Finite Group Databasebeta

← #19145582

Subgroups — #19145582

Order 5504.

444 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 444 conjugacy classes of subgroups — too many to draw. Only its 121 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
1#14583449C211yesmaximal, characteristic, complemented
2#14583289C212yesmaximal, complemented
3#14583258C212yesmaximal, complemented
4#14583111C214yesmaximal, complemented
5#14583038C212yesmaximal, complemented
6#14583033C212yesmaximal, complemented
7#14582956C211yesmaximal, characteristic, complemented
8C2×#124×C43C211yesmaximal, characteristic, complemented
9C2×#10621898—21no—
10C2×#10621884C2214yescomplemented
11C2×#10621882C2214yes—
12#13063325C2211yescharacteristic, complemented
13#13063322C2211yescharacteristic, complemented
14#13063313—21no—
15#13063299—21no—
16#13063299C2212yes—
17C4×D172—21no—
18C4×D172C2212yescomplemented
19C4⋊(C43⋊C8)C2212yescomplemented
20#13063249C2214yescomplemented
21#13063246C2214yes—
22C22⋊(C43⋊C8)C2212yes—
23#13063236C2212yescomplemented
24C22×Q8×C43C2211yescharacteristic
25C22×D4×C43C2211yescharacteristic
26#124×C43—21no—
27#124×C43—21no—
28#124×C43C2212yes—
29#124×C43C2212yes—
30C2×C22⋊C4×C43—21no—
31C2×C22⋊C4×C43—21no—
32C2×C42×C43C2211yescharacteristic
33C24×C43—21no—
34C2×Q8×C43—21no—
35C2×Q8×C43—42no—
36C2×Q8×C43C2312yes—
37C2×D4×C43—21no—
38C2×D4×C43—42no—
39C2×D4×C43C2312yes—
40C22×C4×C43—21no—
41C22×C4×C43D411yescharacteristic
42C22×C4×C43D411yescharacteristic
43C22×C4×C43C2311yescharacteristic
44C2×C22⋊D43—22no—
45#10621898—44no—
46C2×D172—21no—
47C2×D172—21no—
48C2×D172C2312yes—
49C2×C4×D43—22no—
50C2×Dic86—21no—
51C22⋊C4×C43—22no—
52C22⋊C4×C43—22no—
53C22⋊C4×C43—22no—
54C22⋊C4×C43—22no—
55C42×C43D411yescharacteristic
56C42×C43D411yescharacteristic
57C42×C43C2311yescharacteristic
58C42×C43C2311yescharacteristic
59#10621884—44no—
60#10621882—44no—
61(C2×D43)⋊C4—22no—
62(C2×D43)⋊C4—22no—
63C4⋊Dic43—21no—
64C4⋊Dic43C2312yes—
65C2×C43⋊C8C2314yes—
66C23×C43—22no—
67C23×C43—42no—
68C23×C43—42no—
69C23×C43—42no—
70C23×C43C2×D411yescharacteristic
71C22×D43—22no—
72Q8×C43—24no—
73Q8×C43—42no—
74D4×C43—24no—
75D4×C43—42no—
76C2×C4×C43—22no—
77C2×C4×C43—22no—
78C2×C4×C43—22no—
79C2×C4×C43—41no—
80C2×C4×C43—42no—
81C2×C4×C43C2×D411yescharacteristic
82C2×C4×C43C2×D411yescharacteristic
83C2×C4×C43C2×D411yescharacteristic
84C2×C4×C43C2×D411yescharacteristic
85C2×C4×C43C2×D411yescharacteristic
86C2×C4×C43C2411yescharacteristic
87C22⋊D43—44no—
88C2×Dic43—22no—
89D172—24no—
90D172—42no—
91D172—42no—
92C4×D43—44no—
93Dic86—42no—
94C43⋊C8—24no—
95C22×C43—21no—
96C22×C43—21no—
97C22×C43—42no—
98C22×C43—42no—
99C22×C43—42no—
100C22×C43—84no—
101C22×C43AGL(1,ℤ/8)12yes—
102C22×C43C22×D411yescharacteristic
103C2×D43—42no—
104C2×D43—42no—
105C2×D43—42no—
106C4×C43—21no—
107C4×C43—21no—
108C4×C43—21no—
109C4×C43—21no—
110C4×C43—21no—
111C4×C43—42no—
112C4×C43H(5,𝔽2)12yes—
113Dic43—42no—
114#3213—431nomaximal, Sylow
115C2×C43—22no—
116C2×C43—82no—
117C2×C43#53511yescharacteristic
118C2×C43C2×AGL(1,ℤ/8)11yescharacteristic
119C2×C43#57511yescharacteristic
