Finite Group Databasebeta

← #20248319

Subgroups — #20248319

Order 6016.

900 conjugacy classes of subgroups; only the 173 normal subgroups are shown.

normal subgroups only

This group has 900 conjugacy classes of subgroups — too many to draw. Only its 173 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×#13094007C212yesmaximal, complemented
2C2×#13093998C211yesmaximal, characteristic, complemented
3C2×#13093993C212yesmaximal, complemented
4#15689059C212yesmaximal, complemented
5#15689032C212yesmaximal, complemented
6#15689023C214yesmaximal, complemented
7C4×C22⋊Dic47C211yesmaximal, characteristic, complemented
8C22×C22⋊C4×C47C211yesmaximal, characteristic, complemented
9C22×D188C2211yescharacteristic, complemented
10C22×C22⋊D47C2212yes—
11C22×C22⋊D47C2214yes—
12#13094007—28no—
13#13093998—24no—
14#13093993—28no—
15C2×C4⋊Dic47C2211yescharacteristic, complemented
16C2×Dic47⋊C4C2214yescomplemented
17C2×C22⋊Dic47C2214yes—
18C2×C22⋊Dic47C2212yes—
19C2×(C2×D47)⋊C4C2212yescomplemented
20C2×(C2×D47)⋊C4C2214yescomplemented
21C2×C4×Dic47C2212yescomplemented
22C47⋊#95C2212yescomplemented
23C25×C47C2211yescharacteristic
24C23×C4×C47C2211yescharacteristic
25C23×C4×C47C2211yescharacteristic
26C2×C22⋊C4×C47—24no—
27C2×C22⋊C4×C47C2212yes—
28C2×C22⋊C4×C47C2212yes—
29C24×C47—22no—
30C24×C47—24no—
31C24×C47—24no—
32C24×C47—42no—
33C24×C47C2312yes—
34C24×C47C2311yescharacteristic
35C23×D47C2312yes—
36C22×C4×C47—22no—
37C22×C4×C47—24no—
38C22×C4×C47—42no—
39C22×C4×C47D414yescomplemented
40C22×C4×C47C2312yes—
41C22×C4×C47C2311yescharacteristic
42C22×C4×C47C2311yescharacteristic
43C2×C22⋊D47—24no—
44C2×C22⋊D47—24no—
45C2×C22⋊D47—24no—
46C2×C22⋊D47—28no—
47C2×C22⋊D47—28no—
48C2×C22⋊D47—44no—
49C22×Dic47C2312yes—
50C22×Dic47C2314yes—
51C2×D188—22no—
52C2×D188—42no—
53C22⋊C4×C47—24no—
54C22⋊C4×C47—24no—
55C22⋊Dic47—28no—
56C22⋊Dic47D418yescomplemented
57(C2×D47)⋊C4—24no—
58(C2×D47)⋊C4—28no—
59C4⋊Dic47—22no—
60Dic47⋊C4—28no—
61C4×Dic47—42no—
62C23×C47—22no—
63C23×C47—22no—
64C23×C47—28no—
65C23×C47—24no—
66C23×C47—22no—
67C23×C47—22no—
68C23×C47—24no—
69C23×C47—416no—
70C23×C47—44no—
71C23×C47—44no—
72C23×C47C2×D414yes—
73C23×C47C2×D412yes—
74C23×C47#4114yes—
75C23×C47C2411yescharacteristic
76C22×D47—22no—
77C22×D47—22no—
78C22×D47—22no—
79C22×D47—24no—
80C22×D47—24no—
81C2×C4×C47—22no—
82C2×C4×C47—22no—
83C2×C4×C47—24no—
84C2×C4×C47—22no—
85C2×C4×C47—44no—
86C2×C4×C47—44no—
87C2×C4×C47C2×D412yes—
88C2×C4×C47C2×D412yes—
89C22⋊D47—416no—
90C22⋊D47—48no—
91C2×Dic47—24no—
92C2×Dic47—24no—
93C2×Dic47—22no—
94C2×Dic47—22no—
95C2×Dic47—22no—
96C2×Dic47C2×D418yes—
97D188—44no—
98C22×C47—22no—
99C22×C47—22no—
100C22×C47—28no—
101C22×C47—24no—
102C22×C47—28no—
103C22×C47—416no—
104C22×C47—42no—
105C22×C47—42no—
106C22×C47—44no—
107C22×C47#12714yes—
108C22×C47C22×D412yes—
109C22×C47C22×D411yescharacteristic
110C22×C47C2×#4112yes—
111C22×C47H(5,𝔽2)12yes—
112C2×D47—42no—
113C2×D47—42no—
114C2×D47—42no—
115C2×D47—44no—
116C2×D47—44no—
117C4×C47—22no—
118C4×C47—22no—
119C4×C47—42no—
120Dic47—28no—
121Dic47—42no—
122#2539—471nomaximal, Sylow
123C2×C47—24no—
124C2×C47—44no—
125C2×C47#52511yescharacteristic
126C2×C47C2×#12711yescharacteristic
127C2×C47#53411yescharacteristic
