Finite Group Databasebeta

← #20252769

Subgroups — #20252769

Order 6016.

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

normal subgroups only

This group has 704 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
2C2×#13094057C212yesmaximal, complemented
3#15689694C211yesmaximal, characteristic, complemented
4#15689308C214yesmaximal, complemented
5#15689303C214yesmaximal, complemented
6#15689139C212yesmaximal, complemented
7C47×#413C211yesmaximal, characteristic, complemented
8#13094072C2212yes—
9#13094071—22no—
10#13094070—22no—
11#13094069—22no—
12#13094069C2212yes—
13C2×#10625350—22no—
14C2×#10625350C2212yes—
15#41×D47—24no—
16C22×Dic94C2211yescharacteristic, complemented
17#13094057—24no—
18#13094057C2218yescomplemented
19C2×Dic188—22no—
20C2×#10625325—22no—
21#13094022C2212yescomplemented
22#13094011C2212yescomplemented
23#13094005—22no—
24#13094003—22no—
25#13093983C2211yescharacteristic, complemented
26#13093950C2218yescomplemented
27C2×#41×C47C2211yescharacteristic
28C2×M16×C47C2212yescomplemented
29#101×C47C2212yescomplemented
30#100×C47C2212yescomplemented
31#41×C47—22no—
32#41×C47—22no—
33C2×Q8×C47C2311yescharacteristic
34C2×D4×C47D412yes—
35C2×D4×C47C2311yescharacteristic
36C22×C4×C47D412yes—
37C22×C4×C47C2311yescharacteristic
38C2×C22⋊D47—24no—
39C2×C22⋊D47—22no—
40C22×Dic47—21no—
41#10625354—24no—
42Q8×D47—24no—
43#10625352—28no—
44#10625352—24no—
45D4×D47—28no—
46D4×D47—24no—
47#10625350—24no—
48#10625350—24no—
49#10625350—22no—
50#10625350—24no—
51#10625350—22no—
52#10625350D414yes—
53#10625350C2314yes—
54C2×D188—22no—
55C2×D188D412yes—
56C2×C4×D47—24no—
57C2×C4×D47—22no—
58C2×Dic94—22no—
59C2×Dic94—22no—
60C2×Dic94—22no—
61C2×Dic94—21no—
62C2×Dic94D412yes—
63C2×Dic94C2312yes—
64M16×C47—22no—
65M16×C47C2314yes—
66C2×C8×C47—22no—
67C22⋊Dic47—21no—
68C22⋊Dic47—24no—
69C4⋊Dic47—21no—
70Dic47⋊C4—24no—
71C4×Dic47C2312yes—
72Dic188—28no—
73#10625325—28no—
74C23×C47C2×D412yes—
75C23×C47C2×D411yescharacteristic
76C22×D47—24no—
77C22×D47—22no—
78Q8×C47—22no—
79D4×C47—24no—
80D4×C47—22no—
81C2×C4×C47—22no—
82C2×C4×C47—22no—
83C2×C4×C47C2×D412yes—
84C2×C4×C47C2×D411yescharacteristic
85C2×C4×C47C2×D412yes—
86C2×C4×C47C2×D412yes—
87C2×C4×C47C2411yescharacteristic
88C22⋊D47—28no—
89C22⋊D47—24no—
90C22⋊D47—24no—
91C2×Dic47—24no—
92C2×Dic47—22no—
93C2×Dic47—22no—
94C2×Dic47—22no—
95C2×Dic47—42no—
96D188—24no—
97D188—22no—
98D188C2×D414yes—
99C4×D47—28no—
100C4×D47—24no—
101C4×D47—24no—
102Dic94—24no—
103Dic94—22no—
104Dic94—24no—
105Dic94—41no—
106Dic94—41no—
107Dic94C2×D414yes—
108C8×C47—24no—
109C22×C47—22no—
110C22×C47—41no—
111C22×C47—42no—
112C22×C47#12012yes—
113C22×C47C22×D411yescharacteristic
114C2×D47—24no—
115C2×D47—82no—
116C2×D47—84no—
117C4×C47—22no—
118C4×C47#12011yescharacteristic
119C4×C47#12011yescharacteristic
120C4×C47C22×D412yes—
121Dic47—24no—
122Dic47—42no—
123Dic47—42no—
124#3022—471nomaximal, Sylow
125C2×C47—21no—
126C2×C47—22no—
127C2×C47—42no—
128C2×C47C2×#12011yescharacteristic
129D47—44no—
130#585—471no—
131C2×#137—472no—
132#536—471no—
133#456—474no—
134#455—474no—
