Finite Group Databasebeta

← #34115282

Subgroups — #34115282

Order 20096.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23758182C211yesmaximal, characteristic
2#23758180C211yesmaximal, characteristic
3#23757630C211yesmaximal, characteristic
4#19097832—21no—
5#19097830—21no—
6#19097759C2211yescharacteristic
7#19097694—21no—
8#19097691—21no—
9C4×#11929434C411yescharacteristic, complemented
10#125×C157C411yescharacteristic, complemented
11#14578963—41no—
12C22⋊#10597845—41no—
13C2×Dic314D411yescharacteristic
14C2×D628D411yescharacteristic
15C2×#11929434—21no—
16#14578931—41no—
17C4⋊C4×C157—21no—
18C4⋊C4×C157—41no—
19C42×C157C2×C411yescharacteristic
20C2×#10597845—81no—
21#11929441—81no—
22C22×D157—21no—
23Dic314—41no—
24D628—41no—
25C2×Dic157—21no—
26#11929434—41no—
27C2×C4×C157—21no—
28C2×C4×C157—41no—
29C2×C4×C157C22⋊C411yescharacteristic
30C22×C157#9911yescharacteristic
31C2×D157—41no—
32C2×D157—81no—
33#10597845—161no—
34C4×C157—21no—
35C4×C157—41no—
36C4×C157—81no—
37Dic157—41no—
38C2×C157—21no—
39C2×C157#35411yescharacteristic
40D157—81no—
41C157#141411yescharacteristic, complemented, Sylow
42#1414—1571nomaximal, Sylow
43#488—1571no—
44#355—1571no—
45#354—1571no—
46#125#1059784511yescharacteristic, complemented
47#124—1571no—
48#103—3141no—
49#102—3141no—
50#101—3141no—
51#99—3141no—
52C4×C8—1571no—
53C2×Q8—1571no—
54C2×D4—1571no—
55M16—6281no—
56C2×C8—3141no—
57C4⋊C4—21no—
58C4⋊C4—41no—
59C22⋊C4—6281no—
60C22⋊C4—6281no—
61C42C2×#1059784511yescharacteristic
62C23—3141no—
63Q8—6281no—
64D4—6281no—
65C2×C4—21no—
66C2×C4—41no—
67C2×C4—3141no—
68C2×C4—12561no—
69C2×C4C22⋊#1059784511yescharacteristic
70C8—6281no—
71C8—12561no—
72C22—6281no—
73C22—12561no—
74C22#1909782911yescharacteristic
75C4—21no—
76C4—41no—
77C4—81no—
78C4—6281no—
79C4—25121no—
80C2—21no—
81C2—12561no—
82C2#2375817911yescharacteristic
subgroupG/H
centerC2#23758179
commutatorC42×C157C2×C4
FrattiniC42C2×#10597845
Fitting#125×C157C4
socleC2×C157#354
prime radicalC2×D628D4
cosocle#19097759C22
hypercenter#125#10597845
hypocenterC157#1414
LCSG ▷ C42×C157 ▷ C2×C4×C157 ▷ C22×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C42 ◁ #125

Complements

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

NH ≅ G/Ntype
9. C4×#11929434C4semidirect
10. #125×C157C4semidirect
41. C157#1414semidirect
46. #125#10597845semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#237581822
#237581802
#237576302
#1414157