Finite Group Databasebeta

← C3×S4×3−1+2 #14519188

Subgroups — C3×S4×3−1+2 #14519188

Order 1944.

630 conjugacy classes of subgroups; only the 128 normal subgroups are shown.

normal subgroups only

This group has 630 conjugacy classes of subgroups — too many to draw. Only its 128 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×A4×3−1+2C211yesmaximal, characteristic, complemented
2C33×S4C311yesmaximal, characteristic
3S4×3−1+2C319yesmaximal, direct product factor
4C3×C9×S4C313yesmaximal, complemented
5C3×D4×3−1+2—31nomaximal
6C3×D3×3−1+2—41nomaximal
7C33×A4C2×C311yescharacteristic
8C22×C3×3−1+2—31no—
9C22×C3×3−1+2D311yescharacteristic, complemented
10C3×#1094—21no—
11A4×3−1+2—29no—
12A4×3−1+2C2×C319yescomplemented
13C3×C9⋊A4—23no—
14C3×C9×A4C2×C313yescomplemented
15C3×C4×3−1+2—31no—
16C32×3−1+2—41noSylow
17C32×S4—33no—
18C32×S4C3213yes—
19C32×S4C3211yescharacteristic
20C33×D4—31no—
21C9×S4C3219yescomplemented
22D4×3−1+2—39no—
23C3×D4×C9—33no—
24C33×D3—41no—
25C2×C3×3−1+2—31no—
26C2×C3×3−1+2—61no—
27D3×3−1+2—49no—
28C3×D3×C9—43no—
29C22×C33—31no—
30C22×C33C3×D311yescharacteristic
31C32×A4—21no—
32C32×A4—23no—
33C32×A4—33no—
34C32×A4—63no—
35C32×A4C2×C3211yescharacteristic
36C32×A4C2×C3213yes—
37C33×C4—31no—
38C22×3−1+2—39no—
39C22×3−1+2C3×D319yescomplemented
40C22×C3×C9—33no—
41C22×C3×C9C3×D313yescomplemented
42#1094—29no—
43C3×C22⋊C9—23no—
44C9⋊A4—227no—
45C9×A4—29no—
46C9×A4C2×C3219yescomplemented
47C4×3−1+2—39no—
48C3×C4×C9—33no—
49C34—41no—
50C3×3−1+2—49no—
51C3×3−1+2—81no—
52C3×3−1+2—89no—
53C3×3−1+2—83no—
54C3×3−1+2S411yescharacteristic, direct product factor
55C32×C9—43no—
56C3×S4—33no—
57C3×S43−1+213yesdirect product factor
58C3×S4C3311yescharacteristic
59C32×D4—31no—
60C32×D4—33no—
61C32×D4—93no—
62D4×C9—39no—
63C2×C33—31no—
64C2×C33—61no—
65C32×D3—41no—
66C32×D3—43no—
67C32×D3—123no—
68C2×3−1+2—39no—
69C2×3−1+2—69no—
70C2×C3×C9—33no—
71C2×C3×C9—63no—
72D3×C9—49no—
73C22×C32—31no—
74C22×C32—33no—
75C22×C32—33no—
76C22×C32—93no—
77C22×C32C32×D313yes—
78C22×C32C32×D311yescharacteristic
79C3×A4—23no—
80C3×A4—21no—
81C3×A4—23no—
82C3×A4—33no—
83C3×A4—69no—
84C3×A4—63no—
85C3×A4—63no—
86C3×A4C2×3−1+213yescomplemented
87C3×A4C2×C3311yescharacteristic
88C32×C4—31no—
89C32×C4—33no—
90C32×C4—93no—
91C22×C9—39no—
92C22×C9C32×D319yescomplemented
93C22⋊C9—29no—
94C4×C9—39no—
95C33—41no—
96C33—43no—
97C33—83no—
98C33—81no—
99C33—123no—
100C33—243no—
101C33C3×S411yescharacteristic
1023−1+2—89no—
1033−1+2—827no—
1043−1+2C3×S419yesdirect product factor
105C3×C9—49no—
106C3×C9—83no—
107C3×C9—89no—
108C3×C9C3×S413yescomplemented
109S4C3×3−1+211yescharacteristic, direct product factor
110C3×D4—33no—
111C3×D4—31no—
112C3×D4—93no—
113C2×C32—31no—
114C2×C32—33no—
115C2×C32—61no—
116C2×C32—63no—
117C2×C32—93no—
118C2×C32—183no—
119C3×D3—41no—
120C3×D3—43no—
121C3×D3—123no—
122C2×C9—39no—
123C2×C9—69no—
124C22×C3—31no—
125C22×C3—33no—
126C22×C3—33no—
127C22×C3—93no—
128C22×C3D3×3−1+213yescomplemented
129C22×C3C33×D311yescharacteristic
130A4—23no—
131A4—21no—
132A4—63no—
133A4C2×C3×3−1+211yescharacteristic, complemented
134C3×C4—31no—
135C3×C4—33no—
136C3×C4—93no—
137C32—33no—
138C32—41no—
139C32—43no—
140C32—81no—
141C32—83no—
142C32—83no—
143C32—123no—
144C32—243no—
145C32—249no—
146C32—243no—
147C32C32×S413yes—
148C32C32×S411yescharacteristic
149C9—89no—
150C9C32×S419yescomplemented
151D4—31noSylow
152C2×C3—31no—
153C2×C3—33no—
154C2×C3—61no—
155C2×C3—63no—
156C2×C3—93no—
157C2×C3—183no—
158D3—41no—
159C22—31no—
160C22C3×D3×3−1+211yescharacteristic, complemented
161C4—31no—
162C3—33no—
163C3—41no—
164C3—81no—
165C3—83no—
166C3—243no—
167C3S4×3−1+213yesdirect product factor
168C3C33×S411yescharacteristic
169C2—31no—
170C2—61no—
subgroupG/H
centerC32C32×S4
commutator, cosocleC3×A4C2×C33
FrattiniC3C33×S4
FittingC22×C3×3−1+2D3
socleC22×C32C32×D3
prime radicalC33×S4C3
hypercenterC3×3−1+2S4
hypocenterA4C2×C3×3−1+2
LCSG ▷ C3×A4 ▷ A4
UCSC1 ◁ C32 ◁ C3×3−1+2

Complements

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

NH ≅ G/Ntype
1. C3×A4×3−1+2C2semidirect
3. S4×3−1+2C3direct (N × H)
4. C3×C9×S4C3semidirect
9. C22×C3×3−1+2D3semidirect
12. A4×3−1+2C2×C3semidirect
14. C3×C9×A4C2×C3semidirect
21. C9×S4C32semidirect
39. C22×3−1+2C3×D3semidirect
41. C22×C3×C9C3×D3semidirect
46. C9×A4C2×C32semidirect
54. C3×3−1+2S4direct (N × H)
57. C3×S43−1+2direct (N × H)
86. C3×A4C2×3−1+2semidirect
92. C22×C9C32×D3semidirect
104. 3−1+2C3×S4direct (N × H)
108. C3×C9C3×S4semidirect
109. S4C3×3−1+2direct (N × H)
128. C22×C3D3×3−1+2semidirect
133. A4C2×C3×3−1+2semidirect
150. C9C32×S4semidirect
160. C22C3×D3×3−1+2semidirect
167. C3S4×3−1+2direct (N × H)

Maximal subgroups

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

subgroupindex
C3×A4×3−1+22
C33×S43
S4×3−1+23
C3×C9×S43
C3×D4×3−1+23
C3×D3×3−1+24