Finite Group Databasebeta

← C2×C3×A4×3−1+2 #14519344

Subgroups — C2×C3×A4×3−1+2 #14519344

Order 1944.

1304 conjugacy classes of subgroups; only the 532 normal subgroups are shown.

normal subgroups only

This group has 1304 conjugacy classes of subgroups — too many to draw. Only its 532 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, direct product factor
2C2×C33×A4C311yesmaximal, characteristic
3C23×C3×3−1+2C311yesmaximal, characteristic, complemented
4C2×C3×#1094C312yesmaximal, complemented
5C2×A4×3−1+2C3127yesmaximal, direct product factor
6C2×C3×C9⋊A4C316yesmaximal, complemented
7C2×C3×C9×A4C313yesmaximal, complemented
8C2×C32×3−1+2—41nomaximal
9C33×A4C2×C311yescharacteristic
10C22×C3×3−1+2—31no—
11C22×C3×3−1+2—31no—
12C22×C3×3−1+2C2×C311yescharacteristic, complemented
13C3×#1094C2×C312yescomplemented
14A4×3−1+2C2×C3127yesdirect product factor
15C3×C9⋊A4C2×C316yescomplemented
16C3×C9×A4C2×C313yescomplemented
17C32×3−1+2—41noSylow
18C23×C33C3211yescharacteristic
19C2×C32×A4—39no—
20C2×C32×A4C3212yes—
21C2×C32×A4C3219yes—
22C2×C32×A4C3211yescharacteristic
23C23×3−1+2C3219yescomplemented
24C23×C3×C9C3213yescomplemented
25C2×#1094C32118yescomplemented
26C2×C3×C22⋊C9C3216yescomplemented
27C2×C9⋊A4C32154yescomplemented
28C2×C9×A4C32127yescomplemented
29C2×C34—41no—
30C2×C3×3−1+2—31no—
31C2×C3×3−1+2—31no—
32C2×C3×3−1+2—42no—
33C2×C3×3−1+2—427no—
34C2×C3×3−1+2—46no—
35C2×C3×3−1+2A411yescharacteristic, direct product factor
36C2×C32×C9—43no—
37C22×C33—31no—
38C22×C33—31no—
39C22×C33C2×C3211yescharacteristic
40C32×A4—39no—
41C32×A4C2×C3212yes—
42C32×A4C2×C3219yes—
43C32×A4C2×C3211yescharacteristic
44C22×3−1+2—39no—
45C22×3−1+2—39no—
46C22×3−1+2C2×C3219yescomplemented
47C22×C3×C9—33no—
48C22×C3×C9—33no—
49C22×C3×C9C2×C3213yescomplemented
50#1094C2×C32118yescomplemented
51C3×C22⋊C9C2×C3216yescomplemented
52C9⋊A4C2×C32154yescomplemented
53C9×A4C2×C32127yescomplemented
54C34—41no—
55C3×3−1+2—42no—
56C3×3−1+2—427no—
57C3×3−1+2—46no—
58C3×3−1+2C2×A411yescharacteristic, direct product factor
59C32×C9—43no—
60C23×C32—33no—
61C23×C32C3313yes—
62C23×C32C3311yescharacteristic
63C2×C3×A4—36no—
64C2×C3×A4—327no—
65C2×C3×A43−1+219yesdirect product factor
66C2×C3×A4C3316yes—
67C2×C3×A4C3313yes—
68C23×C9C3319yescomplemented
69C2×C22⋊C9C33118yescomplemented
70C2×C33—31no—
71C2×C33—31no—
72C2×C33—41no—
73C2×C33—49no—
74C2×C33—42no—
75C2×C33—129no—
76C2×C33C3×A411yescharacteristic
77C2×3−1+2—39no—
78C2×3−1+2—39no—
79C2×3−1+2—418no—
80C2×3−1+2—454no—
81C2×3−1+2C3×A419yesdirect product factor
82C2×C3×C9—33no—
83C2×C3×C9—33no—
84C2×C3×C9—46no—
85C2×C3×C9—427no—
86C2×C3×C9C3×A413yescomplemented
87C22×C32—31no—
88C22×C32—31no—
89C22×C32—33no—
90C22×C32—33no—
91C22×C32—33no—
92C22×C32—93no—
93C22×C32—93no—
94C22×C32C2×C3313yes—
95C22×C32C2×C3311yescharacteristic
96C3×A4—36no—
97C3×A4—327no—
98C3×A4C2×3−1+219yesdirect product factor
99C3×A4C2×C3316yes—
100C3×A4C2×C3313yes—
101C22×C9—39no—
102C22×C9—39no—
103C22×C9C2×C3319yescomplemented
104C22⋊C9C2×C33118yescomplemented
105C33—41no—
106C33—49no—
107C33—42no—
108C33—129no—
109C33C2×C3×A411yescharacteristic
1103−1+2—418no—
1113−1+2—454no—
1123−1+2C2×C3×A419yesdirect product factor
113C3×C9—46no—
114C3×C9—427no—
115C3×C9C2×C3×A413yescomplemented
116C23×C3—33no—
117C23×C3C3×3−1+213yescomplemented
118C23×C3C3411yescharacteristic
119C2×A4—36no—
120C2×A4C3×3−1+219yesdirect product factor
121C2×C32—31no—
122C2×C32—31no—
123C2×C32—33no—
124C2×C32—33no—
125C2×C32—33no—
126C2×C32—49no—
127C2×C32—43no—
128C2×C32—46no—
129C2×C32—93no—
130C2×C32—93no—
131C2×C32—1227no—
132C2×C32—126no—
133C2×C32C32×A413yes—
134C2×C32C32×A411yescharacteristic
135C2×C9—39no—
136C2×C9—39no—
137C2×C9—418no—
138C2×C9C32×A419yescomplemented
139C22×C3—33no—
140C22×C3—31no—
141C22×C3—33no—
142C22×C3—31no—
143C22×C3—33no—
144C22×C3—93no—
145C22×C3—93no—
146C22×C3C2×C3×3−1+213yescomplemented
147C22×C3C2×C3411yescharacteristic
148A4—36no—
149A4C2×C3×3−1+219yesdirect product factor
150C32—33no—
151C32—43no—
152C32—49no—
153C32—46no—
154C32—1227no—
155C32—126no—
156C32C2×C32×A413yes—
157C32C2×C32×A411yescharacteristic
158C9—418no—
159C9C2×C32×A419yescomplemented
160C23C32×3−1+211yescharacteristic, complemented, Sylow
161C2×C3—31no—
162C2×C3—31no—
163C2×C3—33no—
164C2×C3—33no—
165C2×C3—33no—
166C2×C3—49no—
167C2×C3—93no—
168C2×C3—93no—
169C2×C3—126no—
170C2×C3A4×3−1+213yesdirect product factor
171C2×C3C33×A411yescharacteristic
172C22—31no—
173C22—31no—
174C22C2×C32×3−1+211yescharacteristic, complemented
175C3—33no—
176C3—49no—
177C3—126no—
178C3C2×A4×3−1+213yesdirect product factor
179C3C2×C33×A411yescharacteristic
180C2—31no—
181C2—31no—
182C2C3×A4×3−1+211yescharacteristic, direct product factor
subgroupG/H
centerC2×C32C32×A4
commutator, cosocleC22×C3C2×C34
FrattiniC3C2×C33×A4
FittingC23×C3×3−1+2C3
socleC23×C32C33
prime radicalC2×C33×A4C3
hypercenterC2×C3×3−1+2A4
hypocenterC22C2×C32×3−1+2
LCSG ▷ C22×C3 ▷ C22
UCSC1 ◁ C2×C32 ◁ C2×C3×3−1+2

