Finite Group Databasebeta

← #20252650

Subgroups — #20252650

Order 6016.

754 conjugacy classes of subgroups; only the 153 normal subgroups are shown.

normal subgroups only

This group has 754 conjugacy classes of subgroups — too many to draw. Only its 153 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
1C22×#10625350C211yesmaximal, characteristic
2C2×#13094057C212yesmaximal, complemented
3C2×#13094003C211yesmaximal, characteristic, complemented
4#15689287C214yesmaximal, complemented
5#15689281C212yesmaximal, complemented
6#15689276C212yesmaximal, complemented
7#15689125C212yesmaximal, complemented
8C47×#407C211yesmaximal, characteristic, complemented
9C2×#10625350—21no—
10C2×#10625350—21no—
11C2×#10625350—28no—
12C2×#10625350C2212yes—
13C2×#10625350C2212yes—
14C22×Dic94C2211yescharacteristic
15C22×Dic94C2211yescharacteristic, complemented
16C22×D188C2211yescharacteristic
17C22×C22⋊D47—21no—
18C22×C4×D47—21no—
19#13094057—28no—
20C2×Dic188C2214yescomplemented
21C2×#10625325C2214yescomplemented
22#13094003—21no—
23#13094003—21no—
24#13094003C2212yes—
25#13094003C2212yescomplemented
26C2×C4⋊Dic47C2211yescharacteristic, complemented
27C2×Dic47⋊C4—21no—
28C2×C22⋊Dic47—21no—
29#13093949C2214yescomplemented
30#13093946C2214yescomplemented
31C23×C4×C47C2211yescharacteristic
32C2×M16×C47C2212yescomplemented
33C22⋊C8×C47C2212yes—
34C22⋊C8×C47C2212yescomplemented
35C24×C47D411yescharacteristic
36C23×D47—21no—
37C22×C4×C47—24no—
38C22×C4×C47D411yescharacteristic
39C22×C4×C47D411yescharacteristic
40C22×C4×C47D411yescharacteristic
41C22×C4×C47C2311yescharacteristic
42C22×C4×C47C2311yescharacteristic
43C22×C4×C47C2311yescharacteristic
44C2×C22⋊D47—28no—
45C2×C22⋊D47—22no—
46C2×C22⋊D47—22no—
47C22×Dic47—21no—
48C22×Dic47—21no—
49C22×Dic47—21no—
50#10625350—28no—
51#10625350—28no—
52#10625350—24no—
53#10625350—24no—
54#10625350—24no—
55#10625350D418yes—
56C2×D188—21no—
57C2×D188—24no—
58C2×D188C2312yes—
59C2×C4×D47—28no—
60C2×C4×D47—22no—
61C2×C4×D47—22no—
62C2×Dic94—21no—
63C2×Dic94—24no—
64C2×Dic94—24no—
65C2×Dic94—21no—
66C2×Dic94C2312yes—
67C2×Dic94C2312yes—
68M16×C47—24no—
69C2×C8×C47C2314yes—
70C22⋊Dic47—22no—
71C22⋊Dic47—22no—
72C4⋊Dic47—21no—
73C4⋊Dic47C2312yes—
74Dic47⋊C4—22no—
75Dic47⋊C4—22no—
76Dic188—28no—
77#10625325—28no—
78C23×C47—22no—
79C23×C47—22no—
80C23×C47—41no—
81C23×C47C2×D411yescharacteristic
82C23×C47C2×D411yescharacteristic
83C23×C47C2×D411yescharacteristic
84C22×D47—24no—
85C22×D47—22no—
86C22×D47—42no—
87C22×D47—42no—
88C2×C4×C47—22no—
89C2×C4×C47—22no—
90C2×C4×C47—22no—
91C2×C4×C47—22no—
92C2×C4×C47—22no—
93C2×C4×C47C2×D411yescharacteristic
94C2×C4×C47C2×D411yescharacteristic
95C2×C4×C47C2×D411yescharacteristic
96C2×C4×C47C2×D414yes—
97C2×C4×C47C2411yescharacteristic
98C22⋊D47—28no—
99C22⋊D47—28no—
100C2×Dic47—24no—
101C2×Dic47—22no—
102C2×Dic47—22no—
103C2×Dic47—22no—
104C2×Dic47—42no—
105C2×Dic47—42no—
106D188—24no—
107D188—22no—
108D188C2×D414yes—
109C4×D47—28no—
110C4×D47—28no—
111Dic94—24no—
112Dic94—22no—
113Dic94—24no—
114Dic94—42no—
115Dic94C2×D414yes—
116C8×C47—24no—
117C22×C47—21no—
118C22×C47—21no—
119C22×C47—21no—
120C22×C47—21no—
121C22×C47—21no—
122C22×C47—21no—
123C22×C47—21no—
124C22×C47—44no—
125C22×C47#12012yes—
126C22×C47#13712yescomplemented
127C22×C47C22×D411yescharacteristic
128C2×D47—24no—
129C2×D47—48no—
130C2×D47—42no—
131C2×D47—42no—
132C4×C47—21no—
133C4×C47—21no—
134C4×C47#12012yes—
135C4×C47C22×D412yes—
136Dic47—24no—
137Dic47—42no—
138Dic47—42no—
139#3007—471nomaximal, Sylow
140C2×C47—22no—
141C2×C47—22no—
142C2×C47—41no—
143C2×C47C2×#12011yescharacteristic
144C2×C47C2×#13711yescharacteristic
145C2×C47#57511yescharacteristic
