Finite Group Databasebeta

← C3⋊(#383⋊C9) #13136844

Subgroups — C3⋊(#383⋊C9) #13136844

Order 1728.

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

normal subgroups only

This group has 162 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×#4937C311yesmaximal, characteristic
3#383⋊C9—31nomaximal
4Dic3×C22⋊C9—41nomaximal
5C3×C42⋊C9C411yescharacteristic, complemented
6C2×C32×C42C2×C311yescharacteristic
7C3×C3⋊#95—31no—
8C3×C3⋊#95—31no—
9C2×C42⋊C9—21no—
10C2×C42⋊C9D311yescharacteristic
11C2×C3×C22⋊C9—41no—
12C3×#383—31no—
13#4937C911yescharacteristic, complemented
14C22×C32×C4—31no—
15C22×C3×Dic3—31no—
16C22×C3×Dic3A411yescharacteristic
17C32×C42—31no—
18C32×C42C3×C411yescharacteristic
19C4×C22⋊C9—121no—
20C42⋊C9—21no—
21C42⋊C9Dic311yescharacteristic, complemented
22C3×C22⋊C9—41no—
23C9×Dic3—161no—
24C2×C3×C42—21no—
25C2×C3×C42C2×C911yescharacteristic
26C2×C3×C42C3×D311yescharacteristic
27C3×#95—91no—
28C3×#95—91no—
29C3⋊#95—31no—
30C3⋊#95—31no—
31C23×C32C2×A411yescharacteristic
32C2×C32×C4—31no—
33C2×C32×C4—31no—
34C2×C32×C4—61no—
35C2×C32×C4—61no—
36C2×C3×Dic3—61no—
37C2×C3×Dic3—62no—
38C2×C3×Dic3—61no—
39C2×C22⋊C9—41no—
40C2×C22⋊C9—81no—
41#383—31noSylow
42C2×C3×C9—161no—
43C22×C3×C4—31no—
44C22×C3×C4—31no—
45C22×C3×C4—31no—
46C22×C3×C4—61no—
47C22×C3×C4—91no—
48C22×Dic3—31no—
49C22×Dic3C22⋊C911yescharacteristic
50C3×C42—21no—
51C3×C42—31no—
52C3×C42—31no—
53C3×C42—61no—
54C3×C42C4×C911yescharacteristic, complemented
55C3×C42C3×Dic311yescharacteristic
56C22×C32—31no—
57C22×C32—31no—
58C22×C32C4×A411yescharacteristic
59C32×C4—61no—
60C32×C4—61no—
61C3×Dic3—41no—
62C3×Dic3—121no—
63C22⋊C9—41no—
64C22⋊C9—81no—
65C4×C9—481no—
66C2×C42D3×C911yescharacteristic
67#95—91no—
68#95—91no—
69C3×C9—161noSylow
70C23×C3—21no—
71C23×C3C2×C22⋊C911yescharacteristic
72C23×C3D3×A411yescharacteristic
73C2×C3×C4—31no—
74C2×C3×C4—31no—
75C2×C3×C4—31no—
76C2×C3×C4—31no—
77C2×C3×C4—61no—
78C2×C3×C4—61no—
79C2×C3×C4—61no—
80C2×C3×C4—61no—
81C2×C3×C4—61no—
82C2×C3×C4—61no—
83C2×C3×C4—62no—
84C2×C3×C4—62no—
85C2×C3×C4—181no—
86C2×C3×C4—182no—
87C2×C3×C4—181no—
88C2×Dic3—61no—
89C2×Dic3—62no—
90C2×Dic3—61no—
91C2×C32—31no—
92C2×C32—31no—
93C2×C32#126⋊C311yescharacteristic
94C2×C9—161no—
95C2×C9—321no—
96C22×C4—31no—
97C22×C4—31no—
98C22×C4—91no—
99C42—31no—
100C42C9×Dic311yescharacteristic, complemented
101C22×C3—21no—
102C22×C3—31no—
103C22×C3—31no—
104C22×C3—31no—
105C22×C3—31no—
106C22×C3—61no—
107C22×C3—61no—
108C22×C3C4×C22⋊C911yescharacteristic
109C22×C3Dic3×A411yescharacteristic
110C3×C4—61no—
111C3×C4—61no—
112C3×C4—61no—
113C3×C4—61no—
114C3×C4—62no—
115C3×C4—62no—
116C3×C4—121no—
117C3×C4—361no—
118Dic3—41no—
119Dic3—121no—
120C32#383⋊C311yescharacteristic
121C9—161no—
122C9—321no—
123C23D3×C22⋊C911yescharacteristic
124C2×C4—31no—
125C2×C4—31no—
126C2×C4—61no—
127C2×C4—61no—
128C2×C4—181no—
129C2×C4—182no—
130C2×C4—181no—
131C2×C3—21no—
132C2×C3—31no—
133C2×C3—31no—
134C2×C3—31no—
135C2×C3—31no—
136C2×C3—61no—
137C2×C3—61no—
138C2×C3#126⋊C911yescharacteristic
139C2×C3C3⋊(#126⋊C3)11yescharacteristic
140C22—31no—
141C22—31no—
142C22Dic3×C22⋊C911yescharacteristic
143C4—61no—
144C4—61no—
145C4—121no—
146C4—361no—
147C3—21no—
148C3#383⋊C911yescharacteristic, complemented
149C3C3⋊(#383⋊C3)11yescharacteristic
150C2—31no—
151C2—31no—
152C2C3⋊(#126⋊C9)11yescharacteristic
subgroupG/H
center, hypercenterC2×C3C3⋊(#126⋊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. #4937C9semidirect
21. C42⋊C9Dic3semidirect
54. C3×C42C4×C9semidirect
100. C42C9×Dic3semidirect
148. C3#383⋊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×#49373
#383⋊C93
Dic3×C22⋊C94