Finite Group Databasebeta

← C22×C3⋊D3×3−1+2 #14519365

Subgroups — C22×C3⋊D3×3−1+2 #14519365

Order 1944.

1368 conjugacy classes of subgroups; only the 287 normal subgroups are shown.

normal subgroups only

This group has 1368 conjugacy classes of subgroups — too many to draw. Only its 287 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×C32×3−1+2C211yesmaximal, characteristic, complemented
2C2×C3⋊D3×3−1+2C216yesmaximal, direct product factor
3C22×C32×C3⋊D3C311yesmaximal, characteristic
4C22×C9×C3⋊D3C313yesmaximal, complemented
5C22×D3×3−1+2—34nomaximal
6C2×C32×3−1+2C2213yescomplemented
7C3⋊D3×3−1+2C2214yesdirect product factor
8C22×C34C2×C311yescharacteristic
9C2×C32×C3⋊D3C2×C316yes—
10C22×C3×3−1+2—24no—
11C22×C3×3−1+2—212no—
12C22×C3×3−1+2D314yescomplemented
13C22×C32×C9C2×C313yescomplemented
14C2×C9×C3⋊D3C2×C3118yescomplemented
15C2×D3×3−1+2—324no—
16C32×3−1+2C2311yescharacteristic, complemented, Sylow
17C22×C3×C3⋊D3—31no—
18C22×C3×C3⋊D3C3211yescharacteristic
19C22×C32×D3—34no—
20C23×3−1+2—91no—
21C22×D3×C9—312no—
22C2×C34C22×C313yes—
23C32×C3⋊D3C22×C314yes—
24C2×C3×3−1+2—212no—
25C2×C3×3−1+2—236no—
26C2×C3×3−1+2C2×D3112yescomplemented
27C2×C32×C9C22×C319yescomplemented
28C9×C3⋊D3C22×C3112yescomplemented
29D3×3−1+2—316no—
30C22×C33—24no—
31C22×C33—31no—
32C22×C33—64no—
33C22×C33C3×D314yes—
34C22×C33C2×C3211yescharacteristic
35C2×C3×C3⋊D3—36no—
36C2×C3×C3⋊D3C2×C3216yes—
37C2×C32×D3—324no—
38C22×3−1+2—224no—
39C22×3−1+2—24no—
40C22×3−1+2—212no—
41C22×3−1+2—96no—
42C22×3−1+2C3⋊D311yescharacteristic, direct product factor
43C22×C3×C9—212no—
44C22×C3×C9C3×D3112yescomplemented
45C2×D3×C9—372no—
46C34C23×C311yescharacteristic
47C3×3−1+2—24no—
48C3×3−1+2—212no—
49C3×3−1+2C22×D314yescomplemented
50C32×C9C23×C313yescomplemented
51C23×C32—91no—
52C22×C3⋊D33−1+211yescharacteristic, direct product factor
53C22×C3×D3—34no—
54C22×C3×D3—94no—
55C23×C9—93no—
56C2×C33—212no—
57C2×C33—33no—
58C2×C33—612no—
59C2×C33C2×C3×D3112yes—
60C2×C33C22×C3213yes—
61C3×C3⋊D3—34no—
62C3×C3⋊D3C22×C3214yes—
63C32×D3—316no—
64C2×3−1+2—272no—
65C2×3−1+2—212no—
66C2×3−1+2—236no—
67C2×3−1+2—94no—
68C2×3−1+2C2×C3⋊D313yesdirect product factor
69C2×C3×C9—236no—
70C2×C3×C9C2×C3×D3136yescomplemented
71D3×C9—348no—
72C22×C32—24no—
73C22×C32—24no—
74C22×C32—34no—
75C22×C32—64no—
76C22×C32—68no—
77C22×C32—64no—
78C22×C32—96no—
79C22×C32C2×3−1+211yescharacteristic, complemented
80C22×C32C32×D314yes—
81C22×C32C3×C3⋊D311yescharacteristic
82C2×C3⋊D3C2×3−1+216yesdirect product factor
83C2×C3×D3—324no—
84C2×C3×D3—924no—
85C22×C9—212no—
86C22×C9—918no—
87C22×C9C3×C3⋊D313yescomplemented
88C33—24no—
89C33—31no—
90C33—64no—
91C33C22×C3×D314yes—
92C33C23×C3211yescharacteristic
933−1+2—224no—
943−1+2—24no—
953−1+2—212no—
963−1+2C22×C3⋊D311yescharacteristic, direct product factor
97C3×C9—212no—
98C3×C9C22×C3×D3112yescomplemented
99C23×C3—91no—
100C23×C3—271no—
101C22×D3—34no—
102C2×C32—212no—
103C2×C32—212no—
104C2×C32—312no—
105C2×C32—612no—
106C2×C32—624no—
107C2×C32—612no—
108C2×C32—94no—
109C2×C32C22×3−1+213yescomplemented
110C2×C32C2×C32×D3112yes—
111C2×C32C2×C3×C3⋊D313yes—
112C3⋊D3C22×3−1+214yesdirect product factor
113C3×D3—316no—
114C3×D3—916no—
115C2×C9—236no—
116C2×C9—912no—
117C2×C9C2×C3×C3⋊D319yescomplemented
118C22×C3—24no—
119C22×C3—31no—
120C22×C3—64no—
121C22×C3—96no—
122C22×C3—276no—
123C22×C3D3×3−1+214yescomplemented
124C22×C3C32×C3⋊D311yescharacteristic
125C2×D3—324no—
126C32—24no—
127C32—24no—
128C32—34no—
129C32—64no—
130C32—68no—
131C32—64no—
132C32C23×3−1+211yescharacteristic, complemented
133C32C22×C32×D314yes—
134C32C22×C3×C3⋊D311yescharacteristic
135C9—212no—
136C9C22×C3×C3⋊D313yescomplemented
137C23—91noSylow
138C2×C3—212no—
139C2×C3—33no—
140C2×C3—612no—
141C2×C3—94no—
142C2×C3—274no—
143C2×C3C2×D3×3−1+2112yescomplemented
144C2×C3C2×C32×C3⋊D313yes—
145D3—316no—
146C22—96no—
147C22C3⋊D3×3−1+211yescharacteristic, direct product factor
148C3—24no—
149C3—31no—
150C3—64no—
151C3C22×D3×3−1+214yescomplemented
152C3C22×C32×C3⋊D311yescharacteristic
153C2—94no—
154C2C2×C3⋊D3×3−1+213yesdirect product factor
subgroupG/H
centerC22×C3C32×C3⋊D3
commutator, cosocleC33C23×C32
FrattiniC3C22×C32×C3⋊D3
FittingC22×C32×3−1+2C2
socleC22×C33C2×C32
prime radicalC22×C32×C3⋊D3C3
hypercenterC22×3−1+2C3⋊D3
hypocenterC32C23×3−1+2
LCSG ▷ C33 ▷ C32
UCSC1 ◁ C22×C3 ◁ C22×3−1+2

