Finite Group Databasebeta

← #2810⋊C9 #11919649

Subgroups — #2810⋊C9 #11919649

Order 1152.

145 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#2810C311yesmaximal, characteristic
2C2×C42⋊C9—42nomaximal
3C2×C42⋊C9—41nomaximal
4#95⋊C9—42nomaximal
5C3×#400—32no—
6C3×#389—31no—
7C3×#387—32no—
8C42⋊C9—41no—
9C42⋊C9—42no—
10#2810C911yescharacteristic, complemented, Sylow
11C2×C3×C4⋊C4—32no—
12C2×C3×C4⋊C4—31no—
13C2×C3×C4⋊C4—31no—
14C2×C3×C42A412yes—
15C2×C3×C42A411yescharacteristic
16C3×#95—32no—
17C3×#95—32no—
18C3×#95—32no—
19C3×#95A412yes—
20C2×C22⋊C9—161no—
21#400—32no—
22#389—31no—
23#387—32no—
24C22×C3×C4—31no—
25C22×C3×C4—32no—
26C22×C3×C4—32no—
27C3×C4⋊C4—64no—
28C3×C4⋊C4—62no—
29C3×C4⋊C4—121no—
30C3×C42—41no—
31C3×C42—42no—
32C22⋊C9—161no—
33C2×C4⋊C4—32no—
34C2×C4⋊C4—31no—
35C2×C4⋊C4—31no—
36C2×C42C22⋊C912yes—
37C2×C42C22⋊C911yescharacteristic
38#95—32no—
39#95—32no—
40#95—32no—
41#95C22⋊C912yes—
42C23×C3C22⋊A411yescharacteristic
43C2×C3×C4—32no—
44C2×C3×C4—61no—
45C2×C3×C4—61no—
46C2×C3×C4—62no—
47C2×C3×C4—62no—
48C2×C3×C4—62no—
49C2×C3×C4—62no—
50C2×C3×C4—62no—
51C2×C3×C4—62no—
52C2×C9—641no—
53C22×C4—31no—
54C22×C4—32no—
55C22×C4—32no—
56C4⋊C4—64no—
57C4⋊C4—62no—
58C4⋊C4—121no—
59C42—41no—
60C42—42no—
61C22×C3—31no—
62C22×C3—31no—
63C22×C3#99711yescharacteristic
64C3×C4—62no—
65C3×C4—122no—
66C3×C4—122no—
67C9—641noSylow
68C23C22⋊(C22⋊C9)11yescharacteristic
69C2×C4—32no—
70C2×C4—61no—
71C2×C4—61no—
72C2×C4—62no—
73C2×C4—62no—
74C2×C4—62no—
75C2×C4—62no—
76C2×C4—62no—
77C2×C4—62no—
78C2×C3—31no—
79C2×C3—31no—
80C2×C3#564⋊C311yescharacteristic
81C22—31no—
82C22—31no—
83C22#6370311yescharacteristic
84C4—62no—
85C4—122no—
86C4—122no—
87C3#2810⋊C311yescharacteristic
88C2—31no—
89C2—31no—
90C2#564⋊C911yescharacteristic
subgroupG/H
center, hypercenterC2×C3#564⋊C3
commutator, hypocenter#2810C9
Frattini, socle, prime radicalC23×C3C22⋊A4
Fitting, cosocleC3×#2810C3
LCSG ▷ #2810
UCSC1 ◁ C2×C3

Complements

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

NH ≅ G/Ntype
10. #2810C9semidirect

Maximal subgroups

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

subgroupindex
C3×#28103
C2×C42⋊C94
#95⋊C94