Finite Group Databasebeta

← C3×#1284 #67844

Subgroups — C3×#1284 #67844

Order 384.

226 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 226 conjugacy classes of subgroups — too many to draw. Only its 68 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×#407C211yesmaximal, characteristic
2C3×#381C211yesmaximal, characteristic
3C3×C4×C22⋊C4C211yesmaximal, characteristic
4#1284C311yesmaximal, characteristic, direct product factor, Sylow
5C23×C3×C4C2211yescharacteristic
6C2×C3×M16—21no—
7C2×C3×C22⋊C4—21no—
8C2×C3×C22⋊C4—21no—
9C2×C3×C42C412yescomplemented
10C3×C22⋊C8—21no—
11C3×C22⋊C8C412yescomplemented
12C3×#95—21no—
13C3×#95—21no—
14C3×#95C412yescomplemented
15#407C2×C311yescharacteristic
16#381C2×C311yescharacteristic
17C4×C22⋊C4C2×C311yescharacteristic
18C24×C3D411yescharacteristic
19C22×C3×C4—22no—
20C22×C3×C4—22no—
21C22×C3×C4—42no—
22C22×C3×C4C2×C411yescharacteristic
23C22×C3×C4C2×C411yescharacteristic
24C22×C3×C4C2×C411yescharacteristic
25C22×C3×C4D411yescharacteristic
26C22×C3×C4D411yescharacteristic
27C22×C3×C4Q811yescharacteristic
28C3×M16—42no—
29C2×C3×C8—22no—
30C3×C22⋊C4—24no—
31C3×C22⋊C4—42no—
32C3×C42—42no—
33C23×C4C22×C311yescharacteristic
34C2×M16—21no—
35C2×C22⋊C4—21no—
36C2×C22⋊C4—21no—
37C2×C42C3×C412yescomplemented
38C22⋊C8—21no—
39C22⋊C8C3×C412yescomplemented
40#95—21no—
41#95—21no—
42#95C3×C412yescomplemented
43C23×C3—22no—
44C23×C3—22no—
45C23×C3—41no—
46C23×C3C22⋊C411yescharacteristic
47C23×C3C22⋊C411yescharacteristic
48C23×C3C4⋊C411yescharacteristic
49C2×C3×C4—22no—
50C2×C3×C4—22no—
51C2×C3×C4—24no—
52C2×C3×C4—41no—
53C2×C3×C4—41no—
54C2×C3×C4—41no—
55C2×C3×C4—41no—
56C2×C3×C4—42no—
57C2×C3×C4—42no—
58C2×C3×C4—42no—
59C2×C3×C4—42no—
60C2×C3×C4—42no—
61C2×C3×C4C4211yescharacteristic
62C2×C3×C4C22⋊C411yescharacteristic
63C2×C3×C4C4⋊C411yescharacteristic
64C2×C3×C4C4⋊C411yescharacteristic
65C3×C8—42no—
66C24C3×D411yescharacteristic
67C22×C4—22no—
68C22×C4—22no—
69C22×C4—42no—
70C22×C4C2×C3×C411yescharacteristic
71C22×C4C2×C3×C411yescharacteristic
72C22×C4C2×C3×C411yescharacteristic
73C22×C4C3×D411yescharacteristic
74C22×C4C3×D411yescharacteristic
75C22×C4C3×Q811yescharacteristic
76M16—42no—
77C2×C8—22no—
78C22⋊C4—24no—
79C22⋊C4—42no—
80C42—42no—
81C22×C3—21no—
82C22×C3—21no—
83C22×C3—21no—
84C22×C3—21no—
85C22×C3—21no—
86C22×C3—21no—
87C22×C3—21no—
88C22×C3—44no—
89C22×C3#9511yescharacteristic
90C22×C3#9912yes—
91C22×C3#10412yes—
92C3×C4—21no—
93C3×C4—21no—
94C3×C4—21no—
95C3×C4—21no—
96C3×C4—44no—
97C3×C4—82no—
98C23—22no—
99C23—22no—
100C23—41no—
101C23C3×C22⋊C411yescharacteristic
102C23C3×C22⋊C411yescharacteristic
103C23C3×C4⋊C411yescharacteristic
104C2×C4—22no—
105C2×C4—22no—
106C2×C4—24no—
107C2×C4—41no—
108C2×C4—41no—
109C2×C4—41no—
110C2×C4—41no—
111C2×C4—42no—
112C2×C4—42no—
113C2×C4—42no—
114C2×C4—42no—
115C2×C4—42no—
116C2×C4C3×C4211yescharacteristic
117C2×C4C3×C22⋊C411yescharacteristic
118C2×C4C3×C4⋊C411yescharacteristic
119C2×C4C3×C4⋊C411yescharacteristic
120C8—42no—
121C2×C3—22no—
122C2×C3—22no—
123C2×C3—41no—
124C2×C3H(3,ℤ/4)11yescharacteristic
125C2×C3#33911yescharacteristic
126C2×C3#34211yescharacteristic
127C22—21no—
128C22—21no—
129C22—21no—
130C22—21no—
131C22—21no—
132C22—21no—
133C22—21no—
134C22—44no—
135C22C3×#9511yescharacteristic
136C22C3×#9912yes—
137C22C3×#10412yes—
138C4—21no—
139C4—21no—
140C4—21no—
141C4—21no—
142C4—44no—
143C4—82no—
144C3#128411yescharacteristic, direct product factor, Sylow
145C2—22no—
146C2—22no—
147C2—41no—
148C2C3×H(3,ℤ/4)11yescharacteristic
149C2C3×#33911yescharacteristic
150C2C3×#34211yescharacteristic
subgroupG/H
center, socleC22×C3#95
commutatorC2×C4C3×C42
Frattini, cosocleC23×C4C22×C3
prime radicalC24×C3D4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C3 ◁ C23×C3×C4 ◁ G

Complements

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

NH ≅ G/Ntype
4. #1284C3direct (N × H)
9. C2×C3×C42C4semidirect
11. C3×C22⋊C8C4semidirect
14. C3×#95C4semidirect
37. C2×C42C3×C4semidirect
39. C22⋊C8C3×C4semidirect
42. #95C3×C4semidirect
144. C3#1284direct (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
C3×C4×C22⋊C42
#12843