Finite Group Databasebeta

← #20253329

Subgroups — #20253329

Order 6016.

462 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 462 conjugacy classes of subgroups — too many to draw. Only its 137 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
1C2×#13093998C211yesmaximal, characteristic
2C2×#13093983C211yesmaximal, characteristic, complemented
3#15689448C214yesmaximal, complemented
4#15689442C212yesmaximal, complemented
5#15689437C212yesmaximal, complemented
6#15689165C212yesmaximal, complemented
7#15689129C212yesmaximal, complemented
8C47×#407C211yesmaximal, characteristic, complemented
9C22×D188C2211yescharacteristic
10C22×C22⋊D47—21no—
11#13093998—21no—
12#13093998—21no—
13#13093998C2212yes—
14#13093998C2212yes—
15#13093983—21no—
16#13093983—21no—
17#13093983C2212yes—
18#13093983C2212yescomplemented
19C2×C4⋊Dic47C2211yescharacteristic
20C2×C4⋊Dic47C2211yescharacteristic, complemented
21C2×C4⋊Dic47C2211yescharacteristic, complemented
22C2×C22⋊Dic47—21no—
23C2×(C2×D47)⋊C4—21no—
24C2×C4×Dic47—21no—
25#13093958C2214yescomplemented
26#13093956C2214yescomplemented
27#13093946C2214yescomplemented
28#13093946C2214yescomplemented
29C23×C4×C47C2211yescharacteristic
30C2×M16×C47C2212yes—
31C22⋊C8×C47C2212yescomplemented
32C22⋊C8×C47C2212yescomplemented
33C24×C47D411yescharacteristic
34C23×D47—21no—
35C22×C4×C47—24no—
36C22×C4×C47D411yescharacteristic
37C22×C4×C47D411yescharacteristic
38C22×C4×C47D411yescharacteristic
39C22×C4×C47C2311yescharacteristic
40C22×C4×C47C2311yescharacteristic
41C22×C4×C47C2311yescharacteristic
42C2×C22⋊D47—22no—
43C2×C22⋊D47—22no—
44C2×C22⋊D47—44no—
45C22×Dic47—21no—
46C22×Dic47—21no—
47C22×Dic47—21no—
48C2×D188—24no—
49C2×D188—21no—
50C2×D188C2312yes—
51M16×C47—24no—
52C2×C8×C47C2314yes—
53C22⋊Dic47—22no—
54C22⋊Dic47—22no—
55(C2×D47)⋊C4—22no—
56(C2×D47)⋊C4—22no—
57C4⋊Dic47—21no—
58C4⋊Dic47—21no—
59C4⋊Dic47—21no—
60C4⋊Dic47C2312yes—
61C4⋊Dic47C2312yes—
62C4⋊Dic47C2312yes—
63C4×Dic47—22no—
64C4×Dic47—22no—
65C23×C47—22no—
66C23×C47—22no—
67C23×C47—41no—
68C23×C47C2×D411yescharacteristic
69C23×C47C2×D411yescharacteristic
70C23×C47C2×D411yescharacteristic
71C22×D47—22no—
72C22×D47—42no—
73C22×D47—42no—
74C22×D47—42no—
75C2×C4×C47—22no—
76C2×C4×C47—22no—
77C2×C4×C47—22no—
78C2×C4×C47—22no—
79C2×C4×C47—22no—
80C2×C4×C47C2×D411yescharacteristic
81C2×C4×C47C2×D411yescharacteristic
82C2×C4×C47C2×D411yescharacteristic
83C2×C4×C47#4114yes—
84C2×C4×C47C2411yescharacteristic
85C22⋊D47—44no—
86C22⋊D47—44no—
87C2×Dic47—22no—
88C2×Dic47—22no—
89C2×Dic47—22no—
90C2×Dic47—42no—
91C2×Dic47—42no—
92C2×Dic47—42no—
93D188—24no—
94D188—42no—
95C8×C47—24no—
96C22×C47—21no—
97C22×C47—21no—
98C22×C47—21no—
99C22×C47—21no—
100C22×C47—21no—
101C22×C47—21no—
102C22×C47—21no—
103C22×C47—44no—
104C22×C47#12312yes—
105C22×C47AGL(1,ℤ/8)12yes—
106C22×C47C22×D411yescharacteristic
107C2×D47—42no—
108C2×D47—42no—
109C2×D47—42no—
110C2×D47—84no—
111C4×C47—21no—
112C4×C47—21no—
113C4×C47#12312yes—
114C4×C47C2×#4112yes—
115Dic47—42no—
116Dic47—42no—
117Dic47—42no—
118#3094—471nomaximal, Sylow
119C2×C47—22no—
120C2×C47—22no—
121C2×C47—41no—
122C2×C47C2×#12311yescharacteristic
123C2×C47C2×AGL(1,ℤ/8)11yescharacteristic
124C2×C47#57511yescharacteristic
125D47—82no—
126C2×#121—471no—
