Finite Group Databasebeta

← #20252782

Subgroups — #20252782

Order 6016.

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

normal subgroups only

This group has 766 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, complemented
2#15689635C212yesmaximal, complemented
3#15689630C211yesmaximal, characteristic, complemented
4#15689314C214yesmaximal, complemented
5#15689311C214yesmaximal, complemented
6#15689096C212yesmaximal, complemented
7C47×#410C211yesmaximal, characteristic, complemented
8#13094072—21no—
9#13094071—22no—
10#13094070—22no—
11#13094069—21no—
12#13094069C2214yes—
13C2×#10625350—22no—
14C2×#10625350C2212yes—
15#41×D47—24no—
16C22×C4×D47C2211yescharacteristic, complemented
17#13094008C2214yescomplemented
18#13094005C2212yescomplemented
19#13094004—22no—
20#13094000—21no—
21#13093999—22no—
22#13093995—21no—
23#13093994C2214yescomplemented
24#13093992C2212yescomplemented
25C4×D188—24no—
26C4×C22⋊D47—22no—
27#13093983C2211yescharacteristic, complemented
28#13093938C2218yescomplemented
29C2×#41×C47C2211yescharacteristic
30#117×C47C2212yescomplemented
31#99×C47C2214yescomplemented
32C23×D47C2311yescharacteristic
33#41×C47—22no—
34#41×C47—22no—
35C2×Q8×C47D411yescharacteristic, complemented
36C2×D4×C47D411yescharacteristic, complemented
37C2×D4×C47C2312yes—
38C22×C4×C47D412yescomplemented
39C22×C4×C47C2311yescharacteristic
40C2×C22⋊D47—24no—
41C2×C22⋊D47—22no—
42C2×C22⋊D47C2314yes—
43C22×Dic47C2311yescharacteristic
44#10625354—24no—
45Q8×D47—24no—
46#10625352—24no—
47#10625352—28no—
48D4×D47—24no—
49D4×D47—28no—
50#10625350—24no—
51#10625350—24no—
52#10625350—22no—
53#10625350—22no—
54#10625350—24no—
55#10625350—22no—
56#10625350—22no—
57C2×D188—22no—
58C2×D188—24no—
59C2×D188D412yescomplemented
60C2×C4×D47—24no—
61C2×C4×D47—21no—
62C2×C4×D47—22no—
63C2×C4×D47—21no—
64C2×C4×D47—22no—
65C2×C4×D47D414yescomplemented
66C2×Dic94—22no—
67C2×Dic94D412yescomplemented
68C4⋊C4×C47—22no—
69C22⋊C4×C47C2314yes—
70C42×C47—22no—
71C22⋊Dic47—22no—
72C22⋊Dic47C2312yes—
73(C2×D47)⋊C4—24no—
74(C2×D47)⋊C4—22no—
75(C2×D47)⋊C4—24no—
76C4⋊Dic47—21no—
77C4⋊Dic47—24no—
78Dic47⋊C4—22no—
79C4×Dic47—21no—
80C23×C47C2×D412yes—
81C23×C47C2411yescharacteristic
82C22×D47—22no—
83C22×D47—21no—
84C22×D47—24no—
85C22×D47—42no—
86C22×D47C2×D414yes—
87Q8×C47—22no—
88D4×C47—24no—
89D4×C47—22no—
90C2×C4×C47—22no—
91C2×C4×C47—22no—
92C2×C4×C47—24no—
93C2×C4×C47C2×D412yes—
94C2×C4×C47C2×D411yescharacteristic
95C2×C4×C47C2×D411yescharacteristic
96C2×C4×C47C2×D412yes—
97C2×C4×C47C2×D412yes—
98C22⋊D47—28no—
99C22⋊D47—24no—
100C22⋊D47—24no—
101C22⋊D47—44no—
102C2×Dic47—24no—
103C2×Dic47—22no—
104C2×Dic47—21no—
105C2×Dic47—22no—
106C2×Dic47C2×D414yes—
107D188—24no—
108D188—22no—
109D188—22no—
110D188—48no—
111C4×D47—28no—
112C4×D47—24no—
113C4×D47—24no—
114C4×D47—41no—
115C4×D47—42no—
116C4×D47—41no—
117Dic94—24no—
118Dic94—22no—
119Dic94—22no—
120C22×C47—22no—
121C22×C47—41no—
122C22×C47—42no—
123C22×C47C22×D412yes—
124C22×C47C22×D411yescharacteristic
125C2×D47—24no—
126C2×D47—22no—
127C2×D47—24no—
128C2×D47—41no—
129C2×D47—42no—
130C2×D47—41no—
131C2×D47—44no—
132C2×D47—84no—
133C4×C47—22no—
134C4×C47—44no—
135C4×C47#12011yescharacteristic
136C4×C47#12012yes—
137C4×C47#12011yescharacteristic
138Dic47—24no—
139Dic47—42no—
140Dic47—41no—
141#3025—471nomaximal, Sylow
142C2×C47—21no—
143C2×C47—22no—
144C2×C47—42no—
145C2×C47C2×#12011yescharacteristic
146D47—42no—
147D47—44no—
148#585—471no—
149#525—471no—
150#525—472no—
151#458—474no—
152B(4,𝔽2)—474no—
153#410—472no—
154#410D4711yescharacteristic, complemented
