Finite Group Databasebeta

← #20254208

Subgroups — #20254208

Order 6016.

410 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 410 conjugacy classes of subgroups — too many to draw. Only its 113 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⋊Q8×D47C212yesmaximal
2#15689455C212yesmaximal, complemented
3#15689452C212yesmaximal, complemented
4#15689381C211yesmaximal, characteristic, complemented
5#15689379C212yesmaximal, complemented
6#15689280C212yesmaximal, complemented
7#15689277C212yesmaximal, complemented
8#15689086C211yesmaximal, characteristic
9C47×#470C211yesmaximal, characteristic, complemented
10C2×Q8×D47C2212yes—
11C22×C4×D47C2211yescharacteristic
12C2×Dic188C2211yescharacteristic, complemented
13C2×#10625337C2212yescomplemented
14C2×#10625329C2211yescharacteristic
15#13094004C2212yes—
16#13094003C2212yes—
17#13094002—22no—
18#13094001—22no—
19#13094000C2212yes—
20C4⋊C4×D47—22no—
21C4⋊C4×D47C2212yes—
22C22⋊C4×D47—22no—
23#13093956C2211yescharacteristic, complemented
24#13093955C2212yescomplemented
25#13093949C2212yescomplemented
26#13093948C2212yescomplemented
27#13093947C2212yescomplemented
28(C2×D47)⋊C8C2212yes—
29(C2×D47)⋊C8C2212yes—
30C2×Q16×C47C2211yescharacteristic, complemented
31C2×M16×C47C2211yescharacteristic
32C22⋊Q8×C47C2212yes—
33#106×C47C2211yescharacteristic, complemented
34#103×C47C2212yescomplemented
35C23×D47D411yescharacteristic
36C2×Q8×C47C2312yes—
37C22×C4×C47C2311yescharacteristic
38C22×Dic47D411yescharacteristic
39Q8×D47—42no—
40Q8×D47—42no—
41C2×C4×D47—22no—
42C2×C4×D47—22no—
43C2×C4×D47—41no—
44C2×C4×D47—41no—
45C2×C4×D47D412yes—
46C2×C4×D47C2312yes—
47C2×Dic94—22no—
48C2×Dic94C2312yes—
49Q16×C47—41no—
50M16×C47—41no—
51C2×C8×C47C2311yescharacteristic
52C2×C8×C47C2311yescharacteristic
53C4⋊C4×C47—22no—
54C4⋊C4×C47C2312yes—
55C22⋊C4×C47—22no—
56C22⋊Dic47—22no—
57#10625337—42no—
58(C2×D47)⋊C4—22no—
59(C2×D47)⋊C4—22no—
60C4⋊Dic47—22no—
61C4⋊Dic47C2312yes—
62Dic47⋊C4—22no—
63Dic47⋊C4—22no—
64Dic47⋊C4—22no—
65#10625329—41no—
66C2×C47⋊C8C2312yes—
67Dic188—41no—
68C23×C47C2×D411yescharacteristic
69C22×D47—24no—
70C22×D47—41no—
71C22×D47C2×D412yes—
72Q8×C47—22no—
73Q8×C47—22no—
74C2×C4×C47—21no—
75C2×C4×C47—21no—
76C2×C4×C47—22no—
77C2×C4×C47—22no—
78C2×C4×C47C2×D411yescharacteristic
79C2×C4×C47C2411yescharacteristic
80C2×Dic47—22no—
81C2×Dic47—22no—
82C2×Dic47—41no—
83C2×Dic47C2×D412yes—
84C4×D47—22no—
85C4×D47—22no—
86C4×D47—42no—
87C4×D47—44no—
88C4×D47—44no—
89Dic94—22no—
90Dic94—22no—
91Dic94—44no—
92C8×C47—21no—
93C8×C47—21no—
94C47⋊C8—22no—
95C22×C47—21no—
96C22×C47—22no—
97C22×C47C22×D411yescharacteristic
98C2×D47—22no—
99C2×D47—22no—
100C2×D47—44no—
101C2×D47#13714yes—
102C4×C47—21no—
103C4×C47—42no—
104C4×C47—42no—
105C4×C47H(5,𝔽2)11yescharacteristic
106C4×C47H(5,𝔽2)11yescharacteristic
107Dic47—22no—
108Dic47—42no—
109Dic47—42no—
110#3195—471nomaximal, Sylow
111C2×C47—41no—
112C2×C47#53411yescharacteristic
113C2×C47C2×#13712yes—
114D47—24no—
115C2×C22⋊Q8—472no—
