Finite Group Databasebeta

← #23757494

Subgroups — #23757494

Order 10048.

112 conjugacy classes of subgroups; only the 39 normal subgroups are shown.

normal subgroups only

This group has 112 conjugacy classes of subgroups — too many to draw. Only its 39 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×Dic628C211yesmaximal, characteristic, complemented
2C2×#14578942C211yesmaximal, characteristic
3#19097758C211yesmaximal, characteristic
4#19097736C211yesmaximal, characteristic, complemented
5#19097700C211yesmaximal, characteristic, complemented
6#19097694C211yesmaximal, characteristic, complemented
7#102×C157C211yesmaximal, characteristic
8C2×Dic314C2211yescharacteristic
9C2×Dic314C2211yescharacteristic
10Dic628—22no—
11#14578942—22no—
12C2×#11929434C2211yescharacteristic
13#14578933—21no—
14C22⋊Dic157—21no—
15C22⋊Dic157—21no—
16C4×Dic157—21no—
17C4×Dic157C2211yescharacteristic
18C2×D4×C157C2211yescharacteristic
19C2×C8×C157C2211yescharacteristic
20C4⋊C4×C157C2211yescharacteristic
21Dic314—21no—
22Dic314—21no—
23Dic314—21no—
24Dic314D412yes—
25C2×Dic157—21no—
26C2×Dic157—21no—
27C2×Dic157D411yescharacteristic
28C2×Dic157D411yescharacteristic
29#11929434—21no—
30C23×C157—21no—
31D4×C157—21no—
32D4×C157—21no—
33C2×C4×C157—21no—
34C2×C4×C157C2311yescharacteristic
35C8×C157—21no—
36C22×C157—41no—
37C22×C157—41no—
38C22×C157—41no—
39C22×C157C2×D411yescharacteristic
40C4×C157—41no—
41C4×C157C2×D411yescharacteristic
42C4×C157#4111yescharacteristic
43Dic157—22no—
44Dic157—21no—
45Dic157—21no—
46Dic157—41no—
47C2×C157—81no—
48C2×C157#12111yescharacteristic
49C2×C157#13511yescharacteristic
50C2×C157#13711yescharacteristic
51C157#46411yescharacteristic, complemented, Sylow
52#464—1571nomaximal, Sylow
53C2×Q16—1571no—
54C2×SD16—1571no—
55#124—1571no—
56C4×Q8—1571no—
57C4⋊C8—1571no—
58#103—1571no—
59#102D15711yescharacteristic
60C2×Q8—1571no—
61C2×Q8—1571no—
62C2×D4C2×D15711yescharacteristic
63Q16—3142no—
64SD16—3142no—
65C2×C8—1571no—
66C2×C8C2×D15711yescharacteristic
67C4⋊C4—3141no—
68C4⋊C4C2×D15711yescharacteristic
69C22⋊C4—3141no—
70C22⋊C4—3141no—
71C42—3141no—
72C42—1571no—
73C23—21no—
74Q8—3141no—
75Q8—3141no—
76Q8—3141no—
77Q8—1572no—
78D4—21no—
79D4—21no—
80C2×C4—21no—
81C2×C4—3141no—
82C2×C4—3141no—
83C2×C4—1571no—
84C2×C4—1571no—
85C2×C4C22×D15711yescharacteristic
86C8—21no—
87C8—3141no—
88C22—41no—
89C22—41no—
90C22—41no—
91C22D4×D15711yescharacteristic
92C4—41no—
93C4—3142no—
94C4—3141no—
95C4—3141no—
96C4—6281no—
97C4D4×D15711yescharacteristic
98C4#1457895411yescharacteristic
99C2—81no—
100C2#1909774411yescharacteristic
101C2#1909779011yescharacteristic
102C2#1909780011yescharacteristic
subgroupG/H
centerC22D4×D157
commutator, cosocleC2×C4×C157C23
FrattiniC2×C4C22×D157
Fitting#102×C157C2
socleC22×C157C2×D4
prime radicalC2×D4×C157C22
hypercenter#102D157
hypocenterC157#464
LCSG ▷ C2×C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C22 ◁ C2×C4 ◁ #102

Complements

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

NH ≅ G/Ntype
1. C2×Dic628C2semidirect
4. #19097736C2semidirect
5. #19097700C2semidirect
6. #19097694C2semidirect
51. C157#464semidirect