Finite Group Databasebeta

← (#66366⋊C2)⋊C3 #14518075

Subgroups — (#66366⋊C2)⋊C3 #14518075

Order 1944.

264 conjugacy classes of subgroups; only the 28 normal subgroups are shown.

normal subgroups only

This group has 264 conjugacy classes of subgroups — too many to draw. Only its 28 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
1#11757851C211yesmaximal, characteristic, complemented
2C3×(C3⋊S4)⋊C3—31nomaximal
3C3×(C3⋊S4)⋊C3—31nomaximal
4C3×((C22⋊C9)⋊C2)⋊C3—31nomaximal
5C3×#611⋊C3—31nomaximal
6#66366⋊C2C311yesmaximal, characteristic, complemented
7#4183⋊C3—41nomaximal
8C22×C3×3−1+2D311yescharacteristic, complemented
9C2×C3×AGL(1,ℤ/9)—31no—
10C3×C22⋊H(3,𝔽3)D311yescharacteristic, complemented
11C3×C22⋊H(3,𝔽3)D311yescharacteristic, complemented
12C3×#1094D311yescharacteristic, complemented
13C3×3−1+2⋊C4—31no—
14#66366—21no—
15#66366—21no—
16#66366—21no—
17#66366—21no—
18#66366C2×C311yescharacteristic, complemented
19#6909—41noSylow
20C3×C3⋊S4—31no—
21C3×C3⋊S4—31no—
22C32×#67—91no—
23(C3⋊S4)⋊C3—31no—
24(C3⋊S4)⋊C3—31no—
25(C3⋊S4)⋊C3—31no—
26(C3⋊S4)⋊C3—31no—
27(C3⋊S4)⋊C3—31no—
28(C3⋊S4)⋊C3—31no—
29C3×(C22⋊C9)⋊C2—31no—
30((C22⋊C9)⋊C2)⋊C3—31no—
31((C22⋊C9)⋊C2)⋊C3—31no—
32((C22⋊C9)⋊C2)⋊C3—31no—
33#611⋊C3—31no—
34#611⋊C3—31no—
35#611⋊C3—31no—
36C3×#611—31no—
37C2×C3×3−1+2—31no—
38C3×AGL(1,ℤ/9)—61no—
39C3×AGL(1,ℤ/9)—121no—
40C3×(C3⋊D3)⋊C3—121no—
41C3×(C3⋊D3)⋊C3—121no—
42#4183—41no—
43C22×C33C3⋊D311yescharacteristic
44C2×C32×D3—91no—
45C32×A4—21no—
46C32×A4—31no—
47C32×A4C3×D311yescharacteristic, complemented
48C32×Dic3—91no—
49C22×3−1+2—21no—
50C22×3−1+2—31no—
51C22×3−1+2—31no—
52C22×3−1+2C3×D311yescharacteristic, complemented
53C22×C3×C9—31no—
54C2×AGL(1,ℤ/9)—31no—
55C2×AGL(1,ℤ/9)—31no—
56C2×AGL(1,ℤ/9)—31no—
57C2×C3×D9—31no—
58C22⋊H(3,𝔽3)—21no—
59C22⋊H(3,𝔽3)—31no—
60C22⋊H(3,𝔽3)—31no—
61C22⋊H(3,𝔽3)—31no—
62C22⋊H(3,𝔽3)—31no—
63C22⋊H(3,𝔽3)—31no—
64C22⋊H(3,𝔽3)C3×D311yescharacteristic
65#1094—21no—
66#1094—31no—
67#1094—31no—
68#1094C3×D311yescharacteristic, complemented
69C3×C22⋊C9—31no—
703−1+2⋊C4—31no—
713−1+2⋊C4—31no—
723−1+2⋊C4—31no—
73C3×Dic9—31no—
74C3×3−1+2—41no—
75C3×3−1+2S411yescharacteristic, complemented
76C3×H(3,𝔽3)—41no—
77C3×H(3,𝔽3)—41no—
78AΣL(1,𝔽27)—41no—
79AΣL(1,𝔽27)—81no—
80AΣL(1,𝔽27)—81no—
81AΣL(1,𝔽27)—81no—
82AΣL(1,𝔽27)—81no—
83C3⋊S4—31no—
84C3⋊S4—31no—
85C3×S4—271no—
86C3×S4—271no—
87C32×D4—271no—
88C3×#67—91no—
89C3×#67—91no—
90C3×#67—91no—
91C3×#67—91no—
92(C22⋊C9)⋊C2—31no—
93#611—31no—
94C2×C33—31no—
95C3×C3⋊D3—121no—
96C3×C3⋊D3—121no—
97C32×D3—181no—
98C2×3−1+2—31no—
99C2×3−1+2—31no—
100C2×3−1+2—31no—
101C2×3−1+2—61no—
102C2×3−1+2—61no—
103C2×3−1+2—61no—
104C2×C3×C9—31no—
105C2×C3×C9—61no—
106AGL(1,ℤ/9)—61no—
107AGL(1,ℤ/9)—61no—
108AGL(1,ℤ/9)—61no—
109AGL(1,ℤ/9)—121no—
110AGL(1,ℤ/9)—121no—
111AGL(1,ℤ/9)—121no—
112(C3⋊D3)⋊C3—121no—
113(C3⋊D3)⋊C3—121no—
114(C3⋊D3)⋊C3—121no—
115(C3⋊D3)⋊C3—121no—
116(C3⋊D3)⋊C3—121no—
117(C3⋊D3)⋊C3—121no—
118C3×D9—61no—
119C3×D9—121no—
120C22×C32—91no—
121C22×C32—271no—
122C22×C32#27211yescharacteristic
123C22×C32#27211yescharacteristic
124C22×C32#27211yescharacteristic
