Finite Group Databasebeta

← C3⋊(#399⋊C9) #13136826

Subgroups — C3⋊(#399⋊C9) #13136826

Order 1728.

201 conjugacy classes of subgroups; only the 31 normal subgroups are shown.

normal subgroups only

This group has 201 conjugacy classes of subgroups — too many to draw. Only its 31 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, complemented
2C3×#4677C311yesmaximal, characteristic
3#399⋊C9—31nomaximal
4C2×D3×C22⋊C9—41nomaximal
5C2×C3×(C2×D3)⋊C4—31no—
6C2×C3×C4⋊Dic3—31no—
7C32×#95C2×C311yescharacteristic
8#95⋊C9—21no—
9#95⋊C9D311yescharacteristic, complemented
10C2×C3×C22⋊C9—41no—
11D3×C22⋊C9—42no—
12C3×#399—31no—
13#4677C911yescharacteristic, complemented
14C23×C3×D3A411yescharacteristic
15C22×C32×C4—31no—
16C22×C3×Dic3—31no—
17C22×C22⋊C9—121no—
18C3×(C2×D3)⋊C4—62no—
19C3×C4⋊Dic3—62no—
20C2×D3×C9—161no—
21C3×C22⋊C9—41no—
22C2×C3×C4⋊C4—91no—
23C2×C3×C22⋊C4—91no—
24C2×(C2×D3)⋊C4—31no—
25C2×C4⋊Dic3—31no—
26C3×#95—21no—
27C3×#95C2×C911yescharacteristic, complemented
28C3×#95C3×D311yescharacteristic
29C23×C32C2×A411yescharacteristic
30C22×C3×D3—61no—
31C22×C3×D3—61no—
32C22×C3×D3SL(2,𝔽3)12yes—
33C2×C32×C4—32no—
34C2×C32×C4—62no—
35C2×C3×Dic3—62no—
36C2×C3×Dic3—61no—
37C2×C22⋊C9—41no—
38C2×C22⋊C9—81no—
39C2×C22⋊C9—122no—
40#399—31noSylow
41C2×C3×C9—161no—
42D3×C9—162no—
43C24×C3—31no—
44C23×D3C22⋊C911yescharacteristic
45C22×C3×C4—31no—
46C22×C3×C4—31no—
47C22×C3×C4—61no—
48C22×C3×C4—91no—
49C22×Dic3—31no—
50C3×C4⋊C4—182no—
51C3×C22⋊C4—182no—
52(C2×D3)⋊C4—62no—
53C4⋊Dic3—62no—
54C22×C32—31no—
55C22×C32—31no—
56C22×C32C2×SL(2,𝔽3)11yescharacteristic
57C2×C3×D3—41no—
58C2×C3×D3—62no—
59C2×C3×D3—121no—
60C32×C4—62no—
61C3×Dic3—121no—
62C22×C9—481no—
63C22⋊C9—41no—
64C22⋊C9—81no—
65C2×C4⋊C4—91no—
66C2×C22⋊C4—91no—
67#95D3×C911yescharacteristic, complemented
68C3×C9—161noSylow
69C23×C3—21no—
70C23×C3—32no—
71C23×C3—181no—
72C23×C3—181no—
73C23×C3C2×C22⋊C911yescharacteristic
74C23×C3D3×A411yescharacteristic
75C22×D3—61no—
76C22×D3—61no—
77C22×D3Q8⋊C912yes—
78C2×C3×C4—32no—
79C2×C3×C4—32no—
80C2×C3×C4—62no—
81C2×C3×C4—62no—
82C2×C3×C4—62no—
83C2×C3×C4—122no—
84C2×C3×C4—181no—
85C2×C3×C4—182no—
86C2×Dic3—62no—
87C2×Dic3—61no—
88C2×C32—31no—
89C2×C32—31no—
90C2×C32#127⋊C311yescharacteristic
91C3×D3—42no—
92C2×C9—161no—
93C2×C9—321no—
94C2×C9—482no—
95C24—31no—
96C22×C4—31no—
97C22×C4—91no—
98C4⋊C4—182no—
99C22⋊C4—182no—
100C22×C3—21no—
101C22×C3—31no—
102C22×C3—31no—
103C22×C3—31no—
104C22×C3—31no—
105C22×C3—61no—
106C22×C3—61no—
107C22×C3—121no—
108C22×C3—182no—
109C22×C3—361no—
110C22×C3C2×Q8⋊C911yescharacteristic
111C22×C3D3×SL(2,𝔽3)11yescharacteristic
112C2×D3—41no—
113C2×D3—62no—
114C2×D3—121no—
115C3×C4—62no—
116C3×C4—62no—
117C3×C4—122no—
118C3×C4—361no—
119Dic3—121no—
120C32#399⋊C311yescharacteristic
121C9—161no—
122C9—321no—
123C23—32no—
124C23—181no—
125C23—181no—
126C23D3×C22⋊C911yescharacteristic
127C2×C4—32no—
128C2×C4—62no—
129C2×C4—181no—
130C2×C4—182no—
131C2×C3—21no—
132C2×C3—31no—
133C2×C3—31no—
134C2×C3—31no—
135C2×C3—31no—
136C2×C3—61no—
137C2×C3—61no—
138C2×C3—122no—
139C2×C3#127⋊C911yescharacteristic
140C2×C3C3⋊(#127⋊C3)11yescharacteristic
141D3—42no—
142C22—31no—
143C22—31no—
144C22—121no—
145C22—182no—
146C22—361no—
147C22D3×Q8⋊C911yescharacteristic
148C4—62no—
149C4—361no—
150C3—21no—
151C3#399⋊C911yescharacteristic, complemented
152C3C3⋊(#399⋊C3)11yescharacteristic
153C2—31no—
154C2—31no—
155C2—122no—
156C2C3⋊(#127⋊C9)11yescharacteristic
subgroupG/H
center, hypercenterC2×C3C3⋊(#127⋊C3)
commutator, hypocenterC3×#95C2×C9
FrattiniC23×C3D3×A4
Fitting, cosocleC32×#95C2×C3
socleC23×C32C2×A4
prime radicalC23×C3×D3A4
LCSG ▷ C3×#95
UCSC1 ◁ C2×C3

Complements

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

NH ≅ G/Ntype
1. C3×#95⋊C9C2semidirect
9. #95⋊C9D3semidirect
13. #4677C9semidirect
27. C3×#95C2×C9semidirect
67. #95D3×C9semidirect
151. C3#399⋊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×#46773
#399⋊C93
C2×D3×C22⋊C94