Finite Group Databasebeta

← #20253311

Subgroups — #20253311

Order 6016.

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

normal subgroups only

This group has 458 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
1#15689634C211yesmaximal, characteristic
2#15689458C212yesmaximal, complemented
3#15689453C212yesmaximal, complemented
4#15689441C212yesmaximal, complemented
5#15689436C212yesmaximal, complemented
6#15689163C212yesmaximal, complemented
7#15689122C212yesmaximal, complemented
8#15689087C211yesmaximal, characteristic, complemented
9C22×C4⋊C4×C47C211yesmaximal, characteristic, complemented
10C2×#10625350C2211yescharacteristic
11C2×#10625329C2212yes—
12#13094007—21no—
13#13094003C2211yescharacteristic
14#13094003C2211yescharacteristic
15#13093998C2211yescharacteristic
16#13093998C2211yescharacteristic
17#13093993—21no—
18C4×C22⋊D47—21no—
19C4×C22⋊D47—21no—
20#13093983C2211yescharacteristic
21#13093957C2214yescomplemented
22#13093955C2214yescomplemented
23#13093947C2214yescomplemented
24#13093944C2214yescomplemented
25C22⋊(C47⋊C8)C2212yes—
26C22⋊(C47⋊C8)C2212yes—
27C23×C4×C47—21no—
28C23×C4×C47C2211yescharacteristic
29C2×C4⋊C4×C47—21no—
30C2×C4⋊C4×C47—21no—
31C2×C4⋊C4×C47—21no—
32C2×C4⋊C4×C47C2212yes—
33C2×C4⋊C4×C47C2212yes—
34C2×C4⋊C4×C47C2212yes—
35C24×C47D411yescharacteristic
36C22×C4×C47—24no—
37C22×C4×C47—22no—
38C22×C4×C47—22no—
39C22×C4×C47—22no—
40C22×C4×C47—44no—
41C22×C4×C47D411yescharacteristic
42C22×C4×C47D411yescharacteristic
43C22×C4×C47D411yescharacteristic
44C22×C4×C47C2311yescharacteristic
45C22×C4×C47C2311yescharacteristic
46C22×C4×C47C2311yescharacteristic
47C2×C22⋊D47—21no—
48C2×C22⋊D47—21no—
49C2×C22⋊D47—21no—
50#10625350—24no—
51C2×D188C2311yescharacteristic
52C2×C4×D47—21no—
53C2×Dic94C2311yescharacteristic
54C4⋊C4×C47—22no—
55C4⋊C4×C47—22no—
56C4⋊C4×C47—22no—
57C4⋊C4×C47C2314yes—
58C22⋊Dic47—21no—
59C22⋊Dic47—21no—
60C22⋊Dic47—21no—
61(C2×D47)⋊C4—21no—
62(C2×D47)⋊C4—21no—
63C4⋊Dic47C2311yescharacteristic
64C4⋊Dic47C2311yescharacteristic
65Dic47⋊C4—21no—
66Dic47⋊C4—21no—
67C4×Dic47—21no—
68#10625329—24no—
69C2×C47⋊C8C2314yes—
70C23×C47—22no—
71C23×C47—22no—
72C23×C47—22no—
73C23×C47C2×D411yescharacteristic
74C23×C47C2×D411yescharacteristic
75C23×C47C2×D411yescharacteristic
76C22×D47—21no—
77C2×C4×C47—22no—
78C2×C4×C47—22no—
79C2×C4×C47—22no—
80C2×C4×C47—22no—
81C2×C4×C47—22no—
82C2×C4×C47—24no—
83C2×C4×C47—44no—
84C2×C4×C47—44no—
85C2×C4×C47—44no—
86C2×C4×C47C2×D411yescharacteristic
87C2×C4×C47C2×D411yescharacteristic
88C2×C4×C47C2×D411yescharacteristic
89C2×C4×C47#4114yes—
90C2×C4×C47C2411yescharacteristic
91C22⋊D47—42no—
92C22⋊D47—42no—
93C22⋊D47—42no—
94C2×Dic47—21no—
95C2×Dic47—21no—
96C2×Dic47—21no—
97D188—22no—
98C4×D47—42no—
99Dic94—22no—
100C47⋊C8—24no—
101C22×C47—28no—
102C22×C47—21no—
103C22×C47—21no—
104C22×C47—21no—
105C22×C47—21no—
106C22×C47—21no—
107C22×C47—21no—
108C22×C47#12312yes—
109C22×C47AGL(1,ℤ/8)12yes—
110C22×C47#13712yes—
111C22×C47C22×D411yescharacteristic
112C2×D47—41no—
113C2×D47—41no—
114C2×D47—41no—
115C4×C47—21no—
116C4×C47—21no—
117C4×C47—44no—
118C4×C47#12312yes—
119C4×C47C2×#4112yes—
120Dic47—41no—
121Dic47—41no—
122Dic47—41no—
123#3092—471nomaximal, Sylow
124C2×C47—22no—
125C2×C47—22no—
126C2×C47—22no—
127C2×C47C2×#12311yescharacteristic
