Finite Group Databasebeta

← C3×C3⋊#4207 #13091700

Subgroups — C3×C3⋊#4207 #13091700

Order 1458.

1757 conjugacy classes of subgroups; only the 182 normal subgroups are shown.

normal subgroups only

This group has 1757 conjugacy classes of subgroups — too many to draw. Only its 182 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
1C32×#737C211yesmaximal, characteristic, complemented, Sylow
2C3⋊#4207C313yesmaximal, direct product factor
3C3×C3⋊(C3⋊D9)C311yesmaximal, characteristic, complemented
4C3×#4207—39nomaximal
5C3×C3⋊AGL(1,ℤ/9)—32nomaximal
6C3×C3⋊((C3⋊D3)⋊C3)—31nomaximal
7C32×C3⋊D9—31nomaximal
8C3×#737—227no—
9C3×#737—26no—
10C3×#737—23no—
11C3×#737—23no—
12C3×#737—29no—
13C3×#737D319yescomplemented
14C3×#737C2×C313yescomplemented
15C32×3−1+2—21no—
16C32×3−1+2—22no—
17C32×3−1+2D312yescomplemented
18C32×H(3,𝔽3)D311yescharacteristic
19C33×C9—21no—
20C33×C9D311yescharacteristic, complemented
21C33×C9C2×C311yescharacteristic, complemented
22C3×C3⋊(C3⋊D3)—31no—
23C32×C3⋊D3—91no—
24C3⋊(C3⋊D9)C3211yescharacteristic, complemented
25#4207—327no—
26C3⋊AGL(1,ℤ/9)—36no—
27C3⋊((C3⋊D3)⋊C3)—33no—
28C3×C3⋊D9—31no—
29C3×C3⋊D9—32no—
30C3×C3⋊D9—33no—
31C3×C3⋊D9—39no—
32C3×AGL(1,ℤ/9)—96no—
33C3×(C3⋊D3)⋊C3—93no—
34C32×D9—93no—
35C34—21no—
36C34C3×D311yescharacteristic
37C34C3⋊D311yescharacteristic
38#737—254no—
39#737—2108no—
40#737—254no—
41#737—254no—
42#737—227no—
43#737—227no—
44#737—227no—
45#737C3×D3127yescomplemented
46C3×3−1+2—218no—
47C3×3−1+2—236no—
48C3×3−1+2—26no—
49C3×3−1+2—212no—
50C3×3−1+2—23no—
51C3×3−1+2—29no—
52C3×3−1+2—26no—
53C3×3−1+2—218no—
54C3×3−1+2—26no—
55C3×3−1+2—218no—
56C3×3−1+2—26no—
57C3×3−1+2C3×D316yescomplemented
58C3×3−1+2C3⋊D316yescomplemented
59C3×H(3,𝔽3)—23no—
60C3×H(3,𝔽3)—23no—
61C3×H(3,𝔽3)—29no—
62C3×H(3,𝔽3)C3×D313yes—
63C3×H(3,𝔽3)C3⋊D313yes—
64C32×C9—218no—
65C32×C9—26no—
66C32×C9—21no—
67C32×C9—22no—
68C32×C9—21no—
69C32×C9—23no—
70C32×C9—23no—
71C32×C9—22no—
72C32×C9—21no—
73C32×C9—29no—
74C32×C9—29no—
75C32×C9—23no—
76C32×C9—29no—
77C32×C9C3×D311yescharacteristic
78C32×C9C3×D312yes—
79C32×C9C3×D313yescomplemented
80C32×C9C3×D319yescomplemented
81C32×C9C3⋊D313yescomplemented
82C32×C9C2×C3211yescharacteristic, complemented
83C3⋊(C3⋊D3)—31no—
84C3×C3⋊D3—91no—
85C3×C3⋊D3—93no—
86C3×C3⋊D3—93no—
87C3×C3⋊D3—273no—
88C32×D3—273no—
89C32×D3—271no—
90C3⋊D9—31no—
91C3⋊D9—32no—
92C3⋊D9—39no—
93AGL(1,ℤ/9)—918no—
94(C3⋊D3)⋊C3—99no—
95C3×D9—93no—
96C3×D9—96no—
97C3×D9—99no—
98C33—26no—
99C33—23no—
100C33—21no—
101C33—23no—
102C33—23no—
103C33—21no—
104C33—23no—
105C33—33no—
106C33—33no—
107C33—63no—
108C33—63no—
109C33—66no—
110C33—63no—
111C33C32×D311yescharacteristic
112C33C3×C3⋊D311yescharacteristic
113C33C3×C3⋊D313yes—
114C33C3×C3⋊D313yes—
115C33C3⋊(C3⋊D3)11yescharacteristic
1163−1+2—236no—
1173−1+2—254no—
1183−1+2—2108no—
1193−1+2—227no—
1203−1+2—218no—
1213−1+2—254no—
1223−1+2—218no—
1233−1+2C3×C3⋊D3118yescomplemented
124H(3,𝔽3)—218no—
125H(3,𝔽3)—29no—
126H(3,𝔽3)—29no—
127H(3,𝔽3)C3×C3⋊D319yes—
128C3×C9—212no—
129C3×C9—26no—
130C3×C9—254no—
131C3×C9—218no—
132C3×C9—21no—
133C3×C9—26no—
134C3×C9—22no—
135C3×C9—23no—
136C3×C9—29no—
137C3×C9—26no—
138C3×C9—23no—
139C3×C9—29no—
140C3×C9—23no—
141C3×C9—227no—
142C3×C9—26no—
143C3×C9—218no—
144C3×C9—29no—
145C3×C9—29no—
146C3×C9C32×D311yescharacteristic
147C3×C9C32×D312yes—
148C3×C9C32×D319yescomplemented
149C3×C9C3×C3⋊D313yes—
150C3×C9C3×C3⋊D316yes—
151C3×C9C3×C3⋊D319yescomplemented
152C2×C32—811no—
153C3⋊D3—91no—
154C3⋊D3—93no—
155C3⋊D3—273no—
156C3×D3—279no—
157C3×D3—273no—
158C3×D3—271no—
159C3×D3—273no—
160C3×D3—813no—
161D9—93no—
162D9—96no—
163C32—23no—
164C32—21no—
165C32—23no—
166C32—23no—
167C32—29no—
168C32—33no—
169C32—31no—
170C32—39no—
171C32—33no—
172C32—61no—
173C32—63no—
174C32—69no—
175C32—69no—
176C32—618no—
177C32—62no—
178C32—66no—
179C32—63no—
180C32—69no—
181C32—61no—
182C32—63no—
183C32#420713yescomplemented
184C32C32×C3⋊D313yes—
185C32C32×C3⋊D311yescharacteristic
186C32C3×C3⋊(C3⋊D3)11yescharacteristic
187C32C3×C3⋊(C3⋊D3)13yes—
188C9—23no—
189C9—218no—
190C9—26no—
191C9—29no—
192C9C32×C3⋊D313yes—
193C9C32×C3⋊D316yes—
194C2×C3—813no—
195C2×C3—811no—
196D3—273no—
197D3—271no—
198D3—813no—
199C3—23no—
200C3—21no—
201C3—33no—
202C3—33no—
203C3—63no—
204C3—63no—
205C3—69no—
206C3C3×#420713yescomplemented
207C3C3⋊#420711yescharacteristic, direct product factor
208C3C32×C3⋊(C3⋊D3)11yescharacteristic
209C2—811noSylow
subgroupG/H
center, hypercenterC3C3⋊#4207
commutator, cosocle, hypocenterC32×C9C2×C32
FrattiniC3C32×C3⋊(C3⋊D3)
FittingC32×#737C2
socleC33C3×C3⋊D3
LCSG ▷ C32×C9
UCSC1 ◁ C3

