Finite Group Databasebeta

← #14518023

Subgroups — #14518023

Order 1944.

151 conjugacy classes of subgroups; only the 30 normal subgroups are shown.

normal subgroups only

This group has 151 conjugacy classes of subgroups — too many to draw. Only its 30 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#11757795C211yesmaximal, characteristic, complemented
2#10620045—31nomaximal
3A4⋊D27C311yesmaximal, characteristic, complemented
4((C22⋊C27)⋊C2)⋊C3—32nomaximal
5C3×#6171—31nomaximal
6#92318—41nomaximal
7#66436D311yescharacteristic
8C22×C3×C27D311yescharacteristic, complemented
9C2×C3×D27—31no—
10#66353D312yescomplemented
11C27⋊A4—21no—
12C27⋊A4—22no—
13A4×C27—21no—
14A4×C27C2×C311yescharacteristic, complemented
15C3×Dic27—31no—
16#6903—41noSylow
17C9⋊S4—31no—
18(C3⋊S4)⋊C3—91no—
19((C22⋊C9)⋊C2)⋊C3—92no—
20C3×#611—91no—
21(C22⋊C27)⋊C2—32no—
22#6171—31no—
23#4207—121no—
24C2×C3×C27—31no—
25C3⋊D27—41no—
26D27⋊C3—122no—
27C3×D27—61no—
28C22×C3×C9C3⋊D311yescharacteristic
29C2×C3×D9—91no—
30C22⋊H(3,𝔽3)D911yescharacteristic
31#1094D912yes—
32C9⋊A4—21no—
33C9⋊A4—22no—
34C9×A4—21no—
35C9×A4C3×D311yescharacteristic
36C3×Dic9—91no—
37C22×C27—21no—
38C22×C27C3×D311yescharacteristic
39C2×D27—31no—
40C22⋊C27—22no—
41C22⋊C27C3×D312yes—
42Dic27—31no—
43#737—41no—
44C27⋊C3—42no—
45C27⋊C3—82no—
46C27⋊C3—81no—
47C3×C27—41no—
48C3×C27—81no—
49C3×C27S411yescharacteristic, complemented
50C3⋊S4—91no—
51C3×#67—271no—
52(C22⋊C9)⋊C2—92no—
53#611—91no—
54C2×C3×C9—31no—
55C3⋊D9—121no—
56AGL(1,ℤ/9)—362no—
57(C3⋊D3)⋊C3—361no—
58C3×D9—181no—
59C2×C27—31no—
60C2×C27—61no—
61D27—61no—
62D27—122no—
63C22×C32C3⋊D911yescharacteristic
64C2×C3×D3—271no—
65C3×A4—21no—
66C3×A4C3×D911yescharacteristic
67C3×Dic3—271no—
68C22×C9—21no—
69C22×C9C3×C3⋊D311yescharacteristic
70C2×D9—91no—
71C22⋊C9—22no—
72C22⋊C9C3×D912yes—
73Dic9—91no—
743−1+2—42no—
753−1+2—82no—
763−1+2—81no—
77H(3,𝔽3)—41no—
78C3×C9—41no—
79C3×C9—81no—
80C3×C9C3⋊S411yescharacteristic
81C27—21no—
82C27—42no—
83C27—82no—
84C27C3×S411yescharacteristic
85S4—811no—
86C3×D4—811no—
87#67—271no—
88C2×C32—31no—
89C3⋊D3—361no—
90C3×D3—541no—
91C2×C9—31no—
92C2×C9—61no—
93D9—181no—
94D9—362no—
95C22×C3—31no—
96C22×C3—811no—
97C22×C3C3×C3⋊D911yescharacteristic
98C2×D3—271no—
99A4—31no—
100A4—61no—
101C3×C4—811no—
102Dic3—271no—
103C32—41no—
104C32—81no—
105C32C9⋊S411yescharacteristic
106C9—21no—
107C9—42no—
108C9—82no—
109C9C3×C3⋊S411yescharacteristic
110D4—811noSylow
111C2×C3—31no—
112C2×C3—31no—
113C2×C3—61no—
114C2×C3—1621no—
115D3—541no—
116D3—3241no—
117C22—811no—
118C22#9231811yescharacteristic, complemented
119C4—811no—
120C3—31no—
121C3—121no—
122C3—241no—
123C3C3×C9⋊S411yescharacteristic
124C2—31no—
125C2—1621no—
subgroupG/H
center, hypercenterC1G
commutator, cosocle, hypocenterA4×C27C2×C3
FrattiniC9C3×C3⋊S4
FittingC22×C3×C27D3
socleC22×C3C3×C3⋊D9
LCSG ▷ A4×C27
UCSC1

Complements

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

NH ≅ G/Ntype
1. #11757795C2semidirect
3. A4⋊D27C3semidirect
8. C22×C3×C27D3semidirect
10. #66353D3semidirect
14. A4×C27C2×C3semidirect
49. C3×C27S4semidirect
118. C22#92318semidirect

Maximal subgroups

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

subgroupindex
#117577952
#106200453
A4⋊D273
((C22⋊C27)⋊C2)⋊C33
C3×#61713
#923184