Finite Group Databasebeta

← C3⋊(#66366⋊C2) #14518122

Subgroups — C3⋊(#66366⋊C2) #14518122

Order 1944.

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

normal subgroups only

This group has 483 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×#66366C211yesmaximal, characteristic, complemented
2C3×C3⋊(C3⋊S4)—31nomaximal
3C3⋊((C3⋊S4)⋊C3)—31nomaximal
4C3⋊(((C22⋊C9)⋊C2)⋊C3)—31nomaximal
5#10619980—31nomaximal
6#66366⋊C2—39nomaximal
7C3⋊#4183—41nomaximal
8C33×A4D311yescharacteristic, complemented
9C22×C3×3−1+2D311yescharacteristic, complemented
10C2×C3⋊AGL(1,ℤ/9)—31no—
11C3×C22⋊H(3,𝔽3)D311yescharacteristic, complemented
12C3×#1094D311yescharacteristic, complemented
13C3⋊(3−1+2⋊C4)—31no—
14#66366D319yescomplemented
15C3×AΣL(1,𝔽27)—41noSylow
16C3⋊(C3⋊S4)—31no—
17C3⋊(C3⋊S4)—31no—
18C3×C3⋊S4—99no—
19C3×C3⋊S4—93no—
20C3×#638—91no—
21C3⋊((C22⋊C9)⋊C2)—31no—
22(C3⋊S4)⋊C3—93no—
23((C22⋊C9)⋊C2)⋊C3—93no—
24#6233—31no—
25#611⋊C3—93no—
26C3×C3⋊(C3⋊D3)—121no—
27C2×C3×3−1+2—31no—
28C3⋊AGL(1,ℤ/9)—61no—
29C3⋊AGL(1,ℤ/9)—121no—
30C3⋊((C3⋊D3)⋊C3)—121no—
31#4183—129no—
32C22×C33C3⋊D311yescharacteristic
33C2×C3×C3⋊D3—91no—
34C32×A4—31no—
35C32×A4—39no—
36C32×A4—31no—
37C32×A4—61no—
38C32×A4C3⋊D313yescomplemented
39C3×C3⋊Dic3—91no—
40C22×3−1+2—61no—
41C22×3−1+2C3⋊D313yescomplemented
42C22×C3×C9—31no—
43C2×C3⋊D9—31no—
44C2×AGL(1,ℤ/9)—93no—
45C22⋊H(3,𝔽3)—61no—
46C22⋊H(3,𝔽3)C3⋊D313yescomplemented
47#1094—61no—
48#1094C3⋊D313yescomplemented
49C3×C22⋊C9—31no—
50C3⋊Dic9—31no—
513−1+2⋊C4—93no—
52C34—41no—
53C3×3−1+2—41no—
54C3×3−1+2S411yescharacteristic, complemented
55C3×H(3,𝔽3)—41no—
56AΣL(1,𝔽27)—49no—
57C3⋊S4—99no—
58C3⋊S4—93no—
59C3⋊S4—93no—
60C3⋊S4—273no—
61C3×S4—279no—
62#638—91no—
63C3×#67—273no—
64C3×#67—271no—
65(C22⋊C9)⋊C2—93no—
66#611—93no—
67C2×C33—31no—
68C3⋊(C3⋊D3)—121no—
69C3⋊(C3⋊D3)—121no—
70C3×C3⋊D3—181no—
71C3×C3⋊D3—363no—
72C3×C3⋊D3—369no—
73C2×3−1+2—33no—
74C2×3−1+2—63no—
75C2×C3×C9—31no—
76C2×C3×C9—61no—
77C3⋊D9—61no—
78C3⋊D9—121no—
79AGL(1,ℤ/9)—183no—
80AGL(1,ℤ/9)—363no—
81(C3⋊D3)⋊C3—363no—
82C22×C32—21no—
83C22×C32—33no—
84C22×C32#27211yescharacteristic
85C22×C32C3⋊(C3⋊D3)11yescharacteristic
86C2×C3⋊D3—91no—
87C2×C3×D3—271no—
88C2×C3×D3—273no—
89C3×A4—39no—
90C3×A4—33no—
91C3×A4—39no—
92C3×A4—33no—
93C3×A4—69no—
94C3×A4—93no—
95C3⋊Dic3—91no—
