Finite Group Databasebeta

← #14583087

Subgroups — #14583087

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#13063295C212yesmaximal, complemented
3#13063293C211yesmaximal, characteristic, complemented
4#13063239C212yesmaximal, complemented
5#99×C43C211yesmaximal, characteristic, complemented
6C23×D43C2211yescharacteristic, complemented
7C2×D4×C43C2211yescharacteristic
8C2×C22⋊D43—21no—
9C2×C22⋊D43—21no—
10C2×C22⋊D43C2212yes—
11#10621900—22no—
12D4×D43—22no—
13#10621898—21no—
14C2×D172—22no—
15C22⋊C4×C43C2212yescomplemented
16C22⋊Dic43C2211yescharacteristic, complemented
17(C2×D43)⋊C4—21no—
18(C2×D43)⋊C4—22no—
19C23×C43D411yescharacteristic, complemented
20C23×C43C2311yescharacteristic
21C22×D43—22no—
22C22×D43—21no—
23C22×D43—21no—
24C22×D43—42no—
25C22×D43D412yescomplemented
26D4×C43—22no—
27C2×C4×C43—22no—
28C2×C4×C43D411yescharacteristic, complemented
29C22⋊D43—22no—
30C22⋊D43—22no—
31C22⋊D43—22no—
32C22⋊D43—42no—
33C2×Dic43—21no—
34C2×Dic43—21no—
35C2×Dic43D412yescomplemented
36D172—21no—
37D172—44no—
38C4×D43—22no—
39Dic86—21no—
40C22×C43—21no—
41C22×C43—41no—
42C22×C43—41no—
43C22×C43C2×D411yescharacteristic
44C22×C43C2×D412yes—
45C2×D43—24no—
46C2×D43—22no—
47C2×D43—22no—
48C2×D43—41no—
49C2×D43—42no—
50C2×D43—41no—
51C2×D43—42no—
52C2×D43—81no—
53C4×C43—21no—
54C4×C43—42no—
55Dic43—22no—
56Dic43—41no—
57C2×C43—21no—
58C2×C43—22no—
59C2×C43—41no—
60C2×C43#12011yescharacteristic
61D43—42no—
62D43—42no—
63B(4,𝔽2)—431nomaximal, Sylow
64C43B(4,𝔽2)11yescharacteristic, complemented, Sylow
65H(5,𝔽2)—431no—
66#120—431no—
67#120—432no—
68#99—432no—
69#99D4311yescharacteristic, complemented
70C24—431no—
71#41—862no—
72#41—861no—
73C2×D4—432no—
74C2×D4—862no—
75C2×D4—862no—
76C2×D4—861no—
77C2×D4—861no—
78C2×D4C2×D4311yescharacteristic
79C22⋊C4—431no—
80C22⋊C4—862no—
81C22⋊C4—861no—
82C22⋊C4C2×D4312yescomplemented
83C23—432no—
84C23—861no—
85C23—861no—
86C23—862no—
87C23—1722no—
88C23D17211yescharacteristic, complemented
89C23C22×D4311yescharacteristic
90Q8—861no—
91D4—22no—
92D4—861no—
93D4—862no—
94D4—862no—
95D4—862no—
96D4—1724no—
97D4—1722no—
98C2×C4—22no—
99C2×C4—432no—
100C2×C4—862no—
101C2×C4—861no—
102C2×C4—861no—
103C2×C4D17211yescharacteristic, complemented
104C22—21no—
105C22—41no—
106C22—41no—
107C22—864no—
108C22—862no—
109C22—862no—
110C22—3441no—
111C22—1722no—
112C22—1722no—
113C22—1721no—
114C22—1721no—
115C22C2×D17211yescharacteristic
116C22D4×D4312yes—
117C4—21no—
118C4—42no—
119C4—862no—
120C4—1721no—
121C2—22no—
122C2—21no—
123C2—41no—
124C2—1722no—
125C2—1722no—
126C2#1306329511yescharacteristic
subgroupG/H
centerC2#13063295
commutator, cosocleC23×C43C23
FrattiniC23C22×D43
Fitting#99×C43C2
socleC2×C43#120
hypercenter#99D43
hypocenterC43B(4,𝔽2)
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C23 ◁ #99

Complements

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

NH ≅ G/Ntype
1. #13063370C2semidirect
2. #13063295C2semidirect
3. #13063293C2semidirect
4. #13063239C2semidirect
5. #99×C43C2semidirect
6. C23×D43C22semidirect
15. C22⋊C4×C43C22semidirect
16. C22⋊Dic43C22semidirect
19. C23×C43D4semidirect
25. C22×D43D4semidirect
28. C2×C4×C43D4semidirect
35. C2×Dic43D4semidirect
64. C43B(4,𝔽2)semidirect
69. #99D43semidirect
82. C22⋊C4C2×D43semidirect
88. C23D172semidirect
103. C2×C4D172semidirect

Maximal subgroups

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

subgroupindex
#130633702
#130632952
#130632932
#130632392
#99×C432
B(4,𝔽2)43