Finite Group Databasebeta

← #20247858

Subgroups — #20247858

Order 6016.

708 conjugacy classes of subgroups; only the 169 normal subgroups are shown.

normal subgroups only

This group has 708 conjugacy classes of subgroups — too many to draw. Only its 169 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×#13094006C214yesmaximal, complemented
2C2×#13093995C211yesmaximal, characteristic
3C2×C4⋊C4×D47C211yesmaximal, characteristic, complemented
4#15689059C214yesmaximal, complemented
5#15689026C211yesmaximal, characteristic, complemented
6#15688993C211yesmaximal, characteristic, complemented
7#15688992C211yesmaximal, characteristic, complemented
8C4×(C2×D47)⋊C4C211yesmaximal, characteristic, complemented
9C47×#390C211yesmaximal, characteristic, complemented
10C22×C22⋊D47C2212yes—
11C22×C4×D47C2212yes—
12C22×C4×D47C2211yescharacteristic
13#13094006—216no—
14#13093995—24no—
15C2×C4⋊Dic47C2211yescharacteristic
16C2×C4⋊Dic47C2211yescharacteristic
17C2×C4⋊Dic47C2214yes—
18C2×Dic47⋊C4C2214yes—
19C2×Dic47⋊C4C2212yes—
20C4⋊C4×D47—24no—
21C2×C22⋊Dic47C2214yes—
22C2×C22⋊Dic47C2212yes—
23C2×(C2×D47)⋊C4C2212yes—
24C2×C4×Dic47C2211yescharacteristic
25C47⋊#95C2212yes—
26C22×D4×C47C2211yescharacteristic
27C2×C4⋊C4×C47C2211yescharacteristic
28C2×C22⋊C4×C47C2214yes—
29C2×C42×C47C2211yescharacteristic
30C24×C47C2312yes—
31C23×D47C2311yescharacteristic
32C2×D4×C47—22no—
33C2×D4×C47—22no—
34C2×D4×C47—22no—
35C22×C4×C47C2312yes—
36C22×C4×C47C2312yes—
37C22×C4×C47C2311yescharacteristic
38C2×C22⋊D47—24no—
39C2×C22⋊D47—28no—
40C22×Dic47C2312yes—
41C22×Dic47C2312yes—
42C22×Dic47C2311yescharacteristic
43C22×Dic47C2312yes—
44C2×C4×D47—22no—
45C2×C4×D47—22no—
46C2×C4×D47—24no—
47C2×C4×D47—28no—
48C2×C4×D47D414yes—
49C4⋊C4×C47—22no—
50C22⋊C4×C47—28no—
51C42×C47—22no—
52C22⋊Dic47—24no—
53C22⋊Dic47—28no—
54(C2×D47)⋊C4D418yescomplemented
55C4⋊Dic47—22no—
56C4⋊Dic47—22no—
57C4⋊Dic47—28no—
58Dic47⋊C4—24no—
59Dic47⋊C4—28no—
60C4×Dic47—22no—
61C23×C47—24no—
62C23×C47—22no—
63C23×C47—22no—
64C23×C47—22no—
65C23×C47—24no—
66C23×C47C2411yescharacteristic
67C22×D47—21no—
68C22×D47—21no—
69C22×D47—22no—
70C22×D47C2×D414yes—
71C22×D47C2×D412yes—
72D4×C47—44no—
73C2×C4×C47—22no—
74C2×C4×C47—22no—
75C2×C4×C47—24no—
76C2×C4×C47—22no—
77C2×C4×C47C2×D414yes—
78C2×C4×C47C2×D412yes—
79C2×C4×C47#4112yes—
80C2×C4×C47#4112yes—
81C22⋊D47—48no—
82C2×Dic47—22no—
83C2×Dic47—21no—
84C2×Dic47—21no—
85C2×Dic47—22no—
86C2×Dic47—22no—
87C2×Dic47—24no—
88C2×Dic47—24no—
89C2×Dic47—22no—
90C2×Dic47C2×D414yes—
91C2×Dic47C2×D412yes—
92C4×D47—28no—
93C4×D47—48no—
94C22×C47—42no—
95C22×C47—42no—
96C22×C47—42no—
97C22×C47—44no—
98C22×C47—44no—
99C22×C47C22×D411yescharacteristic
100C22×C47C22×D412yes—
101C22×C47C2×#4111yescharacteristic
102C22×C47C2×#4111yescharacteristic
103C22×C472−1+412yes—
104C2×D47—22no—
105C2×D47—22no—
106C2×D47—24no—
107C2×D47—24no—
108C2×D47#12714yes—
109C4×C47—24no—
110C4×C47—42no—
111C4×C47#12314yescomplemented
112Dic47—22no—
113Dic47—24no—
114Dic47—42no—
115Dic47—42no—
116#2501—471nomaximal, Sylow
117C2×C47—82no—
