Finite Group Databasebeta

← C22×C3×#4207 #14519366

Subgroups — C22×C3×#4207 #14519366

Order 1944.

1194 conjugacy classes of subgroups; only the 256 normal subgroups are shown.

normal subgroups only

This group has 1194 conjugacy classes of subgroups — too many to draw. Only its 256 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
1C22×C3×#737C211yesmaximal, characteristic, complemented
2C2×C3×#4207C216yesmaximal, direct product factor
3C22×#4207C313yesmaximal, direct product factor
4C22×C3×C3⋊D9C311yesmaximal, characteristic, complemented
5C22×C3×AGL(1,ℤ/9)—32nomaximal
6C22×C3×(C3⋊D3)⋊C3—31nomaximal
7C22×C32×D9—31nomaximal
8C2×C3×#737C2213yescomplemented
9C3×#4207C2214yesdirect product factor
10C22×#737—26no—
11C22×#737—23no—
12C22×#737—23no—
13C22×#737C2×C313yescomplemented
14C22×C3×3−1+2—21no—
15C22×C3×3−1+2—22no—
16C22×C3×3−1+2D312yescomplemented
17C22×C3×H(3,𝔽3)D311yescharacteristic
18C22×C32×C9—21no—
19C22×C32×C9D311yescharacteristic, complemented
20C22×C32×C9C2×C311yescharacteristic, complemented
21C2×#4207C2×C3118yesdirect product factor
22C2×C3×C3⋊D9C2×C316yescomplemented
23C2×C3×AGL(1,ℤ/9)—312no—
24C2×C3×(C3⋊D3)⋊C3—36no—
25C2×C32×D9—36no—
26C3×#737C2311yescharacteristic, complemented, Sylow
27C22×C3×C3⋊D3—31no—
28C22×C32×D3—91no—
29C22×C3⋊D9C3211yescharacteristic, complemented
30C22×AGL(1,ℤ/9)—36no—
31C22×(C3⋊D3)⋊C3—33no—
32C22×C3×D9—31no—
33C22×C3×D9—32no—
34C22×C3×D9—33no—
35C2×#737—218no—
36C2×#737—29no—
37C2×#737—29no—
38C2×#737C22×C319yescomplemented
39C2×C3×3−1+2—23no—
40C2×C3×3−1+2—26no—
41C2×C3×3−1+2C2×D316yescomplemented
42C2×C3×H(3,𝔽3)C2×D313yes—
43C2×C32×C9—23no—
44C2×C32×C9C2×D313yescomplemented
45C2×C32×C9C22×C313yescomplemented
46#4207C22×C3112yesdirect product factor
47C3×C3⋊D9C22×C314yescomplemented
48C3×AGL(1,ℤ/9)—38no—
49C3×(C3⋊D3)⋊C3—34no—
50C32×D9—34no—
51C22×C33—21no—
52C22×C33C3×D311yescharacteristic
53C22×C33C3⋊D311yescharacteristic
54C2×C3×C3⋊D3—36no—
55C2×C32×D3—96no—
56C22×3−1+2—26no—
57C22×3−1+2—212no—
58C22×3−1+2—23no—
59C22×3−1+2—26no—
60C22×3−1+2—26no—
61C22×3−1+2C3×D316yescomplemented
62C22×H(3,𝔽3)—23no—
63C22×H(3,𝔽3)C3×D313yes—
64C22×C3×C9—26no—
65C22×C3×C9—21no—
66C22×C3×C9—22no—
67C22×C3×C9—21no—
68C22×C3×C9—23no—
69C22×C3×C9—23no—
70C22×C3×C9—22no—
71C22×C3×C9—21no—
72C22×C3×C9C3×D311yescharacteristic
73C22×C3×C9C3×D312yes—
74C22×C3×C9C3×D313yescomplemented
75C22×C3×C9C2×C3211yescharacteristic, complemented
76C2×C3⋊D9C2×C3216yescomplemented
77C2×AGL(1,ℤ/9)—336no—
78C2×(C3⋊D3)⋊C3—318no—
79C2×C3×D9—36no—
80C2×C3×D9—312no—
81C2×C3×D9—318no—
82#737—26no—
83#737—23no—
84#737—23no—
85#737C23×C313yescomplemented
86C3×3−1+2—21no—
87C3×3−1+2—22no—
88C3×3−1+2C22×D312yescomplemented
89C3×H(3,𝔽3)C22×D311yescharacteristic
90C32×C9—21no—
91C32×C9C22×D311yescharacteristic, complemented
92C32×C9C23×C311yescharacteristic, complemented
93C23×C32—271no—
94C22×C3⋊D3—31no—
95C22×C3×D3—91no—
96C22×C3×D3—93no—
97C22×C3×D3—271no—
98C22×D9—31no—
99C22×D9—32no—
100C2×C33—23no—
101C2×C33C2×C3×D313yes—
102C2×C33C2×C3⋊D313yes—
103C3×C3⋊D3—34no—
104C32×D3—94no—
105C2×3−1+2—218no—
106C2×3−1+2—236no—
107C2×3−1+2—29no—
108C2×3−1+2—218no—
109C2×3−1+2—218no—
110C2×3−1+2C2×C3×D3118yescomplemented
