Finite Group Databasebeta

← #20241889

Subgroups — #20241889

Order 6016.

334 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 334 conjugacy classes of subgroups — too many to draw. Only its 65 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689633C211yesmaximal, characteristic
2#15689085C211yesmaximal, characteristic, complemented
3#95×D47C211yesmaximal, characteristic, complemented
4#15688861C211yesmaximal, characteristic, complemented
5#15688859C211yesmaximal, characteristic, complemented
6#15688857C211yesmaximal, characteristic, complemented
7C47×#327C211yesmaximal, characteristic, complemented
8C2×#10625352C411yescharacteristic, complemented
9C22×C4×D47—21no—
10C22×C4×D47C2211yescharacteristic
11C2×#10625324—21no—
12#13094006—21no—
13#13094004C411yescharacteristic, complemented
14#13094003C2211yescharacteristic
15#13093995C411yescharacteristic, complemented
16#13093992—21no—
17D4×Dic47—21no—
18(C22⋊D47)⋊C4—21no—
19#13093982C411yescharacteristic, complemented
20C22⋊(C47⋊C8)C2211yescharacteristic
21(C2×D47)⋊C8—21no—
22C47⋊#95—21no—
23C47⋊#95C2211yescharacteristic
24#121×C47C2211yescharacteristic
25C22⋊C8×C47C2211yescharacteristic
26#95×C47C2211yescharacteristic
27C23×D47D411yescharacteristic
28C2×D4×C47—21no—
29C2×D4×C47C2×C411yescharacteristic, complemented
30C22×C4×C47—21no—
31C22×C4×C47C2311yescharacteristic
32C2×C22⋊D47—21no—
33C2×C22⋊D47—21no—
34C22×Dic47—21no—
35C22×Dic47—21no—
36C22×Dic47D411yescharacteristic
37#10625352—42no—
38C2×C4×D47—24no—
39C2×C4×D47—42no—
40C2×C4×D47—42no—
41C2×C4×D47—42no—
42C2×C4×D47C2×C411yescharacteristic
43C2×C4×D47C2×C411yescharacteristic
44C2×C4×D47D411yescharacteristic
45C2×C4×D47D411yescharacteristic
46C2×Dic94C2×C411yescharacteristic, complemented
47C2×C8×C47—21no—
48C4⋊C4×C47C2×C411yescharacteristic, complemented
49C22⋊C4×C47—21no—
50C22⋊Dic47—21no—
51C22⋊Dic47—21no—
52(C2×D47)⋊C4—21no—
53(C2×D47)⋊C4—21no—
54C4⋊Dic47—21no—
55C4⋊Dic47C2×C411yescharacteristic, complemented
56Dic47⋊C4—21no—
57C4×Dic47—21no—
58C2×C47⋊C8—21no—
59#10625324—42no—
60C23×C47—21no—
61C23×C47C2×D411yescharacteristic
62C22×D47—21no—
63C22×D47—21no—
64C22×D47—22no—
65C22×D47—22no—
66C22×D47C22⋊C411yescharacteristic
67C22×D47C22⋊C411yescharacteristic
68D4×C47—41no—
69D4×C47—41no—
70D4×C47—41no—
71C2×C4×C47—22no—
72C2×C4×C47—21no—
73C2×C4×C47—41no—
74C2×C4×C47—41no—
75C2×C4×C47—41no—
76C2×C4×C47C22×C411yescharacteristic
77C2×C4×C47C2×D411yescharacteristic
78C22⋊D47—42no—
79C22⋊D47—42no—
80C2×Dic47—22no—
81C2×Dic47—21no—
82C2×Dic47—21no—
83C2×Dic47—41no—
84C2×Dic47—42no—
85C2×Dic47—41no—
86C2×Dic47—41no—
87C2×Dic47C22⋊C411yescharacteristic
88C2×Dic47C22⋊C411yescharacteristic
89C4×D47—22no—
90C4×D47—22no—
91C4×D47—41no—
92C4×D47—41no—
93C4×D47—48no—
94Dic94—41no—
95C8×C47—41no—
96C47⋊C8—41no—
97C22×C47—21no—
98C22×C47—21no—
99C22×C47—41no—
100C22×C47—41no—
101C22×C47—41no—
102C22×C47C2×C22⋊C411yescharacteristic
103C22×C47AGL(1,ℤ/8)11yescharacteristic
104C22×C47#13711yescharacteristic
105C2×D47—24no—
106C2×D47—24no—
107C2×D47—21no—
108C2×D47—21no—
109C2×D47—21no—
110C2×D47—21no—
111C2×D47#9912yes—
112C2×D47#10412yes—
113C4×C47—21no—
114C4×C47—21no—
115C4×C47—42no—
116C4×C47—41no—
117Dic47—21no—
118Dic47—21no—
119Dic47—42no—
120Dic47—41no—
121Dic47—41no—
122#1504—471nomaximal, Sylow
123C2×C47—21no—
