Finite Group Databasebeta

← #20254309

Subgroups — #20254309

Order 6016.

428 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 428 conjugacy classes of subgroups — too many to draw. Only its 125 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#15689671C211yesmaximal, characteristic
2C4⋊Q8×D47C211yesmaximal, characteristic, complemented
3#15689495C211yesmaximal, characteristic, complemented
4#15689474C211yesmaximal, characteristic, complemented
5#15689473C211yesmaximal, characteristic, complemented
6#15689326C214yesmaximal, complemented
7#15689260C214yesmaximal, complemented
8#15689174C211yesmaximal, characteristic, complemented
9C47×#492C211yesmaximal, characteristic, complemented
10C2×#10625352—21no—
11C2×Q8×D47C2212yes—
12C2×#10625335C2214yes—
13#13094024C2211yescharacteristic
14#13094024C2211yescharacteristic
15#13094023—21no—
16#13094023—21no—
17#13094022C2212yes—
18#13094011—21no—
19#13093995—21no—
20#13093995C2212yes—
21D4×Dic47—21no—
22D4×Dic47C2212yes—
23C4⋊C4×D47—21no—
24C4⋊C4×D47—21no—
25C42×D47C2211yescharacteristic
26Dic47⋊C8C2212yes—
27#13093949C2214yes—
28#13093948C2214yes—
29(C2×D47)⋊C8C2212yes—
30C4×C47⋊C8C2211yescharacteristic
31C2×SD16×C47C2214yes—
32C4⋊Q8×C47C2211yescharacteristic
33#127×C47C2211yescharacteristic
34C4×C8×C47C2211yescharacteristic
35C2×Q8×C47C2312yes—
36C2×D4×C47—21no—
37C2×D4×C47—21no—
38C2×D4×C47C2312yes—
39C2×C22⋊D47—22no—
40C22×Dic47—22no—
41Q8×D47—44no—
42#10625352—44no—
43C2×C4×D47—22no—
44C2×C4×D47D411yescharacteristic
45C2×C4×D47D411yescharacteristic
46C2×C4×D47C2311yescharacteristic
47C2×Dic94—21no—
48C2×Dic94—22no—
49C2×Dic94C2312yes—
50SD16×C47—44no—
51C2×C8×C47C2312yes—
52C4⋊C4×C47—21no—
53C4⋊C4×C47—21no—
54C42×C47C2311yescharacteristic
55C22⋊Dic47—22no—
56C22⋊Dic47—22no—
57#10625335—44no—
58C4⋊Dic47—21no—
59C4⋊Dic47—21no—
60C4⋊Dic47—21no—
61C4⋊Dic47C2312yes—
62Dic47⋊C4—22no—
63Dic47⋊C4—22no—
64C4×Dic47D411yescharacteristic
65C4×Dic47D411yescharacteristic
66C4×Dic47C2311yescharacteristic
67C2×C47⋊C8C2312yes—
68C23×C47—22no—
69C22×D47C2×D411yescharacteristic
70Q8×C47—24no—
71D4×C47—24no—
72D4×C47—42no—
73D4×C47—42no—
74C2×C4×C47—22no—
75C2×C4×C47C2×D411yescharacteristic
76C2×C4×C47C2×D411yescharacteristic
77C2×C4×C47C2411yescharacteristic
78C22⋊D47—44no—
79C2×Dic47—22no—
80C2×Dic47—22no—
81C2×Dic47—44no—
82C2×Dic47C2×D411yescharacteristic
83C2×Dic47C2×D411yescharacteristic
84C2×Dic47C2×D411yescharacteristic
85C4×D47—22no—
86C4×D47—22no—
87C4×D47—44no—
88C4×D47SD1614yescomplemented
89Dic94—24no—
90Dic94—44no—
91Dic94—42no—
92C8×C47—22no—
93C47⋊C8—22no—
94C22×C47—42no—
95C22×C47—42no—
96C22×C47—42no—
97C22×C47C22×D411yescharacteristic
98C2×D47—21no—
99C2×D47—21no—
100C2×D47C2×SD1612yes—
101C4×C47—42no—
102C4×C47C2×SD1612yes—
103C4×C47#13712yes—
104C4×C47H(5,𝔽2)12yes—
105Dic47—21no—
106Dic47—21no—
