Finite Group Databasebeta

← C3⋊C8×C42⋊C3 #11920155

Subgroups — C3⋊C8×C42⋊C3 #11920155

Order 1152.

185 conjugacy classes of subgroups; only the 28 normal subgroups are shown.

normal subgroups only

This group has 185 conjugacy classes of subgroups — too many to draw. Only its 28 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×C42⋊C3C211yesmaximal, characteristic
2C42×C3⋊C8C311yesmaximal, characteristic, complemented
3C8×C42⋊C3—31nomaximal
4C2×C3×C42⋊C3C411yescharacteristic
5A4×C3⋊C8—41nomaximal
6C3×C43C2×C311yescharacteristic
7C2×C4×C3⋊C8—31no—
8C2×C4×C3⋊C8—31no—
9C4×C42⋊C3—21no—
10C4×C42⋊C3D311yescharacteristic
11C3×C4×A4—41no—
12C3×C42⋊C3C811yescharacteristic, complemented
13C42×C8—31noSylow
14C2×C3×C42—31no—
15C2×C3×C42—31no—
16C2×C3×C42C3×C411yescharacteristic
17C22×C3⋊C8—31no—
18C22×C3⋊C8A411yescharacteristic
19C8×A4—121no—
20C2×C42⋊C3—21no—
21C2×C42⋊C3Dic311yescharacteristic
22C4×C3⋊C8—34no—
23C4×C3⋊C8—32no—
24C4×C3⋊C8—32no—
25C2×C3×A4—41no—
26C3×C3⋊C8—161no—
27C2×C4×C8—91no—
28C2×C4×C8—91no—
29C43C3×D311yescharacteristic
30C22×C3×C4—31no—
31C22×C3×C4—31no—
32C22×C3×C4C2×A411yescharacteristic
33C4×A4—41no—
34C4×A4—81no—
35C3×C42—31no—
36C3×C42—32no—
37C3×C42—32no—
38C3×C42—34no—
39C3×C42C3×C811yescharacteristic, complemented
40C2×C3⋊C8—32no—
41C2×C3⋊C8—34no—
42C2×C3⋊C8—31no—
43C2×C3⋊C8—31no—
44C42⋊C3—21no—
45C42⋊C3C3⋊C811yescharacteristic, direct product factor
46C3×A4—41no—
47C32×C4—161no—
48C22×C8—31no—
49C22×C8—91no—
50C2×C42—31no—
51C2×C42—31no—
52C2×C42C3×Dic311yescharacteristic
53C4×C8—92no—
54C4×C8—94no—
55C4×C8—92no—
56C23×C3C4×A411yescharacteristic
57C2×A4—41no—
58C2×A4—81no—
59C2×C3×C4—34no—
60C2×C3×C4—32no—
61C2×C3×C4—32no—
62C2×C3×C4—32no—
63C2×C3×C4—31no—
64C2×C3×C4—31no—
65C2×C3×C4—31no—
66C2×C3×C4—31no—
67C3×C8—481no—
68C3⋊C8—34no—
69C3⋊C8—31no—
70C3⋊C8C42⋊C311yescharacteristic, direct product factor
71C2×C32—161no—
72C22×C4—31no—
73C22×C4—31no—
74C22×C4D3×A411yescharacteristic
75C2×C8—91no—
76C2×C8—92no—
77C2×C8—94no—
78C2×C8—91no—
79C42—31no—
80C42—32no—
81C42—32no—
82C42—34no—
83C42C3×C3⋊C811yescharacteristic, complemented
84C22×C3—31no—
85C22×C3—31no—
86C22×C3C8×A411yescharacteristic
87A4—41no—
88A4—81no—
89C3×C4—34no—
90C3×C4—32no—
91C3×C4—32no—
92C3×C4—31no—
93C3×C4—161no—
94C3×C4—321no—
95C3×C4C2×C42⋊C311yescharacteristic
96C32—161noSylow
97C23Dic3×A411yescharacteristic
98C2×C4—32no—
99C2×C4—34no—
100C2×C4—32no—
101C2×C4—32no—
102C2×C4—31no—
103C2×C4—31no—
104C2×C4—31no—
105C2×C4—31no—
106C8—31no—
107C8—94no—
108C8—91no—
109C2×C3—31no—
110C2×C3—31no—
111C2×C3—161no—
112C2×C3—321no—
113C2×C3C4×C42⋊C311yescharacteristic
114C22—31no—
115C22—31no—
116C22A4×C3⋊C811yescharacteristic
117C4—32no—
118C4—32no—
119C4—34no—
120C4—31no—
121C4D3×C42⋊C311yescharacteristic
122C3—161no—
123C3—321no—
124C3C8×C42⋊C311yescharacteristic, complemented
125C2—31no—
126C2—31no—
127C2Dic3×C42⋊C311yescharacteristic
subgroupG/H
center, hypercenterC4D3×C42⋊C3
commutator, hypocenterC3×C42C3×C8
FrattiniC22×C4D3×A4
Fitting, cosocleC3×C43C2×C3
socleC23×C3C4×A4
prime radicalC2×C3×C42⋊C3C4
LCSG ▷ C3×C42
UCSC1 ◁ C4

Complements

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

NH ≅ G/Ntype
2. C42×C3⋊C8C3semidirect
12. C3×C42⋊C3C8semidirect
39. C3×C42C3×C8semidirect
45. C42⋊C3C3⋊C8direct (N × H)
70. C3⋊C8C42⋊C3direct (N × H)
83. C42C3×C3⋊C8semidirect
124. C3C8×C42⋊C3semidirect

Maximal subgroups

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

subgroupindex
C3×C4×C42⋊C32
C42×C3⋊C83
C8×C42⋊C33
A4×C3⋊C84