Finite Group Databasebeta

← #20252614

Subgroups — #20252614

Order 6016.

994 conjugacy classes of subgroups; only the 157 normal subgroups are shown.

normal subgroups only

This group has 994 conjugacy classes of subgroups — too many to draw. Only its 157 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
1C23×D188C211yesmaximal, characteristic, complemented
2C2×#13094049C212yesmaximal, complemented
3#15689273C214yesmaximal, complemented
4#15689256C214yesmaximal, complemented
5#15689127C212yesmaximal, complemented
6#15689087C211yesmaximal, characteristic, complemented
7C47×#525C211yesmaximal, characteristic, complemented
8C24×D47—21no—
9C22×D188—22no—
10C22×D188—21no—
11C22×D188—28no—
12C22×D188C2214yes—
13C22×D188C2212yes—
14#13094049—28no—
15C2×#10625336C2214yescomplemented
16C2×#10625334C2214yescomplemented
17C2×#10625329C2212yescomplemented
18#13093944C2218yescomplemented
19C22⋊(C47⋊C8)C2214yescomplemented
20C2×#41×C47C2211yescharacteristic, complemented
21C23×C4×C47C2211yescharacteristic
22#123×C47—21no—
23C22⋊Q8×C47C2212yescomplemented
24#121×C47C2212yescomplemented
25#120×C47—21no—
26C4×D4×C47—22no—
27#117×C47C2211yescharacteristic, complemented
28C24×C47D411yescharacteristic
29C23×D47—28no—
30C23×D47—24no—
31C23×D47—22no—
32C23×D47—48no—
33#41×C47—24no—
34C2×Q8×C47C2311yescharacteristic, complemented
35C2×D4×C47—22no—
36C2×D4×C47—21no—
37C2×D4×C47C2311yescharacteristic, complemented
38C22×C4×C47—24no—
39C22×C4×C47—21no—
40C22×C4×C47D412yes—
41C22×C4×C47D411yescharacteristic
42C22×C4×C47C2312yes—
43C22×C4×C47C2311yescharacteristic
44C2×D188—28no—
45C2×D188—216no—
46C2×D188—24no—
47C2×D188—22no—
48C2×D188—24no—
49C2×D188—216no—
50C2×D188D418yescomplemented
51C2×D188C2314yes—
52C4⋊C4×C47—22no—
53C4⋊C4×C47C2312yescomplemented
54C22⋊C4×C47—21no—
55C22⋊C4×C47—22no—
56C22⋊C4×C47—22no—
57C42×C47—21no—
58#10625336—28no—
59#10625334—28no—
60#10625329—24no—
61C2×C47⋊C8C2314yescomplemented
62C23×C47—22no—
63C23×C47—24no—
64C23×C47—21no—
65C23×C47C2×D411yescharacteristic
66C23×C47C2×D412yes—
67C22×D47—216no—
68C22×D47—28no—
69C22×D47—24no—
70C22×D47—432no—
71C22×D47—48no—
72C22×D47—48no—
73C22×D47—48no—
74Q8×C47—22no—
75D4×C47—22no—
76D4×C47—42no—
77D4×C47—44no—
78C2×C4×C47—22no—
79C2×C4×C47—24no—
80C2×C4×C47—24no—
81C2×C4×C47—22no—
82C2×C4×C47—21no—
83C2×C4×C47—42no—
84C2×C4×C47C2×D414yes—
85C2×C4×C47C2×D412yes—
86C2×C4×C47C2×D411yescharacteristic
87C2×C4×C47C2411yescharacteristic
88D188—216no—
89D188—28no—
90D188—24no—
91D188C2×D418yes—
92C47⋊C8—24no—
93C22×C47—28no—
94C22×C47—22no—
95C22×C47—22no—
96C22×C47—22no—
97C22×C47—41no—
98C22×C47—42no—
99C22×C47#12012yes—
100C22×C47AGL(1,ℤ/8)14yescomplemented
101C22×C47C22×D411yescharacteristic
102C2×D47—28no—
103C2×D47—416no—
104C2×D47—432no—
105C2×D47—48no—
106C4×C47—22no—
107C4×C47—41no—
108C4×C47—42no—
109C4×C47#12012yes—
110C4×C47C22×D412yes—
111#3003—471nomaximal, Sylow
112C2×C47—22no—
113C2×C47—24no—
114C2×C47—81no—
115C2×C47C2×#12011yescharacteristic
116C2×C47C2×AGL(1,ℤ/8)12yes—
117D47—48no—
118C23×D4—471no—
119C2×AGL(1,ℤ/8)—472no—
120#525D4711yescharacteristic, complemented
121#450—474no—
122#447—474no—
123#418—472no—
124#407—471no—
125C47#300311yescharacteristic, complemented, Sylow
126C25—941no—
127C2×#41C2×D4711yescharacteristic, complemented
128C22×D4—472no—
129C22×D4—474no—
130C22×D4—948no—
131C22×D4—942no—
132C22×D4—941no—
133C23×C4C2×D4711yescharacteristic
134AGL(1,ℤ/8)—948no—
135C2×SD16—474no—
136C2×D8—474no—
137C2×M16—472no—
138#123—21no—
139C22⋊Q8C2×D4712yescomplemented
140#121C2×D4712yescomplemented
141#120—21no—
142C4×D4—22no—
143#117C2×D4711yescharacteristic, complemented
144#102—478no—
145C22⋊C8—474no—
146C24—948no—
147C24—944no—
148C24—942no—
149C24—1888no—
150C24C22⋊D4711yescharacteristic
151#41—24no—
152C2×Q8C22×D4711yescharacteristic, complemented
153C2×D4—22no—
154C2×D4—21no—
155C2×D4—478no—
156C2×D4—474no—
157C2×D4—9416no—
158C2×D4—948no—
159C2×D4—9416no—
160C2×D4—944no—
161C2×D4—944no—
162C2×D4—942no—
163C2×D4C22×D4711yescharacteristic, complemented
164C22×C4—24no—
165C22×C4—21no—
166C22×C4C22⋊D4712yes—
167C22×C4C22⋊D4711yescharacteristic
168C22×C4C22×D4712yes—
169C22×C4C22×D4711yescharacteristic
170SD16—948no—
171D8—948no—
172M16—944no—
173C2×C8—474no—
174C4⋊C4—22no—
175C4⋊C4C22×D4712yescomplemented
176C22⋊C4—21no—
177C22⋊C4—22no—
178C22⋊C4—22no—
179C42—21no—
180C23—22no—
181C23—24no—
182C23—21no—
183C23—9416no—
184C23—948no—
185C23—944no—
186C23—18832no—
187C23—1888no—
188C23—1888no—
189C23—1888no—
190C23C2×C22⋊D4711yescharacteristic
191C23C2×C22⋊D4712yes—
192Q8—22no—
193D4—22no—
194D4—42no—
195D4—44no—
196D4—478no—
197D4—9416no—
198D4—948no—
199D4—944no—
200C2×C4—22no—
201C2×C4—24no—
202C2×C4—24no—
203C2×C4—22no—
204C2×C4—21no—
205C2×C4—42no—
206C2×C4D4×D4714yes—
207C2×C4C2×C22⋊D4712yes—
208C2×C4C2×C22⋊D4711yescharacteristic
209C2×C4C23×D4711yescharacteristic
210C8—944no—
211C22—28no—
212C22—22no—
213C22—22no—
214C22—22no—
215C22—41no—
216C22—42no—
217C22—948no—
218C22—18816no—
219C22—18832no—
220C22—1888no—
221C22#1309399212yes—
222C22#1309404914yescomplemented
223C22C22×C22⋊D4711yescharacteristic
224C4—22no—
225C4—41no—
226C4—42no—
227C4#1309399212yes—
228C4C2×D4×D4712yes—
229C2—22no—
230C2—24no—
231C2—81no—
232C2—1888no—
233C2C2×#1309399211yescharacteristic
234C2C2×#1309404912yes—
subgroupG/H
centerC22C22×C22⋊D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#525C2
socleC22×C47C22×D4
hypercenter#525D47
hypocenterC47#3003
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C23×C4 ◁ #525

