Finite Group Databasebeta

← #10619549⋊C3 #14516916

Subgroups — #10619549⋊C3 #14516916

Order 1944.

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

normal subgroups only

This group has 274 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×#4183⋊C3C211yesmaximal, characteristic, complemented
2C2×#92281C211yesmaximal, characteristic, complemented
3#66322⋊C3C211yesmaximal, characteristic, complemented
4C3×#6200—31nomaximal
5#6290⋊C3—31nomaximal
6#10619549C311yesmaximal, characteristic, complemented
7C2×#6909C2211yescharacteristic
8#4183⋊C3—21no—
9#92281—21no—
10C2×C3×#272D311yescharacteristic, complemented
11C2×C3×AGL(1,ℤ/9)—61no—
12C2×D3×H(3,𝔽3)—31no—
13C2×C3×(C3⋊D3)⋊C3—31no—
14C2×C3×(C3⋊D3)⋊C3—31no—
15C3⋊((C3⋊Dic3)⋊C3)D311yescharacteristic, complemented
16C3×(C3⋊Dic3)⋊C3—31no—
17C2×#4183C2×C311yescharacteristic, complemented
18C2×#4174—21no—
19C2×#4174C2×C311yescharacteristic, complemented
20#66322—21no—
21#66322C2×C311yescharacteristic, complemented
22#6909D411yescharacteristic, complemented, Sylow
23#6290—31no—
24C3×#626—91no—
25C3×#625—91no—
26#638⋊C3—91no—
27#6200—31no—
28C2×C3×3−1+2—21no—
29C2×C3×H(3,𝔽3)C2×D311yescharacteristic
30C2×C3×H(3,𝔽3)C2×D311yescharacteristic
31C3×#272—21no—
32C3×AGL(1,ℤ/9)—62no—
33D3×H(3,𝔽3)—61no—
34C3×(C3⋊D3)⋊C3—61no—
35C3×(C3⋊D3)⋊C3—61no—
36C2×AΣL(1,𝔽27)—21no—
37C2×AΣL(1,𝔽27)—21no—
38C2×AΣL(1,𝔽27)—41no—
39C2×AΣL(1,𝔽27)C22×C311yescharacteristic
40#4183—21no—
41#4174—22no—
42#4174—21no—
43C2×C3×C3⋊D3—31no—
44C2×C3×C3⋊D3—31no—
45C2×C32×D3—31no—
46C2×C32×D3—31no—
47C2×C32×D3—61no—
48C2×C32×D3—91no—
49C2×C32×D3—91no—
50C3⋊(C3⋊Dic3)C3×D311yescharacteristic, complemented
51C3×C3⋊Dic3—31no—
52C32×Dic3—91no—
53C22×H(3,𝔽3)—91no—
54C2×#272C3×D311yescharacteristic
55C2×AGL(1,ℤ/9)—61no—
56C2×AGL(1,ℤ/9)—61no—
57C2×AGL(1,ℤ/9)—61no—
58C2×(C3⋊D3)⋊C3—31no—
59C2×(C3⋊D3)⋊C3—31no—
60C2×(C3⋊D3)⋊C3—61no—
61C2×(C3⋊D3)⋊C3—61no—
62C2×C3×D9—61no—
63(C3⋊Dic3)⋊C3—31no—
64(C3⋊Dic3)⋊C3—61no—
65(C3⋊Dic3)⋊C3—91no—
66C3×3−1+2—21no—
67C3×H(3,𝔽3)D1211yescharacteristic, complemented
68C3×H(3,𝔽3)#6711yescharacteristic, complemented
69AΣL(1,𝔽27)—21no—
70AΣL(1,𝔽27)—21no—
71AΣL(1,𝔽27)—41no—
72AΣL(1,𝔽27)C3×D411yescharacteristic, complemented
73#638—91no—
74C3×#67—271no—
75C3×#67—271no—
76C3×D12—271no—
77#626—91no—
78#625—91no—
79#625—271no—
80C2×C33—21no—
81C2×C33—31no—
82C2×C33D3211yescharacteristic
83C2×C33C2×C3×D311yescharacteristic
84C3×C3⋊D3—61no—
85C3×C3⋊D3—61no—
86C32×D3—62no—
87C32×D3—61no—
88C32×D3—61no—
89C32×D3—181no—
90C32×D3—181no—
91C2×3−1+2—21no—
92C2×3−1+2—41no—
93C2×3−1+2—61no—
94C2×3−1+2—61no—
95C2×H(3,𝔽3)—21no—
96C2×H(3,𝔽3)—31no—
97C2×H(3,𝔽3)—61no—
98C2×H(3,𝔽3)—61no—
99C2×H(3,𝔽3)—181no—
100C2×H(3,𝔽3)C2×C3×D311yescharacteristic
101C2×C3×C9—61no—
102#272—21no—
103AGL(1,ℤ/9)—62no—
104AGL(1,ℤ/9)—62no—
105AGL(1,ℤ/9)—62no—
106(C3⋊D3)⋊C3—61no—
107(C3⋊D3)⋊C3—62no—
108(C3⋊D3)⋊C3—62no—
109(C3⋊D3)⋊C3—61no—
110C3×D9—62no—
111C22×C32—91no—
112C22×C32—91no—
113C22×C32—181no—
114C22×C32—271no—
115C2×C3⋊D3—31no—
116C2×C3⋊D3—31no—
117C2×C3×D3—31no—
118C2×C3×D3—91no—
119C2×C3×D3—91no—
120C2×C3×D3—91no—
121C2×C3×D3—91no—
122C2×C3×D3—91no—