128C2×C47C2×AGL(1,ℤ/8)11yescharacteristic
129C2×C47C2×#13711yescharacteristic
130D47—81no—
131#525—471no—
132C22×C4⋊C4D4711yescharacteristic, complemented
133#484—472no—
134#483—472no—
135#481—472no—
136#480—472no—
137#428—472no—
138#417—472no—
139#407—471no—
140C47#309211yescharacteristic, complemented, Sylow
141C2×#41—471no—
142C23×C4—21no—
143C23×C4C2×D4711yescharacteristic
144C2×M16—472no—
145#123—941no—
146C22⋊Q8—471no—
147C22⋊Q8—471no—
148#121—471no—
149#121—471no—
150#120—941no—
151C4×D4—941no—
152C4×D4—941no—
153#117—471no—
154C2×C4⋊C4—21no—
155C2×C4⋊C4—21no—
156C2×C4⋊C4—21no—
157C2×C4⋊C4C2×D4712yes—
158C2×C4⋊C4C2×D4712yes—
159C2×C4⋊C4C2×D4712yes—
160#107—474no—
161#106—474no—
162#103—474no—
163#102—474no—
164C22⋊C8—472no—
165C22⋊C8—472no—
166C24C22⋊D4711yescharacteristic
167#41—944no—
168C2×Q8—471no—
169C2×D4—471no—
170C2×D4—941no—
171C2×D4—941no—
172C2×D4—941no—
173C22×C4—24no—
174C22×C4—22no—
175C22×C4—22no—
176C22×C4—22no—
177C22×C4—44no—
178C22×C4—941no—
179C22×C4C22⋊D4711yescharacteristic
180C22×C4C22⋊D4711yescharacteristic
181C22×C4C22⋊D4711yescharacteristic
182C22×C4C22×D4711yescharacteristic
183C22×C4C22×D4711yescharacteristic
184C22×C4C22×D4711yescharacteristic
185M16—944no—
186C2×C8—474no—
187C4⋊C4—22no—
188C4⋊C4—22no—
189C4⋊C4—22no—
190C4⋊C4—471no—
191C4⋊C4—471no—
192C4⋊C4—941no—
193C4⋊C4—941no—
194C4⋊C4C22×D4714yes—
195C22⋊C4—941no—
196C22⋊C4—941no—
197C22⋊C4—941no—
198C22⋊C4—941no—
199C22⋊C4—941no—
200C42—941no—
201C23—22no—
202C23—22no—
203C23—22no—
204C23—941no—
205C23C2×C22⋊D4711yescharacteristic
206C23C2×C22⋊D4711yescharacteristic
207C23C2×C22⋊D4711yescharacteristic
208Q8—942no—
209D4—942no—
210D4—1882no—
211D4—1882no—
212D4—1882no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—22no—
216C2×C4—22no—
217C2×C4—22no—
218C2×C4—24no—
219C2×C4—44no—
220C2×C4—44no—
221C2×C4—44no—
222C2×C4—941no—
223C2×C4—941no—
224C2×C4—941no—
225C2×C4—1882no—
226C2×C4#1062535014yes—
227C2×C4C2×C22⋊D4711yescharacteristic
228C2×C4C2×C22⋊D4711yescharacteristic
229C2×C4C2×C22⋊D4711yescharacteristic
230C2×C4C23×D4711yescharacteristic
231C8—944no—
232C22—28no—
233C22—21no—
234C22—21no—
235C22—21no—
236C22—21no—
237C22—21no—
238C22—21no—
239C22—1881no—
240C22—1881no—
241C22—1881no—
242C22#1309400712yes—
243C22#1309405012yes—
244C22#1309405512yes—
245C22C22×C22⋊D4711yescharacteristic
246C4—21no—
247C4—21no—
248C4—44no—
249C4—1881no—
250C4—1881no—
251C4—1881no—
252C4#1309400712yes—
253C4C2×#1062535012yes—
254C2—22no—
255C2—22no—
256C2—22no—
257C2—3761no—
258C2C2×#1309400711yescharacteristic
259C2C2×#1309405011yescharacteristic
260C2C2×#1309405511yescharacteristic
subgroupG/H
centerC22C22×C22⋊D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC22×C4⋊C4×C47C2
socleC22×C47C22×D4
hypercenterC22×C4⋊C4D47
hypocenterC47#3092
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C23×C4 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #15689458C2semidirect
3. #15689453C2semidirect
4. #15689441C2semidirect
5. #15689436C2semidirect
6. #15689163C2semidirect
7. #15689122C2semidirect
8. #15689087C2semidirect
9. C22×C4⋊C4×C47C2semidirect
21. #13093957C22semidirect
22. #13093955C22semidirect
23. #13093947C22semidirect
24. #13093944C22semidirect
132. C22×C4⋊C4D47semidirect
140. C47#3092semidirect