Complements

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

NH ≅ G/Ntype
1. C23×D188C2semidirect
2. C2×#13094049C2semidirect
3. #15689273C2semidirect
4. #15689256C2semidirect
5. #15689127C2semidirect
6. #15689087C2semidirect
7. C47×#525C2semidirect
15. C2×#10625336C22semidirect
16. C2×#10625334C22semidirect
17. C2×#10625329C22semidirect
18. #13093944C22semidirect
19. C22⋊(C47⋊C8)C22semidirect
20. C2×#41×C47C22semidirect
23. C22⋊Q8×C47C22semidirect
24. #121×C47C22semidirect
27. #117×C47C22semidirect
34. C2×Q8×C47C23semidirect
37. C2×D4×C47C23semidirect
50. C2×D188D4semidirect
53. C4⋊C4×C47C23semidirect
61. C2×C47⋊C8C23semidirect
100. C22×C47AGL(1,ℤ/8)semidirect
120. #525D47semidirect
125. C47#3003semidirect
127. C2×#41C2×D47semidirect
139. C22⋊Q8C2×D47semidirect
140. #121C2×D47semidirect
143. #117C2×D47semidirect
152. C2×Q8C22×D47semidirect
163. C2×D4C22×D47semidirect
175. C4⋊C4C22×D47semidirect
222. C22#13094049semidirect