96C3×Dic3—271no—
97C3×Dic3—273no—
98C22×C9—33no—
99C2×D9—93no—
100C22⋊C9—33no—
101Dic9—93no—
102C33—43no—
103C33—129no—
104C33—121no—
105C33—121no—
106C33—241no—
107C33C3⋊S411yescharacteristic
1083−1+2—43no—
1093−1+2—61no—
1103−1+2—241no—
1113−1+2C3⋊S413yescomplemented
112H(3,𝔽3)—43no—
113H(3,𝔽3)—241no—
114C3×C9—31no—
115C3×C9—121no—
116S4—279no—
117S4—813no—
118C3×D4—811no—
119#67—273no—
120#67—271no—
121C2×C32—31no—
122C2×C32—31no—
123C2×C32—61no—
124C2×C32—93no—
125C3⋊D3—181no—
126C3⋊D3—363no—
127C3⋊D3—369no—
128C3⋊D3—363no—
129C3⋊D3—1083no—
130C3×D3—543no—
131C3×D3—541no—
132C3×D3—1089no—
133C2×C9—33no—
134C2×C9—63no—
135D9—183no—
136D9—363no—
137C22×C3—31no—
138C22×C3—61no—
139C22×C3—811no—
140C22×C3#418313yescomplemented
141C22×C3C3⋊#27211yescharacteristic
142C2×D3—271no—
143C2×D3—273no—
144A4—39no—
145A4—93no—
146C3×C4—811no—
147Dic3—271no—
148Dic3—273no—
149C32—21no—
150C32—33no—
151C32—129no—
152C32—129no—
153C32—123no—
154C32—123no—
155C32—249no—
156C32—363no—
157C32#625811yescharacteristic
158C32C3⋊(C3⋊S4)11yescharacteristic
159C9—33no—
160C9—123no—
161D4—811noSylow
162C2×C3—33no—
163C2×C3—31no—
164C2×C3—91no—
165C2×C3—181no—
166C2×C3—1621no—
167D3—543no—
168D3—541no—
169D3—3243no—
170D3—1089no—
171C22—811no—
172C22C3⋊#418311yescharacteristic, complemented
173C4—811no—
174C3—31no—
175C3—61no—
176C3—129no—
177C3—363no—
178C3#66366⋊C213yescomplemented
179C3C3⋊#625811yescharacteristic
180C2—31no—
181C2—1621no—
subgroupG/H
center, hypercenterC1G
commutator, cosocle, hypocenterC3×#66366C2
FrattiniC32C3⋊(C3⋊S4)
FittingC22×C3×3−1+2D3
socleC22×C32#272
LCSG ▷ C3×#66366
UCSC1

Complements

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

NH ≅ G/Ntype
1. C3×#66366C2semidirect
8. C33×A4D3semidirect
9. C22×C3×3−1+2D3semidirect
11. C3×C22⋊H(3,𝔽3)D3semidirect
12. C3×#1094D3semidirect
14. #66366D3semidirect
38. C32×A4C3⋊D3semidirect
41. C22×3−1+2C3⋊D3semidirect
46. C22⋊H(3,𝔽3)C3⋊D3semidirect
48. #1094C3⋊D3semidirect
54. C3×3−1+2S4semidirect
111. 3−1+2C3⋊S4semidirect
140. C22×C3#4183semidirect
172. C22C3⋊#4183semidirect
178. C3#66366⋊C2semidirect

Maximal subgroups

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

subgroupindex
C3×#663662
C3×C3⋊(C3⋊S4)3
C3⋊((C3⋊S4)⋊C3)3
C3⋊(((C22⋊C9)⋊C2)⋊C3)3
#106199803
#66366⋊C23
C3⋊#41834