Finite Group Databasebeta

← #20249728

Subgroups — #20249728

Order 6016.

568 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 568 conjugacy classes of subgroups — too many to draw. Only its 141 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×#13094009C212yesmaximal
2C2×#13094002C212yesmaximal, complemented
3#15689054C212yesmaximal, complemented
4#15689049C212yesmaximal, complemented
5#15689043C211yesmaximal, characteristic, complemented
6#15689040C211yesmaximal, characteristic
7#15689014C212yesmaximal, complemented
8#15688994C212yesmaximal, complemented
9C47×#384C211yesmaximal, characteristic, complemented
10C22×Dic94C2211yescharacteristic
11C22×D188C2211yescharacteristic
12C22×C4×D47C2212yes—
13#13094009—28no—
14#13094002—28no—
15C2×Dic47⋊C4C2212yes—
16C2×Dic47⋊C4C2212yes—
17C2×Dic47⋊C4C2212yes—
18C2×(C2×D47)⋊C4C2212yes—
19C2×(C2×D47)⋊C4C2212yes—
20C2×(C2×D47)⋊C4C2212yes—
21C2×(C2×D47)⋊C4C2212yes—
22C2×(C2×D47)⋊C4C2212yes—
23C47⋊#95C2212yes—
24C47⋊#95C2212yes—
25C47⋊#95C2212yes—
26C47⋊#95C2211yescharacteristic
27C47⋊#95C2211yescharacteristic
28C2×C4⋊C4×C47C2212yes—
29C2×C4⋊C4×C47C2212yes—
30C2×C4⋊C4×C47C2211yescharacteristic
31C2×C4⋊C4×C47C2211yescharacteristic
32C2×C42×C47C2211yescharacteristic
33C23×D47C2312yes—
34C22×C4×C47C2311yescharacteristic
35C22×C4×C47C2312yes—
36C22×C4×C47C2311yescharacteristic
37C22×C4×C47C2312yes—
38C22×C4×C47C2311yescharacteristic
39C22×Dic47C2312yes—
40C22×Dic47C2312yes—
41C22×Dic47C2312yes—
42C2×D188—24no—
43C2×D188—41no—
44C2×C4×D47—24no—
45C2×C4×D47—24no—
46C2×C4×D47—42no—
47C2×Dic94—24no—
48C2×Dic94—41no—
49C4⋊C4×C47—24no—
50C4⋊C4×C47—24no—
51C4⋊C4×C47—41no—
52C4⋊C4×C47—41no—
53C42×C47—22no—
54(C2×D47)⋊C4—24no—
55(C2×D47)⋊C4—24no—
56(C2×D47)⋊C4—24no—
57(C2×D47)⋊C4—24no—
58(C2×D47)⋊C4D418yes—
59Dic47⋊C4—24no—
60Dic47⋊C4—24no—
61Dic47⋊C4—24no—
62C23×C47C2411yescharacteristic
63C22×D47—22no—
64C22×D47—22no—
65C22×D47—22no—
66C22×D47—22no—
67C22×D47—22no—
68C22×D47—22no—
69C22×D47C2×D414yes—
70C2×C4×C47—22no—
71C2×C4×C47—21no—
72C2×C4×C47—21no—
73C2×C4×C47—22no—
74C2×C4×C47—22no—
75C2×C4×C47—22no—
76C2×C4×C47—22no—
77C2×C4×C47—22no—
78C2×C4×C47—21no—
79C2×C4×C47—22no—
80C2×C4×C47—21no—
81C2×C4×C47C2×D414yes—
82C2×C4×C47#4112yes—
83C2×Dic47—22no—
84C2×Dic47—22no—
85C2×Dic47—22no—
86C2×Dic47—22no—
87C2×Dic47—22no—
88C2×Dic47—22no—
89C2×Dic47—22no—
90C2×Dic47—22no—
91C2×Dic47C2×D414yes—
92D188—44no—
93C4×D47—48no—
94Dic94—44no—
95C22×C47C22×D412yes—
96C22×C47C2×#4111yescharacteristic
97C22×C47H(5,𝔽2)11yescharacteristic
98C22×C472−1+411yescharacteristic
99C22×C472−1+412yes—
100C2×D47—24no—
101C2×D47—24no—
102C2×D47—24no—
103C2×D47—42no—
104C2×D47—42no—
105C2×D47—42no—
106C2×D47—42no—
107C4×C47—22no—
108C4×C47—24no—
109C4×C47—41no—
110C4×C47—42no—
111C4×C47—41no—
112Dic47—24no—
113Dic47—42no—
114Dic47—42no—
115#2680—471nomaximal, Sylow
116C2×C47#53612yes—