107Dic47—42no—
108Dic47—42no—
109Dic47C2×SD1612yes—
110#3206—471nomaximal, Sylow
111C2×C47—82no—
112C2×C47#53511yescharacteristic
113C2×C47C22×SD1611yescharacteristic
114C2×C47C2×#13711yescharacteristic
115D47—22no—
116#532—471no—
117C2×C4⋊Q8—471no—
118#492—471no—
119#492D4711yescharacteristic, complemented
120#487—471no—
121#487—471no—
122#461—474no—
123#448—474no—
124#431—471no—
125C47#320611yescharacteristic, complemented, Sylow
126C2×#41—941no—
127C22×Q8—472no—
128C2×SD16—474no—
129C2×SD16C2×D4714yes—
130C4⋊Q8—472no—
131C4⋊Q8—471no—
132C4⋊Q8—471no—
133C4⋊Q8—941no—
134C4⋊Q8—941no—
135C4⋊Q8C2×D4711yescharacteristic
136#127C2×D4711yescharacteristic
137#124—941no—
138#121—472no—
139#121—941no—
140C4×D4—472no—
141C4×D4—941no—
142C2×C4⋊C4—941no—
143C2×C4⋊C4—941no—
144C2×C42—471no—
145C4⋊C8—472no—
146#103—474no—
147#103—474no—
148C22⋊C8—472no—
149C4×C8—471no—
150C4×C8C2×D4711yescharacteristic
151#41—1884no—
152C2×Q8—472no—
153C2×Q8—942no—
154C2×Q8—941no—
155C2×Q8—1884no—
156C2×Q8C22×D4712yes—
157C2×D4—21no—
158C2×D4—21no—
159C2×D4—942no—
160C2×D4C22×D4712yes—
161C22×C4—471no—
162C22×C4—471no—
163C22×C4—471no—
164C22×C4—942no—
165C22×C4—942no—
166SD16—44no—
167SD16—1884no—
168C2×C8—472no—
169C2×C8C22×D4712yes—
170C4⋊C4—21no—
171C4⋊C4—21no—
172C4⋊C4—472no—
173C4⋊C4—942no—
174C4⋊C4—942no—
175C4⋊C4—941no—
176C4⋊C4—941no—
177C4⋊C4—941no—
178C22⋊C4—942no—
179C22⋊C4—942no—
180C42—471no—
181C42—471no—
182C42—471no—
183C42C22×D4711yescharacteristic
184C23—22no—
185C23—471no—
186Q8—24no—
187Q8—944no—
188Q8—1884no—
189Q8—1882no—
190D4—24no—
191D4—42no—
192D4—42no—
193D4—1884no—
194C2×C4—22no—
195C2×C4—471no—
196C2×C4—474no—
197C2×C4—471no—
198C2×C4—471no—
199C2×C4—942no—
200C2×C4—942no—
201C2×C4—942no—
202C2×C4—942no—
203C2×C4—1884no—
204C2×C4—1884no—
205C2×C4D4×D4711yescharacteristic
206C2×C4D4×D4711yescharacteristic
207C2×C4C23×D4711yescharacteristic
208C8—22no—
209C8—942no—
210C22—42no—
211C22—42no—
212C22—42no—
213C22—472no—
214C22—941no—
215C22—941no—
216C22C2×D4×D4711yescharacteristic
217C4—42no—
218C4—472no—
219C4—941no—
220C4—941no—
221C4—1882no—
222C4—1882no—
223C4SD16×D4712yes—
224C4#1309405312yes—
225C4#1309406912yes—
226C2—82no—
227C2—942no—
228C2#1568968611yescharacteristic
229C2C2×SD16×D4711yescharacteristic
230C2C2×#1309405311yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#492C2
socleC22×C47C22×D4
hypercenter#492D47
hypocenterC47#3206
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #492

Complements

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

NH ≅ G/Ntype
2. C4⋊Q8×D47C2semidirect
3. #15689495C2semidirect
4. #15689474C2semidirect
5. #15689473C2semidirect
6. #15689326C2semidirect
7. #15689260C2semidirect
8. #15689174C2semidirect
9. C47×#492C2semidirect
88. C4×D47SD16semidirect
119. #492D47semidirect
125. C47#3206semidirect