Finite Group Databasebeta

← C3×#1821 #72536

Subgroups — C3×#1821 #72536

Order 384.

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

normal subgroups only

This group has 316 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×C4⋊C4C211yesmaximal, characteristic
2C3×#407C212yesmaximal
3C3×#343C214yesmaximal, complemented
4#1821C311yesmaximal, characteristic, direct product factor, Sylow
5C23×C3×C4C412yes—
6C23×C3×C4C2211yescharacteristic
7C2×C3×M16C2214yes—
8C2×C3×C4⋊C4—22no—
9C2×C3×C4⋊C4—22no—
10C2×C3×C4⋊C4C412yes—
11C2×C3×C4⋊C4C2212yes—
12C3×C22⋊C8—22no—
13C3×C22⋊C8—22no—
14C22×C4⋊C4C2×C311yescharacteristic
15#407C2×C312yes—
16#343C2×C314yescomplemented
17C24×C3C2×C411yescharacteristic
18C22×C3×C4—24no—
19C22×C3×C4—22no—
20C22×C3×C4—22no—
21C22×C3×C4—44no—
22C22×C3×C4C2×C411yescharacteristic
23C22×C3×C4C2×C414yes—
24C22×C3×C4D412yes—
25C22×C3×C4D412yes—
26C22×C3×C4C2311yescharacteristic
27C3×M16—28no—
28C2×C3×C8—24no—
29C3×C4⋊C4—24no—
30C3×C4⋊C4—24no—
31C23×C4C3×C412yes—
32C23×C4C22×C311yescharacteristic
33C2×M16C22×C314yes—
34C2×C4⋊C4—22no—
35C2×C4⋊C4—22no—
36C2×C4⋊C4C3×C412yes—
37C2×C4⋊C4C22×C312yes—
38C22⋊C8—22no—
39C22⋊C8—22no—
40C23×C3—22no—
41C23×C3—22no—
42C23×C3—22no—
43C23×C3C22⋊C411yescharacteristic
44C23×C3C22⋊C411yescharacteristic
45C23×C3C22×C411yescharacteristic
46C2×C3×C4—22no—
47C2×C3×C4—24no—
48C2×C3×C4—24no—
49C2×C3×C4—24no—
50C2×C3×C4—44no—
51C2×C3×C4—44no—
52C2×C3×C4—44no—
53C2×C3×C4C22⋊C412yes—
54C2×C3×C4C2×D412yes—
55C2×C3×C4#4114yes—
56C3×C8—44no—
57C24C2×C3×C411yescharacteristic
58C22×C4—24no—
59C22×C4—22no—
60C22×C4—22no—
61C22×C4—44no—
62C22×C4C2×C3×C411yescharacteristic
63C22×C4C2×C3×C414yes—
64C22×C4C3×D412yes—
65C22×C4C3×D412yes—
66C22×C4C23×C311yescharacteristic
67M16—28no—
68C2×C8—24no—
69C4⋊C4—24no—
70C4⋊C4—24no—
71C22×C3—28no—
72C22×C3—21no—
73C22×C3—21no—
74C22×C3—21no—
75C22×C3—21no—
76C22×C3—21no—
77C22×C3—21no—
78C22×C3#10012yes—
79C22×C3#10112yes—
80C22×C3C2×C22⋊C411yescharacteristic
81C22×C3#11712yes—
82C3×C4—22no—
83C3×C4—44no—
84C3×C4#12314yes—
85C23—22no—
86C23—22no—
87C23—22no—
88C23C3×C22⋊C411yescharacteristic
89C23C3×C22⋊C411yescharacteristic
90C23C22×C3×C411yescharacteristic
91C2×C4—22no—
92C2×C4—24no—
93C2×C4—24no—
94C2×C4—24no—
95C2×C4—44no—
96C2×C4—44no—
97C2×C4—44no—
98C2×C4C3×C22⋊C412yes—
99C2×C4C2×C3×D412yes—
100C2×C4C3×#4114yes—
101C8—44no—
102C2×C3—22no—
103C2×C3—22no—
104C2×C3—22no—
105C2×C3#38111yescharacteristic
106C2×C3C2×#10011yescharacteristic
107C2×C3C2×#10111yescharacteristic
108C22—28no—
109C22—21no—
110C22—21no—
111C22—21no—
112C22—21no—
113C22—21no—
114C22—21no—
115C22C3×#10012yes—
116C22C3×#10112yes—
117C22C2×C3×C22⋊C411yescharacteristic
118C22C3×#11712yes—
119C4—22no—
120C4—44no—
121C4C3×#12314yes—
122C3#182111yescharacteristic, direct product factor, Sylow
123C2—22no—
124C2—22no—
125C2—22no—
126C2C3×#38111yescharacteristic
127C2C2×C3×#10011yescharacteristic
128C2C2×C3×#10111yescharacteristic
subgroupG/H
center, socleC22×C3C2×C22⋊C4
commutatorC23C22×C3×C4
Frattini, cosocleC22×C4C23×C3
prime radicalC24×C3C2×C4
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C3 ◁ C23×C3×C4 ◁ G

Complements

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

NH ≅ G/Ntype
3. C3×#343C2semidirect
4. #1821C3direct (N × H)
16. #343C2×C3semidirect
122. C3#1821direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×C4⋊C42
C3×#4072
C3×#3432
#18213