Finite Group Databasebeta

← D13⋊#208 #11929182

Subgroups — D13⋊#208 #11929182

Order 1248.

136 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 136 conjugacy classes of subgroups — too many to draw. Only its 61 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×C3×C4×D13C211yesmaximal, characteristic
2#10597728C212yesmaximal, complemented
3#10597724C212yesmaximal, complemented
4D13⋊(C3⋊C8)C212yesmaximal, complemented
5D13⋊M16—31nomaximal, Hall
6C22×C3×D13C411yescharacteristic
7C2×C3×C4×C13C411yescharacteristic
8C2×C3×Dic13C2211yescharacteristic
9C3×C4×D13C411yescharacteristic
10C3×C4×D13C411yescharacteristic
11C3×C4×D13C2211yescharacteristic
12C3×C4×D13C2211yescharacteristic
13C3⋊#1057C2214yescomplemented
14C2×C4×D13D311yescharacteristic
15#6122—32no—
16#6118—32no—
17D13⋊C8—32no—
18C22×C3×C13C2×C411yescharacteristic
19C2×C3×D13—22no—
20C2×C3×D13C2×C411yescharacteristic
21C2×C3×D13C2×C411yescharacteristic
22C3×C4×C13C2×C411yescharacteristic
23C3×C4×C13C2×C411yescharacteristic
24C3×Dic13C2×C411yescharacteristic
25C3×Dic13C2311yescharacteristic
26C22×D13Dic311yescharacteristic
27C2×C4×C13Dic311yescharacteristic
28C2×Dic13C2×D311yescharacteristic
29C4×D13Dic311yescharacteristic
30C4×D13Dic311yescharacteristic
31C4×D13C2×D311yescharacteristic
32C4×D13C2×D311yescharacteristic
33#1057—34no—
34C2×#208—131nomaximal, Hall
35C2×C3×C13—21no—
36C2×C3×C13C22×C411yescharacteristic
37C3×D13—21no—
38C3×D13M1612yescomplemented
39C22×C13C2×Dic311yescharacteristic
40C2×D13—22no—
41C2×D13C2×Dic311yescharacteristic
42C2×D13C2×Dic311yescharacteristic
43C4×C13C2×Dic311yescharacteristic
44C4×C13C2×Dic311yescharacteristic
45Dic13C2×Dic311yescharacteristic
46Dic13C22×D311yescharacteristic
47C22×C3×C4—131no—
48#208—132no—
49#208—132no—
50C2×C3⋊C8—132no—
51C3×C13C2×M1611yescharacteristic, complemented, Hall
52C2×M16—391noSylow
53C2×C13—21no—
54C2×C13C22×Dic311yescharacteristic
55D13—21no—
56D13#20812yescomplemented
57C23×C3—131no—
58C2×C3×C4—131no—
59C2×C3×C4—131no—
60C2×C3×C4—131no—
61C2×C3×C4—131no—
62C2×C3×C4—131no—
63C2×C3×C4#26111yescharacteristic
64C3⋊C8—134no—
65C22×C4—131no—
66M16—392no—
67M16—392no—
68C2×C8—392no—
69C13C2×#20811yescharacteristic, complemented, Sylow
70C22×C3—131no—
71C22×C3—131no—
72C22×C3—262no—
73C22×C3C2×#26111yescharacteristic
74C3×C4—131no—
75C3×C4—131no—
76C3×C4C2×#26111yescharacteristic
77C3×C4C2×#26111yescharacteristic
78C23—131no—
79C2×C4—131no—
80C2×C4—131no—
81C2×C4—131no—
82C2×C4—131no—
83C2×C4—131no—
84C2×C4C3⋊#26111yescharacteristic
85C8—394no—
86C2×C3—21no—
87C2×C3—132no—
88C2×C3—261no—
89C2×C3C22×#26111yescharacteristic
90C22—131no—
91C22—131no—
92C22—262no—
93C22C2×C3⋊#26111yescharacteristic
94C4—131no—
95C4—131no—
96C4C2×C3⋊#26111yescharacteristic
97C4C2×C3⋊#26111yescharacteristic
98C3D13⋊M1611yescharacteristic, complemented, Sylow
99C2—21no—
100C2—132no—
101C2—261no—
102C2C22×C3⋊#26111yescharacteristic
subgroupG/H
centerC4C2×C3⋊#261
commutator, socleC2×C3×C13C22×C4
FrattiniC2C22×C3⋊#261
FittingC2×C3×C4×C13C4
prime radicalC22×C3×D13C4
cosocleC3×Dic13C23
hypercenterC2×C4C3⋊#261
hypocenterC3×C13C2×M16
LCSG ▷ C2×C3×C13 ▷ C3×C13
UCSC1 ◁ C4 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
2. #10597728C2semidirect
3. #10597724C2semidirect
4. D13⋊(C3⋊C8)C2semidirect
13. C3⋊#1057C22semidirect
38. C3×D13M16semidirect
51. C3×C13C2×M16semidirect
56. D13#208semidirect
69. C13C2×#208semidirect
98. C3D13⋊M16semidirect

Maximal subgroups

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

subgroupindex
C2×C3×C4×D132
#105977282
#105977242
D13⋊(C3⋊C8)2
D13⋊M163
C2×#20813