Finite Group Databasebeta

← #10619556⋊C3 #14516923

Subgroups — #10619556⋊C3 #14516923

Order 1944.

248 conjugacy classes of subgroups; only the 34 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 34 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×#4184⋊C3C211yesmaximal, characteristic, complemented
2C2×#92283C211yesmaximal, characteristic, complemented
3#66324⋊C3C211yesmaximal, characteristic, complemented
4#6194⋊C3—31nomaximal
5C3×#6200—31nomaximal
6#10619556C311yesmaximal, characteristic, complemented
7C2×#6910C2211yescharacteristic
8#4184⋊C3—21no—
9#92283—21no—
10C2×C3×#272D311yescharacteristic
11C2×D3×3−1+2—31no—
12C2×C3×AGL(1,ℤ/9)—31no—
13C2×C3×AGL(1,ℤ/9)—61no—
14C2×C3×(C3⋊D3)⋊C3—31no—
15C3⋊(3−1+2⋊C4)D311yescharacteristic, complemented
16C3×(C3⋊Dic3)⋊C3—31no—
17C2×#4184C2×C311yescharacteristic, complemented
18C2×#4176—21no—
19C2×#4176C2×C311yescharacteristic, complemented
20#66324—21no—
21#66324C2×C311yescharacteristic, complemented
22#6910D411yescharacteristic, complemented, Sylow
23C3×#626—91no—
24C3×#625—91no—
25#611⋊C3—91no—
26#6200—31no—
27#6194—31no—
28C2×C3×3−1+2—21no—
29C2×C3×3−1+2C2×D311yescharacteristic
30C2×C3×H(3,𝔽3)C2×D311yescharacteristic
31C3×#272—21no—
32D3×3−1+2—61no—
33C3×AGL(1,ℤ/9)—62no—
34C3×AGL(1,ℤ/9)—61no—
35C3×(C3⋊D3)⋊C3—61no—
36C2×#731—21no—
37C2×#731—21no—
38C2×#731—41no—
39C2×#731C22×C311yescharacteristic
40#4184—21no—
41#4176—22no—
42#4176—21no—
43C2×C3×C3⋊D3—31no—
44C2×C32×D3—31no—
45C2×C32×D3—91no—
46C2×C32×D3—91no—
47C3×C3⋊Dic3—31no—
48C32×Dic3—91no—
49C22×3−1+2—91no—
50C2×#272C3×D311yescharacteristic
51C2×AGL(1,ℤ/9)—31no—
52C2×AGL(1,ℤ/9)—61no—
53C2×AGL(1,ℤ/9)—61no—
54C2×AGL(1,ℤ/9)—61no—
55C2×AGL(1,ℤ/9)—61no—
56C2×(C3⋊D3)⋊C3—31no—
57C2×(C3⋊D3)⋊C3—61no—
58C2×D3×C9—31no—
59C2×D3×C9—61no—
60C2×C3×D9—31no—
61C2×C3×D9—61no—
62C3⋊Dic9C3×D311yescharacteristic, complemented
633−1+2⋊C4—91no—
64(C3⋊Dic3)⋊C3—31no—
65(C3⋊Dic3)⋊C3—61no—
66C3×3−1+2—21no—
67C3×3−1+2D1211yescharacteristic, complemented
68C3×H(3,𝔽3)#6711yescharacteristic
69#731—21no—
70#731—21no—
71#731—41no—
72#731C3×D411yescharacteristic, complemented
73C3×#67—271no—
74C3×#67—271no—
75C3×D12—271no—
76#626—91no—
77#625—91no—
78#611—91no—
79C2×C33—31no—
80C2×C33D3211yescharacteristic
81C3×C3⋊D3—61no—
82C32×D3—61no—
83C32×D3—181no—
84C32×D3—181no—
85C2×3−1+2—21no—
86C2×3−1+2—31no—
87C2×3−1+2—41no—
88C2×3−1+2—61no—
89C2×3−1+2—61no—
90C2×3−1+2—61no—
91C2×3−1+2—181no—
92C2×H(3,𝔽3)—21no—
93C2×H(3,𝔽3)—61no—
94C2×H(3,𝔽3)C2×C3×D311yescharacteristic
95C2×C3×C9—21no—
96C2×C3×C9—61no—
97C2×C3×C9C2×C3×D311yescharacteristic
98#272—21no—
99AGL(1,ℤ/9)—62no—
100AGL(1,ℤ/9)—61no—
101AGL(1,ℤ/9)—62no—
102AGL(1,ℤ/9)—62no—
103AGL(1,ℤ/9)—62no—
104(C3⋊D3)⋊C3—62no—
105(C3⋊D3)⋊C3—61no—
106D3×C9—62no—
107D3×C9—61no—
108C3×D9—62no—
109C3×D9—61no—
110C22×C32—91no—
111C22×C32—271no—