127C2×#117—471no—
128#482—474no—
129#481—472no—
130#480—472no—
131#428—472no—
132#418—472no—
133#407D4711yescharacteristic, complemented
134C47#309411yescharacteristic, complemented, Sylow
135C22×D4—471no—
136C22×D4—941no—
137C23×C4C2×D4711yescharacteristic
138C2×M16C2×D4712yes—
139#121—472no—
140#121—472no—
141#121—941no—
142#121—941no—
143#117—472no—
144#117—472no—
145#117—941no—
146#117—941no—
147C2×C4⋊C4—471no—
148C2×C4⋊C4—471no—
149C2×C4⋊C4—471no—
150C2×C22⋊C4—941no—
151C2×C22⋊C4—941no—
152C2×C42—941no—
153#107—474no—
154#106—474no—
155#102—474no—
156#102—474no—
157C22⋊C8C2×D4712yescomplemented
158C22⋊C8C2×D4712yescomplemented
159C24—941no—
160C24D18811yescharacteristic
161C2×D4—472no—
162C2×D4—942no—
163C2×D4—942no—
164C2×D4—941no—
165C2×D4—944no—
166C2×D4—1884no—
167C22×C4—24no—
168C22×C4—941no—
169C22×C4—941no—
170C22×C4—941no—
171C22×C4D18811yescharacteristic
172C22×C4D18811yescharacteristic
173C22×C4D18811yescharacteristic
174C22×C4C22×D4711yescharacteristic
175C22×C4C22×D4711yescharacteristic
176C22×C4C22×D4711yescharacteristic
177M16—24no—
178C2×C8C22×D4714yes—
179C4⋊C4—472no—
180C4⋊C4—472no—
181C4⋊C4—472no—
182C4⋊C4—941no—
183C4⋊C4—941no—
184C4⋊C4—941no—
185C22⋊C4—942no—
186C22⋊C4—942no—
187C22⋊C4—942no—
188C22⋊C4—942no—
189C42—942no—
190C42—942no—
191C23—22no—
192C23—22no—
193C23—41no—
194C23—942no—
195C23—1882no—
196C23—1882no—
197C23—1882no—
198C23C2×D18811yescharacteristic
199C23C2×D18811yescharacteristic
200C23C2×D18811yescharacteristic
201D4—944no—
202D4—1884no—
203D4—1884no—
204D4—1882no—
205C2×C4—22no—
206C2×C4—22no—
207C2×C4—22no—
208C2×C4—22no—
209C2×C4—22no—
210C2×C4—942no—
211C2×C4—942no—
212C2×C4—942no—
213C2×C4—1882no—
214C2×C4—1882no—
215C2×C4—1882no—
216C2×C4C2×D18811yescharacteristic
217C2×C4C2×D18811yescharacteristic
218C2×C4C2×D18811yescharacteristic
219C2×C4#1062535214yes—
220C2×C4C23×D4711yescharacteristic
221C8—24no—
222C22—21no—
223C22—21no—
224C22—21no—
225C22—21no—
226C22—21no—
227C22—21no—
228C22—21no—
229C22—44no—
230C22—3764no—
231C22—1882no—
232C22—1882no—
233C22—1882no—
234C22#1309400812yes—
235C22#1309405212yes—
236C22C22×D18811yescharacteristic
237C4—21no—
238C4—21no—
239C4—1882no—
240C4—1882no—
241C4—1882no—
242C4#1309400812yes—
243C4C2×#1062535212yes—
244C2—22no—
245C2—22no—
246C2—41no—
247C2—3762no—
248C2C2×#1309400811yescharacteristic
249C2C2×#1309405211yescharacteristic
250C2#1568992311yescharacteristic
subgroupG/H
centerC22C22×D188
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#407C2
socleC22×C47C22×D4
hypercenter#407D47
hypocenterC47#3094
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C23×C4 ◁ #407

Complements

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

NH ≅ G/Ntype
2. C2×#13093983C2semidirect
3. #15689448C2semidirect
4. #15689442C2semidirect
5. #15689437C2semidirect
6. #15689165C2semidirect
7. #15689129C2semidirect
8. C47×#407C2semidirect
18. #13093983C22semidirect
20. C2×C4⋊Dic47C22semidirect
21. C2×C4⋊Dic47C22semidirect
25. #13093958C22semidirect
26. #13093956C22semidirect
27. #13093946C22semidirect
28. #13093946C22semidirect
31. C22⋊C8×C47C22semidirect
32. C22⋊C8×C47C22semidirect
133. #407D47semidirect
134. C47#3094semidirect
157. C22⋊C8C2×D47semidirect
158. C22⋊C8C2×D47semidirect