Finite Group Databasebeta

← C47×#20347 #26060045

Subgroups — C47×#20347 #26060045

Order 12032.

2270 conjugacy classes of subgroups.

The subgroup lattice has 298 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×M16×C47C211yesmaximal, characteristic
2C22×#117×C47C212yesmaximal
3C47×#1736C218yesmaximal, complemented
4C47×#1735C214yesmaximal, complemented
5C24×C4×C47C2211yescharacteristic
6C22×M16×C47—28no—
7C22×M16×C47C418yescomplemented
8C22×M16×C47C2214yes—
9C23×C8×C47C2212yes—
10C2×#117×C47—28no—
11C2×#117×C47—22no—
12C2×#117×C47—22no—
13C2×#117×C47C4116yescomplemented
14C2×#117×C47C2214yes—
15C2×#117×C47C2214yes—
16C22×C4⋊C4×C47C2214yes—
17C22×C22⋊C4×C47—22no—
18C22×C42×C47—22no—
19C47×#340C22116yescomplemented
20C25×C47D411yescharacteristic
21C23×C4×C47—24no—
22C23×C4×C47C2×C414yes—
23C23×C4×C47C2×C418yes—
24C23×C4×C47D411yescharacteristic
25C23×C4×C47D412yes—
26C23×C4×C47D418yes—
27C23×C4×C47Q814yes—
28C23×C4×C47C2312yes—
29C23×C4×C47C2311yescharacteristic
30C2×M16×C47—232no—
31C2×M16×C47—28no—
32C2×M16×C47—28no—
33C2×M16×C47C2×C4116yescomplemented
34C22×C8×C47—28no—
35C22×C8×C47C2×C418yescomplemented
36C22×C8×C47C2314yes—
37#117×C47—216no—
38#117×C47—216no—
39#117×C47—28no—
40#117×C47—28no—
41#117×C47C2×C4116yes—
42#117×C47C2×C4116yescomplemented
43C2×C4⋊C4×C47—24no—
44C2×C4⋊C4×C47—28no—
45C2×C4⋊C4×C47C2×C4116yescomplemented
46C2×C4⋊C4×C47C2318yes—
47C2×C22⋊C4×C47—216no—
48C2×C22⋊C4×C47—24no—
49C2×C22⋊C4×C47—24no—
50C2×C42×C47—216no—
51C2×C42×C47—24no—
52C2×C42×C47—24no—
53C24×C47—44no—
54C24×C47C22⋊C418yes—
55C24×C47C4⋊C414yes—
56C24×C47C2×D411yescharacteristic
57C24×C47C2×D412yes—
58C22×C4×C47—216no—
59C22×C4×C47—28no—
60C22×C4×C47—416no—
61C22×C4×C47C42116yes—
62C22×C4×C47C22⋊C418yes—
63C22×C4×C47C22⋊C418yes—
64C22×C4×C47C22⋊C418yes—
65C22×C4×C47C22⋊C4116yes—
66C22×C4×C47C4⋊C414yes—
67C22×C4×C47C4⋊C418yes—
68C22×C4×C47C4⋊C4132yes—
69C22×C4×C47C22×C412yes—
70C22×C4×C47C22×C414yes—
71C22×C4×C47C22×C414yes—
72C22×C4×C47C22×C414yes—
73C22×C4×C47C22×C414yes—
74C22×C4×C47C2×D412yes—
75C22×C4×C47C2×D414yes—
76C22×C4×C47C2×D414yes—
77C22×C4×C47C2×D414yes—
78C22×C4×C47C2×D411yescharacteristic
79C22×C4×C47C2×Q814yes—
80C22×C4×C47C2×Q812yes—
81C22×C4×C47C2411yescharacteristic
82M16×C47—232no—
83C2×C8×C47—216no—
84C2×C8×C47—28no—
85C2×C8×C47C22×C418yes—
86C4⋊C4×C47—216no—
87C4⋊C4×C47—28no—
88C4⋊C4×C47C22×C4116yes—
89C22⋊C4×C47—216no—
90C22⋊C4×C47—216no—
91C42×C47—216no—
92C42×C47—216no—
93C23×C47—28no—
94C23×C47—24no—
95C23×C47—416no—
96C23×C47—48no—
97C23×C47#95116yes—
98C23×C47C2×C22⋊C414yes—
99C23×C47C2×C22⋊C414yes—
100C23×C47C2×C22⋊C414yes—
101C23×C47C2×C4⋊C412yes—
102C23×C47C2×C4⋊C414yes—
103C23×C47C22×D411yescharacteristic
104C2×C4×C47—216no—
105C2×C4×C47—432no—
106C2×C4×C47—416no—
107C2×C4×C47#95132yes—
