Finite Group Databasebeta

← #20252795

Subgroups — #20252795

Order 6016.

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

normal subgroups only

This group has 716 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
1#15689959C211yesmaximal, characteristic
2#15689699C212yesmaximal, complemented
3#15689694C211yesmaximal, characteristic, complemented
4#15689314C218yesmaximal, complemented
5#15689096C212yesmaximal, complemented
6C47×#410C211yesmaximal, characteristic, complemented
7#13094072—21no—
8#13094071—22no—
9#13094070—22no—
10#13094069—21no—
11#13094069C2214yes—
12C2×#10625350—22no—
13C2×#10625350C2212yes—
14#41×D47—24no—
15C22×Dic94C2211yescharacteristic, complemented
16#13094024—22no—
17#13094022—21no—
18#13094012—22no—
19#13094011—21no—
20#13094008C2218yescomplemented
21#13094005C2214yescomplemented
22#13094004—24no—
23#13094003—22no—
24#13093983C2211yescharacteristic, complemented
25#13093938C2218yescomplemented
26C2×#41×C47C2211yescharacteristic
27#117×C47C2212yescomplemented
28#99×C47C2214yescomplemented
29#41×C47—22no—
30#41×C47—22no—
31C2×Q8×C47D411yescharacteristic
32C2×D4×C47D411yescharacteristic
33C2×D4×C47C2312yes—
34C22×C4×C47D412yes—
35C22×C4×C47C2311yescharacteristic
36C2×C22⋊D47—24no—
37C2×C22⋊D47C2314yes—
38C22×Dic47C2312yes—
39#10625354—24no—
40Q8×D47—24no—
41#10625352—24no—
42#10625352—28no—
43D4×D47—24no—
44D4×D47—28no—
45#10625350—24no—
46#10625350—24no—
47#10625350—22no—
48#10625350—22no—
49#10625350—24no—
50#10625350—22no—
51#10625350—22no—
52C2×D188—22no—
53C2×D188D412yes—
54C2×C4×D47—24no—
55C2×C4×D47D414yes—
56C2×Dic94—22no—
57C2×Dic94—21no—
58C2×Dic94—22no—
59C2×Dic94—21no—
60C2×Dic94—22no—
61C2×Dic94D412yes—
62C4⋊C4×C47—22no—
63C22⋊C4×C47C2314yes—
64C42×C47—22no—
65C22⋊Dic47—24no—
66C22⋊Dic47C2312yes—
67(C2×D47)⋊C4—28no—
68C4⋊Dic47—21no—
69C4⋊Dic47—28no—
70Dic47⋊C4—24no—
71C4×Dic47—21no—
72C23×C47C2×D412yes—
73C23×C47C2411yescharacteristic
74C22×D47—24no—
75C22×D47C2×D414yes—
76Q8×C47—22no—
77D4×C47—24no—
78D4×C47—22no—
79C2×C4×C47—22no—
80C2×C4×C47—22no—
81C2×C4×C47—24no—
82C2×C4×C47C2×D412yes—
83C2×C4×C47C2×D411yescharacteristic
84C2×C4×C47C2×D411yescharacteristic
85C2×C4×C47C2×D412yes—
86C2×C4×C47C2×D412yes—
87C22⋊D47—28no—
88C22⋊D47—24no—
89C22⋊D47—24no—
90C2×Dic47—24no—
91C2×Dic47—22no—
92C2×Dic47—22no—
93C2×Dic47—24no—
94C2×Dic47C2×D414yes—
95D188—24no—
96D188—22no—
97D188—22no—
98C4×D47—28no—
99C4×D47—24no—
100C4×D47—24no—
101Dic94—24no—
102Dic94—22no—
103Dic94—22no—
104Dic94—41no—
105Dic94—42no—
106Dic94—41no—
107C22×C47—22no—
108C22×C47—41no—
109C22×C47—42no—
110C22×C47C22×D412yes—
111C22×C47C22×D411yescharacteristic
112C2×D47—24no—
113C2×D47—44no—
114C2×D47—84no—
115C4×C47—22no—
116C4×C47—44no—
117C4×C47#12011yescharacteristic
118C4×C47#12012yes—
119C4×C47#12011yescharacteristic
120Dic47—24no—
121Dic47—42no—
122Dic47—42no—
123#3028—471nomaximal, Sylow
124C2×C47—21no—
125C2×C47—22no—
126C2×C47—42no—
127C2×C47C2×#12011yescharacteristic
128D47—44no—
129#585—471no—
