Finite Group Databasebeta

← C3×D12×3−1+2 #14518889

Subgroups — C3×D12×3−1+2 #14518889

Order 1944.

926 conjugacy classes of subgroups; only the 288 normal subgroups are shown.

normal subgroups only

This group has 926 conjugacy classes of subgroups — too many to draw. Only its 288 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×C3×D3×3−1+2C212yesmaximal, complemented
2C32×C4×3−1+2C211yesmaximal, characteristic, complemented
3C33×D12C311yesmaximal, characteristic
4C3×D4×3−1+2—31nomaximal
5D12×3−1+2C319yesmaximal, direct product factor
6C3×C9×D12C313yesmaximal, complemented
7C2×C32×3−1+2C2211yescharacteristic
8C3×D3×3−1+2—22no—
9C2×C33×D3C2×C312yes—
10C34×C4C2×C311yescharacteristic
11C22×C3×3−1+2—32no—
12C2×D3×3−1+2C2×C3118yescomplemented
13C2×C3×D3×C9C2×C316yescomplemented
14C3×C4×3−1+2—21no—
15C3×C4×3−1+2—29no—
16C3×C4×3−1+2—23no—
17C3×C4×3−1+2D311yescharacteristic, complemented
18C3×C4×3−1+2C2×C319yescomplemented
19C32×C4×C9C2×C313yescomplemented
20C32×3−1+2D411yescharacteristic, complemented, Sylow
21C33×D4—31no—
22C32×D12—33no—
23C32×D12C3213yes—
24C32×D12C3211yescharacteristic
25D4×3−1+2—39no—
26C3×D4×C9—33no—
27C9×D12C3219yescomplemented
28C2×C34C22×C311yescharacteristic
29C33×D3—22no—
30C2×C3×3−1+2—21no—
31C2×C3×3−1+2—29no—
32C2×C3×3−1+2—23no—
33C2×C3×3−1+2—62no—
34C2×C3×3−1+2C2×D311yescharacteristic
35C2×C3×3−1+2C22×C319yes—
36C2×C32×C9C22×C313yes—
37D3×3−1+2—218no—
38C3×D3×C9—26no—
39C22×C33—32no—
40C2×C32×D3—36no—
41C2×C32×D3C2×C3216yes—
42C2×C32×D3C2×C3212yes—
43C33×C4—23no—
44C33×C4—21no—
45C33×C4—33no—
46C33×C4—63no—
47C33×C4C3×D311yescharacteristic
48C33×C4C2×C3211yescharacteristic
49C33×C4C2×C3213yes—
50C22×3−1+2—318no—
51C22×C3×C9—36no—
52C2×D3×C9C2×C32118yescomplemented
53C4×3−1+2—29no—
54C4×3−1+2—227no—
55C4×3−1+2C3×D319yescomplemented
56C3×C4×C9—23no—
57C3×C4×C9—29no—
58C3×C4×C9C3×D313yescomplemented
59C3×C4×C9C2×C3219yescomplemented
60C34C3×D411yescharacteristic
61C3×3−1+2—21no—
62C3×3−1+2—29no—
63C3×3−1+2—23no—
64C3×3−1+2D1211yescharacteristic, direct product factor
65C3×3−1+2C3×D419yescomplemented
66C32×C9C3×D413yescomplemented
67C32×D4—31no—
68C32×D4—33no—
69C32×D4—93no—
70C3×D12—33no—
71C3×D123−1+213yesdirect product factor
72C3×D12C3311yescharacteristic
73D4×C9—39no—
74C2×C33—23no—
75C2×C33—21no—
76C2×C33—33no—
77C2×C33—63no—
78C2×C33—62no—
79C2×C33C2×C3×D311yescharacteristic
80C2×C33C22×C3211yescharacteristic
81C2×C33C22×C3213yes—
82C32×D3—22no—
83C32×D3—26no—
84C32×D3—66no—
85C2×3−1+2—29no—
86C2×3−1+2—227no—
87C2×3−1+2—618no—
88C2×3−1+2C2×C3×D319yes—
89C2×C3×C9—23no—
90C2×C3×C9—29no—
91C2×C3×C9—66no—
92C2×C3×C9C2×C3×D313yes—
93C2×C3×C9C22×C3219yes—
94D3×C9—218no—
95C22×C32—32no—
96C22×C32—36no—
97C22×C32—96no—
98C2×C3×D3—36no—
99C2×C3×D3C2×3−1+216yescomplemented
100C2×C3×D3C2×C3312yes—
101C32×C4—23no—
102C32×C4—21no—
103C32×C4—23no—
104C32×C4—33no—
105C32×C4—33no—
106C32×C4—69no—
107C32×C4—63no—
108C32×C4—63no—
109C32×C4C2×3−1+213yescomplemented
110C32×C4C32×D313yes—
111C32×C4C32×D311yescharacteristic
112C32×C4C2×C3311yescharacteristic
113C22×C9—318no—
114C4×C9—29no—
115C4×C9C32×D319yescomplemented
116C33—23no—
117C33—21no—
118C33—33no—
119C33—63no—
120C33C3×D1211yescharacteristic
121C33C32×D411yescharacteristic
122C33C32×D413yes—
1233−1+2—29no—
1243−1+2—227no—
1253−1+2C3×D1219yesdirect product factor
126C3×C9—23no—
127C3×C9—29no—
128C3×C9C3×D1213yescomplemented
129C3×C9C32×D419yescomplemented
130C3×D4—33no—
131C3×D4—31no—
132C3×D4—93no—
133D12C3×3−1+211yescharacteristic, direct product factor
134C2×C32—23no—
135C2×C32—21no—
136C2×C32—23no—
137C2×C32—33no—
138C2×C32—33no—
139C2×C32—69no—
140C2×C32—63no—
141C2×C32—62no—
142C2×C32—63no—
143C2×C32—66no—
144C2×C32—186no—
145C2×C32C22×3−1+213yes—
146C2×C32C2×C32×D313yes—
147C2×C32C2×C32×D311yescharacteristic
148C2×C32C22×C3311yescharacteristic
149C3×D3—26no—
150C3×D3—22no—
151C3×D3—66no—
152C2×C9—29no—
153C2×C9—618no—
154C2×C9C2×C32×D319yes—
155C22×C3—36no—
156C22×C3—32no—
157C22×C3—96no—
158C2×D3C2×C3×3−1+212yescomplemented
159C3×C4—23no—
160C3×C4—21no—
161C3×C4—33no—
162C3×C4—63no—
163C3×C4D3×3−1+213yescomplemented
164C3×C4C2×C3×3−1+211yescharacteristic, complemented
165C3×C4C33×D311yescharacteristic
166C32—21no—
167C32—23no—
168C32—23no—
169C32—33no—
170C32—33no—
171C32—63no—
172C32—69no—
173C32—63no—
174C32D4×3−1+213yescomplemented
175C32C32×D1213yes—
176C32C32×D1211yescharacteristic
177C32C33×D411yescharacteristic
178C9—29no—
179C9C32×D1219yescomplemented
180D4—31noSylow
181C2×C3—23no—
182C2×C3—21no—
183C2×C3—33no—
184C2×C3—62no—
185C2×C3—66no—
186C2×C3—63no—
187C2×C3—186no—
188C2×C3C2×D3×3−1+213yes—
189C2×C3C22×C3×3−1+211yescharacteristic
190C2×C3C2×C33×D311yescharacteristic
191D3—22no—
192C22—32no—
193C4C3×D3×3−1+211yescharacteristic, complemented
194C3—23no—
195C3—21no—
196C3—33no—
197C3—63no—
198C3D12×3−1+213yesdirect product factor
199C3C3×D4×3−1+211yescharacteristic, complemented
200C3C33×D1211yescharacteristic
201C2—62no—
202C2C2×C3×D3×3−1+211yescharacteristic
subgroupG/H
centerC2×C32C2×C32×D3
commutator, cosocleC2×C32C22×C33
FrattiniC2×C3C2×C33×D3
FittingC32×C4×3−1+2C2
socleC2×C33C22×C32
prime radicalC33×D12C3
hypercenterC3×C4×3−1+2D3
hypocenterC3C3×D4×3−1+2
LCSG ▷ C2×C32 ▷ C3
UCSC1 ◁ C2×C32 ◁ C3×C4×3−1+2

