Finite Group Databasebeta

← C3⋊(#384⋊C9) #13136843

Subgroups — C3⋊(#384⋊C9) #13136843

Order 1728.

194 conjugacy classes of subgroups; only the 33 normal subgroups are shown.

normal subgroups only

This group has 194 conjugacy classes of subgroups — too many to draw. Only its 33 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×#4935C311yesmaximal, characteristic
3#384⋊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×#384—31no—
13#4935C911yescharacteristic, complemented
14C22×C32×C4—31no—
15C22×C3×Dic3—31no—
16C22×C3×Dic3A411yescharacteristic
17C32×C42—31no—
18C32×C42C3×C411yescharacteristic
19C3×C4⋊Dic3—62no—
20C3×C4⋊Dic3—62no—
21C4×C22⋊C9—121no—
22C42⋊C9—21no—
23C42⋊C9Dic311yescharacteristic, complemented
24C3×C22⋊C9—41no—
25C9×Dic3—161no—
26C2×C3×C4⋊C4—91no—
27C2×C3×C4⋊C4—91no—
28C2×C3×C42—21no—
29C2×C3×C42C2×C911yescharacteristic
30C2×C3×C42C3×D311yescharacteristic
31C2×C4⋊Dic3—31no—
32C2×C4⋊Dic3—31no—
33C23×C32C2×A411yescharacteristic
34C2×C32×C4—32no—
35C2×C32×C4—32no—
36C2×C32×C4—31no—
37C2×C32×C4—31no—
38C2×C3×Dic3—61no—
39C2×C3×Dic3—61no—
40C2×C3×Dic3—62no—
41C2×C22⋊C9—41no—
42C2×C22⋊C9—81no—
43#384—31noSylow
44C2×C3×C9—161no—
45C22×C3×C4—31no—
46C22×C3×C4—31no—
47C22×C3×C4—31no—
48C22×C3×C4—61no—
49C22×C3×C4—91no—
50C22×Dic3—31no—
51C22×Dic3C22⋊C911yescharacteristic
52C3×C4⋊C4—182no—
53C3×C4⋊C4—182no—
54C3×C42—21no—
55C3×C42—31no—
56C3×C42—31no—
57C3×C42—61no—
58C3×C42C4×C911yescharacteristic, complemented
59C3×C42C3×Dic311yescharacteristic
60C4⋊Dic3—62no—
61C4⋊Dic3—62no—
62C22×C32—31no—
63C22×C32—31no—
64C22×C32C4×A411yescharacteristic
65C32×C4—32no—
66C32×C4—32no—
67C3×Dic3—41no—
68C3×Dic3—121no—
69C22⋊C9—41no—
70C22⋊C9—81no—
71C4×C9—481no—
72C2×C4⋊C4—91no—
73C2×C4⋊C4—91no—
74C2×C42D3×C911yescharacteristic
75C3×C9—161noSylow
76C23×C3—21no—
77C23×C3C2×C22⋊C911yescharacteristic
78C23×C3D3×A411yescharacteristic
79C2×C3×C4—32no—
80C2×C3×C4—32no—
81C2×C3×C4—32no—
82C2×C3×C4—32no—
83C2×C3×C4—31no—
84C2×C3×C4—31no—
85C2×C3×C4—31no—
86C2×C3×C4—31no—
87C2×C3×C4—61no—
88C2×C3×C4—61no—
89C2×C3×C4—62no—
90C2×C3×C4—62no—
91C2×C3×C4—181no—
92C2×C3×C4—181no—
93C2×C3×C4—182no—
94C2×Dic3—61no—
95C2×Dic3—61no—
96C2×Dic3—62no—
97C2×C32—31no—
98C2×C32—31no—
99C2×C32#127⋊C311yescharacteristic
100C2×C9—161no—
101C2×C9—321no—
102C22×C4—31no—
103C22×C4—31no—
104C22×C4—91no—
105C4⋊C4—182no—
106C4⋊C4—182no—
107C42—31no—
108C42C9×Dic311yescharacteristic, complemented
109C22×C3—21no—
110C22×C3—31no—
111C22×C3—31no—
112C22×C3—31no—
113C22×C3—31no—
114C22×C3—61no—
115C22×C3—61no—
116C22×C3C4×C22⋊C911yescharacteristic
117C22×C3Dic3×A411yescharacteristic
118C3×C4—32no—
119C3×C4—32no—
120C3×C4—32no—
121C3×C4—32no—
122C3×C4—62no—
123C3×C4—62no—
124C3×C4—121no—
125C3×C4—361no—
126Dic3—41no—
127Dic3—121no—
128C32#384⋊C311yescharacteristic
129C9—161no—
130C9—321no—
131C23D3×C22⋊C911yescharacteristic
132C2×C4—32no—
133C2×C4—32no—
134C2×C4—31no—
135C2×C4—31no—
136C2×C4—181no—
137C2×C4—181no—
138C2×C4—182no—
139C2×C3—21no—
140C2×C3—31no—
141C2×C3—31no—
142C2×C3—31no—
143C2×C3—31no—
144C2×C3—61no—
145C2×C3—61no—
146C2×C3#127⋊C911yescharacteristic
147C2×C3C3⋊(#127⋊C3)11yescharacteristic
148C22—31no—
149C22—31no—
150C22Dic3×C22⋊C911yescharacteristic
151C4—32no—
152C4—32no—
153C4—121no—
154C4—361no—
155C3—21no—
156C3#384⋊C911yescharacteristic, complemented
157C3C3⋊(#384⋊C3)11yescharacteristic
158C2—31no—
159C2—31no—
160C2C3⋊(#127⋊C9)11yescharacteristic
subgroupG/H
center, hypercenterC2×C3C3⋊(#127⋊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. #4935C9semidirect
23. C42⋊C9Dic3semidirect
58. C3×C42C4×C9semidirect
108. C42C9×Dic3semidirect
156. C3#384⋊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×#49353
#384⋊C93
Dic3×C22⋊C94