Finite Group Databasebeta

← C3⋊#10619754 #14518113

Subgroups — C3⋊#10619754 #14518113

Order 1944.

489 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 489 conjugacy classes of subgroups — too many to draw. Only its 73 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×(C3×A4)⋊C9C211yesmaximal, characteristic, complemented
2C3×C3⋊(C3⋊S4)—31nomaximal
3C3×C3⋊((C22⋊C9)⋊C2)—32nomaximal
4C3×#6233—31nomaximal
5#10619754—39nomaximal
6C3⋊#4181—41nomaximal
7C33×A4D311yescharacteristic
8C22×C32×C9D311yescharacteristic, complemented
9C2×C3×C3⋊D9—31no—
10C32×C22⋊C9D312yescomplemented
11C3×C3⋊Dic9—31no—
12(C3×A4)⋊C9D319yescomplemented
13C3×C32⋊C9—41noSylow
14C3⋊(C3⋊S4)—31no—
15C3×C3⋊S4—99no—
16C3×C3⋊S4—93no—
17C3×#638—91no—
18C3⋊((C22⋊C9)⋊C2)—32no—
19C3×(C22⋊C9)⋊C2—96no—
20#6233—31no—
21C3×#611—93no—
22C3×C3⋊(C3⋊D3)—121no—
23C2×C32×C9—31no—
24C3×C3⋊D9—61no—
25C3×C3⋊D9—122no—
26#4181—129no—
27C22×C33C3⋊D311yescharacteristic
28C2×C3×C3⋊D3—91no—
29C32×A4—31no—
30C32×A4—63no—
31C32×A4—61no—
32C32×A4D919yescomplemented
33C32×A4C3⋊D313yes—
34C3×C3⋊Dic3—91no—
35C22×C3×C9—31no—
36C22×C3×C9—61no—
37C22×C3×C9C3⋊D313yescomplemented
38C2×C3⋊D9—31no—
39C2×C3×D9—93no—
40C3×C22⋊C9—32no—
41C3×C22⋊C9—62no—
42C3×C22⋊C9C3⋊D316yescomplemented
43C3⋊Dic9—31no—
44C3×Dic9—93no—
45C34—41no—
46C32×C9—42no—
47C32×C9S411yescharacteristic, complemented
48C32⋊C9—49no—
49C3⋊S4—99no—
50C3⋊S4—93no—
51C3×S4—279no—
52#638—91no—
53C3×#67—273no—
54C3×#67—271no—
55(C22⋊C9)⋊C2—96no—
56#611—93no—
57C2×C33—31no—
58C3⋊(C3⋊D3)—121no—
59C3×C3⋊D3—181no—
60C3×C3⋊D3—363no—
61C3×C3⋊D3—369no—
62C2×C3×C9—31no—
63C2×C3×C9—33no—
64C2×C3×C9—63no—
65C2×C3×C9—61no—
66C3⋊D9—61no—
67C3⋊D9—122no—
68C3×D9—183no—
69C3×D9—366no—
70C22×C32—23no—
71C22×C32—21no—
72C22×C32C3⋊D913yes—
73C22×C32#27211yescharacteristic
74C22×C32C3⋊(C3⋊D3)11yescharacteristic
75C2×C3⋊D3—91no—
76C2×C3×D3—271no—
77C2×C3×D3—273no—
78C3×A4—39no—
79C3×A4—33no—
80C3×A4—69no—
81C3×A4—63no—
82C3×A4C3⋊D919yescomplemented
83C3⋊Dic3—91no—
84C3×Dic3—271no—
85C3×Dic3—273no—
86C22×C9—33no—
87C2×D9—93no—
88C22⋊C9—36no—
89Dic9—93no—
90C33—49no—
91C33—43no—
92C33—121no—
93C33—243no—
94C33—241no—
95C33C3⋊S411yescharacteristic
96C3×C9—31no—
97C3×C9—46no—
98C3×C9—61no—
99C3×C9—122no—
100C3×C9—242no—
101C3×C9C3⋊S413yescomplemented
102S4—279no—
103C3×D4—811no—
104#67—273no—
105#67—271no—
106C2×C32—31no—
107C2×C32—33no—
108C2×C32—31no—
109C2×C32—61no—
110C2×C32—63no—
111C3⋊D3—181no—
112C3⋊D3—369no—
113C3⋊D3—363no—
114C3×D3—543no—
115C3×D3—541no—
116C3×D3—1089no—
117C2×C9—33no—
118C2×C9—63no—
119D9—183no—
120D9—366no—
121C22×C3—23no—
122C22×C3—21no—
123C22×C3—811no—
124C22×C3#418113yescomplemented
125C22×C3C3⋊(C3⋊D9)11yescharacteristic
126C22×C3C3⋊#27211yescharacteristic
127C2×D3—271no—
128C2×D3—273no—
129A4—39no—
130C3×C4—811no—
131Dic3—271no—
132Dic3—273no—
133C32—23no—
134C32—21no—
135C32—49no—
136C32—129no—
137C32—123no—
138C32—249no—
139C32—243no—
140C32C9⋊S413yes—
141C32#625811yescharacteristic
142C32C3⋊(C3⋊S4)11yescharacteristic
143C9—33no—
144C9—126no—
145D4—811noSylow
146C2×C3—33no—
147C2×C3—31no—
148C2×C3—31no—
149C2×C3—63no—
150C2×C3—61no—
151C2×C3—1621no—
152D3—543no—
153D3—541no—
154D3—1089no—
155C22—811no—
156C22C3⋊#418111yescharacteristic, complemented
157C4—811no—
158C3—23no—
159C3—21no—
160C3—129no—
161C3#1061975413yescomplemented
162C3C3⋊(C9⋊S4)11yescharacteristic
163C3C3⋊#625811yescharacteristic
164C2—31no—
165C2—1621no—
subgroupG/H
center, hypercenterC3C3⋊(C9⋊S4)
commutator, cosocle, hypocenterC3×(C3×A4)⋊C9C2
FrattiniC32C3⋊(C3⋊S4)
FittingC22×C32×C9D3
socleC22×C33C3⋊D3
LCSG ▷ C3×(C3×A4)⋊C9
UCSC1 ◁ C3

Complements

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

NH ≅ G/Ntype
1. C3×(C3×A4)⋊C9C2semidirect
8. C22×C32×C9D3semidirect
10. C32×C22⋊C9D3semidirect
12. (C3×A4)⋊C9D3semidirect
32. C32×A4D9semidirect
37. C22×C3×C9C3⋊D3semidirect
42. C3×C22⋊C9C3⋊D3semidirect
47. C32×C9S4semidirect
82. C3×A4C3⋊D9semidirect
101. C3×C9C3⋊S4semidirect
124. C22×C3#4181semidirect
156. C22C3⋊#4181semidirect
161. C3#10619754semidirect

Maximal subgroups

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

subgroupindex
C3×(C3×A4)⋊C92
C3×C3⋊(C3⋊S4)3
C3×C3⋊((C22⋊C9)⋊C2)3
C3×#62333
#106197543
C3⋊#41814