Finite Group Databasebeta

← C3⋊C8×C22⋊A4 #11923431

Subgroups — C3⋊C8×C22⋊A4 #11923431

Order 1152.

773 conjugacy classes of subgroups; only the 56 normal subgroups are shown.

normal subgroups only

This group has 773 conjugacy classes of subgroups — too many to draw. Only its 56 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⋊A4—31nomaximal
4C2×C3×C22⋊A4C411yescharacteristic
5A4×C3⋊C8—45nomaximal
6C24×C3×C4C2×C311yescharacteristic
7C4×C22⋊A4—21no—
8C4×C22⋊A4D311yescharacteristic
9C23×C3⋊C8—35no—
10C23×C3⋊C8—35no—
11C3×C22⋊A4C811yescharacteristic, complemented
12C3×C4×A4—45no—
13C24×C8—31noSylow
14C25×C3C3×C411yescharacteristic
15C2×C22⋊A4—21no—
16C2×C22⋊A4Dic311yescharacteristic
17C23×C3×C4—35no—
18C23×C3×C4—35no—
19C22×C3⋊C8—330no—
20C22×C3⋊C8—310no—
21C22×C3⋊C8—35no—
22C22×C3⋊C8A415yescomplemented
23C8×A4—125no—
24C2×C3×A4—45no—
25C3×C3⋊C8—161no—
26C24×C4C3×D311yescharacteristic
27C23×C8—95no—
28C23×C8—95no—
29C24×C3—35no—
30C24×C3—35no—
31C24×C3C3×C811yescharacteristic, complemented
32C22⋊A4—21no—
33C22⋊A4C3⋊C811yescharacteristic, direct product factor
34C22×C3×C4—310no—
35C22×C3×C4—330no—
36C22×C3×C4—35no—
37C22×C3×C4C2×A415yes—
38C4×A4—45no—
39C4×A4—85no—
40C2×C3⋊C8—330no—
41C2×C3⋊C8—35no—
42C2×C3⋊C8—35no—
43C3×A4—45no—
44C32×C4—161no—
45C25C3×Dic311yescharacteristic
46C23×C4—35no—
47C23×C4—35no—
48C22×C8—35no—
49C22×C8—910no—
50C22×C8—930no—
51C22×C8—95no—
52C23×C3—310no—
53C23×C3—330no—
54C23×C3—35no—
55C23×C3—35no—
56C23×C3C4×A415yes—
57C2×A4—45no—
58C2×A4—85no—
59C2×C3×C4—330no—
60C2×C3×C4—35no—
61C2×C3×C4—35no—
62C3×C8—481no—
63C3⋊C8—35no—
64C3⋊C8C22⋊A411yescharacteristic, direct product factor
65C2×C32—161no—
66C24—35no—
67C24—35no—
68C24C3×C3⋊C811yescharacteristic, complemented
69C22×C4—310no—
70C22×C4—330no—
71C22×C4—35no—
72C22×C4D3×A415yes—
73C2×C8—95no—
74C2×C8—930no—
75C2×C8—95no—
76C22×C3—35no—
77C22×C3—330no—
78C22×C3—310no—
79C22×C3—35no—
80C22×C3C8×A415yescomplemented
81A4—45no—
82A4—85no—
83C3×C4—35no—
84C3×C4—161no—
85C3×C4—321no—
86C3×C4C2×C22⋊A411yescharacteristic
87C32—161noSylow
88C23—310no—
89C23—330no—
90C23—35no—
91C23—35no—
92C23Dic3×A415yes—
93C2×C4—330no—
94C2×C4—35no—
95C2×C4—35no—
96C8—31no—
97C8—95no—
98C2×C3—35no—
99C2×C3—35no—
100C2×C3—161no—
101C2×C3—321no—
102C2×C3C4×C22⋊A411yescharacteristic
103C22—35no—
104C22—310no—
105C22—330no—
106C22—35no—
107C22A4×C3⋊C815yescomplemented
108C4—35no—
109C4D3×C22⋊A411yescharacteristic
110C3—161no—
111C3—321no—
112C3C8×C22⋊A411yescharacteristic, complemented
113C2—35no—
114C2—35no—
115C2Dic3×C22⋊A411yescharacteristic
subgroupG/H
center, Frattini, hypercenterC4D3×C22⋊A4
commutator, hypocenterC24×C3C3×C8
Fitting, cosocleC24×C3×C4C2×C3
socleC25×C3C3×C4
prime radicalC2×C3×C22⋊A4C4
LCSG ▷ C24×C3
UCSC1 ◁ C4

Complements

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

NH ≅ G/Ntype
2. C24×C3⋊C8C3semidirect
11. C3×C22⋊A4C8semidirect
22. C22×C3⋊C8A4semidirect
31. C24×C3C3×C8semidirect
33. C22⋊A4C3⋊C8direct (N × H)
64. C3⋊C8C22⋊A4direct (N × H)
68. C24C3×C3⋊C8semidirect
80. C22×C3C8×A4semidirect
107. C22A4×C3⋊C8semidirect
112. C3C8×C22⋊A4semidirect

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
A4×C3⋊C84