Finite Group Databasebeta

← #23758146

Subgroups — #23758146

Order 10048.

114 conjugacy classes of subgroups; only the 46 normal subgroups are shown.

normal subgroups only

This group has 114 conjugacy classes of subgroups — too many to draw. Only its 46 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
1C2×D157⋊C8C211yesmaximal, characteristic
2C2×C4⋊#10597845C211yesmaximal, characteristic
3C4⋊C4×D157C211yesmaximal, characteristic
4C22×#10597845—21no—
5D157⋊C8—21no—
6D157⋊C8C412yescomplemented
7C2×#11929441—21no—
8C4⋊#10597845—21no—
9C4⋊#10597845C412yescomplemented
10C2×C4×D157—21no—
11C2×C4×D157C2211yescharacteristic
12C4⋊Dic157C411yescharacteristic, complemented
13#14578933—21no—
14C4⋊C4×C157C411yescharacteristic, complemented
15C2×#10597845—22no—
16C2×#10597845—41no—
17C2×#10597845—41no—
18#11929441—22no—
19C22×D157D411yescharacteristic
20C2×Dic157—21no—
21C2×Dic157D411yescharacteristic
22C4×D157—41no—
23C4×D157—41no—
24C4×D157C2×C411yescharacteristic
25C4×D157C2×C411yescharacteristic
26C4×D157D411yescharacteristic
27C4×D157Q811yescharacteristic
28C2×C4×C157—21no—
29C2×C4×C157C2×C411yescharacteristic
30C22×C157C22⋊C411yescharacteristic
31C2×D157C22⋊C411yescharacteristic
32C2×D157C4⋊C411yescharacteristic
33C2×D157D811yescharacteristic
34C2×D157SD1611yescharacteristic
35C2×D157SD1611yescharacteristic
36C2×D157Q1611yescharacteristic
37#10597845—42no—
38C4×C157—41no—
39C4×C157C4211yescharacteristic
40C4×C157C4⋊C411yescharacteristic
41Dic157—41no—
42Dic157C22⋊C411yescharacteristic
43Dic157C4⋊C411yescharacteristic
44C2×C157#9511yescharacteristic
45C2×C157#10211yescharacteristic
46C2×C157#10311yescharacteristic
47D157#10211yescharacteristic
48D157#10311yescharacteristic
49D157#10611yescharacteristic
50D157#10711yescharacteristic
51C157#34011yescharacteristic, complemented, Sylow
52#340—1571nomaximal, Sylow
53C22×C8—1571no—
54C2×C4⋊C4—1571no—
55C2×C4⋊C4—1571no—
56C22×C4—3141no—
57C22×C4—3141no—
58C22×C4—1571no—
59C2×C8—3141no—
60C2×C8—3141no—
61C2×C8—1572no—
62C4⋊C4—3141no—
63C4⋊C4—3141no—
64C4⋊C4—1572no—
65C4⋊C4—1571no—
66C4⋊C4#1059784511yescharacteristic, complemented
67C23—1571no—
68C2×C4—21no—
69C2×C4—3142no—
70C2×C4—3141no—
71C2×C4—6281no—
72C2×C4—6281no—
73C2×C4—6281no—
74C2×C4—6281no—
75C2×C4—1571no—
76C2×C4—1571no—
77C2×C4—1571no—
78C2×C4—1571no—
79C2×C4—1571no—
80C2×C4C2×#1059784511yescharacteristic
81C8—3142no—
82C22—1571no—
83C22—1571no—
84C22—1571no—
85C22—1571no—
86C22—1571no—
87C22—1571no—
88C22C22⋊#1059784511yescharacteristic
89C4—41no—
90C4—6282no—
91C4—6281no—
92C4—1571no—
93C4—1571no—
94C4C4×#1059784511yescharacteristic
95C4C4⋊#1059784511yescharacteristic
96C2—1571no—
97C2—1571no—
98C2—1571no—
99C2—1571no—
100C2(C2×#10597845)⋊C411yescharacteristic
101C2#1909783311yescharacteristic
102C2#1909783411yescharacteristic
subgroupG/H
centerC22C22⋊#10597845
commutatorC4×C157C42
FrattiniC2×C4C2×#10597845
FittingC4⋊C4×C157C4
socleC22×C157C22⋊C4
prime radicalC22×D157D4
cosocleC2×C4×D157C22
hypercenterC4⋊C4#10597845
hypocenterC157#340
LCSG ▷ C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C22 ◁ C2×C4 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
6. D157⋊C8C4semidirect
9. C4⋊#10597845C4semidirect
12. C4⋊Dic157C4semidirect
14. C4⋊C4×C157C4semidirect
51. C157#340semidirect
66. C4⋊C4#10597845semidirect