Finite Group Databasebeta

← #20251864

Subgroups — #20251864

Order 6016.

756 conjugacy classes of subgroups; only the 209 normal subgroups are shown.

normal subgroups only

This group has 756 conjugacy classes of subgroups — too many to draw. Only its 209 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×#13094069C211yesmaximal, characteristic
2#15689889C212yesmaximal, complemented
3#15689105C212yesmaximal, complemented
4#15689104C214yesmaximal, complemented
5C2×#13093941C211yesmaximal, characteristic, complemented
6#100×D47C214yesmaximal, complemented
7C2×#100×C47C211yesmaximal, characteristic, complemented
8#13094069—24no—
9#13094069—24no—
10C2×#10625350C2211yescharacteristic
11C2×#10625350C2211yescharacteristic
12C2×#10625352C412yes—
13C2×#10625352C2212yes—
14C22×C22⋊D47C414yes—
15C2×D4×D47C412yes—
16C2×D4×D47C2212yes—
17#13094032—24no—
18#13094030—24no—
19C2×#10625329C2212yescomplemented
20M16×D47C2218yescomplemented
21#13093942C2214yescomplemented
22#13093941C2214yescomplemented
23#13093940C2214yescomplemented
24C22×D4×C47C2211yescharacteristic
25C2×M16×C47C2212yescomplemented
26#100×C47C2214yescomplemented
27C24×C47C2×C412yes—
28C23×D47C2×C414yes—
29C2×D4×C47—22no—
30C2×D4×C47—22no—
31C2×D4×C47C2×C412yes—
32C2×D4×C47C2312yes—
33C22×C4×C47C2311yescharacteristic
34C2×C22⋊D47—28no—
35C2×C22⋊D47—28no—
36C2×C22⋊D47C2×C414yes—
37C2×C22⋊D47C2×C414yes—
38C2×C22⋊D47C2×C412yes—
39C2×C22⋊D47C2×C412yes—
40C22×Dic47C2×C414yes—
41#10625352—28no—
42#10625352—28no—
43D4×D47—28no—
44D4×D47—28no—
45#10625350—22no—
46#10625350—22no—
47#10625350D414yes—
48#10625350D414yes—
49C2×D188C2×C411yescharacteristic
50C2×D188C2311yescharacteristic
51C2×C4×D47C2×C412yes—
52C2×C4×D47C2312yes—
53C2×Dic94C2×C411yescharacteristic
54C2×Dic94C2311yescharacteristic
55M16×C47—22no—
56M16×C47C2314yes—
57C2×C8×C47—22no—
58#10625329—22no—
59#10625329C2314yes—
60C2×C47⋊C8—22no—
61#10625324—28no—
62C8×D47—28no—
63C23×C47—22no—
64C23×C47—22no—
65C23×C47—82no—
66C23×C47C22×C414yes—
67C23×C47C22×C411yescharacteristic
68C22×D47—28no—
69C22×D47—84no—
70C22×D47C22×C412yes—
71C22×D47C22×C412yes—
72D4×C47—24no—
73D4×C47—24no—
74C2×C4×C47C22×C411yescharacteristic
75C2×C4×C47C2×D412yes—
76C2×C4×C47C2×D412yes—
77C2×C4×C47C2411yescharacteristic
78C22⋊D47—22no—
79C22⋊D47—22no—
80C22⋊D47—28no—
81C22⋊D47—28no—
82C22⋊D47C22⋊C414yes—
83C22⋊D47C22⋊C414yes—
84C2×Dic47—28no—
85C2×Dic47C22×C412yes—
86C2×Dic47C22×C412yes—
87D188—22no—
88D188C22⋊C414yes—
89C4×D47—24no—
90C4×D47C2×D418yes—
91Dic94—22no—
92Dic94C22⋊C414yes—
93C8×C47—24no—
94C47⋊C8—24no—
95C22×C47—24no—
96C22×C47—41no—
97C22×C47—44no—
98C22×C47—82no—
99C22×C47—82no—
100C22×C47C2×C22⋊C411yescharacteristic
101C22×C47C2×C22⋊C411yescharacteristic
102C22×C47C23×C411yescharacteristic
103C2×D47—22no—
104C2×D47—42no—
105C2×D47—42no—
106C2×D47—88no—
107C2×D47C2×C22⋊C414yes—
108C4×C47C2×C22⋊C412yes—
109C4×C47C22×D412yes—
110Dic47—22no—
111Dic47C2×C22⋊C414yes—
112#2888—471nomaximal, Sylow
113C2×C47—21no—
114C2×C47—21no—
