Finite Group Databasebeta

← C22×Dic3×C3⋊D3 #11724601

Subgroups — C22×Dic3×C3⋊D3 #11724601

Order 864.

1632 conjugacy classes of subgroups; only the 400 normal subgroups are shown.

normal subgroups only

This group has 1632 conjugacy classes of subgroups — too many to draw. Only its 400 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
1C23×C3×C3⋊D3C211yesmaximal, characteristic
2C22×C3⋊(C3⋊Dic3)C211yesmaximal, characteristic, complemented
3C22×C32×Dic3C211yesmaximal, characteristic, complemented
4C2×Dic3×C3⋊D3C2112yesmaximal, direct product factor
5C22×C4×C3⋊D3—31nomaximal
6C22×D3×Dic3—34nomaximal
7C23×C33C2211yescharacteristic
8C22×C3×C3⋊D3C418yescomplemented
9C22×C3×C3⋊D3C2216yes—
10C2×C3⋊(C3⋊Dic3)C2216yescomplemented
11C2×C32×Dic3C2216yescomplemented
12Dic3×C3⋊D3C22116yesdirect product factor
13C23×C3⋊D3D311yescharacteristic
14C23×C3×D3—34no—
15C22×C32×C4—31no—
16C22×C3⋊Dic3—31no—
17C22×C3⋊Dic3—34no—
18C22×C3⋊Dic3—64no—
19C2×C4×C3⋊D3—312no—
20C22×C3×Dic3D314yescomplemented
21C2×D3×Dic3—348no—
22C22×C33C2×C414yescomplemented
23C22×C33C2313yes—
24C2×C3×C3⋊D3C2×C4124yescomplemented
25C2×C3×C3⋊D3C2314yes—
26C3⋊(C3⋊Dic3)C2314yescomplemented
27C32×Dic3C2314yescomplemented
28C23×Dic3—91no—
29C22×C4×D3—94no—
30C23×C32—24no—
31C23×C32C2×D314yes—
32C23×C32C2×D311yescharacteristic
33C22×C3⋊D3Dic318yesdirect product factor
34C22×C3⋊D3C2×D316yes—
35C22×C3×D3—332no—
36C22×C3×D3—324no—
37C2×C32×C4—36no—
38C2×C3⋊Dic3—36no—
39C2×C3⋊Dic3—324no—
40C2×C3⋊Dic3—624no—
41C4×C3⋊D3—316no—
42C2×C3×Dic3C2×D3124yescomplemented
43D3×Dic3—364no—
44C2×C33C22×C416yescomplemented
45C2×C33C2411yescharacteristic
46C3×C3⋊D3C22×C418yescomplemented
47C24×C3—91no—
48C23×D3—34no—
49C22×C3×C4—34no—
50C22×Dic3—94no—
51C22×Dic3—91no—
52C22×Dic3—912no—
53C22×Dic3—184no—
54C22×Dic3C3⋊D311yescharacteristic, direct product factor
55C2×C4×D3—948no—
56C22×C32—216no—
57C22×C32—212no—
58C22×C32C4×D3116yescomplemented
59C22×C32C2×Dic314yescomplemented
60C22×C32C22×D3112yes—
61C22×C32C22×D313yes—
62C2×C3⋊D3C2×Dic3124yesdirect product factor
63C2×C3⋊D3C22×D314yes—
64C2×C3×D3—396no—
65C2×C3×D3—316no—
66C32×C4—34no—
67C3⋊Dic3—34no—
68C3⋊Dic3—316no—
69C3⋊Dic3—616no—
70C3×Dic3C22×D3116yescomplemented
71C23×C4—271noSylow
72C33C23×C411yescharacteristic, complemented, Sylow
73C23×C3—24no—
74C23×C3—98no—
75C23×C3—96no—
76C23×C3D3214yes—
77C23×C3C2×C3⋊D311yescharacteristic
78C22×D3—332no—
79C22×D3—324no—
80C2×C3×C4—324no—
81C2×Dic3—924no—
82C2×Dic3—96no—
83C2×Dic3—916no—
84C2×Dic3—1824no—
85C2×Dic3C2×C3⋊D316yesdirect product factor
86C4×D3—964no—
87C2×C32—24no—
88C2×C32—224no—
89C2×C32C2×C4×D3124yescomplemented
90C2×C32C22×Dic316yescomplemented
91C2×C32C23×D314yes—
92C2×C32C23×D311yescharacteristic
93C3⋊D3C22×Dic318yesdirect product factor
94C3×D3—332no—
95C24—91no—
96C22×C4—31no—
97C22×C4—2712no—
98C22×C4—271no—
99C22×C3—216no—
100C22×C3—212no—
101C22×C3—94no—
102C22×C3—924no—
103C22×C3D3×Dic3116yescomplemented
104C22×C3C4×C3⋊D314yescomplemented
105C22×C3C2×D32112yes—
106C22×C3C22×C3⋊D313yes—
107C2×D3—316no—
108C2×D3—396no—
109C3×C4—316no—
110Dic3—916no—
111Dic3—94no—
112Dic3—1816no—
113Dic3C22×C3⋊D314yesdirect product factor
114C32—24no—
115C32C22×C4×D314yescomplemented
116C32C23×Dic311yescharacteristic, complemented
117C23—98no—
118C23—96no—
119C23D3×C3⋊D311yescharacteristic
120C2×C4—36no—
121C2×C4—2716no—
122C2×C4—276no—
123C2×C3—24no—
124C2×C3—224no—
125C2×C3—98no—
126C2×C3C2×D3×Dic3124yescomplemented
127C2×C3C2×C4×C3⋊D316yescomplemented
128C2×C3C22×D3214yes—
129C2×C3C23×C3⋊D311yescharacteristic
130D3—332no—
131C22—94no—
132C22—924no—
133C22Dic3×C3⋊D314yesdirect product factor
134C22C2×D3×C3⋊D313yes—
135C4—34no—
136C4—274no—
137C3—24no—
138C3C22×D3×Dic314yescomplemented
139C3C22×C4×C3⋊D311yescharacteristic, complemented
140C2—98no—
141C2C2×Dic3×C3⋊D316yesdirect product factor
142C2C22×D3×C3⋊D311yescharacteristic
subgroupG/H
center, hypercenterC23D3×C3⋊D3
commutator, hypocenterC33C23×C4
FrattiniC2C22×D3×C3⋊D3
Fitting, socleC23×C33C22
prime radicalC23×C3×C3⋊D3C2
cosocleC2×C33C24
LCSG ▷ C33
UCSC1 ◁ C23