108C2×C4×C47#95116yes—
109C2×C4×C47C2×C4214yes—
110C2×C4×C47C2×C4218yes—
111C2×C4×C47C2×C22⋊C414yes—
112C2×C4×C47C2×C22⋊C418yes—
113C2×C4×C47C2×C22⋊C414yes—
114C2×C4×C47C2×C22⋊C414yes—
115C2×C4×C47C2×C22⋊C414yes—
116C2×C4×C47C2×C4⋊C418yes—
117C2×C4×C47C2×C4⋊C418yes—
118C2×C4×C47C2×C4⋊C418yes—
119C2×C4×C47C2×C4⋊C414yes—
120C2×C4×C47C2×C4⋊C412yes—
121C2×C4×C47C23×C411yescharacteristic
122C2×C4×C47C23×C412yes—
123C2×C4×C47C22×D412yes—
124C2×C4×C47C22×Q811yescharacteristic
125C8×C47—28no—
126#20347C4711yesmaximal, characteristic, direct product factor, Sylow
127C22×C47—28no—
128C22×C47—28no—
129C22×C47—28no—
130C22×C47—28no—
131C22×C47—24no—
132C22×C47—416no—
133C22×C47C2×#9514yes—
134C22×C47C2×#9518yes—
135C22×C47C22×C22⋊C412yes—
136C22×C47C22×C4⋊C411yescharacteristic
137C22×C47#57514yes—
138C4×C47—416no—
139C4×C47C2×#9514yes—
140C4×C47C2×#9518yes—
141C4×C47C22×C4211yescharacteristic
142C4×C47C22×C22⋊C411yescharacteristic
143C4×C47C22×C4⋊C412yes—
144C23×M16C2×C4711yescharacteristic
145C22×#117C2×C4712yes—
146#1736C2×C4718yescomplemented
147#1735C2×C4714yescomplemented
148C2×C47—28no—
149C2×C47—24no—
150C2×C47C22×#9511yescharacteristic
151C2×C47#289614yes—
152C2×C47#291112yes—
153C24×C4C22×C4711yescharacteristic
154C22×M16—28no—
155C22×M16C4×C4718yescomplemented
156C22×M16C22×C4714yes—
157C23×C8C22×C4712yes—
158C2×#117—28no—
159C2×#117—22no—
160C2×#117—22no—
161C2×#117C4×C47116yescomplemented
162C2×#117C22×C4714yes—
163C2×#117C22×C4714yes—
164C22×C4⋊C4C22×C4714yes—
165C22×C22⋊C4—22no—
166C22×C42—22no—
167#340C22×C47116yescomplemented
168C47#2034711yescharacteristic, direct product factor, Sylow
169C25D4×C4711yescharacteristic
170C23×C4—24no—
171C23×C4C2×C4×C4714yes—
172C23×C4C2×C4×C4718yes—
173C23×C4D4×C4711yescharacteristic
174C23×C4D4×C4712yes—
175C23×C4D4×C4718yes—
176C23×C4Q8×C4714yes—
177C23×C4C23×C4712yes—
178C23×C4C23×C4711yescharacteristic
179C2×M16—232no—
180C2×M16—28no—
181C2×M16—28no—
182C2×M16C2×C4×C47116yescomplemented
183C22×C8—28no—
184C22×C8C2×C4×C4718yescomplemented
185C22×C8C23×C4714yes—
186#117—216no—
187#117—216no—
188#117—28no—
189#117—28no—
190#117C2×C4×C47116yes—
191#117C2×C4×C47116yescomplemented
192C2×C4⋊C4—24no—
193C2×C4⋊C4—28no—
194C2×C4⋊C4C2×C4×C47116yescomplemented
195C2×C4⋊C4C23×C4718yes—
196C2×C22⋊C4—216no—
197C2×C22⋊C4—24no—
198C2×C22⋊C4—24no—
199C2×C42—216no—
200C2×C42—24no—
201C2×C42—24no—
202C24—44no—
203C24C22⋊C4×C4718yes—
204C24C4⋊C4×C4714yes—
205C24C2×D4×C4711yescharacteristic
206C24C2×D4×C4712yes—
207C22×C4—216no—
208C22×C4—28no—
209C22×C4—416no—
210C22×C4C42×C47116yes—
211C22×C4C22⋊C4×C47116yes—
212C22×C4C22⋊C4×C4718yes—
213C22×C4C22⋊C4×C4718yes—
214C22×C4C22⋊C4×C4718yes—
215C22×C4C4⋊C4×C47132yes—
216C22×C4C4⋊C4×C4714yes—
217C22×C4C4⋊C4×C4718yes—
218C22×C4C22×C4×C4712yes—
219C22×C4C22×C4×C4714yes—
