Finite Group Databasebeta

← C3×D13⋊M16 #11929169

Subgroups — C3×D13⋊M16 #11929169

Order 1248.

136 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 136 conjugacy classes of subgroups — too many to draw. Only its 72 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
2C3×#6122C212yesmaximal, complemented
3C3×#6118C212yesmaximal, complemented
4C3×D13⋊C8C212yesmaximal, complemented
5D13⋊M16C311yesmaximal, characteristic, direct product factor, 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×D13C2×C311yescharacteristic
15#6122C2×C312yescomplemented
16#6118C2×C312yescomplemented
17D13⋊C8C2×C312yescomplemented
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×D13C3×C411yescharacteristic
27C2×C4×C13C3×C411yescharacteristic
28C2×Dic13C22×C311yescharacteristic
29C4×D13C3×C411yescharacteristic
30C4×D13C3×C411yescharacteristic
31C4×D13C22×C311yescharacteristic
32C4×D13C22×C311yescharacteristic
33#1057C22×C314yescomplemented
34C2×C3×M16—131nomaximal, Hall
35C2×C3×C13—21no—
36C2×C3×C13C22×C411yescharacteristic
37C3×D13—21no—
38C3×D13M1612yescomplemented
39C22×C13C2×C3×C411yescharacteristic
40C2×D13—22no—
41C2×D13C2×C3×C411yescharacteristic
42C2×D13C2×C3×C411yescharacteristic
43C4×C13C2×C3×C411yescharacteristic
44C4×C13C2×C3×C411yescharacteristic
45Dic13C2×C3×C411yescharacteristic
46Dic13C23×C311yescharacteristic
47C22×C3×C4—131no—
48C3×M16—132no—
49C3×M16—132no—
50C2×C3×C8—132no—
51C3×C13C2×M1611yescharacteristic, complemented, Hall
52C2×M16—131noSylow
53C2×C13—21no—
54C2×C13C22×C3×C411yescharacteristic
55D13—21no—
56D13C3×M1612yescomplemented
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—132no—
67M16—132no—
68C2×C8—132no—
69C13C2×C3×M1611yescharacteristic, 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—134no—
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, direct product factor, Sylow
99C2—21no—
100C2—132no—
101C2—261no—
102C2C22×C3×#26111yescharacteristic
subgroupG/H
centerC3×C4C2×#261
commutatorC2×C13C22×C3×C4
FrattiniC2C22×C3×#261
FittingC2×C3×C4×C13C4
socleC2×C3×C13C22×C4
prime radicalC22×C3×D13C4
cosocleDic13C23×C3
hypercenterC2×C3×C4#261
hypocenterC13C2×C3×M16
LCSG ▷ C2×C13 ▷ C13
UCSC1 ◁ C3×C4 ◁ C2×C3×C4

Complements

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

NH ≅ G/Ntype
2. C3×#6122C2semidirect
3. C3×#6118C2semidirect
4. C3×D13⋊C8C2semidirect
5. D13⋊M16C3direct (N × H)
13. C3×#1057C22semidirect
15. #6122C2×C3semidirect
16. #6118C2×C3semidirect
17. D13⋊C8C2×C3semidirect
33. #1057C22×C3semidirect
38. C3×D13M16semidirect
51. C3×C13C2×M16semidirect
56. D13C3×M16semidirect
69. C13C2×C3×M16semidirect
98. C3D13⋊M16direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×C4×D132
C3×#61222
C3×#61182
C3×D13⋊C82
D13⋊M163
C2×C3×M1613