Finite Group Databasebeta

← C2×D9×C22⋊C9 #13048128

Subgroups — C2×D9×C22⋊C9 #13048128

Order 1296.

240 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 45 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×C9×C22⋊C9C211yesmaximal, characteristic, complemented
2D9×C22⋊C9C212yesmaximal, direct product factor
3C23×C3×D9C311yesmaximal, characteristic
4C2×D3×C22⋊C9—31nomaximal
5C2×C9×D9—41nomaximal
6C9×C22⋊C9C2211yescharacteristic, complemented
7C23×C3×C9C2×C311yescharacteristic
8C22×C3×D9—31no—
9C22×C3×D9—31no—
10C22×C3×D9—32no—
11C22×C3×D9C2×C312yes—
12C2×C3×C22⋊C9—21no—
13C2×C3×C22⋊C9D311yescharacteristic
14D3×C22⋊C9—32no—
15C2×C92—41no—
16C9×D9—42no—
17C23×C3×D3—31no—
18C23×D9C911yescharacteristic, complemented
19C22×C22⋊C9—91no—
20C22×C3×C9—31no—
21C22×C3×C9—31no—
22C22×C3×C9C22×C311yescharacteristic
23C2×D3×C9—121no—
24C2×C3×D9—32no—
25C2×C3×D9—31no—
26C2×C3×D9—32no—
27C2×C3×D9—32no—
28C2×C3×D9—32no—
29C2×C3×D9A411yescharacteristic
30C3×C22⋊C9—21no—
31C3×C22⋊C9C2×D311yescharacteristic
32C92—41noSylow
33C23×C32C3×D311yescharacteristic
34C22×C3×D3—32no—
35C22×C3×D3—91no—
36C22×C3×D3—92no—
37C22×C3×D3—91no—
38C23×C9—21no—
39C23×C9C2×C911yescharacteristic, complemented
40C22×D9—31no—
41C22×D9—31no—
42C22×D9—32no—
43C22×D9C2×C912yescomplemented
44C2×C22⋊C9—23no—
45C2×C22⋊C9—21no—
46C2×C22⋊C9—92no—
47C2×C22⋊C9D911yescharacteristic, direct product factor
48C2×C3×C9—31no—
49C2×C3×C9—31no—
50C2×C3×C9—41no—
51C2×C3×C9—81no—
52C2×C3×C9C2×A411yescharacteristic
53D3×C9—122no—
54C3×D9—32no—
55C3×D9C2×A412yes—
56C24×C3—91no—
57C23×D3—31no—
58C22×C32—31no—
59C22×C32—31no—
60C22×C32C2×C3×D311yescharacteristic
61C2×C3×D3—31no—
62C2×C3×D3—92no—
63C2×C3×D3—92no—
64C2×C3×D3—92no—
65C2×C3×D3—91no—
66C2×C3×D3—92no—
67C22×C9—21no—
68C22×C9—31no—
69C22×C9—31no—
70C22×C9—61no—
71C22×C9—61no—
72C22×C9—361no—
73C22×C9C22×C911yescharacteristic, complemented
74C2×D9—32no—
75C2×D9—31no—
76C2×D9—32no—
77C2×D9—32no—
78C2×D9—32no—
79C2×D9C22⋊C911yescharacteristic, direct product factor
80C22⋊C9—23no—
81C22⋊C9—21no—
82C22⋊C9C2×D911yescharacteristic, direct product factor
83C3×C9—41no—
84C3×C9—81no—
85C3×C9C22×A411yescharacteristic
86C23×C3—21no—
87C23×C3—92no—
88C23×C3—271no—
89C23×C3—272no—
90C23×C3—271no—
91C23×C3C3×D911yescharacteristic
92C23×C3D3×C911yescharacteristic
93C22×D3—32no—
94C22×D3—91no—
95C22×D3—92no—
96C22×D3—91no—
97C2×C32—31no—
98C2×C32—31no—
99C2×C32D3×A411yescharacteristic
100C3×D3—32no—
101C3×D3—92no—
102C2×C9—21no—
103C2×C9—31no—
104C2×C9—31no—
105C2×C9—41no—
106C2×C9—61no—
107C2×C9—61no—
108C2×C9—83no—
109C2×C9—81no—
110C2×C9—362no—
111C2×C9C2×C22⋊C911yescharacteristic, complemented
112D9—32no—
113D9C2×C22⋊C912yesdirect product factor
114C24—91noSylow
115C22×C3—21no—
116C22×C3—31no—
117C22×C3—31no—
118C22×C3—31no—
119C22×C3—31no—
120C22×C3—61no—
121C22×C3—61no—
122C22×C3—91no—
123C22×C3—272no—
124C22×C3—272no—
125C22×C3—272no—
126C22×C3—272no—
127C22×C3—271no—
128C22×C3C2×C3×D911yescharacteristic
129C22×C3C2×D3×C911yescharacteristic
130C2×D3—31no—
131C2×D3—92no—
132C2×D3—92no—
133C2×D3—92no—
134C2×D3—91no—
135C2×D3—92no—
136C32C2×D3×A411yescharacteristic
137C9—21no—
138C9—41no—
139C9—83no—
140C9—81no—
141C9C22×C22⋊C911yescharacteristic, complemented
142C23—92no—
143C23—271no—
144C23—272no—
145C23—271no—
146C23C9×D911yescharacteristic, complemented
147C2×C3—21no—
148C2×C3—31no—
149C2×C3—31no—
150C2×C3—31no—
151C2×C3—31no—
152C2×C3—61no—
153C2×C3—61no—
154C2×C3—92no—
155C2×C3—272no—
156C2×C3A4×D911yescharacteristic
157C2×C3D3×C22⋊C911yescharacteristic
158D3—32no—
159D3—92no—
160C22—31no—
161C22—31no—
162C22—91no—
163C22—272no—
164C22—272no—
165C22—272no—
166C22—272no—
167C22—271no—
168C22C2×C9×D911yescharacteristic, complemented
169C3—21no—
170C3C2×A4×D911yescharacteristic
171C3C2×D3×C22⋊C911yescharacteristic
172C2—31no—
173C2—31no—
174C2—92no—
175C2—272no—
176C2D9×C22⋊C911yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2×C3A4×D9
commutator, hypocenterC22×C9C22×C9
FrattiniC32C2×D3×A4
FittingC23×C3×C9C2×C3
socleC23×C32C3×D3
prime radicalC23×C3×D9C3
cosocleC22×C3×C9C22×C3
LCSG ▷ C22×C9
UCSC1 ◁ C2×C3

Complements

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

NH ≅ G/Ntype
1. C2×C9×C22⋊C9C2semidirect
2. D9×C22⋊C9C2direct (N × H)
6. C9×C22⋊C9C22semidirect
18. C23×D9C9semidirect
39. C23×C9C2×C9semidirect
43. C22×D9C2×C9semidirect
47. C2×C22⋊C9D9direct (N × H)
73. C22×C9C22×C9semidirect
79. C2×D9C22⋊C9direct (N × H)
82. C22⋊C9C2×D9direct (N × H)
111. C2×C9C2×C22⋊C9semidirect
113. D9C2×C22⋊C9direct (N × H)
141. C9C22×C22⋊C9semidirect
146. C23C9×D9semidirect
168. C22C2×C9×D9semidirect
176. C2D9×C22⋊C9direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C9×C22⋊C92
D9×C22⋊C92
C23×C3×D93
C2×D3×C22⋊C93
C2×C9×D94