Finite Group Databasebeta

← #14517678

Subgroups — #14517678

Order 1944.

428 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 428 conjugacy classes of subgroups — too many to draw. Only its 93 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
1C22×#6900C211yesmaximal, characteristic, complemented
2C2×#92314C211yesmaximal, characteristic, complemented
3#11757618C211yesmaximal, characteristic, complemented
4#10619980—34nomaximal
5#10619673C311yesmaximal, characteristic, complemented
6C2×#6900—21no—
7C2×#6900C2211yescharacteristic
8#92314—21no—
9C22×C3×3−1+2D314yes—
10C2×C3⋊AGL(1,ℤ/9)—34no—
11C3⋊(3−1+2⋊C4)—34no—
12C22×C9⋊C9—24no—
13C22×C92C2×C311yescharacteristic, complemented
14C2×C9⋊D9C2×C311yescharacteristic, complemented
15C9⋊Dic9C2×C311yescharacteristic, complemented
16#6900D411yescharacteristic, complemented, Sylow
17C3×#638—91no—
18#6233—34no—
19#611⋊C3—912no—
20C2×C3×3−1+2—24no—
21C2×C3×3−1+2C2×D314yes—
22C3⋊AGL(1,ℤ/9)—64no—
23C2×C9⋊C9—28no—
24C2×C9⋊C9—24no—
25C2×C92—21no—
26C2×C92C22×C311yescharacteristic
27C9⋊D9—21no—
28C22×C33C3⋊D311yescharacteristic
29C2×C3×C3⋊D3—91no—
30C3×C3⋊Dic3—91no—
31C22×3−1+2—312no—
32C22×C3×C9—24no—
33C22×C3×C9C3×D314yes—
34C2×C3⋊D9—34no—
35C2×AGL(1,ℤ/9)—912no—
36C3⋊Dic9—34no—
373−1+2⋊C4—912no—
38C3×3−1+2#6714yes—
39C9⋊C9—24no—
40C92C3×D411yescharacteristic, complemented
41#638—91no—
42C3×#67—274no—
43#611—912no—
44C2×C33—21no—
45C2×C33C2×C3⋊D311yescharacteristic
46C3×C3⋊D3—181no—
47C2×3−1+2—312no—
48C2×3−1+2—612no—
49C2×C3×C9—24no—
50C2×C3×C9—28no—
51C2×C3×C9—24no—
52C2×C3×C9C2×C3×D314yes—
53C3⋊D9—64no—
54AGL(1,ℤ/9)—1812no—
55C22×C32—34no—
56C22×C32C3×C3⋊D311yescharacteristic
57C2×C3⋊D3—91no—
58C2×C3×D3—274no—
59C3⋊Dic3—91no—
60C3×Dic3—274no—
61C22×C9—64no—
62C22×C9AGL(1,ℤ/9)112yescomplemented
63C2×D9—912no—
64Dic9—912no—
65C33#63811yescharacteristic
663−1+2—312no—
67C3×C9—24no—
68C3×C9C3×#6714yes—
69C3×D4—811no—
70#67—274no—
71C2×C32—21no—
72C2×C32—34no—
73C2×C32—64no—
74C2×C32C2×C3×C3⋊D311yescharacteristic
75C3⋊D3—181no—
76C3×D3—544no—
77C2×C9—212no—
78C2×C9—68no—
79C2×C9—64no—
80C2×C9C2×AGL(1,ℤ/9)112yes—
81D9—1812no—
82C22×C3—91no—
83C22×C3—811no—
84C22×C3C3⋊AGL(1,ℤ/9)14yes—
85C2×D3—274no—
86C3×C4—811no—
87Dic3—274no—
88C32—34no—
89C32C3×#63811yescharacteristic
90C9—64no—
91C9#611⋊C3112yescomplemented
92D4—811noSylow
93C2×C3—24no—
94C2×C3—91no—
95C2×C3—181no—
96C2×C3—1621no—
97C2×C3C2×C3⋊AGL(1,ℤ/9)14yes—
98D3—544no—
99C22—811no—
100C22#9231411yescharacteristic, complemented
101C4—811no—
102C3—91no—
103C3#1061998014yes—
104C2—21no—
105C2—1621no—
106C2C2×#9231411yescharacteristic
subgroupG/H
centerC2C2×#92314
commutator, cosocleC2×C92C22×C3
Frattini, socleC2×C32C2×C3×C3⋊D3
FittingC22×#6900C2
hypercenterC22#92314
hypocenterC92C3×D4
LCSG ▷ C2×C92 ▷ C92
UCSC1 ◁ C2 ◁ C22

Complements

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

NH ≅ G/Ntype
1. C22×#6900C2semidirect
2. C2×#92314C2semidirect
3. #11757618C2semidirect
5. #10619673C3semidirect
13. C22×C92C2×C3semidirect
14. C2×C9⋊D9C2×C3semidirect
15. C9⋊Dic9C2×C3semidirect
16. #6900D4semidirect
40. C92C3×D4semidirect
62. C22×C9AGL(1,ℤ/9)semidirect
91. C9#611⋊C3semidirect
100. C22#92314semidirect

Maximal subgroups

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

subgroupindex
C22×#69002
C2×#923142
#117576182
#106199803
#106196733