Finite Group Databasebeta

← #13091515

Subgroups — #13091515

Order 1458.

425 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 425 conjugacy classes of subgroups — too many to draw. Only its 55 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
1#10624896C211yesmaximal, characteristic, complemented, Sylow
2C3⋊#4207C311yesmaximal, characteristic, complemented
3C3×C3⋊AGL(1,ℤ/9)—31nomaximal
4#92303C312yesmaximal, complemented
5#92297C311yesmaximal, characteristic, complemented
6#4169⋊C3—31nomaximal
7#92258—31nomaximal
8C3×#4169—31nomaximal
9C3×#737—21no—
10C3×#737C2×C311yescharacteristic, complemented
11C32×3−1+2D311yescharacteristic, complemented
12#6893—21no—
13#6893—21no—
14#6893—21no—
15C9⋊H(3,𝔽3)—22no—
16C9⋊H(3,𝔽3)—22no—
17C9⋊H(3,𝔽3)—21no—
18C9⋊H(3,𝔽3)—21no—
19C9⋊H(3,𝔽3)—22no—
20C9⋊H(3,𝔽3)—21no—
21C9⋊H(3,𝔽3)—22no—
22C9⋊H(3,𝔽3)C2×C312yescomplemented
23#6891D311yescharacteristic, complemented
24C32⋊H(3,𝔽3)D311yescharacteristic
25C9×H(3,𝔽3)—21no—
26C9×H(3,𝔽3)C2×C311yescharacteristic, complemented
27C3×C32⋊C9D311yescharacteristic, complemented
28C32×C3⋊D3—91no—
29C3⋊(C3⋊D9)C3211yescharacteristic, complemented
30#4207—93no—
31C3⋊AGL(1,ℤ/9)—32no—
32C3⋊AGL(1,ℤ/9)—31no—
33C3⋊AGL(1,ℤ/9)—31no—
34C3⋊((C3⋊D3)⋊C3)—31no—
35C3⋊((C3⋊D3)⋊C3)—32no—
36C3⋊((C3⋊D3)⋊C3)—31no—
37C3×C3⋊D9—31no—
38C3×C3⋊D9—31no—
39C3×AGL(1,ℤ/9)—93no—
40#4169—31no—
41#4169—32no—
42#4169—31no—
43#4169—32no—
44C34C3⋊D311yescharacteristic
45#737—33no—
46#737—63no—
47#737—66no—
48#737—63no—
49C3×3−1+2—22no—
50C3×3−1+2—22no—
51C3×3−1+2—21no—
52C3×3−1+2—22no—
53C3×3−1+2—21no—
54C3×3−1+2—21no—
55C3×3−1+2—22no—
56C3×3−1+2—21no—
57C3×3−1+2—21no—
58C3×3−1+2—33no—
59C3×3−1+2—63no—
60C3×3−1+2C3×D311yescharacteristic
61C3×3−1+2C3×D312yes—
62C3×3−1+2C3×D311yescharacteristic
63C3×H(3,𝔽3)—21no—
64C3×H(3,𝔽3)—21no—
65C3×H(3,𝔽3)—22no—
66C3×H(3,𝔽3)C3×D311yescharacteristic
67C3×H(3,𝔽3)C3×D311yescharacteristic
68C3×H(3,𝔽3)C3×D312yes—
69C32×C9—22no—
70C32×C9—21no—
71C32×C9—21no—
72C32×C9—21no—
73C32×C9—21no—
74C32×C9C3×D311yescharacteristic
75C32×C9C3×D311yescharacteristic
76C32×C9C2×C3211yescharacteristic, complemented
77C32⋊C9—22no—
78C32⋊C9—22no—
79C32⋊C9—22no—
80C32⋊C9—22no—
81C32⋊C9—22no—
82C32⋊C9—22no—
83C32⋊C9—22no—
84C32⋊C9—22no—
85C32⋊C9—22no—
86C32⋊C9—21no—
87C32⋊C9—22no—
88C32⋊C9—22no—
89C32⋊C9—21no—
90C32⋊C9—21no—
91C32⋊C9—22no—
92C32⋊C9—22no—
93C32⋊C9—21no—
94C32⋊C9—21no—
95C32⋊C9—22no—
96C32⋊C9C3×D311yescharacteristic
97C32⋊C9C3×D312yes—
98C32⋊C9C3×D311yescharacteristic
99C32⋊C9C3×D312yes—
100C3⋊(C3⋊D3)—31no—
101C3×C3⋊D3—91no—
102C3×C3⋊D3—92no—
103C3×C3⋊D3—91no—
104C32×D3—271no—
105C32×D3—271no—
106C32×D3—272no—
107C3⋊D9—31no—
108C3⋊D9—31no—
109C3⋊D9—31no—
110C3⋊D9—93no—
111AGL(1,ℤ/9)—96no—
112AGL(1,ℤ/9)—93no—
113AGL(1,ℤ/9)—271no—
114(C3⋊D3)⋊C3—271no—
115(C3⋊D3)⋊C3—271no—
116(C3⋊D3)⋊C3—272no—
117C3×D9—93no—
118C3×D9—271no—
119C33—21no—
120C33—21no—
121C33—22no—
122C33—31no—
123C33—31no—
124C33—61no—
125C33—61no—
126C33—92no—
