Finite Group Databasebeta

← C3×#2810⋊C3 #11919648

Subgroups — C3×#2810⋊C3 #11919648

Order 1152.

184 conjugacy classes of subgroups; only the 24 normal subgroups are shown.

normal subgroups only

This group has 184 conjugacy classes of subgroups — too many to draw. Only its 24 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×#2810C311yesmaximal, characteristic, complemented
2#2810⋊C3C313yesmaximal, direct product factor
3C2×C3×C42⋊C3—42nomaximal
4C2×C3×C42⋊C3—41nomaximal
5C3×#95⋊C3—42nomaximal
6C3×#400—32no—
7C3×#389—31no—
8C3×#387—32no—
9C3×C42⋊C3—41no—
10C3×C42⋊C3—42no—
11#2810C3211yescharacteristic, complemented, Sylow
12C2×C3×C4⋊C4—32no—
13C2×C3×C4⋊C4—31no—
14C2×C3×C4⋊C4—31no—
15C2×C3×C42A412yes—
16C2×C3×C42A411yescharacteristic
17C2×C42⋊C3—46no—
18C2×C42⋊C3—43no—
19C3×#95—32no—
20C3×#95—32no—
21C3×#95—32no—
22C3×#95A412yes—
23#95⋊C3—46no—
24C2×C3×A4—161no—
25#400—32no—
26#389—31no—
27#387—32no—
28C22×C3×C4—31no—
29C22×C3×C4—32no—
30C22×C3×C4—32no—
31C3×C4⋊C4—64no—
32C3×C4⋊C4—62no—
33C3×C4⋊C4—121no—
34C3×C42—41no—
35C3×C42—42no—
36C42⋊C3—43no—
37C42⋊C3—46no—
38C3×A4—161no—
39C2×C4⋊C4—32no—
40C2×C4⋊C4—31no—
41C2×C4⋊C4—31no—
42C2×C42C3×A412yes—
43C2×C42C3×A411yescharacteristic
44#95—32no—
45#95—32no—
46#95—32no—
47#95C3×A412yes—
48C23×C3C22⋊A411yescharacteristic
49C2×A4—163no—
50C2×C3×C4—32no—
51C2×C3×C4—61no—
52C2×C3×C4—61no—
53C2×C3×C4—62no—
54C2×C3×C4—62no—
55C2×C3×C4—62no—
56C2×C3×C4—62no—
57C2×C3×C4—62no—
58C2×C3×C4—62no—
59C2×C32—641no—
60C22×C4—31no—
61C22×C4—32no—
62C22×C4—32no—
63C4⋊C4—64no—
64C4⋊C4—62no—
65C4⋊C4—121no—
66C42—41no—
67C42—42no—
68C22×C3—31no—
69C22×C3—31no—
70C22×C3#99711yescharacteristic
71A4—163no—
72C3×C4—62no—
73C3×C4—122no—
74C3×C4—122no—
75C32—641noSylow
76C23C3×C22⋊A411yescharacteristic
77C2×C4—32no—
78C2×C4—61no—
79C2×C4—61no—
80C2×C4—62no—
81C2×C4—62no—
82C2×C4—62no—
83C2×C4—62no—
84C2×C4—62no—
85C2×C4—62no—
86C2×C3—31no—
87C2×C3—31no—
88C2×C3—643no—
89C2×C3#564⋊C311yescharacteristic
90C22—31no—
91C22—31no—
92C22C3×#99711yescharacteristic
93C4—62no—
94C4—122no—
95C4—122no—
96C3—643no—
97C3#2810⋊C311yescharacteristic, direct product factor
98C2—31no—
99C2—31no—
100C2C3×#564⋊C311yescharacteristic
subgroupG/H
center, hypercenterC2×C3#564⋊C3
commutator, cosocle, hypocenter#2810C32
FrattiniC23C3×C22⋊A4
FittingC3×#2810C3
socleC23×C3C22⋊A4
LCSG ▷ #2810
UCSC1 ◁ C2×C3

Complements

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

NH ≅ G/Ntype
1. C3×#2810C3semidirect
2. #2810⋊C3C3direct (N × H)
11. #2810C32semidirect
97. C3#2810⋊C3direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#28103
#2810⋊C33
C2×C3×C42⋊C34
C3×#95⋊C34