Finite Group Databasebeta

← #14516478

Subgroups — #14516478

Order 1944.

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

normal subgroups only

This group has 119 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#11757428C211yesmaximal, characteristic, complemented
2#10620045—31nomaximal
3((C22⋊C27)⋊C2)⋊C3—32nomaximal
4C3×#6171—31nomaximal
5#92213—41nomaximal
6#66436D311yescharacteristic
7C22×C3×C27D311yescharacteristic, complemented
8C2×C3×D27—31no—
9#66353D312yescomplemented
10C3×Dic27—31no—
11#6872—41noSylow
12C9⋊S4—31no—
13(C3⋊S4)⋊C3—91no—
14((C22⋊C9)⋊C2)⋊C3—92no—
15C3×#611—91no—
16(C22⋊C27)⋊C2—32no—
17#6171—31no—
18#4207—121no—
19C2×C3×C27—31no—
20D27⋊C3—122no—
21C3×D27—61no—
22C22×C3×C9C3⋊D311yescharacteristic
23C2×C3×D9—91no—
24C22⋊H(3,𝔽3)D911yescharacteristic
25#1094D912yes—
26C9⋊A4—61no—
27C9×A4—31no—
28C3×Dic9—91no—
29C22×C27—31no—
30C2×D27—31no—
31C22⋊C27—32no—
32Dic27—31no—
33#737—41no—
34C27⋊C3—42no—
35C3×C27S411yescharacteristic, complemented
36C3⋊S4—91no—
37C3×#67—271no—
38(C22⋊C9)⋊C2—92no—
39#611—91no—
40C2×C3×C9—31no—
41C3⋊D9—121no—
42AGL(1,ℤ/9)—362no—
43(C3⋊D3)⋊C3—361no—
44C3×D9—181no—
45C2×C27—31no—
46C2×C27—61no—
47D27—61no—
48D27—122no—
49C22×C32C3⋊D911yescharacteristic
50C2×C3×D3—271no—
51C3×A4—31no—
52C3×Dic3—271no—
53C22×C9—21no—
54C22×C9#27211yescharacteristic
55C2×D9—91no—
56C22⋊C9—32no—
57Dic9—91no—
583−1+2—42no—
593−1+2—241no—
60H(3,𝔽3)—41no—
61C3×C9—121no—
62C3×C9C3⋊S411yescharacteristic
63C27—31no—
64C27—122no—
65S4—811no—
66C3×D4—811no—
67#67—271no—
68C2×C32—31no—
69C3⋊D3—361no—
70C3×D3—541no—
71C2×C9—31no—
72C2×C9—61no—
73D9—181no—
74D9—362no—
75C22×C3—31no—
76C22×C3—811no—
77C22×C3#418111yescharacteristic
78C2×D3—271no—
79A4—91no—
80C3×C4—811no—
81Dic3—271no—
82C32—121no—
83C32C9⋊S411yescharacteristic
84C9—21no—
85C9—122no—
86C9#625811yescharacteristic
87D4—811noSylow
88C2×C3—31no—
89C2×C3—31no—
90C2×C3—61no—
91C2×C3—1621no—
92D3—541no—
93D3—3241no—
94C22—811no—
95C22#9221311yescharacteristic, complemented
96C4—811no—
97C3—31no—
98C3—361no—
99C3#1061975411yescharacteristic
100C2—31no—
101C2—1621no—
subgroupG/H
center, hypercenterC1G
commutator, cosocle, hypocenter#11757428C2
FrattiniC3×C9C3⋊S4
FittingC22×C3×C27D3
socleC22×C3#4181
LCSG ▷ #11757428
UCSC1

Complements

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

NH ≅ G/Ntype
1. #11757428C2semidirect
7. C22×C3×C27D3semidirect
9. #66353D3semidirect
35. C3×C27S4semidirect
95. C22#92213semidirect

Maximal subgroups

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

subgroupindex
#117574282
#106200453
((C22⋊C27)⋊C2)⋊C33
C3×#61713
#922134