118C2×C47C2×#12311yescharacteristic
119C2×C47C2×#12711yescharacteristic
120C2×C47#53611yescharacteristic
121C2×C47#54712yes—
122C2×C47#54712yes—
123D47—24no—
124C2×#123—474no—
125C2×#121—471no—
126C22×C4⋊C4—471no—
127#399—474no—
128#390—471no—
129#390D4711yescharacteristic, complemented
130#384—471no—
131#384—471no—
132C4×C22⋊C4—471no—
133C47#250111yescharacteristic, complemented, Sylow
134C22×D4—472no—
135C22×D4C2×D4711yescharacteristic
136C23×C4—471no—
137C23×C4—472no—
138#123—9416no—
139#121—944no—
140C2×C4⋊C4—472no—
141C2×C4⋊C4—471no—
142C2×C4⋊C4—471no—
143C2×C4⋊C4—474no—
144C2×C4⋊C4—474no—
145C2×C4⋊C4—944no—
146C2×C4⋊C4C2×D4711yescharacteristic
147C2×C22⋊C4—472no—
148C2×C22⋊C4—472no—
149C2×C22⋊C4—474no—
150C2×C22⋊C4C2×D4714yes—
151C2×C42—471no—
152C2×C42C2×D4711yescharacteristic
153#95—472no—
154C24—471no—
155C24C22×D4712yes—
156C2×D4—22no—
157C2×D4—22no—
158C2×D4—22no—
159C2×D4—944no—
160C2×D4—948no—
161C22×C4—471no—
162C22×C4—472no—
163C22×C4—474no—
164C22×C4—472no—
165C22×C4—472no—
166C22×C4—944no—
167C22×C4—948no—
168C22×C4—942no—
169C22×C4—942no—
170C22×C4C22×D4712yes—
171C22×C4C22×D4712yes—
172C22×C4C22×D4711yescharacteristic
173C4⋊C4—22no—
174C4⋊C4—944no—
175C4⋊C4—948no—
176C4⋊C4—942no—
177C4⋊C4—942no—
178C4⋊C4—948no—
179C22⋊C4—28no—
180C22⋊C4—478no—
181C22⋊C4—944no—
182C22⋊C4—948no—
183C42—22no—
184C42—942no—
185C23—24no—
186C23—22no—
187C23—22no—
188C23—22no—
189C23—24no—
190C23—474no—
191C23—472no—
192C23—941no—
193C23—941no—
194C23—942no—
195C23C23×D4711yescharacteristic
196D4—44no—
197D4—1888no—
198C2×C4—22no—
199C2×C4—22no—
200C2×C4—24no—
201C2×C4—22no—
202C2×C4—474no—
203C2×C4—472no—
204C2×C4—941no—
205C2×C4—942no—
206C2×C4—941no—
207C2×C4—942no—
208C2×C4—948no—
209C2×C4—944no—
210C2×C4—942no—
211C2×C4—942no—
212C2×C4—944no—
213C2×C4—1888no—
214C2×C4#1062535012yes—
215C2×C4D4×D4714yes—
216C2×C4D4×D4712yes—
217C2×C4#1062535212yes—
218C22—44no—
219C22—44no—
220C22—42no—
221C22—42no—
222C22—42no—
223C22—474no—
224C22—944no—
225C22—944no—
226C22—942no—
227C22—942no—
228C22C2×D4×D4712yes—
229C22C2×D4×D4711yescharacteristic
230C22C2×#1062535211yescharacteristic
231C22C2×#1062535011yescharacteristic
232C22#1309407112yes—
233C4—24no—
234C4—42no—
235C4—944no—
236C4—942no—
237C4—1882no—
238C4—1882no—
239C4#1309400614yescomplemented
240C2—82no—
241C2—944no—
242C2C2×#1309400611yescharacteristic
243C2#127×D4711yescharacteristic
244C2#1568969311yescharacteristic
245C2#1568977312yes—
246C2#1568977812yes—
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#390C2
hypercenter#390D47
hypocenterC47#2501
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #390

Complements

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

NH ≅ G/Ntype
1. C2×#13094006C2semidirect
3. C2×C4⋊C4×D47C2semidirect
4. #15689059C2semidirect
5. #15689026C2semidirect
6. #15688993C2semidirect
7. #15688992C2semidirect
8. C4×(C2×D47)⋊C4C2semidirect
9. C47×#390C2semidirect
54. (C2×D47)⋊C4D4semidirect
111. C4×C47#123semidirect
129. #390D47semidirect
133. C47#2501semidirect
239. C4#13094006semidirect