Finite Group Databasebeta

← #10619551⋊C3 #14516917

Subgroups — #10619551⋊C3 #14516917

Order 1944.

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

normal subgroups only

This group has 270 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×#4175⋊C3C211yesmaximal, characteristic, complemented
3#11757585C211yesmaximal, characteristic, complemented
4C3×#6198—31nomaximal
5#6292⋊C3—31nomaximal
6#10619551C311yesmaximal, characteristic, complemented
7C2×#6909C2211yescharacteristic
8#4183⋊C3—21no—
9#4175⋊C3—21no—
10C2×C3⋊((C3⋊D3)⋊C3)D311yescharacteristic, complemented
11C2×C3×AGL(1,ℤ/9)—61no—
12C2×C3×(C3⋊D3)⋊C3—31no—
13C2×C3×(C3⋊D3)⋊C3—31no—
14C2×C3×(C3⋊D3)⋊C3—31no—
15C3×#1084D311yescharacteristic, complemented
16Dic3×H(3,𝔽3)—31no—
17C2×#4183C2×C311yescharacteristic, complemented
18C2×#4175—21no—
19C2×#4175C2×C311yescharacteristic, complemented
20#66321—21no—
21#66321C2×C311yescharacteristic, complemented
22#6909D411yescharacteristic, complemented, Sylow
23#6292—31no—
24C3×#626—91no—
25C3×#626—91no—
26C4⋊((C3⋊D3)⋊C3)—91no—
27#6198—31no—
28C2×C3×3−1+2—21no—
29C2×C3×H(3,𝔽3)C2×D311yescharacteristic
30C2×C3×H(3,𝔽3)C2×D311yescharacteristic
31C3⋊((C3⋊D3)⋊C3)—21no—
32C3×AGL(1,ℤ/9)—62no—
33C3×(C3⋊D3)⋊C3—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#4175—22no—
42#4175—21no—
43C2×C3⋊(C3⋊D3)C3×D311yescharacteristic, complemented
44C2×C3×C3⋊D3—31no—
45C2×C3×C3⋊D3—31no—
46C2×C3×C3⋊D3—31no—
47C2×C32×D3—91no—
48C2×C32×D3—91no—
49C32×Dic3—31no—
50C32×Dic3—31no—
51C32×Dic3—61no—
52C32×Dic3—91no—
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—31no—
58C2×(C3⋊D3)⋊C3—31no—
59C2×(C3⋊D3)⋊C3—61no—
60C2×(C3⋊D3)⋊C3—61no—
61C2×(C3⋊D3)⋊C3—61no—
62C2×(C3⋊D3)⋊C3—91no—
63C2×C3×D9—61no—
64C4×H(3,𝔽3)—91no—
65#1084C3×D311yescharacteristic
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
73C4⋊(C3⋊D3)—91no—
74C3×#67—271no—
75C3×#67—271no—
76C3×D12—271no—
77#626—91no—
78#626—91no—
79#626—271no—
80C2×C33—21no—
81C2×C33—31no—
82C2×C33D3211yescharacteristic
83C2×C33C2×C3×D311yescharacteristic
84C3⋊(C3⋊D3)—21no—
85C3×C3⋊D3—61no—
86C3×C3⋊D3—61no—
87C3×C3⋊D3—61no—
88C32×D3—181no—
89C32×D3—181no—
90C2×3−1+2—21no—
91C2×3−1+2—41no—
92C2×3−1+2—61no—
93C2×3−1+2—61no—
94C2×H(3,𝔽3)—21no—
95C2×H(3,𝔽3)—31no—
96C2×H(3,𝔽3)—61no—
97C2×H(3,𝔽3)—61no—
98C2×H(3,𝔽3)C2×C3×D311yescharacteristic
99C2×C3×C9—61no—
100AGL(1,ℤ/9)—62no—
101AGL(1,ℤ/9)—62no—
102AGL(1,ℤ/9)—62no—
103(C3⋊D3)⋊C3—62no—
104(C3⋊D3)⋊C3—61no—
105(C3⋊D3)⋊C3—62no—
106(C3⋊D3)⋊C3—62no—
107(C3⋊D3)⋊C3—61no—
108(C3⋊D3)⋊C3—61no—
109(C3⋊D3)⋊C3—181no—
110C3×D9—62no—
111C22×C32—271no—
112C22×C32—271no—
113C2×C3⋊D3—31no—
114C2×C3⋊D3—31no—
115C2×C3⋊D3—31no—
116C2×C3⋊D3—91no—
117C2×C3⋊D3—271no—
