Finite Group Databasebeta

← C22×C3×SL(2,ℤ/4) #10596570

Subgroups — C22×C3×SL(2,ℤ/4) #10596570

Order 576.

586 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 586 conjugacy classes of subgroups — too many to draw. Only its 118 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×A4C211yesmaximal, characteristic
2C2×C3×SL(2,ℤ/4)C216yesmaximal, direct product factor
3C22×SL(2,ℤ/4)C311yesmaximal, characteristic, direct product factor
4C22×C3×C22⋊C4—31nomaximal
5C22×C3×A4C414yescomplemented
6C22×C3×A4C2213yes—
7C22×C3×Dic3—41nomaximal
8C3×SL(2,ℤ/4)C2214yesdirect product factor
9C25×C3D311yescharacteristic
10C23×A4—21no—
11C23×A4C2×C311yescharacteristic
12C23×C3×C4—31no—
13C23×C3×C4—31no—
14C2×SL(2,ℤ/4)C2×C316yesdirect product factor
15C2×C3×C22⋊C4—36no—
16C2×C3×C22⋊C4—36no—
17C23×C32—41no—
18C2×C3×A4C2×C416yescomplemented
19C2×C3×A4C2311yescharacteristic
20C2×C3×Dic3—46no—
21C22×C22⋊C4—31noSylow
22C24×C3—31no—
23C24×C3—34no—
24C24×C3—33no—
25C24×C3Dic314yescomplemented
26C24×C3C2×D313yes—
27C22×A4—24no—
28C22×A4—23no—
29C22×A4C3×C414yescomplemented
30C22×A4C22×C313yes—
31C22×C3×C4—36no—
32C22×C3×C4—36no—
33C22×C3×C4—64no—
34C22×C3×C4—63no—
35C22×C3×C4—61no—
36C22×Dic3—41no—
37SL(2,ℤ/4)C22×C314yesdirect product factor
38C3×C22⋊C4—312no—
39C3×C22⋊C4—34no—
40C22×C32—44no—
41C22×C32—43no—
42C3×A4C22×C411yescharacteristic, complemented
43C3×Dic3—44no—
44C25C3×D311yescharacteristic
45C23×C4—31no—
46C23×C4—31no—
47C2×C22⋊C4—36no—
48C2×C22⋊C4—36no—
49C23×C3—34no—
50C23×C3—34no—
51C23×C3—33no—
52C23×C3—33no—
53C23×C3—33no—
54C23×C3—312no—
55C23×C3—36no—
56C23×C3—41no—
57C23×C3—66no—
58C23×C3—61no—
59C23×C3—81no—
60C23×C3C2×Dic316yescomplemented
61C23×C3S411yescharacteristic
62C23×C3C22×D311yescharacteristic
63C2×A4—26no—
64C2×A4—21no—
65C2×A4C2×C3×C416yescomplemented
66C2×A4C23×C311yescharacteristic
67C2×C3×C4—34no—
68C2×C3×C4—34no—
69C2×C3×C4—612no—
70C2×C3×C4—66no—
71C2×C3×C4—66no—
72C2×Dic3—46no—
73C2×C32—46no—
74C2×C32—41no—
75C24—31no—
76C24—33no—
77C24—34no—
78C24C3×Dic314yescomplemented
79C24C2×C3×D313yes—
80C22×C4—36no—
81C22×C4—36no—
82C22×C4—64no—
83C22×C4—63no—
84C22×C4—61no—
85C22⋊C4—312no—
86C22⋊C4—34no—
87C22×C3—36no—
88C22×C3—31no—
89C22×C3—36no—
90C22×C3—36no—
91C22×C3—312no—
92C22×C3—31no—
93C22×C3—33no—
94C22×C3—43no—
95C22×C3—44no—
96C22×C3—63no—
97C22×C3—64no—
98C22×C3—83no—
99C22×C3—84no—
100C22×C3SL(2,ℤ/4)14yesdirect product factor
101C22×C3C22×Dic311yescharacteristic, complemented
102C22×C3C2×S413yes—
103A4—21no—
104A4C22×C3×C411yescharacteristic, complemented
105C3×C4—64no—
106C3×C4—64no—
107Dic3—44no—
108C32—41noSylow
109C23—33no—
110C23—33no—
111C23—34no—
112C23—34no—
113C23—33no—
114C23—312no—
115C23—36no—
116C23—66no—
117C23—61no—
118C23C2×C3×Dic316yescomplemented
119C23C3×S411yescharacteristic
120C23C22×C3×D311yescharacteristic
121C2×C4—34no—
122C2×C4—34no—
123C2×C4—612no—
124C2×C4—66no—
125C2×C4—66no—
126C2×C3—31no—
127C2×C3—31no—
128C2×C3—36no—
129C2×C3—46no—
130C2×C3—41no—
131C2×C3—86no—
132C2×C3—81no—
133C2×C3C2×SL(2,ℤ/4)16yesdirect product factor
134C2×C3C22×S411yescharacteristic
135C22—36no—
136C22—31no—
137C22—36no—
138C22—36no—
139C22—312no—
140C22—31no—
141C22—33no—
142C22—63no—
143C22—64no—
144C22C3×SL(2,ℤ/4)14yesdirect product factor
145C22C22×C3×Dic311yescharacteristic, complemented
146C22C2×C3×S413yes—
147C4—64no—
148C4—64no—
149C3—41no—
150C3—81no—
151C3C22×SL(2,ℤ/4)11yescharacteristic, direct product factor
152C2—31no—
153C2—31no—
154C2—36no—
155C2C2×C3×SL(2,ℤ/4)16yesdirect product factor
156C2C22×C3×S411yescharacteristic
subgroupG/H
center, hypercenterC23×C3S4
commutator, hypocenterA4C22×C3×C4
FrattiniC2C22×C3×S4
Fitting, socleC25×C3D3
prime radicalC23×C3×A4C2
cosocleC2×A4C23×C3
LCSG ▷ A4
UCSC1 ◁ C23×C3

Complements

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

NH ≅ G/Ntype
2. C2×C3×SL(2,ℤ/4)C2direct (N × H)
3. C22×SL(2,ℤ/4)C3direct (N × H)
5. C22×C3×A4C4semidirect
8. C3×SL(2,ℤ/4)C22direct (N × H)
14. C2×SL(2,ℤ/4)C2×C3direct (N × H)
18. C2×C3×A4C2×C4semidirect
25. C24×C3Dic3semidirect
29. C22×A4C3×C4semidirect
37. SL(2,ℤ/4)C22×C3direct (N × H)
42. C3×A4C22×C4semidirect
60. C23×C3C2×Dic3semidirect
65. C2×A4C2×C3×C4semidirect
78. C24C3×Dic3semidirect
100. C22×C3SL(2,ℤ/4)direct (N × H)
101. C22×C3C22×Dic3semidirect
104. A4C22×C3×C4semidirect
118. C23C2×C3×Dic3semidirect
133. C2×C3C2×SL(2,ℤ/4)direct (N × H)
144. C22C3×SL(2,ℤ/4)direct (N × H)
145. C22C22×C3×Dic3semidirect
151. C3C22×SL(2,ℤ/4)direct (N × H)
155. C2C2×C3×SL(2,ℤ/4)direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C3×A42
C2×C3×SL(2,ℤ/4)2
C22×SL(2,ℤ/4)3
C22×C3×C22⋊C43
C22×C3×Dic34