Finite Group Databasebeta

← #19145584

Subgroups — #19145584

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
2C2×#13063313C211yesmaximal, characteristic, complemented
3#14583288C212yesmaximal, complemented
4#14583259C212yesmaximal, complemented
5#14583115C214yesmaximal, complemented
6#14583040C212yesmaximal, complemented
7#14583035C212yesmaximal, complemented
8C43×#432C211yesmaximal, characteristic, complemented
9C2×#10621898—21no—
10C22×Dic86C2211yescharacteristic
11C22×D172C2211yescharacteristic
12C2×#10621873C2214yescomplemented
13C2×D344C2214yes—
14#13063325C2211yescharacteristic, complemented
15#13063322C2211yescharacteristic, complemented
16#13063313—21no—
17#13063313—21no—
18#13063313—21no—
19#13063313C2212yes—
20#13063313C2212yes—
21#13063299—21no—
22#13063299C2212yes—
23C4×D172—21no—
24C4×D172C2212yescomplemented
25C2×(C2×D43)⋊C4—21no—
26C2×(C2×D43)⋊C4—21no—
27#13063250C2214yescomplemented
28#13063247C2214yes—
29C2×C42×C43C2211yescharacteristic
30C4⋊C8×C43C2212yescomplemented
31C22⋊C8×C43C2212yes—
32#97×C43C2212yescomplemented
33C23×D43—21no—
34C22×C4×C43D411yescharacteristic
35C22×C4×C43D411yescharacteristic
36C22×C4×C43C2311yescharacteristic
37C2×C22⋊D43—22no—
38C22×Dic43—21no—
39#10621898—44no—
40C2×D172—21no—
41C2×D172—21no—
42C2×D172—21no—
43C2×D172—42no—
44C2×D172C2312yes—
45C2×D172C2312yes—
46C2×C4×D43—22no—
47C2×Dic86—21no—
48C2×Dic86—21no—
49C2×Dic86—42no—
50C2×Dic86C2312yes—
51C2×C8×C43C2314yes—
52C42×C43D411yescharacteristic
53C42×C43D411yescharacteristic
54C42×C43C2311yescharacteristic
55C42×C43C2311yescharacteristic
56(C2×D43)⋊C4—22no—
57(C2×D43)⋊C4—22no—
58(C2×D43)⋊C4—22no—
59(C2×D43)⋊C4—22no—
60(C2×D43)⋊C4—22no—
61(C2×D43)⋊C4—22no—
62C4⋊Dic43—21no—
63C4⋊Dic43C2312yes—
64D344—44no—
65#10621873—44no—
66C23×C43C2×D411yescharacteristic
67C22×D43—22no—
68C22×D43—22no—
69C22×D43—42no—
70C22×D43—42no—
71C22×D43—42no—
72C2×C4×C43—22no—
73C2×C4×C43—22no—
74C2×C4×C43—41no—
75C2×C4×C43C2×D411yescharacteristic
76C2×C4×C43C2×D411yescharacteristic
77C2×C4×C43C2×D411yescharacteristic
78C2×C4×C43C2×D411yescharacteristic
79C2×C4×C43C2×D411yescharacteristic
80C2×C4×C43C2411yescharacteristic
81C22⋊D43—44no—
82C2×Dic43—22no—
83C2×Dic43—22no—
84C2×Dic43—42no—
85D172—24no—
86D172—24no—
87D172—42no—
88D172—42no—
89D172—42no—
90C4×D43—44no—
91Dic86—24no—
92Dic86—42no—
93Dic86—42no—
94C8×C43—24no—
95C22×C43—21no—
96C22×C43—21no—
97C22×C43AGL(1,ℤ/8)12yes—
98C22×C43C22×D411yescharacteristic
99C2×D43—42no—
100C2×D43—42no—
101C2×D43—42no—
102C2×D43—42no—
103C2×D43—42no—
104C2×D43—42no—
105C2×D43—84no—
106C4×C43—21no—
107C4×C43—21no—
108C4×C43—21no—
109C4×C43—21no—
110C4×C43—21no—
111C4×C43H(5,𝔽2)12yes—
112Dic43—42no—
113Dic43—42no—
114#3213—431nomaximal, Sylow
115C2×C43—22no—
116C2×C43#53511yescharacteristic
117C2×C43C2×AGL(1,ℤ/8)11yescharacteristic
118C2×C43#57511yescharacteristic
119D43—82no—
120D43—82no—
121#532—431no—
122C2×#124—431no—
123#496—432no—
124#489—432no—
125#463—434no—
126#448—432no—
127#447—432no—
