Finite Group Databasebeta

← D9⋊(#95⋊C3) #13136803

Subgroups — D9⋊(#95⋊C3) #13136803

Order 1728.

230 conjugacy classes of subgroups; only the 25 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 25 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
1C9⋊(#95⋊C3)C211yesmaximal, characteristic, complemented
2D3×#95⋊C3—31nomaximal
3D9×#95C311yesmaximal, characteristic, complemented
4C2×D9⋊A4—41nomaximal
5C22×C4×D9—31no—
6C3×#95⋊C3D311yescharacteristic
7C9×#95C2×C311yescharacteristic, complemented
8C9⋊#95—31no—
9#95⋊C9—21no—
10C2×C9⋊A4—41no—
11D9⋊A4—42no—
12D3×#95—31no—
13C2×#95⋊C3—91no—
14C2×D3×A4—121no—
15C23×D9A411yescharacteristic
16C22×C4×C9—31no—
17C22×Dic9—31no—
18C2×C4×D9—32no—
19C2×C4×D9—32no—
20C2×C4×D9—64no—
21C2×AGL(1,ℤ/9)—161no—
22C9⋊A4—41no—
23C22×C4×D3—91no—
24C3×#95C3×D311yescharacteristic
25C3⋊#95—91no—
26#95⋊C3—31no—
27C2×C3×A4—41no—
28D3×A4—122no—
29C23×C9C2×A411yescharacteristic
30C22×D9—31no—
31C22×D9—31no—
32C22×D9—32no—
33C22×D9SL(2,𝔽3)12yes—
34C2×C22⋊C9—81no—
35C2×C4×C9—32no—
36C2×C4×C9—62no—
37C2×Dic9—32no—
38C2×Dic9—62no—
39C4×D9—64no—
40C4×D9—64no—
41C2×#95—91noSylow
42C2×3−1+2—161no—
43AGL(1,ℤ/9)—162no—
44C23×D3—31no—
45C22×A4—361no—
46C22×C3×C4—31no—
47C22×Dic3—91no—
48C2×C4×D3—92no—
49C2×C4×D3—92no—
50C2×C4×D3—184no—
51C2×C3×D3—481no—
52C3×A4—41no—
53C22×C9—31no—
54C22×C9—31no—
55C22×C9C2×SL(2,𝔽3)11yescharacteristic
56C2×D9—32no—
57C2×D9—31no—
58C2×D9—32no—
59C2×D9—32no—
60C2×D9—32no—
61C2×D9C42⋊C311yescharacteristic
62C22⋊C9—81no—
63C4×C9—62no—
64Dic9—62no—
65C23×C4—271no—
66#95—271no—
67#95AGL(1,ℤ/9)11yescharacteristic, complemented
683−1+2—161noSylow
69C23×C3D3×A411yescharacteristic
70C22×D3—32no—
71C22×D3—91no—
72C22×D3—91no—
73C22×D3—92no—
74C2×A4—121no—
75C2×A4—362no—
76C2×C3×C4—32no—
77C2×C3×C4—62no—
78C2×Dic3—92no—
79C2×Dic3—182no—
80C4×D3—184no—
81C4×D3—184no—
82C2×C32—161no—
83C3×D3—482no—
84C2×C9—31no—
85C2×C9—31no—
86C2×C9—321no—
87C2×C9C2×C42⋊C311yescharacteristic
88D9—32no—
89D9#95⋊C312yescomplemented
90C24—91no—
91C22×C4—31no—
92C22×C4—272no—
93C22×C4—272no—
94C22×C4—271no—
95C22×C4—544no—
96C22×C3—31no—
97C22×C3—31no—
98C22×C3—1441no—
99C22×C3D3×SL(2,𝔽3)11yescharacteristic
100C2×D3—31no—
101C2×D3—92no—
102C2×D3—92no—
103C2×D3—92no—
104C2×D3—91no—
105C2×D3—92no—
106A4—121no—
107C3×C4—62no—
108Dic3—182no—
109C32—161no—
110C9—321no—
111C9C2×#95⋊C311yescharacteristic, complemented
112C23—92no—
113C23—271no—
114C23—271no—
115C23—272no—
116C23D9⋊A411yescharacteristic
117C2×C4—32no—
118C2×C4—62no—
119C2×C4—272no—
120C2×C4—544no—
121C2×C4—544no—
122C2×C4—542no—
123C2×C3—31no—
124C2×C3—31no—
125C2×C3—481no—
126C2×C3—1442no—
127C2×C3D3×C42⋊C311yescharacteristic
128D3—32no—
129D3—92no—
130C22—31no—
131C22—31no—
132C22—91no—
133C22—272no—
134C22—272no—
135C22—272no—
136C22—272no—
137C22—271no—
138C22D9⋊SL(2,𝔽3)11yescharacteristic
139C4—62no—
140C4—542no—
141C3—481no—
142C3D3×#95⋊C311yescharacteristic
143C2—31no—
144C2—31no—
145C2—92no—
146C2—272no—
147C2D9⋊(C42⋊C3)11yescharacteristic
subgroupG/H
center, hypercenterC2D9⋊(C42⋊C3)
commutator, Fitting, cosocle, hypocenterC9×#95C2×C3
Frattini, socleC23×C3D3×A4
LCSG ▷ C9×#95
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
1. C9⋊(#95⋊C3)C2semidirect
3. D9×#95C3semidirect
7. C9×#95C2×C3semidirect
67. #95AGL(1,ℤ/9)semidirect
89. D9#95⋊C3semidirect
111. C9C2×#95⋊C3semidirect

Maximal subgroups

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

subgroupindex
C9⋊(#95⋊C3)2
D3×#95⋊C33
D9×#953
C2×D9⋊A44