Finite Group Databasebeta

← C23×C3×C42⋊C3 #11919662

Subgroups — C23×C3×C42⋊C3 #11919662

Order 1152.

1256 conjugacy classes of subgroups; only the 160 normal subgroups are shown.

normal subgroups only

This group has 1256 conjugacy classes of subgroups — too many to draw. Only its 160 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×C42⋊C3C217yesmaximal, direct product factor
2C23×C3×C42C311yesmaximal, characteristic, complemented
3C23×C42⋊C3C313yesmaximal, direct product factor
4C23×C3×A4—41nomaximal
5C2×C3×C42⋊C3C2217yesdirect product factor
6C24×C3×C4—31no—
7C22×C3×C42—37no—
8C22×C3×C42C2×C317yescomplemented
9C22×C42⋊C3C2×C3121yesdirect product factor
10C22×C3×A4—47no—
11C3×C42⋊C3C2311yescharacteristic, direct product factor
12C23×C42C3211yescharacteristic, complemented, Sylow
13C25×C3A411yescharacteristic
14C23×A4—43no—
15C23×C3×C4—314no—
16C23×C3×C4—32no—
17C23×C3×C4—37no—
18C23×C3×C4—37no—
19C2×C3×C42—321no—
20C2×C3×C42—314no—
21C2×C3×C42C22×C317yescomplemented
22C2×C42⋊C3C22×C3121yesdirect product factor
23C23×C32—161no—
24C2×C3×A4—47no—
25C24×C4—31no—
26C22×C42—37no—
27C22×C42C2×C3217yescomplemented
28C24×C3—37no—
29C24×C3—31no—
30C24×C3C2×A417yes—
31C22×A4—421no—
32C22×C3×C4—342no—
33C22×C3×C4—342no—
34C22×C3×C4—314no—
35C22×C3×C4—314no—
36C22×C3×C4—37no—
37C22×C3×C4—321no—
38C3×C42—37no—
39C3×C42—314no—
40C3×C42C23×C311yescharacteristic, complemented
41C42⋊C3C23×C313yesdirect product factor
42C22×C32—167no—
43C3×A4—41no—
44C25C3×A411yescharacteristic
45C23×C4—314no—
46C23×C4—32no—
47C23×C4—37no—
48C23×C4—37no—
49C2×C42—321no—
50C2×C42—314no—
51C2×C42C22×C3217yescomplemented
52C23×C3—321no—
53C23×C3—314no—
54C23×C3—37no—
55C23×C3—37no—
56C23×C3—163no—
57C23×C3C42⋊C311yescharacteristic, direct product factor
58C23×C3C22×A417yes—
59C2×A4—421no—
60C2×C3×C4—314no—
61C2×C3×C4—342no—
62C2×C3×C4—314no—
63C2×C3×C4—342no—
64C2×C3×C4—31no—
65C2×C3×C4—37no—
66C2×C32—167no—
67C24—37no—
68C24—31no—
69C24C2×C3×A417yes—
70C22×C4—342no—
71C22×C4—342no—
72C22×C4—314no—
73C22×C4—314no—
74C22×C4—37no—
75C22×C4—321no—
76C42—37no—
77C42—314no—
78C42C23×C3211yescharacteristic, complemented
79C22×C3—37no—
80C22×C3—314no—
81C22×C3—37no—
82C22×C3—321no—
83C22×C3—1621no—
84C22×C3C2×C42⋊C317yesdirect product factor
85C22×C3C23×A411yescharacteristic
86A4—43no—
87C3×C4—32no—
88C3×C4—314no—
89C32—161noSylow
90C23—321no—
91C23—314no—
92C23—37no—
93C23—37no—
94C23C3×C42⋊C311yescharacteristic, direct product factor
95C23C22×C3×A417yes—
96C2×C4—314no—
97C2×C4—342no—
98C2×C4—314no—
99C2×C4—342no—
100C2×C4—31no—
101C2×C4—37no—
102C2×C3—31no—
103C2×C3—37no—
104C2×C3—1621no—
105C2×C3C22×C42⋊C317yesdirect product factor
106C22—37no—
107C22—314no—
108C22—37no—
109C22—321no—
110C22C2×C3×C42⋊C317yesdirect product factor
111C22C23×C3×A411yescharacteristic
112C4—32no—
113C4—314no—
114C3—163no—
115C3C23×C42⋊C311yescharacteristic, direct product factor
116C2—31no—
117C2—37no—
118C2C22×C3×C42⋊C317yesdirect product factor
subgroupG/H
center, hypercenterC23×C3C42⋊C3
commutator, cosocle, hypocenterC42C23×C32
FrattiniC22C23×C3×A4
FittingC23×C3×C42C3
socleC25×C3A4
LCSG ▷ C42
UCSC1 ◁ C23×C3

Complements

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

NH ≅ G/Ntype
1. C22×C3×C42⋊C3C2direct (N × H)
2. C23×C3×C42C3semidirect
3. C23×C42⋊C3C3direct (N × H)
5. C2×C3×C42⋊C3C22direct (N × H)
8. C22×C3×C42C2×C3semidirect
9. C22×C42⋊C3C2×C3direct (N × H)
11. C3×C42⋊C3C23direct (N × H)
12. C23×C42C32semidirect
21. C2×C3×C42C22×C3semidirect
22. C2×C42⋊C3C22×C3direct (N × H)
27. C22×C42C2×C32semidirect
40. C3×C42C23×C3semidirect
41. C42⋊C3C23×C3direct (N × H)
51. C2×C42C22×C32semidirect
57. C23×C3C42⋊C3direct (N × H)
78. C42C23×C32semidirect
84. C22×C3C2×C42⋊C3direct (N × H)
94. C23C3×C42⋊C3direct (N × H)
105. C2×C3C22×C42⋊C3direct (N × H)
110. C22C2×C3×C42⋊C3direct (N × H)
115. C3C23×C42⋊C3direct (N × H)
118. C2C22×C3×C42⋊C3direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×C42⋊C32
C23×C3×C423
C23×C42⋊C33
C23×C3×A44