Finite Group Databasebeta

← #10593737⋊C3 #13165842

Subgroups — #10593737⋊C3 #13165842

Order 1728.

144 conjugacy classes of subgroups; only the 15 normal subgroups are shown.

normal subgroups only

This group has 144 conjugacy classes of subgroups — too many to draw. Only its 15 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⋊D3×C42⋊C3C211yesmaximal, characteristic
2#10593737C311yesmaximal, characteristic, complemented
3A4×#157—41nomaximal
4C32×C42⋊C3C411yescharacteristic, complemented
5C42×C3⋊D3C2×C311yescharacteristic
6#63781—31no—
7#63781—31no—
8D3×C42⋊C3—62no—
9A4×C3⋊D3—41no—
10#383⋊C3—91nomaximal
11C22×#157—31no—
12C22×#157A411yescharacteristic
13C2×C4×C3⋊D3—31no—
14C32×C42C3×C411yescharacteristic, complemented
15C4×C3⋊Dic3—31no—
16C3×C42⋊C3—22no—
17C3×C42⋊C3—42no—
18C32×A4—41no—
19C3×#157—161no—
20C42×D3—62no—
21C2×C42⋊C3—91no—
22C22×C3⋊D3C2×A411yescharacteristic
23C2×#157—61no—
24C2×#157—61no—
25C2×#157—62no—
26D3×A4—242no—
27C2×C32×C4—31no—
28C2×C3⋊Dic3—31no—
29C4×C3⋊D3—61no—
30C4×C3⋊D3—61no—
31#383—91noSylow
32C3×C3⋊D3—161no—
33C2×C4×D3—182no—
34C4×A4—361no—
35C3×C42—22no—
36C4×Dic3—182no—
37C42⋊C3—42no—
38C42⋊C3#15711yescharacteristic, complemented
39C22×C32C4×A411yescharacteristic
40C2×C3⋊D3—31no—
41C2×C3⋊D3—31no—
42C3×A4—82no—
43C3×A4—162no—
44#157—41no—
45#157—121no—
46C32×C4—61no—
47C3⋊Dic3—61no—
48C2×C42—91no—
49#95—271no—
50#95—271no—
51C33—161noSylow
52C22×D3—62no—
53C2×A4—361no—
54C2×C3×C4—62no—
55C2×Dic3—182no—
56C4×D3—184no—
57C4×D3—184no—
58C2×C32—31no—
59C3⋊D3—31no—
60C3⋊D3#126⋊C311yescharacteristic
61C3×D3—962no—
62C22×C4—91no—
63C22×C4—271no—
64C22×C4—271no—
65C42—271no—
66C42C3×#15711yescharacteristic, complemented
67C22×C3—22no—
68C2×D3—182no—
69C2×D3—182no—
70A4—41no—
71A4—162no—
72C3×C4—64no—
73C3×C4—1441no—
74Dic3—184no—
75C32—322no—
76C32—642no—
77C32#383⋊C311yescharacteristic, complemented
78C23—91no—
79C2×C4—31no—
80C2×C4—271no—
81C2×C4—541no—
82C2×C4—541no—
83C2×C4—541no—
84C2×C4—541no—
85C2×C4—542no—
86C2×C3—62no—
87C2×C3—1441no—
88D3—62no—
89D3—182no—
90C22—271no—
91C22—271no—
92C22A4×#15711yescharacteristic
93C4—61no—
94C4—361no—
95C4—541no—
96C4—1081no—
97C3—22no—
98C3—161no—
99C3—642no—
100C2—31no—
101C2—91no—
102C2—271no—
subgroupG/H
center, hypercenterC1G
commutator, Fitting, hypocenterC32×C42C3×C4
FrattiniC22A4×#157
socleC22×C32C4×A4
prime radicalC3⋊D3×C42⋊C3C2
cosocleC42×C3⋊D3C2×C3
LCSG ▷ C32×C42
UCSC1

Complements

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

NH ≅ G/Ntype
2. #10593737C3semidirect
4. C32×C42⋊C3C4semidirect
14. C32×C42C3×C4semidirect
38. C42⋊C3#157semidirect
66. C42C3×#157semidirect
77. C32#383⋊C3semidirect

Maximal subgroups

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

subgroupindex
C3⋊D3×C42⋊C32
#105937373
A4×#1574
#383⋊C39