111C2×H(3,𝔽3)—29no—
112C2×H(3,𝔽3)C2×C3×D319yes—
113C2×C3×C9—218no—
114C2×C3×C9—23no—
115C2×C3×C9—26no—
116C2×C3×C9—23no—
117C2×C3×C9—29no—
118C2×C3×C9—29no—
119C2×C3×C9—26no—
120C2×C3×C9—23no—
121C2×C3×C9C2×C3×D313yes—
122C2×C3×C9C2×C3×D316yes—
123C2×C3×C9C2×C3×D319yescomplemented
124C2×C3×C9C22×C3213yescomplemented
125C3⋊D9C22×C3214yescomplemented
126AGL(1,ℤ/9)—324no—
127(C3⋊D3)⋊C3—312no—
128C3×D9—34no—
129C3×D9—38no—
130C3×D9—312no—
131C22×C32—21no—
132C22×C32—23no—
133C22×C32—31no—
134C22×C32—31no—
135C22×C32—61no—
136C22×C32—61no—
137C22×C32—62no—
138C22×C32—61no—
139C22×C32—276no—
140C22×C32C32×D311yescharacteristic
141C22×C32C3×C3⋊D311yescharacteristic
142C22×C32C3×C3⋊D313yes—
143C2×C3⋊D3—36no—
144C2×C3×D3—96no—
145C2×C3×D3—918no—
146C2×C3×D3—276no—
147C22×C9—21no—
148C22×C9—26no—
149C22×C9—22no—
150C22×C9—23no—
151C22×C9C32×D311yescharacteristic
152C22×C9C32×D312yes—
153C2×D9—36no—
154C2×D9—312no—
155C33—21no—
156C33C22×C3×D311yescharacteristic
157C33C22×C3⋊D311yescharacteristic
1583−1+2—26no—
1593−1+2—212no—
1603−1+2—23no—
1613−1+2—26no—
1623−1+2—26no—
1633−1+2C22×C3×D316yescomplemented
164H(3,𝔽3)—23no—
165H(3,𝔽3)C22×C3×D313yes—
166C3×C9—26no—
167C3×C9—21no—
168C3×C9—22no—
169C3×C9—21no—
170C3×C9—23no—
171C3×C9—23no—
172C3×C9—22no—
173C3×C9—21no—
174C3×C9C22×C3×D311yescharacteristic
175C3×C9C22×C3×D312yes—
176C3×C9C22×C3×D313yescomplemented
177C3×C9C23×C3211yescharacteristic, complemented
178C23×C3—273no—
179C23×C3—271no—
180C22×D3—91no—
181C22×D3—271no—
182C2×C32—23no—
183C2×C32—29no—
184C2×C32—33no—
185C2×C32—33no—
186C2×C32—63no—
187C2×C32—63no—
188C2×C32—66no—
189C2×C32—63no—
190C2×C32—274no—
191C2×C32C2×C32×D313yes—
192C2×C32C2×C3×C3⋊D313yes—
193C2×C32C2×C3×C3⋊D319yes—
194C3⋊D3—34no—
195C3×D3—94no—
196C3×D3—912no—
197C3×D3—274no—
198C2×C9—23no—
199C2×C9—218no—
200C2×C9—26no—
201C2×C9—29no—
202C2×C9C2×C32×D313yes—
203C2×C9C2×C32×D316yes—
204D9—34no—
205D9—38no—
206C22×C3—21no—
207C22×C3—31no—
208C22×C3—33no—
209C22×C3—61no—
210C22×C3—63no—
211C22×C3—2718no—
212C22×C3—276no—
213C22×C3#420711yescharacteristic, direct product factor
214C22×C3C32×C3⋊D311yescharacteristic
215C2×D3—96no—
216C2×D3—276no—
217C32—21no—
218C32—23no—
219C32—31no—
220C32—31no—
221C32—61no—
222C32—61no—
223C32—62no—
224C32—61no—
225C32C22×C32×D311yescharacteristic
226C32C22×C3×C3⋊D311yescharacteristic
227C32C22×C3×C3⋊D313yes—
228C9—21no—
229C9—26no—
230C9—22no—
231C9—23no—
232C9C22×C32×D311yescharacteristic
233C9C22×C32×D312yes—
234C23—271noSylow
235C2×C3—23no—
236C2×C3—33no—
237C2×C3—39no—
238C2×C3—63no—
239C2×C3—69no—
240C2×C3—2712no—
241C2×C3—274no—
242C2×C3C2×#420713yesdirect product factor
243C2×C3C2×C32×C3⋊D313yes—
244D3—94no—
245D3—274no—
246C22—276no—
247C22C3×#420711yescharacteristic, direct product factor
248C3—21no—
249C3—31no—
250C3—33no—
251C3—61no—
252C3—63no—
253C3C22×#420711yescharacteristic, direct product factor
254C3C22×C32×C3⋊D311yescharacteristic
255C2—274no—
256C2C2×C3×#420713yesdirect product factor
subgroupG/H
center, hypercenterC22×C3#4207
commutator, cosocle, hypocenterC3×C9C23×C32
FrattiniC3C22×C32×C3⋊D3
FittingC22×C3×#737C2
socleC22×C32C3×C3⋊D3
LCSG ▷ C3×C9
UCSC1 ◁ C22×C3

