Finite Group Databasebeta

← #20252902

Subgroups — #20252902

Order 6016.

494 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 494 conjugacy classes of subgroups — too many to draw. Only its 141 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
1C22×#10625335C211yesmaximal, characteristic, complemented
2#15689694C211yesmaximal, characteristic, complemented
3#15689598C211yesmaximal, characteristic, complemented
4#15689336C214yesmaximal, complemented
5#15689326C214yesmaximal, complemented
6#15689151C211yesmaximal, characteristic, complemented
7#15689133C211yesmaximal, characteristic, complemented
8#15689119C211yesmaximal, characteristic, complemented
9C2×AGL(1,ℤ/8)×C47C211yesmaximal, characteristic
10C22×Dic94C2211yescharacteristic
11C2×#10625335—24no—
12C2×#10625335C2214yes—
13C22×C47⋊C8C2211yescharacteristic
14#13094022C2212yescomplemented
15#13094011C2212yescomplemented
16#13094005—22no—
17#13094003—22no—
18D4×Dic47—22no—
19D4×Dic47C2214yes—
20#13093983C2211yescharacteristic
21#13093983C2211yescharacteristic
22C2×C22⋊Dic47—22no—
23Dic47⋊C8C2214yescomplemented
24#13093949C2214yescomplemented
25#13093948C2212yescomplemented
26#13093945C2212yescomplemented
27C2×#41×C47C2211yescharacteristic
28C22×D4×C47C2211yescharacteristic
29AGL(1,ℤ/8)×C47—24no—
30C2×SD16×C47C2212yes—
31C2×D8×C47C2212yes—
32C2×M16×C47C2211yescharacteristic
33C24×C47—21no—
34#41×C47—22no—
35#41×C47—22no—
36C2×Q8×C47C2311yescharacteristic
37C2×D4×C47—21no—
38C2×D4×C47—21no—
39C2×D4×C47—22no—
40C2×D4×C47D414yes—
41C2×D4×C47C2311yescharacteristic
42C2×D4×C47C2312yes—
43C22×C4×C47—21no—
44C22×C4×C47C2311yescharacteristic
45C22×Dic47—21no—
46C22×Dic47—24no—
47C2×Dic94—22no—
48C2×Dic94—22no—
49C2×Dic94—21no—
50C2×Dic94C2312yes—
51SD16×C47—24no—
52D8×C47—24no—
53M16×C47—22no—
54C2×C8×C47C2312yes—
55C22⋊Dic47—21no—
56C22⋊Dic47—24no—
57C22⋊Dic47—24no—
58C22⋊Dic47D412yes—
59#10625335—28no—
60C4⋊Dic47D412yes—
61C4⋊Dic47C2312yes—
62Dic47⋊C4—24no—
63C4×Dic47—21no—
64C4×Dic47C2312yes—
65C2×C47⋊C8—22no—
66C2×C47⋊C8C2312yes—
67C23×C47—22no—
68C23×C47—24no—
69C23×C47—21no—
70C23×C47—82no—
71C23×C47C2×D411yescharacteristic
72Q8×C47—21no—
73Q8×C47—21no—
74D4×C47—24no—
75D4×C47—21no—
76D4×C47—22no—
77D4×C47—21no—
78D4×C47—42no—
79D4×C47C2×D414yes—
80C2×C4×C47—21no—
81C2×C4×C47—42no—
82C2×C4×C47C2×D411yescharacteristic
83C2×C4×C47C2×D412yes—
84C2×C4×C47#4112yes—
85C2×C4×C47C2411yescharacteristic
86C2×Dic47—22no—
87C2×Dic47—22no—
88C2×Dic47—42no—
89C2×Dic47—84no—
90C2×Dic47C2×D414yes—
91Dic94—22no—
92Dic94—22no—
93Dic94—42no—
94C8×C47—22no—
95C47⋊C8—22no—
96C22×C47—22no—
97C22×C47—24no—
98C22×C47—44no—
99C22×C47—41no—
100C22×C47—42no—
101C22×C47—84no—
102C22×C47#12112yes—
103C22×C47C22×D411yescharacteristic
104C4×C47—41no—
105C4×C47#12112yes—
106C4×C47C22×D411yescharacteristic
107C4×C47C2×#4111yescharacteristic
108Dic47—24no—
109Dic47—42no—
