Finite Group Databasebeta

← #20252752

Subgroups — #20252752

Order 6016.

698 conjugacy classes of subgroups; only the 161 normal subgroups are shown.

normal subgroups only

This group has 698 conjugacy classes of subgroups — too many to draw. Only its 161 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#15689921C212yesmaximal, complemented
2#15689697C211yesmaximal, characteristic, complemented
3#15689306C214yesmaximal, complemented
4#15689296C214yesmaximal, complemented
5#15689140C212yesmaximal, complemented
6C2×#13093943C211yesmaximal, characteristic, complemented
7C2×2−1+4×C47C211yesmaximal, characteristic, complemented
8C2×#10625350C2211yescharacteristic
9#13094055—22no—
10#13094054C2214yescomplemented
11#13094050—22no—
12#13094049C2214yescomplemented
13#13094044—24no—
14C2×#10625329C2212yes—
15#13094022C2212yescomplemented
16#13094013C2212yescomplemented
17#13094007—22no—
18#13094000—22no—
19#13093983C2211yescharacteristic
20#13093951C2218yescomplemented
21#13093943C2214yescomplemented
222−1+4×C47—24no—
232−1+4×C47—22no—
242−1+4×C47C2214yes—
25C2×#41×C47—22no—
26C2×#41×C47—22no—
27C2×#41×C47C2212yes—
28C22×Q8×C47—22no—
29C22×Q8×C47C2211yescharacteristic
30#41×C47—28no—
31#41×C47—28no—
32#41×C47—28no—
33#41×C47—28no—
34#41×C47—22no—
35#41×C47—22no—
36#41×C47D414yes—
37#41×C47C2314yes—
38C2×Q8×C47—22no—
39C2×Q8×C47—28no—
40C2×Q8×C47—28no—
41C2×Q8×C47—22no—
42C2×Q8×C47—22no—
43C2×Q8×C47D412yes—
44C2×Q8×C47D412yes—
45C2×Q8×C47C2312yes—
46C2×D4×C47—22no—
47C2×D4×C47—22no—
48C2×D4×C47D412yes—
49C22×C4×C47—24no—
50C22×C4×C47—22no—
51C22×C4×C47D412yes—
52C22×C4×C47C2311yescharacteristic
53C2×C22⋊D47—21no—
54#10625350—22no—
55#10625350—22no—
56C2×D188C2311yescharacteristic
57C2×C4×D47—21no—
58C2×Dic94C2311yescharacteristic
59C22⋊Dic47—21no—
60#10625337—24no—
61#10625336—24no—
62#10625335—24no—
63#10625334—24no—
64(C2×D47)⋊C4—24no—
65C4⋊Dic47—21no—
66Dic47⋊C4—24no—
67C4×Dic47C2312yes—
68#10625329—22no—
69#10625329C2314yes—
70C2×C47⋊C8—22no—
71C23×C47—22no—
72C23×C47C2×D411yescharacteristic
73C22×D47—21no—
74Q8×C47—28no—
75Q8×C47—22no—
76Q8×C47—24no—
77Q8×C47—24no—
78Q8×C47C2×D414yes—
79D4×C47—28no—
80D4×C47—24no—
81D4×C47—24no—
82D4×C47—22no—
83D4×C47C2×D414yes—
84C2×C4×C47—216no—
85C2×C4×C47—22no—
86C2×C4×C47—22no—
87C2×C4×C47—22no—
88C2×C4×C47—24no—
89C2×C4×C47—24no—
90C2×C4×C47C2×D414yes—
91C2×C4×C47C2×D411yescharacteristic
92C2×C4×C47C2×D412yes—
93C2×C4×C47C2×D412yes—
94C2×C4×C47C2411yescharacteristic
95C22⋊D47—41no—
96C22⋊D47—41no—
97C2×Dic47—22no—
98C2×Dic47—21no—
99D188—22no—
100C4×D47—42no—
101Dic94—22no—
102C47⋊C8—24no—
103C22×C47—24no—
104C22×C47—41no—
105C22×C47—44no—
106C22×C47#12011yescharacteristic
107C22×C47#12011yescharacteristic
108C22×C47C22×D411yescharacteristic
109C2×D47—42no—
110C2×D47—41no—
111C4×C47—24no—
112C4×C47—24no—
113C4×C47#12012yes—
114C4×C47C22×D412yes—
115Dic47—42no—
116Dic47—41no—
117#3020—471nomaximal, Sylow
118C2×C47—21no—
119C2×C47—21no—
120C2×C47—21no—
