Finite Group Databasebeta

← Dic9×C42⋊C3 #13136809

Subgroups — Dic9×C42⋊C3 #13136809

Order 1728.

186 conjugacy classes of subgroups; only the 28 normal subgroups are shown.

normal subgroups only

This group has 186 conjugacy classes of subgroups — too many to draw. Only its 28 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×C9×C42⋊C3C211yesmaximal, characteristic
2Dic3×C42⋊C3—31nomaximal
3C42×Dic9C311yesmaximal, characteristic, complemented
4A4×Dic9—41nomaximal
5C9×C42⋊C3C411yescharacteristic, complemented
6C2×C3×C42⋊C3D311yescharacteristic
7C2×C42×C9C2×C311yescharacteristic
8C2×C4×Dic9—31no—
9C2×C4×Dic9—31no—
10C2×C42⋊C9—21no—
11C2×C9×A4—41no—
12C42×Dic3—31no—
13C4×C42⋊C3—91no—
14Dic3×A4—121no—
15C3×C42⋊C3Dic311yescharacteristic
16C22×C4×C9—31no—
17C22×Dic9—31no—
18C22×Dic9A411yescharacteristic
19C42×C9—31no—
20C42×C9C3×C411yescharacteristic, complemented
21C4×Dic9—34no—
22C4×Dic9—32no—
23C4×Dic9—32no—
24C42⋊C9—21no—
25C9×A4—41no—
26C3×Dic9—161no—
27C2×C3×C42C3×D311yescharacteristic
28C2×C4×Dic3—91no—
29C2×C4×Dic3—91no—
30C2×C42⋊C3—21no—
31C2×C42⋊C3D911yescharacteristic
32C2×C3×A4—41no—
33C23×C9C2×A411yescharacteristic
34C2×C22⋊C9—81no—
35C2×C4×C9—32no—
36C2×C4×C9—32no—
37C2×C4×C9—31no—
38C2×C4×C9—31no—
39C2×Dic9—34no—
40C2×Dic9—32no—
41C2×Dic9—31no—
42C2×Dic9—31no—
43C43—91noSylow
44C2×C3×C9—161no—
45C22×C3×C4—31no—
46C22×Dic3—31no—
47C22×Dic3—91no—
48C4×A4—361no—
49C3×C42—31no—
50C3×C42C3×Dic311yescharacteristic
51C4×Dic3—92no—
52C4×Dic3—94no—
53C4×Dic3—92no—
54C42⋊C3—21no—
55C42⋊C3Dic911yescharacteristic, direct product factor
56C3×A4—41no—
57C3×Dic3—481no—
58C22×C9—31no—
59C22×C9—31no—
60C22×C9C4×A411yescharacteristic
61C22⋊C9—81no—
62C4×C9—32no—
63C4×C9—32no—
64Dic9—34no—
65Dic9—31no—
66Dic9C42⋊C311yescharacteristic, direct product factor
67C2×C42—271no—
68C2×C42—271no—
69C2×C42C3×D911yescharacteristic
70C3×C9—161noSylow
71C23×C3D3×A411yescharacteristic
72C2×A4—41no—
73C2×A4—81no—
74C2×C3×C4—32no—
75C2×C3×C4—32no—
76C2×C3×C4—31no—
77C2×C3×C4—31no—
78C2×Dic3—91no—
79C2×Dic3—94no—
80C2×Dic3—92no—
81C2×Dic3—91no—
82C2×C32—161no—
83C2×C9—31no—
84C2×C9—31no—
85C2×C9—321no—
86C2×C9C2×C42⋊C311yescharacteristic
87C22×C4—31no—
88C22×C4—91no—
89C22×C4—271no—
90C42—31no—
91C42—272no—
92C42—274no—
93C42—272no—
94C42C3×Dic911yescharacteristic, complemented
95C22×C3—31no—
96C22×C3—31no—
97C22×C3Dic3×A411yescharacteristic
98A4—41no—
99A4—81no—
100C3×C4—32no—
101C3×C4—32no—
102C3×C4—1441no—
103Dic3—31no—
104Dic3—94no—
105Dic3—91no—
106C32—161no—
107C9—321no—
108C9C4×C42⋊C311yescharacteristic, complemented
109C23A4×D911yescharacteristic
110C2×C4—32no—
111C2×C4—32no—
112C2×C4—31no—
113C2×C4—31no—
114C2×C4—271no—
115C2×C4—274no—
116C2×C4—272no—
117C2×C4—271no—
118C2×C3—31no—
119C2×C3—31no—
120C2×C3—161no—
121C2×C3—321no—
122C2×C3D3×C42⋊C311yescharacteristic
123C22—31no—
124C22—31no—
125C22A4×Dic911yescharacteristic
126C4—32no—
127C4—32no—
128C4—91no—
129C4—274no—
130C4—271no—
131C3—161no—
132C3—321no—
133C3Dic3×C42⋊C311yescharacteristic
134C2—31no—
135C2—31no—
136C2D9×C42⋊C311yescharacteristic
subgroupG/H
center, hypercenterC2D9×C42⋊C3
commutator, hypocenterC42×C9C3×C4
Frattini, socleC23×C3D3×A4
Fitting, cosocleC2×C42×C9C2×C3
prime radicalC2×C3×C42⋊C3D3
LCSG ▷ C42×C9
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
3. C42×Dic9C3semidirect
5. C9×C42⋊C3C4semidirect
20. C42×C9C3×C4semidirect
55. C42⋊C3Dic9direct (N × H)
66. Dic9C42⋊C3direct (N × H)
94. C42C3×Dic9semidirect
108. C9C4×C42⋊C3semidirect

Maximal subgroups

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

subgroupindex
C2×C9×C42⋊C32
Dic3×C42⋊C33
C42×Dic93
A4×Dic94