Complements

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

NH ≅ G/Ntype
2. C22×C3⋊(C3⋊Dic3)C2semidirect
3. C22×C32×Dic3C2semidirect
4. C2×Dic3×C3⋊D3C2direct (N × H)
8. C22×C3×C3⋊D3C4semidirect
10. C2×C3⋊(C3⋊Dic3)C22semidirect
11. C2×C32×Dic3C22semidirect
12. Dic3×C3⋊D3C22direct (N × H)
20. C22×C3×Dic3D3semidirect
22. C22×C33C2×C4semidirect
24. C2×C3×C3⋊D3C2×C4semidirect
26. C3⋊(C3⋊Dic3)C23semidirect
27. C32×Dic3C23semidirect
33. C22×C3⋊D3Dic3direct (N × H)
42. C2×C3×Dic3C2×D3semidirect
44. C2×C33C22×C4semidirect
46. C3×C3⋊D3C22×C4semidirect
54. C22×Dic3C3⋊D3direct (N × H)
58. C22×C32C4×D3semidirect
59. C22×C32C2×Dic3semidirect
62. C2×C3⋊D3C2×Dic3direct (N × H)
70. C3×Dic3C22×D3semidirect
72. C33C23×C4semidirect
85. C2×Dic3C2×C3⋊D3direct (N × H)
89. C2×C32C2×C4×D3semidirect
90. C2×C32C22×Dic3semidirect
93. C3⋊D3C22×Dic3direct (N × H)
103. C22×C3D3×Dic3semidirect
104. C22×C3C4×C3⋊D3semidirect
113. Dic3C22×C3⋊D3direct (N × H)
115. C32C22×C4×D3semidirect
116. C32C23×Dic3semidirect
126. C2×C3C2×D3×Dic3semidirect
127. C2×C3C2×C4×C3⋊D3semidirect
133. C22Dic3×C3⋊D3direct (N × H)
138. C3C22×D3×Dic3semidirect
139. C3C22×C4×C3⋊D3semidirect
141. C2C2×Dic3×C3⋊D3direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C3×C3⋊D32
C22×C3⋊(C3⋊Dic3)2
C22×C32×Dic32
C2×Dic3×C3⋊D32
C22×C4×C3⋊D33
C22×D3×Dic33