124C2×C47—21no—
125C2×C47—81no—
126C2×C47C2×#9911yescharacteristic
127C2×C47#41711yescharacteristic
128C2×C47C2×#10411yescharacteristic
129D47—22no—
130D47—22no—
131#525—471no—
132#407—471no—
133C2×#95—471no—
134#328—471no—
135#328—471no—
136#327—471no—
137#327D4711yescharacteristic, complemented
138C47#150411yescharacteristic, complemented, Sylow
139C2×#41—471no—
140C23×C4—471no—
141C23×C4—941no—
142C2×M16—941no—
143#123—941no—
144C22⋊Q8—471no—
145C22⋊Q8—471no—
146#121—471no—
147#121C2×D4711yescharacteristic
148#120—941no—
149C4×D4—941no—
150C4×D4—941no—
151#117—471no—
152C22⋊C8—471no—
153C22⋊C8—941no—
154C22⋊C8C2×D4711yescharacteristic
155#95—471no—
156#95—941no—
157#95C2×D4711yescharacteristic
158C24—471no—
159#41—1882no—
160C2×Q8—471no—
161C2×D4—21no—
162C2×D4—941no—
163C2×D4—941no—
164C2×D4C4×D4711yescharacteristic, complemented
165C22×C4—21no—
166C22×C4—471no—
167C22×C4—471no—
168C22×C4—471no—
169C22×C4—471no—
170C22×C4—471no—
171C22×C4—944no—
172C22×C4—941no—
173C22×C4—941no—
174C22×C4—1882no—
175C22×C4—1882no—
176C22×C4—1882no—
177C22×C4C22×D4711yescharacteristic
178M16—1882no—
179C2×C8—21no—
180C2×C8—941no—
181C4⋊C4—471no—
182C4⋊C4—941no—
183C4⋊C4—941no—
184C4⋊C4C4×D4711yescharacteristic, complemented
185C22⋊C4—21no—
186C22⋊C4—941no—
187C22⋊C4—941no—
188C22⋊C4—941no—
189C22⋊C4—941no—
190C42—941no—
191C23—21no—
192C23—471no—
193C23—471no—
194C23—942no—
195C23—942no—
196C23—941no—
197C23—941no—
198C23D4×D4711yescharacteristic
199Q8—1881no—
200D4—41no—
201D4—41no—
202D4—41no—
203D4—1882no—
204D4—1882no—
205C2×C4—22no—
206C2×C4—21no—
207C2×C4—41no—
208C2×C4—41no—
209C2×C4—41no—
210C2×C4—471no—
211C2×C4—471no—
212C2×C4—942no—
213C2×C4—942no—
214C2×C4—942no—
215C2×C4—941no—
216C2×C4—941no—
217C2×C4—1881no—
218C2×C4—1881no—
219C2×C4—1888no—
220C2×C4—1881no—
221C2×C4—1882no—
222C2×C4—1881no—
223C2×C4—1881no—
224C2×C4C2×C4×D4711yescharacteristic
225C2×C4D4×D4711yescharacteristic
226C8—41no—
227C8—1881no—
228C22—21no—
229C22—21no—
230C22—41no—
231C22—41no—
232C22—41no—
233C22—472no—
234C22—472no—
235C22—944no—
236C22—944no—
237C22—941no—
238C22—941no—
239C22—941no—
240C22—941no—
241C22C22⋊C4×D4711yescharacteristic
242C22#1309404811yescharacteristic
243C22#1309405311yescharacteristic
244C4—21no—
245C4—21no—
246C4—42no—
247C4—41no—
248C4—941no—
249C4—941no—
250C4—1882no—
251C4—1881no—
252C4—1881no—
253C2—21no—
254C2—21no—
255C2—81no—
256C2—942no—
257C2—942no—
258C2#99×D4711yescharacteristic
259C2#1568912111yescharacteristic
260C2#104×D4711yescharacteristic
subgroupG/H
centerC22C22⋊C4×D47
commutatorC2×C4×C47C22×C4
FrattiniC22×C4C22×D47
FittingC47×#327C2
socleC22×C47C2×C22⋊C4
hypercenter#327D47
hypocenterC47#1504
LCSG ▷ C2×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #327

Complements

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

NH ≅ G/Ntype
2. #15689085C2semidirect
3. #95×D47C2semidirect
4. #15688861C2semidirect
5. #15688859C2semidirect
6. #15688857C2semidirect
7. C47×#327C2semidirect
8. C2×#10625352C4semidirect
13. #13094004C4semidirect
15. #13093995C4semidirect
19. #13093982C4semidirect
29. C2×D4×C47C2×C4semidirect
46. C2×Dic94C2×C4semidirect
48. C4⋊C4×C47C2×C4semidirect
55. C4⋊Dic47C2×C4semidirect
137. #327D47semidirect
138. C47#1504semidirect
164. C2×D4C4×D47semidirect
184. C4⋊C4C4×D47semidirect