135#421—472no—
136#413D4711yescharacteristic, complemented
137C47#302211yescharacteristic, complemented, Sylow
1382−1+4—472no—
1392−1+4—942no—
140H(5,𝔽2)—472no—
141H(5,𝔽2)—942no—
142H(5,𝔽2)—942no—
143C2×#41—472no—
144C2×#41—944no—
145C2×#41—942no—
146C2×#41C2×D4711yescharacteristic
147C22×Q8—471no—
148#137—478no—
149#137—944no—
150C2×Q16—942no—
151C2×SD16—942no—
152C2×M16C2×D4712yescomplemented
153C4⋊Q8—472no—
154#124—472no—
155#123—942no—
156C22⋊Q8—942no—
157#117—471no—
158#104—478no—
159#101C2×D4712yescomplemented
160#100C2×D4712yescomplemented
161#41—22no—
162#41—22no—
163#41—474no—
164#41—474no—
165#41—944no—
166#41—944no—
167#41—944no—
168#41—948no—
169#41—944no—
170#41—942no—
171#41—944no—
172#41—942no—
173C2×Q8—472no—
174C2×Q8—472no—
175C2×Q8—942no—
176C2×Q8—944no—
177C2×Q8—941no—
178C2×Q8—942no—
179C2×Q8—942no—
180C2×Q8C22×D4711yescharacteristic
181C2×D4—472no—
182C2×D4—942no—
183C2×D4—944no—
184C2×D4—948no—
185C2×D4—942no—
186C2×D4—944no—
187C2×D4D18812yes—
188C2×D4C22×D4711yescharacteristic
189C22×C4—944no—
190C22×C4—942no—
191C22×C4—941no—
192C22×C4D18812yes—
193C22×C4C22×D4711yescharacteristic
194Q16—948no—
195SD16—948no—
196M16—22no—
197M16C22×D4714yes—
198C2×C8—22no—
199C4⋊C4—944no—
200C4⋊C4—941no—
201C22⋊C4—941no—
202C22⋊C4—944no—
203C42—472no—
204C23—944no—
205C23—942no—
206C23C2×D18812yes—
207C23C2×D18811yescharacteristic
208Q8—22no—
209Q8—474no—
210Q8—944no—
211Q8—942no—
212Q8—944no—
213Q8—1881no—
214Q8—1881no—
215D4—24no—
216D4—22no—
217D4—474no—
218D4—944no—
219D4—948no—
220D4—944no—
221D4—944no—
222D4—942no—
223C2×C4—22no—
224C2×C4—22no—
225C2×C4—948no—
226C2×C4—944no—
227C2×C4—942no—
228C2×C4—944no—
229C2×C4—944no—
230C2×C4—942no—
231C2×C4—942no—
232C2×C4—1882no—
233C2×C4C2×D18812yes—
234C2×C4C2×D18811yescharacteristic
235C2×C4D4×D4712yes—
236C2×C4D4×D4712yes—
237C2×C4C23×D4711yescharacteristic
238C8—24no—
239C22—22no—
240C22—41no—
241C22—42no—
242C22—944no—
243C22—3762no—
244C22—3764no—
245C22#1309399412yes—
246C22C22×D18811yescharacteristic
247C4—22no—
248C4—944no—
249C4—1882no—
250C4—1882no—
251C4#1309399411yescharacteristic
252C4#1309399411yescharacteristic
253C4C2×D4×D4712yes—
254C2—21no—
255C2—22no—
256C2—42no—
257C2—1884no—
258C2C2×#1309399411yescharacteristic
subgroupG/H
centerC2C2×#13093994
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#413C2
socleC2×C47C2×#120
hypercenter#413D47
hypocenterC47#3022
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2 ◁ C22×C4 ◁ #413

Complements

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

NH ≅ G/Ntype
2. C2×#13094057C2semidirect
3. #15689694C2semidirect
4. #15689308C2semidirect
5. #15689303C2semidirect
6. #15689139C2semidirect
7. C47×#413C2semidirect
16. C22×Dic94C22semidirect
18. #13094057C22semidirect
21. #13094022C22semidirect
22. #13094011C22semidirect
25. #13093983C22semidirect
26. #13093950C22semidirect
28. C2×M16×C47C22semidirect
29. #101×C47C22semidirect
30. #100×C47C22semidirect
136. #413D47semidirect
137. C47#3022semidirect
152. C2×M16C2×D47semidirect
159. #101C2×D47semidirect
160. #100C2×D47semidirect