Finite Group Databasebeta

← #13048645

Subgroups — #13048645

Order 1296.

488 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 488 conjugacy classes of subgroups — too many to draw. Only its 89 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
1C4×C3⋊(C3⋊D9)C211yesmaximal, characteristic, complemented
2C4×C9×C3⋊D3C211yesmaximal, characteristic, complemented
3C32×C4×D9C211yesmaximal, characteristic, complemented
4#10619878C211yesmaximal, characteristic, complemented
5#10619877C211yesmaximal, characteristic, complemented
6#10619873C211yesmaximal, characteristic, complemented
7#10619867C211yesmaximal, characteristic, complemented
8#89020—31nomaximal
9#88640—34nomaximal
10C2×C3⋊(C3⋊D9)C2211yescharacteristic
11C2×C9×C3⋊D3C2211yescharacteristic
12C2×C32×D9C2211yescharacteristic
13C32×C4×C9C2211yescharacteristic
14C3⋊(C3⋊Dic9)C2211yescharacteristic
15C9×C3⋊Dic3C2211yescharacteristic
16C32×Dic9C2211yescharacteristic
17C4×C3⋊(C3⋊D3)—31no—
18C3×C4×C3⋊D3D311yescharacteristic
19C32×C4×D3—31no—
20#6293—31no—
21#6292—31no—
22#6291—31no—
23#6290—31no—
24C4×C3⋊D9—34no—
25C4×C3⋊D9—64no—
26C4×D3×C9—34no—
27C3×C4×D9D314yescomplemented
28#6195—34no—
29#6194—34no—
30#6192—34no—
31#6189—34no—
32C2×C32×C9C2311yescharacteristic
33C3⋊(C3⋊D9)—21no—
34C9×C3⋊D3—21no—
35C32×D9—21no—
36#3828—91no—
37#3798—94no—
38#3697—91no—
39C2×C3⋊(C3⋊D3)—31no—
40C2×C3×C3⋊D3C2×D311yescharacteristic
41C2×C32×D3—31no—
42C33×C4C2×D311yescharacteristic
43C3⋊(C3⋊Dic3)—31no—
44C3×C3⋊Dic3C2×D311yescharacteristic
45C32×Dic3—31no—
46C2×C3⋊D9—34no—
47C2×C3⋊D9—64no—
48C2×D3×C9—34no—
49C2×C3×D9C2×D314yes—
50C3×C4×C9—24no—
51C3×C4×C9C2×D314yes—
52C3⋊Dic9—34no—
53C3⋊Dic9—64no—
54C9×Dic3—34no—
55C3×Dic9C2×D314yes—
56C32×C9#4111yescharacteristic, complemented, Sylow
57C2×C32×C4—91no—
58#638—91no—
59#638—91no—
60C4⋊(C3⋊D3)—91no—
61C4×C3⋊D3—91no—
62C4×C3⋊D3—94no—
63C4×C3⋊D3—184no—
64C4×C3⋊D3D911yescharacteristic, complemented
65#634—91no—
66C3×C4×D3—34no—
67C3×C4×D3—34no—
68#627—94no—
69#626—94no—
70#626—94no—
71#625—94no—
72C2×C4×C9—91no—
73#611—91no—
74#611—91no—
75D36—91no—
76C4×D9—91no—
77C4×D9—184no—
78C4×D9C3⋊D311yescharacteristic, complemented
79Dic18—91no—
80C2×C33C22×D311yescharacteristic
81C3⋊(C3⋊D3)—61no—
82C3×C3⋊D3—21no—
83C32×D3—61no—
84C2×C3×C9—24no—
85C2×C3×C9C22×D314yes—
86C3⋊D9—68no—
87C3⋊D9—64no—
88D3×C9—64no—
89C3×D9—24no—
90#235—271no—
91#235—274no—
92C22×C32—91no—
93C2×C3⋊D3—91no—
94C2×C3⋊D3—94no—
95C2×C3⋊D3—184no—
96C2×C3⋊D3C2×D911yescharacteristic
97C2×C3×D3—34no—
98C2×C3×D3—34no—
99C32×C4—24no—
100C32×C4—91no—
101C32×C4C2×D911yescharacteristic
102C32×C4D3214yes—
103C3⋊Dic3—91no—
104C3⋊Dic3—94no—
105C3⋊Dic3—184no—
106C3⋊Dic3C2×D911yescharacteristic