128C2×C47#54614yes—
129D47—82no—
130C2×#123—472no—
131C2×#121—471no—
132C2×#120—472no—
133C22×C22⋊C4D4711yescharacteristic, complemented
134#399—472no—
135#392—472no—
136#390—474no—
137C4×C22⋊C4—471no—
138C47#253911yescharacteristic, complemented, Sylow
139C25C2×D4711yescharacteristic
140C22×D4—472no—
141C22×D4—474no—
142C22×D4—471no—
143C23×C4C2×D4711yescharacteristic
144C23×C4C2×D4711yescharacteristic
145#123—948no—
146#121—944no—
147#120—948no—
148C2×C4⋊C4—471no—
149C2×C4⋊C4—474no—
150C2×C22⋊C4—24no—
151C2×C22⋊C4—472no—
152C2×C22⋊C4—474no—
153C2×C22⋊C4—472no—
154C2×C22⋊C4—474no—
155C2×C22⋊C4C2×D4712yes—
156C2×C22⋊C4C2×D4712yes—
157C2×C42—472no—
158#95—472no—
159C24—24no—
160C24—22no—
161C24—24no—
162C24—42no—
163C24—472no—
164C24C22×D4712yes—
165C24C22×D4711yescharacteristic
166C2×D4—948no—
167C2×D4—948no—
168C2×D4—944no—
169C2×D4—944no—
170C2×D4—944no—
171C2×D4—942no—
172C2×D4—1882no—
173C2×D4—1884no—
174C22×C4—24no—
175C22×C4—22no—
176C22×C4—42no—
177C22×C4—474no—
178C22×C4—472no—
179C22×C4C22⋊D4714yescomplemented
180C22×C4C22×D4712yes—
181C22×C4C22×D4711yescharacteristic
182C22×C4C22×D4711yescharacteristic
183C4⋊C4—948no—
184C4⋊C4—942no—
185C22⋊C4—24no—
186C22⋊C4—24no—
187C22⋊C4—478no—
188C22⋊C4—948no—
189C22⋊C4—948no—
190C22⋊C4—944no—
191C42—1882no—
192C23—22no—
193C23—22no—
194C23—28no—
195C23—24no—
196C23—22no—
197C23—22no—
198C23—24no—
199C23—416no—
200C23—44no—
201C23—44no—
202C23—942no—
203C23—942no—
204C23—942no—
205C23—944no—
206C23—944no—
207C23#1062535014yes—
208C23D4×D4714yes—
209C23C2×C22⋊D4712yes—
210C23C23×D4711yescharacteristic
211D4—1884no—
212D4—18816no—
213D4—1888no—
214C2×C4—22no—
215C2×C4—22no—
216C2×C4—24no—
217C2×C4—22no—
218C2×C4—44no—
219C2×C4—44no—
220C2×C4—478no—
221C2×C4—944no—
222C2×C4—944no—
223C2×C4—942no—
224C2×C4—942no—
225C2×C4—942no—
226C2×C4C2×C22⋊D4712yes—
227C2×C4C2×C22⋊D4712yes—
228C22—28no—
229C22—22no—
230C22—22no—
231C22—28no—
232C22—24no—
233C22—416no—
234C22—44no—
235C22—42no—
236C22—42no—
237C22—1884no—
238C22—1884no—
239C22—1882no—
240C22—1882no—
241C22—1882no—
242C22#1309402014yes—
243C22C2×D4×D4712yes—
244C22C22×C22⋊D4711yescharacteristic
245C22C2×#1062535012yes—
246C22#1309406912yes—
247C4—22no—
248C4—22no—
249C4—42no—
250C4—948no—
251C4—1882no—
252C2—24no—
253C2—44no—
254C2—3762no—
255C2#1568963411yescharacteristic
256C2C2×#1309402011yescharacteristic
257C2#1568968211yescharacteristic
258C2#1568976314yes—
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC22×C22⋊C4×C47C2
hypercenterC22×C22⋊C4D47
hypocenterC47#2539
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ C22×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#13094007C2semidirect
2. C2×#13093998C2semidirect
3. C2×#13093993C2semidirect
4. #15689059C2semidirect
5. #15689032C2semidirect
6. #15689023C2semidirect
7. C4×C22⋊Dic47C2semidirect
8. C22×C22⋊C4×C47C2semidirect
9. C22×D188C22semidirect
15. C2×C4⋊Dic47C22semidirect
16. C2×Dic47⋊C4C22semidirect
19. C2×(C2×D47)⋊C4C22semidirect
20. C2×(C2×D47)⋊C4C22semidirect
21. C2×C4×Dic47C22semidirect
22. C47⋊#95C22semidirect
39. C22×C4×C47D4semidirect
56. C22⋊Dic47D4semidirect
133. C22×C22⋊C4D47semidirect
138. C47#2539semidirect
179. C22×C4C22⋊D47semidirect