Finite Group Databasebeta

← C3⋊(#401⋊C9) #13136824

Subgroups — C3⋊(#401⋊C9) #13136824

Order 1728.

137 conjugacy classes of subgroups; only the 27 normal subgroups are shown.

normal subgroups only

This group has 137 conjugacy classes of subgroups — too many to draw. Only its 27 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
1C3×#95⋊C9C211yesmaximal, characteristic
2C3×C3⋊#401C311yesmaximal, characteristic
3#401⋊C9—31nomaximal
4Dic3×C22⋊C9—41nomaximal
5C32×#95C2×C311yescharacteristic
6C3×C3⋊#95—31no—
7C3×C3⋊#95—31no—
8#95⋊C9—21no—
9#95⋊C9D311yescharacteristic
10C2×C3×C22⋊C9—41no—
11C3×#401—31no—
12C3⋊#401C911yescharacteristic, complemented
13C22×C32×C4—31no—
14C22×C3×Dic3—31no—
15C22×C3×Dic3A411yescharacteristic
16C4×C22⋊C9—121no—
17C3×C22⋊C9—41no—
18C9×Dic3—161no—
19C3×#95—21no—
20C3×#95—91no—
21C3×#95—91no—
22C3×#95C2×C911yescharacteristic
23C3×#95C3×D311yescharacteristic
24C3⋊#95—31no—
25C3⋊#95—31no—
26C23×C32C2×A411yescharacteristic
27C2×C32×C4—61no—
28C2×C32×C4—62no—
29C2×C3×Dic3—61no—
30C2×C3×Dic3—61no—
31C2×C3×Dic3—61no—
32C2×C3×Dic3—61no—
33C2×C22⋊C9—41no—
34C2×C22⋊C9—81no—
35#401—31noSylow
36C2×C3×C9—161no—
37C22×C3×C4—31no—
38C22×C3×C4—31no—
39C22×C3×C4—31no—
40C22×C3×C4—61no—
41C22×C3×C4—91no—
42C22×Dic3—31no—
43C22×Dic3C22⋊C911yescharacteristic
44C22×C32—31no—
45C22×C32—31no—
46C22×C32#41⋊C311yescharacteristic
47C32×C4—121no—
48C3×Dic3—41no—
49C3×Dic3—121no—
50C22⋊C9—41no—
51C22⋊C9—81no—
52C4×C9—481no—
53#95—91no—
54#95—91no—
55#95D3×C911yescharacteristic
56C3×C9—161noSylow
57C23×C3—21no—
58C23×C3C2×C22⋊C911yescharacteristic
59C23×C3D3×A411yescharacteristic
60C2×C3×C4—61no—
61C2×C3×C4—61no—
62C2×C3×C4—62no—
63C2×C3×C4—62no—
64C2×C3×C4—62no—
65C2×C3×C4—122no—
66C2×C3×C4—181no—
67C2×C3×C4—181no—
68C2×C3×C4—181no—
69C2×C3×C4—181no—
70C2×Dic3—61no—
71C2×Dic3—61no—
72C2×Dic3—61no—
73C2×Dic3—61no—
74C2×C32—31no—
75C2×C32—31no—
76C2×C32#126⋊C311yescharacteristic
77C2×C9—161no—
78C2×C9—321no—
79C22×C4—31no—
80C22×C4—31no—
81C22×C4—91no—
82C22×C3—21no—
83C22×C3—31no—
84C22×C3—31no—
85C22×C3—31no—
86C22×C3—31no—
87C22×C3—61no—
88C22×C3—61no—
89C22×C3#41⋊C911yescharacteristic
90C22×C3C3⋊(#41⋊C3)11yescharacteristic
91C3×C4—121no—
92C3×C4—121no—
93C3×C4—122no—
94C3×C4—121no—
95C3×C4—361no—
96Dic3—41no—
97Dic3—121no—
98C32#401⋊C311yescharacteristic
99C9—161no—
100C9—321no—
101C23D3×C22⋊C911yescharacteristic
102C2×C4—61no—
103C2×C4—62no—
104C2×C4—181no—
105C2×C4—181no—
106C2×C4—181no—
107C2×C4—181no—
108C2×C3—21no—
109C2×C3—31no—
110C2×C3—31no—
111C2×C3—31no—
112C2×C3—31no—
113C2×C3—61no—
114C2×C3—61no—
115C2×C3#126⋊C911yescharacteristic
116C2×C3C3⋊(#126⋊C3)11yescharacteristic
117C22—31no—
118C22—31no—
119C22C3⋊(#41⋊C9)11yescharacteristic
120C4—121no—
121C4—121no—
122C4—361no—
123C3—21no—
124C3#401⋊C911yescharacteristic, complemented
125C3C3⋊(#401⋊C3)11yescharacteristic
126C2—31no—
127C2—31no—
128C2C3⋊(#126⋊C9)11yescharacteristic
subgroupG/H
center, hypercenterC2×C3C3⋊(#126⋊C3)
commutator, hypocenterC3×#95C2×C9
FrattiniC23×C3D3×A4
Fitting, cosocleC32×#95C2×C3
socle, prime radicalC23×C32C2×A4
LCSG ▷ C3×#95
UCSC1 ◁ C2×C3

Complements

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

NH ≅ G/Ntype
12. C3⋊#401C9semidirect
124. C3#401⋊C9semidirect

Maximal subgroups

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

subgroupindex
C3×#95⋊C92
C3×C3⋊#4013
#401⋊C93
Dic3×C22⋊C94