107C3×Dic3—34no—
108C3×Dic3—34no—
109C22×C9—91no—
110C2×D9—91no—
111C2×D9—184no—
112C2×D9C2×C3⋊D311yescharacteristic
113C4×C9—24no—
114C4×C9—91no—
115C4×C9C2×C3⋊D311yescharacteristic
116Dic9—91no—
117Dic9—184no—
118Dic9C2×C3⋊D311yescharacteristic
119C33#23511yescharacteristic
120C3×C9—24no—
121C3×C9#23514yescomplemented
122C2×C3×C4—94no—
123C2×C3×C4—91no—
124#67—271no—
125#67—274no—
126#67—271no—
127#67—274no—
128D12—271no—
129D12—274no—
130C4×D3—34no—
131C4×D3—31no—
132C4×D3—274no—
133C4×D3—271no—
134C4×D3—544no—
135Dic6—271no—
136Dic6—274no—
137C2×C32—24no—
138C2×C32—181no—
139C2×C32C22×D911yescharacteristic
140C2×C32C2×D3214yes—
141C3⋊D3—21no—
142C3⋊D3—188no—
143C3⋊D3—181no—
144C3⋊D3—184no—
145C3×D3—64no—
146C3×D3—64no—
147C2×C9—24no—
148C2×C9—181no—
149C2×C9C22×C3⋊D311yescharacteristic
150D9—21no—
151D9—188no—
152D9—181no—
153#41—811noSylow
154C22×C3—94no—
155C22×C3—91no—
156C2×D3—34no—
157C2×D3—31no—
158C2×D3—274no—
159C2×D3—271no—
160C2×D3—544no—
161C3×C4—24no—
162C3×C4—94no—
163C3×C4—91no—
164C3×C4D3×D914yes—
165C3×C4D3×C3⋊D311yescharacteristic
166Dic3—34no—
167Dic3—31no—
168Dic3—274no—
169Dic3—271no—
170Dic3—544no—
171C32—24no—
172C32#369711yescharacteristic, complemented
173C32#379814yes—
174C9—24no—
175C9#382811yescharacteristic, complemented
176Q8—811no—
177D4—811no—
178D4—811no—
179D4—811no—
180C2×C4—91no—
181C2×C4—91no—
182C2×C4—811no—
183C2×C3—24no—
184C2×C3—184no—
185C2×C3—181no—
186C2×C3C2×D3×D914yes—
187C2×C3C2×D3×C3⋊D311yescharacteristic
188D3—64no—
189D3—61no—
190D3—548no—
191D3—544no—
192D3—541no—
193C22—91no—
194C22—91no—
195C22—811no—
196C4—91no—
197C4—91no—
198C4—811no—
199C4D9×C3⋊D311yescharacteristic
200C3—24no—
201C3#8864014yescomplemented
202C3#8902011yescharacteristic
203C2—181no—
204C2—181no—
205C2—1621no—
206C2C2×D9×C3⋊D311yescharacteristic
subgroupG/H
center, hypercenterC4D9×C3⋊D3
commutator, cosocleC2×C32×C9C23
FrattiniC2×C3C2×D3×C3⋊D3
FittingC32×C4×C9C22
socleC2×C33C22×D3
hypocenterC32×C9#41
LCSG ▷ C2×C32×C9 ▷ C32×C9
UCSC1 ◁ C4

Complements

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

NH ≅ G/Ntype
1. C4×C3⋊(C3⋊D9)C2semidirect
2. C4×C9×C3⋊D3C2semidirect
3. C32×C4×D9C2semidirect
4. #10619878C2semidirect
5. #10619877C2semidirect
6. #10619873C2semidirect
7. #10619867C2semidirect
27. C3×C4×D9D3semidirect
56. C32×C9#41semidirect
64. C4×C3⋊D3D9semidirect
78. C4×D9C3⋊D3semidirect
121. C3×C9#235semidirect
172. C32#3697semidirect
175. C9#3828semidirect
201. C3#88640semidirect

Maximal subgroups

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

subgroupindex
C4×C3⋊(C3⋊D9)2
C4×C9×C3⋊D32
C32×C4×D92
#106198782
#106198772
#106198732
#106198672
#890203
#886403