130#536—471no—
131#536—472no—
132#458—478no—
133#410—472no—
134#410D4711yescharacteristic, complemented
135C47#302811yescharacteristic, complemented, Sylow
1362−1+4—942no—
1372−1+4—941no—
138H(5,𝔽2)—474no—
139H(5,𝔽2)—942no—
140H(5,𝔽2)—941no—
141C2×#41—472no—
142C2×#41—944no—
143C2×#41—942no—
144C2×#41C2×D4711yescharacteristic
145C22×Q8—471no—
146C4⋊Q8—942no—
147C4⋊Q8—941no—
148#124—942no—
149#124—941no—
150#123—474no—
151#123—478no—
152C22⋊Q8—944no—
153C22⋊Q8—942no—
154#117—471no—
155#117C2×D4712yescomplemented
156#99—478no—
157#99C2×D4714yescomplemented
158#41—22no—
159#41—22no—
160#41—944no—
161#41—944no—
162#41—948no—
163#41—944no—
164#41—944no—
165#41—942no—
166#41—942no—
167#41—944no—
168#41—942no—
169#41—942no—
170C2×Q8—472no—
171C2×Q8—942no—
172C2×Q8—944no—
173C2×Q8—941no—
174C2×Q8—941no—
175C2×Q8—942no—
176C2×Q8—942no—
177C2×Q8D18811yescharacteristic
178C2×D4—474no—
179C2×D4—472no—
180C2×D4—942no—
181C2×D4—948no—
182C2×D4—944no—
183C2×D4—944no—
184C2×D4D18811yescharacteristic
185C2×D4C22×D4712yes—
186C22×C4—474no—
187C22×C4—472no—
188C22×C4—944no—
189C22×C4D18812yes—
190C22×C4C22×D4711yescharacteristic
191C4⋊C4—22no—
192C4⋊C4—948no—
193C4⋊C4—944no—
194C4⋊C4—941no—
195C22⋊C4—472no—
196C22⋊C4—948no—
197C22⋊C4—944no—
198C22⋊C4C22×D4714yes—
199C42—22no—
200C42—941no—
201C23—474no—
202C23—944no—
203C23C2×D18812yes—
204C23C23×D4711yescharacteristic
205Q8—22no—
206Q8—944no—
207Q8—942no—
208Q8—942no—
209Q8—1881no—
210Q8—1881no—
211Q8—1882no—
212D4—24no—
213D4—22no—
214D4—944no—
215D4—948no—
216D4—944no—
217D4—944no—
218D4—942no—
219D4—942no—
220C2×C4—22no—
221C2×C4—22no—
222C2×C4—24no—
223C2×C4—474no—
224C2×C4—948no—
225C2×C4—944no—
226C2×C4—944no—
227C2×C4—944no—
228C2×C4—944no—
229C2×C4—942no—
230C2×C4—942no—
231C2×C4C2×D18812yes—
232C2×C4C2×D18811yescharacteristic
233C2×C4C2×D18811yescharacteristic
234C2×C4D4×D4712yes—
235C2×C4D4×D4712yes—
236C22—22no—
237C22—41no—
238C22—42no—
239C22—944no—
240C22—3764no—
241C22—1884no—
242C22C2×D4×D4712yes—
243C22C22×D18811yescharacteristic
244C4—22no—
245C4—44no—
246C4—944no—
247C4—1882no—
248C4—1882no—
249C4#1309399411yescharacteristic
250C4#1309399411yescharacteristic
251C4#1309399412yes—
252C2—22no—
253C2—21no—
254C2—42no—
255C2—1884no—
256C2C2×#1309399411yescharacteristic
subgroupG/H
centerC2C2×#13093994
commutatorC23×C47C24
FrattiniC23C23×D47
FittingC47×#410C2
socleC2×C47C2×#120
hypercenter#410D47
hypocenterC47#3028
LCSG ▷ C23×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2 ◁ C22×C4 ◁ #410

Complements

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

NH ≅ G/Ntype
2. #15689699C2semidirect
3. #15689694C2semidirect
4. #15689314C2semidirect
5. #15689096C2semidirect
6. C47×#410C2semidirect
15. C22×Dic94C22semidirect
20. #13094008C22semidirect
21. #13094005C22semidirect
24. #13093983C22semidirect
25. #13093938C22semidirect
27. #117×C47C22semidirect
28. #99×C47C22semidirect
134. #410D47semidirect
135. C47#3028semidirect
155. #117C2×D47semidirect
157. #99C2×D47semidirect