123C2×C3×D3—91no—
124C2×C3×D3—181no—
125C2×C3×D3—181no—
126C2×C3×D3—181no—
127C2×C3×D3—271no—
128C2×C3×D3—271no—
129C32×C4—271no—
130C3⋊Dic3—31no—
131C3⋊Dic3—91no—
132C3⋊Dic3—271no—
133C3×Dic3—91no—
134C3×Dic3—91no—
135C3×Dic3—181no—
136C3×Dic3—271no—
137C2×D9—61no—
138C33—21no—
139C33—31no—
140C33#62611yescharacteristic
141C33C3×D1211yescharacteristic, complemented
1423−1+2—21no—
1433−1+2—41no—
1443−1+2—61no—
1453−1+2—61no—
146H(3,𝔽3)—21no—
147H(3,𝔽3)—31no—
148H(3,𝔽3)—61no—
149H(3,𝔽3)—61no—
150H(3,𝔽3)C3×#6711yescharacteristic
151C3×C9—61no—
152C3×D4—811no—
153#67—271no—
154#67—271no—
155#67—811no—
156D12—271no—
157C2×C32—21no—
158C2×C32—31no—
159C2×C32—31no—
160C2×C32—61no—
161C2×C32—61no—
162C2×C32—91no—
163C2×C32—91no—
164C2×C32—91no—
165C2×C32—181no—
166C2×C32—181no—
167C2×C32—181no—
168C2×C32—182no—
169C2×C32—181no—
170C2×C32—541no—
171C2×C32((C3⋊D3)⋊C3)⋊C211yescharacteristic
172C2×C32C3×D3211yescharacteristic
173C3⋊D3—61no—
174C3⋊D3—61no—
175C3×D3—61no—
176C3×D3—181no—
177C3×D3—181no—
178C3×D3—182no—
179C3×D3—181no—
180C3×D3—182no—
181C3×D3—181no—
182C3×D3—182no—
183C3×D3—181no—
184C3×D3—181no—
185C3×D3—541no—
186C3×D3—541no—
187C2×C9—61no—
188C2×C9—121no—
189D9—62no—
190C22×C3—91no—
191C22×C3—271no—
192C22×C3—271no—
193C22×C3—271no—
194C22×C3—271no—
195C22×C3—541no—
196C22×C3—541no—
197C2×D3—31no—
198C2×D3—91no—
199C2×D3—91no—
200C2×D3—271no—
201C2×D3—271no—
202C3×C4—271no—
203C3×C4—271no—
204C3×C4—541no—
205Dic3—91no—
206Dic3—271no—
207Dic3—811no—
208C32—21no—
209C32—31no—
210C32—31no—
211C32—61no—
212C32—61no—
213C32—91no—
214C32—91no—
215C32—91no—
216C32—181no—
217C32—181no—
218C32#620011yescharacteristic
219C32C3×#62611yescharacteristic
220C9—61no—
221C9—121no—
222D4—811noSylow
223C2×C3—31no—
224C2×C3—31no—
225C2×C3—61no—
226C2×C3—91no—
227C2×C3—91no—
228C2×C3—181no—
229C2×C3—181no—
230C2×C3—181no—
231C2×C3—541no—
232C2×C3—541no—
233C2×C3—542no—
234C2×C3—541no—
235C2×C3—541no—
236C2×C3—542no—
237C2×C3C3×((C3⋊D3)⋊C3)⋊C211yescharacteristic
238D3—61no—
239D3—181no—
240D3—181no—
241D3—541no—
242D3—541no—
243C22—91no—
244C22—271no—
245C4—271no—
246C3—31no—
247C3—31no—
248C3—61no—
249C3—91no—
250C3—91no—
251C3—181no—
252C3—181no—
253C3C3×#620011yescharacteristic
254C2—181no—
255C2—541no—
256C2(#4174⋊C2)⋊C311yescharacteristic
subgroupG/H
center, hypercenterC2(#4174⋊C2)⋊C3
commutator, cosocleC2×AΣL(1,𝔽27)C22×C3
FrattiniC2×C32C3×D32
FittingC2×#6909C22
socleC2×C3C3×((C3⋊D3)⋊C3)⋊C2
hypocenterAΣL(1,𝔽27)C3×D4
LCSG ▷ C2×AΣL(1,𝔽27) ▷ AΣL(1,𝔽27)
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
1. C2×#4183⋊C3C2semidirect
2. C2×#92281C2semidirect
3. #66322⋊C3C2semidirect
6. #10619549C3semidirect
10. C2×C3×#272D3semidirect
15. C3⋊((C3⋊Dic3)⋊C3)D3semidirect
17. C2×#4183C2×C3semidirect
19. C2×#4174C2×C3semidirect
21. #66322C2×C3semidirect
22. #6909D4semidirect
50. C3⋊(C3⋊Dic3)C3×D3semidirect
67. C3×H(3,𝔽3)D12semidirect
68. C3×H(3,𝔽3)#67semidirect
72. AΣL(1,𝔽27)C3×D4semidirect
141. C33C3×D12semidirect

Maximal subgroups

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

subgroupindex
C2×#4183⋊C32
C2×#922812
#66322⋊C32
C3×#62003
#6290⋊C33
#106195493