Finite Group Databasebeta

← #20252663

Subgroups — #20252663

Order 6016.

752 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 752 conjugacy classes of subgroups — too many to draw. Only its 149 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×#13094070C211yesmaximal, characteristic
2C2×#13094055C211yesmaximal, characteristic, complemented
3C22×#10625336C211yesmaximal, characteristic, complemented
4#15689283C214yesmaximal, complemented
5#15689273C214yesmaximal, complemented
6#15689127C211yesmaximal, characteristic, complemented
7#15689117C211yesmaximal, characteristic, complemented
8#15689090C211yesmaximal, characteristic, complemented
9C47×#536C211yesmaximal, characteristic, complemented
10#13094070—24no—
11#13094070—24no—
12C2×#10625354—21no—
13C2×#10625350C2212yes—
14C2×#10625350C2211yescharacteristic
15C22×D188C2212yes—
16C22×D188C2211yescharacteristic
17C2×D4×D47—22no—
18C2×D4×D47—21no—
19#13094055—24no—
20C2×#10625337C2212yescomplemented
21C2×#10625336—24no—
22C2×#10625336C2212yescomplemented
23C2×#10625336C2214yescomplemented
24C2×#10625329C2211yescharacteristic, complemented
25C22×C47⋊C8C2211yescharacteristic, complemented
26#13093947C2212yescomplemented
27#13093944C2212yescomplemented
28#13093944C2214yescomplemented
29C22⋊(C47⋊C8)C2214yescomplemented
30C2×#41×C47C2211yescharacteristic
31C22×Q8×C47C2211yescharacteristic, complemented
32C4⋊Q8×C47—21no—
33#124×C47—21no—
34#123×C47—22no—
35C22⋊Q8×C47C2214yescomplemented
36#117×C47C2211yescharacteristic, complemented
37C23×D47—22no—
38C23×D47—21no—
39#41×C47—22no—
40#41×C47—22no—
41C2×Q8×C47—21no—
42C2×Q8×C47—22no—
43C2×Q8×C47—22no—
44C2×Q8×C47D411yescharacteristic
45C2×Q8×C47C2312yes—
46C2×D4×C47D412yes—
47C2×D4×C47D411yescharacteristic
48C22×C4×C47—21no—
49C22×C4×C47C2312yes—
50C22×C4×C47C2311yescharacteristic
51C2×C22⋊D47—22no—
52C2×C22⋊D47—21no—
53#10625354—28no—
54D4×D47—216no—
55D4×D47—28no—
56#10625350—22no—
57#10625350—24no—
58#10625350—24no—
59#10625350D414yes—
60C2×D188—22no—
61C2×D188—21no—
62C2×D188—22no—
63C2×D188—24no—
64C2×D188—24no—
65C2×D188D414yes—
66C2×D188C2311yescharacteristic
67C2×D188C2312yes—
68C2×C4×D47—22no—
69C2×C4×D47—21no—
70C2×Dic94C2311yescharacteristic
71C4⋊C4×C47—24no—
72C4⋊C4×C47C2312yes—
73C22⋊C4×C47—21no—
74C22⋊C4×C47—24no—
75C42×C47—21no—
76#10625337—24no—
77#10625336—28no—
78#10625336—24no—
79#10625329—22no—
80C2×C47⋊C8—22no—
81C2×C47⋊C8C2312yes—
82C2×C47⋊C8C2312yes—
83C23×C47C2×D412yes—
84C23×C47C2×D411yescharacteristic
85C22×D47—22no—
86C22×D47—21no—
87C22×D47—28no—
88C22×D47—24no—
89C22×D47—82no—
90C22×D47—84no—
91Q8×C47—22no—
92Q8×C47—22no—
93Q8×C47—22no—
94Q8×C47—42no—
95D4×C47—24no—
96D4×C47—22no—
97C2×C4×C47—22no—
98C2×C4×C47—22no—
99C2×C4×C47—22no—
100C2×C4×C47—22no—
101C2×C4×C47—42no—
102C2×C4×C47C2×D412yes—
103C2×C4×C47C2×D412yes—
104C2×C4×C47C2×D412yes—
105C2×C4×C47C2×D411yescharacteristic
106C2×C4×C47C2411yescharacteristic
107C22⋊D47—28no—
108C22⋊D47—24no—
109C2×Dic47—21no—
110D188—28no—
111D188—24no—
112D188—21no—
113D188—22no—
114D188C2×D412yes—
115D188C2×D414yes—
116C4×D47—28no—
117C4×D47—24no—
118Dic94—21no—
119Dic94C2×D412yes—
120C47⋊C8—22no—
121C47⋊C8—22no—
122C22×C47—22no—
123C22×C47—22no—
124C22×C47—24no—
125C22×C47#12012yes—
126C22×C47C22×D411yescharacteristic
127C2×D47—24no—
128C2×D47—22no—
129C2×D47—44no—
130C2×D47—42no—
131C2×D47—84no—
132C2×D47—88no—
133C4×C47—22no—
134C4×C47—42no—
135C4×C47—42no—
136C4×C47#12012yes—
137C4×C47C22×D411yescharacteristic
138C4×C47C22×D411yescharacteristic
139Dic47—22no—
140#3009—471nomaximal, Sylow
141C2×C47—22no—
142C2×C47—42no—
143C2×C47C2×#12011yescharacteristic
144C2×C47#57712yes—
145D47—44no—
