C2×C4×C47C2×SD1611yescharacteristic
136C2×C4×C47C2×SD1611yescharacteristic
137C2×C4×C47C2×Q1611yescharacteristic
138C2×Dic47—42no—
139C2×Dic47—42no—
140C2×Dic47—82no—
141C2×Dic47#10211yescharacteristic
142C2×Dic47#10212yes—
143C2×Dic47#10211yescharacteristic
144C2×Dic47#10712yes—
145C4×D47—88no—
146C4×D47—84no—
147C4×D47#9512yes—
148C4×D47#9512yes—
149C4×D47#10312yes—
150C4×D47#10312yes—
151C4×D47#10312yes—
152C4×D47#10312yes—
153C4×D47#10612yes—
154C4×D47#10612yes—
155C8×C47C2×C4211yescharacteristic
156C8×C47C2×C22⋊C411yescharacteristic
157C8×C47C2×C4⋊C411yescharacteristic
158C8×C47C2×C4⋊C411yescharacteristic
159C47⋊C8#9512yes—
160C47⋊C8#9512yes—
161C2×#1386—471nomaximal, Sylow
162C22×C47—22no—
163C22×C47C2×#10211yescharacteristic
164C22×C47C2×#10211yescharacteristic
165C22×C47C2×#10711yescharacteristic
166C2×D47—22no—
167C2×D47—24no—
168C2×D47—24no—
169C2×D47#34012yes—
170C2×D47#34012yes—
171C2×D47#36014yes—
172C4×C47—82no—
173C4×C47—82no—
174C4×C47C2×#9511yescharacteristic
175C4×C47C2×#10311yescharacteristic
176C4×C47C2×#10311yescharacteristic
177C4×C47C2×#10611yescharacteristic
178Dic47—82no—
179Dic47—82no—
180Dic47#34012yes—
181Dic47#34012yes—
182C22×M32—471no—
183C2×#427—471no—
184C22×#106—471no—
185#1386—471no—
186#1386—471no—
187#1386—471no—
188#1386D4711yescharacteristic, direct product factor
189C2×C47—21no—
190C2×C47—21no—
191C2×C47C2×#34011yescharacteristic
192C2×C47C2×#36012yes—
193D47—22no—
194D47#138614yesdirect product factor
195C23×C8—471no—
196C2×#117—941no—
197C22×C4⋊C4—941no—
198C2×M32—471no—
199C2×M32—474no—
200C2×M32—941no—
201C2×M32—942no—
202C2×M32C2×D4711yescharacteristic
203C22×C16—941no—
204#427—471no—
205#427—472no—
206#427—941no—
207#427—941no—
208#427C2×D4711yescharacteristic
209C2×#107—472no—
210C2×#106—471no—
211C2×#106—474no—
212C2×#106—942no—
213C2×#106—941no—
214C2×#106—941no—
215C2×#106C2×D4711yescharacteristic
216C47C2×#138611yescharacteristic, complemented, Sylow
217C23×C4—471no—
218C23×C4—1881no—
219C22×C8—471no—
220C22×C8—472no—
221C22×C8—471no—
222C22×C8—471no—
223C22×C8—472no—
224C22×C8—471no—
225C22×C8—472no—
226C22×C8—471no—
227C22×C8—472no—
228C22×C8C22×D4711yescharacteristic
229#117—21no—
230#117—942no—
231#117—941no—
232#117—1881no—
233#117—1881no—
234C2×C4⋊C4—21no—
235C2×C4⋊C4—944no—
236C2×C4⋊C4—942no—
237C2×C4⋊C4—941no—
238C2×C4⋊C4—1882no—
239C2×C4⋊C4—1881no—
240C2×C22⋊C4—1881no—
241C2×C42—1881no—
242M32—21no—
243M32—472no—
244M32—944no—
245M32—941no—
246M32C4×D4712yescomplemented
247C2×C16—21no—
248C2×C16—944no—
249C2×C16—941no—
250#107—472no—
251#107—942no—
252#107C4×D4712yescomplemented
253#106—21no—
254#106—21no—
255#106—472no—
256#106—944no—
257#106—942no—
258#106—941no—
259#106—941no—
260#106C4×D4712yescomplemented
261C24—471no—
262C22×C4—41no—
263C22×C4—471no—
264C22×C4—472no—
265C22×C4—471no—
266C22×C4—471no—
267C22×C4—472no—
268C22×C4—471no—
269C22×C4—472no—
270C22×C4—471no—
271C22×C4—472no—
272C22×C4—3764no—
273C22×C4—1882no—
274C22×C4—1884no—
275C22×C4—1881no—
276C22×C4D4×D4711yescharacteristic
277C2×C8—472no—
