Finite Group Databasebeta

← #10593838⋊C3 #13165845

Subgroups — #10593838⋊C3 #13165845

Order 1728.

122 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3⋊(C3⋊(#131⋊C3))C211yesmaximal, characteristic
2#10593838C311yesmaximal, characteristic, complemented
3C32×#41⋊C3C411yescharacteristic
4C3×#3708—41nomaximal
5#64157C2×C311yescharacteristic
6#63773—31no—
7C2×#3708—31no—
8C3⋊(#131⋊C3)—62no—
9C32×SL(2,𝔽3)C811yescharacteristic
10C3×C3⋊(C3⋊C8)—41no—
11#504⋊C3—91nomaximal
12C32×#41C3×C411yescharacteristic
13C3×#41⋊C3—22no—
14C3×#41⋊C3—42no—
15#3748—31no—
16C2×C3⋊(C3⋊C8)—31no—
17#3708—31no—
18#3708A411yescharacteristic
19C33×C4—41no—
20#948—62no—
21#131⋊C3—91no—
22C32×Q8C3×C811yescharacteristic
23C32×D4—31no—
24C2×C32×C4—31no—
25C3×SL(2,𝔽3)—22no—
26C3×SL(2,𝔽3)—42no—
27C3⋊(C3⋊C8)—31no—
28C3⋊(C3⋊C8)C2×A411yescharacteristic
29C3×C3⋊C8—242no—
30#504—91noSylow
31C2×C33—41no—
32C3×#41—22no—
33#41⋊C3—42no—
34#41⋊C3#15711yescharacteristic
35#208—182no—
36C2×C3⋊C8—182no—
37C3×C16—361no—
38C22×C32—31no—
39C32×C4—31no—
40C32×C4—82no—
41C32×C4—162no—
42C32×C4C4×A411yescharacteristic
43#131—91no—
44M32—271no—
45C2×C16—271no—
46C33—41noSylow
47C3×Q8—22no—
48C3×D4—62no—
49C2×C3×C4—62no—
50SL(2,𝔽3)—42no—
51SL(2,𝔽3)#62211yescharacteristic
52C3×C8—361no—
53C3⋊C8—62no—
54C3⋊C8—182no—
55C2×C32—61no—
56C2×C32—82no—
57C2×C32—162no—
58C2×C32C8×A411yescharacteristic
59#41C3×#15711yescharacteristic
60M16—271no—
61C2×C8—271no—
62C16—91no—
63C16—271no—
64C22×C3—62no—
65C3×C4—22no—
66C3×C4—41no—
67C3×C4—62no—
68C3×C4—162no—
69C32—82no—
70C32—162no—
71C32#504⋊C311yescharacteristic, complemented
72Q8C3×#62211yescharacteristic
73D4—31no—
74C2×C4—31no—
75C8—91no—
76C8—271no—
77C2×C3—22no—
78C2×C3—41no—
79C2×C3—122no—
80C2×C3—162no—
81C22—31no—
82C4—31no—
83C4A4×#15711yescharacteristic
84C3—22no—
85C3—41no—
86C3—162no—
87C2—61no—
88C2A4×#62211yescharacteristic
subgroupG/H
center, Frattini, hypercenterC4A4×#157
commutator, hypocenterC32×Q8C3×C8
FittingC32×#41C3×C4
socleC2×C32C8×A4
prime radicalC32×#41⋊C3C4
cosocle#64157C2×C3
LCSG ▷ C32×Q8
UCSC1 ◁ C4

Complements

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

NH ≅ G/Ntype
2. #10593838C3semidirect
71. C32#504⋊C3semidirect

Maximal subgroups

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

subgroupindex
C3⋊(C3⋊(#131⋊C3))2
#105938383
C3×#37084
#504⋊C39