Finite Group Databasebeta

← C3⋊#10619751 #14518108

Subgroups — C3⋊#10619751 #14518108

Order 1944.

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

normal subgroups only

This group has 327 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×#66357C211yesmaximal, characteristic, complemented
2C3⋊((C3⋊S4)⋊C3)—31nomaximal
3C3⋊(((C22⋊C9)⋊C2)⋊C3)—32nomaximal
4C3×#6233—31nomaximal
5#10619751—39nomaximal
6C3⋊#4184—41nomaximal
7C22×C32×C9D311yescharacteristic, complemented
8C2×C3×C3⋊D9—31no—
9C3×C22⋊H(3,𝔽3)D311yescharacteristic
10C3×#1094D312yescomplemented
11C3×C3⋊Dic9—31no—
12#66357D319yescomplemented
13C3×#731—41noSylow
14C3⋊(C3⋊S4)—31no—
15C3×#638—91no—
16C3⋊((C22⋊C9)⋊C2)—32no—
17(C3⋊S4)⋊C3—93no—
18((C22⋊C9)⋊C2)⋊C3—96no—
19#6233—31no—
20C3×#611—93no—
21C2×C32×C9—31no—
22C3⋊AGL(1,ℤ/9)—122no—
23C3⋊((C3⋊D3)⋊C3)—121no—
24C3×C3⋊D9—61no—
25#4184—129no—
26C22×C33C3⋊D311yescharacteristic
27C2×C3×C3⋊D3—91no—
28C32×A4—31no—
29C3×C3⋊Dic3—91no—
30C22×C3×C9—31no—
31C22×C3×C9—61no—
32C22×C3×C9C3⋊D313yescomplemented
33C2×C3⋊D9—31no—
34C2×C3×D9—93no—
35C22⋊H(3,𝔽3)—61no—
36C22⋊H(3,𝔽3)C3⋊D313yes—
37#1094—62no—
38#1094C3⋊D316yescomplemented
39C3×C22⋊C9—32no—
40C3⋊Dic9—31no—
41C3×Dic9—93no—
42C3×3−1+2—42no—
43C3×H(3,𝔽3)—41no—
44C32×C9S411yescharacteristic, complemented
45#731—49no—
46C3⋊S4—93no—
47C3⋊S4—273no—
48#638—91no—
49C3×#67—273no—
50C3×#67—271no—
51(C22⋊C9)⋊C2—96no—
52#611—93no—
53C2×C33—31no—
54C3⋊(C3⋊D3)—121no—
55C3×C3⋊D3—181no—
56C2×C3×C9—31no—
57C2×C3×C9—33no—
58C2×C3×C9—63no—
59C2×C3×C9—61no—
60C3⋊D9—61no—
61C3⋊D9—122no—
62AGL(1,ℤ/9)—366no—
63(C3⋊D3)⋊C3—363no—
64C3×D9—183no—
65C22×C32—21no—
66C22×C32—33no—
67C22×C32#27211yescharacteristic
68C22×C32C3⋊(C3⋊D3)11yescharacteristic
69C2×C3⋊D3—91no—
70C2×C3×D3—271no—
71C2×C3×D3—273no—
72C3×A4—33no—
73C3×A4—93no—
74C3⋊Dic3—91no—
75C3×Dic3—271no—
76C3×Dic3—273no—
77C22×C9—33no—
78C2×D9—93no—
79C22⋊C9—36no—
80Dic9—93no—
81C33—121no—
82C33C3⋊S411yescharacteristic
833−1+2—46no—
843−1+2—242no—
85H(3,𝔽3)—43no—
86H(3,𝔽3)—241no—
87C3×C9—31no—
88C3×C9—61no—
89C3×C9—122no—
90C3×C9C3⋊S413yescomplemented
91S4—813no—
92C3×D4—811no—
93#67—273no—
94#67—271no—
95C2×C32—31no—
96C2×C32—33no—
97C2×C32—31no—
98C2×C32—61no—
99C2×C32—63no—
100C3⋊D3—181no—
101C3⋊D3—363no—
102C3⋊D3—1083no—
103C3×D3—543no—
104C3×D3—541no—
105C2×C9—33no—
106C2×C9—63no—
107D9—183no—
108D9—366no—
109C22×C3—31no—
110C22×C3—61no—
111C22×C3—811no—
112C22×C3#418413yescomplemented
113C22×C3C3⋊#27211yescharacteristic
114C2×D3—271no—
115C2×D3—273no—
116A4—93no—
117C3×C4—811no—
118Dic3—271no—
119Dic3—273no—
120C32—21no—
121C32—33no—
122C32—123no—
123C32—363no—
124C32#625811yescharacteristic
125C32C3⋊(C3⋊S4)11yescharacteristic
126C9—33no—
127C9—126no—
128D4—811noSylow
129C2×C3—31no—
130C2×C3—33no—
131C2×C3—31no—
132C2×C3—61no—
133C2×C3—63no—
134C2×C3—1621no—
135D3—543no—
136D3—541no—
137D3—3243no—
138C22—811no—
139C22C3⋊#418411yescharacteristic, complemented
140C4—811no—
141C3—31no—
142C3—61no—
143C3—363no—
144C3#1061975113yescomplemented
145C3C3⋊#625811yescharacteristic
146C2—31no—
147C2—1621no—
subgroupG/H
center, hypercenterC1G
commutator, cosocle, hypocenterC3×#66357C2
FrattiniC32C3⋊(C3⋊S4)
FittingC22×C32×C9D3
socleC22×C32#272
LCSG ▷ C3×#66357
UCSC1

Complements

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

NH ≅ G/Ntype
1. C3×#66357C2semidirect
7. C22×C32×C9D3semidirect
10. C3×#1094D3semidirect
12. #66357D3semidirect
32. C22×C3×C9C3⋊D3semidirect
38. #1094C3⋊D3semidirect
44. C32×C9S4semidirect
90. C3×C9C3⋊S4semidirect
112. C22×C3#4184semidirect
139. C22C3⋊#4184semidirect
144. C3#10619751semidirect

Maximal subgroups

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

subgroupindex
C3×#663572
C3⋊((C3⋊S4)⋊C3)3
C3⋊(((C22⋊C9)⋊C2)⋊C3)3
C3×#62333
#106197513
C3⋊#41844