112C2×C3⋊D3—31no—
113C2×C3×D3—31no—
114C2×C3×D3—91no—
115C2×C3×D3—91no—
116C2×C3×D3—91no—
117C2×C3×D3—91no—
118C2×C3×D3—91no—
119C2×C3×D3—181no—
120C2×C3×D3—181no—
121C2×C3×D3—271no—
122C32×C4—271no—
123C3⋊Dic3—31no—
124C3×Dic3—91no—
125C3×Dic3—91no—
126C3×Dic3—181no—
127C3×Dic3—271no—
128C22×C9—91no—
129C22×C9—181no—
130C2×D9—31no—
131C2×D9—61no—
132Dic9—91no—
133C33—31no—
134C33#62611yescharacteristic
1353−1+2—21no—
1363−1+2—31no—
1373−1+2—41no—
1383−1+2—61no—
1393−1+2—61no—
1403−1+2—61no—
141H(3,𝔽3)—21no—
142H(3,𝔽3)—61no—
143H(3,𝔽3)C3×#6711yescharacteristic
144C3×C9—21no—
145C3×C9—61no—
146C3×C9C3×D1211yescharacteristic, complemented
147C3×D4—811no—
148#67—271no—
149#67—271no—
150D12—271no—
151C2×C32—21no—
152C2×C32—31no—
153C2×C32—61no—
154C2×C32—91no—
155C2×C32—91no—
156C2×C32—181no—
157C2×C32—181no—
158C2×C32—541no—
159C2×C32((C3⋊D3)⋊C3)⋊C211yescharacteristic
160C2×C32C3×D3211yescharacteristic
161C3⋊D3—61no—
162C3×D3—61no—
163C3×D3—181no—
164C3×D3—181no—
165C3×D3—182no—
166C3×D3—181no—
167C3×D3—182no—
168C3×D3—181no—
169C3×D3—181no—
170C3×D3—541no—
171C2×C9—31no—
172C2×C9—61no—
173C2×C9—61no—
174C2×C9—121no—
175C2×C9—181no—
176C2×C9—182no—
177D9—61no—
178D9—62no—
179C22×C3—91no—
180C22×C3—271no—
181C22×C3—271no—
182C22×C3—271no—
183C22×C3—541no—
184C2×D3—31no—
185C2×D3—91no—
186C2×D3—91no—
187C2×D3—271no—
188C3×C4—271no—
189C3×C4—271no—
190C3×C4—541no—
191Dic3—91no—
192Dic3—271no—
193C32—21no—
194C32—31no—
195C32—61no—
196C32—91no—
197C32—91no—
198C32—181no—
199C32#620011yescharacteristic
200C32C3×#62611yescharacteristic
201C9—31no—
202C9—61no—
203C9—61no—
204C9—121no—
205D4—811noSylow
206C2×C3—31no—
207C2×C3—31no—
208C2×C3—61no—
209C2×C3—91no—
210C2×C3—181no—
211C2×C3—181no—
212C2×C3—541no—
213C2×C3—541no—
214C2×C3—541no—
215C2×C3—542no—
216C2×C3C3×((C3⋊D3)⋊C3)⋊C211yescharacteristic
217D3—61no—
218D3—181no—
219D3—181no—
220D3—541no—
221C22—91no—
222C22—271no—
223C4—271no—
224C3—31no—
225C3—31no—
226C3—61no—
227C3—91no—
228C3—181no—
229C3C3×#620011yescharacteristic
230C2—181no—
231C2—541no—
232C2(#4176⋊C2)⋊C311yescharacteristic
subgroupG/H
center, hypercenterC2(#4176⋊C2)⋊C3
commutator, cosocleC2×#731C22×C3
FrattiniC2×C32C3×D32
FittingC2×#6910C22
socleC2×C3C3×((C3⋊D3)⋊C3)⋊C2
hypocenter#731C3×D4
LCSG ▷ C2×#731 ▷ #731
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
1. C2×#4184⋊C3C2semidirect
2. C2×#92283C2semidirect
3. #66324⋊C3C2semidirect
6. #10619556C3semidirect
15. C3⋊(3−1+2⋊C4)D3semidirect
17. C2×#4184C2×C3semidirect
19. C2×#4176C2×C3semidirect
21. #66324C2×C3semidirect
22. #6910D4semidirect
62. C3⋊Dic9C3×D3semidirect
67. C3×3−1+2D12semidirect
72. #731C3×D4semidirect
146. C3×C9C3×D12semidirect

Maximal subgroups

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

subgroupindex
C2×#4184⋊C32
C2×#922832
#66324⋊C32
#6194⋊C33
C3×#62003
#106195563