Finite Group Databasebeta

← D47×#2110 #26368933

Subgroups — D47×#2110 #26368933

Order 12032.

738 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×M32×D47C212yesmaximal
2#405×D47C211yesmaximal, characteristic
3#20244993C211yesmaximal, characteristic, complemented
4#20244992C212yesmaximal, complemented
5#20244991C214yesmaximal, complemented
6#347×D47C214yesmaximal, complemented
7C47×#2110C211yesmaximal, characteristic, complemented
8C2×M16×D47C411yescharacteristic
9C22×C8×D47C2211yescharacteristic
10#117×D47C411yescharacteristic
11C2×#13093964C2212yes—
12C2×#13093963C414yescomplemented
13M32×D47C414yescomplemented
14M32×D47C414yescomplemented
15M32×D47C2214yes—
16M32×D47C2214yes—
17C2×C16×D47C414yescomplemented
18#15689081C411yescharacteristic
19#15689080C2212yes—
20#15689079C411yescharacteristic
21#15689078C2211yescharacteristic
22#15689077C412yes—
23#97×D47C2212yes—
24C4×C8×D47C412yes—
25#15688901C2214yescomplemented
26#15688900C2218yescomplemented
27C2×M32×C47C2212yes—
28C47×#405C2211yescharacteristic
29C47×#347C2214yescomplemented
30C22×C4×D47C2×C411yescharacteristic
31C2×#10625329C2×C411yescharacteristic
32C2×#10625324C2×C412yes—
33M16×D47—22no—
34M16×D47—22no—
35C22×C47⋊C8C2×C411yescharacteristic
36C2×C8×D47C2×C412yes—
37C2×C8×D47C2×C411yescharacteristic
38C2×C8×D47C2×C411yescharacteristic
39C2×C8×D47C2×C412yes—
40C2×C8×D47C2×C412yes—
41C2×C8×D47C2×C412yes—
42C2×C8×D47C2×C412yes—
43C2×C8×D47C2311yescharacteristic
44C2×C8×D47C2311yescharacteristic
45#13093983C2×C411yescharacteristic
46#13093982—21no—
47#13093981C2×C412yes—
48#13093980—21no—
49C4⋊C4×D47—21no—
50C22⋊C4×D47—21no—
51C42×D47C2×C412yes—
52#13093964C2×C414yescomplemented
53#13093964C2314yes—
54#13093963C2×C418yes—
55#13093963C2×C418yescomplemented
56C2×C47⋊C16C2×C414yescomplemented
57C16×D47C2×C418yes—
58C16×D47C2×C418yescomplemented
59#13093935C2×C412yes—
60#13093934C2×C412yes—
61#13093934C2312yes—
62C4×C47⋊C8C2×C412yes—
63C8×Dic47C2×C412yes—
64C8×Dic47C2×C412yes—
65C2×M16×C47C2×C411yescharacteristic
66C22×C8×C47C2311yescharacteristic
67#117×C47C2×C411yescharacteristic
68M32×C47C2×C414yescomplemented
69M32×C47C2314yes—
70C2×C16×C47C2×C414yescomplemented
71#97×C47C2312yes—
72C4×C8×C47C2×C412yes—
73C23×D47M1611yescharacteristic
74C22×C4×C47C22×C411yescharacteristic
75C22×Dic47M1611yescharacteristic
76C2×C4×D47—22no—
77C2×C4×D47C4212yes—
78C2×C4×D47C4212yes—
79C2×C4×D47M1611yescharacteristic
80C2×C4×D47M1611yescharacteristic
81C2×C4×D47M1612yes—
82C2×C4×D47M1612yes—
83C2×C4×D47C22×C411yescharacteristic
84C2×C4×D47C22×C411yescharacteristic
85M16×C47—22no—
86C2×C8×C47C22×C412yes—
87C2×C8×C47C22×C411yescharacteristic
88C2×C8×C47C22×C412yes—
89C2×C8×C47C22×C412yes—
90C2×C8×C47C2411yescharacteristic
91C4⋊C4×C47—21no—
92C22⋊C4×C47—21no—
93C42×C47C22×C412yes—
94C22⋊Dic47—21no—
95(C2×D47)⋊C4—22no—
96C4⋊Dic47—21no—
97Dic47⋊C4—22no—
98C4×Dic47—22no—
99C4×Dic47C22×C412yes—
100#10625329—22no—
101C2×C47⋊C8C4212yes—
102C2×C47⋊C8C4212yes—
103C2×C47⋊C8C22×C412yes—
104C2×C47⋊C8C22×C411yescharacteristic
105C2×C47⋊C8C22×C411yescharacteristic
106#10625324—24no—
107C8×D47—22no—
108C8×D47—22no—
109C8×D47C4211yescharacteristic
