Finite Group Databasebeta

← #14518697

Subgroups — #14518697

Order 1944.

602 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 602 conjugacy classes of subgroups — too many to draw. Only its 85 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⋊(C3⋊AGL(1,ℤ/9))C211yesmaximal, characteristic
23−1+2×C3⋊Dic3C211yesmaximal, characteristic, complemented
3C32×3−1+2⋊C4C211yesmaximal, characteristic, complemented
4C3×#6289—31nomaximal
5#10619870C311yesmaximal, characteristic, complemented
6(C3⋊AGL(1,ℤ/9))⋊C4—34nomaximal
7C2×C32×3−1+2C2211yescharacteristic
8C3⋊(C3⋊AGL(1,ℤ/9))C412yescomplemented
9C2×C3×C3⋊(C3⋊D3)—31no—
10C32×C3⋊Dic3D311yescharacteristic
11C33×Dic3—31no—
12C2×C3⋊(C3⋊D9)C2×C311yescharacteristic
13C2×C3⋊AGL(1,ℤ/9)—34no—
14C2×C3⋊AGL(1,ℤ/9)—64no—
15C9×C3⋊Dic3—21no—
16C9×C3⋊Dic3C2×C311yescharacteristic, complemented
17Dic3×3−1+2—34no—
18C3×3−1+2⋊C4—24no—
19C3×3−1+2⋊C4D314yescomplemented
20C32×Dic9C2×C311yescharacteristic, complemented
21C32×3−1+2C2×C411yescharacteristic, complemented, Sylow
22C3×C4×C3⋊D3—91no—
23#6289—31no—
24C3×#624—94no—
25C4×AGL(1,ℤ/9)—91no—
26(C3⋊D9)⋊C4—34no—
27C2×C34C2×D311yescharacteristic
28C3×C3⋊(C3⋊D3)—32no—
29C2×C3×3−1+2—24no—
30C2×C3×3−1+2—24no—
31C2×C3×3−1+2—44no—
32C2×C3×3−1+2C2×D314yes—
33C2×C32×C9—21no—
34C2×C32×C9C22×C311yescharacteristic
35C3⋊(C3⋊D9)C3×C412yescomplemented
36C3⋊AGL(1,ℤ/9)—38no—
37C3⋊AGL(1,ℤ/9)—68no—
38C2×C3⋊(C3⋊D3)—31no—
39C2×C3×C3⋊D3—91no—
40C2×C3×C3⋊D3—94no—
41C2×C3×C3⋊D3—184no—
42C33×C4—91no—
43C3×C3⋊Dic3—31no—
44C3×C3⋊Dic3C3×D311yescharacteristic
45C32×Dic3—34no—
46C32×Dic3—34no—
47C32×Dic3—31no—
48C32×Dic3—64no—
49C2×C3⋊D9—34no—
50C2×C3⋊D9—64no—
51C2×AGL(1,ℤ/9)—91no—
52C2×AGL(1,ℤ/9)—184no—
53C4×3−1+2—91no—
543−1+2⋊C4—24no—
553−1+2⋊C4C3⋊D311yescharacteristic, complemented
56C9×Dic3—34no—
57C9×Dic3—64no—
58C3×Dic9C3×D314yescomplemented
59C34C4×D311yescharacteristic
60C3×3−1+2—24no—
61C3×3−1+2—24no—
62C3×3−1+2—44no—
63C3×3−1+2C4×D314yescomplemented
64C32×C9—21no—
65C32×C9C2×C3×C411yescharacteristic, complemented
66C4×C3⋊D3—91no—
67C3×C4×D3—271no—
68C3×C4×D3—274no—
69#624—94no—
70C4×D9—91no—
71C2×C33—24no—
72C2×C33—31no—
73C2×C33—64no—
74C2×C33D3214yes—
75C2×C33C2×C3×D311yescharacteristic
76C3⋊(C3⋊D3)—32no—
77C3×C3⋊D3—92no—
78C3×C3⋊D3—98no—
79C3×C3⋊D3—188no—
80C2×3−1+2—24no—
81C2×3−1+2—24no—
82C2×3−1+2—44no—
83C2×3−1+2—412no—
84C2×3−1+2C2×C3⋊D311yescharacteristic
85C2×C3×C9—24no—
86C2×C3×C9—24no—
87C2×C3×C9—44no—
88C2×C3×C9C2×C3×D314yes—
89C3⋊D9—38no—
90C3⋊D9—68no—
91AGL(1,ℤ/9)—92no—
92AGL(1,ℤ/9)—188no—
93C2×C3⋊D3—91no—
94C2×C3⋊D3—94no—
95C2×C3⋊D3—184no—
96C2×C3×D3—274no—
97C2×C3×D3—271no—
98C2×C3×D3—544no—
99C32×C4—91no—
100C32×C4—94no—
101C32×C4—91no—
102C32×C4—184no—
103C3⋊Dic3AGL(1,ℤ/9)11yescharacteristic, complemented
104C3×Dic3—34no—
105C3×Dic3—34no—
