Finite Group Databasebeta

← C3×#66440⋊C2 #14519206

Subgroups — C3×#66440⋊C2 #14519206

Order 1944.

436 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 436 conjugacy classes of subgroups — too many to draw. Only its 58 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
1C3×#66440C211yesmaximal, characteristic, complemented
2#66440⋊C2C313yesmaximal, direct product factor
3C3×C9⋊S4C311yesmaximal, characteristic, complemented
4C3×(C3⋊S4)⋊C3—31nomaximal
5C32×(C22⋊C9)⋊C2—31nomaximal
6C3×((C22⋊C9)⋊C2)⋊C3—31nomaximal
7C3×#611⋊C3—31nomaximal
8C3×#4207—41nomaximal
9C22×C3×3−1+2D311yescharacteristic, complemented
10C2×C3×AGL(1,ℤ/9)—31no—
11C3×C22⋊H(3,𝔽3)D311yescharacteristic
12C3×#1094D311yescharacteristic, complemented
13C32×C22⋊C9D311yescharacteristic, complemented
14#66440—23no—
15#66440—23no—
16#66440—23no—
17#66440—23no—
18#66440C2×C313yescomplemented
19C3×C9⋊A4—21no—
20C3×C9⋊A4—21no—
21C3×C9⋊A4—21no—
22C3×C9×A4—21no—
23C3×C9×A4C2×C311yescharacteristic, complemented
24C3×3−1+2⋊C4—31no—
25C3×#737—41noSylow
26C3×C3⋊S4—31no—
27C32×#67—91no—
28C9⋊S4C3211yescharacteristic, complemented
29(C3⋊S4)⋊C3—33no—
30C3×(C22⋊C9)⋊C2—31no—
31C3×(C22⋊C9)⋊C2—31no—
32C3×(C22⋊C9)⋊C2—33no—
33((C22⋊C9)⋊C2)⋊C3—33no—
34#611⋊C3—33no—
35C3×#611—31no—
36C2×C3×3−1+2—31no—
37#4207—43no—
38C3×C3⋊D9—41no—
39C3×AGL(1,ℤ/9)—61no—
40C3×AGL(1,ℤ/9)—121no—
41C3×(C3⋊D3)⋊C3—121no—
42C32×D9—121no—
43C22×C33C3⋊D311yescharacteristic
44C2×C32×D3—91no—
45C32×A4—21no—
46C32×A4C3×D311yescharacteristic
47C32×Dic3—91no—
48C22×3−1+2—23no—
49C22×3−1+2C3×D313yescomplemented
50C22×C3×C9—21no—
51C22×C3×C9C3×D311yescharacteristic
52C2×AGL(1,ℤ/9)—33no—
53C2×C3×D9—31no—
54C22⋊H(3,𝔽3)—23no—
55C22⋊H(3,𝔽3)C3×D313yes—
56#1094—23no—
57#1094C3×D313yescomplemented
58C3×C22⋊C9—21no—
59C3×C22⋊C9—21no—
60C3×C22⋊C9—23no—
61C3×C22⋊C9C3×D311yescharacteristic
62C3×C22⋊C9C3×D311yescharacteristic
63C3×C22⋊C9C3×D313yescomplemented
64C9⋊A4—26no—
65C9⋊A4—26no—
66C9⋊A4—26no—
67C9⋊A4—23no—
68C9⋊A4—23no—
69C9⋊A4—23no—
70C9×A4—26no—
71C9×A4—21no—
72C9×A4—21no—
73C9×A4—23no—
74C9×A4—21no—
75C9×A4—21no—
76C9×A4C2×C3211yescharacteristic, complemented
773−1+2⋊C4—33no—
78C3×Dic9—31no—
79#737—43no—
80#737—83no—
81#737—83no—
82#737—83no—
83#737—83no—
84C3×3−1+2—41no—
85C3×3−1+2—81no—
86C3×3−1+2—81no—
87C3×3−1+2—81no—
88C3×3−1+2S411yescharacteristic, complemented
89C3×H(3,𝔽3)—41no—
90C32×C9—41no—
91C32×C9—41no—
92C32×C9—81no—
93C3⋊S4—31no—
94C3×S4—271no—
95C32×D4—271no—
96C3×#67—91no—
97C3×#67—93no—
98(C22⋊C9)⋊C2—31no—
99(C22⋊C9)⋊C2—31no—
100#611—31no—
101C2×C33—31no—
102C3×C3⋊D3—121no—
103C32×D3—181no—
104C2×3−1+2—33no—
105C2×3−1+2—63no—
106C2×C3×C9—31no—
107C2×C3×C9—61no—
108C3⋊D9—41no—
109AGL(1,ℤ/9)—63no—
110AGL(1,ℤ/9)—123no—
111(C3⋊D3)⋊C3—123no—
112C3×D9—61no—
113C3×D9—121no—
114C3×D9—123no—
115C3×D9—121no—
116C22×C32—31no—
117C22×C32—61no—
118C22×C32—271no—
119C22×C32C3×C3⋊D311yescharacteristic
120C22×C32C3×C3⋊D313yes—
121C2×C3×D3—91no—
122C2×C3×D3—93no—
123C3×A4—21no—
124C3×A4—23no—
125C3×A4—31no—
