Finite Group Databasebeta

← #23757198

Subgroups — #23757198

Order 10048.

170 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 170 conjugacy classes of subgroups — too many to draw. Only its 59 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×C4⋊Dic157C211yesmaximal, characteristic, complemented
2C2×C22⋊Dic157C212yesmaximal
3#19097678C211yesmaximal, characteristic, complemented
4#19097678C212yesmaximal, complemented
5C2×C22⋊C4×C157C211yesmaximal, characteristic
6C22×Dic157C2212yes—
7C22×Dic157C2212yes—
8C4⋊Dic157—22no—
9C22⋊Dic157—24no—
10C24×C157C2211yescharacteristic
11C22×C4×C157C2211yescharacteristic
12C22×C4×C157C2211yescharacteristic
13C22⋊C4×C157—22no—
14C2×Dic157—22no—
15C2×Dic157—22no—
16C2×Dic157—22no—
17C2×Dic157—22no—
18C2×Dic157—22no—
19C2×Dic157—22no—
20C23×C157—21no—
21C23×C157—22no—
22C23×C157—22no—
23C23×C157—21no—
24C23×C157D412yes—
25C23×C157C2311yescharacteristic
26C2×C4×C157—22no—
27C2×C4×C157—21no—
28C2×C4×C157—22no—
29C2×C4×C157D412yes—
30C22×C157—22no—
31C22×C157—24no—
32C22×C157—41no—
33C22×C157—41no—
34C22×C157—42no—
35C22×C157C2×D411yescharacteristic
36C22×C157C2×D411yescharacteristic
37C22×C157#4112yes—
38C22×C157#4112yes—
39C22×C157#4111yescharacteristic
40C4×C157—22no—
41C4×C157—41no—
42Dic157—42no—
43Dic157—42no—
44C2×C157—42no—
45C2×C157#12111yescharacteristic
46C2×C157#12311yescharacteristic
47C2×C157#12312yes—
48C2×C157#12411yescharacteristic
49C2×C157#12612yes—
50C157#39711yescharacteristic, complemented, Sylow
51#397—1571nomaximal, Sylow
52C2×C4⋊C4—1571no—
53C2×C22⋊C4—1572no—
54C2×C22⋊C4D15711yescharacteristic
55#95—1571no—
56#95—1572no—
57C24C2×D15711yescharacteristic
58C22×C4—1572no—
59C22×C4—1572no—
60C22×C4C2×D15711yescharacteristic
61C22×C4C2×D15711yescharacteristic
62C4⋊C4—3142no—
63C22⋊C4—22no—
64C22⋊C4—3144no—
65C23—21no—
66C23—22no—
67C23—22no—
68C23—21no—
69C23D62812yes—
70C23C22×D15711yescharacteristic
71C2×C4—22no—
72C2×C4—21no—
73C2×C4—22no—
74C2×C4—3142no—
75C2×C4—3142no—
76C2×C4—3142no—
77C2×C4—3142no—
78C2×C4—3142no—
79C2×C4—3142no—
80C2×C4C22⋊D15712yes—
81C22—22no—
82C22—24no—
83C22—41no—
84C22—41no—
85C22—42no—
86C22C2×C22⋊D15711yescharacteristic
87C22C2×D62811yescharacteristic
88C22#1457895312yes—
89C22#1457895312yes—
90C22#1457895411yescharacteristic
91C4—22no—
92C4—41no—
93C4—6282no—
94C4—6282no—
95C2—42no—
96C2#1909774511yescharacteristic
97C2#1909775211yescharacteristic
98C2#1909775512yes—
99C2#1909775811yescharacteristic
100C2#1909776412yes—
subgroupG/H
center, FrattiniC23C22×D157
commutator, socle, cosocleC23×C157C23
FittingC2×C22⋊C4×C157C2
prime radicalC24×C157C22
hypercenterC2×C22⋊C4D157
hypocenterC157#397
LCSG ▷ C23×C157 ▷ C157
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×C4⋊Dic157C2semidirect
3. #19097678C2semidirect
4. #19097678C2semidirect
50. C157#397semidirect