110C8×D47C4211yescharacteristic
111C8×D47C4212yes—
112C8×D47C4211yescharacteristic
113C8×D47C4211yescharacteristic
114C8×D47C4212yes—
115C8×D47C22×C412yes—
116C8×D47C22×C412yes—
117C8×D47C22×C412yes—
118C8×D47C22×C412yes—
119C16×C47C22×C418yes—
120C47⋊C16C22×C418yes—
121C23×C47C2×M1611yescharacteristic
122C22×D47—42no—
123C22×D47#9712yes—
124C22×D47#9712yes—
125C22×D47C2×M1611yescharacteristic
126C22×D47C2×M1611yescharacteristic
127C2×C4×C47—22no—
128C2×C4×C47C2×C4212yes—
129C2×C4×C47C2×M1612yes—
130C2×C4×C47C2×M1611yescharacteristic
131C2×C4×C47C23×C411yescharacteristic
132C2×Dic47—22no—
133C2×Dic47#9712yes—
134C2×Dic47#9712yes—
135C2×Dic47C2×M1611yescharacteristic
136C2×Dic47C2×M1611yescharacteristic
137C4×D47—44no—
138C4×D47#9712yes—
139C4×D47#9712yes—
140C4×D47#9712yes—
141C4×D47#9712yes—
142C4×D47C2×C4212yes—
143C4×D47C2×C4211yescharacteristic
144C4×D47C2×C4211yescharacteristic
145C4×D47C2×M1611yescharacteristic
146C4×D47C2×M1611yescharacteristic
147C4×D47C2×M1612yes—
148C8×C47—22no—
149C8×C47C2×C4211yescharacteristic
150C8×C47C2×C4211yescharacteristic
151C8×C47C23×C412yes—
152C47⋊C8—22no—
153C47⋊C8C2×C4212yes—
154C47⋊C8C2×C4211yescharacteristic
155C47⋊C8C2×C4211yescharacteristic
156C2×#2110—471nomaximal, Sylow
157C22×C47—41no—
158C22×C47C2×#9712yes—
159C22×C47C22×M1611yescharacteristic
160C2×D47—22no—
161C2×D47—24no—
162C2×D47—42no—
163C2×D47—41no—
164C2×D47C2×#9711yescharacteristic
165C2×D47C2×#9712yes—
166C2×D47C2×#9711yescharacteristic
167C4×C47—42no—
168C4×C47C2×#9712yes—
169C4×C47C22×C4211yescharacteristic
170C4×C47C22×M1611yescharacteristic
171Dic47—42no—
172Dic47C2×#9711yescharacteristic
173Dic47C2×#9711yescharacteristic
174Dic47C2×#9712yes—
175C22×M32—472no—
176C2×#405—471no—
177#2110—472no—
178#2110—471no—
179#2110—474no—
180#2110D4711yescharacteristic, direct product factor
181C2×#347—474no—
182C2×C47—21no—
183C2×C47—22no—
184C2×C47C22×#9711yescharacteristic
185D47—21no—
186D47—22no—
187D47#211012yesdirect product factor
188C22×M16—471no—
189C23×C8—471no—
190C2×#117—471no—
191C2×M32—472no—
192C2×M32—474no—
193C2×M32—474no—
194C2×M32—474no—
195C2×M32—474no—
196C2×M32—474no—
197C2×M32C2×D4712yes—
198C22×C16—474no—
199#405—471no—
200#405—471no—
201#405—471no—
202#405—472no—
203#405—472no—
204#405C2×D4711yescharacteristic
205C2×#97—472no—
206C2×C4×C8—472no—
207#347—478no—
208#347—474no—
209#347C2×D4714yescomplemented
210C47C2×#211011yescharacteristic, complemented, Sylow
211C23×C4—471no—
212C2×M16—471no—
213C2×M16—472no—
214C2×M16—942no—
215C2×M16—942no—
216C2×M16C4×D4711yescharacteristic
217C22×C8—471no—
218C22×C8—471no—
219C22×C8—471no—
220C22×C8—472no—
221C22×C8—472no—
222C22×C8—472no—
223C22×C8—472no—
224C22×C8—471no—
225C22×C8—471no—
226C22×C8—472no—
227C22×C8C22×D4711yescharacteristic
228#117—471no—
229#117—472no—
230#117—941no—
231#117—941no—
232#117C4×D4711yescharacteristic
233C2×C4⋊C4—941no—
234C2×C22⋊C4—941no—
235C2×C42—472no—
236M32—474no—
237M32—474no—
238M32—478no—
239M32—478no—
240M32C4×D4714yescomplemented
241M32C22×D4714yes—
242C2×C16—474no—
243C2×C16—478no—
244C2×C16—478no—
245C2×C16C4×D4714yescomplemented
246#97—472no—
247#97—472no—
248#97—472no—
249#97C22×D4712yes—
