Finite Group Databasebeta

← C3×#1466 #72181

Subgroups — C3×#1466 #72181

Order 384.

300 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 300 conjugacy classes of subgroups — too many to draw. Only its 100 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
1C2×C3×C4×D4C211yesmaximal, characteristic
2C3×#432C212yesmaximal, complemented
3C3×#323C214yesmaximal, complemented
4#1466C311yesmaximal, characteristic, direct product factor, Sylow
5C22×C3×D4C411yescharacteristic
6C23×C3×C4C412yes—
7C3×C4×D4—22no—
8C3×C4×D4—22no—
9C2×C3×C4⋊C4C411yescharacteristic
10C2×C3×C22⋊C4C2212yes—
11C2×C3×C42C2211yescharacteristic
12C3×C4⋊C8—22no—
13C3×C22⋊C8C2214yes—
14C3×#97—22no—
15C2×C4×D4C2×C311yescharacteristic
16#432C2×C312yescomplemented
17#323C2×C314yescomplemented
18C24×C3C2×C412yes—
19C2×C3×D4—24no—
20C2×C3×D4—22no—
21C22×C3×C4—22no—
22C22×C3×C4—22no—
23C22×C3×C4—44no—
24C22×C3×C4C2×C411yescharacteristic
25C22×C3×C4C2×C411yescharacteristic
26C22×C3×C4C2×C412yes—
27C22×C3×C4C2311yescharacteristic
28C2×C3×C8—24no—
29C3×C4⋊C4—22no—
30C3×C22⋊C4—24no—
31C3×C42D412yes—
32C3×C42D412yes—
33C22×D4C3×C411yescharacteristic
34C23×C4C3×C412yes—
35C4×D4—22no—
36C4×D4—22no—
37C2×C4⋊C4C3×C411yescharacteristic
38C2×C22⋊C4C22×C312yes—
39C2×C42C22×C311yescharacteristic
40C4⋊C8—22no—
41C22⋊C8C22×C314yes—
42#97—22no—
43C23×C3—22no—
44C23×C3—22no—
45C23×C3—42no—
46C23×C3—42no—
47C23×C3M1614yes—
48C23×C3C22×C411yescharacteristic
49C3×D4—28no—
50C2×C3×C4—22no—
51C2×C3×C4—22no—
52C2×C3×C4—22no—
53C2×C3×C4—41no—
54C2×C3×C4—44no—
55C2×C3×C4—44no—
56C2×C3×C4—42no—
57C2×C3×C4C22⋊C412yes—
58C2×C3×C4C22⋊C411yescharacteristic
59C2×C3×C4C22⋊C411yescharacteristic
60C2×C3×C4C2×D412yes—
61C3×C8—44no—
62C24C2×C3×C412yes—
63C2×D4—24no—
64C2×D4—22no—
65C22×C4—22no—
66C22×C4—22no—
67C22×C4—44no—
68C22×C4C2×C3×C411yescharacteristic
69C22×C4C2×C3×C411yescharacteristic
70C22×C4C2×C3×C412yes—
71C22×C4C23×C311yescharacteristic
72C2×C8—24no—
73C4⋊C4—22no—
74C22⋊C4—24no—
75C42C3×D412yes—
76C42C3×D412yes—
77C22×C3—21no—
78C22×C3—21no—
79C22×C3—24no—
80C22×C3—44no—
81C22×C3—44no—
82C22×C3—42no—
83C22×C3—42no—
84C22×C3C2×C22⋊C411yescharacteristic
85C22×C3C2×M1612yes—
86C3×C4—22no—
87C3×C4—22no—
88C3×C4—21no—
89C3×C4—42no—
90C3×C4#10012yes—
91C23—22no—
92C23—22no—
93C23—42no—
94C23—42no—
95C23C3×M1614yes—
96C23C22×C3×C411yescharacteristic
97D4—28no—
98C2×C4—22no—
99C2×C4—22no—
100C2×C4—22no—
101C2×C4—41no—
102C2×C4—44no—
103C2×C4—44no—
104C2×C4—42no—
105C2×C4C3×C22⋊C412yes—
106C2×C4C3×C22⋊C411yescharacteristic
107C2×C4C3×C22⋊C411yescharacteristic
108C2×C4C2×C3×D412yes—
109C8—44no—
110C2×C3—22no—
111C2×C3—44no—
112C2×C3#40711yescharacteristic
113C2×C3#41011yescharacteristic
114C2×C3C2×#10011yescharacteristic
115C22—21no—
116C22—21no—
117C22—24no—
118C22—44no—
119C22—44no—
120C22—42no—
121C22—42no—
122C22C2×C3×C22⋊C411yescharacteristic
123C22C2×C3×M1612yes—
124C4—22no—
125C4—22no—
126C4—21no—
127C4—42no—
128C4C3×#10012yes—
129C3#146611yescharacteristic, direct product factor, Sylow
130C2—22no—
131C2—44no—
132C2C3×#40711yescharacteristic
133C2C3×#41011yescharacteristic
134C2C2×C3×#10011yescharacteristic
subgroupG/H
center, socleC22×C3C2×C22⋊C4
commutatorC23C22×C3×C4
Frattini, cosocleC22×C4C23×C3
prime radicalC22×C3×D4C4
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C3 ◁ C2×C3×C42 ◁ G

Complements

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

NH ≅ G/Ntype
2. C3×#432C2semidirect
3. C3×#323C2semidirect
4. #1466C3direct (N × H)
16. #432C2×C3semidirect
17. #323C2×C3semidirect
129. C3#1466direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×C4×D42
C3×#4322
C3×#3232
#14663