Finite Group Databasebeta

← #20253771

Subgroups — #20253771

Order 6016.

400 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 117 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#15689679C211yesmaximal, characteristic, complemented
2#124×D47C211yesmaximal, characteristic
3#15689484C212yesmaximal, complemented
4#15689481C212yesmaximal, complemented
5#15689480C211yesmaximal, characteristic, complemented
6#15689478C211yesmaximal, characteristic, complemented
7#15689477C211yesmaximal, characteristic, complemented
8#15689130C212yesmaximal, complemented
9#15689126C212yesmaximal
10C4×#10625324C211yesmaximal, characteristic, complemented
11C47×#488C211yesmaximal, characteristic, complemented
12C2×Q8×D47C2211yescharacteristic
13C2×D4×D47C2211yescharacteristic
14C2×#10625324C2212yes—
15#13094023C2212yescomplemented
16#13094016C2211yescharacteristic, complemented
17#13094013C2211yescharacteristic
18#13094012C2211yescharacteristic
19#13094011C2211yescharacteristic
20#13094010—22no—
21#13094002—22no—
22#13093989—22no—
23#13093982C2212yes—
24C22⋊C4×D47—22no—
25C42×D47C2211yescharacteristic
26#13093949C2212yescomplemented
27#13093948C2212yescomplemented
28#13093947C2212yescomplemented
29#13093946C2212yes—
30#13093945C2212yes—
31#13093944C2212yes—
32#13093934C2212yescomplemented
33C4×C47⋊C8C2211yescharacteristic, complemented
34#125×C47C2211yescharacteristic, complemented
35#124×C47C2211yescharacteristic
36#103×C47C2212yescomplemented
37#102×C47C2212yes—
38C4×C8×C47C2211yescharacteristic, complemented
39C23×D47—21no—
40C2×Q8×C47C2311yescharacteristic
41C2×D4×C47C2311yescharacteristic
42C2×C22⋊D47—21no—
43Q8×D47—24no—
44D4×D47—24no—
45C2×D188C2311yescharacteristic
46C2×C4×D47—21no—
47C2×C4×D47D412yes—
48C2×C4×D47C2311yescharacteristic
49C2×Dic94—22no—
50C2×Dic94—21no—
51C2×Dic94C2311yescharacteristic
52C2×C8×C47C2312yes—
53C4⋊C4×C47—22no—
54C4⋊C4×C47C2312yes—
55C22⋊C4×C47—22no—
56C42×C47C2311yescharacteristic
57C22⋊Dic47—22no—
58(C2×D47)⋊C4—22no—
59(C2×D47)⋊C4—22no—
60(C2×D47)⋊C4—22no—
61C4⋊Dic47C2312yes—
62Dic47⋊C4—22no—
63Dic47⋊C4—22no—
64C4×Dic47—22no—
65C4×Dic47D412yes—
66C4×Dic47C2311yescharacteristic
67C2×C47⋊C8C2312yes—
68#10625324—24no—
69C23×C47—21no—
70C22×D47—21no—
71C22×D47—44no—
72C22×D47—42no—
73C22×D47C2×D411yescharacteristic
74Q8×C47—22no—
75D4×C47—22no—
76C2×C4×C47—22no—
77C2×C4×C47—21no—
78C2×C4×C47C2×D412yes—
79C2×C4×C47C2411yescharacteristic
80C22⋊D47—42no—
81C2×Dic47—22no—
82C2×Dic47—21no—
83C2×Dic47C2×D412yes—
84C2×Dic47C2×D411yescharacteristic
85D188—22no—
86C4×D47—42no—
87C4×D47—42no—
88C4×D47#4114yes—
89Dic94—22no—
90Dic94—44no—
91Dic94—42no—
92C8×C47—22no—
93C47⋊C8—22no—
94C22×C47—41no—
95C22×C47—42no—
96C22×C47C22×D411yescharacteristic
97C2×D47—22no—
98C2×D47—41no—
99C2×D47—42no—
100C2×D47—84no—
101C2×D47#12412yes—
102C4×C47—22no—
103C4×C47—41no—
104C4×C47—42no—
105C4×C47C2×#4112yes—
106Dic47—22no—
107Dic47—41no—
108Dic47—42no—
109Dic47#12412yes—
110#3140—471nomaximal, Sylow
111C2×C47—81no—
112C2×C47C2×#12411yescharacteristic
