Finite Group Databasebeta

← #13048710

Subgroups — #13048710

Order 1296.

742 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 742 conjugacy classes of subgroups — too many to draw. Only its 91 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
1C22×C3⋊(C3⋊D9)C211yesmaximal, characteristic, complemented
2C2×D9×C3⋊D3C211yesmaximal, characteristic, complemented
3C9×#638C211yesmaximal, characteristic, complemented
4C32×#611C211yesmaximal, characteristic, complemented
5#10619878C211yesmaximal, characteristic, complemented
6#10619873C211yesmaximal, characteristic, complemented
7#10619870C211yesmaximal, characteristic, complemented
8#89039—31nomaximal
9#88668—34nomaximal
10C22×C32×C9C2211yescharacteristic, complemented
11C2×C3⋊(C3⋊D9)—22no—
12C2×C3⋊(C3⋊D9)C2211yescharacteristic
13C2×C3⋊(C3⋊D9)C2211yescharacteristic, complemented
14C2×C9×C3⋊D3C2211yescharacteristic, complemented
15C2×C32×D9C2211yescharacteristic, complemented
16D9×C3⋊D3—22no—
17C9×C3⋊Dic3C2211yescharacteristic, complemented
18C32×Dic9C2211yescharacteristic, complemented
19C22×C3⋊(C3⋊D3)—31no—
20C2×D3×C3⋊D3—31no—
21C3×#638D311yescharacteristic
22C32×#67—31no—
23#6292—31no—
24#6291—31no—
25#6289—31no—
26C22×C3⋊D9—34no—
27C22×C3⋊D9—64no—
28C2×D3×D9—34no—
29C9×#67—34no—
30C3×#611D314yescomplemented
31#6195—34no—
32#6192—34no—
33(C3⋊D9)⋊C4—34no—
34C2×C32×C9—21no—
35C2×C32×C9C2311yescharacteristic
36C3⋊(C3⋊D9)—21no—
37C3⋊(C3⋊D9)D412yescomplemented
38C9×C3⋊D3—21no—
39C32×D9—21no—
40D4×C3⋊D3—91no—
41#3811—94no—
42D4×D9—91no—
43C22×C33C2×D311yescharacteristic
44C2×C3⋊(C3⋊D3)—31no—
45C2×C3⋊(C3⋊D3)—31no—
46C2×C3⋊(C3⋊D3)—62no—
47C2×C3×C3⋊D3C2×D311yescharacteristic
48C2×C32×D3—31no—
49D3×C3⋊D3—62no—
50C3×C3⋊Dic3C2×D311yescharacteristic
51C32×Dic3—31no—
52C22×C3×C9—24no—
53C22×C3×C9C2×D314yescomplemented
54C2×C3⋊D9—34no—
55C2×C3⋊D9—34no—
56C2×C3⋊D9—68no—
57C2×C3⋊D9—64no—
58C2×C3⋊D9—64no—
59C2×C3⋊D9—616no—
60C2×D3×C9—34no—
61C2×C3×D9C2×D314yescomplemented
62D3×D9—68no—
63C9×Dic3—34no—
64C3×Dic9C2×D314yescomplemented
65C32×C9C2×D411yescharacteristic, complemented, Sylow
66C22×C3⋊D3—91no—
67C22×C3⋊D3—91no—
68C22×C3⋊D3—94no—
69C22×C3⋊D3—184no—
70C2×D32—94no—
71C32×D4—91no—
72#638—91no—
73#638D911yescharacteristic, complemented
74C4⋊(C3⋊D3)—91no—
75C4×C3⋊D3—91no—
76C3×#67—34no—
77C3×#67—34no—
78#626—94no—
79#626—94no—
80#624—94no—
81C22×D9—91no—
82C22×D9—91no—
83C22×D9—184no—
84D4×C9—91no—
85#611—91no—
86#611C3⋊D311yescharacteristic, complemented
87D36—91no—
88C4×D9—91no—
89C2×C33—21no—
90C2×C33C22×D311yescharacteristic
91C3⋊(C3⋊D3)—32no—
92C3⋊(C3⋊D3)—61no—
93C3×C3⋊D3—21no—
94C32×D3—61no—
95C2×C3×C9—28no—
96C2×C3×C9—24no—
97C2×C3×C9—24no—
98C2×C3×C9C22×D314yes—
99C3⋊D9—38no—
100C3⋊D9—68no—
101C3⋊D9—68no—
102C3⋊D9—64no—
103D3×C9—64no—
104C3×D9—24no—
105D3×D4—271no—
106D3×D4—274no—
107C22×C32—24no—
108C22×C32—91no—
109C22×C32C2×D911yescharacteristic, complemented
110C22×C32D3214yes—
111C2×C3⋊D3—91no—
112C2×C3⋊D3—91no—
113C2×C3⋊D3—94no—
114C2×C3⋊D3—94no—
115C2×C3⋊D3—184no—
116C2×C3⋊D3—184no—
117C2×C3⋊D3—182no—
118C2×C3⋊D3—188no—
119C2×C3⋊D3—182no—
120C2×C3⋊D3—1816no—
121C2×C3⋊D3C2×D911yescharacteristic, complemented
122C2×C3×D3—34no—
123C2×C3×D3—34no—
124D32—188no—
125C32×C4—91no—
126C3⋊Dic3C2×D911yescharacteristic, complemented
127C3×Dic3—34no—
128C3×Dic3—34no—
129C22×C9—24no—
130C22×C9—91no—
131C22×C9C2×C3⋊D311yescharacteristic, complemented
132C2×D9—91no—
133C2×D9—91no—
134C2×D9—184no—
135C2×D9—184no—
136C2×D9—182no—
137C2×D9—182no—
138C2×D9—1816no—
139C2×D9C2×C3⋊D311yescharacteristic, complemented
140C4×C9—91no—
141Dic9C2×C3⋊D311yescharacteristic, complemented
142C33D3×D411yescharacteristic
143C3×C9—24no—
144C3×C9D3×D414yescomplemented
145C22×D3—271no—
146C22×D3—274no—
147C22×D3—274no—
148C22×D3—271no—
149C22×D3—544no—
150C3×D4—94no—
151C3×D4—91no—
152#67—34no—
153#67—31no—
154#67—271no—
155#67—274no—
156D12—271no—
157D12—274no—
158C4×D3—271no—
159C4×D3—274no—
160C2×C32—28no—
161C2×C32—21no—
162C2×C32—24no—
163C2×C32—24no—
164C2×C32—181no—
165C2×C32C22×D911yescharacteristic
166C2×C32C2×D3214yes—
167C3⋊D3—21no—
168C3⋊D3—92no—
169C3⋊D3—98no—
170C3⋊D3—188no—
171C3⋊D3—188no—
172C3⋊D3—181no—
173C3⋊D3—184no—
174C3×D3—64no—
175C3×D3—64no—
176C2×C9—28no—
177C2×C9—21no—
178C2×C9—24no—
179C2×C9—181no—
180C2×C9C22×C3⋊D311yescharacteristic
181D9—21no—
182D9—92no—
183D9—188no—
184D9—188no—
185D9—181no—
186C2×D4—811noSylow
187C22×C3—24no—
188C22×C3—94no—
189C22×C3—91no—
190C22×C3D3×D914yescomplemented
191C22×C3D3×C3⋊D311yescharacteristic
192C2×D3—34no—
193C2×D3—31no—
194C2×D3—274no—
195C2×D3—271no—
196C2×D3—274no—
197C2×D3—271no—
198C2×D3—544no—
199C2×D3—544no—
200C2×D3—542no—
201C2×D3—548no—
202C2×D3—542no—
203C2×D3—548no—
204C2×D3—5416no—
205C3×C4—94no—
206C3×C4—91no—
207Dic3—34no—
208Dic3—31no—
209C32—24no—
210C32D4×D911yescharacteristic, complemented
211C32#381114yes—
212C9—24no—
213C9D4×C3⋊D311yescharacteristic, complemented
214C23—811no—
215C23—811no—
216D4—91no—
217D4—91no—
218D4—811no—
219D4—811no—
220C2×C4—811no—
221C2×C3—28no—
222C2×C3—24no—
223C2×C3—21no—
224C2×C3—24no—
225C2×C3—184no—
226C2×C3—181no—
227C2×C3C2×D3×D914yes—
228C2×C3C2×D3×C3⋊D311yescharacteristic
229D3—64no—
230D3—61no—
231D3—278no—
232D3—272no—
233D3—548no—
234D3—548no—
235D3—544no—
236D3—541no—
237C22—91no—
238C22—91no—
239C22—811no—
240C22—811no—
241C22—1622no—
242C22—1622no—
243C22D9×C3⋊D311yescharacteristic, complemented
244C4—91no—
245C4—91no—
246C3—24no—
247C3#8866814yescomplemented
248C3#8903911yescharacteristic
249C2—21no—
250C2—181no—
251C2—181no—
252C2—812no—
253C2—1621no—
254C2C2×D9×C3⋊D311yescharacteristic
subgroupG/H
centerC2C2×D9×C3⋊D3
commutator, cosocleC2×C32×C9C23
FrattiniC2×C3C2×D3×C3⋊D3
FittingC22×C32×C9C22
socleC2×C33C22×D3
hypercenterC22D9×C3⋊D3
hypocenterC32×C9C2×D4
LCSG ▷ C2×C32×C9 ▷ C32×C9
UCSC1 ◁ C2 ◁ C22

