Finite Group Databasebeta

← #20252676

Subgroups — #20252676

Order 6016.

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

normal subgroups only

This group has 732 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×#13094071C211yesmaximal, characteristic, complemented
2C2×#13094052C211yesmaximal, characteristic, complemented
3C22×#10625325C211yesmaximal, characteristic, complemented
4#15689687C211yesmaximal, characteristic, complemented
5#15689270C214yesmaximal, complemented
6#15689264C214yesmaximal, complemented
7#15689133C211yesmaximal, characteristic, complemented
8#15689120C211yesmaximal, characteristic, complemented
9C47×#408C211yesmaximal, characteristic, complemented
10#13094071—24no—
11#13094071—24no—
12C2×#10625350C2211yescharacteristic
13C2×#10625350C2212yescomplemented
14C2×#10625352—21no—
15C2×#10625352—22no—
16C22×Dic94C2211yescharacteristic
17C22×Dic94C2212yescomplemented
18C2×Q8×D47—21no—
19C22×D188C2211yescharacteristic
20#13094052—24no—
21C2×#10625325—24no—
22C2×#10625325C2212yes—
23C2×#10625325C2214yes—
24C2×D376C2212yes—
25#13094020—21no—
26#13094013—21no—
27#13093998C2214yes—
28#13093992—22no—
29#13093983C2211yescharacteristic
30#13093949C2212yescomplemented
31#13093949C2214yescomplemented
32#13093946C2212yescomplemented
33C2×#41×C47C2211yescharacteristic
34C2×M16×C47C2211yescharacteristic
35C22×C8×C47C2211yescharacteristic
36C22⋊C8×C47C2214yescomplemented
37C23×D47—21no—
38#41×C47—22no—
39#41×C47—22no—
40C2×Q8×C47D411yescharacteristic
41C2×D4×C47D412yes—
42C2×D4×C47D411yescharacteristic
43C22×C4×C47C2312yes—
44C22×C4×C47C2311yescharacteristic
45C2×C22⋊D47—21no—
46C2×C22⋊D47—22no—
47C2×C22⋊D47—24no—
48C22×Dic47—21no—
49C22×Dic47—22no—
50Q8×D47—28no—
51#10625352—216no—
52#10625352—28no—
53#10625350—22no—
54#10625350—24no—
55#10625350—24no—
56#10625350D414yescomplemented
57C2×D188—22no—
58C2×D188—22no—
59C2×D188—21no—
60C2×D188C2312yes—
61C2×D188C2311yescharacteristic
62C2×C4×D47—21no—
63C2×C4×D47—22no—
64C2×Dic94—21no—
65C2×Dic94—22no—
66C2×Dic94—22no—
67C2×Dic94—24no—
68C2×Dic94—24no—
69C2×Dic94D414yescomplemented
70C2×Dic94C2312yes—
71C2×Dic94C2311yescharacteristic
72M16×C47—22no—
73C2×C8×C47—22no—
74C2×C8×C47C2312yes—
75C2×C8×C47C2312yes—
76C22⋊Dic47—21no—
77(C2×D47)⋊C4—24no—
78C4⋊Dic47C2312yes—
79C4×Dic47—21no—
80D376—24no—
81#10625325—28no—
82#10625325—24no—
83C23×C47C2×D412yes—
84C23×C47C2×D411yescharacteristic
85C22×D47—21no—
86C22×D47—22no—
87C22×D47—42no—
88C22×D47—82no—
89Q8×C47—22no—
90D4×C47—24no—
91D4×C47—22no—
92C2×C4×C47—22no—
93C2×C4×C47—22no—
94C2×C4×C47C2×D412yes—
95C2×C4×C47C2×D411yescharacteristic
96C2×C4×C47C2×D412yes—
97C2×C4×C47C2×D412yes—
98C2×C4×C47C2411yescharacteristic
99C22⋊D47—28no—
100C22⋊D47—24no—
101C22⋊D47—84no—
102C2×Dic47—28no—
103C2×Dic47—24no—
104C2×Dic47—22no—
105C2×Dic47—21no—
106C2×Dic47—22no—
107D188—21no—
108D188—22no—
109D188—22no—
110D188—42no—
111D188C2×D412yes—
112C4×D47—28no—
113C4×D47—24no—
114Dic94—28no—
115Dic94—24no—
116Dic94—22no—
117Dic94—21no—
118Dic94C2×D412yes—
119Dic94C2×D414yes—
120C8×C47—22no—
121C8×C47—22no—
122C22×C47—22no—
123C22×C47—22no—
124C22×C47—24no—
125C22×C47#12012yes—
126C22×C47C22×D411yescharacteristic
127C2×D47—22no—
128C2×D47—42no—
129C2×D47—42no—
130C2×D47—44no—
131C2×D47—84no—
132C4×C47—22no—
133C4×C47#12012yes—
134C4×C47C22×D411yescharacteristic
135C4×C47C22×D411yescharacteristic
136Dic47—22no—
137Dic47—24no—
138Dic47—42no—
139#3010—471nomaximal, Sylow
140C2×C47—22no—
141C2×C47—42no—
