Finite Group Databasebeta

← #19145437

Subgroups — #19145437

Order 5504.

418 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 418 conjugacy classes of subgroups — too many to draw. Only its 117 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#14583410C212yesmaximal, complemented
2#14583241C212yesmaximal, complemented
3#14583224C212yesmaximal, complemented
4#14583157C211yesmaximal, characteristic, complemented
5#14583152C211yesmaximal, characteristic, complemented
6#14583145C212yesmaximal, complemented
7#14583063C212yesmaximal, complemented
8#14583046C212yesmaximal, complemented
9C43×#407C211yesmaximal, characteristic, complemented
10C2×#10621898C2212yes—
11C2×Dic172C2211yescharacteristic, complemented
12C2×#10621873C2212yescomplemented
13C2×D344C2211yescharacteristic, complemented
14#13063308—22no—
15#13063304C2212yes—
16#13063304C2212yes—
17#13063299C2212yes—
18#13063299C2212yes—
19#13063294—22no—
20C4×C22⋊D43—22no—
21C4×C22⋊D43—22no—
22#13063284C2212yes—
23#13063259C2212yescomplemented
24#13063257C2211yescharacteristic, complemented
25#13063257C2211yescharacteristic, complemented
26#13063250C2212yescomplemented
27#13063250C2212yescomplemented
28#13063247C2212yescomplemented
29#13063247C2212yescomplemented
30C23×C4×C43C2211yescharacteristic
31C2×M16×C43C2211yescharacteristic
32C2×M16×C43C2211yescharacteristic
33C22⋊C8×C43C2212yes—
34C22⋊C8×C43C2212yes—
35C24×C43D411yescharacteristic
36C22×C4×C43—41no—
37C22×C4×C43—41no—
38C22×C4×C43D411yescharacteristic
39C22×C4×C43D412yes—
40C22×C4×C43C2312yes—
41C22×C4×C43C2311yescharacteristic
42C2×C22⋊D43—22no—
43C2×C22⋊D43—22no—
44C2×C22⋊D43—22no—
45#10621898—42no—
46#10621898—42no—
47C2×D172C2312yes—
48C2×C4×D43—22no—
49C2×Dic86C2312yes—
50M16×C43—41no—
51M16×C43—41no—
52C2×C8×C43C2311yescharacteristic
53C2×C8×C43C2312yes—
54C2×C8×C43C2311yescharacteristic
55C22⋊Dic43—22no—
56C22⋊Dic43—22no—
57C22⋊Dic43—22no—
58(C2×D43)⋊C4—22no—
59(C2×D43)⋊C4—22no—
60C4⋊Dic43C2312yes—
61C4⋊Dic43C2312yes—
62Dic43⋊C4—22no—
63Dic43⋊C4—22no—
64C4×Dic43—22no—
65Dic172—41no—
66D344—41no—
67#10621873—42no—
68C23×C43—41no—
69C23×C43—42no—
70C23×C43C2×D412yes—
71C23×C43C2×D411yescharacteristic
72C22×D43—22no—
73C2×C4×C43—21no—
74C2×C4×C43—21no—
75C2×C4×C43—22no—
76C2×C4×C43—22no—
77C2×C4×C43—41no—
78C2×C4×C43—42no—
79C2×C4×C43C2×D412yes—
80C2×C4×C43C2×D411yescharacteristic
81C2×C4×C43C2411yescharacteristic
82C22⋊D43—44no—
83C22⋊D43—44no—
84C22⋊D43—44no—
85C2×Dic43—22no—
86C2×Dic43—22no—
87C2×Dic43—22no—
88D172—22no—
89D172—22no—
90C4×D43—44no—
91Dic86—22no—
92Dic86—22no—
93C8×C43—22no—
94C8×C43—21no—
95C8×C43—21no—
96C22×C43—22no—
97C22×C43—21no—
98C22×C43—22no—
99C22×C43—22no—
100C22×C43—22no—
101C22×C43—44no—
102C22×C43C22×D411yescharacteristic
103C2×D43—42no—
104C2×D43—42no—
105C2×D43—42no—
106C4×C43—22no—
107C4×C43—21no—
108C4×C43H(5,𝔽2)11yescharacteristic
109C4×C43H(5,𝔽2)11yescharacteristic
110Dic43—42no—
111Dic43—42no—
112Dic43—42no—
113#3197—431nomaximal, Sylow
114C2×C43—42no—
115C2×C43—41no—
116C2×C43#53411yescharacteristic
