Finite Group Databasebeta

← C3×#1819 #72534

Subgroups — C3×#1819 #72534

Order 384.

504 conjugacy classes of subgroups; only the 112 normal subgroups are shown.

normal subgroups only

This group has 504 conjugacy classes of subgroups — too many to draw. Only its 112 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
1C22×C3×C22⋊C4C211yesmaximal, characteristic
2C3×#379C212yesmaximal
3C3×#342C214yesmaximal, complemented
4#1819C311yesmaximal, characteristic, direct product factor, Sylow
5C25×C3C2211yescharacteristic
6C23×C3×C4C412yescomplemented
7C2×C3×C22⋊C4—24no—
8C2×C3×C22⋊C4—24no—
9C2×C3×C22⋊C4C412yescomplemented
10C2×C3×C22⋊C4C2214yes—
11C2×C3×C22⋊C4C2212yes—
12C22×C22⋊C4C2×C311yescharacteristic
13#379C2×C312yes—
14#342C2×C314yescomplemented
15C24×C3—24no—
16C24×C3—44no—
17C24×C3C2×C411yescharacteristic
18C24×C3C2×C411yescharacteristic
19C24×C3D414yes—
20C24×C3C2311yescharacteristic
21C22×C3×C4—22no—
22C22×C3×C4—22no—
23C22×C3×C4—24no—
24C22×C3×C4—44no—
25C22×C3×C4C2×C414yes—
26C3×C22⋊C4—24no—
27C3×C22⋊C4—24no—
28C3×C22⋊C4—28no—
29C3×C22⋊C4—48no—
30C25C22×C311yescharacteristic
31C23×C4C3×C412yescomplemented
32C2×C22⋊C4—24no—
33C2×C22⋊C4—24no—
34C2×C22⋊C4C3×C412yescomplemented
35C2×C22⋊C4C22×C314yes—
36C2×C22⋊C4C22×C312yes—
37C23×C3—24no—
38C23×C3—22no—
39C23×C3—28no—
40C23×C3—22no—
41C23×C3—28no—
42C23×C3—42no—
43C23×C3—44no—
44C23×C3—42no—
45C23×C3—416no—
46C23×C3C22⋊C412yes—
47C23×C3C22⋊C412yes—
48C23×C3C22×C411yescharacteristic
49C23×C3C2×D412yes—
50C23×C3#4114yes—
51C2×C3×C4—24no—
52C2×C3×C4—44no—
53C2×C3×C4—44no—
54C2×C3×C4—44no—
55C2×C3×C4—48no—
56C2×C3×C4—44no—
57C24—24no—
58C24—44no—
59C24C2×C3×C411yescharacteristic
60C24C2×C3×C411yescharacteristic
61C24C3×D414yes—
62C24C23×C311yescharacteristic
63C22×C4—22no—
64C22×C4—22no—
65C22×C4—24no—
66C22×C4—44no—
67C22×C4C2×C3×C414yes—
68C22⋊C4—24no—
69C22⋊C4—24no—
70C22⋊C4—28no—
71C22⋊C4—48no—
72C22×C3—28no—
73C22×C3—22no—
74C22×C3—22no—
75C22×C3—22no—
76C22×C3—24no—
77C22×C3—22no—
78C22×C3—24no—
79C22×C3—44no—
80C22×C3—416no—
81C22×C3—44no—
82C22×C3#9914yes—
83C22×C3C2×C22⋊C411yescharacteristic
84C22×C3#11712yes—
85C22×C3#12314yes—
86C3×C4—44no—
87C3×C4—84no—
88C23—24no—
89C23—22no—
90C23—28no—
91C23—22no—
92C23—28no—
93C23—42no—
94C23—44no—
95C23—42no—
96C23—416no—
97C23C3×C22⋊C412yes—
98C23C3×C22⋊C412yes—
99C23C22×C3×C411yescharacteristic
100C23C2×C3×D412yes—
101C23C3×#4114yes—
102C2×C4—24no—
103C2×C4—44no—
104C2×C4—44no—
105C2×C4—44no—
106C2×C4—48no—
107C2×C4—44no—
108C2×C3—24no—
109C2×C3—24no—
110C2×C3—22no—
111C2×C3—42no—
112C2×C3#38111yescharacteristic
113C2×C3C2×#9912yes—
114C22—28no—
115C22—22no—
116C22—22no—
117C22—22no—
118C22—24no—
119C22—22no—
120C22—24no—
121C22—44no—
122C22—416no—
123C22—44no—
124C22C3×#9914yes—
125C22C2×C3×C22⋊C411yescharacteristic
126C22C3×#11712yes—
127C22C3×#12314yes—
128C4—44no—
129C4—84no—
130C3#181911yescharacteristic, direct product factor, Sylow
131C2—24no—
132C2—24no—
133C2—22no—
134C2—42no—
135C2C3×#38111yescharacteristic
136C2C2×C3×#9912yes—
subgroupG/H
center, socleC22×C3C2×C22⋊C4
commutatorC23C22×C3×C4
Frattini, cosocleC24C23×C3
prime radicalC25×C3C22
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C3 ◁ C25×C3 ◁ G

Complements

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

NH ≅ G/Ntype
3. C3×#342C2semidirect
4. #1819C3direct (N × H)
6. C23×C3×C4C4semidirect
9. C2×C3×C22⋊C4C4semidirect
14. #342C2×C3semidirect
31. C23×C4C3×C4semidirect
34. C2×C22⋊C4C3×C4semidirect
130. C3#1819direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×C22⋊C42
C3×#3792
C3×#3422
#18193