Finite Group Databasebeta

← C3⋊#10619750 #14518109

Subgroups — C3⋊#10619750 #14518109

Order 1944.

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

normal subgroups only

This group has 375 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×#66358C211yesmaximal, characteristic, complemented
2C3⋊((C3⋊S4)⋊C3)—33nomaximal
3C3×#6233—31nomaximal
4#10619750—39nomaximal
5C3⋊#4185—41nomaximal
6C22×C32×C9D311yescharacteristic, complemented
7C2×C3×C3⋊D9—31no—
8C3×C22⋊H(3,𝔽3)D313yescomplemented
9C3×C3⋊Dic9—31no—
10#66358D319yescomplemented
11C3×#732—41noSylow
12C3⋊(C3⋊S4)—33no—
13C3×#638—91no—
14(C3⋊S4)⋊C3—99no—
15#6233—31no—
16C3×#611—93no—
17C2×C32×C9—31no—
18C3⋊((C3⋊D3)⋊C3)—123no—
19C3×C3⋊D9—61no—
20#4185—129no—
21C22×C33C3⋊D311yescharacteristic
22C2×C3×C3⋊D3—91no—
23C32×A4—33no—
24C3×C3⋊Dic3—91no—
25C22×C3×C9—31no—
26C22×C3×C9—61no—
27C22×C3×C9C3⋊D313yescomplemented
28C2×C3⋊D9—31no—
29C2×C3×D9—93no—
30C22⋊H(3,𝔽3)—63no—
31C22⋊H(3,𝔽3)C3⋊D319yescomplemented
32C3⋊Dic9—31no—
33C3×Dic9—93no—
34C3×H(3,𝔽3)—43no—
35C32×C9S411yescharacteristic, complemented
36#732—49no—
37C3⋊S4—99no—
38C3⋊S4—279no—
39#638—91no—
40C3×#67—273no—
41C3×#67—271no—
42#611—93no—
43C2×C33—31no—
44C3⋊(C3⋊D3)—123no—
45C3×C3⋊D3—181no—
46C2×C3×C9—31no—
47C2×C3×C9—33no—
48C2×C3×C9—63no—
49C2×C3×C9—61no—
50C3⋊D9—61no—
51(C3⋊D3)⋊C3—369no—
52C3×D9—183no—
53C22×C32—21no—
54C22×C32—33no—
55C22×C32#27211yescharacteristic
56C22×C32C3⋊(C3⋊D3)11yescharacteristic
57C2×C3⋊D3—91no—
58C2×C3×D3—271no—
59C2×C3×D3—273no—
60C3×A4—39no—
61C3×A4—99no—
62C3⋊Dic3—91no—
63C3×Dic3—271no—
64C3×Dic3—273no—
65C22×C9—33no—
66C2×D9—93no—
67Dic9—93no—
68C33—123no—
69C33C3⋊S411yescharacteristic
70H(3,𝔽3)—49no—
71H(3,𝔽3)—243no—
72C3×C9—31no—
73C3×C9—61no—
74C3×C9C3⋊S413yescomplemented
75S4—819no—
76C3×D4—811no—
77#67—273no—
78#67—271no—
79C2×C32—31no—
80C2×C32—33no—
81C2×C32—31no—
82C2×C32—61no—
83C2×C32—63no—
84C3⋊D3—181no—
85C3⋊D3—369no—
86C3⋊D3—1089no—
87C3×D3—543no—
88C3×D3—541no—
89C2×C9—33no—
90C2×C9—63no—
91D9—183no—
92C22×C3—31no—
93C22×C3—61no—
94C22×C3—811no—
95C22×C3#418513yescomplemented
96C22×C3C3⋊#27211yescharacteristic
97C2×D3—271no—
98C2×D3—273no—
99A4—99no—
100C3×C4—811no—
101Dic3—271no—
102Dic3—273no—
103C32—21no—
104C32—33no—
105C32—129no—
106C32—369no—
107C32#625811yescharacteristic
108C32C3⋊(C3⋊S4)11yescharacteristic
109C9—33no—
110D4—811noSylow
111C2×C3—31no—
112C2×C3—33no—
113C2×C3—31no—
114C2×C3—61no—
115C2×C3—63no—
116C2×C3—1621no—
117D3—543no—
118D3—541no—
119D3—3249no—
120C22—811no—
121C22C3⋊#418511yescharacteristic, complemented
122C4—811no—
123C3—31no—
124C3—61no—
125C3—369no—
126C3#1061975013yescomplemented
127C3C3⋊#625811yescharacteristic
128C2—31no—
129C2—1621no—
subgroupG/H
center, hypercenterC1G
commutator, cosocle, hypocenterC3×#66358C2
FrattiniC32C3⋊(C3⋊S4)
FittingC22×C32×C9D3
socleC22×C32#272
LCSG ▷ C3×#66358
UCSC1

Complements

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

NH ≅ G/Ntype
1. C3×#66358C2semidirect
6. C22×C32×C9D3semidirect
8. C3×C22⋊H(3,𝔽3)D3semidirect
10. #66358D3semidirect
27. C22×C3×C9C3⋊D3semidirect
31. C22⋊H(3,𝔽3)C3⋊D3semidirect
35. C32×C9S4semidirect
74. C3×C9C3⋊S4semidirect
95. C22×C3#4185semidirect
121. C22C3⋊#4185semidirect
126. C3#10619750semidirect

Maximal subgroups

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

subgroupindex
C3×#663582
C3⋊((C3⋊S4)⋊C3)3
C3×#62333
#106197503
C3⋊#41854