126C3×A4—61no—
127C3×A4—62no—
128C3×A4—61no—
129C3×A4C32×D311yescharacteristic
130C32×C4—271no—
131C3×Dic3—91no—
132C3×Dic3—93no—
133C22×C9—23no—
134C22×C9—21no—
135C22×C9C32×D311yescharacteristic
136C2×D9—31no—
137C22⋊C9—21no—
138C22⋊C9—23no—
139C22⋊C9—21no—
140C22⋊C9—23no—
141C22⋊C9C32×D311yescharacteristic
142C22⋊C9C32×D311yescharacteristic
143Dic9—31no—
144C33—41no—
145C33—81no—
146C33C3⋊S411yescharacteristic
1473−1+2—23no—
1483−1+2—43no—
1493−1+2—83no—
1503−1+2—83no—
1513−1+2—86no—
1523−1+2—86no—
1533−1+2—86no—
1543−1+2—83no—
1553−1+2—83no—
1563−1+2C3×S413yescomplemented
157H(3,𝔽3)—43no—
158H(3,𝔽3)—83no—
159C3×C9—21no—
160C3×C9—41no—
161C3×C9—41no—
162C3×C9—41no—
163C3×C9—43no—
164C3×C9—81no—
165C3×C9—81no—
166C3×C9—83no—
167C3×C9—81no—
168C3×C9—86no—
169C3×C9—81no—
170C3×C9—83no—
171C3×C9—81no—
172C3×C9—81no—
173C3×C9C3×S411yescharacteristic
174S4—271no—
175C3×D4—273no—
176C3×D4—271no—
177#67—91no—
178C2×C32—31no—
179C2×C32—33no—
180C2×C32—91no—
181C2×C32—181no—
182C2×C32—541no—
183C3⋊D3—121no—
184C3×D3—181no—
185C3×D3—183no—
186C3×D3—1081no—
187C2×C9—31no—
188C2×C9—61no—
189C2×C9—63no—
190D9—61no—
191D9—121no—
192D9—121no—
193C22×C3—21no—
194C22×C3—33no—
195C22×C3—271no—
196C22×C3—273no—
197C22×C3#420711yescharacteristic, complemented
198C22×C3C32×C3⋊D311yescharacteristic
199C2×D3—91no—
200A4—31no—
201A4—61no—
202A4—63no—
203C3×C4—271no—
204C3×C4—273no—
205Dic3—91no—
206C32—31no—
207C32—41no—
208C32—61no—
209C32—83no—
210C32—81no—
211C32—121no—
212C32—241no—
213C32—242no—
214C32—241no—
215C32C3×C3⋊S411yescharacteristic
216C32C3×C3⋊S413yes—
217C9—23no—
218C9—21no—
219C9—41no—
220C9—41no—
221C9—81no—
222C9—81no—
223C9—83no—
224C9—83no—
225C9C32×S411yescharacteristic
226D4—271noSylow
227C2×C3—31no—
228C2×C3—31no—
229C2×C3—61no—
230C2×C3—93no—
231C2×C3—543no—
232C2×C3—541no—
233D3—181no—
234D3—1081no—
235C22—271no—
236C22C3×#420711yescharacteristic, complemented
237C4—271no—
238C3—21no—
239C3—33no—
240C3—121no—
241C3—241no—
242C3—243no—
243C3#66440⋊C211yescharacteristic, direct product factor
244C3C32×C3⋊S411yescharacteristic
245C2—31no—
246C2—541no—
subgroupG/H
center, hypercenterC3#66440⋊C2
commutator, cosocle, hypocenterC9×A4C2×C32
FrattiniC3C32×C3⋊S4
FittingC22×C3×3−1+2D3
socleC22×C32C3×C3⋊D3
LCSG ▷ C9×A4
UCSC1 ◁ C3

Complements

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

NH ≅ G/Ntype
1. C3×#66440C2semidirect
2. #66440⋊C2C3direct (N × H)
3. C3×C9⋊S4C3semidirect
9. C22×C3×3−1+2D3semidirect
12. C3×#1094D3semidirect
13. C32×C22⋊C9D3semidirect
18. #66440C2×C3semidirect
23. C3×C9×A4C2×C3semidirect
28. C9⋊S4C32semidirect
49. C22×3−1+2C3×D3semidirect
57. #1094C3×D3semidirect
63. C3×C22⋊C9C3×D3semidirect
76. C9×A4C2×C32semidirect
88. C3×3−1+2S4semidirect
156. 3−1+2C3×S4semidirect
197. C22×C3#4207semidirect
236. C22C3×#4207semidirect
243. C3#66440⋊C2direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#664402
#66440⋊C23
C3×C9⋊S43
C3×(C3⋊S4)⋊C33
C32×(C22⋊C9)⋊C23
C3×((C22⋊C9)⋊C2)⋊C33
C3×#611⋊C33
C3×#42074