Finite Group Databasebeta

← #23757529

Subgroups — #23757529

Order 10048.

110 conjugacy classes of subgroups; only the 41 normal subgroups are shown.

normal subgroups only

This group has 110 conjugacy classes of subgroups — too many to draw. Only its 41 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×#14578944C211yesmaximal, characteristic, complemented
2C2×#14578938C211yesmaximal, characteristic
3#19097750C211yesmaximal, characteristic
4#19097702C211yesmaximal, characteristic, complemented
5#19097695C211yesmaximal, characteristic, complemented
6#19097694C211yesmaximal, characteristic, complemented
7C22⋊Q8×C157C211yesmaximal, characteristic
8C2×Dic314C2211yescharacteristic
9#14578944—22no—
10#14578938—22no—
11C2×#11929434C2211yescharacteristic
12C2×#11929434C2211yescharacteristic
13C4⋊Dic157C2211yescharacteristic
14#14578933—21no—
15C22⋊Dic157—21no—
16C2×Q8×C157C2211yescharacteristic
17C22×C4×C157C2211yescharacteristic
18C4⋊C4×C157—21no—
19C4⋊C4×C157C2211yescharacteristic
20C22⋊C4×C157—21no—
21Dic314—21no—
22Dic314—21no—
23C2×Dic157—21no—
24C2×Dic157—21no—
25#11929434—21no—
26#11929434D412yes—
27C23×C157D411yescharacteristic
28Q8×C157—21no—
29Q8×C157—21no—
30C2×C4×C157—21no—
31C2×C4×C157—21no—
32C2×C4×C157—21no—
33C2×C4×C157—21no—
34C2×C4×C157D411yescharacteristic
35C2×C4×C157C2311yescharacteristic
36C22×C157—21no—
37C22×C157—21no—
38C22×C157—21no—
39C22×C157C2×D411yescharacteristic
40C4×C157—21no—
41C4×C157—41no—
42C4×C157—41no—
43C4×C157C2×D411yescharacteristic
44C4×C157#4111yescharacteristic
45Dic157—41no—
46Dic157—41no—
47C2×C157—41no—
48C2×C157#12111yescharacteristic
49C2×C157#13711yescharacteristic
50C2×C157#13711yescharacteristic
51C157#47011yescharacteristic, complemented, Sylow
52#470—1571nomaximal, Sylow
53C2×Q16—1571no—
54C2×M16—1571no—
55C22⋊Q8—1571no—
56C22⋊Q8D15711yescharacteristic
57#106—1571no—
58#103—1571no—
59#103—1571no—
60C2×Q8—1571no—
61C2×Q8C2×D15711yescharacteristic
62C22×C4C2×D15711yescharacteristic
63Q16—3142no—
64M16—3142no—
65C2×C8—1571no—
66C2×C8—1571no—
67C4⋊C4—21no—
68C4⋊C4—3141no—
69C4⋊C4—1571no—
70C4⋊C4C2×D15711yescharacteristic
71C22⋊C4—21no—
72C22⋊C4—3141no—
73C23C22⋊D15711yescharacteristic
74Q8—21no—
75Q8—21no—
76Q8—3141no—
77Q8—3141no—
78C2×C4—21no—
79C2×C4—21no—
80C2×C4—21no—
81C2×C4—21no—
82C2×C4—3141no—
83C2×C4—3141no—
84C2×C4C22⋊D15711yescharacteristic
85C2×C4C22×D15711yescharacteristic
86C8—3141no—
87C8—1572no—
88C22—21no—
89C22—21no—
90C22—21no—
91C22C2×C22⋊D15711yescharacteristic
92C4—21no—
93C4—41no—
94C4—41no—
95C4—6281no—
96C4—6281no—
97C4D4×D15711yescharacteristic
98C4#1457895311yescharacteristic
99C2—41no—
100C2#1909774311yescharacteristic
101C2#1909780111yescharacteristic
102C2#1909780211yescharacteristic
subgroupG/H
centerC22C2×C22⋊D157
commutator, cosocleC2×C4×C157C23
FrattiniC2×C4C22×D157
FittingC22⋊Q8×C157C2
socleC22×C157C2×D4
prime radicalC23×C157D4
hypercenterC22⋊Q8D157
hypocenterC157#470
LCSG ▷ C2×C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C2×#14578944C2semidirect
4. #19097702C2semidirect
5. #19097695C2semidirect
6. #19097694C2semidirect
51. C157#470semidirect