Finite Group Databasebeta

← #23757274

Subgroups — #23757274

Order 10048.

162 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 162 conjugacy classes of subgroups — too many to draw. Only its 71 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×#14578938C211yesmaximal, characteristic, complemented
2C2×C4⋊Dic157C211yesmaximal, characteristic, complemented
3#19097695C212yesmaximal, complemented
4#19097692C212yesmaximal, complemented
5C2×#41×C157C211yesmaximal, characteristic
6C22×Dic157—21no—
7#14578938—22no—
8C2×#11929434C2212yes—
9C4⋊Dic157—21no—
10C4⋊Dic157C2212yes—
11#41×C157—22no—
12#41×C157C414yescomplemented
13C2×Q8×C157C2211yescharacteristic
14C2×D4×C157—21no—
15C2×D4×C157C2211yescharacteristic
16C22×C4×C157—21no—
17C22×C4×C157C2211yescharacteristic
18C2×Dic157—22no—
19C2×Dic157—42no—
20#11929434—22no—
21C23×C157—21no—
22C23×C157D411yescharacteristic
23Q8×C157—21no—
24Q8×C157C2×C412yescomplemented
25D4×C157—24no—
26D4×C157—21no—
27D4×C157C2×C412yescomplemented
28C2×C4×C157—21no—
29C2×C4×C157—24no—
30C2×C4×C157C2×C412yes—
31C2×C4×C157D411yescharacteristic
32C2×C4×C157D412yes—
33C2×C4×C157C2311yescharacteristic
34C22×C157—21no—
35C22×C157—21no—
36C22×C157—22no—
37C22×C157—41no—
38C22×C157—41no—
39C22×C157C22⋊C412yes—
40C22×C157C2×D411yescharacteristic
41C4×C157—22no—
42C4×C157C22⋊C412yes—
43C4×C157C22×C411yescharacteristic
44C4×C157C2×D411yescharacteristic
45Dic157—42no—
46C2×C157—22no—
47C2×C157—42no—
48C2×C157C2×C22⋊C411yescharacteristic
49C2×C157AGL(1,ℤ/8)11yescharacteristic
50C2×C157#13711yescharacteristic
51C157#41711yescharacteristic, complemented, Sylow
52#417—1571nomaximal, Sylow
53C2×#41D15711yescharacteristic
54C2×M16—1571no—
55C2×C4⋊C4—1571no—
56#103—1572no—
57#102—1572no—
58#41—22no—
59#41Dic15714yescomplemented
60C2×Q8C2×D15711yescharacteristic
61C2×D4—21no—
62C2×D4C2×D15711yescharacteristic
63C22×C4—21no—
64C22×C4—3141no—
65C22×C4C2×D15711yescharacteristic
66M16—3142no—
67C2×C8—1572no—
68C4⋊C4—3141no—
69C4⋊C4—1572no—
70C23—21no—
71C23C22⋊D15711yescharacteristic
72Q8—21no—
73Q8C2×Dic15712yescomplemented
74D4—24no—
75D4—21no—
76D4C2×Dic15712yescomplemented
77C2×C4—21no—
78C2×C4—24no—
79C2×C4—3142no—
80C2×C4—6282no—
81C2×C4C2×Dic15712yes—
82C2×C4C22⋊D15712yes—
83C2×C4C22⋊D15711yescharacteristic
84C2×C4C22×D15711yescharacteristic
85C8—3142no—
86C22—21no—
87C22—21no—
88C22—22no—
89C22—41no—
90C22—41no—
91C22C22⋊Dic15712yes—
92C22C2×C22⋊D15711yescharacteristic
93C4—22no—
94C4—6282no—
95C4C22⋊Dic15712yes—
96C4C22×Dic15711yescharacteristic
97C4C2×C22⋊D15711yescharacteristic
98C2—22no—
99C2—42no—
100C2C2×C22⋊Dic15711yescharacteristic
101C2#1909779611yescharacteristic
102C2#1909780111yescharacteristic
subgroupG/H
centerC22C2×C22⋊D157
commutatorC4×C157C22×C4
FrattiniC2×C4C22×D157
Fitting, prime radicalC2×#41×C157C2
socleC22×C157C2×D4
cosocleC2×C4×C157C23
hypercenterC2×#41D157
hypocenterC157#417
LCSG ▷ C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C2×#14578938C2semidirect
2. C2×C4⋊Dic157C2semidirect
3. #19097695C2semidirect
4. #19097692C2semidirect
12. #41×C157C4semidirect
24. Q8×C157C2×C4semidirect
27. D4×C157C2×C4semidirect
51. C157#417semidirect
59. #41Dic157semidirect
73. Q8C2×Dic157semidirect
76. D4C2×Dic157semidirect