117C2×C43#57512yes—
118D43—82no—
119#525—432no—
120#485—432no—
121#482—432no—
122#470—431no—
123#469—431no—
124#468—432no—
125#452—432no—
126#449—432no—
127#407D4311yescharacteristic, complemented
128C43#319711yescharacteristic, complemented, Sylow
129C2×#41—432no—
130C23×C4C2×D4311yescharacteristic
131C2×Q16—431no—
132C2×SD16—432no—
133C2×D8—431no—
134C2×M16C2×D4311yescharacteristic
135C2×M16C2×D4311yescharacteristic
136#123—862no—
137C22⋊Q8—432no—
138C22⋊Q8—432no—
139#121—432no—
140#121—432no—
141#120—862no—
142C4×D4—862no—
143C4×D4—862no—
144#117—432no—
145#107—432no—
146#106—431no—
147#106—431no—
148#103—432no—
149#103—432no—
150#102—432no—
151#102—432no—
152C22⋊C8C2×D4312yes—
153C22⋊C8C2×D4312yes—
154C24D17211yescharacteristic
155#41—1722no—
156#41—1722no—
157C2×Q8—432no—
158C2×D4—432no—
159C2×D4—862no—
160C2×D4—862no—
161C2×D4—862no—
162C22×C4—41no—
163C22×C4—41no—
164C22×C4—862no—
165C22×C4D17211yescharacteristic
166C22×C4D17212yes—
167C22×C4C22×D4312yes—
168C22×C4C22×D4311yescharacteristic
169Q16—1721no—
170SD16—1722no—
171D8—1721no—
172M16—41no—
173M16—41no—
174C2×C8C22×D4311yescharacteristic
175C2×C8C22×D4312yes—
176C2×C8C22×D4311yescharacteristic
177C4⋊C4—432no—
178C4⋊C4—432no—
179C4⋊C4—862no—
180C4⋊C4—862no—
181C22⋊C4—862no—
182C22⋊C4—862no—
183C22⋊C4—862no—
184C22⋊C4—862no—
185C22⋊C4—862no—
186C42—862no—
187C23—41no—
188C23—42no—
189C23—862no—
190C23C2×D17211yescharacteristic
191C23C2×D17212yes—
192Q8—862no—
193Q8—862no—
194D4—862no—
195D4—862no—
196D4—1724no—
197D4—1724no—
198D4—1724no—
199C2×C4—21no—
200C2×C4—21no—
201C2×C4—22no—
202C2×C4—22no—
203C2×C4—41no—
204C2×C4—42no—
205C2×C4—862no—
206C2×C4—862no—
207C2×C4—862no—
208C2×C4—1724no—
209C2×C4C2×D17212yes—
210C2×C4C2×D17211yescharacteristic
211C2×C4C23×D4311yescharacteristic
212C8—21no—
213C8—22no—
214C8—21no—
215C22—22no—
216C22—22no—
217C22—22no—
218C22—22no—
219C22—21no—
220C22—44no—
221C22—1722no—
222C22—1722no—
223C22—1722no—
224C22C22×D17211yescharacteristic
225C4—22no—
226C4—21no—
227C4—1722no—
228C4—1722no—
229C4—1722no—
230C4#1306337011yescharacteristic
231C4#1306337011yescharacteristic
232C2—41no—
233C2—42no—
234C2—3442no—
235C2#1458346111yescharacteristic
236C2#1458369912yes—
subgroupG/H
centerC22C22×D172
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#407C2
socleC22×C43C22×D4
hypercenter#407D43
hypocenterC43#3197
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #407

Complements

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

NH ≅ G/Ntype
1. #14583410C2semidirect
2. #14583241C2semidirect
3. #14583224C2semidirect
4. #14583157C2semidirect
5. #14583152C2semidirect
6. #14583145C2semidirect
7. #14583063C2semidirect
8. #14583046C2semidirect
9. C43×#407C2semidirect
11. C2×Dic172C22semidirect
12. C2×#10621873C22semidirect
13. C2×D344C22semidirect
23. #13063259C22semidirect
24. #13063257C22semidirect
25. #13063257C22semidirect
26. #13063250C22semidirect
27. #13063250C22semidirect
28. #13063247C22semidirect
29. #13063247C22semidirect
127. #407D43semidirect
128. C43#3197semidirect