Complements

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

NH ≅ G/Ntype
1. C2×C3×D3×3−1+2C2semidirect
2. C32×C4×3−1+2C2semidirect
5. D12×3−1+2C3direct (N × H)
6. C3×C9×D12C3semidirect
12. C2×D3×3−1+2C2×C3semidirect
13. C2×C3×D3×C9C2×C3semidirect
17. C3×C4×3−1+2D3semidirect
18. C3×C4×3−1+2C2×C3semidirect
19. C32×C4×C9C2×C3semidirect
20. C32×3−1+2D4semidirect
27. C9×D12C32semidirect
52. C2×D3×C9C2×C32semidirect
55. C4×3−1+2C3×D3semidirect
58. C3×C4×C9C3×D3semidirect
59. C3×C4×C9C2×C32semidirect
64. C3×3−1+2D12direct (N × H)
65. C3×3−1+2C3×D4semidirect
66. C32×C9C3×D4semidirect
71. C3×D123−1+2direct (N × H)
99. C2×C3×D3C2×3−1+2semidirect
109. C32×C4C2×3−1+2semidirect
115. C4×C9C32×D3semidirect
125. 3−1+2C3×D12direct (N × H)
128. C3×C9C3×D12semidirect
129. C3×C9C32×D4semidirect
133. D12C3×3−1+2direct (N × H)
158. C2×D3C2×C3×3−1+2semidirect
163. C3×C4D3×3−1+2semidirect
164. C3×C4C2×C3×3−1+2semidirect
174. C32D4×3−1+2semidirect
179. C9C32×D12semidirect
193. C4C3×D3×3−1+2semidirect
198. C3D12×3−1+2direct (N × H)
199. C3C3×D4×3−1+2semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D3×3−1+22
C32×C4×3−1+22
C33×D123
C3×D4×3−1+23
D12×3−1+23
C3×C9×D123