Finite Group Databasebeta

← C3⋊Dic3×C22⋊A4 #13181486

Subgroups — C3⋊Dic3×C22⋊A4 #13181486

Order 1728.

1684 conjugacy classes of subgroups; only the 104 normal subgroups are shown.

normal subgroups only

This group has 1684 conjugacy classes of subgroups — too many to draw. Only its 104 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
1C2×C32×C22⋊A4C211yesmaximal, characteristic
2C24×C3⋊Dic3C311yesmaximal, characteristic, complemented
3Dic3×C22⋊A4—34nomaximal
4C32×C22⋊A4C411yescharacteristic, complemented
5A4×C3⋊Dic3—45nomaximal
6C25×C32C2×C311yescharacteristic
7C2×C3×C22⋊A4—24no—
8C2×C3×C22⋊A4D314yes—
9C23×C3⋊Dic3—35no—
10C23×C3⋊Dic3—35no—
11C2×C32×A4—45no—
12C24×Dic3—34no—
13C4×C22⋊A4—91no—
14C24×C32—35no—
15C24×C32—35no—
16C24×C32C3×C411yescharacteristic, complemented
17C3×C22⋊A4—24no—
18C3×C22⋊A4Dic314yescomplemented
19C22×C3⋊Dic3—330no—
20C22×C3⋊Dic3—310no—
21C22×C3⋊Dic3—35no—
22C22×C3⋊Dic3A415yescomplemented
23Dic3×A4—1220no—
24C32×A4—45no—
25C3×C3⋊Dic3—161no—
26C25×C3C3×D314yes—
27C2×C22⋊A4—24no—
28C2×C22⋊A4C3⋊D311yescharacteristic
29C23×Dic3—920no—
30C23×Dic3—920no—
31C23×C32—330no—
32C23×C32—310no—
33C23×C32—35no—
34C23×C32—35no—
35C23×C32C2×A415yes—
36C2×C3×A4—420no—
37C2×C3×A4—820no—
38C2×C3⋊Dic3—330no—
39C2×C3⋊Dic3—35no—
40C2×C3⋊Dic3—35no—
41C24×C4—91noSylow
42C2×C33—161no—
43C24×C3—320no—
44C24×C3—320no—
45C24×C3C3×Dic314yescomplemented
46C22⋊A4—24no—
47C22⋊A4C3⋊Dic311yescharacteristic, direct product factor
48C22×Dic3—320no—
49C22×Dic3—940no—
50C22×Dic3—9120no—
51C22×Dic3—920no—
52C4×A4—365no—
53C22×C32—35no—
54C22×C32—330no—
55C22×C32—310no—
56C22×C32—35no—
57C22×C32C4×A415yescomplemented
58C3×A4—420no—
59C3×A4—820no—
60C3⋊Dic3—35no—
61C3⋊Dic3C22⋊A411yescharacteristic, direct product factor
62C3×Dic3—484no—
63C25C3×C3⋊D311yescharacteristic
64C23×C4—275no—
65C23×C4—275no—
66C33—161noSylow
67C23×C3—340no—
68C23×C3—3120no—
69C23×C3—320no—
70C23×C3—320no—
71C23×C3D3×A4120yes—
72C2×A4—45no—
73C2×A4—820no—
74C2×Dic3—920no—
75C2×Dic3—9120no—
76C2×Dic3—920no—
77C2×C32—35no—
78C2×C32—35no—
79C2×C32—164no—
80C2×C32—324no—
81C2×C32C2×C22⋊A411yescharacteristic
82C24—35no—
83C24—35no—
84C24C3×C3⋊Dic311yescharacteristic, complemented
85C22×C4—95no—
86C22×C4—2710no—
87C22×C4—2730no—
88C22×C4—275no—
89C22×C3—320no—
90C22×C3—340no—
91C22×C3—3120no—
92C22×C3—320no—
93C22×C3Dic3×A4120yescomplemented
94A4—45no—
95A4—820no—
96C3×C4—1441no—
97Dic3—34no—
98Dic3—920no—
99C32—164no—
100C32—324no—
101C32C4×C22⋊A411yescharacteristic, complemented
102C23—310no—
103C23—330no—
104C23—35no—
105C23—35no—
106C23A4×C3⋊D315yes—
107C2×C4—275no—
108C2×C4—2730no—
109C2×C4—275no—
110C2×C3—320no—
111C2×C3—320no—
112C2×C3—161no—
113C2×C3—324no—
114C2×C3D3×C22⋊A414yes—
115C22—35no—
116C22—310no—
117C22—330no—
118C22—35no—
119C22A4×C3⋊Dic315yescomplemented
120C4—91no—
121C4—275no—
122C3—161no—
123C3—324no—
124C3Dic3×C22⋊A414yescomplemented
125C2—35no—
126C2—35no—
127C2C3⋊D3×C22⋊A411yescharacteristic
subgroupG/H
center, Frattini, hypercenterC2C3⋊D3×C22⋊A4
commutator, hypocenterC24×C32C3×C4
Fitting, socle, cosocleC25×C32C2×C3
prime radicalC2×C32×C22⋊A4C2
LCSG ▷ C24×C32
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
2. C24×C3⋊Dic3C3semidirect
4. C32×C22⋊A4C4semidirect
16. C24×C32C3×C4semidirect
18. C3×C22⋊A4Dic3semidirect
22. C22×C3⋊Dic3A4semidirect
45. C24×C3C3×Dic3semidirect
47. C22⋊A4C3⋊Dic3direct (N × H)
57. C22×C32C4×A4semidirect
61. C3⋊Dic3C22⋊A4direct (N × H)
84. C24C3×C3⋊Dic3semidirect
93. C22×C3Dic3×A4semidirect
101. C32C4×C22⋊A4semidirect
119. C22A4×C3⋊Dic3semidirect
124. C3Dic3×C22⋊A4semidirect

Maximal subgroups

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

subgroupindex
C2×C32×C22⋊A42
C24×C3⋊Dic33
Dic3×C22⋊A43
A4×C3⋊Dic34