116#483—472no—
117#483—472no—
118#470—471no—
119#470—472no—
120#470D4711yescharacteristic, complemented
121#451—472no—
122#451—472no—
123#407—471no—
124C47#319511yescharacteristic, complemented, Sylow
125C22×Q8—472no—
126C23×C4—471no—
127C2×Q16—472no—
128C2×Q16—471no—
129C2×Q16C2×D4711yescharacteristic, complemented
130C2×M16—471no—
131C2×M16C2×D4711yescharacteristic
132C22⋊Q8—472no—
133C22⋊Q8—472no—
134C22⋊Q8—472no—
135C22⋊Q8—942no—
136C22⋊Q8—942no—
137C22⋊Q8C2×D4712yes—
138C2×C4⋊C4—472no—
139C2×C4⋊C4—942no—
140C2×C22⋊C4—942no—
141#106—471no—
142#106—472no—
143#106C2×D4711yescharacteristic, complemented
144#103—472no—
145#103—472no—
146#103—472no—
147#103C2×D4712yescomplemented
148C22⋊C8—472no—
149C22⋊C8—472no—
150C24—471no—
151C2×Q8—472no—
152C2×Q8—942no—
153C2×Q8—1882no—
154C2×Q8—1882no—
155C2×Q8C22×D4712yes—
156C22×C4—471no—
157C22×C4—472no—
158C22×C4—472no—
159C22×C4—942no—
160C22×C4—942no—
161C22×C4—1881no—
162C22×C4—1881no—
163C22×C4C22×D4711yescharacteristic
164Q16—41no—
165Q16—1881no—
166Q16—1882no—
167M16—41no—
168M16—1881no—
169C2×C8—472no—
170C2×C8C22×D4711yescharacteristic
171C2×C8C22×D4711yescharacteristic
172C4⋊C4—22no—
173C4⋊C4—472no—
174C4⋊C4—942no—
175C4⋊C4—942no—
176C4⋊C4—942no—
177C4⋊C4—942no—
178C4⋊C4C22×D4712yes—
179C22⋊C4—22no—
180C22⋊C4—942no—
181C22⋊C4—942no—
182C22⋊C4—942no—
183C23—472no—
184C23—944no—
185C23—1881no—
186C23D4×D4711yescharacteristic
187Q8—22no—
188Q8—22no—
189Q8—942no—
190Q8—942no—
191Q8—1884no—
192C2×C4—21no—
193C2×C4—21no—
194C2×C4—22no—
195C2×C4—22no—
196C2×C4—472no—
197C2×C4—942no—
198C2×C4—942no—
199C2×C4—942no—
200C2×C4—942no—
201C2×C4—1882no—
202C2×C4—1884no—
203C2×C4—1884no—
204C2×C4—1881no—
205C2×C4D4×D4711yescharacteristic
206C2×C4C23×D4711yescharacteristic
207C8—21no—
208C8—21no—
209C8—942no—
210C22—22no—
211C22—21no—
212C22—474no—
213C22—942no—
214C22—942no—
215C22—1884no—
216C22C2×D4×D4711yescharacteristic
217C4—21no—
218C4—42no—
219C4—42no—
220C4—942no—
221C4—1882no—
222C4—1882no—
223C4#1309406911yescharacteristic
224C4#1309407011yescharacteristic
225C2—41no—
226C2—944no—
227C2#1568968111yescharacteristic
228C2#137×D4712yes—
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#470C2
socleC22×C47C22×D4
hypercenter#470D47
hypocenterC47#3195
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #470

Complements

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

NH ≅ G/Ntype
2. #15689455C2semidirect
3. #15689452C2semidirect
4. #15689381C2semidirect
5. #15689379C2semidirect
6. #15689280C2semidirect
7. #15689277C2semidirect
9. C47×#470C2semidirect
12. C2×Dic188C22semidirect
13. C2×#10625337C22semidirect
23. #13093956C22semidirect
24. #13093955C22semidirect
25. #13093949C22semidirect
26. #13093948C22semidirect
27. #13093947C22semidirect
30. C2×Q16×C47C22semidirect
33. #106×C47C22semidirect
34. #103×C47C22semidirect
120. #470D47semidirect
124. C47#3195semidirect
129. C2×Q16C2×D47semidirect
143. #106C2×D47semidirect
147. #103C2×D47semidirect