155C47#302511yescharacteristic, complemented, Sylow
1562−1+4—942no—
1572−1+4—941no—
158H(5,𝔽2)—474no—
159H(5,𝔽2)—942no—
160H(5,𝔽2)—941no—
161C2×#41—472no—
162C2×#41—944no—
163C2×#41—942no—
164C2×#41C2×D4711yescharacteristic
165C23×C4—471no—
166#123—472no—
167#123—474no—
168C22⋊Q8—942no—
169C22⋊Q8—941no—
170#121—942no—
171#121—941no—
172#120—472no—
173#120—474no—
174C4×D4—944no—
175C4×D4—942no—
176#117—471no—
177#117C2×D4712yescomplemented
178#99—478no—
179#99C2×D4714yescomplemented
180C24—471no—
181#41—22no—
182#41—22no—
183#41—944no—
184#41—944no—
185#41—948no—
186#41—944no—
187#41—944no—
188#41—942no—
189#41—942no—
190#41—944no—
191#41—942no—
192#41—942no—
193C2×Q8—472no—
194C2×Q8—942no—
195C2×Q8—944no—
196C2×Q8D18811yescharacteristic, complemented
197C2×D4—474no—
198C2×D4—472no—
199C2×D4—942no—
200C2×D4—944no—
201C2×D4—948no—
202C2×D4—944no—
203C2×D4—944no—
204C2×D4—942no—
205C2×D4D18811yescharacteristic, complemented
206C2×D4C22×D4712yes—
207C22×C4—474no—
208C22×C4—471no—
209C22×C4—944no—
210C22×C4—941no—
211C22×C4—941no—
212C22×C4—942no—
213C22×C4—942no—
214C22×C4D18812yescomplemented
215C22×C4C22×D4711yescharacteristic
216C4⋊C4—22no—
217C4⋊C4—944no—
218C4⋊C4—942no—
219C4⋊C4—941no—
220C22⋊C4—472no—
221C22⋊C4—944no—
222C22⋊C4—944no—
223C22⋊C4—942no—
224C22⋊C4—942no—
225C22⋊C4C22×D4714yes—
226C42—22no—
227C42—941no—
228C23—474no—
229C23—944no—
230C23—942no—
231C23—941no—
232C23—1882no—
233C23C2×D18812yes—
234C23C23×D4711yescharacteristic
235Q8—22no—
236Q8—944no—
237Q8—942no—
238Q8—942no—
239D4—24no—
240D4—22no—
241D4—944no—
242D4—948no—
243D4—944no—
244D4—944no—
245D4—942no—
246D4—942no—
247D4—1888no—
248D4—1884no—
249C2×C4—22no—
250C2×C4—22no—
251C2×C4—24no—
252C2×C4—474no—
253C2×C4—948no—
254C2×C4—944no—
255C2×C4—944no—
256C2×C4—944no—
257C2×C4—942no—
258C2×C4—942no—
259C2×C4—941no—
260C2×C4—1881no—
261C2×C4—1882no—
262C2×C4—1881no—
263C2×C4C2×D18812yes—
264C2×C4C2×D18811yescharacteristic
265C2×C4C2×D18811yescharacteristic
266C2×C4D4×D4712yes—
267C2×C4D4×D4712yes—
268C22—22no—
269C22—41no—
270C22—42no—
271C22—944no—
272C22—942no—
273C22—944no—
274C22—3764no—
275C22—1884no—
276C22—1882no—
277C22—1881no—
278C22—1881no—
279C22C2×D4×D4712yes—
280C22C22×D18811yescharacteristic
281C4—22no—
282C4—44no—
283C4—944no—
284C4—1882no—
285C4—1881no—
286C4#1309399411yescharacteristic
287C4#1309399412yes—
288C4#1309399411yescharacteristic
289C2—22no—
290C2—21no—
291C2—42no—
292C2—1882no—
293C2—1884no—
294C2C2×#1309399411yescharacteristic
subgroupG/H
centerC4#13093994
commutatorC23×C47C24
FrattiniC23C23×D47
FittingC47×#410C2
socleC2×C47C2×#120
hypercenter#410D47
hypocenterC47#3025
LCSG ▷ C23×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C4 ◁ C22×C4 ◁ #410

Complements

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

NH ≅ G/Ntype
1. #15689959C2semidirect
2. #15689635C2semidirect
3. #15689630C2semidirect
4. #15689314C2semidirect
5. #15689311C2semidirect
6. #15689096C2semidirect
7. C47×#410C2semidirect
16. C22×C4×D47C22semidirect
17. #13094008C22semidirect
18. #13094005C22semidirect
23. #13093994C22semidirect
24. #13093992C22semidirect
27. #13093983C22semidirect
28. #13093938C22semidirect
30. #117×C47C22semidirect
31. #99×C47C22semidirect
35. C2×Q8×C47D4semidirect
36. C2×D4×C47D4semidirect
38. C22×C4×C47D4semidirect
59. C2×D188D4semidirect
65. C2×C4×D47D4semidirect
67. C2×Dic94D4semidirect
154. #410D47semidirect
155. C47#3025semidirect
177. #117C2×D47semidirect
179. #99C2×D47semidirect
196. C2×Q8D188semidirect
205. C2×D4D188semidirect
214. C22×C4D188semidirect