Finite Group Databasebeta

← #20253337

Subgroups — #20253337

Order 6016.

410 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 410 conjugacy classes of subgroups — too many to draw. Only its 137 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×#13094003C211yesmaximal, characteristic
2C2×#13093983C211yesmaximal, characteristic
3#15689465C214yesmaximal, complemented
4#15689459C212yesmaximal, complemented
5#15689454C212yesmaximal, complemented
6#15689165C212yesmaximal, complemented
7#15689133C212yesmaximal, complemented
8C47×#407C211yesmaximal, characteristic
9C22×Dic94C2211yescharacteristic
10#13094003—21no—
11#13094003—21no—
12#13094003C2212yes—
13#13094003C2212yes—
14#13093983—21no—
15#13093983—21no—
16#13093983C2212yes—
17#13093983C2212yes—
18C2×C4⋊Dic47C2211yescharacteristic
19C2×C4⋊Dic47C2211yescharacteristic
20C2×C4⋊Dic47C2211yescharacteristic
21C2×Dic47⋊C4—21no—
22C2×C22⋊Dic47—21no—
23C2×C22⋊Dic47—21no—
24C2×C4×Dic47—21no—
25#13093958C2214yescomplemented
26#13093956C2214yescomplemented
27#13093949C2214yescomplemented
28#13093949C2214yescomplemented
29C23×C4×C47C2211yescharacteristic
30C2×M16×C47C2212yes—
31C22⋊C8×C47C2212yes—
32C22⋊C8×C47C2212yes—
33C24×C47D411yescharacteristic
34C22×C4×C47—24no—
35C22×C4×C47D411yescharacteristic
36C22×C4×C47D411yescharacteristic
37C22×C4×C47D411yescharacteristic
38C22×C4×C47C2311yescharacteristic
39C22×C4×C47C2311yescharacteristic
40C22×C4×C47C2311yescharacteristic
41C22×Dic47—21no—
42C22×Dic47—21no—
43C22×Dic47—21no—
44C22×Dic47—21no—
45C2×Dic94—24no—
46C2×Dic94—21no—
47C2×Dic94C2312yes—
48M16×C47—24no—
49C2×C8×C47C2314yes—
50C22⋊Dic47—22no—
51C22⋊Dic47—22no—
52C22⋊Dic47—22no—
53C22⋊Dic47—22no—
54C4⋊Dic47—21no—
55C4⋊Dic47—21no—
56C4⋊Dic47—21no—
57C4⋊Dic47C2312yes—
58C4⋊Dic47C2312yes—
59C4⋊Dic47C2312yes—
60Dic47⋊C4—22no—
61Dic47⋊C4—22no—
62C4×Dic47—22no—
63C4×Dic47—22no—
64C23×C47—22no—
65C23×C47—22no—
66C23×C47—41no—
67C23×C47C2×D411yescharacteristic
68C23×C47C2×D411yescharacteristic
69C23×C47C2×D411yescharacteristic
70C2×C4×C47—22no—
71C2×C4×C47—22no—
72C2×C4×C47—22no—
73C2×C4×C47—22no—
74C2×C4×C47—22no—
75C2×C4×C47C2×D411yescharacteristic
76C2×C4×C47C2×D411yescharacteristic
77C2×C4×C47C2×D411yescharacteristic
78C2×C4×C47#4114yes—
79C2×C4×C47C2411yescharacteristic
80C2×Dic47—22no—
81C2×Dic47—22no—
82C2×Dic47—22no—
83C2×Dic47—22no—
84C2×Dic47—42no—
85C2×Dic47—42no—
86C2×Dic47—42no—
87C2×Dic47—42no—
88Dic94—24no—
89Dic94—42no—
90C8×C47—24no—
91C22×C47—21no—
92C22×C47—21no—
93C22×C47—21no—
94C22×C47—21no—
95C22×C47—21no—
96C22×C47—21no—
97C22×C47—21no—
98C22×C47—44no—
99C22×C47#12312yes—
100C22×C47#13712yes—
101C22×C47C22×D411yescharacteristic
102C4×C47—21no—
103C4×C47—21no—
104C4×C47#12312yes—
105C4×C47C2×#4112yes—
106Dic47—42no—
107Dic47—42no—
108Dic47—42no—
109Dic47—42no—
110#3095—471nomaximal, Sylow
111C2×C47—22no—
112C2×C47—22no—
113C2×C47—41no—
114C2×C47C2×#12311yescharacteristic