Complements

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

NH ≅ G/Ntype
1. C22×C3⋊(C3⋊D9)C2semidirect
2. C2×D9×C3⋊D3C2semidirect
3. C9×#638C2semidirect
4. C32×#611C2semidirect
5. #10619878C2semidirect
6. #10619873C2semidirect
7. #10619870C2semidirect
10. C22×C32×C9C22semidirect
13. C2×C3⋊(C3⋊D9)C22semidirect
14. C2×C9×C3⋊D3C22semidirect
15. C2×C32×D9C22semidirect
17. C9×C3⋊Dic3C22semidirect
18. C32×Dic9C22semidirect
30. C3×#611D3semidirect
37. C3⋊(C3⋊D9)D4semidirect
53. C22×C3×C9C2×D3semidirect
61. C2×C3×D9C2×D3semidirect
64. C3×Dic9C2×D3semidirect
65. C32×C9C2×D4semidirect
73. #638D9semidirect
86. #611C3⋊D3semidirect
109. C22×C32C2×D9semidirect
121. C2×C3⋊D3C2×D9semidirect
126. C3⋊Dic3C2×D9semidirect
131. C22×C9C2×C3⋊D3semidirect
139. C2×D9C2×C3⋊D3semidirect
141. Dic9C2×C3⋊D3semidirect
144. C3×C9D3×D4semidirect
190. C22×C3D3×D9semidirect
210. C32D4×D9semidirect
213. C9D4×C3⋊D3semidirect
243. C22D9×C3⋊D3semidirect
247. C3#88668semidirect

Maximal subgroups

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

subgroupindex
C22×C3⋊(C3⋊D9)2
C2×D9×C3⋊D32
C9×#6382
C32×#6112
#106198782
#106198732
#106198702
#890393
#886683