Finite Group Databasebeta

← #19145460

Subgroups — #19145460

Order 5504.

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

normal subgroups only

This group has 442 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#14583463C212yesmaximal, complemented
2#14583224C214yesmaximal, complemented
3#14583152C212yesmaximal, complemented
4#14583135C212yesmaximal, complemented
5#14583035C214yesmaximal, complemented
6C43×#408C211yesmaximal, characteristic, complemented
7C22×D172C2212yescomplemented
8C2×D344C2212yes—
9C2×D344C2212yes—
10#13063321—22no—
11#13063314—22no—
12#13063299C2214yes—
13#13063299C2214yescomplemented
14#13063293—22no—
15#13063293—22no—
16#13063284C2212yescomplemented
17#13063259C2212yescomplemented
18#13063257C2212yescomplemented
19#13063247C2214yescomplemented
20#13063247C2214yescomplemented
21C2×#41×C43C2211yescharacteristic
22C2×M16×C43C2211yescharacteristic, complemented
23C22×C8×C43C2211yescharacteristic, complemented
24C22⋊C8×C43C2214yescomplemented
25C23×D43—22no—
26#41×C43—41no—
27#41×C43—41no—
28C2×Q8×C43D411yescharacteristic
29C2×D4×C43D411yescharacteristic
30C2×D4×C43D412yes—
31C22×C4×C43C2312yes—
32C22×C4×C43C2311yescharacteristic
33C2×C22⋊D43—24no—
34C2×C22⋊D43—24no—
35C2×D172—22no—
36C2×D172—42no—
37C2×D172—42no—
38C2×D172C2314yes—
39M16×C43—41no—
40C2×C8×C43—41no—
41C2×C8×C43C2312yes—
42C2×C8×C43C2312yes—
43C22⋊Dic43—22no—
44(C2×D43)⋊C4—24no—
45(C2×D43)⋊C4—24no—
46C4⋊Dic43C2314yes—
47C4×Dic43—22no—
48D344—42no—
49D344—42no—
50C23×C43C2×D412yes—
51C23×C43C2×D411yescharacteristic
52C22×D43—24no—
53C22×D43—44no—
54C22×D43—84no—
55Q8×C43—41no—
56D4×C43—42no—
57D4×C43—41no—
58C2×C4×C43—21no—
59C2×C4×C43—21no—
60C2×C4×C43—22no—
61C2×C4×C43—22no—
62C2×C4×C43C2×D412yes—
63C2×C4×C43C2×D411yescharacteristic
64C2×C4×C43C2411yescharacteristic
65C22⋊D43—84no—
66C22⋊D43—84no—
67C2×Dic43—24no—
68D172—24no—
69D172—24no—
70D172—44no—
71C8×C43—22no—
72C8×C43—22no—
73C22×C43—22no—
74C22×C43—21no—
75C22×C43—24no—
76C22×C43—22no—
77C22×C43C22×D411yescharacteristic
78C2×D43—44no—
79C2×D43—44no—
80C2×D43—44no—
81C2×D43—88no—
82C4×C43—22no—
83C4×C43—21no—
84C4×C43H(5,𝔽2)11yescharacteristic
85C4×C43H(5,𝔽2)11yescharacteristic
86Dic43—44no—
87#3199—431nomaximal, Sylow
88C2×C43—42no—
89C2×C43—41no—
90C2×C43#53411yescharacteristic
91C2×C43#57612yes—
92D43—84no—
93#535—432no—
94#482—434no—
95#469—432no—
96#466—432no—
97#447—434no—
98#408D4311yescharacteristic, complemented
99C43#319911yescharacteristic, complemented, Sylow
100C2×#41C2×D4311yescharacteristic
101C22×D4—432no—
102C2×D8—432no—
103C2×D8—432no—
104C2×M16C2×D4311yescharacteristic, complemented
105C22×C8C2×D4311yescharacteristic, complemented
106#127—862no—
107#124—862no—
108#121—434no—
109#121—434no—
110#120—862no—
111#120—862no—
112#117—432no—
113#107—432no—
114#106—432no—
115#102—434no—
116#102—434no—
117C22⋊C8C2×D4314yescomplemented
118C24—862no—
119#41—41no—
120#41—41no—
121C2×Q8D17211yescharacteristic
122C2×D4—434no—
123C2×D4—864no—
124C2×D4—864no—
125C2×D4—862no—
126C2×D4—1722no—
127C2×D4—1722no—
128C2×D4D17211yescharacteristic
129C2×D4D17212yes—
130C22×C4C22×D4312yes—
131C22×C4C22×D4311yescharacteristic
132D8—1722no—
133D8—1722no—
134M16—41no—
135C2×C8—41no—
136C2×C8C22×D4312yes—
137C2×C8C22×D4312yes—
138C4⋊C4—434no—
139C22⋊C4—862no—
140C22⋊C4—864no—
141C22⋊C4—864no—
142C42—862no—
143C23—864no—
144C23—3444no—
145C23—1724no—
146C23C2×D17212yes—
147C23C2×D17211yescharacteristic
148Q8—41no—
149D4—42no—
150D4—41no—
151D4—864no—
152D4—864no—
153D4—3444no—
154D4—3444no—
155D4—1724no—
156C2×C4—21no—
157C2×C4—21no—
158C2×C4—22no—
159C2×C4—22no—
160C2×C4—864no—
161C2×C4C2×D17212yes—
162C2×C4C2×D17211yescharacteristic
163C2×C4C23×D4311yescharacteristic
164C8—22no—
165C8—22no—
166C22—22no—
167C22—24no—
168C22—22no—
169C22—21no—
170C22—3448no—
171C22—1724no—
172C22—1724no—
173C22—1724no—
174C22C22×D17211yescharacteristic
175C4—22no—
176C4—21no—
177C4—1724no—
178C4#1306337011yescharacteristic
179C4#1306337011yescharacteristic
180C2—42no—
181C2—41no—
182C2—3444no—
183C2#1458346111yescharacteristic
184C2#1458370412yes—
subgroupG/H
centerC22C22×D172
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#408C2
socleC22×C43C22×D4
hypercenter#408D43
hypocenterC43#3199
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×#41 ◁ #408

Complements

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

NH ≅ G/Ntype
1. #14583463C2semidirect
2. #14583224C2semidirect
3. #14583152C2semidirect
4. #14583135C2semidirect
5. #14583035C2semidirect
6. C43×#408C2semidirect
7. C22×D172C22semidirect
13. #13063299C22semidirect
16. #13063284C22semidirect
17. #13063259C22semidirect
18. #13063257C22semidirect
19. #13063247C22semidirect
20. #13063247C22semidirect
22. C2×M16×C43C22semidirect
23. C22×C8×C43C22semidirect
24. C22⋊C8×C43C22semidirect
98. #408D43semidirect
99. C43#3199semidirect
104. C2×M16C2×D43semidirect
105. C22×C8C2×D43semidirect
117. C22⋊C8C2×D43semidirect