128#432D4311yescharacteristic, complemented
129C43#321311yescharacteristic, complemented, Sylow
130C2×#41—861no—
131C22×Q8—431no—
132C22×D4—431no—
133C2×SD16—434no—
134C2×D8—434no—
135C4⋊Q8—431no—
136#127—431no—
137#124—432no—
138#124—432no—
139#124—861no—
140#124—861no—
141#124—861no—
142#121—432no—
143#121—861no—
144C4×D4—432no—
145C4×D4—861no—
146C2×C22⋊C4—861no—
147C2×C22⋊C4—861no—
148C2×C42C2×D4311yescharacteristic
149C4⋊C8C2×D4312yescomplemented
150#103—434no—
151#102—434no—
152C22⋊C8C2×D4312yes—
153#97C2×D4312yescomplemented
154C24—861no—
155#41—1724no—
156C2×Q8—432no—
157C2×Q8—861no—
158C2×Q8—861no—
159C2×Q8—1722no—
160C2×D4—432no—
161C2×D4—432no—
162C2×D4—862no—
163C2×D4—861no—
164C2×D4—861no—
165C2×D4—861no—
166C2×D4—1722no—
167C22×C4—861no—
168C22×C4—862no—
169C22×C4D17211yescharacteristic
170C22×C4D17211yescharacteristic
171C22×C4C22×D4311yescharacteristic
172SD16—1724no—
173D8—1724no—
174C2×C8C22×D4314yes—
175C4⋊C4—432no—
176C4⋊C4—861no—
177C22⋊C4—862no—
178C22⋊C4—862no—
179C22⋊C4—862no—
180C22⋊C4—862no—
181C22⋊C4—862no—
182C22⋊C4—862no—
183C42D17211yescharacteristic
184C42D17211yescharacteristic
185C42C22×D4311yescharacteristic
186C42C22×D4311yescharacteristic
187C23—862no—
188C23—862no—
189C23—1722no—
190C23—1722no—
191C23—1722no—
192C23C2×D17211yescharacteristic
193Q8—864no—
194Q8—1722no—
195Q8—1722no—
196D4—864no—
197D4—864no—
198D4—1722no—
199D4—1722no—
200D4—1722no—
201D4—1724no—
202C2×C4—22no—
203C2×C4—22no—
204C2×C4—41no—
205C2×C4—862no—
206C2×C4—862no—
207C2×C4—1724no—
208C2×C4—1722no—
209C2×C4C2×D17211yescharacteristic
210C2×C4C2×D17211yescharacteristic
211C2×C4C2×D17211yescharacteristic
212C2×C4C2×D17211yescharacteristic
213C2×C4C2×D17211yescharacteristic
214C2×C4C23×D4311yescharacteristic
215C8—24no—
216C22—21no—
217C22—21no—
218C22—3444no—
219C22—1722no—
220C22—1722no—
221C22—1722no—
222C22—1722no—
223C22—1722no—
224C22—1722no—
225C22#1306335312yes—
226C22C22×D17211yescharacteristic
227C4—21no—
228C4—21no—
229C4—21no—
230C4—21no—
231C4—21no—
232C4—1722no—
233C4—1722no—
234C4#1306337112yes—
235C2—22no—
236C2—3442no—
237C2—3442no—
238C2#1458346811yescharacteristic
239C2C2×#1306335311yescharacteristic
240C2#1458369911yescharacteristic
subgroupG/H
centerC22C22×D172
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#432C2
socleC22×C43C22×D4
hypercenter#432D43
hypocenterC43#3213
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #432

Complements

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

NH ≅ G/Ntype
1. #14583449C2semidirect
2. C2×#13063313C2semidirect
3. #14583288C2semidirect
4. #14583259C2semidirect
5. #14583115C2semidirect
6. #14583040C2semidirect
7. #14583035C2semidirect
8. C43×#432C2semidirect
12. C2×#10621873C22semidirect
14. #13063325C22semidirect
15. #13063322C22semidirect
24. C4×D172C22semidirect
27. #13063250C22semidirect
30. C4⋊C8×C43C22semidirect
32. #97×C43C22semidirect
128. #432D43semidirect
129. C43#3213semidirect
149. C4⋊C8C2×D43semidirect
153. #97C2×D43semidirect