120D43—82no—
121#532—431no—
122C2×#124D4311yescharacteristic, complemented
123#496—432no—
124#489—432no—
125#463—434no—
126#448—432no—
127#447—432no—
128#432—431no—
129C43#321311yescharacteristic, complemented, Sylow
130C2×#41—861no—
131C22×Q8C2×D4311yescharacteristic
132C22×D4C2×D4311yescharacteristic
133C2×SD16—434no—
134C2×D8—434no—
135C4⋊Q8—431no—
136#127—431no—
137#124—21no—
138#124—21no—
139#124—861no—
140#124C2×D4312yes—
141#124C2×D4312yes—
142#121—432no—
143#121—861no—
144C4×D4—432no—
145C4×D4—861no—
146C2×C22⋊C4—21no—
147C2×C22⋊C4—21no—
148C2×C42C2×D4311yescharacteristic
149C4⋊C8—432no—
150#103—434no—
151#102—434no—
152C22⋊C8—432no—
153#97—432no—
154C24—21no—
155#41—1724no—
156C2×Q8—21no—
157C2×Q8—42no—
158C2×Q8—861no—
159C2×Q8C22×D4312yes—
160C2×D4—21no—
161C2×D4—42no—
162C2×D4—432no—
163C2×D4—862no—
164C2×D4—861no—
165C2×D4—861no—
166C2×D4C22×D4312yes—
167C22×C4—21no—
168C22×C4—862no—
169C22×C4C22⋊D4311yescharacteristic
170C22×C4C22⋊D4311yescharacteristic
171C22×C4C22×D4311yescharacteristic
172SD16—1724no—
173D8—1724no—
174C2×C8—434no—
175C4⋊C4—432no—
176C4⋊C4—861no—
177C22⋊C4—22no—
178C22⋊C4—22no—
179C22⋊C4—22no—
180C22⋊C4—22no—
181C22⋊C4—862no—
182C22⋊C4—862no—
183C42C22⋊D4311yescharacteristic
184C42C22⋊D4311yescharacteristic
185C42C22×D4311yescharacteristic
186C42C22×D4311yescharacteristic
187C23—22no—
188C23—42no—
189C23—42no—
190C23—42no—
191C23—862no—
192C23C2×C22⋊D4311yescharacteristic
193Q8—24no—
194Q8—42no—
195Q8—1722no—
196D4—24no—
197D4—42no—
198D4—864no—
199D4—1722no—
200D4—1722no—
201D4—1724no—
202C2×C4—22no—
203C2×C4—22no—
204C2×C4—22no—
205C2×C4—41no—
206C2×C4—42no—
207C2×C4—862no—
208C2×C4—1724no—
209C2×C4C2×C22⋊D4311yescharacteristic
210C2×C4C2×C22⋊D4311yescharacteristic
211C2×C4C2×C22⋊D4311yescharacteristic
212C2×C4C2×C22⋊D4311yescharacteristic
213C2×C4C2×C22⋊D4311yescharacteristic
214C2×C4C23×D4311yescharacteristic
215C8—864no—
216C22—21no—
217C22—21no—
218C22—42no—
219C22—42no—
220C22—42no—
221C22—84no—
222C22—1722no—
223C22—1722no—
224C22—1722no—
225C22#1306335012yes—
226C22C22×C22⋊D4311yescharacteristic
227C4—21no—
228C4—21no—
229C4—21no—
230C4—21no—
231C4—21no—
232C4—42no—
233C4—1722no—
234C4#1306337012yes—
235C2—22no—
236C2—82no—
237C2—3442no—
238C2#1458346611yescharacteristic
239C2C2×#1306335011yescharacteristic
240C2#1458369711yescharacteristic
subgroupG/H
centerC22C22×C22⋊D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC2×#124×C43C2
socleC22×C43C22×D4
hypercenterC2×#124D43
hypocenterC43#3213
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#124

Complements

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

NH ≅ G/Ntype
1. #14583449C2semidirect
2. #14583289C2semidirect
3. #14583258C2semidirect
4. #14583111C2semidirect
5. #14583038C2semidirect
6. #14583033C2semidirect
7. #14582956C2semidirect
8. C2×#124×C43C2semidirect
10. C2×#10621884C22semidirect
12. #13063325C22semidirect
13. #13063322C22semidirect
18. C4×D172C22semidirect
19. C4⋊(C43⋊C8)C22semidirect
20. #13063249C22semidirect
23. #13063236C22semidirect
122. C2×#124D43semidirect
129. C43#3213semidirect