Finite Group Databasebeta

← M16×D13⋊C3 #11928271

Subgroups — M16×D13⋊C3 #11928271

Order 1248.

136 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 136 conjugacy classes of subgroups — too many to draw. Only its 69 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×C4×D13⋊C3C211yesmaximal, characteristic
2M16×C13⋊C3C211yesmaximal, characteristic, complemented
3#6099⋊C3C211yesmaximal, characteristic, complemented
4#6094⋊C3C212yesmaximal, complemented
5C8×D13⋊C3C212yesmaximal, complemented
6M16×D13C311yesmaximal, characteristic, complemented, Hall
7C22×D13⋊C3C411yescharacteristic
8C2×C4×C13⋊C3C2211yescharacteristic
9C2×Dic13⋊C3C411yescharacteristic
10C4×D13⋊C3C411yescharacteristic
11C4×D13⋊C3C411yescharacteristic
12C4×D13⋊C3C2211yescharacteristic
13C4×D13⋊C3C2211yescharacteristic
14C8×C13⋊C3C2212yescomplemented
15#1055⋊C3C2212yescomplemented
16C2×C4×D13C2×C311yescharacteristic
17C13×M16C2×C311yescharacteristic, complemented
18#6099C2×C311yescharacteristic, complemented
19#6094C2×C312yescomplemented
20C8×D13C2×C312yescomplemented
21C22×C13⋊C3C2×C411yescharacteristic
22C2×D13⋊C3—22no—
23C2×D13⋊C3C2×C411yescharacteristic
24C2×D13⋊C3C2×C411yescharacteristic
25C4×C13⋊C3C2×C411yescharacteristic
26C4×C13⋊C3C2311yescharacteristic
27Dic13⋊C3C2×C411yescharacteristic
28Dic13⋊C3C2×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×C13⋊C3—21no—
40C2×C13⋊C3C22×C411yescharacteristic
41D13⋊C3—21no—
42D13⋊C3M1612yesdirect 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—132no—
53C3×M16—131no—
54C3×M16—131no—
55C2×C3×C8—132no—
56C13⋊C3C2×M1611yescharacteristic, complemented, Hall
57C2×M16—131noSylow
58C2×C13—21no—
59C2×C13C22×C3×C411yescharacteristic
60D13—21no—
61D13C3×M1612yescomplemented
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×C4—131no—
69C3×C8—132no—
70C3×C8—132no—
71C22×C4—131no—
72M16—131no—
73M16—132no—
74M16D13⋊C311yescharacteristic, direct product factor
75C2×C8—132no—
76C13C2×C3×M1611yescharacteristic, complemented, Sylow
77C22×C3—131no—
78C22×C3—131no—
79C22×C3—131no—
80C22×C3—262no—
81C3×C4—131no—
82C3×C4—131no—
83C3×C4—131no—
84C3×C4—131no—
85C23—131no—
86C2×C4—131no—
87C2×C4—131no—
88C2×C4—131no—
89C2×C4—131no—
90C2×C4—131no—
91C2×C4C2×D13⋊C311yescharacteristic
92C8—132no—
93C8C2×D13⋊C312yescomplemented
94C2×C3—132no—
95C2×C3—131no—
96C2×C3—261no—
97C2×C3—261no—
98C22—131no—
99C22—131no—
100C22—262no—
101C22C4×D13⋊C311yescharacteristic
102C4—131no—
103C4—131no—
104C4C4×D13⋊C311yescharacteristic
105C4C22×D13⋊C311yescharacteristic
106C3—131noSylow
107C2—21no—
108C2—132no—
109C2—261no—
110C2C2×C4×D13⋊C311yescharacteristic
subgroupG/H
center, FrattiniC4C22×D13⋊C3
commutator, socleC2×C13C22×C3×C4
FittingC13×M16C2×C3
prime radicalC22×D13⋊C3C4
cosocleC4×C13C23×C3
hypercenterM16D13⋊C3
hypocenterC13C2×C3×M16
LCSG ▷ C2×C13 ▷ C13
UCSC1 ◁ C4 ◁ M16

Complements

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

NH ≅ G/Ntype
2. M16×C13⋊C3C2semidirect
3. #6099⋊C3C2semidirect
4. #6094⋊C3C2semidirect
5. C8×D13⋊C3C2semidirect
6. M16×D13C3semidirect
14. C8×C13⋊C3C22semidirect
15. #1055⋊C3C22semidirect
17. C13×M16C2×C3semidirect
18. #6099C2×C3semidirect
19. #6094C2×C3semidirect
20. C8×D13C2×C3semidirect
36. C8×C13C22×C3semidirect
37. #1055C22×C3semidirect
42. D13⋊C3M16direct (N × H)
56. C13⋊C3C2×M16semidirect
61. D13C3×M16semidirect
74. M16D13⋊C3direct (N × H)
76. C13C2×C3×M16semidirect
93. C8C2×D13⋊C3semidirect

Maximal subgroups

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

subgroupindex
C2×C4×D13⋊C32
M16×C13⋊C32
#6099⋊C32
#6094⋊C32
C8×D13⋊C32
M16×D133
C2×C3×M1613