Finite Group Databasebeta

← #20252751

Subgroups — #20252751

Order 6016.

698 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 698 conjugacy classes of subgroups — too many to draw. Only its 145 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×#13094072C211yesmaximal, characteristic, complemented
2#15689921C212yesmaximal, complemented
3#15689305C214yesmaximal, complemented
4#15689295C214yesmaximal, complemented
5#15689141C212yesmaximal, complemented
6C2×#13093943C211yesmaximal, characteristic, complemented
7C47×#536C211yesmaximal, characteristic, complemented
8#13094072—22no—
9#13094072—24no—
10#13094072C2214yes—
11C2×#10625354—22no—
12C2×#10625350—22no—
13C2×#10625350C2212yes—
14C2×Q8×D47—22no—
15#13094055C2214yescomplemented
16#13094054—22no—
17#13094050C2214yescomplemented
18#13094049—22no—
19#13094044—24no—
20C2×#10625329C2212yes—
21#13093952C2218yescomplemented
22#13093943C2214yescomplemented
23C2×#41×C47C2211yescharacteristic
24C22×Q8×C47C2211yescharacteristic
25C4⋊Q8×C47C2212yescomplemented
26#124×C47C2212yescomplemented
27#123×C47—22no—
28C22⋊Q8×C47—22no—
29#117×C47C2211yescharacteristic
30#41×C47—22no—
31#41×C47—22no—
32C2×Q8×C47—22no—
33C2×Q8×C47—22no—
34C2×Q8×C47D412yes—
35C2×Q8×C47C2311yescharacteristic
36C2×Q8×C47C2312yes—
37C2×D4×C47—21no—
38C2×D4×C47C2311yescharacteristic
39C22×C4×C47—21no—
40C22×C4×C47D412yes—
41C22×C4×C47C2311yescharacteristic
42C2×C22⋊D47—22no—
43#10625354—28no—
44#10625354—28no—
45Q8×D47—28no—
46Q8×D47—28no—
47#10625350—28no—
48#10625350—28no—
49#10625350—22no—
50#10625350—22no—
51#10625350D414yes—
52#10625350C2314yes—
53C2×D188—22no—
54C2×D188D412yes—
55C2×C4×D47—24no—
56C2×C4×D47—22no—
57C2×Dic94—22no—
58C2×Dic94D412yes—
59C4⋊C4×C47—21no—
60C4⋊C4×C47—24no—
61C22⋊C4×C47—21no—
62C22⋊C4×C47—24no—
63C42×C47C2312yes—
64#10625337—24no—
65#10625336—24no—
66#10625335—24no—
67#10625334—24no—
68#10625329—22no—
69#10625329C2314yes—
70C2×C47⋊C8—22no—
71C23×C47—21no—
72C23×C47C2×D411yescharacteristic
73C22×D47—22no—
74Q8×C47—24no—
75Q8×C47—24no—
76Q8×C47—22no—
77D4×C47—22no—
78D4×C47—41no—
79D4×C47—41no—
80C2×C4×C47—22no—
81C2×C4×C47—22no—
82C2×C4×C47—22no—
83C2×C4×C47—21no—
84C2×C4×C47—42no—
85C2×C4×C47C2×D412yes—
86C2×C4×C47C2×D412yes—
87C2×C4×C47C2×D414yes—
88C2×C4×C47C2×D411yescharacteristic
89C2×C4×C47C2411yescharacteristic
90C22⋊D47—24no—
91C22⋊D47—24no—
92C2×Dic47—22no—
93D188—28no—
94D188—22no—
95D188C2×D414yes—
96C4×D47—216no—
97C4×D47—24no—
98C4×D47—24no—
99Dic94—28no—
100Dic94—22no—
101Dic94C2×D414yes—
102C47⋊C8—24no—
103C22×C47—41no—
104C22×C47—42no—
105C22×C47—41no—
106C22×C47#12011yescharacteristic
107C22×C47#12011yescharacteristic
108C22×C47C22×D411yescharacteristic
109C2×D47—24no—
110C2×D47—44no—
111C4×C47—24no—
112C4×C47—42no—
113C4×C47—41no—
114C4×C47#12012yes—
115C4×C47C22×D412yes—
116Dic47—24no—
117#3020—471nomaximal, Sylow
118C2×C47—21no—
119C2×C47—21no—
120C2×C47—21no—
121C2×C47—81no—
122C2×C47C2×#12011yescharacteristic
