Finite Group Databasebeta

← #11757433⋊C2 #14516482

Subgroups — #11757433⋊C2 #14516482

Order 1944.

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

normal subgroups only

This group has 118 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#11757433C211yesmaximal, characteristic, complemented
2#10620045—31nomaximal
3C3×(C22⋊C27)⋊C2—31nomaximal
4((C22⋊C27)⋊C2)⋊C3—31nomaximal
5#6171⋊C3—31nomaximal
6#92213—41nomaximal
7#66436D311yescharacteristic
8C22×C27⋊C3D311yescharacteristic, complemented
9C2×D27⋊C3—31no—
10#66353D311yescharacteristic, complemented
11C3×C22⋊C27D311yescharacteristic, complemented
12(C27⋊C3)⋊C4—31no—
13#6872—41noSylow
14C9⋊S4—31no—
15(C3⋊S4)⋊C3—91no—
16((C22⋊C9)⋊C2)⋊C3—92no—
17C3×#611—91no—
18(C22⋊C27)⋊C2—31no—
19(C22⋊C27)⋊C2—31no—
20#6171—31no—
21#4207—121no—
22C2×C27⋊C3—31no—
23D27⋊C3—61no—
24D27⋊C3—121no—
25C3×D27—121no—
26C22×C3×C9C3⋊D311yescharacteristic
27C2×C3×D9—91no—
28C22⋊H(3,𝔽3)D911yescharacteristic
29#1094D912yes—
30C9⋊A4—61no—
31C9×A4—31no—
32C3×Dic9—91no—
33C22×C27—31no—
34C2×D27—31no—
35C22⋊C27—31no—
36C22⋊C27—31no—
37Dic27—31no—
38#737—41no—
39C27⋊C3—41no—
40C27⋊C3S411yescharacteristic, complemented
41C3×C27—41no—
42C3⋊S4—91no—
43C3×#67—271no—
44(C22⋊C9)⋊C2—92no—
45#611—91no—
46C2×C3×C9—31no—
47C3⋊D9—121no—
48AGL(1,ℤ/9)—362no—
49(C3⋊D3)⋊C3—361no—
50C3×D9—181no—
51C2×C27—31no—
52C2×C27—61no—
53D27—61no—
54D27—121no—
55D27—121no—
56C22×C32C3⋊D911yescharacteristic
57C2×C3×D3—271no—
58C3×A4—31no—
59C3×Dic3—271no—
60C22×C9—21no—
61C22×C9#27211yescharacteristic
62C2×D9—91no—
63C22⋊C9—32no—
64Dic9—91no—
653−1+2—42no—
663−1+2—241no—
67H(3,𝔽3)—41no—
68C3×C9—121no—
69C3×C9C3⋊S411yescharacteristic
70C27—31no—
71C27—121no—
72C27—121no—
73S4—811no—
74C3×D4—811no—
75#67—271no—
76C2×C32—31no—
77C3⋊D3—361no—
78C3×D3—541no—
79C2×C9—31no—
80C2×C9—61no—
81D9—181no—
82D9—362no—
83C22×C3—31no—
84C22×C3—811no—
85C22×C3#418111yescharacteristic
86C2×D3—271no—
87A4—91no—
88C3×C4—811no—
89Dic3—271no—
90C32—121no—
91C32C9⋊S411yescharacteristic
92C9—21no—
93C9—122no—
94C9#625811yescharacteristic
95D4—811noSylow
96C2×C3—31no—
97C2×C3—91no—
98C2×C3—1621no—
99D3—541no—
100D3—3241no—
101C22—811no—
102C22#9221311yescharacteristic, complemented
103C4—811no—
104C3—31no—
105C3—361no—
106C3#1061975411yescharacteristic
107C2—31no—
108C2—1621no—
subgroupG/H
center, hypercenterC1G
commutator, cosocle, hypocenter#11757433C2
FrattiniC3×C9C3⋊S4
FittingC22×C27⋊C3D3
socleC22×C3#4181
LCSG ▷ #11757433
UCSC1

Complements

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

NH ≅ G/Ntype
1. #11757433C2semidirect
8. C22×C27⋊C3D3semidirect
10. #66353D3semidirect
11. C3×C22⋊C27D3semidirect
40. C27⋊C3S4semidirect
102. C22#92213semidirect

Maximal subgroups

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

subgroupindex
#117574332
#106200453
C3×(C22⋊C27)⋊C23
((C22⋊C27)⋊C2)⋊C33
#6171⋊C33
#922134