Finite Group Databasebeta

← #11757431⋊C2 #14516480

Subgroups — #11757431⋊C2 #14516480

Order 1944.

138 conjugacy classes of subgroups; only the 20 normal subgroups are shown.

normal subgroups only

This group has 138 conjugacy classes of subgroups — too many to draw. Only its 20 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
1#11757431C211yesmaximal, characteristic, complemented
2C3×C9⋊S4—31nomaximal
3((C22⋊C27)⋊C2)⋊C3—32nomaximal
4#6171⋊C3—31nomaximal
5#6869⋊C2—41nomaximal
6C3×C9×A4D311yescharacteristic
7C22×C27⋊C3D311yescharacteristic, complemented
8C2×D27⋊C3—31no—
9#66353D312yescomplemented
10(C27⋊C3)⋊C4—31no—
11#6869—41noSylow
12C3×C3⋊S4—91no—
13C9⋊S4—31no—
14C3×(C22⋊C9)⋊C2—92no—
15C3×#611—91no—
16(C22⋊C27)⋊C2—32no—
17#6171—31no—
18C3×C3⋊D9—121no—
19C2×C27⋊C3—31no—
20D27⋊C3—61no—
21D27⋊C3—122no—
22C32×A4D911yescharacteristic
23C22×C3×C9C3⋊D311yescharacteristic
24C2×C3×D9—91no—
25C3×C22⋊C9D912yes—
26C9×A4—31no—
27C9×A4—61no—
28C3×Dic9—91no—
29C22×C27—31no—
30C2×D27—31no—
31C22⋊C27—32no—
32Dic27—31no—
33C32×C9—41no—
34C27⋊C3—42no—
35C27⋊C3S411yescharacteristic, complemented
36C3⋊S4—91no—
37C3×S4—273no—
38C3×#67—271no—
39(C22⋊C9)⋊C2—92no—
40#611—91no—
41C3×C3⋊D3—361no—
42C2×C3×C9—31no—
43C3⋊D9—121no—
44C3×D9—181no—
45C3×D9—362no—
46C2×C27—31no—
47C2×C27—61no—
48D27—61no—
49D27—122no—
50C22×C32C3⋊D911yescharacteristic
51C2×C3×D3—271no—
52C3×A4—31no—
53C3×A4—33no—
54C3×Dic3—271no—
55C22×C9—21no—
56C22×C9#27211yescharacteristic
57C2×D9—91no—
58C22⋊C9—32no—
59Dic9—91no—
60C33—41no—
61C3×C9—42no—
62C3×C9—121no—
63C3×C9—241no—
64C3×C9C3⋊S411yescharacteristic
65C27—31no—
66C27—122no—
67S4—273no—
68C3×D4—811no—
69#67—271no—
70C2×C32—31no—
71C3⋊D3—361no—
72C3×D3—541no—
73C3×D3—1083no—
74C2×C9—31no—
75C2×C9—61no—
76D9—181no—
77D9—362no—
78C22×C3—31no—
79C22×C3—811no—
80C22×C3#418111yescharacteristic
81C2×D3—271no—
82A4—33no—
83C3×C4—811no—
84Dic3—271no—
85C32—123no—
86C32—121no—
87C32C9⋊S411yescharacteristic
88C9—21no—
89C9—122no—
90C9#625811yescharacteristic
91D4—811noSylow
92C2×C3—31no—
93C2×C3—91no—
94C2×C3—1621no—
95D3—541no—
96D3—1083no—
97C22—811no—
98C22#6869⋊C211yescharacteristic, complemented
99C4—811no—
100C3—31no—
101C3—123no—
102C3#1061975411yescharacteristic
103C2—31no—
104C2—1621no—
subgroupG/H
center, hypercenterC1G
commutator, cosocle, hypocenter#11757431C2
FrattiniC3×C9C3⋊S4
FittingC22×C27⋊C3D3
socleC22×C3#4181
LCSG ▷ #11757431
UCSC1

Complements

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

NH ≅ G/Ntype
1. #11757431C2semidirect
7. C22×C27⋊C3D3semidirect
9. #66353D3semidirect
35. C27⋊C3S4semidirect
98. C22#6869⋊C2semidirect

Maximal subgroups

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

subgroupindex
#117574312
C3×C9⋊S43
((C22⋊C27)⋊C2)⋊C33
#6171⋊C33
#6869⋊C24