110Dic47—42no—
111#3042—471nomaximal, Sylow
112C2×C47—22no—
113C2×C47—44no—
114C2×C47—81no—
115C2×C47C2×#12111yescharacteristic
116C2×C47#57712yes—
117C2×AGL(1,ℤ/8)D4711yescharacteristic
118C22×SD16—471no—
119#536—471no—
120#518—471no—
121#463—474no—
122#461—474no—
123#424—471no—
124#419—471no—
125#416—471no—
126C47#304211yescharacteristic, complemented, Sylow
127C2×#41C2×D4711yescharacteristic
128C22×Q8—471no—
129C22×D4C2×D4711yescharacteristic
130AGL(1,ℤ/8)—24no—
131C2×SD16—474no—
132C2×SD16—944no—
133C2×SD16C2×D4712yes—
134C2×D8C2×D4712yes—
135C2×M16C2×D4711yescharacteristic
136C22×C8—471no—
137C4⋊Q8—472no—
138#124—472no—
139#123—942no—
140C22⋊Q8—942no—
141C4×D4—474no—
142C4×D4—942no—
143#117—471no—
144#117—471no—
145C2×C22⋊C4—942no—
146C4⋊C8—474no—
147#103—472no—
148#103—474no—
149#102—472no—
150C24—21no—
151#41—22no—
152#41—22no—
153C2×Q8—472no—
154C2×Q8—941no—
155C2×Q8—942no—
156C2×Q8—942no—
157C2×Q8C22×D4711yescharacteristic
158C2×D4—21no—
159C2×D4—21no—
160C2×D4—22no—
161C2×D4C22⋊D4714yes—
162C2×D4C22×D4711yescharacteristic
163C2×D4C22×D4712yes—
164C22×C4—21no—
165C22×C4—944no—
166C22×C4—941no—
167C22×C4C22×D4711yescharacteristic
168SD16—24no—
169SD16—948no—
170D8—24no—
171M16—22no—
172C2×C8—472no—
173C2×C8—942no—
174C2×C8C22×D4712yes—
175C4⋊C4—472no—
176C4⋊C4—472no—
177C4⋊C4—944no—
178C22⋊C4—472no—
179C22⋊C4—944no—
180C22⋊C4—944no—
181C22⋊C4—941no—
182C42—472no—
183C42—941no—
184C23—22no—
185C23—24no—
186C23—21no—
187C23—82no—
188C23D4×D4711yescharacteristic
189Q8—21no—
190Q8—21no—
191Q8—942no—
192Q8—942no—
193Q8—1882no—
194D4—24no—
195D4—21no—
196D4—22no—
197D4—21no—
198D4—42no—
199D4C2×C22⋊D4714yes—
200C2×C4—21no—
201C2×C4—42no—
202C2×C4—474no—
203C2×C4—942no—
204C2×C4—942no—
205C2×C4—3764no—
206C2×C4—1882no—
207C2×C4D4×D4711yescharacteristic
208C2×C4#1062535212yes—
209C2×C4C2×C22⋊D4712yes—
210C2×C4C23×D4711yescharacteristic
211C8—22no—
212C8—942no—
213C22—22no—
214C22—24no—
215C22—44no—
216C22—41no—
217C22—42no—
218C22—84no—
219C22#1309399612yes—
220C22C2×D4×D4711yescharacteristic
221C4—41no—
222C4—944no—
223C4—1882no—
224C4—1882no—
225C4#1309399612yes—
226C4C22×C22⋊D4711yescharacteristic
227C4C2×#1062535211yescharacteristic
228C2—22no—
229C2—44no—
230C2—81no—
231C2C2×#1309399611yescharacteristic
232C2#1568993312yes—
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC2×AGL(1,ℤ/8)×C47C2
socleC22×C47C22×D4
hypercenterC2×AGL(1,ℤ/8)D47
hypocenterC47#3042
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. C22×#10625335C2semidirect
2. #15689694C2semidirect
3. #15689598C2semidirect
4. #15689336C2semidirect
5. #15689326C2semidirect
6. #15689151C2semidirect
7. #15689133C2semidirect
8. #15689119C2semidirect
14. #13094022C22semidirect
15. #13094011C22semidirect
23. Dic47⋊C8C22semidirect
24. #13093949C22semidirect
25. #13093948C22semidirect
26. #13093945C22semidirect
126. C47#3042semidirect