118C2×C3×D3—91no—
119C2×C3×D3—91no—
120C2×C3×D3—91no—
121C2×C3×D3—91no—
122C2×C3×D3—181no—
123C2×C3×D3—181no—
124C2×C3×D3—271no—
125C2×C3×D3—271no—
126C2×C3×D3—271no—
127C32×C4—91no—
128C32×C4—91no—
129C32×C4—181no—
130C3×Dic3—31no—
131C3×Dic3—91no—
132C3×Dic3—91no—
133C3×Dic3—91no—
134C3×Dic3—91no—
135C3×Dic3—181no—
136C3×Dic3—181no—
137C2×D9—61no—
138C33—21no—
139C33—31no—
140C33#62611yescharacteristic
141C33C3×#6711yescharacteristic, 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×D1211yescharacteristic
151C3×C9—61no—
152C3×D4—811no—
153#67—271no—
154#67—271no—
155D12—271no—
156D12—811no—
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—541no—
168C2×C32—541no—
169C2×C32((C3⋊D3)⋊C3)⋊C211yescharacteristic
170C2×C32C3×D3211yescharacteristic
171C3⋊D3—61no—
172C3⋊D3—61no—
173C3⋊D3—61no—
174C3⋊D3—181no—
175C3⋊D3—541no—
176C3×D3—182no—
177C3×D3—181no—
178C3×D3—182no—
179C3×D3—181no—
180C3×D3—181no—
181C3×D3—181no—
182C3×D3—541no—
183C3×D3—541no—
184C3×D3—541no—
185C2×C9—61no—
186C2×C9—121no—
187D9—62no—
188C22×C3—271no—
189C22×C3—271no—
190C22×C3—271no—
191C22×C3—271no—
192C22×C3—541no—
193C22×C3—541no—
194C2×D3—91no—
195C2×D3—91no—
196C2×D3—271no—
197C2×D3—271no—
198C2×D3—271no—
199C2×D3—811no—
200C3×C4—91no—
201C3×C4—271no—
202C3×C4—271no—
203C3×C4—541no—
204Dic3—31no—
205Dic3—91no—
206C32—21no—
207C32—31no—
208C32—31no—
209C32—61no—
210C32—61no—
211C32—91no—
212C32—91no—
213C32—91no—
214C32—181no—
215C32—181no—
216C32#620011yescharacteristic
217C32C3×#62611yescharacteristic
218C9—61no—
219C9—121no—
220D4—811noSylow
221C2×C3—31no—
222C2×C3—31no—
223C2×C3—61no—
224C2×C3—91no—
225C2×C3—91no—
226C2×C3—181no—
227C2×C3—181no—
228C2×C3—541no—
229C2×C3—541no—
230C2×C3—541no—
231C2×C3—542no—
232C2×C3—541no—
233C2×C3—542no—
234C2×C3C3×((C3⋊D3)⋊C3)⋊C211yescharacteristic
235D3—181no—
236D3—181no—
237D3—541no—
238D3—541no—
239D3—541no—
240D3—1621no—
241C22—271no—
242C22—271no—
243C4—91no—
244C3—31no—
245C3—31no—
246C3—61no—
247C3—91no—
248C3—91no—
249C3—181no—
250C3—181no—
251C3C3×#620011yescharacteristic
252C2—541no—
253C2—541no—
254C2(#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×#4175⋊C3C2semidirect
3. #11757585C2semidirect
6. #10619551C3semidirect
10. C2×C3⋊((C3⋊D3)⋊C3)D3semidirect
15. C3×#1084D3semidirect
17. C2×#4183C2×C3semidirect
19. C2×#4175C2×C3semidirect
21. #66321C2×C3semidirect
22. #6909D4semidirect
43. C2×C3⋊(C3⋊D3)C3×D3semidirect
67. C3×H(3,𝔽3)D12semidirect
68. C3×H(3,𝔽3)#67semidirect
72. AΣL(1,𝔽27)C3×D4semidirect
141. C33C3×#67semidirect

Maximal subgroups

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

subgroupindex
C2×#4183⋊C32
C2×#4175⋊C32
#117575852
C3×#61983
#6292⋊C33
#106195513