220C22×C4C22×C4×C4714yes—
221C22×C4C22×C4×C4714yes—
222C22×C4C22×C4×C4714yes—
223C22×C4C2×D4×C4712yes—
224C22×C4C2×D4×C4711yescharacteristic
225C22×C4C2×D4×C4714yes—
226C22×C4C2×D4×C4714yes—
227C22×C4C2×D4×C4714yes—
228C22×C4C2×Q8×C4714yes—
229C22×C4C2×Q8×C4712yes—
230C22×C4C24×C4711yescharacteristic
231M16—232no—
232C2×C8—216no—
233C2×C8—28no—
234C2×C8C22×C4×C4718yes—
235C4⋊C4—216no—
236C4⋊C4—28no—
237C4⋊C4C22×C4×C47116yes—
238C22⋊C4—216no—
239C22⋊C4—216no—
240C42—216no—
241C42—216no—
242C23—28no—
243C23—24no—
244C23—416no—
245C23—48no—
246C23#95×C47116yes—
247C23C2×C22⋊C4×C4714yes—
248C23C2×C22⋊C4×C4714yes—
249C23C2×C22⋊C4×C4714yes—
250C23C2×C4⋊C4×C4712yes—
251C23C2×C4⋊C4×C4714yes—
252C23C22×D4×C4711yescharacteristic
253C2×C4—216no—
254C2×C4—432no—
255C2×C4—416no—
256C2×C4#95×C47132yes—
257C2×C4#95×C47116yes—
258C2×C4C2×C42×C4714yes—
259C2×C4C2×C42×C4718yes—
260C2×C4C2×C22⋊C4×C4714yes—
261C2×C4C2×C22⋊C4×C4718yes—
262C2×C4C2×C22⋊C4×C4714yes—
263C2×C4C2×C22⋊C4×C4714yes—
264C2×C4C2×C22⋊C4×C4714yes—
265C2×C4C2×C4⋊C4×C4718yes—
266C2×C4C2×C4⋊C4×C4718yes—
267C2×C4C2×C4⋊C4×C4718yes—
268C2×C4C2×C4⋊C4×C4714yes—
269C2×C4C2×C4⋊C4×C4712yes—
270C2×C4C23×C4×C4711yescharacteristic
271C2×C4C23×C4×C4712yes—
272C2×C4C22×D4×C4712yes—
273C2×C4C22×Q8×C4711yescharacteristic
274C8—28no—
275C22—28no—
276C22—28no—
277C22—28no—
278C22—28no—
279C22—24no—
280C22—416no—
281C22C2×#95×C4714yes—
282C22C2×#95×C4718yes—
283C22C22×C22⋊C4×C4712yes—
284C22C22×C4⋊C4×C4711yescharacteristic
285C22C47×#57514yes—
286C4—416no—
287C4C2×#95×C4714yes—
288C4C2×#95×C4718yes—
289C4C22×C42×C4711yescharacteristic
290C4C22×C22⋊C4×C4711yescharacteristic
291C4C22×C4⋊C4×C4712yes—
292C2—28no—
293C2—24no—
294C2C22×#95×C4711yescharacteristic
295C2C47×#289614yes—
296C2C47×#291112yes—
subgroupG/H
centerC22×C4×C47C2×D4
commutatorC4C22×C42×C47
Frattini, cosocleC22×C4C24×C47
socleC23×C47C22×D4
prime radicalC25×C47D4
LCSG ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4×C47 ◁ C24×C4×C47 ◁ G

Complements

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

NH ≅ G/Ntype
3. C47×#1736C2semidirect
4. C47×#1735C2semidirect
7. C22×M16×C47C4semidirect
13. C2×#117×C47C4semidirect
19. C47×#340C22semidirect
33. C2×M16×C47C2×C4semidirect
35. C22×C8×C47C2×C4semidirect
42. #117×C47C2×C4semidirect
45. C2×C4⋊C4×C47C2×C4semidirect
126. #20347C47direct (N × H)
146. #1736C2×C47semidirect
147. #1735C2×C47semidirect
155. C22×M16C4×C47semidirect
161. C2×#117C4×C47semidirect
167. #340C22×C47semidirect
168. C47#20347direct (N × H)
182. C2×M16C2×C4×C47semidirect
184. C22×C8C2×C4×C47semidirect
191. #117C2×C4×C47semidirect
194. C2×C4⋊C4C2×C4×C47semidirect

Maximal subgroups

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

subgroupindex
C23×M16×C472
C22×#117×C472
C47×#17362
C47×#17352
#2034747