115C2×C47C2×#13711yescharacteristic
116C2×C47#57511yescharacteristic
117C2×C22⋊Q8—471no—
118C2×#117—471no—
119#485—474no—
120#484—472no—
121#483—472no—
122#428—472no—
123#419—472no—
124#407D4711yescharacteristic
125C47#309511yescharacteristic, complemented, Sylow
126C22×Q8—471no—
127C23×C4C2×D4711yescharacteristic
128C2×M16C2×D4712yes—
129C22⋊Q8—472no—
130C22⋊Q8—472no—
131C22⋊Q8—941no—
132C22⋊Q8—941no—
133#117—472no—
134#117—472no—
135#117—941no—
136#117—941no—
137C2×C4⋊C4—471no—
138C2×C4⋊C4—471no—
139C2×C4⋊C4—471no—
140C2×C4⋊C4—941no—
141C2×C22⋊C4—941no—
142C2×C22⋊C4—941no—
143C2×C42—941no—
144#107—474no—
145#106—474no—
146#103—474no—
147#103—474no—
148C22⋊C8C2×D4712yes—
149C22⋊C8C2×D4712yes—
150C24D18811yescharacteristic
151C2×Q8—472no—
152C2×Q8—941no—
153C2×Q8—944no—
154C22×C4—24no—
155C22×C4—941no—
156C22×C4—941no—
157C22×C4—941no—
158C22×C4—941no—
159C22×C4D18811yescharacteristic
160C22×C4D18811yescharacteristic
161C22×C4D18811yescharacteristic
162C22×C4C22×D4711yescharacteristic
163C22×C4C22×D4711yescharacteristic
164C22×C4C22×D4711yescharacteristic
165M16—24no—
166C2×C8C22×D4714yes—
167C4⋊C4—472no—
168C4⋊C4—472no—
169C4⋊C4—472no—
170C4⋊C4—942no—
171C4⋊C4—942no—
172C4⋊C4—941no—
173C4⋊C4—941no—
174C4⋊C4—941no—
175C22⋊C4—942no—
176C22⋊C4—942no—
177C22⋊C4—942no—
178C22⋊C4—942no—
179C42—942no—
180C42—942no—
181C23—22no—
182C23—22no—
183C23—41no—
184C23C2×D18811yescharacteristic
185C23C2×D18811yescharacteristic
186C23C2×D18811yescharacteristic
187Q8—944no—
188Q8—1882no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—22no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—942no—
195C2×C4—942no—
196C2×C4—942no—
197C2×C4—942no—
198C2×C4—1882no—
199C2×C4—1882no—
200C2×C4—1882no—
201C2×C4—1882no—
202C2×C4C2×D18811yescharacteristic
203C2×C4C2×D18811yescharacteristic
204C2×C4C2×D18811yescharacteristic
205C2×C4#1062535214yes—
206C2×C4C23×D4711yescharacteristic
207C8—24no—
208C22—21no—
209C22—21no—
210C22—21no—
211C22—21no—
212C22—21no—
213C22—21no—
214C22—21no—
215C22—44no—
216C22#1309400812yes—
217C22#1309405712yes—
218C22C22×D18811yescharacteristic
219C4—21no—
220C4—21no—
221C4—1882no—
222C4—1882no—
223C4—1882no—
224C4—1882no—
225C4#1309400812yes—
226C4C2×#1062535212yes—
227C2—22no—
228C2—22no—
229C2—41no—
230C2C2×#1309400811yescharacteristic
231C2C2×#1309405711yescharacteristic
232C2#1568992311yescharacteristic
subgroupG/H
centerC22C22×D188
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#407C2
socleC22×C47C22×D4
hypercenter#407D47
hypocenterC47#3095
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C23×C4 ◁ #407

Complements

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

NH ≅ G/Ntype
3. #15689465C2semidirect
4. #15689459C2semidirect
5. #15689454C2semidirect
6. #15689165C2semidirect
7. #15689133C2semidirect
25. #13093958C22semidirect
26. #13093956C22semidirect
27. #13093949C22semidirect
28. #13093949C22semidirect
125. C47#3095semidirect