117C2×C47#53911yescharacteristic
118C2×C47D4211yescharacteristic
119C2×C47#54712yes—
120C2×C47#56311yescharacteristic
121D47—44no—
122C2×#123—472no—
123C2×C22⋊Q8—472no—
124#398—472no—
125#397—472no—
126#395—471no—
127#394—471no—
128#388—472no—
129#385—472no—
130#384D4711yescharacteristic, complemented
131C47#268011yescharacteristic, complemented, Sylow
132C22×Q8—471no—
133C22×D4—471no—
134C23×C4—472no—
135#123—948no—
136C22⋊Q8—948no—
137C2×C4⋊C4—472no—
138C2×C4⋊C4—472no—
139C2×C4⋊C4—472no—
140C2×C4⋊C4C2×D4712yes—
141C2×C4⋊C4C2×D4712yes—
142C2×C4⋊C4C2×D4711yescharacteristic
143C2×C4⋊C4C2×D4711yescharacteristic
144C2×C22⋊C4—472no—
145C2×C22⋊C4—472no—
146C2×C22⋊C4—472no—
147C2×C22⋊C4—472no—
148C2×C22⋊C4—472no—
149C2×C42C2×D4711yescharacteristic
150#95—472no—
151#95—472no—
152#95—472no—
153#95—471no—
154#95—471no—
155C24—472no—
156C2×Q8—944no—
157C2×Q8—1881no—
158C2×D4—944no—
159C2×D4—1881no—
160C22×C4—472no—
161C22×C4—472no—
162C22×C4—472no—
163C22×C4—944no—
164C22×C4—944no—
165C22×C4—1882no—
166C22×C4C22×D4711yescharacteristic
167C22×C4C22×D4712yes—
168C22×C4C22×D4711yescharacteristic
169C22×C4C22×D4711yescharacteristic
170C22×C4C22×D4712yes—
171C4⋊C4—24no—
172C4⋊C4—24no—
173C4⋊C4—41no—
174C4⋊C4—41no—
175C4⋊C4—944no—
176C4⋊C4—944no—
177C4⋊C4—944no—
178C22⋊C4—478no—
179C22⋊C4—944no—
180C22⋊C4—944no—
181C22⋊C4—944no—
182C22⋊C4—944no—
183C42—22no—
184C23—474no—
185C23—942no—
186C23—942no—
187C23—942no—
188C23—942no—
189C23—942no—
190C23—942no—
191C23C23×D4711yescharacteristic
192Q8—1884no—
193D4—1884no—
194C2×C4—22no—
195C2×C4—21no—
196C2×C4—22no—
197C2×C4—21no—
198C2×C4—22no—
199C2×C4—22no—
200C2×C4—22no—
201C2×C4—22no—
202C2×C4—22no—
203C2×C4—21no—
204C2×C4—21no—
205C2×C4—474no—
206C2×C4—942no—
207C2×C4—942no—
208C2×C4—942no—
209C2×C4—942no—
210C2×C4—942no—
211C2×C4—942no—
212C2×C4—942no—
213C2×C4—942no—
214C2×C4—1888no—
215C2×C4#1062535012yes—
216C2×C4D4×D4714yes—
217C22—944no—
218C22—944no—
219C22—944no—
220C22—1882no—
221C22—1882no—
222C22—1882no—
223C22—1882no—
224C22C2×D4×D4712yes—
225C22C2×#1062535011yescharacteristic
226C22#1309406911yescharacteristic
227C22#1309407212yes—
228C22#1309407211yescharacteristic
229C4—24no—
230C4—22no—
231C4—42no—
232C4—41no—
233C4—41no—
234C4—944no—
235C4—1882no—
236C4—1882no—
237C2—1884no—
238C2#1568969812yes—
239C2#1568972011yescharacteristic
240C2#1568975811yescharacteristic
241C2#1568977412yes—
242C2#1568987211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#384C2
hypercenter#384D47
hypocenterC47#2680
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #384

Complements

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

NH ≅ G/Ntype
2. C2×#13094002C2semidirect
3. #15689054C2semidirect
4. #15689049C2semidirect
5. #15689043C2semidirect
7. #15689014C2semidirect
8. #15688994C2semidirect
9. C47×#384C2semidirect
130. #384D47semidirect
131. C47#2680semidirect