Finite Group Databasebeta

← C3⋊#10619762 #14518125

Subgroups — C3⋊#10619762 #14518125

Order 1944.

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

normal subgroups only

This group has 660 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×#66368C211yesmaximal, characteristic, complemented
2C3×#6312—31nomaximal
3C3⋊((C3⋊S4)⋊C3)—31nomaximal
4C3⋊(((C22⋊C9)⋊C2)⋊C3)—32nomaximal
5#10619762—39nomaximal
6C3⋊#4183—41nomaximal
7C22×C34D311yescharacteristic, complemented
8C2×C3×C3⋊(C3⋊D3)—31no—
9C3×C3⋊(C3⋊Dic3)—31no—
10C3×C22⋊H(3,𝔽3)D311yescharacteristic, complemented
11C3×#1094D312yescomplemented
12#66368D319yescomplemented
13C3×AΣL(1,𝔽27)—41noSylow
14C3⋊(C3⋊S4)—31no—
15#6312—31no—
16C3×#638—99no—
17C3×#638—91no—
18C3×#638—93no—
19C3⋊((C22⋊C9)⋊C2)—32no—
20(C3⋊S4)⋊C3—93no—
21((C22⋊C9)⋊C2)⋊C3—96no—
22C2×C34—31no—
23C3×C3⋊(C3⋊D3)—61no—
24C3⋊AGL(1,ℤ/9)—122no—
25C3⋊((C3⋊D3)⋊C3)—121no—
26#4183—129no—
27C22×C33—31no—
28C22×C33—39no—
29C22×C33—61no—
30C22×C33C3⋊D311yescharacteristic
31C22×C33C3⋊D313yescomplemented
32C2×C3⋊(C3⋊D3)—31no—
33C2×C3×C3⋊D3—99no—
34C2×C3×C3⋊D3—91no—
35C2×C3×C3⋊D3—93no—
36C32×A4—31no—
37C3⋊(C3⋊Dic3)—31no—
38C3×C3⋊Dic3—99no—
39C3×C3⋊Dic3—91no—
40C3×C3⋊Dic3—93no—
41C22⋊H(3,𝔽3)—61no—
42C22⋊H(3,𝔽3)C3⋊D313yescomplemented
43#1094—62no—
44#1094C3⋊D316yescomplemented
45C3×C22⋊C9—32no—
46C34S411yescharacteristic, complemented
47C3×3−1+2—42no—
48C3×H(3,𝔽3)—41no—
49AΣL(1,𝔽27)—49no—
50C3⋊S4—93no—
51C3⋊S4—273no—
52#638—99no—
53#638—93no—
54#638—91no—
55C3×#67—279no—
56C3×#67—273no—
57C3×#67—271no—
58(C22⋊C9)⋊C2—96no—
59C2×C33—31no—
60C2×C33—39no—
61C2×C33—31no—
62C2×C33—33no—
63C2×C33—69no—
64C2×C33—61no—
65C2×C33—63no—
66C3⋊(C3⋊D3)—61no—
67C3⋊(C3⋊D3)—121no—
68C3×C3⋊D3—189no—
69C3×C3⋊D3—181no—
70C3×C3⋊D3—183no—
71C3⋊D9—122no—
72AGL(1,ℤ/9)—366no—
73(C3⋊D3)⋊C3—363no—
74C22×C32—21no—
75C22×C32—39no—
76C22×C32—33no—
77C22×C32—39no—
78C22×C32—33no—
79C22×C32—69no—
80C22×C32#27211yescharacteristic
81C22×C32C3⋊(C3⋊D3)11yescharacteristic
82C2×C3⋊D3—99no—
83C2×C3⋊D3—93no—
84C2×C3⋊D3—91no—
85C2×C3×D3—279no—
86C2×C3×D3—273no—
87C2×C3×D3—271no—
88C3×A4—33no—
89C3×A4—93no—
90C3⋊Dic3—99no—
91C3⋊Dic3—93no—
92C3⋊Dic3—91no—
93C3×Dic3—279no—
94C3×Dic3—273no—
95C3×Dic3—271no—
96C22⋊C9—36no—
97C33—31no—
98C33—39no—
99C33—61no—
100C33—121no—
101C33C3⋊S411yescharacteristic
102C33C3⋊S413yescomplemented
1033−1+2—46no—
1043−1+2—242no—
105H(3,𝔽3)—43no—
106H(3,𝔽3)—241no—
107C3×C9—122no—
108S4—813no—
109C3×D4—811no—
110#67—279no—
111#67—273no—
112#67—271no—
113C2×C32—39no—
114C2×C32—33no—
115C2×C32—31no—
116C2×C32—39no—
117C2×C32—33no—
118C2×C32—31no—
119C2×C32—61no—
120C2×C32—69no—
121C2×C32—69no—
122C2×C32—63no—
123C2×C32—63no—
124C2×C32—627no—
125C3⋊D3—189no—
126C3⋊D3—183no—
127C3⋊D3—181no—
128C3⋊D3—363no—
129C3⋊D3—1083no—
130C3×D3—549no—
131C3×D3—543no—
132C3×D3—541no—
133D9—366no—
134C22×C3—39no—
135C22×C3—31no—
136C22×C3—61no—
137C22×C3—811no—
138C22×C3#418313yescomplemented
139C22×C3C3⋊#27211yescharacteristic
140C2×D3—279no—
141C2×D3—273no—
142C2×D3—271no—
143A4—93no—
144C3×C4—811no—
145Dic3—279no—
146Dic3—273no—
147Dic3—271no—
148C32—21no—
149C32—39no—
150C32—39no—
151C32—33no—
152C32—33no—
153C32—69no—
154C32—123no—
155C32—363no—
156C32#625811yescharacteristic
157C32C3⋊(C3⋊S4)11yescharacteristic
158C9—126no—
159D4—811noSylow
160C2×C3—39no—
161C2×C3—31no—
162C2×C3—33no—
163C2×C3—31no—
164C2×C3—69no—
165C2×C3—61no—
166C2×C3—63no—
167C2×C3—1621no—
168D3—549no—
169D3—543no—
170D3—541no—
171D3—3243no—
172C22—811no—
173C22C3⋊#418311yescharacteristic, complemented
174C4—811no—
175C3—39no—
176C3—31no—
177C3—61no—
178C3—363no—
179C3#1061976213yescomplemented
180C3C3⋊#625811yescharacteristic
181C2—31no—
182C2—1621no—
subgroupG/H
center, hypercenterC1G
commutator, cosocle, hypocenterC3×#66368C2
FrattiniC32C3⋊(C3⋊S4)
FittingC22×C34D3
socleC22×C32#272
LCSG ▷ C3×#66368
UCSC1

Complements

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

NH ≅ G/Ntype
1. C3×#66368C2semidirect
7. C22×C34D3semidirect
10. C3×C22⋊H(3,𝔽3)D3semidirect
11. C3×#1094D3semidirect
12. #66368D3semidirect
31. C22×C33C3⋊D3semidirect
42. C22⋊H(3,𝔽3)C3⋊D3semidirect
44. #1094C3⋊D3semidirect
46. C34S4semidirect
102. C33C3⋊S4semidirect
138. C22×C3#4183semidirect
173. C22C3⋊#4183semidirect
179. C3#10619762semidirect

Maximal subgroups

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

subgroupindex
C3×#663682
C3×#63123
C3⋊((C3⋊S4)⋊C3)3
C3⋊(((C22⋊C9)⋊C2)⋊C3)3
#106197623
C3⋊#41834