Finite Group Databasebeta

← C3⋊(#1747⋊C3) #11920149

Subgroups — C3⋊(#1747⋊C3) #11920149

Order 1152.

107 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#338⋊C3C211yesmaximal, characteristic
2#68717C311yesmaximal, characteristic, complemented
3#1747⋊C3—31nomaximal
4A4×C3⋊C8—41nomaximal
5#5122—31no—
6C3×#338C2×C311yescharacteristic
7#4557—31no—
8#338⋊C3—21no—
9#338⋊C3D311yescharacteristic
10C3×C4×A4—41no—
11#1747—31noSylow
12C2×C3×M16—31no—
13#926—31no—
14C22×C3⋊C8A411yescharacteristic
15C8×A4—121no—
16#815—32no—
17C8×Dic3—32no—
18C2×C3×A4—41no—
19C3×C3⋊C8—161no—
20#405—91no—
21#338C3×D311yescharacteristic
22H(3,ℤ/4)—91no—
23C22×C3×C4C2×A411yescharacteristic
24C4×A4—41no—
25C4×A4—81no—
26C3×M16—62no—
27C2×C3×C8—32no—
28#217—61no—
29C4⋊Dic3—61no—
30C4×Dic3—32no—
31C2×C3⋊C8—31no—
32C2×C3⋊C8—31no—
33C3×A4—41no—
34C32×C4—161no—
35C2×M16—31no—
36C22×C8—31no—
37#117—91no—
38#97—92no—
39C4×C8—92no—
40C23×C3#41⋊C311yescharacteristic
41C2×A4—41no—
42C2×A4—81no—
43C2×C3×C4—31no—
44C2×C3×C4—31no—
45C2×Dic3—62no—
46C3×C8—62no—
47C3×C8—481no—
48C3⋊C8—31no—
49C3⋊C8C42⋊C311yescharacteristic
50C2×C32—161no—
51C22×C4D3×A411yescharacteristic
52M16—62no—
53C2×C8—32no—
54C2×C8—91no—
55C2×C8—91no—
56C4⋊C4—181no—
57C22⋊C4—181no—
58C42—92no—
59C22×C3—31no—
60C22×C3—41no—
61A4—41no—
62A4—81no—
63C3×C4—31no—
64C3×C4—161no—
65C3×C4—321no—
66C3×C4C2×C42⋊C311yescharacteristic
67Dic3—122no—
68C32—161noSylow
69C23C3⋊(#41⋊C3)11yescharacteristic
70C2×C4—31no—
71C2×C4—31no—
72C2×C4—182no—
73C8—31no—
74C8—62no—
75C8—91no—
76C2×C3—61no—
77C2×C3—161no—
78C2×C3—321no—
79C2×C3#376⋊C311yescharacteristic
80C22—31no—
81C22—41no—
82C4—31no—
83C4—362no—
84C4D3×C42⋊C311yescharacteristic
85C3—161no—
86C3—321no—
87C3#1747⋊C311yescharacteristic, complemented
88C2—61no—
89C2C3⋊(#376⋊C3)11yescharacteristic
subgroupG/H
center, hypercenterC4D3×C42⋊C3
commutator, Fitting, cosocle, hypocenterC3×#338C2×C3
FrattiniC22×C4D3×A4
socleC2×C3#376⋊C3
prime radicalC3×#338⋊C3C2
LCSG ▷ C3×#338
UCSC1 ◁ C4

Complements

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

NH ≅ G/Ntype
2. #68717C3semidirect
87. C3#1747⋊C3semidirect

Maximal subgroups

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

subgroupindex
C3×#338⋊C32
#687173
#1747⋊C33
A4×C3⋊C84