146D47—42no—
147C2×H(5,𝔽2)—471no—
148C2×#137—471no—
149C22×SD16—471no—
150#536D4711yescharacteristic, complemented
151#452—474no—
152#450—474no—
153#418—471no—
154#416—471no—
155#408—471no—
156C47#300911yescharacteristic, complemented, Sylow
157H(5,𝔽2)—944no—
158H(5,𝔽2)—944no—
159C2×#41—471no—
160C2×#41—472no—
161C2×#41—941no—
162C2×#41C2×D4711yescharacteristic
163C22×Q8C2×D4711yescharacteristic, complemented
164C22×D4—471no—
165C22×D4—472no—
166C22×D4—942no—
167C22×D4—941no—
168#137—944no—
169C2×Q16—472no—
170C2×SD16—474no—
171C2×SD16—472no—
172C2×SD16—944no—
173C2×M16—471no—
174C22×C8—471no—
175C4⋊Q8—21no—
176#124—21no—
177#123—22no—
178C22⋊Q8C2×D4714yescomplemented
179#117C2×D4711yescharacteristic, complemented
180#103—472no—
181#102—472no—
182#102—474no—
183C22⋊C8—474no—
184C24—942no—
185C24—941no—
186#41—22no—
187#41—22no—
188#41—474no—
189#41—944no—
190#41—944no—
191#41—948no—
192#41—942no—
193C2×Q8—21no—
194C2×Q8—22no—
195C2×Q8—22no—
196C2×Q8—471no—
197C2×Q8C22⋊D4711yescharacteristic
198C2×Q8C22×D4712yes—
199C2×D4—474no—
200C2×D4—472no—
201C2×D4—471no—
202C2×D4—944no—
203C2×D4—944no—
204C2×D4—9416no—
205C2×D4—948no—
206C2×D4—942no—
207C2×D4—941no—
208C2×D4—942no—
209C2×D4—942no—
210C2×D4—941no—
211C2×D4C22⋊D4712yes—
212C2×D4C22⋊D4711yescharacteristic
213C22×C4—21no—
214C22×C4—942no—
215C22×C4—941no—
216C22×C4C22×D4712yes—
217C22×C4C22×D4711yescharacteristic
218Q16—944no—
219SD16—948no—
220SD16—944no—
221M16—942no—
222C2×C8—472no—
223C2×C8—472no—
224C2×C8—942no—
225C4⋊C4—24no—
226C4⋊C4C22×D4712yes—
227C22⋊C4—21no—
228C22⋊C4—24no—
229C42—21no—
230C23—948no—
231C23—944no—
232C23—942no—
233C23—941no—
234C23—3762no—
235C23—3764no—
236C23C2×C22⋊D4712yes—
237C23C2×C22⋊D4711yescharacteristic
238Q8—22no—
239Q8—22no—
240Q8—22no—
241Q8—42no—
242Q8—472no—
243Q8—941no—
244D4—24no—
245D4—22no—
246D4—474no—
247D4—472no—
248D4—948no—
249D4—948no—
250D4—944no—
251D4—944no—
252D4—941no—
253D4—942no—
254C2×C4—22no—
255C2×C4—22no—
256C2×C4—22no—
257C2×C4—22no—
258C2×C4—42no—
259C2×C4—948no—
260C2×C4—941no—
261C2×C4—944no—
262C2×C4D4×D4712yes—
263C2×C4D4×D4712yes—
264C2×C4C2×C22⋊D4712yes—
265C2×C4C2×C22⋊D4711yescharacteristic
266C2×C4C23×D4711yescharacteristic
267C8—942no—
268C8—942no—
269C22—22no—
270C22—22no—
271C22—24no—
272C22—944no—
273C22—942no—
274C22—3764no—
275C22—3768no—
276C22—1884no—
277C22—1882no—
278C22#1309399212yes—
279C22C22×C22⋊D4711yescharacteristic
280C4—22no—
281C4—42no—
282C4—42no—
283C4—942no—
284C4#1309399212yes—
285C4C2×D4×D4711yescharacteristic
286C4C2×D4×D4711yescharacteristic
287C2—22no—
288C2—42no—
289C2—1884no—
290C2—1882no—
291C2C2×#1309399211yescharacteristic
292C2#1568993112yes—
subgroupG/H
centerC22C22×C22⋊D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#536C2
socleC22×C47C22×D4
hypercenter#536D47
hypocenterC47#3009
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×#41 ◁ #536

Complements

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

NH ≅ G/Ntype
2. C2×#13094055C2semidirect
3. C22×#10625336C2semidirect
4. #15689283C2semidirect
5. #15689273C2semidirect
6. #15689127C2semidirect
7. #15689117C2semidirect
8. #15689090C2semidirect
9. C47×#536C2semidirect
20. C2×#10625337C22semidirect
22. C2×#10625336C22semidirect
23. C2×#10625336C22semidirect
24. C2×#10625329C22semidirect
25. C22×C47⋊C8C22semidirect
26. #13093947C22semidirect
27. #13093944C22semidirect
28. #13093944C22semidirect
29. C22⋊(C47⋊C8)C22semidirect
31. C22×Q8×C47C22semidirect
35. C22⋊Q8×C47C22semidirect
36. #117×C47C22semidirect
150. #536D47semidirect
156. C47#3009semidirect
163. C22×Q8C2×D47semidirect
178. C22⋊Q8C2×D47semidirect
179. #117C2×D47semidirect