Complements

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

NH ≅ G/Ntype
1. C3×A4×3−1+2C2direct (N × H)
3. C23×C3×3−1+2C3semidirect
4. C2×C3×#1094C3semidirect
5. C2×A4×3−1+2C3direct (N × H)
6. C2×C3×C9⋊A4C3semidirect
7. C2×C3×C9×A4C3semidirect
12. C22×C3×3−1+2C2×C3semidirect
13. C3×#1094C2×C3semidirect
14. A4×3−1+2C2×C3direct (N × H)
15. C3×C9⋊A4C2×C3semidirect
16. C3×C9×A4C2×C3semidirect
23. C23×3−1+2C32semidirect
24. C23×C3×C9C32semidirect
25. C2×#1094C32semidirect
26. C2×C3×C22⋊C9C32semidirect
27. C2×C9⋊A4C32semidirect
28. C2×C9×A4C32semidirect
35. C2×C3×3−1+2A4direct (N × H)
46. C22×3−1+2C2×C32semidirect
49. C22×C3×C9C2×C32semidirect
50. #1094C2×C32semidirect
51. C3×C22⋊C9C2×C32semidirect
52. C9⋊A4C2×C32semidirect
53. C9×A4C2×C32semidirect
58. C3×3−1+2C2×A4direct (N × H)
65. C2×C3×A43−1+2direct (N × H)
68. C23×C9C33semidirect
69. C2×C22⋊C9C33semidirect
81. C2×3−1+2C3×A4direct (N × H)
86. C2×C3×C9C3×A4semidirect
98. C3×A4C2×3−1+2direct (N × H)
103. C22×C9C2×C33semidirect
104. C22⋊C9C2×C33semidirect
112. 3−1+2C2×C3×A4direct (N × H)
115. C3×C9C2×C3×A4semidirect
117. C23×C3C3×3−1+2semidirect
120. C2×A4C3×3−1+2direct (N × H)
138. C2×C9C32×A4semidirect
146. C22×C3C2×C3×3−1+2semidirect
149. A4C2×C3×3−1+2direct (N × H)
159. C9C2×C32×A4semidirect
160. C23C32×3−1+2semidirect
170. C2×C3A4×3−1+2direct (N × H)
174. C22C2×C32×3−1+2semidirect
178. C3C2×A4×3−1+2direct (N × H)
182. C2C3×A4×3−1+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
C2×C33×A43
C23×C3×3−1+23
C2×C3×#10943
C2×A4×3−1+23
C2×C3×C9⋊A43
C2×C3×C9×A43
C2×C32×3−1+24