Finite Group Databasebeta

← #23757364

Subgroups — #23757364

Order 10048.

122 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 122 conjugacy classes of subgroups — too many to draw. Only its 51 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×#14578942C211yesmaximal, characteristic
2#19097736C211yesmaximal, characteristic, complemented
3D4×Dic157C211yesmaximal, characteristic
4#19097702C211yesmaximal, characteristic, complemented
5#19097696C211yesmaximal, characteristic, complemented
6C8×Dic157C211yesmaximal, characteristic, complemented
7#102×C157C211yesmaximal, characteristic
8C2×Dic314C2211yescharacteristic
9C22×Dic157—21no—
10#14578942C414yescomplemented
11C2×#11929434C2211yescharacteristic
12C4⋊Dic157C2211yescharacteristic
13#14578933—21no—
14C22⋊Dic157—21no—
15C4×Dic157—21no—
16C4×Dic157C2211yescharacteristic
17C2×D4×C157C2211yescharacteristic
18C2×C8×C157C2211yescharacteristic
19C4⋊C4×C157C2211yescharacteristic
20Dic314—21no—
21Dic314C2×C412yescomplemented
22C2×Dic157—21no—
23C2×Dic157—21no—
24C2×Dic157—42no—
25C2×Dic157D411yescharacteristic
26C2×Dic157D411yescharacteristic
27#11929434C2×C412yescomplemented
28C23×C157—21no—
29D4×C157—21no—
30D4×C157C2×C412yes—
31C2×C4×C157—21no—
32C2×C4×C157C2311yescharacteristic
33C8×C157—21no—
34C22×C157—22no—
35C22×C157—41no—
36C22×C157—41no—
37C22×C157C2×D411yescharacteristic
38C4×C157—41no—
39C4×C157C22×C411yescharacteristic
40C4×C157#4111yescharacteristic
41Dic157—22no—
42Dic157—21no—
43Dic157—41no—
44Dic157SD1612yescomplemented
45C2×C157—42no—
46C2×C157C4×D411yescharacteristic
47C2×C157C2×SD1611yescharacteristic
48C2×C157#13511yescharacteristic
49C157C4×SD1611yescharacteristic, complemented, Sylow
50C4×SD16—1571nomaximal, Sylow
51C2×SD16—1571no—
52C4×Q8—1571no—
53C4×D4—1571no—
54#106—1571no—
55#103—1571no—
56#102D15711yescharacteristic
57C4×C8—1571no—
58C2×Q8—1571no—
59C2×D4C2×D15711yescharacteristic
60C22×C4—3141no—
61SD16—1574no—
62C2×C8—1571no—
63C2×C8C2×D15711yescharacteristic
64C4⋊C4—3141no—
65C4⋊C4—1571no—
66C4⋊C4C2×D15711yescharacteristic
67C22⋊C4—3141no—
68C42—3141no—
69C42—1571no—
70C23—21no—
71Q8—3141no—
72Q8—1572no—
73D4—21no—
74D4C4×D15712yes—
75C2×C4—21no—
76C2×C4—3141no—
77C2×C4—3141no—
78C2×C4—6282no—
79C2×C4—1571no—
80C2×C4—1571no—
81C2×C4C22×D15711yescharacteristic
82C8—21no—
83C8—1572no—
84C22—22no—
85C22—41no—
86C22—41no—
87C22D4×D15711yescharacteristic
88C4—41no—
89C4—3142no—
90C4—3141no—
91C4—6281no—
92C4—1572no—
93C4C2×C4×D15711yescharacteristic
94C4#1457895311yescharacteristic
95C2—42no—
96C2#1909773111yescharacteristic
97C2SD16×D15711yescharacteristic
98C2#1909779011yescharacteristic
subgroupG/H
centerC22D4×D157
commutatorC4×C157C22×C4
FrattiniC2×C4C22×D157
Fitting#102×C157C2
socleC22×C157C2×D4
prime radicalC2×D4×C157C22
cosocleC2×C4×C157C23
hypercenter#102D157
hypocenterC157C4×SD16
LCSG ▷ C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C22 ◁ C2×C4 ◁ #102

Complements

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

NH ≅ G/Ntype
2. #19097736C2semidirect
4. #19097702C2semidirect
5. #19097696C2semidirect
6. C8×Dic157C2semidirect
10. #14578942C4semidirect
21. Dic314C2×C4semidirect
27. #11929434C2×C4semidirect
44. Dic157SD16semidirect
49. C157C4×SD16semidirect