250C4×C8—472no—
251C4×C8—472no—
252C4×C8—472no—
253C4×C8C4×D4712yes—
254C24—471no—
255C22×C4—471no—
256C22×C4—472no—
257C22×C4—472no—
258C22×C4—471no—
259C22×C4—471no—
260C22×C4—472no—
261C22×C4—472no—
262C22×C4—471no—
263C22×C4—471no—
264C22×C4—942no—
265C22×C4C2×C4×D4711yescharacteristic
266M16—22no—
267M16—944no—
268M16—942no—
269C2×C8—472no—
270C2×C8—472no—
271C2×C8—471no—
272C2×C8—471no—
273C2×C8—471no—
274C2×C8—471no—
275C2×C8—472no—
276C2×C8—471no—
277C2×C8—471no—
278C2×C8—472no—
279C2×C8—472no—
280C2×C8—472no—
281C2×C8—472no—
282C2×C8—472no—
283C2×C8—472no—
284C2×C8—942no—
285C2×C8—942no—
286C2×C8C2×C4×D4712yes—
287C2×C8C2×C4×D4711yescharacteristic
288C2×C8C2×C4×D4712yes—
289C2×C8C2×C4×D4712yes—
290C2×C8C23×D4711yescharacteristic
291C4⋊C4—21no—
292C4⋊C4—942no—
293C4⋊C4—941no—
294C22⋊C4—21no—
295C22⋊C4—942no—
296C22⋊C4—941no—
297C42—472no—
298C42—942no—
299C42C2×C4×D4712yes—
300C16—478no—
301C16C2×C4×D4718yes—
302C23—472no—
303C23—471no—
304C23—472no—
305C23—471no—
306C23—1882no—
307C23M16×D4711yescharacteristic
308C2×C4—22no—
309C2×C4—472no—
310C2×C4—472no—
311C2×C4—471no—
312C2×C4—471no—
313C2×C4—471no—
314C2×C4—472no—
315C2×C4—471no—
316C2×C4—472no—
317C2×C4—472no—
318C2×C4—472no—
319C2×C4—472no—
320C2×C4—471no—
321C2×C4—471no—
322C2×C4—472no—
323C2×C4—942no—
324C2×C4—1884no—
325C2×C4C42×D4712yes—
326C2×C4M16×D4711yescharacteristic
327C2×C4M16×D4712yes—
328C2×C4C22×C4×D4711yescharacteristic
329C8—22no—
330C8—471no—
331C8—471no—
332C8—472no—
333C8—942no—
334C8C42×D4711yescharacteristic
335C8C42×D4711yescharacteristic
336C8C22×C4×D4712yes—
337C22—41no—
338C22—471no—
339C22—471no—
340C22—472no—
341C22—942no—
342C22—944no—
343C22—1881no—
344C22—1882no—
345C22#97×D4712yes—
346C22C2×M16×D4711yescharacteristic
347C4—42no—
348C4—471no—
349C4—471no—
350C4—472no—
351C4—1882no—
352C4#97×D4712yes—
353C4C2×C42×D4711yescharacteristic
354C4C2×M16×D4711yescharacteristic
355C2—21no—
356C2—22no—
357C2—472no—
358C2—941no—
359C2—942no—
360C2C2×#97×D4711yescharacteristic
subgroupG/H
centerC8C42×D47
commutatorC4×C47C22×C42
FrattiniC2×C8C23×D47
FittingC47×#2110C2
socleC2×C47C22×#97
prime radicalC23×D47M16
cosocleC2×C8×C47C24
hypercenter#2110D47
hypocenterC47C2×#2110
LCSG ▷ C4×C47 ▷ C47
UCSC1 ◁ C8 ◁ #2110

Complements

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

NH ≅ G/Ntype
3. #20244993C2semidirect
4. #20244992C2semidirect
5. #20244991C2semidirect
6. #347×D47C2semidirect
7. C47×#2110C2semidirect
12. C2×#13093963C4semidirect
13. M32×D47C4semidirect
14. M32×D47C4semidirect
17. C2×C16×D47C4semidirect
25. #15688901C22semidirect
26. #15688900C22semidirect
29. C47×#347C22semidirect
52. #13093964C2×C4semidirect
55. #13093963C2×C4semidirect
56. C2×C47⋊C16C2×C4semidirect
58. C16×D47C2×C4semidirect
68. M32×C47C2×C4semidirect
70. C2×C16×C47C2×C4semidirect
180. #2110D47direct (N × H)
187. D47#2110direct (N × H)
209. #347C2×D47semidirect
210. C47C2×#2110semidirect
240. M32C4×D47semidirect
245. C2×C16C4×D47semidirect

Maximal subgroups

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

subgroupindex
C2×M32×D472
#405×D472
#202449932
#202449922
#202449912
#347×D472
C47×#21102
C2×#211047