Finite Group Databasebeta

← #10593735⋊C3 #13165841

Subgroups — #10593735⋊C3 #13165841

Order 1728.

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

normal subgroups only

This group has 160 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#10593735C311yesmaximal, characteristic, complemented
3A4×#157—41nomaximal
4C32×C42⋊C3C411yescharacteristic, complemented
5C2×C4⋊#157—31no—
6C2×C4⋊#157—31no—
7C42×C3⋊D3C2×C311yescharacteristic
8D3×C42⋊C3—62no—
9A4×C3⋊D3—41no—
10#384⋊C3—91nomaximal
11C22×#157—31no—
12C22×#157A411yescharacteristic
13C2×C4×C3⋊D3—31no—
14C4⋊#157—62no—
15C4⋊#157—62no—
16C32×C42C3×C411yescharacteristic, complemented
17C4×C3⋊Dic3—31no—
18C3×C42⋊C3—22no—
19C3×C42⋊C3—42no—
20C32×A4—41no—
21C3×#157—161no—
22C42×D3—62no—
23C2×C42⋊C3—91no—
24C22×C3⋊D3C2×A411yescharacteristic
25C2×#157—61no—
26C2×#157—61no—
27C2×#157—62no—
28D3×A4—242no—
29C2×C32×C4—31no—
30C2×C3⋊Dic3—31no—
31C4×C3⋊D3—32no—
32C4×C3⋊D3—32no—
33#384—91noSylow
34C3×C3⋊D3—161no—
35C2×C4×D3—182no—
36C4×A4—361no—
37C3×C42—22no—
38C4×Dic3—182no—
39C42⋊C3—42no—
40C42⋊C3#15711yescharacteristic, complemented
41C22×C32C4×A411yescharacteristic
42C2×C3⋊D3—31no—
43C2×C3⋊D3—31no—
44C3×A4—82no—
45C3×A4—162no—
46#157—41no—
47#157—121no—
48C32×C4—32no—
49C3⋊Dic3—32no—
50C2×C4⋊C4—271no—
51C2×C4⋊C4—271no—
52C2×C42—91no—
53C33—161noSylow
54C22×D3—62no—
55C2×A4—361no—
56C2×C3×C4—62no—
57C2×Dic3—182no—
58C4×D3—184no—
59C4×D3—184no—
60C2×C32—31no—
61C3⋊D3—31no—
62C3⋊D3#127⋊C311yescharacteristic
63C3×D3—962no—
64C22×C4—91no—
65C22×C4—271no—
66C22×C4—271no—
67C4⋊C4—542no—
68C4⋊C4—542no—
69C42—271no—
70C42C3×#15711yescharacteristic, complemented
71C22×C3—22no—
72C2×D3—182no—
73C2×D3—182no—
74A4—41no—
75A4—162no—
76C3×C4—64no—
77C3×C4—1441no—
78Dic3—184no—
79C32—322no—
80C32—642no—
81C32#384⋊C311yescharacteristic, complemented
82C23—91no—
83C2×C4—31no—
84C2×C4—272no—
85C2×C4—272no—
86C2×C4—271no—
87C2×C4—541no—
88C2×C4—541no—
89C2×C4—542no—
90C2×C3—62no—
91C2×C3—1441no—
92D3—62no—
93D3—182no—
94C22—271no—
95C22—271no—
96C22A4×#15711yescharacteristic
97C4—32no—
98C4—272no—
99C4—361no—
100C4—1081no—
101C3—22no—
102C3—161no—
103C3—642no—
104C2—31no—
105C2—91no—
106C2—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. #10593735C3semidirect
4. C32×C42⋊C3C4semidirect
16. C32×C42C3×C4semidirect
40. C42⋊C3#157semidirect
70. C42C3×#157semidirect
81. C32#384⋊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
#105937353
A4×#1574
#384⋊C39