Complements

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

NH ≅ G/Ntype
1. C22×C32×3−1+2C2semidirect
2. C2×C3⋊D3×3−1+2C2direct (N × H)
4. C22×C9×C3⋊D3C3semidirect
6. C2×C32×3−1+2C22semidirect
7. C3⋊D3×3−1+2C22direct (N × H)
12. C22×C3×3−1+2D3semidirect
13. C22×C32×C9C2×C3semidirect
14. C2×C9×C3⋊D3C2×C3semidirect
16. C32×3−1+2C23semidirect
26. C2×C3×3−1+2C2×D3semidirect
27. C2×C32×C9C22×C3semidirect
28. C9×C3⋊D3C22×C3semidirect
42. C22×3−1+2C3⋊D3direct (N × H)
44. C22×C3×C9C3×D3semidirect
49. C3×3−1+2C22×D3semidirect
50. C32×C9C23×C3semidirect
52. C22×C3⋊D33−1+2direct (N × H)
68. C2×3−1+2C2×C3⋊D3direct (N × H)
70. C2×C3×C9C2×C3×D3semidirect
79. C22×C32C2×3−1+2semidirect
82. C2×C3⋊D3C2×3−1+2direct (N × H)
87. C22×C9C3×C3⋊D3semidirect
96. 3−1+2C22×C3⋊D3direct (N × H)
98. C3×C9C22×C3×D3semidirect
109. C2×C32C22×3−1+2semidirect
112. C3⋊D3C22×3−1+2direct (N × H)
117. C2×C9C2×C3×C3⋊D3semidirect
123. C22×C3D3×3−1+2semidirect
132. C32C23×3−1+2semidirect
136. C9C22×C3×C3⋊D3semidirect
143. C2×C3C2×D3×3−1+2semidirect
147. C22C3⋊D3×3−1+2direct (N × H)
151. C3C22×D3×3−1+2semidirect
154. C2C2×C3⋊D3×3−1+2direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C32×3−1+22
C2×C3⋊D3×3−1+22
C22×C32×C3⋊D33
C22×C9×C3⋊D33
C22×D3×3−1+23