115C2×C47—21no—
116C2×C47—44no—
117C2×C47C22×C22⋊C411yescharacteristic
118D47—24no—
119D47—42no—
120C2×H(5,𝔽2)—471no—
121#568—472no—
122#413—472no—
123#413—474no—
124C2×#100—471no—
125C2×#100—474no—
126C2×#100D4711yescharacteristic, complemented
127C47#288811yescharacteristic, complemented, Sylow
128H(5,𝔽2)—944no—
129H(5,𝔽2)—944no—
130C2×#41—472no—
131C2×#41—472no—
132C2×#41—471no—
133C2×#41—471no—
134C22×D4—474no—
135C22×D4—472no—
136C22×D4—472no—
137C22×D4C2×D4711yescharacteristic
138#131—944no—
139#131—944no—
140C2×M16—472no—
141C2×M16—478no—
142C2×M16C2×D4712yescomplemented
143#101—474no—
144#100—474no—
145#100—474no—
146#100C2×D4714yescomplemented
147C24—474no—
148C24C4×D4712yes—
149#41—474no—
150#41—474no—
151#41—948no—
152#41—948no—
153#41—942no—
154#41—942no—
155C2×Q8—471no—
156C2×Q8—471no—
157C2×D4—22no—
158C2×D4—22no—
159C2×D4—472no—
160C2×D4—474no—
161C2×D4—474no—
162C2×D4—472no—
163C2×D4—471no—
164C2×D4—471no—
165C2×D4—948no—
166C2×D4—948no—
167C2×D4—948no—
168C2×D4—948no—
169C2×D4C4×D4712yes—
170C2×D4C22×D4712yes—
171C22×C4—472no—
172C22×C4—474no—
173C22×C4—472no—
174C22×C4C22×D4711yescharacteristic
175M16—22no—
176M16—474no—
177M16—948no—
178M16—942no—
179M16C22×D4714yes—
180C2×C8—22no—
181C2×C8—948no—
182C2×C8—942no—
183C23—22no—
184C23—22no—
185C23—82no—
186C23—472no—
187C23—472no—
188C23—948no—
189C23—3764no—
190C23C2×C4×D4714yes—
191C23C2×C4×D4711yescharacteristic
192Q8—474no—
193Q8—942no—
194D4—24no—
195D4—24no—
196D4—474no—
197D4—474no—
198D4—474no—
199D4—948no—
200D4—948no—
201D4—942no—
202D4—942no—
203D4—942no—
204C2×C4—472no—
205C2×C4—478no—
206C2×C4—472no—
207C2×C4—948no—
208C2×C4—944no—
209C2×C4C2×C4×D4711yescharacteristic
210C2×C4D4×D4712yes—
211C2×C4D4×D4712yes—
212C2×C4C23×D4711yescharacteristic
213C8—24no—
214C8—944no—
215C22—24no—
216C22—41no—
217C22—44no—
218C22—82no—
219C22—82no—
220C22—474no—
221C22—942no—
222C22—3768no—
223C22—1882no—
224C22—1882no—
225C22C22⋊C4×D4711yescharacteristic
226C22C22⋊C4×D4711yescharacteristic
227C22C22×C4×D4711yescharacteristic
228C4—474no—
229C4—942no—
230C4C22⋊C4×D4712yes—
231C4C2×D4×D4712yes—
232C2—21no—
233C2—21no—
234C2—21no—
235C2—44no—
236C2—944no—
237C2—1882no—
238C2C2×C22⋊C4×D4711yescharacteristic
subgroupG/H
centerC2C2×C22⋊C4×D47
commutatorC22×C47C23×C4
FrattiniC2×C4C23×D47
FittingC2×#100×C47C2
socleC2×C47C22×C22⋊C4
hypercenterC2×#100D47
hypocenterC47#2888
LCSG ▷ C22×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×#100

Complements

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

NH ≅ G/Ntype
2. #15689889C2semidirect
3. #15689105C2semidirect
4. #15689104C2semidirect
5. C2×#13093941C2semidirect
6. #100×D47C2semidirect
7. C2×#100×C47C2semidirect
19. C2×#10625329C22semidirect
20. M16×D47C22semidirect
21. #13093942C22semidirect
22. #13093941C22semidirect
23. #13093940C22semidirect
25. C2×M16×C47C22semidirect
26. #100×C47C22semidirect
126. C2×#100D47semidirect
127. C47#2888semidirect
142. C2×M16C2×D47semidirect
146. #100C2×D47semidirect