Complements

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

NH ≅ G/Ntype
1. C22×C3×#737C2semidirect
2. C2×C3×#4207C2direct (N × H)
3. C22×#4207C3direct (N × H)
4. C22×C3×C3⋊D9C3semidirect
8. C2×C3×#737C22semidirect
9. C3×#4207C22direct (N × H)
13. C22×#737C2×C3semidirect
16. C22×C3×3−1+2D3semidirect
19. C22×C32×C9D3semidirect
20. C22×C32×C9C2×C3semidirect
21. C2×#4207C2×C3direct (N × H)
22. C2×C3×C3⋊D9C2×C3semidirect
26. C3×#737C23semidirect
29. C22×C3⋊D9C32semidirect
38. C2×#737C22×C3semidirect
41. C2×C3×3−1+2C2×D3semidirect
44. C2×C32×C9C2×D3semidirect
45. C2×C32×C9C22×C3semidirect
46. #4207C22×C3direct (N × H)
47. C3×C3⋊D9C22×C3semidirect
61. C22×3−1+2C3×D3semidirect
74. C22×C3×C9C3×D3semidirect
75. C22×C3×C9C2×C32semidirect
76. C2×C3⋊D9C2×C32semidirect
85. #737C23×C3semidirect
88. C3×3−1+2C22×D3semidirect
91. C32×C9C22×D3semidirect
92. C32×C9C23×C3semidirect
110. C2×3−1+2C2×C3×D3semidirect
123. C2×C3×C9C2×C3×D3semidirect
124. C2×C3×C9C22×C32semidirect
125. C3⋊D9C22×C32semidirect
163. 3−1+2C22×C3×D3semidirect
176. C3×C9C22×C3×D3semidirect
177. C3×C9C23×C32semidirect
213. C22×C3#4207direct (N × H)
242. C2×C3C2×#4207direct (N × H)
247. C22C3×#4207direct (N × H)
253. C3C22×#4207direct (N × H)
256. C2C2×C3×#4207direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×#7372
C2×C3×#42072
C22×#42073
C22×C3×C3⋊D93
C22×C3×AGL(1,ℤ/9)3
C22×C3×(C3⋊D3)⋊C33
C22×C32×D93