121C2×C47—44no—
122C2×C47C2×#12011yescharacteristic
123D47—81no—
124C2×2−1+4D4711yescharacteristic, complemented
125#575—472no—
126#536—471no—
127#456—474no—
128#454—474no—
129#421—472no—
130C2×#101—471no—
131C47#302011yescharacteristic, complemented, Sylow
1322−1+4—24no—
1332−1+4—22no—
1342−1+4C2×D4714yes—
135C2×#41—22no—
136C2×#41—22no—
137C2×#41—471no—
138C2×#41C2×D4712yes—
139C22×Q8—22no—
140C22×Q8C2×D4711yescharacteristic
141#137—474no—
142#137—942no—
143AGL(1,ℤ/8)—474no—
144AGL(1,ℤ/8)—942no—
145#135—944no—
146C2×M16—472no—
147C4⋊Q8—472no—
148#124—472no—
149#123—942no—
150C22⋊Q8—942no—
151#117—471no—
152#104—478no—
153#101—474no—
154#41—28no—
155#41—28no—
156#41—28no—
157#41—28no—
158#41—22no—
159#41—22no—
160#41—942no—
161#41—942no—
162#41C22⋊D4714yes—
163#41C22×D4714yes—
164C2×Q8—22no—
165C2×Q8—28no—
166C2×Q8—28no—
167C2×Q8—22no—
168C2×Q8—22no—
169C2×Q8—471no—
170C2×Q8C22⋊D4712yes—
171C2×Q8C22⋊D4712yes—
172C2×Q8C22×D4712yes—
173C2×D4—22no—
174C2×D4—22no—
175C2×D4—471no—
176C2×D4—941no—
177C2×D4C22⋊D4712yes—
178C22×C4—24no—
179C22×C4—22no—
180C22×C4—941no—
181C22×C4C22⋊D4712yes—
182C22×C4C22×D4711yescharacteristic
183Q16—944no—
184SD16—944no—
185SD16—944no—
186D8—944no—
187M16—474no—
188M16—942no—
189C2×C8—942no—
190C4⋊C4—944no—
191C4⋊C4—941no—
192C22⋊C4—941no—
193C22⋊C4—944no—
194C42—472no—
195C23—22no—
196C23—941no—
197C23C2×C22⋊D4711yescharacteristic
198Q8—28no—
199Q8—22no—
200Q8—24no—
201Q8—24no—
202Q8—942no—
203Q8C2×C22⋊D4714yes—
204D4—28no—
205D4—24no—
206D4—24no—
207D4—22no—
208D4—942no—
209D4—1881no—
210D4—1881no—
211D4C2×C22⋊D4714yes—
212C2×C4—216no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—22no—
216C2×C4—24no—
217C2×C4—24no—
218C2×C4—942no—
219C2×C4—941no—
220C2×C4—1882no—
221C2×C4C2×C22⋊D4714yes—
222C2×C4C2×C22⋊D4711yescharacteristic
223C2×C4C2×C22⋊D4712yes—
224C2×C4C2×C22⋊D4712yes—
225C2×C4C23×D4711yescharacteristic
226C8—944no—
227C22—24no—
228C22—41no—
229C22—44no—
230C22—1882no—
231C22—1881no—
232C22#1309399311yescharacteristic
233C22#1309399311yescharacteristic
234C22C22×C22⋊D4711yescharacteristic
235C4—24no—
236C4—24no—
237C4—1882no—
238C4—1881no—
239C4#1309399312yes—
240C4C22×C22⋊D4712yes—
241C2—21no—
242C2—21no—
243C2—21no—
244C2—44no—
245C2—3761no—
246C2C2×#1309399311yescharacteristic
subgroupG/H
centerC2C2×#13093993
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC2×2−1+4×C47C2
socleC2×C47C2×#120
hypercenterC2×2−1+4D47
hypocenterC47#3020
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×2−1+4

Complements

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

NH ≅ G/Ntype
1. #15689921C2semidirect
2. #15689697C2semidirect
3. #15689306C2semidirect
4. #15689296C2semidirect
5. #15689140C2semidirect
6. C2×#13093943C2semidirect
7. C2×2−1+4×C47C2semidirect
10. #13094054C22semidirect
12. #13094049C22semidirect
15. #13094022C22semidirect
16. #13094013C22semidirect
20. #13093951C22semidirect
21. #13093943C22semidirect
124. C2×2−1+4D47semidirect
131. C47#3020semidirect