Finite Group Databasebeta

← C3×#1306 #67866

Subgroups — C3×#1306 #67866

Order 384.

192 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 192 conjugacy classes of subgroups — too many to draw. Only its 64 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×#407C212yesmaximal
2C3×#381C211yesmaximal, characteristic
3#1306C311yesmaximal, characteristic, direct product factor, Sylow
4C23×C3×C4C2211yescharacteristic
5C2×C3×M16—22no—
6C2×C3×C22⋊C4C412yes—
7C3×C22⋊C8—22no—
8C3×C22⋊C8C414yescomplemented
9C3×#95—22no—
10#407C2×C312yes—
11#381C2×C311yescharacteristic
12C24×C3C2×C411yescharacteristic
13C22×C3×C4—22no—
14C22×C3×C4—42no—
15C22×C3×C4C2×C412yes—
16C22×C3×C4D412yes—
17C22×C3×C4D411yescharacteristic
18C22×C3×C4Q811yescharacteristic
19C3×M16—44no—
20C2×C3×C8—24no—
21C3×C22⋊C4—42no—
22C23×C4C22×C311yescharacteristic
23C2×M16—22no—
24C2×C22⋊C4C3×C412yes—
25C22⋊C8—22no—
26C22⋊C8C3×C414yescomplemented
27#95—22no—
28C23×C3—22no—
29C23×C3—42no—
30C23×C3C4211yescharacteristic
31C23×C3C22⋊C411yescharacteristic
32C23×C3C4⋊C411yescharacteristic
33C2×C3×C4—24no—
34C2×C3×C4—42no—
35C2×C3×C4—41no—
36C2×C3×C4—41no—
37C2×C3×C4—44no—
38C2×C3×C4—42no—
39C2×C3×C4C22⋊C412yes—
40C2×C3×C4C4⋊C412yes—
41C3×C8—44no—
42C24C2×C3×C411yescharacteristic
43C22×C4—22no—
44C22×C4—42no—
45C22×C4C2×C3×C412yes—
46C22×C4C3×D412yes—
47C22×C4C3×D411yescharacteristic
48C22×C4C3×Q811yescharacteristic
49M16—44no—
50C2×C8—24no—
51C22⋊C4—42no—
52C22×C3—22no—
53C22×C3—21no—
54C22×C3—21no—
55C22×C3—22no—
56C22×C3—22no—
57C22×C3—44no—
58C22×C3#9511yescharacteristic
59C22×C3#9912yes—
60C3×C4—22no—
61C3×C4—22no—
62C3×C4—82no—
63C23—22no—
64C23—42no—
65C23C3×C4211yescharacteristic
66C23C3×C22⋊C411yescharacteristic
67C23C3×C4⋊C411yescharacteristic
68C2×C4—24no—
69C2×C4—42no—
70C2×C4—41no—
71C2×C4—41no—
72C2×C4—44no—
73C2×C4—42no—
74C2×C4C3×C22⋊C412yes—
75C2×C4C3×C4⋊C412yes—
76C8—44no—
77C2×C3—22no—
78C2×C3—41no—
79C2×C3—41no—
80C2×C3#34211yescharacteristic
81C2×C3#34412yes—
82C22—22no—
83C22—21no—
84C22—21no—
85C22—22no—
86C22—22no—
87C22—44no—
88C22C3×#9511yescharacteristic
89C22C3×#9912yes—
90C4—22no—
91C4—22no—
92C4—82no—
93C3#130611yescharacteristic, direct product factor, Sylow
94C2—22no—
95C2—41no—
96C2—41no—
97C2C3×#34211yescharacteristic
98C2C3×#34412yes—
subgroupG/H
center, socleC22×C3#95
commutatorC23C3×C42
Frattini, cosocleC23×C4C22×C3
prime radicalC24×C3C2×C4
LCSG ▷ C23 ▷ C22 ▷ C1
UCSC1 ◁ C22×C3 ◁ C23×C3×C4 ◁ G

Complements

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

NH ≅ G/Ntype
3. #1306C3direct (N × H)
8. C3×C22⋊C8C4semidirect
26. C22⋊C8C3×C4semidirect
93. C3#1306direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#4072
C3×#3812
#13063