Finite Group Databasebeta

← #10619557⋊C3 #14516925

Subgroups — #10619557⋊C3 #14516925

Order 1944.

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

normal subgroups only

This group has 236 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×#4177⋊C3C211yesmaximal, characteristic, complemented
2C2×#92283C211yesmaximal, characteristic, complemented
3#66331⋊C3C211yesmaximal, characteristic, complemented
4#6195⋊C3—31nomaximal
5C3×#6200—31nomaximal
6#10619557C311yesmaximal, characteristic, complemented
7C2×#6910C2211yescharacteristic
8#4177⋊C3—21no—
9#92283—21no—
10C2×C3⋊AGL(1,ℤ/9)D311yescharacteristic, complemented
11C2×C3×#272D311yescharacteristic
12C2×D3×3−1+2—31no—
13C2×C3×(C3⋊D3)⋊C3—31no—
14C3×3−1+2⋊C4—31no—
15C3×3−1+2⋊C4—61no—
16C3×(C3⋊Dic3)⋊C3—31no—
17C2×#4177—21no—
18C2×#4177C2×C311yescharacteristic, complemented
19C2×#4176—21no—
20C2×#4176C2×C311yescharacteristic, complemented
21#66331C2×C311yescharacteristic, complemented
22#6910D411yescharacteristic, complemented, Sylow
23C3×#626—91no—
24C3×#625—91no—
25#611⋊C3—91no—
26#6200—31no—
27#6195—31no—
28C2×C3×3−1+2—21no—
29C2×C3×3−1+2C2×D311yescharacteristic
30C2×C3×H(3,𝔽3)C2×D311yescharacteristic
31C3⋊AGL(1,ℤ/9)—21no—
32C3×#272—21no—
33D3×3−1+2—61no—
34C3×(C3⋊D3)⋊C3—61no—
35C2×#731—21no—
36C2×#731—21no—
37C2×#731—41no—
38C2×#731C22×C311yescharacteristic
39#4177—22no—
40#4177—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×C3⋊D9C3×D311yescharacteristic, complemented
52C2×AGL(1,ℤ/9)—91no—
53C2×(C3⋊D3)⋊C3—31no—
54C2×(C3⋊D3)⋊C3—61no—
55C2×D3×C9—31no—
56C2×D3×C9—61no—
573−1+2⋊C4—31no—
583−1+2⋊C4—61no—
593−1+2⋊C4—61no—
603−1+2⋊C4—61no—
613−1+2⋊C4—61no—
62(C3⋊Dic3)⋊C3—31no—
63(C3⋊Dic3)⋊C3—61no—
64C3×Dic9—31no—
65C3×Dic9—61no—
66C3×3−1+2—21no—
67C3×3−1+2#6711yescharacteristic, 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—
99C3⋊D9—21no—
100AGL(1,ℤ/9)—181no—
101(C3⋊D3)⋊C3—62no—
102(C3⋊D3)⋊C3—61no—
103D3×C9—62no—
104D3×C9—61no—
105C22×C32—91no—
106C22×C32—271no—
107C2×C3⋊D3—31no—
108C2×C3×D3—31no—
109C2×C3×D3—91no—
110C2×C3×D3—91no—
111C2×C3×D3—91no—
112C2×C3×D3—91no—
113C2×C3×D3—91no—
114C2×C3×D3—181no—
115C2×C3×D3—181no—
116C2×C3×D3—271no—
117C32×C4—271no—
118C3⋊Dic3—31no—
119C3×Dic3—91no—
120C3×Dic3—91no—
121C3×Dic3—181no—
122C3×Dic3—271no—
123C22×C9—91no—
124C22×C9—181no—
125C2×D9—91no—
126Dic9—31no—
127Dic9—61no—
128C33—31no—
129C33#62511yescharacteristic
1303−1+2—21no—
1313−1+2—31no—
1323−1+2—41no—
1333−1+2—61no—
1343−1+2—61no—
1353−1+2—61no—
136H(3,𝔽3)—21no—
137H(3,𝔽3)—61no—
138H(3,𝔽3)C3×#6711yescharacteristic
139C3×C9—21no—
140C3×C9—61no—
141C3×C9C3×#6711yescharacteristic, complemented
142C3×D4—811no—
143#67—271no—
144#67—271no—
145D12—271no—
146C2×C32—21no—
147C2×C32—31no—
148C2×C32—61no—
149C2×C32—91no—
150C2×C32—91no—
151C2×C32—181no—
152C2×C32—181no—
153C2×C32—541no—
154C2×C32((C3⋊D3)⋊C3)⋊C211yescharacteristic
155C2×C32C3×D3211yescharacteristic
156C3⋊D3—61no—
157C3×D3—61no—
158C3×D3—181no—
159C3×D3—181no—
160C3×D3—181no—
161C3×D3—182no—
162C3×D3—181no—
163C3×D3—182no—
164C3×D3—181no—
165C3×D3—541no—
166C2×C9—31no—
167C2×C9—61no—
168C2×C9—61no—
169C2×C9—121no—
170C2×C9—181no—
171C2×C9—182no—
172D9—181no—
173C22×C3—91no—
174C22×C3—271no—
175C22×C3—271no—
176C22×C3—271no—
177C22×C3—541no—
178C2×D3—31no—
179C2×D3—91no—
180C2×D3—91no—
181C2×D3—271no—
182C3×C4—271no—
183C3×C4—271no—
184C3×C4—541no—
185Dic3—91no—
186Dic3—271no—
187C32—21no—
188C32—31no—
189C32—61no—
190C32—91no—
191C32—91no—
192C32—181no—
193C32#619811yescharacteristic
194C32C3×#62511yescharacteristic
195C9—31no—
196C9—61no—
197C9—61no—
198C9—121no—
199D4—811noSylow
200C2×C3—31no—
201C2×C3—31no—
202C2×C3—61no—
203C2×C3—91no—
204C2×C3—181no—
205C2×C3—181no—
206C2×C3—541no—
207C2×C3—541no—
208C2×C3—541no—
209C2×C3—542no—
210C2×C3C3×((C3⋊D3)⋊C3)⋊C211yescharacteristic
211D3—61no—
212D3—181no—
213D3—181no—
214D3—541no—
215C22—91no—
216C22—271no—
217C4—271no—
218C3—31no—
219C3—31no—
220C3—61no—
221C3—91no—
222C3—181no—
223C3C3×#619811yescharacteristic
224C2—181no—
225C2—541no—
226C2(#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×#4177⋊C3C2semidirect
2. C2×#92283C2semidirect
3. #66331⋊C3C2semidirect
6. #10619557C3semidirect
10. C2×C3⋊AGL(1,ℤ/9)D3semidirect
18. C2×#4177C2×C3semidirect
20. C2×#4176C2×C3semidirect
21. #66331C2×C3semidirect
22. #6910D4semidirect
51. C2×C3⋊D9C3×D3semidirect
67. C3×3−1+2#67semidirect
72. #731C3×D4semidirect
141. C3×C9C3×#67semidirect

Maximal subgroups

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

subgroupindex
C2×#4177⋊C32
C2×#922832
#66331⋊C32
#6195⋊C33
C3×#62003
#106195573