106C3×Dic3—31no—
107C3×Dic3—64no—
108C3×Dic3—94no—
109C2×D9—91no—
110C2×D9—184no—
111C4×C9—91no—
112C4×C9—181no—
113Dic9C3×C3⋊D311yescharacteristic, complemented
114C33—24no—
115C33—31no—
116C33—64no—
117C33#62414yes—
118C33C3×C4×D311yescharacteristic
1193−1+2—24no—
1203−1+2—24no—
1213−1+2—44no—
1223−1+2—412no—
1233−1+2C4×C3⋊D311yescharacteristic, complemented
124C3×C9—24no—
125C3×C9—24no—
126C3×C9—44no—
127C3×C9C3×C4×D314yescomplemented
128C2×C3×C4—811no—
129C4×D3—271no—
130C4×D3—274no—
131C2×C32—24no—
132C2×C32—24no—
133C2×C32—34no—
134C2×C32—64no—
135C2×C32—64no—
136C2×C32—124no—
137C2×C32C2×AGL(1,ℤ/9)11yescharacteristic
138C2×C32C3×D3214yes—
139C2×C32D3×C3⋊D311yescharacteristic
140C3⋊D3—92no—
141C3⋊D3—98no—
142C3⋊D3—188no—
143C3×D3—278no—
144C3×D3—272no—
145C3×D3—548no—
146C2×C9—21no—
147C2×C9—24no—
148C2×C9—44no—
149C2×C9C2×C3×C3⋊D311yescharacteristic
150D9—92no—
151D9—188no—
152C22×C3—811no—
153C2×D3—274no—
154C2×D3—271no—
155C2×D3—544no—
156C3×C4—91no—
157C3×C4—94no—
158C3×C4—91no—
159C3×C4—184no—
160C3×C4—271no—
161Dic3—34no—
162Dic3—31no—
163C32—24no—
164C32—24no—
165C32—34no—
166C32—64no—
167C32—64no—
168C32—124no—
169C32C4×AGL(1,ℤ/9)11yescharacteristic, complemented
170C32C3×#62414yes—
171C32#628911yescharacteristic
172C9—24no—
173C9—21no—
174C9—44no—
175C9C3×C4×C3⋊D311yescharacteristic, complemented
176C2×C4—811noSylow
177C2×C3—24no—
178C2×C3—31no—
179C2×C3—64no—
180C2×C3—812no—
181C2×C3D3×AGL(1,ℤ/9)14yes—
182C2×C3C3×D3×C3⋊D311yescharacteristic
183D3—278no—
184D3—272no—
185D3—548no—
186C22—811no—
187C4—91no—
188C4—91no—
189C3—24no—
190C3—31no—
191C3—64no—
192C3(C3⋊AGL(1,ℤ/9))⋊C414yescomplemented
193C3C3×#628911yescharacteristic
194C2—812no—
195C2C3⋊D3×AGL(1,ℤ/9)11yescharacteristic
subgroupG/H
center, hypercenterC2C3⋊D3×AGL(1,ℤ/9)
commutator, hypocenterC32×C9C2×C3×C4
FrattiniC2×C3C3×D3×C3⋊D3
FittingC2×C32×3−1+2C22
socleC2×C33C2×C3×D3
prime radicalC2×C3⋊(C3⋊AGL(1,ℤ/9))C2
cosocleC2×C32×C9C22×C3
LCSG ▷ C32×C9
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
2. 3−1+2×C3⋊Dic3C2semidirect
3. C32×3−1+2⋊C4C2semidirect
5. #10619870C3semidirect
8. C3⋊(C3⋊AGL(1,ℤ/9))C4semidirect
16. C9×C3⋊Dic3C2×C3semidirect
19. C3×3−1+2⋊C4D3semidirect
20. C32×Dic9C2×C3semidirect
21. C32×3−1+2C2×C4semidirect
35. C3⋊(C3⋊D9)C3×C4semidirect
55. 3−1+2⋊C4C3⋊D3semidirect
58. C3×Dic9C3×D3semidirect
63. C3×3−1+2C4×D3semidirect
65. C32×C9C2×C3×C4semidirect
103. C3⋊Dic3AGL(1,ℤ/9)semidirect
113. Dic9C3×C3⋊D3semidirect
123. 3−1+2C4×C3⋊D3semidirect
127. C3×C9C3×C4×D3semidirect
169. C32C4×AGL(1,ℤ/9)semidirect
175. C9C3×C4×C3⋊D3semidirect
192. C3(C3⋊AGL(1,ℤ/9))⋊C4semidirect

Maximal subgroups

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

subgroupindex
C2×C3⋊(C3⋊AGL(1,ℤ/9))2
3−1+2×C3⋊Dic32
C32×3−1+2⋊C42
C3×#62893
#106198703
(C3⋊AGL(1,ℤ/9))⋊C43