Finite Group Databasebeta

← #11757854⋊C2 #14518079

Subgroups — #11757854⋊C2 #14518079

Order 1944.

240 conjugacy classes of subgroups; only the 28 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 28 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#11757854C211yesmaximal, characteristic, complemented
2C3×((C22⋊C9)⋊C2)⋊C3—33nomaximal
3C3×#611⋊C3—31nomaximal
4#66359⋊C2C311yesmaximal, characteristic, complemented
5#6912⋊C2—41nomaximal
6C22×C3×3−1+2D311yescharacteristic
7C2×C3×AGL(1,ℤ/9)—31no—
8C3×#1094D313yes—
9C3×3−1+2⋊C4—31no—
10#66359—21no—
11#66359—23no—
12#66359C2×C311yescharacteristic, complemented
13#6912—41noSylow
14C32×#67—91no—
15C3×(C22⋊C9)⋊C2—33no—
16((C22⋊C9)⋊C2)⋊C3—36no—
17((C22⋊C9)⋊C2)⋊C3—33no—
18#611⋊C3—33no—
19C3×#611—31no—
20C2×C3×3−1+2—31no—
21C3×AGL(1,ℤ/9)—61no—
22C3×AGL(1,ℤ/9)—123no—
23#733⋊C2—41no—
24C22×C33C3⋊D311yescharacteristic
25C2×C32×D3—91no—
26C32×Dic3—91no—
27C22×3−1+2—33no—
28C22×C3×C9—21no—
29C22×C3×C9C3×D311yescharacteristic
30C2×AGL(1,ℤ/9)—33no—
31C2×C3×D9—31no—
32#1094—23no—
33#1094—36no—
34#1094C3×D313yes—
35C3×C22⋊C9—33no—
363−1+2⋊C4—33no—
37C3×Dic9—31no—
38C3×3−1+2—43no—
39C3×3−1+2S411yescharacteristic
40#733—41no—
41#733—83no—
42#733—81no—
43C32×D4—271no—
44C3×#67—93no—
45C3×#67—91no—
46(C22⋊C9)⋊C2—33no—
47#611—31no—
48C2×C33—31no—
49C32×D3—181no—
50C2×3−1+2—33no—
51C2×3−1+2—63no—
52C2×C3×C9—31no—
53C2×C3×C9—61no—
54AGL(1,ℤ/9)—63no—
55AGL(1,ℤ/9)—123no—
56AGL(1,ℤ/9)—126no—
57C3×D9—61no—
58C3×D9—123no—
59C22×C32—91no—
60C22×C32—271no—
61C22×C32#27213yes—
62C22×C32C3×C3⋊D311yescharacteristic
63C2×C3×D3—91no—
64C2×C3×D3—93no—
65C32×C4—271no—
66C3×Dic3—91no—
67C3×Dic3—93no—
68C22×C9—31no—
69C22×C9—61no—
70C2×D9—31no—
71C22⋊C9—33no—
72C22⋊C9—63no—
73Dic9—31no—
74C33C3⋊S411yescharacteristic
753−1+2—33no—
763−1+2—43no—
773−1+2—83no—
783−1+2—126no—
79C3×C9—21no—
80C3×C9—123no—
81C3×C9C3×S411yescharacteristic
82C3×D4—271no—
83C3×D4—273no—
84#67—91no—
85C2×C32—31no—
86C2×C32—33no—
87C2×C32—91no—
88C2×C32—181no—
89C2×C32—541no—
90C3×D3—183no—
91C3×D3—181no—
92C2×C9—31no—
93C2×C9—61no—
94C2×C9—63no—
95D9—61no—
96D9—123no—
97C22×C3—31no—
98C22×C3—33no—
99C22×C3—271no—
100C22×C3—273no—
101C22×C3C3×#27211yescharacteristic
102C2×D3—91no—
103C3×C4—271no—
104C3×C4—273no—
105Dic3—91no—
106C32—91no—
107C32#625813yes—
108C32C3×C3⋊S411yescharacteristic
109C9—31no—
110C9—61no—
111C9—123no—
112C9—243no—
113D4—271noSylow
114C2×C3—31no—
115C2×C3—31no—
116C2×C3—61no—
117C2×C3—93no—
118C2×C3—541no—
119C2×C3—543no—
120D3—181no—
121C22—271no—
122C22#6912⋊C211yescharacteristic, complemented
123C4—271no—
124C3—31no—
125C3—33no—
126C3C3×#625811yescharacteristic
127C2—31no—
128C2—541no—
subgroupG/H
center, hypercenterC1G
commutator, cosocle, hypocenter#66359C2×C3
FrattiniC32C3×C3⋊S4
FittingC22×C3×3−1+2D3
socleC22×C3C3×#272
LCSG ▷ #66359
UCSC1

Complements

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

NH ≅ G/Ntype
1. #11757854C2semidirect
4. #66359⋊C2C3semidirect
12. #66359C2×C3semidirect
122. C22#6912⋊C2semidirect

Maximal subgroups

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

subgroupindex
#117578542
C3×((C22⋊C9)⋊C2)⋊C33
C3×#611⋊C33
#66359⋊C23
#6912⋊C24