Finite Group Databasebeta

← Dic3×C42⋊C9 #13136842

Subgroups — Dic3×C42⋊C9 #13136842

Order 1728.

242 conjugacy classes of subgroups; only the 35 normal subgroups are shown.

normal subgroups only

This group has 242 conjugacy classes of subgroups — too many to draw. Only its 35 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×C3×C42⋊C9C211yesmaximal, characteristic
2C3×C42×Dic3C311yesmaximal, characteristic
3C4×C42⋊C9—31nomaximal
4Dic3×C22⋊C9—41nomaximal
5C3×C42⋊C9C411yescharacteristic, complemented
6C2×C32×C42C2×C311yescharacteristic
7C2×C3×C4×Dic3—31no—
8C2×C3×C4×Dic3—31no—
9C2×C42⋊C9—21no—
10C2×C42⋊C9D311yescharacteristic
11C2×C3×C22⋊C9—41no—
12C3×C43—31no—
13C42×Dic3C911yescharacteristic, complemented
14C22×C32×C4—31no—
15C22×C3×Dic3—31no—
16C22×C3×Dic3A411yescharacteristic
17C32×C42—31no—
18C32×C42C3×C411yescharacteristic
19C3×C4×Dic3—34no—
20C3×C4×Dic3—32no—
21C3×C4×Dic3—32no—
22C4×C22⋊C9—121no—
23C42⋊C9—21no—
24C42⋊C9Dic311yescharacteristic, direct product factor
25C3×C22⋊C9—41no—
26C9×Dic3—161no—
27C2×C3×C42—21no—
28C2×C3×C42—91no—
29C2×C3×C42—91no—
30C2×C3×C42C2×C911yescharacteristic
31C2×C3×C42C3×D311yescharacteristic
32C2×C4×Dic3—31no—
33C2×C4×Dic3—31no—
34C23×C32C2×A411yescharacteristic
35C2×C32×C4—32no—
36C2×C32×C4—32no—
37C2×C32×C4—31no—
38C2×C32×C4—31no—
39C2×C3×Dic3—34no—
40C2×C3×Dic3—32no—
41C2×C3×Dic3—31no—
42C2×C3×Dic3—31no—
43C2×C22⋊C9—41no—
44C2×C22⋊C9—81no—
45C43—31noSylow
46C2×C3×C9—161no—
47C22×C3×C4—31no—
48C22×C3×C4—31no—
49C22×C3×C4—31no—
50C22×C3×C4—61no—
51C22×C3×C4—91no—
52C22×Dic3—31no—
53C22×Dic3C22⋊C911yescharacteristic
54C3×C42—21no—
55C3×C42—31no—
56C3×C42—31no—
57C3×C42—61no—
58C3×C42—92no—
59C3×C42—94no—
60C3×C42—92no—
61C3×C42C4×C911yescharacteristic, complemented
62C3×C42C3×Dic311yescharacteristic
63C4×Dic3—34no—
64C4×Dic3—32no—
65C4×Dic3—32no—
66C22×C32—31no—
67C22×C32—31no—
68C22×C32C4×A411yescharacteristic
69C32×C4—32no—
70C32×C4—32no—
71C3×Dic3—34no—
72C3×Dic3—31no—
73C3×Dic3C42⋊C311yescharacteristic
74C22⋊C9—41no—
75C22⋊C9—81no—
76C4×C9—481no—
77C2×C42—91no—
78C2×C42—91no—
79C2×C42D3×C911yescharacteristic
80C3×C9—161noSylow
81C23×C3—21no—
82C23×C3C2×C22⋊C911yescharacteristic
83C23×C3D3×A411yescharacteristic
84C2×C3×C4—32no—
85C2×C3×C4—32no—
86C2×C3×C4—32no—
87C2×C3×C4—32no—
88C2×C3×C4—31no—
89C2×C3×C4—31no—
90C2×C3×C4—31no—
91C2×C3×C4—31no—
92C2×C3×C4—61no—
93C2×C3×C4—61no—
94C2×C3×C4—62no—
95C2×C3×C4—62no—
96C2×C3×C4—91no—
97C2×C3×C4—94no—
98C2×C3×C4—92no—
99C2×C3×C4—91no—
100C2×Dic3—34no—
101C2×Dic3—32no—
102C2×Dic3—31no—
103C2×Dic3—31no—
104C2×C32—31no—
105C2×C32—31no—
106C2×C32C2×C42⋊C311yescharacteristic
107C2×C9—161no—
108C2×C9—321no—
109C22×C4—31no—
110C22×C4—31no—
111C22×C4—91no—
112C42—31no—
113C42—92no—
114C42—94no—
115C42—92no—
116C42C9×Dic311yescharacteristic, complemented
117C22×C3—21no—
118C22×C3—31no—
119C22×C3—31no—
120C22×C3—31no—
121C22×C3—31no—
122C22×C3—61no—
123C22×C3—61no—
124C22×C3C4×C22⋊C911yescharacteristic
125C22×C3Dic3×A411yescharacteristic
126C3×C4—32no—
127C3×C4—32no—
128C3×C4—32no—
129C3×C4—32no—
130C3×C4—31no—
131C3×C4—62no—
132C3×C4—62no—
133C3×C4—94no—
134C3×C4—91no—
135Dic3—34no—
136Dic3—31no—
137Dic3C42⋊C911yescharacteristic, direct product factor
138C32C4×C42⋊C311yescharacteristic
139C9—161no—
140C9—321no—
141C23D3×C22⋊C911yescharacteristic
142C2×C4—32no—
143C2×C4—32no—
144C2×C4—31no—
145C2×C4—31no—
146C2×C4—91no—
147C2×C4—94no—
148C2×C4—92no—
149C2×C4—91no—
150C2×C3—21no—
151C2×C3—31no—
152C2×C3—31no—
153C2×C3—31no—
154C2×C3—31no—
155C2×C3—61no—
156C2×C3—61no—
157C2×C3C2×C42⋊C911yescharacteristic
158C2×C3D3×C42⋊C311yescharacteristic
159C22—31no—
160C22—31no—
161C22Dic3×C22⋊C911yescharacteristic
162C4—32no—
163C4—32no—
164C4—31no—
165C4—94no—
166C4—91no—
167C3—21no—
168C3C4×C42⋊C911yescharacteristic, complemented
169C3Dic3×C42⋊C311yescharacteristic
170C2—31no—
171C2—31no—
172C2D3×C42⋊C911yescharacteristic
subgroupG/H
center, hypercenterC2×C3D3×C42⋊C3
commutator, hypocenterC3×C42C4×C9
FrattiniC23×C3D3×A4
Fitting, cosocleC2×C32×C42C2×C3
socle, prime radicalC23×C32C2×A4
LCSG ▷ C3×C42
UCSC1 ◁ C2×C3

Complements

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

NH ≅ G/Ntype
5. C3×C42⋊C9C4semidirect
13. C42×Dic3C9semidirect
24. C42⋊C9Dic3direct (N × H)
61. C3×C42C4×C9semidirect
116. C42C9×Dic3semidirect
137. Dic3C42⋊C9direct (N × H)
168. C3C4×C42⋊C9semidirect

Maximal subgroups

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

subgroupindex
C2×C3×C42⋊C92
C3×C42×Dic33
C4×C42⋊C93
Dic3×C22⋊C94