Finite Group Databasebeta

← #23757495

Subgroups — #23757495

Order 10048.

112 conjugacy classes of subgroups; only the 43 normal subgroups are shown.

normal subgroups only

This group has 112 conjugacy classes of subgroups — too many to draw. Only its 43 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×#14578941C211yesmaximal, characteristic
3#19097759C211yesmaximal, characteristic
4C4⋊#11929434C211yesmaximal, characteristic, complemented
5#19097694C211yesmaximal, characteristic, complemented
6#19097691C211yesmaximal, characteristic
7C4×Q8×C157C211yesmaximal, characteristic, complemented
8C2×Dic314C2211yescharacteristic
9C2×D628C2211yescharacteristic
10#14578944—22no—
11#14578941—22no—
12C2×#11929434C2211yescharacteristic
13C2×#11929434C2211yescharacteristic
14#14578931—21no—
15#14578931—21no—
16C2×Q8×C157C2211yescharacteristic
17C4⋊C4×C157—21no—
18C4⋊C4×C157C2211yescharacteristic
19C42×C157—21no—
20C42×C157C2211yescharacteristic
21C22×D157—21no—
22Dic314—21no—
23Dic314—21no—
24D628—21no—
25D628—21no—
26C2×Dic157—21no—
27#11929434—21no—
28#11929434—21no—
29Q8×C157—21no—
30Q8×C157D412yes—
31C2×C4×C157—21no—
32C2×C4×C157—21no—
33C2×C4×C157D411yescharacteristic
34C2×C4×C157D411yescharacteristic
35C2×C4×C157C2311yescharacteristic
36C22×C157C2×D411yescharacteristic
37C2×D157—41no—
38C2×D157—41no—
39C2×D157—41no—
40C4×C157—22no—
41C4×C157—21no—
42C4×C157—21no—
43C4×C157—41no—
44C4×C157C2×D411yescharacteristic
45C4×C157#4111yescharacteristic
46Dic157—41no—
47C2×C157#12111yescharacteristic
48C2×C157#13511yescharacteristic
49C2×C157#13711yescharacteristic
50D157—81no—
51C157#46411yescharacteristic, complemented, Sylow
52#464—1571nomaximal, Sylow
53C2×Q16—1571no—
54C2×SD16—1571no—
55#124—1571no—
56C4×Q8D15711yescharacteristic, complemented
57C4⋊C8—1571no—
58#103—1571no—
59#102—1571no—
60C2×Q8—1571no—
61C2×Q8C2×D15711yescharacteristic
62C2×D4—1571no—
63Q16—3142no—
64SD16—3142no—
65C2×C8—1571no—
66C2×C8—1571no—
67C4⋊C4—21no—
68C4⋊C4C2×D15711yescharacteristic
69C22⋊C4—3141no—
70C22⋊C4—3141no—
71C42—21no—
72C42C2×D15711yescharacteristic
73C23—3141no—
74Q8—21no—
75Q8—3141no—
76Q8—3141no—
77Q8D62812yes—
78D4—3141no—
79D4—3141no—
80C2×C4—21no—
81C2×C4—21no—
82C2×C4—3141no—
83C2×C4C22⋊D15711yescharacteristic
84C2×C4C22⋊D15711yescharacteristic
85C2×C4C22×D15711yescharacteristic
86C8—3141no—
87C8—3141no—
88C22—6281no—
89C22—6281no—
90C22—6281no—
91C22C2×C22⋊D15711yescharacteristic
92C4—22no—
93C4—21no—
94C4—21no—
95C4—41no—
96C4—6281no—
97C4C2×D62811yescharacteristic
98C4#1457895411yescharacteristic
99C2—12561no—
100C2#1909774511yescharacteristic
101C2#1909779111yescharacteristic
102C2#1909780211yescharacteristic
subgroupG/H
centerC22C2×C22⋊D157
commutator, cosocleC2×C4×C157C23
FrattiniC2×C4C22×D157
FittingC4×Q8×C157C2
socleC22×C157C2×D4
prime radicalC2×D628C22
hypercenterC4×Q8D157
hypocenterC157#464
LCSG ▷ C2×C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
1. C2×#14578944C2semidirect
4. C4⋊#11929434C2semidirect
5. #19097694C2semidirect
7. C4×Q8×C157C2semidirect
51. C157#464semidirect
56. C4×Q8D157semidirect