Finite Group Databasebeta

← #99×Dic47 #20243178

Subgroups — #99×Dic47 #20243178

Order 6016.

412 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 412 conjugacy classes of subgroups — too many to draw. Only its 119 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×D4×Dic47C211yesmaximal, characteristic
2C2×#13093939C211yesmaximal, characteristic
3C22⋊C4×Dic47C212yesmaximal, complemented
4#15688889C212yesmaximal, complemented
5C2×#99×C47C211yesmaximal, characteristic
6C23×Dic47C411yescharacteristic, complemented
7C23×Dic47C2211yescharacteristic
8D4×Dic47—22no—
9D4×Dic47—22no—
10C2×C4⋊Dic47C411yescharacteristic, complemented
11C2×C22⋊Dic47C411yescharacteristic, complemented
12C2×C22⋊Dic47C2211yescharacteristic
13C2×C22⋊Dic47C2212yes—
14C2×C4×Dic47—22no—
15C2×C4×Dic47C411yescharacteristic, complemented
16#13093939C414yescomplemented
17C47⋊#95—22no—
18C22×D4×C47C2211yescharacteristic
19C2×C22⋊C4×C47C2212yes—
20#99×C47C414yescomplemented
21C24×C47C2×C411yescharacteristic
22C24×C47C2311yescharacteristic
23C2×D4×C47—22no—
24C2×D4×C47—22no—
25C2×D4×C47C2×C412yes—
26C2×D4×C47C2×C412yes—
27C22×C4×C47—22no—
28C22×C4×C47C2×C411yescharacteristic
29C22×Dic47—22no—
30C22×Dic47—21no—
31C22×Dic47—21no—
32C22×Dic47—42no—
33C22×Dic47—42no—
34C22×Dic47C2×C411yescharacteristic
35C22×Dic47C2×C411yescharacteristic
36C22×Dic47C2×C411yescharacteristic
37C22×Dic47C2×C411yescharacteristic
38C22×Dic47D412yes—
39C22×Dic47D412yes—
40C22⋊C4×C47—22no—
41C22⋊C4×C47C2×C414yescomplemented
42C22⋊Dic47—22no—
43C22⋊Dic47—22no—
44C22⋊Dic47—22no—
45C22⋊Dic47C2×C414yescomplemented
46C4⋊Dic47—22no—
47C4×Dic47—21no—
48C4×Dic47—21no—
49C4×Dic47—44no—
50C23×C47—21no—
51C23×C47—21no—
52C23×C47—41no—
53C23×C47—41no—
54C23×C47—41no—
55C23×C47—41no—
56C23×C47C4212yescomplemented
57C23×C47C22×C411yescharacteristic
58C23×C47C22×C411yescharacteristic
59C23×C47C22×C411yescharacteristic
60C23×C47C2×D412yes—
61C23×C47#4112yes—
62D4×C47—24no—
63D4×C47—24no—
64C2×C4×C47—21no—
65C2×C4×C47—21no—
66C2×C4×C47—24no—
67C2×C4×C47—42no—
68C2×C4×C47—42no—
69C2×C4×C47C4212yescomplemented
70C2×Dic47—24no—
71C2×Dic47—22no—
72C2×Dic47—21no—
73C2×Dic47—21no—
74C2×Dic47—24no—
75C2×Dic47—41no—
76C2×Dic47—42no—
77C2×Dic47—42no—
78C2×Dic47—42no—
79C2×Dic47—42no—
80C2×Dic47—42no—
81C2×Dic47—41no—
82C2×Dic47—41no—
83C2×Dic47C22⋊C411yescharacteristic
84C2×Dic47C22⋊C412yes—
85C2×Dic47C22⋊C411yescharacteristic
86C22×C47—22no—
87C22×C47—21no—
88C22×C47—22no—
89C22×C47—21no—
90C22×C47—22no—
91C22×C47—41no—
92C22×C47—41no—
93C22×C47—42no—
94C22×C47—42no—
95C22×C47—42no—
96C22×C47—41no—
97C22×C47—41no—
98C22×C47C2×C4211yescharacteristic
99C22×C47C2×C22⋊C411yescharacteristic
100C22×C47#11711yescharacteristic
101C22×C47C4×D412yes—
102C22×C47C4×D412yes—
103C4×C47—22no—
104C4×C47—44no—
105Dic47—21no—
106Dic47—22no—
107Dic47—44no—
108Dic47—41no—
109Dic47—41no—
110Dic47#9912yesdirect product factor
111C4×#99—471nomaximal, Sylow
112C2×C47—22no—
113C2×C47—22no—
114C2×C47—21no—
115C2×C47—21no—
116C2×C47—42no—
117C2×C47C4×C22⋊C411yescharacteristic
118C2×C47C2×#9911yescharacteristic
