Finite Group Databasebeta

← C22×C3×D3×C8 #10595833

Subgroups — C22×C3×D3×C8 #10595833

Order 576.

714 conjugacy classes of subgroups; only the 414 normal subgroups are shown.

normal subgroups only

This group has 714 conjugacy classes of subgroups — too many to draw. Only its 414 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×C3×C4×D3C211yesmaximal, characteristic
2C22×C32×C8C211yesmaximal, characteristic, complemented
3C22×C3×C3⋊C8C211yesmaximal, characteristic, complemented
4C2×C3×D3×C8C2112yesmaximal, direct product factor
5C23×C3×C8—31nomaximal
6C22×D3×C8C311yesmaximal, characteristic, direct product factor
7C23×C3×D3C411yescharacteristic
8C22×C32×C4C2211yescharacteristic
9C22×C3×Dic3C411yescharacteristic
10C2×C3×C4×D3C416yes—
11C2×C3×C4×D3C2216yes—
12C2×C32×C8C2216yescomplemented
13C2×C3×C3⋊C8C2216yescomplemented
14C3×D3×C8C22116yesdirect product factor
15C23×C3×C4—31no—
16C22×C4×D3C2×C311yescharacteristic
17C22×C3×C8—21no—
18C22×C3×C8—31no—
19C22×C3×C8—312no—
20C22×C3×C8D311yescharacteristic, direct product factor
21C22×C3×C8C2×C311yescharacteristic, complemented
22C22×C3⋊C8C2×C311yescharacteristic, complemented
23C2×D3×C8C2×C3112yesdirect product factor
24C23×C32C2×C411yescharacteristic
25C22×C3×D3C818yesdirect product factor
26C22×C3×D3C2×C416yes—
27C2×C32×C4C2×C413yes—
28C2×C32×C4C2313yes—
29C2×C3×Dic3C2×C416yes—
30C3×C4×D3C2×C4112yes—
31C3×C4×D3C2314yes—
32C32×C8C2314yescomplemented
33C3×C3⋊C8C2314yescomplemented
34C23×C8—31noSylow
35C24×C3—31no—
36C23×D3C3×C411yescharacteristic
37C22×C3×C4—21no—
38C22×C3×C4—31no—
39C22×C3×C4—36no—
40C22×C3×C4—36no—
41C22×C3×C4C2×D311yescharacteristic
42C22×C3×C4C22×C311yescharacteristic
43C22×Dic3C3×C411yescharacteristic
44C2×C4×D3C3×C416yes—
45C2×C4×D3C22×C316yes—
46C2×C3×C8—26no—
47C2×C3×C8—36no—
48C2×C3×C8—316no—
49C2×C3×C8C2×D316yesdirect product factor
50C2×C3×C8C22×C316yescomplemented
51C2×C3⋊C8C22×C316yescomplemented
52D3×C8C22×C3116yesdirect product factor
53C22×C32C2×C814yescomplemented
54C22×C32C22×C413yes—
55C2×C3×D3C2×C8124yesdirect product factor
56C2×C3×D3C22×C414yes—
57C32×C4C22×C413yes—
58C32×C4C2411yescharacteristic
59C3×Dic3C22×C414yes—
60C23×C4—31no—
61C22×C8—31no—
62C22×C8—312no—
63C22×C8C3×D311yescharacteristic, direct product factor
64C23×C3—21no—
65C23×C3—38no—
66C23×C3—36no—
67C23×C3C4×D311yescharacteristic
68C23×C3C2×C3×C411yescharacteristic
69C22×D3C3×C818yesdirect product factor
70C22×D3C2×C3×C416yes—
71C2×C3×C4—23no—
72C2×C3×C4—23no—
73C2×C3×C4—36no—
74C2×C3×C4—312no—
75C2×C3×C4—34no—
76C2×C3×C4C4×D313yes—
77C2×C3×C4C2×C3×C413yes—
78C2×C3×C4C22×D313yes—
79C2×C3×C4C23×C313yes—
80C2×Dic3C2×C3×C416yes—
81C4×D3C2×C3×C4112yes—
82C4×D3C23×C314yes—
83C3×C8—24no—
84C3×C8—34no—
85C3×C8C22×D314yesdirect product factor
86C3×C8C23×C314yescomplemented
87C3⋊C8C23×C314yescomplemented
88C2×C32C22×C816yescomplemented
89C2×C32C23×C411yescharacteristic
90C3×D3C22×C818yesdirect product factor
91C24—31no—
92C22×C4—31no—
93C22×C4—36no—
94C22×C4—36no—
95C22×C4C2×C3×D311yescharacteristic
96C2×C8—36no—
97C2×C8—316no—
98C2×C8C2×C3×D316yesdirect product factor
99C22×C3—24no—
100C22×C3—23no—
101C22×C3—324no—
102C22×C3—34no—
103C22×C3D3×C814yesdirect product factor
104C22×C3C2×C3×C814yescomplemented
105C22×C3C2×C4×D313yes—
106C22×C3C22×C3×C413yes—
107C2×D3C2×C3×C8124yesdirect product factor
108C2×D3C22×C3×C414yes—
109C3×C4—21no—
110C3×C4—23no—
111C3×C4—34no—
112C3×C4C2×C4×D313yes—
113C3×C4C22×C3×C413yes—
114C3×C4C23×D311yescharacteristic
115C3×C4C24×C311yescharacteristic
116Dic3C22×C3×C414yes—
117C32C23×C811yescharacteristic, complemented, Sylow
118C23—38no—
119C23—36no—
120C23C3×C4×D311yescharacteristic
121C2×C4—36no—
122C2×C4—34no—
123C2×C4—312no—
124C2×C4C3×C4×D313yes—
125C2×C4C22×C3×D313yes—
126C8—34no—
127C8C22×C3×D314yesdirect product factor
128C2×C3—26no—
129C2×C3—21no—
130C2×C3—38no—
131C2×C3C2×D3×C816yesdirect product factor
132C2×C3C22×C3×C816yescomplemented
133C2×C3C22×C4×D311yescharacteristic
134C2×C3C23×C3×C411yescharacteristic
135D3C22×C3×C818yesdirect product factor
136C22—324no—
137C22—34no—
138C22C3×D3×C814yesdirect product factor
139C22C2×C3×C4×D313yes—
140C4—34no—
141C4C2×C3×C4×D313yes—
142C4C23×C3×D311yescharacteristic
143C3—21no—
144C3C22×D3×C811yescharacteristic, direct product factor
145C3C23×C3×C811yescharacteristic, complemented
146C2—38no—
147C2C2×C3×D3×C816yesdirect product factor
148C2C22×C3×C4×D311yescharacteristic
subgroupG/H
center, hypercenterC22×C3×C8D3
commutator, hypocenterC3C23×C3×C8
FrattiniC4C23×C3×D3
FittingC22×C32×C8C2
socleC23×C32C2×C4
prime radicalC23×C3×D3C4
cosocleC3×C4C24×C3
LCSG ▷ C3
UCSC1 ◁ C22×C3×C8

