Finite Group Databasebeta

← C3⋊(#66364⋊C2) #14518120

Subgroups — C3⋊(#66364⋊C2) #14518120

Order 1944.

297 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 297 conjugacy classes of subgroups — too many to draw. Only its 47 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
1C3×#66364C211yesmaximal, characteristic, complemented
2C3×C3⋊((C22⋊C9)⋊C2)—31nomaximal
3C3⋊(((C22⋊C9)⋊C2)⋊C3)—32nomaximal
4#10619980—31nomaximal
5#66364⋊C2—39nomaximal
6C3⋊(#733⋊C2)—41nomaximal
7C22×C3×3−1+2D311yescharacteristic
8C2×C3⋊AGL(1,ℤ/9)—31no—
9C3×#1094D312yes—
10C32×C22⋊C9D311yescharacteristic
11C3⋊(3−1+2⋊C4)—31no—
12#66364D319yescomplemented
13C3×#733—41noSylow
14C3×#638—91no—
15C3⋊((C22⋊C9)⋊C2)—32no—
16C3⋊((C22⋊C9)⋊C2)—31no—
17C3×(C22⋊C9)⋊C2—93no—
18((C22⋊C9)⋊C2)⋊C3—96no—
19#6233—31no—
20#611⋊C3—93no—
21C2×C3×3−1+2—31no—
22C3⋊AGL(1,ℤ/9)—61no—
23C3⋊AGL(1,ℤ/9)—122no—
24C3×C3⋊D9—121no—
25#733⋊C2—129no—
26C22×C33C3⋊D311yescharacteristic
27C2×C3×C3⋊D3—91no—
28C3×C3⋊Dic3—91no—
29C22×3−1+2—61no—
30C22×3−1+2C3⋊D313yes—
31C22×C3×C9—31no—
32C2×C3⋊D9—31no—
33C2×AGL(1,ℤ/9)—93no—
34#1094—62no—
35#1094C3⋊D316yes—
36C3×C22⋊C9—31no—
37C3×C22⋊C9—32no—
38C3×C22⋊C9—61no—
39C3×C22⋊C9C3⋊D313yes—
40C3⋊Dic9—31no—
413−1+2⋊C4—93no—
42C3×3−1+2—42no—
43C3×3−1+2S411yescharacteristic
44C32×C9—41no—
45#733—49no—
46#638—91no—
47C3×#67—273no—
48C3×#67—271no—
49(C22⋊C9)⋊C2—96no—
50(C22⋊C9)⋊C2—93no—
51#611—93no—
52C2×C33—31no—
53C3×C3⋊D3—181no—
54C2×3−1+2—33no—
55C2×3−1+2—63no—
56C2×C3×C9—31no—
57C2×C3×C9—61no—
58C3⋊D9—61no—
59C3⋊D9—121no—
60C3⋊D9—122no—
61AGL(1,ℤ/9)—183no—
62AGL(1,ℤ/9)—366no—
63C3×D9—363no—
64C22×C32—21no—
65C22×C32—33no—
66C22×C32#27211yescharacteristic
67C22×C32C3⋊(C3⋊D3)11yescharacteristic
68C2×C3⋊D3—91no—
69C2×C3×D3—271no—
70C2×C3×D3—273no—
71C3⋊Dic3—91no—
72C3×Dic3—271no—
73C3×Dic3—273no—
74C22×C9—33no—
75C2×D9—93no—
76C22⋊C9—33no—
77C22⋊C9—36no—
78Dic9—93no—
79C33C3⋊S411yescharacteristic
803−1+2—46no—
813−1+2—61no—
823−1+2—242no—
833−1+2C3⋊S413yes—
84C3×C9—31no—
85C3×C9—43no—
86C3×C9—121no—
87C3×C9—122no—
88C3×C9—241no—
89C3×D4—811no—
90#67—273no—
91#67—271no—
92C2×C32—31no—
93C2×C32—31no—
94C2×C32—61no—
95C2×C32—93no—
96C3⋊D3—181no—
97C3×D3—543no—
98C3×D3—541no—
99C2×C9—33no—
100C2×C9—63no—
101D9—183no—
102D9—363no—
103D9—366no—
104C22×C3—31no—
105C22×C3—61no—
106C22×C3—811no—
107C22×C3#733⋊C213yescomplemented
108C22×C3C3⋊#27211yescharacteristic
109C2×D3—271no—
110C2×D3—273no—
111C3×C4—811no—
112Dic3—271no—
113Dic3—273no—
114C32—21no—
115C32—33no—
116C32#625811yescharacteristic
117C32C3⋊(C3⋊S4)11yescharacteristic
118C9—33no—
119C9—123no—
120C9—126no—
121D4—811noSylow
122C2×C3—33no—
123C2×C3—31no—
124C2×C3—91no—
125C2×C3—181no—
126C2×C3—1621no—
127D3—543no—
128D3—541no—
129C22—811no—
130C22C3⋊(#733⋊C2)11yescharacteristic, complemented
131C4—811no—
132C3—31no—
133C3—61no—
134C3#66364⋊C213yescomplemented
135C3C3⋊#625811yescharacteristic
136C2—31no—
137C2—1621no—
subgroupG/H
center, hypercenterC1G
commutator, cosocle, hypocenterC3×#66364C2
FrattiniC32C3⋊(C3⋊S4)
FittingC22×C3×3−1+2D3
socleC22×C32#272
LCSG ▷ C3×#66364
UCSC1

Complements

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

NH ≅ G/Ntype
1. C3×#66364C2semidirect
12. #66364D3semidirect
107. C22×C3#733⋊C2semidirect
130. C22C3⋊(#733⋊C2)semidirect
134. C3#66364⋊C2semidirect

Maximal subgroups

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

subgroupindex
C3×#663642
C3×C3⋊((C22⋊C9)⋊C2)3
C3⋊(((C22⋊C9)⋊C2)⋊C3)3
#106199803
#66364⋊C23
C3⋊(#733⋊C2)4