123D47—44no—
124C2×2−1+4—471no—
125#575—472no—
126#536D4711yescharacteristic, complemented
127#456—474no—
128#454—474no—
129#421—472no—
130C2×#101—471no—
131C47#302011yescharacteristic, complemented, Sylow
1322−1+4—474no—
1332−1+4—944no—
1342−1+4—942no—
135C2×#41—472no—
136C2×#41—942no—
137C2×#41—942no—
138C2×#41C2×D4711yescharacteristic
139C22×Q8—942no—
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⋊Q8C2×D4712yescomplemented
148#124C2×D4712yescomplemented
149#123—22no—
150C22⋊Q8—22no—
151#117C2×D4711yescharacteristic
152#104—478no—
153#101—474no—
154#41—22no—
155#41—22no—
156#41—474no—
157#41—474no—
158#41—948no—
159#41—948no—
160#41—948no—
161#41—942no—
162#41—942no—
163#41—948no—
164C2×Q8—22no—
165C2×Q8—22no—
166C2×Q8—472no—
167C2×Q8—942no—
168C2×Q8—948no—
169C2×Q8—948no—
170C2×Q8C22⋊D4712yes—
171C2×Q8C22×D4711yescharacteristic
172C2×Q8C22×D4712yes—
173C2×D4—21no—
174C2×D4—472no—
175C2×D4—942no—
176C2×D4—942no—
177C2×D4C22×D4711yescharacteristic
178C22×C4—21no—
179C22×C4—944no—
180C22×C4—942no—
181C22×C4C22⋊D4712yes—
182C22×C4C22×D4711yescharacteristic
183Q16—944no—
184SD16—944no—
185SD16—944no—
186D8—944no—
187M16—474no—
188M16—942no—
189C2×C8—942no—
190C4⋊C4—21no—
191C4⋊C4—24no—
192C22⋊C4—21no—
193C22⋊C4—24no—
194C42C22×D4712yes—
195C23—21no—
196C23—942no—
197C23C2×C22⋊D4711yescharacteristic
198Q8—24no—
199Q8—24no—
200Q8—22no—
201Q8—474no—
202Q8—948no—
203Q8—942no—
204D4—22no—
205D4—41no—
206D4—41no—
207D4—474no—
208D4—948no—
209D4—944no—
210D4—944no—
211D4—942no—
212C2×C4—22no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—21no—
216C2×C4—42no—
217C2×C4—9416no—
218C2×C4—942no—
219C2×C4—944no—
220C2×C4—944no—
221C2×C4D4×D4712yes—
222C2×C4D4×D4712yes—
223C2×C4C2×C22⋊D4714yes—
224C2×C4C2×C22⋊D4711yescharacteristic
225C2×C4C23×D4711yescharacteristic
226C8—944no—
227C22—41no—
228C22—42no—
229C22—41no—
230C22—944no—
231C22—1884no—
232C22#1309399211yescharacteristic
233C22#1309399211yescharacteristic
234C22C22×C22⋊D4711yescharacteristic
235C4—24no—
236C4—42no—
237C4—41no—
238C4—944no—
239C4#1309399212yes—
240C4C2×D4×D4712yes—
241C2—21no—
242C2—21no—
243C2—21no—
244C2—81no—
245C2—1884no—
246C2C2×#1309399211yescharacteristic
subgroupG/H
centerC2C2×#13093992
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#536C2
socleC2×C47C2×#120
hypercenter#536D47
hypocenterC47#3020
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2 ◁ C22×C4 ◁ #536

Complements

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

NH ≅ G/Ntype
1. C2×#13094072C2semidirect
2. #15689921C2semidirect
3. #15689305C2semidirect
4. #15689295C2semidirect
5. #15689141C2semidirect
6. C2×#13093943C2semidirect
7. C47×#536C2semidirect
15. #13094055C22semidirect
17. #13094050C22semidirect
21. #13093952C22semidirect
22. #13093943C22semidirect
25. C4⋊Q8×C47C22semidirect
26. #124×C47C22semidirect
126. #536D47semidirect
131. C47#3020semidirect
147. C4⋊Q8C2×D47semidirect
148. #124C2×D47semidirect