Finite Group Databasebeta

← C3⋊#10619757 #14518119

Subgroups — C3⋊#10619757 #14518119

Order 1944.

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

normal subgroups only

This group has 507 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×#66363C211yesmaximal, characteristic, complemented
2C3×C3⋊(C3⋊S4)—31nomaximal
3C3⋊(((C22⋊C9)⋊C2)⋊C3)—32nomaximal
4#10619977—31nomaximal
5#10619757—39nomaximal
6C3⋊#4183—41nomaximal
7C33×A4D311yescharacteristic, complemented
8C22×C3×H(3,𝔽3)D311yescharacteristic, complemented
9C2×C3⋊((C3⋊D3)⋊C3)—31no—
10C3×#1094D312yescomplemented
11C3⋊((C3⋊Dic3)⋊C3)—31no—
12#66363D319yescomplemented
13C3×AΣL(1,𝔽27)—41noSylow
14C3⋊(C3⋊S4)—31no—
15C3×C3⋊S4—99no—
16C3×C3⋊S4—93no—
17#6312—31no—
18C3×#638—91no—
19C3⋊((C22⋊C9)⋊C2)—32no—
20((C22⋊C9)⋊C2)⋊C3—96no—
21#638⋊C3—93no—
22C3×C3⋊(C3⋊D3)—121no—
23C2×C3×H(3,𝔽3)—31no—
24C3⋊AGL(1,ℤ/9)—122no—
25C3⋊((C3⋊D3)⋊C3)—61no—
26#4183—129no—
27C22×C33—31no—
28C22×C33C3⋊D311yescharacteristic
29C2×C3⋊(C3⋊D3)—31no—
30C2×C3×C3⋊D3—91no—
31C32×A4—31no—
32C32×A4—39no—
33C32×A4—61no—
34C32×A4C3⋊D313yescomplemented
35C3⋊(C3⋊Dic3)—31no—
36C3×C3⋊Dic3—91no—
37C22×H(3,𝔽3)—61no—
38C22×H(3,𝔽3)C3⋊D313yescomplemented
39C2×(C3⋊D3)⋊C3—93no—
40#1094—62no—
41#1094C3⋊D316yescomplemented
42C3×C22⋊C9—32no—
43(C3⋊Dic3)⋊C3—93no—
44C34—41no—
45C3×3−1+2—42no—
46C3×H(3,𝔽3)S411yescharacteristic, complemented
47AΣL(1,𝔽27)—49no—
48C3⋊S4—99no—
49C3⋊S4—93no—
50C3×S4—279no—
51#638—91no—
52#638—93no—
53#638—273no—
54C3×#67—273no—
55C3×#67—271no—
56(C22⋊C9)⋊C2—96no—
57C2×C33—31no—
58C2×C33—31no—
59C2×C33—61no—
60C3⋊(C3⋊D3)—61no—
61C3⋊(C3⋊D3)—121no—
62C3×C3⋊D3—181no—
63C3×C3⋊D3—363no—
64C3×C3⋊D3—369no—
65C2×H(3,𝔽3)—33no—
66C2×H(3,𝔽3)—63no—
67C3⋊D9—122no—
68AGL(1,ℤ/9)—366no—
69(C3⋊D3)⋊C3—183no—
70C22×C32—21no—
71C22×C32—33no—
72C22×C32—33no—
73C22×C32—93no—
74C22×C32#27211yescharacteristic
75C22×C32C3⋊(C3⋊D3)11yescharacteristic
76C2×C3⋊D3—91no—
77C2×C3⋊D3—93no—
78C2×C3⋊D3—273no—
79C2×C3×D3—271no—
80C2×C3×D3—273no—
81C3×A4—39no—
82C3×A4—33no—
83C3×A4—39no—
84C3×A4—69no—
85C3⋊Dic3—91no—
86C3⋊Dic3—93no—
87C3⋊Dic3—273no—
88C3×Dic3—271no—
89C3×Dic3—273no—
90C22⋊C9—36no—
91C33—31no—
92C33—43no—
93C33—129no—
94C33—121no—
95C33—241no—
96C33C3⋊S411yescharacteristic
973−1+2—46no—
983−1+2—242no—
99H(3,𝔽3)—61no—
100H(3,𝔽3)C3⋊S413yescomplemented
101C3×C9—122no—
102S4—279no—
103C3×D4—811no—
104#67—273no—
105#67—271no—
106#67—813no—
107C2×C32—31no—
108C2×C32—33no—
109C2×C32—31no—
110C2×C32—61no—
111C2×C32—63no—
112C2×C32—93no—
113C2×C32—93no—
114C2×C32—183no—
115C3⋊D3—181no—
116C3⋊D3—183no—
117C3⋊D3—369no—
118C3⋊D3—363no—
119C3⋊D3—543no—
120C3×D3—543no—
121C3×D3—541no—
122C3×D3—1089no—
123D9—366no—
124C22×C3—31no—
125C22×C3—61no—
126C22×C3—93no—
127C22×C3—811no—
128C22×C3#418313yescomplemented
129C22×C3C3⋊#27211yescharacteristic
130C2×D3—271no—
131C2×D3—273no—
132C2×D3—813no—
133A4—39no—
134C3×C4—811no—
135Dic3—271no—
136Dic3—273no—
137Dic3—813no—
138C32—21no—
139C32—33no—
140C32—33no—
141C32—93no—
142C32—129no—
143C32—129no—
144C32—123no—
145C32—249no—
146C32#625811yescharacteristic
147C32C3⋊(C3⋊S4)11yescharacteristic
148C9—126no—
149D4—811noSylow
150C2×C3—33no—
151C2×C3—31no—
152C2×C3—91no—
153C2×C3—93no—
154C2×C3—181no—
155C2×C3—183no—
156C2×C3—1621no—
157D3—543no—
158D3—541no—
159D3—1089no—
160D3—1623no—
161C22—811no—
162C22C3⋊#418311yescharacteristic, complemented
163C4—811no—
164C3—31no—
165C3—61no—
166C3—93no—
167C3—129no—
168C3#1061975713yescomplemented
169C3C3⋊#625811yescharacteristic
170C2—31no—
171C2—1621no—
subgroupG/H
center, hypercenterC1G
commutator, cosocle, hypocenterC3×#66363C2
FrattiniC32C3⋊(C3⋊S4)
FittingC22×C3×H(3,𝔽3)D3
socleC22×C32#272
LCSG ▷ C3×#66363
UCSC1

Complements

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

NH ≅ G/Ntype
1. C3×#66363C2semidirect
7. C33×A4D3semidirect
8. C22×C3×H(3,𝔽3)D3semidirect
10. C3×#1094D3semidirect
12. #66363D3semidirect
34. C32×A4C3⋊D3semidirect
38. C22×H(3,𝔽3)C3⋊D3semidirect
41. #1094C3⋊D3semidirect
46. C3×H(3,𝔽3)S4semidirect
100. H(3,𝔽3)C3⋊S4semidirect
128. C22×C3#4183semidirect
162. C22C3⋊#4183semidirect
168. C3#10619757semidirect

Maximal subgroups

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

subgroupindex
C3×#663632
C3×C3⋊(C3⋊S4)3
C3⋊(((C22⋊C9)⋊C2)⋊C3)3
#106199773
#106197573
C3⋊#41834