278C2×C8—471no—
279C2×C8—471no—
280C2×C8—472no—
281C2×C8—472no—
282C2×C8—472no—
283C2×C8—472no—
284C2×C8—472no—
285C2×C8—472no—
286C2×C8—472no—
287C2×C8—472no—
288C2×C8—472no—
289C2×C8C2×C4×D4711yescharacteristic
290C2×C8C2×C4×D4711yescharacteristic
291C2×C8C2×C4×D4711yescharacteristic
292C2×C8D4×D4711yescharacteristic
293C2×C8D4×D4711yescharacteristic
294C2×C8Q8×D4711yescharacteristic
295C4⋊C4—22no—
296C4⋊C4—22no—
297C4⋊C4—41no—
298C4⋊C4—942no—
299C4⋊C4—942no—
300C4⋊C4—1884no—
301C4⋊C4—1882no—
302C4⋊C4—1881no—
303C22⋊C4—41no—
304C22⋊C4—1882no—
305C22⋊C4—1881no—
306C42—41no—
307C42—1882no—
308C42—1881no—
309C16—22no—
310C16—942no—
311C23—471no—
312C23—472no—
313C23—471no—
314C23—472no—
315C23—944no—
316C23D8×D4711yescharacteristic
317C2×C4—42no—
318C2×C4—42no—
319C2×C4—82no—
320C2×C4—472no—
321C2×C4—471no—
322C2×C4—471no—
323C2×C4—472no—
324C2×C4—472no—
325C2×C4—472no—
326C2×C4—472no—
327C2×C4—472no—
328C2×C4—472no—
329C2×C4—472no—
330C2×C4—472no—
331C2×C4—472no—
332C2×C4—3764no—
333C2×C4—3768no—
334C2×C4—3762no—
335C2×C4—1882no—
336C2×C4—1882no—
337C2×C4C22⋊C4×D4711yescharacteristic
338C2×C4C22⋊C4×D4711yescharacteristic
339C2×C4C4⋊C4×D4711yescharacteristic
340C2×C4SD16×D4711yescharacteristic
341C2×C4SD16×D4711yescharacteristic
342C2×C4Q16×D4711yescharacteristic
343C8—472no—
344C8—472no—
345C8C42×D4711yescharacteristic
346C8C22⋊C4×D4711yescharacteristic
347C8C4⋊C4×D4711yescharacteristic
348C8C4⋊C4×D4711yescharacteristic
349C22—22no—
350C22—474no—
351C22—472no—
352C22—472no—
353C22—944no—
354C22—944no—
355C22—942no—
356C22#102×D4711yescharacteristic
357C22#102×D4711yescharacteristic
358C22#107×D4711yescharacteristic
359C4—82no—
360C4—82no—
361C4—472no—
362C4—472no—
363C4—3762no—
364C4—3762no—
365C4#95×D4711yescharacteristic
366C4#103×D4711yescharacteristic
367C4#103×D4711yescharacteristic
368C4#106×D4711yescharacteristic
369C2—21no—
370C2—21no—
371C2—474no—
372C2—942no—
373C2#340×D4711yescharacteristic
374C2#360×D4712yes—
subgroupG/H
centerC22#102×D47
commutatorC8×C47C2×C42
FrattiniC22×C8C22×D47
FittingC47×#1386C2
socleC22×C47C2×#102
prime radicalC23×D47D8
cosocleC22×C8×C47C23
hypercenter#1386D47
hypocenterC47C2×#1386
LCSG ▷ C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #1386

Complements

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

NH ≅ G/Ntype
4. #20241495C2semidirect
5. #20241494C2semidirect
6. #20241493C2semidirect
7. C47×#1386C2semidirect
14. M32×D47C4semidirect
17. #15689160C4semidirect
20. #107×D47C4semidirect
25. #106×D47C4semidirect
52. #13093964C2×C4semidirect
56. #13093958C2×C4semidirect
60. #13093956C2×C4semidirect
67. M32×C47C2×C4semidirect
69. #107×C47C2×C4semidirect
72. #106×C47C2×C4semidirect
188. #1386D47direct (N × H)
194. D47#1386direct (N × H)
216. C47C2×#1386semidirect
246. M32C4×D47semidirect
252. #107C4×D47semidirect
260. #106C4×D47semidirect

Maximal subgroups

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

subgroupindex
C2×M32×D472
#427×D472
C2×#106×D472
#202414952
#202414942
#202414932
C47×#13862
C2×#138647