Finite Group Databasebeta

← C3⋊(#1658⋊C3) #11920175

Subgroups — C3⋊(#1658⋊C3) #11920175

Order 1152.

102 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#564⋊C3C211yesmaximal, characteristic, complemented
2#71960C311yesmaximal, characteristic, complemented
3#1658⋊C3—31nomaximal
4C3⋊(#127⋊C3)—41nomaximal
5C3×#564C2×C311yescharacteristic, complemented
6#564⋊C3—21no—
7#564⋊C3D311yescharacteristic, complemented
8#5067—31no—
9#4543—31no—
10C3×C42⋊C3—41no—
11C3×C42⋊C3—82no—
12#1658—31noSylow
13C3×#125—31no—
14C3×#125—62no—
15#874A411yescharacteristic
16#127⋊C3—121no—
17#809—62no—
18#803—31no—
19D3×A4—161no—
20#564C3×D311yescharacteristic, complemented
21#490—91no—
22#330—91no—
23C2×D12—61no—
24C3×C4⋊C4—32no—
25C3×C4⋊C4—62no—
26C3×C4⋊C4—62no—
27C3×C42—22no—
28C3×C42C2×A411yescharacteristic
29C2×C3⋊C8—61no—
30C42⋊C3—41no—
31C42⋊C3—82no—
32C42⋊C3—84no—
33C42⋊C3—81no—
34C3×A4—161no—
35#127—31no—
36#125—31no—
37#125—62no—
38#102—182no—
39#97—91no—
40C22×D3—41no—
41C2×A4—481no—
42C2×C3×C4—31no—
43C2×C3×C4—62no—
44D12—122no—
45C3⋊C8—121no—
46C3×D3—641no—
47C2×D4—181no—
48C2×C8—181no—
49C4⋊C4—32no—
50C4⋊C4—62no—
51C4⋊C4—62no—
52C42—22no—
53C42D3×A411yescharacteristic
54C22×C3#120⋊C311yescharacteristic
55C2×D3—241no—
56A4—161no—
57A4—321no—
58C3×C4—61no—
59C3×C4—122no—
60C32—641noSylow
61C23—121no—
62D4—362no—
63C2×C4—31no—
64C2×C4—62no—
65C8—361no—
66C2×C3—31no—
67C2×C3—1921no—
68D3—161no—
69C22—721no—
70C22C3⋊(#120⋊C3)11yescharacteristic
71C4—61no—
72C4—122no—
73C3—641no—
74C3—1281no—
75C3#1658⋊C311yescharacteristic, complemented
76C2—31no—
77C2—481no—
subgroupG/H
center, hypercenterC1G
commutator, Fitting, cosocle, hypocenterC3×#564C2×C3
FrattiniC42D3×A4
socleC22×C3#120⋊C3
LCSG ▷ C3×#564
UCSC1

Complements

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

NH ≅ G/Ntype
1. C3×#564⋊C3C2semidirect
2. #71960C3semidirect
5. C3×#564C2×C3semidirect
7. #564⋊C3D3semidirect
20. #564C3×D3semidirect
75. C3#1658⋊C3semidirect

Maximal subgroups

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

subgroupindex
C3×#564⋊C32
#719603
#1658⋊C33
C3⋊(#127⋊C3)4