Finite Group Databasebeta

← #14583085

Subgroups — #14583085

Order 2752.

198 conjugacy classes of subgroups; only the 39 normal subgroups are shown.

normal subgroups only

This group has 198 conjugacy classes of subgroups — too many to draw. Only its 39 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#13063370C211yesmaximal, characteristic, complemented
2#13063294C212yesmaximal, complemented
3#13063240C211yesmaximal, characteristic, complemented
4#13063239C212yesmaximal, complemented
5#120×C43C211yesmaximal, characteristic, complemented
6C24×C43C2211yescharacteristic, complemented
7C2×D4×C43—21no—
8C2×D4×C43C2211yescharacteristic
9C2×C22⋊D43—21no—
10C2×C22⋊D43—22no—
11C2×C22⋊D43C2212yes—
12#10621900—22no—
13D4×D43—22no—
14#10621898—21no—
15C22⋊C4×C43—21no—
16C22⋊C4×C43C2211yescharacteristic, complemented
17C22⋊Dic43—22no—
18C22⋊Dic43C2212yescomplemented
19C23×C43—22no—
20C23×C43—21no—
21C23×C43—42no—
22C23×C43D411yescharacteristic, complemented
23C23×C43C2311yescharacteristic
24C22×D43—21no—
25C22×D43D412yescomplemented
26D4×C43—22no—
27D4×C43—42no—
28C2×C4×C43—21no—
29C2×C4×C43D411yescharacteristic, complemented
30C22⋊D43—22no—
31C22⋊D43—22no—
32C22⋊D43—22no—
33C22⋊D43—44no—
34C2×Dic43—21no—
35C2×Dic43—22no—
36C2×Dic43D412yescomplemented
37D172—21no—
38C4×D43—22no—
39Dic86—21no—
40C22×C43—24no—
41C22×C43—22no—
42C22×C43—21no—
43C22×C43—41no—
44C22×C43—41no—
45C22×C43—42no—
46C22×C43—41no—
47C22×C43—41no—
48C22×C43C2×D412yes—
49C22×C43C2×D411yescharacteristic
50C2×D43—22no—
51C2×D43—42no—
52C2×D43—81no—
53C4×C43—21no—
54C4×C43—41no—
55Dic43—22no—
56Dic43—42no—
57C2×C43—22no—
58C2×C43—21no—
59C2×C43—41no—
60C2×C43—42no—
61C2×C43#12011yescharacteristic
62D43—42no—
63B(4,𝔽2)—431nomaximal, Sylow
64C43B(4,𝔽2)11yescharacteristic, complemented, Sylow
65H(5,𝔽2)—431no—
66#120—432no—
67#120D4311yescharacteristic, complemented
68#99—431no—
69#99—432no—
70C24C2×D4311yescharacteristic, complemented
71#41—862no—
72#41—861no—
73C2×D4—21no—
74C2×D4—432no—
75C2×D4—862no—
76C2×D4—861no—
77C2×D4—862no—
78C2×D4C2×D4311yescharacteristic
79C22⋊C4—21no—
80C22⋊C4—432no—
81C22⋊C4—862no—
82C22⋊C4C2×D4311yescharacteristic, complemented
83C23—22no—
84C23—21no—
85C23—42no—
86C23—432no—
87C23—861no—
88C23C22⋊D4311yescharacteristic, complemented
89C23C22×D4311yescharacteristic
90Q8—861no—
91D4—22no—
92D4—42no—
93D4—861no—
94D4—862no—
95D4—862no—
96D4—862no—
97D4—1724no—
98C2×C4—21no—
99C2×C4—432no—
100C2×C4—862no—
101C2×C4—861no—
102C2×C4—862no—
103C2×C4C22⋊D4311yescharacteristic, complemented
104C22—22no—
105C22—24no—
106C22—21no—
107C22—41no—
108C22—41no—
109C22—41no—
110C22—42no—
111C22—41no—
112C22—862no—
113C22—3441no—
114C22—1722no—
115C22D4×D4312yes—
116C22C2×C22⋊D4311yescharacteristic
117C4—21no—
118C4—41no—
119C4—862no—
120C4—1722no—
121C2—21no—
122C2—22no—
123C2—42no—
124C2—41no—
125C2—1722no—
126C2#1306329311yescharacteristic
subgroupG/H
centerC2#13063293
commutator, cosocleC23×C43C23
FrattiniC23C22×D43
Fitting#120×C43C2
socleC2×C43#120
hypercenter#120D43
hypocenterC43B(4,𝔽2)
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C23 ◁ #120

Complements

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

NH ≅ G/Ntype
1. #13063370C2semidirect
2. #13063294C2semidirect
3. #13063240C2semidirect
4. #13063239C2semidirect
5. #120×C43C2semidirect
6. C24×C43C22semidirect
16. C22⋊C4×C43C22semidirect
18. C22⋊Dic43C22semidirect
22. C23×C43D4semidirect
25. C22×D43D4semidirect
29. C2×C4×C43D4semidirect
36. C2×Dic43D4semidirect
64. C43B(4,𝔽2)semidirect
67. #120D43semidirect
70. C24C2×D43semidirect
82. C22⋊C4C2×D43semidirect
88. C23C22⋊D43semidirect
103. C2×C4C22⋊D43semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#130633702
#130632942
#130632402
#130632392
#120×C432
B(4,𝔽2)43