Finite Group Databasebeta

← #23757461

Subgroups — #23757461

Order 10048.

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#19097816C211yesmaximal, characteristic, complemented
2#19097741C212yesmaximal, complemented
3#19097739C211yesmaximal, characteristic, complemented
4#19097685C212yesmaximal, complemented
5#99×C157C211yesmaximal, characteristic, complemented
6C23×D157C2211yescharacteristic, complemented
7#14578954—21no—
8#14578953—22no—
9C2×D628—22no—
10C2×C22⋊D157—21no—
11C2×C22⋊D157—21no—
12C2×C22⋊D157C2212yes—
13D4×D157—22no—
14C22⋊Dic157C2211yescharacteristic, complemented
15#14578931—22no—
16#14578931—21no—
17C2×D4×C157C2211yescharacteristic
18C22⋊C4×C157C2212yescomplemented
19C22×D157—21no—
20C22×D157—22no—
21C22×D157—21no—
22C22×D157—42no—
23C22×D157D412yescomplemented
24Dic314—21no—
25D628—21no—
26D628—44no—
27C22⋊D157—22no—
28C22⋊D157—22no—
29C22⋊D157—22no—
30C22⋊D157—42no—
31C2×Dic157—21no—
32C2×Dic157—21no—
33C2×Dic157D412yescomplemented
34C4×D157—22no—
35C23×C157D411yescharacteristic, complemented
36C23×C157C2311yescharacteristic
37D4×C157—22no—
38C2×C4×C157—22no—
39C2×C4×C157D411yescharacteristic, complemented
40C22×C157—21no—
41C22×C157—41no—
42C22×C157—41no—
43C22×C157C2×D412yes—
44C22×C157C2×D411yescharacteristic
45C2×D157—22no—
46C2×D157—24no—
47C2×D157—22no—
48C2×D157—41no—
49C2×D157—42no—
50C2×D157—41no—
51C2×D157—42no—
52C2×D157—81no—
53C4×C157—21no—
54C4×C157—42no—
55Dic157—22no—
56Dic157—41no—
57C2×C157—21no—
58C2×C157—22no—
59C2×C157—41no—
60C2×C157#12011yescharacteristic
61D157—42no—
62D157—42no—
63C157B(4,𝔽2)11yescharacteristic, complemented, Sylow
64B(4,𝔽2)—1571nomaximal, Sylow
65H(5,𝔽2)—1571no—
66#120—1571no—
67#120—1572no—
68#99—1572no—
69#99D15711yescharacteristic, complemented
70C24—1571no—
71#41—3142no—
72#41—3141no—
73C2×D4—3142no—
74C2×D4—3142no—
75C2×D4—3141no—
76C2×D4—3141no—
77C2×D4—1572no—
78C2×D4C2×D15711yescharacteristic
79C22⋊C4—3142no—
80C22⋊C4—3141no—
81C22⋊C4—1571no—
82C22⋊C4C2×D15712yescomplemented
83C23—3141no—
84C23—3142no—
85C23—3141no—
86C23—6282no—
87C23—1572no—
88C23D62811yescharacteristic, complemented
89C23C22×D15711yescharacteristic
90Q8—3141no—
91D4—22no—
92D4—3141no—
93D4—3142no—
94D4—3142no—
95D4—3142no—
96D4—6284no—
97D4—6282no—
98C2×C4—22no—
99C2×C4—3142no—
100C2×C4—3141no—
101C2×C4—3141no—
102C2×C4—1572no—
103C2×C4D62811yescharacteristic, complemented
104C22—21no—
105C22—41no—
106C22—41no—
107C22—3144no—
108C22—3142no—
109C22—3142no—
110C22—6282no—
111C22—6282no—
112C22—6281no—
113C22—6281no—
114C22—12561no—
115C22D4×D15712yes—
116C22C2×D62811yescharacteristic
117C4—21no—
118C4—42no—
119C4—3142no—
120C4—6281no—
121C2—22no—
122C2—21no—
123C2—41no—
124C2—6282no—
125C2—6282no—
126C2#1909774111yescharacteristic
subgroupG/H
centerC2#19097741
commutator, cosocleC23×C157C23
FrattiniC23C22×D157
Fitting#99×C157C2
socleC2×C157#120
hypercenter#99D157
hypocenterC157B(4,𝔽2)
LCSG ▷ C23×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C2 ◁ C23 ◁ #99

Complements

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

NH ≅ G/Ntype
1. #19097816C2semidirect
2. #19097741C2semidirect
3. #19097739C2semidirect
4. #19097685C2semidirect
5. #99×C157C2semidirect
6. C23×D157C22semidirect
14. C22⋊Dic157C22semidirect
18. C22⋊C4×C157C22semidirect
23. C22×D157D4semidirect
33. C2×Dic157D4semidirect
35. C23×C157D4semidirect
39. C2×C4×C157D4semidirect
63. C157B(4,𝔽2)semidirect
69. #99D157semidirect
82. C22⋊C4C2×D157semidirect
88. C23D628semidirect
103. C2×C4D628semidirect