127C33C32×D311yescharacteristic
128C33C3×C3⋊D311yescharacteristic
129C33C3×C3⋊D311yescharacteristic
130C33C3×C3⋊D312yes—
1313−1+2—23no—
1323−1+2—31no—
1333−1+2—36no—
1343−1+2—63no—
1353−1+2—66no—
1363−1+2—63no—
1373−1+2—66no—
1383−1+2—66no—
1393−1+2—61no—
1403−1+2—62no—
1413−1+2—62no—
1423−1+2—61no—
1433−1+2—61no—
1443−1+2—63no—
1453−1+2—66no—
1463−1+2(C3⋊D3)⋊C313yescomplemented
147H(3,𝔽3)—31no—
148H(3,𝔽3)—31no—
149H(3,𝔽3)—61no—
150H(3,𝔽3)—61no—
151H(3,𝔽3)—62no—
152H(3,𝔽3)—62no—
153H(3,𝔽3)—61no—
154H(3,𝔽3)—61no—
155H(3,𝔽3)—92no—
156H(3,𝔽3)—182no—
157C3×C9—21no—
158C3×C9—22no—
159C3×C9—21no—
160C3×C9—21no—
161C3×C9—21no—
162C3×C9—21no—
163C3×C9—22no—
164C3×C9—21no—
165C3×C9—22no—
166C3×C9—33no—
167C3×C9—31no—
168C3×C9—33no—
169C3×C9—63no—
170C3×C9—63no—
171C3×C9—66no—
172C3×C9—61no—
173C3×C9—62no—
174C3×C9—61no—
175C3×C9—63no—
176C3×C9C32×D311yescharacteristic
177C3×C9C32×D311yescharacteristic
178C3×C9C32×D311yescharacteristic
179C2×C32—811no—
180C3⋊D3—91no—
181C3⋊D3—271no—
182C3⋊D3—271no—
183C3⋊D3—272no—
184C3×D3—271no—
185C3×D3—272no—
186C3×D3—272no—
187C3×D3—271no—
188C3×D3—272no—
189C3×D3—272no—
190C3×D3—272no—
191C3×D3—272no—
192C3×D3—271no—
193C3×D3—271no—
194D9—93no—
195D9—271no—
196D9—271no—
197C32—21no—
198C32—21no—
199C32—31no—
200C32—31no—
201C32—32no—
202C32—32no—
203C32—32no—
204C32—31no—
205C32—32no—
206C32—31no—
207C32—32no—
208C32—32no—
209C32—32no—
210C32—61no—
211C32—62no—
212C32—61no—
213C32—61no—
214C32—61no—
215C32—62no—
216C32—62no—
217C32—62no—
218C32—62no—
219C32—62no—
220C32—91no—
221C32—181no—
222C32—181no—
223C32—182no—
224C32C3⋊((C3⋊D3)⋊C3)11yescharacteristic
225C32#420711yescharacteristic, complemented
226C32C32×C3⋊D311yescharacteristic
227C9—23no—
228C9—31no—
229C9—31no—
230C9—61no—
231C9—61no—
232C9—61no—
233C9—62no—
234C9—61no—
235C9—62no—
236C9—62no—
237C9—61no—
238C9C3×(C3⋊D3)⋊C313yes—
239C2×C3—811no—
240C2×C3—811no—
241C2×C3—812no—
242D3—271no—
243D3—271no—
244D3—272no—
245D3—2431no—
246C3—31no—
247C3—31no—
248C3—61no—
249C3—61no—
250C3—91no—
251C3—92no—
252C3—181no—
253C3—181no—
254C3—182no—
255C3C3×C3⋊((C3⋊D3)⋊C3)11yescharacteristic
256C3C3×#420711yescharacteristic
257C3#4207⋊C312yes—
258C2—811noSylow
subgroupG/H
center, hypercenterC1G
commutator, cosocle, hypocenterC32×C9C2×C32
Frattini, socleC32C32×C3⋊D3
Fitting#10624896C2
LCSG ▷ C32×C9
UCSC1

Complements

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

NH ≅ G/Ntype
1. #10624896C2semidirect
2. C3⋊#4207C3semidirect
4. #92303C3semidirect
5. #92297C3semidirect
10. C3×#737C2×C3semidirect
11. C32×3−1+2D3semidirect
22. C9⋊H(3,𝔽3)C2×C3semidirect
23. #6891D3semidirect
26. C9×H(3,𝔽3)C2×C3semidirect
27. C3×C32⋊C9D3semidirect
29. C3⋊(C3⋊D9)C32semidirect
76. C32×C9C2×C32semidirect
146. 3−1+2(C3⋊D3)⋊C3semidirect
225. C32#4207semidirect

Maximal subgroups

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

subgroupindex
#106248962
C3⋊#42073
C3×C3⋊AGL(1,ℤ/9)3
#923033
#922973
#4169⋊C33
#922583
C3×#41693