125C22×C32C3×C3⋊D311yescharacteristic
126C2×C3×D3—91no—
127C2×C3×D3—91no—
128C2×C3×D3—91no—
129C2×C3×D3—91no—
130C3×A4—31no—
131C3×A4—31no—
132C3×A4—61no—
133C3×A4—61no—
134C3×A4—91no—
135C3×A4—91no—
136C3×A4—181no—
137C3×A4—181no—
138C32×C4—271no—
139C3×Dic3—91no—
140C3×Dic3—91no—
141C3×Dic3—91no—
142C3×Dic3—91no—
143C22×C9—31no—
144C22×C9—61no—
145C2×D9—31no—
146C22⋊C9—31no—
147C22⋊C9—61no—
148Dic9—31no—
149C33—41no—
150C33—81no—
151C33—121no—
152C33C3⋊S411yescharacteristic
1533−1+2—21no—
1543−1+2—31no—
1553−1+2—31no—
1563−1+2—41no—
1573−1+2—81no—
1583−1+2—121no—
1593−1+2—121no—
1603−1+2C3×S411yescharacteristic, complemented
161H(3,𝔽3)—41no—
162H(3,𝔽3)—81no—
163H(3,𝔽3)—121no—
164H(3,𝔽3)—121no—
165H(3,𝔽3)—121no—
166H(3,𝔽3)—121no—
167H(3,𝔽3)—121no—
168C3×C9—31no—
169C3×C9—121no—
170S4—271no—
171S4—271no—
172C3×D4—271no—
173C3×D4—271no—
174C3×D4—271no—
175C3×D4—271no—
176#67—91no—
177C2×C32—31no—
178C2×C32—31no—
179C2×C32—31no—
180C2×C32—31no—
181C2×C32—91no—
182C2×C32—181no—
183C2×C32—541no—
184C3⋊D3—121no—
185C3⋊D3—121no—
186C3×D3—181no—
187C3×D3—181no—
188C3×D3—181no—
189C3×D3—181no—
190C3×D3—1081no—
191C3×D3—1081no—
192C2×C9—31no—
193C2×C9—61no—
194C2×C9—61no—
195C2×C9—61no—
196C2×C9—61no—
197D9—61no—
198D9—121no—
199C22×C3—31no—
200C22×C3—31no—
201C22×C3—31no—
202C22×C3—31no—
203C22×C3—271no—
204C22×C3—271no—
205C22×C3—271no—
206C22×C3—271no—
207C22×C3C3×#27211yescharacteristic
208C2×D3—91no—
209A4—91no—
210A4—91no—
211A4—181no—
212A4—181no—
213C3×C4—271no—
214C3×C4—271no—
215C3×C4—271no—
216C3×C4—271no—
217Dic3—91no—
218C32—91no—
219C32—121no—
220C32—121no—
221C32—241no—
222C32—241no—
223C32—361no—
224C32—361no—
225C32—721no—
226C32—721no—
227C32#625811yescharacteristic
228C32#625811yescharacteristic
229C32#625811yescharacteristic
230C32C3×C3⋊S411yescharacteristic
231C9—31no—
232C9—61no—
233C9—121no—
234C9—241no—
235D4—271noSylow
236C2×C3—31no—
237C2×C3—31no—
238C2×C3—61no—
239C2×C3—91no—
240C2×C3—91no—
241C2×C3—91no—
242C2×C3—541no—
243C2×C3—541no—
244C2×C3—541no—
245C2×C3—541no—
246D3—181no—
247D3—1081no—
248D3—1081no—
249C22—271no—
250C22#4183⋊C311yescharacteristic, complemented
251C4—271no—
252C3—31no—
253C3—31no—
254C3—31no—
255C3—31no—
256C3—361no—
257C3—361no—
258C3—721no—
259C3—721no—
260C3C3×#625811yescharacteristic
261C2—31no—
262C2—541no—
subgroupG/H
center, hypercenterC1G
commutator, cosocle, hypocenter#66366C2×C3
FrattiniC32C3×C3⋊S4
FittingC22×C3×3−1+2D3
socleC22×C3C3×#272
LCSG ▷ #66366
UCSC1

Complements

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

NH ≅ G/Ntype
1. #11757851C2semidirect
6. #66366⋊C2C3semidirect
8. C22×C3×3−1+2D3semidirect
10. C3×C22⋊H(3,𝔽3)D3semidirect
11. C3×C22⋊H(3,𝔽3)D3semidirect
12. C3×#1094D3semidirect
18. #66366C2×C3semidirect
47. C32×A4C3×D3semidirect
52. C22×3−1+2C3×D3semidirect
68. #1094C3×D3semidirect
75. C3×3−1+2S4semidirect
160. 3−1+2C3×S4semidirect
250. C22#4183⋊C3semidirect

Maximal subgroups

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

subgroupindex
#117578512
C3×(C3⋊S4)⋊C33
C3×((C22⋊C9)⋊C2)⋊C33
C3×#611⋊C33
#66366⋊C23
#4183⋊C34