Finite Group Databasebeta

← C3⋊(#66365⋊C2) #14518121

Subgroups — C3⋊(#66365⋊C2) #14518121

Order 1944.

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

normal subgroups only

This group has 321 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×#66365C211yesmaximal, characteristic, complemented
2C3⋊((C3⋊S4)⋊C3)—31nomaximal
3C3×C3⋊((C22⋊C9)⋊C2)—31nomaximal
4C3⋊(((C22⋊C9)⋊C2)⋊C3)—31nomaximal
5#10619980—31nomaximal
6#66365⋊C2—39nomaximal
7C3⋊#4184—41nomaximal
8C22×C3×3−1+2D311yescharacteristic, complemented
9C2×C3⋊AGL(1,ℤ/9)—31no—
10C3×C22⋊H(3,𝔽3)D311yescharacteristic
11C3×#1094D311yescharacteristic, complemented
12C32×C22⋊C9D311yescharacteristic, complemented
13C3⋊(3−1+2⋊C4)—31no—
14#66365D319yescomplemented
15C3×#731—41noSylow
16C3⋊(C3⋊S4)—31no—
17C3×#638—91no—
18C3⋊((C22⋊C9)⋊C2)—31no—
19C3⋊((C22⋊C9)⋊C2)—31no—
20(C3⋊S4)⋊C3—93no—
21C3×(C22⋊C9)⋊C2—93no—
22((C22⋊C9)⋊C2)⋊C3—93no—
23#6233—31no—
24#611⋊C3—93no—
25C2×C3×3−1+2—31no—
26C3⋊AGL(1,ℤ/9)—61no—
27C3⋊AGL(1,ℤ/9)—121no—
28C3⋊((C3⋊D3)⋊C3)—121no—
29C3×C3⋊D9—121no—
30#4184—129no—
31C22×C33C3⋊D311yescharacteristic
32C2×C3×C3⋊D3—91no—
33C32×A4—31no—
34C3×C3⋊Dic3—91no—
35C22×3−1+2—61no—
36C22×3−1+2C3⋊D313yescomplemented
37C22×C3×C9—31no—
38C2×C3⋊D9—31no—
39C2×AGL(1,ℤ/9)—93no—
40C22⋊H(3,𝔽3)—61no—
41C22⋊H(3,𝔽3)C3⋊D313yes—
42#1094—61no—
43#1094C3⋊D313yescomplemented
44C3×C22⋊C9—31no—
45C3×C22⋊C9—31no—
46C3×C22⋊C9—61no—
47C3×C22⋊C9C3⋊D313yescomplemented
48C3⋊Dic9—31no—
493−1+2⋊C4—93no—
50C3×3−1+2—41no—
51C3×3−1+2S411yescharacteristic, complemented
52C3×H(3,𝔽3)—41no—
53C32×C9—41no—
54#731—49no—
55C3⋊S4—93no—
56C3⋊S4—273no—
57#638—91no—
58C3×#67—273no—
59C3×#67—271no—
60(C22⋊C9)⋊C2—93no—
61(C22⋊C9)⋊C2—93no—
62#611—93no—
63C2×C33—31no—
64C3⋊(C3⋊D3)—121no—
65C3×C3⋊D3—181no—
66C2×3−1+2—33no—
67C2×3−1+2—63no—
68C2×C3×C9—31no—
69C2×C3×C9—61no—
70C3⋊D9—61no—
71C3⋊D9—121no—
72C3⋊D9—121no—
73AGL(1,ℤ/9)—183no—
74AGL(1,ℤ/9)—363no—
75(C3⋊D3)⋊C3—363no—
76C3×D9—363no—
77C22×C32—21no—
78C22×C32—33no—
79C22×C32#27211yescharacteristic
80C22×C32C3⋊(C3⋊D3)11yescharacteristic
81C2×C3⋊D3—91no—
82C2×C3×D3—271no—
83C2×C3×D3—273no—
84C3×A4—33no—
85C3×A4—93no—
86C3⋊Dic3—91no—
87C3×Dic3—271no—
88C3×Dic3—273no—
89C22×C9—33no—
90C2×D9—93no—
91C22⋊C9—33no—
92C22⋊C9—33no—
93Dic9—93no—
94C33—121no—
95C33C3⋊S411yescharacteristic
963−1+2—43no—
973−1+2—61no—
983−1+2—241no—
993−1+2C3⋊S413yescomplemented
100H(3,𝔽3)—43no—
101H(3,𝔽3)—241no—
102C3×C9—31no—
103C3×C9—43no—
104C3×C9—121no—
105C3×C9—121no—
106C3×C9—241no—
107S4—813no—
108C3×D4—811no—
109#67—273no—
110#67—271no—
111C2×C32—31no—
112C2×C32—31no—
113C2×C32—61no—
114C2×C32—93no—
115C3⋊D3—181no—
116C3⋊D3—363no—
117C3⋊D3—1083no—
118C3×D3—543no—
119C3×D3—541no—
120C2×C9—33no—
121C2×C9—63no—
122D9—183no—
123D9—363no—
124D9—363no—
125C22×C3—31no—
126C22×C3—61no—
127C22×C3—811no—
128C22×C3#418413yescomplemented
129C22×C3C3⋊#27211yescharacteristic
130C2×D3—271no—
131C2×D3—273no—
132A4—93no—
133C3×C4—811no—
134Dic3—271no—
135Dic3—273no—
136C32—21no—
137C32—33no—
138C32—123no—
139C32—363no—
140C32#625811yescharacteristic
141C32C3⋊(C3⋊S4)11yescharacteristic
142C9—33no—
143C9—123no—
144C9—123no—
145D4—811noSylow
146C2×C3—33no—
147C2×C3—31no—
148C2×C3—91no—
149C2×C3—181no—
150C2×C3—1621no—
151D3—543no—
152D3—541no—
153D3—3243no—
154C22—811no—
155C22C3⋊#418411yescharacteristic, complemented
156C4—811no—
157C3—31no—
158C3—61no—
159C3—363no—
160C3#66365⋊C213yescomplemented
161C3C3⋊#625811yescharacteristic
162C2—31no—
163C2—1621no—
subgroupG/H
center, hypercenterC1G
commutator, cosocle, hypocenterC3×#66365C2
FrattiniC32C3⋊(C3⋊S4)
FittingC22×C3×3−1+2D3
socleC22×C32#272
LCSG ▷ C3×#66365
UCSC1

Complements

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

NH ≅ G/Ntype
1. C3×#66365C2semidirect
8. C22×C3×3−1+2D3semidirect
11. C3×#1094D3semidirect
12. C32×C22⋊C9D3semidirect
14. #66365D3semidirect
36. C22×3−1+2C3⋊D3semidirect
43. #1094C3⋊D3semidirect
47. C3×C22⋊C9C3⋊D3semidirect
51. C3×3−1+2S4semidirect
99. 3−1+2C3⋊S4semidirect
128. C22×C3#4184semidirect
155. C22C3⋊#4184semidirect
160. C3#66365⋊C2semidirect

Maximal subgroups

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

subgroupindex
C3×#663652
C3⋊((C3⋊S4)⋊C3)3
C3×C3⋊((C22⋊C9)⋊C2)3
C3⋊(((C22⋊C9)⋊C2)⋊C3)3
#106199803
#66365⋊C23
C3⋊#41844