142C2×C47C2×#12011yescharacteristic
143C2×C47#57712yes—
144D47—42no—
145D47—82no—
146C2×2−1+4—471no—
147C2×AGL(1,ℤ/8)—471no—
148C22×SD16—471no—
149#535—471no—
150#449—474no—
151#448—474no—
152#419—471no—
153#416—471no—
154#408D4711yescharacteristic, complemented
155C47#301011yescharacteristic, complemented, Sylow
1562−1+4—944no—
1572−1+4—944no—
158C2×#41—471no—
159C2×#41—472no—
160C2×#41—942no—
161C2×#41—941no—
162C2×#41C2×D4711yescharacteristic
163C22×Q8—471no—
164C22×Q8—472no—
165C22×Q8—941no—
166C22×D4—471no—
167AGL(1,ℤ/8)—944no—
168C2×SD16—474no—
169C2×SD16—472no—
170C2×SD16—944no—
171C2×D8—472no—
172C2×M16C2×D4711yescharacteristic
173C22×C8C2×D4711yescharacteristic
174#127—941no—
175#124—941no—
176#121—474no—
177#120—942no—
178#117—471no—
179#103—472no—
180#103—474no—
181#102—472no—
182C22⋊C8C2×D4714yescomplemented
183C24—941no—
184#41—22no—
185#41—22no—
186#41—474no—
187#41—944no—
188#41—944no—
189#41—9416no—
190#41—948no—
191#41—942no—
192C2×Q8—474no—
193C2×Q8—472no—
194C2×Q8—471no—
195C2×Q8—944no—
196C2×Q8—944no—
197C2×Q8—948no—
198C2×Q8—942no—
199C2×Q8—941no—
200C2×Q8—942no—
201C2×Q8D18811yescharacteristic
202C2×D4—471no—
203C2×D4—472no—
204C2×D4—942no—
205C2×D4—941no—
206C2×D4—944no—
207C2×D4—941no—
208C2×D4—942no—
209C2×D4—942no—
210C2×D4D18812yes—
211C2×D4D18811yescharacteristic
212C22×C4—942no—
213C22×C4—941no—
214C22×C4—942no—
215C22×C4—941no—
216C22×C4C22×D4712yes—
217C22×C4C22×D4711yescharacteristic
218SD16—948no—
219SD16—944no—
220D8—944no—
221M16—22no—
222C2×C8—22no—
223C2×C8C22×D4712yes—
224C2×C8C22×D4712yes—
225C4⋊C4—472no—
226C22⋊C4—941no—
227C22⋊C4—944no—
228C42—941no—
229C23—941no—
230C23—942no—
231C23—3762no—
232C23—1882no—
233C23C2×D18812yes—
234C23C2×D18811yescharacteristic
235Q8—22no—
236Q8—474no—
237Q8—472no—
238Q8—948no—
239Q8—944no—
240Q8—942no—
241Q8—941no—
242D4—24no—
243D4—22no—
244D4—472no—
245D4—948no—
246D4—944no—
247D4—941no—
248D4—942no—
249D4—942no—
250D4—3764no—
251D4—1882no—
252C2×C4—22no—
253C2×C4—22no—
254C2×C4—948no—
255C2×C4—948no—
256C2×C4—944no—
257C2×C4—942no—
258C2×C4—941no—
259C2×C4—944no—
260C2×C4—942no—
261C2×C4C2×D18812yes—
262C2×C4C2×D18811yescharacteristic
263C2×C4D4×D4712yes—
264C2×C4D4×D4712yes—
265C2×C4C23×D4711yescharacteristic
266C8—22no—
267C8—22no—
268C22—22no—
269C22—22no—
270C22—24no—
271C22—942no—
272C22—3764no—
273C22—1882no—
274C22—1884no—
275C22—1882no—
276C22#1309399412yes—
277C22C22×D18811yescharacteristic
278C4—22no—
279C4—944no—
280C4—942no—
281C4—1882no—
282C4#1309399412yes—
283C4C2×D4×D4711yescharacteristic
284C4C2×D4×D4711yescharacteristic
285C2—22no—
286C2—42no—
287C2—3762no—
288C2—1882no—
289C2C2×#1309399411yescharacteristic
290C2#1568993512yes—
subgroupG/H
centerC22C22×D188
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#408C2
socleC22×C47C22×D4
hypercenter#408D47
hypocenterC47#3010
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×#41 ◁ #408

Complements

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

NH ≅ G/Ntype
1. C2×#13094071C2semidirect
2. C2×#13094052C2semidirect
3. C22×#10625325C2semidirect
4. #15689687C2semidirect
5. #15689270C2semidirect
6. #15689264C2semidirect
7. #15689133C2semidirect
8. #15689120C2semidirect
9. C47×#408C2semidirect
13. C2×#10625350C22semidirect
17. C22×Dic94C22semidirect
30. #13093949C22semidirect
31. #13093949C22semidirect
32. #13093946C22semidirect
36. C22⋊C8×C47C22semidirect
56. #10625350D4semidirect
69. C2×Dic94D4semidirect
154. #408D47semidirect
155. C47#3010semidirect
182. C22⋊C8C2×D47semidirect