113C2×C47#57512yes—
114D47—22no—
115D47—81no—
116#533—471no—
117C2×#124—471no—
118#489—472no—
119#489—472no—
120#488—471no—
121#488—471no—
122#488—471no—
123#488D4711yescharacteristic, complemented
124#419—472no—
125#418—472no—
126C4×M16—471no—
127C47#314011yescharacteristic, complemented, Sylow
128C22×Q8—471no—
129C22×D4—471no—
130C2×M16—472no—
131C4⋊Q8—472no—
132#125—471no—
133#125C2×D4711yescharacteristic, complemented
134#124—471no—
135#124—471no—
136#124—471no—
137#124—942no—
138#124C2×D4711yescharacteristic
139C22⋊Q8—942no—
140C4×Q8—942no—
141#117—472no—
142C2×C22⋊C4—942no—
143C2×C42—471no—
144#103—472no—
145#103—472no—
146#103—472no—
147#103C2×D4712yescomplemented
148#102—472no—
149#102—472no—
150#102—472no—
151#102C2×D4712yes—
152#97—472no—
153C4×C8—471no—
154C4×C8C2×D4711yescharacteristic, complemented
155C24—941no—
156C2×Q8—471no—
157C2×Q8—942no—
158C2×Q8—941no—
159C2×Q8—944no—
160C2×Q8C22×D4711yescharacteristic
161C2×D4—471no—
162C2×D4—944no—
163C2×D4—941no—
164C2×D4C22×D4711yescharacteristic
165C22×C4—471no—
166C22×C4—472no—
167C22×C4—941no—
168M16—944no—
169C2×C8—472no—
170C2×C8C22×D4712yes—
171C4⋊C4—22no—
172C4⋊C4—472no—
173C4⋊C4—942no—
174C4⋊C4—942no—
175C4⋊C4C22×D4712yes—
176C22⋊C4—22no—
177C22⋊C4—942no—
178C22⋊C4—942no—
179C22⋊C4—942no—
180C22⋊C4—942no—
181C42—472no—
182C42—471no—
183C42—942no—
184C42C22×D4711yescharacteristic
185C23—21no—
186C23—471no—
187C23—941no—
188C23—1882no—
189C23—1884no—
190Q8—22no—
191Q8—942no—
192Q8—1882no—
193Q8—1884no—
194D4—22no—
195D4—942no—
196D4—1882no—
197C2×C4—22no—
198C2×C4—21no—
199C2×C4—471no—
200C2×C4—474no—
201C2×C4—472no—
202C2×C4—942no—
203C2×C4—941no—
204C2×C4—1882no—
205C2×C4—1882no—
206C2×C4D4×D4712yes—
207C2×C4C23×D4711yescharacteristic
208C8—22no—
209C8—942no—
210C22—41no—
211C22—42no—
212C22—472no—
213C22—942no—
214C22—3764no—
215C22—1881no—
216C22—1882no—
217C22C2×D4×D4711yescharacteristic
218C4—22no—
219C4—41no—
220C4—42no—
221C4—472no—
222C4—942no—
223C4—1881no—
224C4—1882no—
225C4#41×D4712yes—
226C2—81no—
227C2—942no—
228C2—3761no—
229C2#124×D4711yescharacteristic
230C2#1568992012yes—
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#488C2
socleC22×C47C22×D4
hypercenter#488D47
hypocenterC47#3140
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #488

Complements

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

NH ≅ G/Ntype
1. #15689679C2semidirect
3. #15689484C2semidirect
4. #15689481C2semidirect
5. #15689480C2semidirect
6. #15689478C2semidirect
7. #15689477C2semidirect
8. #15689130C2semidirect
10. C4×#10625324C2semidirect
11. C47×#488C2semidirect
15. #13094023C22semidirect
16. #13094016C22semidirect
26. #13093949C22semidirect
27. #13093948C22semidirect
28. #13093947C22semidirect
32. #13093934C22semidirect
33. C4×C47⋊C8C22semidirect
34. #125×C47C22semidirect
36. #103×C47C22semidirect
38. C4×C8×C47C22semidirect
123. #488D47semidirect
127. C47#3140semidirect
133. #125C2×D47semidirect
147. #103C2×D47semidirect
154. C4×C8C2×D47semidirect