Finite Group Databasebeta

← C3×M16×D13 #11928796

Subgroups — C3×M16×D13 #11928796

Order 1248.

136 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 136 conjugacy classes of subgroups — too many to draw. Only its 78 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×C13×M16C211yesmaximal, characteristic, complemented
3C3×#6099C211yesmaximal, characteristic, complemented
4C3×#6094C212yesmaximal, complemented
5C3×C8×D13C212yesmaximal, complemented
6M16×D13C311yesmaximal, characteristic, direct product factor, Hall
7C22×C3×D13C411yescharacteristic
8C2×C3×C4×C13C2211yescharacteristic
9C2×C3×Dic13C411yescharacteristic
10C3×C4×D13C411yescharacteristic
11C3×C4×D13C411yescharacteristic
12C3×C4×D13C2211yescharacteristic
13C3×C4×D13C2211yescharacteristic
14C3×C8×C13C2212yescomplemented
15C3×#1055C2212yescomplemented
16C2×C4×D13C2×C311yescharacteristic
17C13×M16C2×C311yescharacteristic, complemented
18#6099C2×C311yescharacteristic, complemented
19#6094C2×C312yescomplemented
20C8×D13C2×C312yescomplemented
21C22×C3×C13C2×C411yescharacteristic
22C2×C3×D13—22no—
23C2×C3×D13C2×C411yescharacteristic
24C2×C3×D13C2×C411yescharacteristic
25C3×C4×C13C2×C411yescharacteristic
26C3×C4×C13C2311yescharacteristic
27C3×Dic13C2×C411yescharacteristic
28C3×Dic13C2×C411yescharacteristic
29C22×D13C3×C411yescharacteristic
30C2×C4×C13C22×C311yescharacteristic
31C2×Dic13C3×C411yescharacteristic
32C4×D13C3×C411yescharacteristic
33C4×D13C3×C411yescharacteristic
34C4×D13C22×C311yescharacteristic
35C4×D13C22×C311yescharacteristic
36C8×C13C22×C312yescomplemented
37#1055C22×C312yescomplemented
38C2×C3×M16—131nomaximal, Hall
39C2×C3×C13—21no—
40C2×C3×C13C22×C411yescharacteristic
41C3×D13—21no—
42C3×D13M1612yesdirect product factor
43C22×C13C2×C3×C411yescharacteristic
44C2×D13—22no—
45C2×D13C2×C3×C411yescharacteristic
46C2×D13C2×C3×C411yescharacteristic
47C4×C13C2×C3×C411yescharacteristic
48C4×C13C23×C311yescharacteristic
49Dic13C2×C3×C411yescharacteristic
50Dic13C2×C3×C411yescharacteristic
51C22×C3×C4—131no—
52C3×M16—131no—
53C3×M16—132no—
54C3×M16D1311yescharacteristic, direct product factor
55C2×C3×C8—132no—
56C3×C13C2×M1611yescharacteristic, complemented, Hall
57C2×M16—131noSylow
58C2×C13—21no—
59C2×C13C22×C3×C411yescharacteristic
60D13—21no—
61D13C3×M1612yesdirect product factor
62C23×C3—131no—
63C2×C3×C4—131no—
64C2×C3×C4—131no—
65C2×C3×C4—131no—
66C2×C3×C4—131no—
67C2×C3×C4—131no—
68C2×C3×C4C2×D1311yescharacteristic
69C3×C8—132no—
70C3×C8C2×D1312yescomplemented
71C22×C4—131no—
72M16—131no—
73M16—132no—
74M16C3×D1311yescharacteristic, direct product factor
75C2×C8—132no—
76C13C2×C3×M1611yescharacteristic, complemented, Sylow
77C22×C3—131no—
78C22×C3—131no—
79C22×C3—262no—
80C22×C3C4×D1311yescharacteristic
81C3×C4—131no—
82C3×C4—131no—
83C3×C4C4×D1311yescharacteristic
84C3×C4C22×D1311yescharacteristic
85C23—131no—
86C2×C4—131no—
87C2×C4—131no—
88C2×C4—131no—
89C2×C4—131no—
90C2×C4—131no—
91C2×C4C2×C3×D1311yescharacteristic
92C8—132no—
93C8C2×C3×D1312yescomplemented
94C2×C3—21no—
95C2×C3—132no—
96C2×C3—261no—
97C2×C3C2×C4×D1311yescharacteristic
98C22—131no—
99C22—131no—
100C22—262no—
101C22C3×C4×D1311yescharacteristic
102C4—131no—
103C4—131no—
104C4C3×C4×D1311yescharacteristic
105C4C22×C3×D1311yescharacteristic
106C3M16×D1311yescharacteristic, direct product factor, Sylow
107C2—21no—
108C2—132no—
109C2—261no—
110C2C2×C3×C4×D1311yescharacteristic
subgroupG/H
centerC3×C4C22×D13
commutatorC2×C13C22×C3×C4
FrattiniC4C22×C3×D13
FittingC3×C13×M16C2
socleC2×C3×C13C22×C4
prime radicalC22×C3×D13C4
cosocleC4×C13C23×C3
hypercenterC3×M16D13
hypocenterC13C2×C3×M16
LCSG ▷ C2×C13 ▷ C13
UCSC1 ◁ C3×C4 ◁ C3×M16

Complements

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

NH ≅ G/Ntype
2. C3×C13×M16C2semidirect
3. C3×#6099C2semidirect
4. C3×#6094C2semidirect
5. C3×C8×D13C2semidirect
6. M16×D13C3direct (N × H)
14. C3×C8×C13C22semidirect
15. C3×#1055C22semidirect
17. C13×M16C2×C3semidirect
18. #6099C2×C3semidirect
19. #6094C2×C3semidirect
20. C8×D13C2×C3semidirect
36. C8×C13C22×C3semidirect
37. #1055C22×C3semidirect
42. C3×D13M16direct (N × H)
54. C3×M16D13direct (N × H)
56. C3×C13C2×M16semidirect
61. D13C3×M16direct (N × H)
70. C3×C8C2×D13semidirect
74. M16C3×D13direct (N × H)
76. C13C2×C3×M16semidirect
93. C8C2×C3×D13semidirect
106. C3M16×D13direct (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×C13×M162
C3×#60992
C3×#60942
C3×C8×D132
M16×D133
C2×C3×M1613