Complements

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

NH ≅ G/Ntype
2. C22×C32×C8C2semidirect
3. C22×C3×C3⋊C8C2semidirect
4. C2×C3×D3×C8C2direct (N × H)
6. C22×D3×C8C3direct (N × H)
12. C2×C32×C8C22semidirect
13. C2×C3×C3⋊C8C22semidirect
14. C3×D3×C8C22direct (N × H)
20. C22×C3×C8D3direct (N × H)
21. C22×C3×C8C2×C3semidirect
22. C22×C3⋊C8C2×C3semidirect
23. C2×D3×C8C2×C3direct (N × H)
25. C22×C3×D3C8direct (N × H)
32. C32×C8C23semidirect
33. C3×C3⋊C8C23semidirect
49. C2×C3×C8C2×D3direct (N × H)
50. C2×C3×C8C22×C3semidirect
51. C2×C3⋊C8C22×C3semidirect
52. D3×C8C22×C3direct (N × H)
53. C22×C32C2×C8semidirect
55. C2×C3×D3C2×C8direct (N × H)
63. C22×C8C3×D3direct (N × H)
69. C22×D3C3×C8direct (N × H)
85. C3×C8C22×D3direct (N × H)
86. C3×C8C23×C3semidirect
87. C3⋊C8C23×C3semidirect
88. C2×C32C22×C8semidirect
90. C3×D3C22×C8direct (N × H)
98. C2×C8C2×C3×D3direct (N × H)
103. C22×C3D3×C8direct (N × H)
104. C22×C3C2×C3×C8semidirect
107. C2×D3C2×C3×C8direct (N × H)
117. C32C23×C8semidirect
127. C8C22×C3×D3direct (N × H)
131. C2×C3C2×D3×C8direct (N × H)
132. C2×C3C22×C3×C8semidirect
135. D3C22×C3×C8direct (N × H)
138. C22C3×D3×C8direct (N × H)
144. C3C22×D3×C8direct (N × H)
145. C3C23×C3×C8semidirect
147. C2C2×C3×D3×C8direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×C4×D32
C22×C32×C82
C22×C3×C3⋊C82
C2×C3×D3×C82
C23×C3×C83
C22×D3×C83