Finite Group Databasebeta

← #23758260

Subgroups — #23758260

Order 10048.

150 conjugacy classes of subgroups; only the 48 normal subgroups are shown.

normal subgroups only

This group has 150 conjugacy classes of subgroups — too many to draw. Only its 48 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×#14578963C212yesmaximal, complemented
2#19097832C212yesmaximal, complemented
3#19097831C212yesmaximal, complemented
4C2×#14578953C211yesmaximal, characteristic
5#14578963—22no—
6#14578963C2214yes—
7C2×#11929441—22no—
8#14578953—22no—
9#14578953—22no—
10C2×Dic314C2211yescharacteristic
11C2×C22⋊D157C411yescharacteristic
12C2×C22⋊D157C2211yescharacteristic
13C22×Dic157C411yescharacteristic
14C22×Dic157C2211yescharacteristic
15C2×C4×D157C411yescharacteristic
16C2×D4×C157C411yescharacteristic
17#11929441—24no—
18C22×D157C2×C411yescharacteristic
19Dic314—22no—
20C22⋊D157—22no—
21C22⋊D157—22no—
22C2×Dic157—21no—
23C2×Dic157—21no—
24C2×Dic157C2×C411yescharacteristic
25C2×Dic157C2×C411yescharacteristic
26C2×Dic157D412yes—
27C2×Dic157D412yes—
28C2×Dic157C2311yescharacteristic
29C4×D157—21no—
30C4×D157—21no—
31C23×C157C2×C411yescharacteristic
32C23×C157C2×C411yescharacteristic
33D4×C157—22no—
34C2×C4×C157C2×C411yescharacteristic
35C22×C157—21no—
36C22×C157—41no—
37C22×C157—41no—
38C22×C157C22⋊C412yes—
39C22×C157C22×C411yescharacteristic
40C2×D157—21no—
41C2×D157—41no—
42C4×C157—21no—
43Dic157—21no—
44Dic157C22⋊C411yescharacteristic
45Dic157C22⋊C411yescharacteristic
46Dic157C2×D412yes—
47C2×C157—21no—
48C2×C157—22no—
49C2×C157—41no—
50C2×C157C2×C22⋊C411yescharacteristic
51D157—41no—
52C157#41311yescharacteristic, complemented, Sylow
53#413—1571nomaximal, Sylow
54C2×#41—1571no—
55C2×M16—1572no—
56#101—1572no—
57#100—1572no—
58#41—3142no—
59#41—3142no—
60C2×Q8—1571no—
61C2×D4—1571no—
62C2×D4—1571no—
63C2×D4#1059784511yescharacteristic
64C22×C4—1571no—
65C22×C4—1571no—
66C22×C4—1571no—
67M16—3142no—
68M16—1574no—
69C2×C8—3142no—
70C23—1571no—
71C23C2×#1059784511yescharacteristic
72C23C2×#1059784511yescharacteristic
73Q8—3142no—
74D4—22no—
75D4—3142no—
76D4—3142no—
77C2×C4—3141no—
78C2×C4—3141no—
79C2×C4—3141no—
80C2×C4—3141no—
81C2×C4—1571no—
82C2×C4—1572no—
83C2×C4—1572no—
84C2×C4—1571no—
85C2×C4—1571no—
86C2×C4C2×#1059784511yescharacteristic
87C8—3144no—
88C22—21no—
89C22—41no—
90C22—41no—
91C22—3141no—
92C22—6281no—
93C22C22⋊#1059784512yes—
94C22C22×#1059784511yescharacteristic
95C4—21no—
96C4—3141no—
97C4—1572no—
98C4—1571no—
99C4—1571no—
100C2—21no—
101C2—22no—
102C2—41no—
103C2—6281no—
104C2C2×C22⋊#1059784511yescharacteristic
subgroupG/H
centerC2C2×C22⋊#10597845
commutatorC22×C157C22×C4
FrattiniC22C22×#10597845
FittingC2×D4×C157C4
socleC2×C157C2×C22⋊C4
prime radicalC2×#14578953C2
cosocleC2×Dic157C23
hypercenterC2×D4#10597845
hypocenterC157#413
LCSG ▷ C22×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C2 ◁ C23 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
1. C2×#14578963C2semidirect
2. #19097832C2semidirect
3. #19097831C2semidirect
52. C157#413semidirect