Finite Group Databasebeta

← C3×#1463 #72178

Subgroups — C3×#1463 #72178

Order 384.

312 conjugacy classes of subgroups; only the 104 normal subgroups are shown.

normal subgroups only

This group has 312 conjugacy classes of subgroups — too many to draw. Only its 104 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×#324C214yesmaximal, complemented
4#1463C311yesmaximal, characteristic, direct product factor, Sylow
5C23×C3×C4C411yescharacteristic
6C23×C3×C4C411yescharacteristic
7C23×C3×C4C2211yescharacteristic
8C2×C3×M16—22no—
9C2×C3×C4⋊C4—22no—
10C2×C3×C4⋊C4—22no—
11C2×C3×C4⋊C4C412yes—
12C2×C3×C4⋊C4C2212yes—
13C3×C22⋊C8—22no—
14C3×C22⋊C8C2214yes—
15C22×C4⋊C4C2×C311yescharacteristic
16#407C2×C312yes—
17#324C2×C314yescomplemented
18C24×C3C2×C411yescharacteristic
19C22×C3×C4—21no—
20C22×C3×C4—21no—
21C22×C3×C4—24no—
22C22×C3×C4—21no—
23C22×C3×C4—21no—
24C22×C3×C4—42no—
25C22×C3×C4—42no—
26C22×C3×C4C2×C412yes—
27C22×C3×C4C2×C412yes—
28C22×C3×C4C2×C411yescharacteristic
29C22×C3×C4D412yes—
30C22×C3×C4D412yes—
31C22×C3×C4C2311yescharacteristic
32C3×M16—44no—
33C2×C3×C8—24no—
34C3×C4⋊C4—24no—
35C3×C4⋊C4—24no—
36C23×C4C3×C411yescharacteristic
37C23×C4C3×C411yescharacteristic
38C23×C4C22×C311yescharacteristic
39C2×M16—22no—
40C2×C4⋊C4—22no—
41C2×C4⋊C4—22no—
42C2×C4⋊C4C3×C412yes—
43C2×C4⋊C4C22×C312yes—
44C22⋊C8—22no—
45C22⋊C8C22×C314yes—
46C23×C3—22no—
47C23×C3—22no—
48C23×C3—22no—
49C23×C3C22⋊C411yescharacteristic
50C23×C3C22⋊C411yescharacteristic
51C23×C3C22×C411yescharacteristic
52C2×C3×C4—24no—
53C2×C3×C4—24no—
54C2×C3×C4—24no—
55C2×C3×C4—22no—
56C2×C3×C4—22no—
57C2×C3×C4—22no—
58C2×C3×C4—41no—
59C2×C3×C4—42no—
60C2×C3×C4—41no—
61C2×C3×C4—42no—
62C2×C3×C4—42no—
63C2×C3×C4—42no—
64C2×C3×C4C22⋊C412yes—
65C2×C3×C4M1614yescomplemented
66C2×C3×C4C2×D412yes—
67C3×C8—44no—
68C24C2×C3×C411yescharacteristic
69C22×C4—21no—
70C22×C4—21no—
71C22×C4—24no—
72C22×C4—21no—
73C22×C4—21no—
74C22×C4—42no—
75C22×C4—42no—
76C22×C4C2×C3×C412yes—
77C22×C4C2×C3×C412yes—
78C22×C4C2×C3×C411yescharacteristic
79C22×C4C3×D412yes—
80C22×C4C3×D412yes—
81C22×C4C23×C311yescharacteristic
82M16—44no—
83C2×C8—24no—
84C4⋊C4—24no—
85C4⋊C4—24no—
86C22×C3—28no—
87C22×C3—21no—
88C22×C3—21no—
89C22×C3—21no—
90C22×C3—21no—
91C22×C3—21no—
92C22×C3—21no—
93C22×C3#9912yes—
94C22×C3#10112yes—
95C22×C3C2×C22⋊C411yescharacteristic
96C22×C3C2×M1612yes—
97C3×C4—24no—
98C3×C4—22no—
99C3×C4—22no—
100C3×C4—42no—
101C23—22no—
102C23—22no—
103C23—22no—
104C23C3×C22⋊C411yescharacteristic
105C23C3×C22⋊C411yescharacteristic
106C23C22×C3×C411yescharacteristic
107C2×C4—24no—
108C2×C4—24no—
109C2×C4—24no—
110C2×C4—22no—
111C2×C4—22no—
112C2×C4—22no—
113C2×C4—41no—
114C2×C4—42no—
115C2×C4—41no—
116C2×C4—42no—
117C2×C4—42no—
118C2×C4—42no—
119C2×C4C3×C22⋊C412yes—
120C2×C4C3×M1614yescomplemented
121C2×C4C2×C3×D412yes—
122C8—44no—
123C2×C3—22no—
124C2×C3—22no—
125C2×C3—22no—
126C2×C3#40711yescharacteristic
127C2×C3C2×#9911yescharacteristic
128C2×C3C2×#10111yescharacteristic
129C22—28no—
130C22—21no—
131C22—21no—
132C22—21no—
133C22—21no—
134C22—21no—
135C22—21no—
136C22C3×#9912yes—
137C22C3×#10112yes—
138C22C2×C3×C22⋊C411yescharacteristic
139C22C2×C3×M1612yes—
140C4—24no—
141C4—22no—
142C4—22no—
143C4—42no—
144C3#146311yescharacteristic, direct product factor, Sylow
145C2—22no—
146C2—22no—
147C2—22no—
148C2C3×#40711yescharacteristic
149C2C2×C3×#9911yescharacteristic
150C2C2×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×#324C2semidirect
4. #1463C3direct (N × H)
17. #324C2×C3semidirect
65. C2×C3×C4M16semidirect
120. C2×C4C3×M16semidirect
144. C3#1463direct (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×#3242
#14633