119C2×C47#41011yescharacteristic
120C2×C4×D4—471no—
121C2×#99—471no—
122C2×#99D4711yescharacteristic
123C4×C22⋊C4—472no—
124#342—472no—
125C47C4×#9911yescharacteristic, complemented, Sylow
126C22×D4C2×D4711yescharacteristic
127C23×C4—471no—
128C23×C4—471no—
129C4×D4—942no—
130C4×D4—942no—
131C2×C4⋊C4—471no—
132C2×C22⋊C4—472no—
133C2×C22⋊C4—471no—
134C2×C22⋊C4—471no—
135C2×C22⋊C4C2×D4712yes—
136C2×C42—471no—
137C2×C42—942no—
138#99—474no—
139#99Dic4714yesdirect product factor
140#95—942no—
141C24C4×D4711yescharacteristic
142C24C22×D4711yescharacteristic
143C2×D4—22no—
144C2×D4—22no—
145C2×D4C4×D4712yes—
146C2×D4C2×Dic4712yes—
147C22×C4—22no—
148C22×C4—471no—
149C22×C4—472no—
150C22×C4—471no—
151C22×C4—472no—
152C22×C4—471no—
153C22×C4—471no—
154C22×C4—941no—
155C22×C4—941no—
156C22×C4—942no—
157C22×C4—1882no—
158C22×C4—1882no—
159C22×C4C4×D4711yescharacteristic
160C4⋊C4—942no—
161C22⋊C4—22no—
162C22⋊C4—474no—
163C22⋊C4—942no—
164C22⋊C4—942no—
165C22⋊C4—942no—
166C22⋊C4C2×Dic4714yescomplemented
167C42—941no—
168C42—941no—
169C42—1884no—
170C23—21no—
171C23—21no—
172C23—41no—
173C23—41no—
174C23—41no—
175C23—41no—
176C23C4×Dic4712yescomplemented
177C23C2×C4×D4711yescharacteristic
178C23C2×C4×D4711yescharacteristic
179C23D4×D4712yes—
180C23#1062535212yes—
181C23C22×Dic4711yescharacteristic
182D4—24no—
183D4—24no—
184C2×C4—21no—
185C2×C4—21no—
186C2×C4—24no—
187C2×C4—42no—
188C2×C4—42no—
189C2×C4—471no—
190C2×C4—471no—
191C2×C4—472no—
192C2×C4—944no—
193C2×C4—942no—
194C2×C4—941no—
195C2×C4—941no—
196C2×C4—944no—
197C2×C4—1882no—
198C2×C4—1882no—
199C2×C4—1881no—
200C2×C4—1882no—
201C2×C4—1882no—
202C2×C4—1882no—
203C2×C4—1881no—
204C2×C4—1881no—
205C2×C4C4×Dic4712yescomplemented
206C22—22no—
207C22—21no—
208C22—22no—
209C22—21no—
210C22—22no—
211C22—41no—
212C22—42no—
213C22—41no—
214C22—42no—
215C22—42no—
216C22—41no—
217C22—41no—
218C22C2×C4×Dic4711yescharacteristic
219C22C22⋊C4×D4711yescharacteristic
220C22#1309398011yescharacteristic
221C22(C22⋊D47)⋊C412yes—
222C22D4×Dic4712yes—
223C4—22no—
224C4—44no—
225C4—472no—
226C4—941no—
227C4—942no—
228C4—1884no—
229C4—1881no—
230C4—1881no—
231C2—22no—
232C2—22no—
233C2—21no—
234C2—21no—
235C2—42no—
236C2C22⋊C4×Dic4711yescharacteristic
237C2#99×D4711yescharacteristic
238C2#1568909511yescharacteristic
subgroupG/H
centerC22C22⋊C4×D47
commutatorC22×C47C2×C42
FrattiniC24C22×D47
FittingC2×#99×C47C2
socleC22×C47C2×C22⋊C4
hypercenterC2×#99D47
hypocenterC47C4×#99
LCSG ▷ C22×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C24 ◁ C2×#99

Complements

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

NH ≅ G/Ntype
3. C22⋊C4×Dic47C2semidirect
4. #15688889C2semidirect
6. C23×Dic47C4semidirect
10. C2×C4⋊Dic47C4semidirect
11. C2×C22⋊Dic47C4semidirect
15. C2×C4×Dic47C4semidirect
16. #13093939C4semidirect
20. #99×C47C4semidirect
41. C22⋊C4×C47C2×C4semidirect
45. C22⋊Dic47C2×C4semidirect
56. C23×C47C42semidirect
69. C2×C4×C47C42semidirect
110. Dic47#99direct (N × H)
125. C47C4×#99semidirect
139. #99Dic47direct (N × H)
166. C22⋊C4C2×Dic47semidirect
176. C23C4×Dic47semidirect
205. C2×C4C4×Dic47semidirect