146D47—44no—
147C22×#41—471no—
148C2×#137—472no—
149C2×C22⋊Q8—471no—
150#452—474no—
151#451—472no—
152#450—472no—
153#417—472no—
154#407D4711yescharacteristic, complemented
155C47#300711yescharacteristic, complemented, Sylow
156C2×#41—472no—
157C2×#41—472no—
158C2×#41—948no—
159C2×#41—941no—
160C2×#41—941no—
161C22×Q8—471no—
162C22×Q8—471no—
163C22×D4—471no—
164C22×D4—941no—
165C23×C4—941no—
166C23×C4C2×D4711yescharacteristic
167#137—948no—
168C2×Q16—474no—
169C2×SD16—474no—
170C2×M16C2×D4712yescomplemented
171C22⋊Q8—472no—
172C22⋊Q8—472no—
173C22⋊Q8—941no—
174C22⋊Q8—941no—
175C2×C4⋊C4—471no—
176C2×C4⋊C4—941no—
177C2×C22⋊C4—941no—
178#103—474no—
179#102—474no—
180C22⋊C8C2×D4712yes—
181C22⋊C8C2×D4712yescomplemented
182C24—941no—
183C24D18811yescharacteristic
184#41—478no—
185#41—944no—
186#41—944no—
187#41—948no—
188#41—948no—
189#41—944no—
190C2×Q8—472no—
191C2×Q8—472no—
192C2×Q8—944no—
193C2×Q8—941no—
194C2×Q8—941no—
195C2×Q8—944no—
196C2×D4—472no—
197C2×D4—944no—
198C2×D4—948no—
199C2×D4—942no—
200C2×D4—942no—
201C2×D4—941no—
202C22×C4—24no—
203C22×C4—948no—
204C22×C4—941no—
205C22×C4—942no—
206C22×C4—942no—
207C22×C4—941no—
208C22×C4—941no—
209C22×C4D18811yescharacteristic
210C22×C4D18811yescharacteristic
211C22×C4D18811yescharacteristic
212C22×C4C22×D4711yescharacteristic
213C22×C4C22×D4711yescharacteristic
214C22×C4C22×D4711yescharacteristic
215Q16—948no—
216SD16—948no—
217M16—24no—
218C2×C8C22×D4714yes—
219C4⋊C4—472no—
220C4⋊C4—942no—
221C4⋊C4—942no—
222C4⋊C4—941no—
223C22⋊C4—942no—
224C22⋊C4—942no—
225C23—22no—
226C23—22no—
227C23—41no—
228C23—944no—
229C23—942no—
230C23—1882no—
231C23—1882no—
232C23C2×D18811yescharacteristic
233C23C2×D18811yescharacteristic
234C23C2×D18811yescharacteristic
235Q8—474no—
236Q8—944no—
237Q8—942no—
238Q8—944no—
239Q8—1882no—
240D4—474no—
241D4—944no—
242D4—948no—
243D4—948no—
244D4—942no—
245C2×C4—22no—
246C2×C4—22no—
247C2×C4—22no—
248C2×C4—22no—
249C2×C4—22no—
250C2×C4—948no—
251C2×C4—944no—
252C2×C4—942no—
253C2×C4—948no—
254C2×C4—942no—
255C2×C4—942no—
256C2×C4—1882no—
257C2×C4—1882no—
258C2×C4C2×D18811yescharacteristic
259C2×C4C2×D18811yescharacteristic
260C2×C4C2×D18811yescharacteristic
261C2×C4D4×D4714yes—
262C2×C4C23×D4711yescharacteristic
263C8—24no—
264C22—21no—
265C22—21no—
266C22—21no—
267C22—21no—
268C22—21no—
269C22—21no—
270C22—21no—
271C22—44no—
272C22—944no—
273C22—1888no—
274C22—1882no—
275C22—1882no—
276C22#1309399412yes—
277C22#1309405712yescomplemented
278C22C22×D18811yescharacteristic
279C4—21no—
280C4—21no—
281C4—944no—
282C4—1882no—
283C4—1882no—
284C4#1309399412yes—
285C4C2×D4×D4712yes—
286C2—22no—
287C2—22no—
288C2—41no—
289C2—1884no—
290C2C2×#1309399411yescharacteristic
291C2C2×#1309405711yescharacteristic
292C2#1568992311yescharacteristic
subgroupG/H
centerC22C22×D188
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#407C2
socleC22×C47C22×D4
hypercenter#407D47
hypocenterC47#3007
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C23×C4 ◁ #407

Complements

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

NH ≅ G/Ntype
2. C2×#13094057C2semidirect
3. C2×#13094003C2semidirect
4. #15689287C2semidirect
5. #15689281C2semidirect
6. #15689276C2semidirect
7. #15689125C2semidirect
8. C47×#407C2semidirect
15. C22×Dic94C22semidirect
20. C2×Dic188C22semidirect
21. C2×#10625325C22semidirect
25. #13094003C22semidirect
26. C2×C4⋊Dic47C22semidirect
29. #13093949C22semidirect
30. #13093946C22semidirect
32. C2×M16×C47C22semidirect
34. C22⋊C8×C47C22semidirect
126. C22×C47#137semidirect
154. #407D47semidirect
155. C47#3007semidirect
170. C2×M16C2×D47semidirect
181. C22⋊C8C2×D47semidirect
277. C22#13094057semidirect