Finite Group Databasebeta

← C3⋊D3×#125 #10596158

Subgroups — C3⋊D3×#125 #10596158

Order 576.

678 conjugacy classes of subgroups; only the 199 normal subgroups are shown.

normal subgroups only

This group has 678 conjugacy classes of subgroups — too many to draw. Only its 199 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
1C32×#125C211yesmaximal, characteristic, complemented
2C4⋊C4×C3⋊D3C214yesmaximal
3C4⋊C4×C3⋊D3C212yesmaximal
4#64099C212yesmaximal, complemented
5#64098C214yesmaximal, complemented
6C42×C3⋊D3C211yesmaximal, characteristic
7#64079C211yesmaximal, characteristic, complemented
8D3×#125—34nomaximal
9C2×C4×C3⋊D3C2212yes—
10C2×C4×C3⋊D3C2214yes—
11C2×C4×C3⋊D3C2211yescharacteristic
12C32×C4⋊C4C2214yes—
13C32×C4⋊C4C2212yes—
14C32×C42C2211yescharacteristic
15C4⋊(C3⋊Dic3)C2212yes—
16C4⋊(C3⋊Dic3)C2214yes—
17#3750C2214yes—
18#3750C2214yes—
19#3750C2214yes—
20C4×C3⋊Dic3C2212yes—
21C4×C3⋊Dic3C2211yescharacteristic
22C3×#125D314yescomplemented
23D3×C4⋊C4—316no—
24D3×C4⋊C4—38no—
25#890—38no—
26#889—316no—
27C42×D3—34no—
28#870—34no—
29C22×C3⋊D3C2311yescharacteristic
30C2×C32×C4C2312yes—
31C2×C32×C4C2314yes—
32C2×C32×C4C2311yescharacteristic
33C2×C3⋊Dic3C2312yes—
34C2×C3⋊Dic3C2314yes—
35C2×C3⋊Dic3C2311yescharacteristic
36C4×C3⋊D3—24no—
37C4×C3⋊D3—28no—
38C4×C3⋊D3Q814yes—
39C2×#125—91noSylow
40C2×C4×D3—34no—
41C2×C4×D3—38no—
42C2×C4×D3—316no—
43C3×C4⋊C4C2×D3116yes—
44C3×C4⋊C4C2×D318yes—
45C3×C42C2×D314yes—
46C4⋊Dic3—38no—
47C4⋊Dic3—316no—
48Dic3⋊C4—316no—
49Dic3⋊C4—316no—
50Dic3⋊C4—316no—
51C4×Dic3—38no—
52C4×Dic3—34no—
53C22×C32C2411yescharacteristic
54C2×C3⋊D3C2×Q812yes—
55C2×C3⋊D3#4114yes—
56C32×C4—22no—
57C32×C4—24no—
58C32×C4C2×Q812yes—
59C3⋊Dic3—22no—
60C3⋊Dic3—24no—
61C3⋊Dic3C2×Q812yes—
62#125—94no—
63#125—92no—
64#125—91no—
65#125C3⋊D311yescharacteristic, direct product factor
66C2×C4⋊C4—92no—
67C2×C4⋊C4—94no—
68C2×C42—91no—
69C22×D3—34no—
70C2×C3×C4C22×D318yes—
71C2×C3×C4C22×D3116yes—
72C2×C3×C4C22×D314yes—
73C2×Dic3—34no—
74C2×Dic3—38no—
75C2×Dic3—316no—
76C4×D3—316no—
77C4×D3—616no—
78C4×D3—632no—
79C2×C32C22×Q811yescharacteristic
80C2×C32C2×#4112yes—
81C3⋊D3#12514yesdirect product factor
82C22×C4—91no—
83C22×C4—92no—
84C22×C4—94no—
85C4⋊C4—94no—
86C4⋊C4—94no—
87C4⋊C4—94no—
88C4⋊C4—94no—
89C4⋊C4—92no—
90C4⋊C4C2×C3⋊D314yes—
91C4⋊C4C2×C3⋊D312yes—
92C42—92no—
93C42—91no—
94C42C2×C3⋊D311yescharacteristic
95C22×C3C23×D314yes—
96C2×D3—38no—
97C2×D3—316no—
98C3×C4—28no—
99C3×C4—216no—
100C3×C4D3×Q818yes—
101Dic3—38no—
102Dic3—68no—
103Dic3—616no—
104C32C2×#12511yescharacteristic, complemented, Sylow
105C23—91no—
106C2×C4—91no—
107C2×C4—94no—
108C2×C4—92no—
109C2×C4—94no—
110C2×C4—184no—
111C2×C4—188no—
112C2×C4C22×C3⋊D312yes—
113C2×C4C22×C3⋊D314yes—
114C2×C4C22×C3⋊D311yescharacteristic
115C2×C3C2×D3×Q814yes—
116C2×C3D3×#4118yes—
117D3—316no—
118C22—92no—
119C22—94no—
120C22C23×C3⋊D311yescharacteristic
121C4—22no—
122C4—24no—
123C4—92no—
124C4—182no—
125C4—184no—
126C4Q8×C3⋊D312yes—
127C3D3×#12514yescomplemented
128C2—94no—
129C2C2×Q8×C3⋊D311yescharacteristic
130C2#41×C3⋊D312yes—
subgroupG/H
center, FrattiniC22C23×C3⋊D3
commutator, socle, cosocleC22×C32C24
FittingC32×#125C2
prime radicalC22×C3⋊D3C23
hypercenter#125C3⋊D3
hypocenterC32C2×#125
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ #125

Complements

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

NH ≅ G/Ntype
1. C32×#125C2semidirect
4. #64099C2semidirect
5. #64098C2semidirect
7. #64079C2semidirect
22. C3×#125D3semidirect
65. #125C3⋊D3direct (N × H)
81. C3⋊D3#125direct (N × H)
104. C32C2×#125semidirect
127. C3D3×#125semidirect

Maximal subgroups

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

subgroupindex
C32×#1252
C4⋊C4×C3⋊D32
#640992
#640982
C42×C3⋊D32
#640792
D3×#1253