Complements

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

NH ≅ G/Ntype
1. C32×#737C2semidirect
2. C3⋊#4207C3direct (N × H)
3. C3×C3⋊(C3⋊D9)C3semidirect
13. C3×#737D3semidirect
14. C3×#737C2×C3semidirect
17. C32×3−1+2D3semidirect
20. C33×C9D3semidirect
21. C33×C9C2×C3semidirect
24. C3⋊(C3⋊D9)C32semidirect
45. #737C3×D3semidirect
57. C3×3−1+2C3×D3semidirect
58. C3×3−1+2C3⋊D3semidirect
79. C32×C9C3×D3semidirect
80. C32×C9C3×D3semidirect
81. C32×C9C3⋊D3semidirect
82. C32×C9C2×C32semidirect
123. 3−1+2C3×C3⋊D3semidirect
148. C3×C9C32×D3semidirect
151. C3×C9C3×C3⋊D3semidirect
183. C32#4207semidirect
206. C3C3×#4207semidirect
207. C3C3⋊#4207direct (N × H)

Maximal subgroups

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

subgroupindex
C32×#7372
C3⋊#42073
C3×C3⋊(C3⋊D9)3
C3×#42073
C3×C3⋊AGL(1,ℤ/9)3
C3×C3⋊((C3⋊D3)⋊C3)3
C32×C3⋊D93