Finite Group Databasebeta

← #11757847⋊C2 #14518083

Subgroups — #11757847⋊C2 #14518083

Order 1944.

217 conjugacy classes of subgroups; only the 34 normal subgroups are shown.

normal subgroups only

This group has 217 conjugacy classes of subgroups — too many to draw. Only its 34 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#11757847C211yesmaximal, characteristic, complemented
2#10619980—31nomaximal
3C9⋊((C22⋊C9)⋊C2)C311yesmaximal, characteristic, complemented
4#10619746—33nomaximal
5#6899⋊C2—41nomaximal
6C22×C3×3−1+2D311yescharacteristic
7C2×C3⋊AGL(1,ℤ/9)—31no—
8C3⋊(3−1+2⋊C4)—31no—
9C32⋊(C22⋊C9)D313yes—
10C9⋊(C22⋊C9)—21no—
11(C22⋊C9)⋊C9—23no—
12C9×C22⋊C9C2×C311yescharacteristic, complemented
13#6899—41noSylow
14C3×#638—91no—
15C3⋊((C22⋊C9)⋊C2)—33no—
16#6233—31no—
17#611⋊C3—93no—
18C2×C3×3−1+2—31no—
19C3⋊AGL(1,ℤ/9)—61no—
20C9⋊D9—41no—
21#4169—123no—
22C22×C33C3⋊D311yescharacteristic
23C2×C3×C3⋊D3—91no—
24C3×C3⋊Dic3—91no—
25C22×3−1+2—33no—
26C22×C3×C9—21no—
27C22×C3×C9C3×D311yescharacteristic
28C2×C3⋊D9—31no—
29C2×AGL(1,ℤ/9)—93no—
30C3×C22⋊C9—23no—
31C3×C22⋊C9C3×D313yes—
32C3⋊Dic9—31no—
333−1+2⋊C4—93no—
34C3×3−1+2S411yescharacteristic
35C9⋊C9—83no—
36C9⋊C9—81no—
37C32⋊C9—43no—
38C92—41no—
39#638—91no—
40C3×#67—271no—
41C3×#67—273no—
42(C22⋊C9)⋊C2—273no—
43#611—93no—
44C2×C33—31no—
45C3×C3⋊D3—181no—
46C2×3−1+2—33no—
47C2×3−1+2—63no—
48C2×C3×C9—31no—
49C2×C3×C9—61no—
50C3⋊D9—61no—
51C3⋊D9—123no—
52AGL(1,ℤ/9)—183no—
53C22×C32—31no—
54C22×C32—33no—
55C22×C32C3×C3⋊D311yescharacteristic
56C2×C3⋊D3—91no—
57C2×C3×D3—271no—
58C2×C3×D3—273no—
59C3⋊Dic3—91no—
60C3×Dic3—271no—
61C3×Dic3—273no—
62C22×C9—61no—
63C22×C9AGL(1,ℤ/9)13yes—
64C2×D9—93no—
65C22⋊C9—33no—
66C22⋊C9—63no—
67Dic9—93no—
68C33C3⋊S411yescharacteristic
693−1+2—33no—
70C3×C9—21no—
71C3×C9—43no—
72C3×C9—83no—
73C3×C9C3×S411yescharacteristic
74C3×D4—811no—
75#67—271no—
76#67—273no—
77C2×C32—31no—
78C2×C32—31no—
79C2×C32—61no—
80C2×C32—93no—
81C3⋊D3—181no—
82C3×D3—541no—
83C3×D3—543no—
84C2×C9—33no—
85C2×C9—63no—
86D9—183no—
87D9—1083no—
88C22×C3—91no—
89C22×C3—811no—
90C22×C3C3⋊AGL(1,ℤ/9)11yescharacteristic
91C22×C3#420713yes—
92C2×D3—271no—
93C2×D3—273no—
94C3×C4—811no—
95Dic3—271no—
96Dic3—273no—
97C32—33no—
98C32—31no—
99C32C3×C3⋊S411yescharacteristic
100C9—61no—
101C9—123no—
102C9—243no—
103C9((C22⋊C9)⋊C2)⋊C313yes—
104D4—811noSylow
105C2×C3—33no—
106C2×C3—31no—
107C2×C3—91no—
108C2×C3—181no—
109C2×C3—1621no—
110D3—543no—
111D3—541no—
112C22—811no—
113C22#6899⋊C211yescharacteristic, complemented
114C4—811no—
115C3—91no—
116C3#66440⋊C213yes—
117C3C3⋊(((C22⋊C9)⋊C2)⋊C3)11yescharacteristic
118C2—31no—
119C2—1621no—
subgroupG/H
center, hypercenterC1G
commutator, cosocle, hypocenterC9×C22⋊C9C2×C3
FrattiniC32C3×C3⋊S4
FittingC22×C3×3−1+2D3
socleC22×C32C3×C3⋊D3
LCSG ▷ C9×C22⋊C9
UCSC1

Complements

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

NH ≅ G/Ntype
1. #11757847C2semidirect
3. C9⋊((C22⋊C9)⋊C2)C3semidirect
12. C9×C22⋊C9C2×C3semidirect
113. C22#6899⋊C2semidirect

Maximal subgroups

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

subgroupindex
#117578472
#106199803
C9⋊((C22⋊C9)⋊C2)3
#106197463
#6899⋊C24