Finite Group Databasebeta

← C3×C8×C22⋊A4 #11919854

Subgroups — C3×C8×C22⋊A4 #11919854

Order 1152.

808 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 808 conjugacy classes of subgroups — too many to draw. Only its 72 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
1C3×C4×C22⋊A4C211yesmaximal, characteristic
2C24×C3×C8C311yesmaximal, characteristic, complemented
3C8×C22⋊A4C313yesmaximal, direct product factor
4C2×C3×C22⋊A4C411yescharacteristic
5C3×C8×A4—45nomaximal
6C24×C3×C4C2×C311yescharacteristic
7C4×C22⋊A4C2×C313yes—
8C23×C3×C8—35no—
9C23×C3×C8—35no—
10C3×C22⋊A4C811yescharacteristic, direct product factor
11C3×C4×A4—45no—
12C24×C8C3211yescharacteristic, complemented, Sylow
13C25×C3C3×C411yescharacteristic
14C2×C22⋊A4C3×C413yes—
15C23×C3×C4—35no—
16C23×C3×C4—35no—
17C22×C3×C8—330no—
18C22×C3×C8—310no—
19C22×C3×C8—35no—
20C22×C3×C8A415yescomplemented
21C8×A4—415no—
22C2×C3×A4—45no—
23C32×C8—161no—
24C24×C4C2×C3211yescharacteristic
25C23×C8—35no—
26C23×C8—35no—
27C24×C3—35no—
28C24×C3—35no—
29C24×C3C3×C811yescharacteristic, complemented
30C22⋊A4C3×C813yesdirect product factor
31C22×C3×C4—310no—
32C22×C3×C4—330no—
33C22×C3×C4—35no—
34C22×C3×C4C2×A415yes—
35C4×A4—415no—
36C2×C3×C8—330no—
37C2×C3×C8—35no—
38C2×C3×C8—35no—
39C3×A4—45no—
40C32×C4—161no—
41C25C32×C411yescharacteristic
42C23×C4—35no—
43C23×C4—35no—
44C22×C8—330no—
45C22×C8—310no—
46C22×C8—35no—
47C22×C8C3×A415yescomplemented
48C23×C3—310no—
49C23×C3—330no—
50C23×C3—35no—
51C23×C3—35no—
52C23×C3C4×A415yes—
53C2×A4—415no—
54C2×C3×C4—330no—
55C2×C3×C4—35no—
56C2×C3×C4—35no—
57C3×C8—35no—
58C3×C8—163no—
59C3×C8C22⋊A411yescharacteristic, direct product factor
60C2×C32—161no—
61C24—35no—
62C24—35no—
63C24C32×C811yescharacteristic, complemented
64C22×C4—310no—
65C22×C4—330no—
66C22×C4—35no—
67C22×C4C2×C3×A415yes—
68C2×C8—330no—
69C2×C8—35no—
70C2×C8—35no—
71C22×C3—35no—
72C22×C3—330no—
73C22×C3—310no—
74C22×C3—35no—
75C22×C3C8×A415yescomplemented
76A4—415no—
77C3×C4—35no—
78C3×C4—163no—
79C3×C4C2×C22⋊A411yescharacteristic
80C32—161noSylow
81C23—310no—
82C23—330no—
83C23—35no—
84C23—35no—
85C23C3×C4×A415yes—
86C2×C4—330no—
87C2×C4—35no—
88C2×C4—35no—
89C8—35no—
90C8C3×C22⋊A411yescharacteristic, direct product factor
91C2×C3—35no—
92C2×C3—35no—
93C2×C3—163no—
94C2×C3C4×C22⋊A411yescharacteristic
95C22—35no—
96C22—310no—
97C22—330no—
98C22—35no—
99C22C3×C8×A415yescomplemented
100C4—35no—
101C4C2×C3×C22⋊A411yescharacteristic
102C3—163no—
103C3C8×C22⋊A411yescharacteristic, direct product factor
104C2—35no—
105C2—35no—
106C2C3×C4×C22⋊A411yescharacteristic
subgroupG/H
center, hypercenterC3×C8C22⋊A4
commutator, hypocenterC24C32×C8
FrattiniC4C2×C3×C22⋊A4
FittingC24×C3×C8C3
socleC25×C3C3×C4
prime radicalC2×C3×C22⋊A4C4
cosocleC24×C4C2×C32
LCSG ▷ C24
UCSC1 ◁ C3×C8

Complements

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

NH ≅ G/Ntype
2. C24×C3×C8C3semidirect
3. C8×C22⋊A4C3direct (N × H)
10. C3×C22⋊A4C8direct (N × H)
12. C24×C8C32semidirect
20. C22×C3×C8A4semidirect
29. C24×C3C3×C8semidirect
30. C22⋊A4C3×C8direct (N × H)
47. C22×C8C3×A4semidirect
59. C3×C8C22⋊A4direct (N × H)
63. C24C32×C8semidirect
75. C22×C3C8×A4semidirect
90. C8C3×C22⋊A4direct (N × H)
99. C22C3×C8×A4semidirect
103. C3C8×C22⋊A4direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C4×C22⋊A42
C24×C3×C83
C8×C22⋊A43
C3×C8×A44