Finite Group Databasebeta

← C3×#1326 #67886

Subgroups — C3×#1326 #67886

Order 384.

158 conjugacy classes of subgroups; only the 44 normal subgroups are shown.

normal subgroups only

This group has 158 conjugacy classes of subgroups — too many to draw. Only its 44 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×#385C211yesmaximal, characteristic
2C3×#323C211yesmaximal, characteristic
3C3×#323C211yesmaximal, characteristic
4#1326C311yesmaximal, characteristic, direct product factor, Sylow
5C23×C3×C4C411yescharacteristic
6C2×C3×C4⋊C4—21no—
7C2×C3×C22⋊C4C411yescharacteristic
8C2×C3×C22⋊C4C2211yescharacteristic
9C3×C22⋊C8—21no—
10C3×C22⋊C8—21no—
11C3×#95—21no—
12#385C2×C311yescharacteristic
13#323C2×C311yescharacteristic
14#323C2×C311yescharacteristic
15C24×C3C2×C411yescharacteristic
16C22×C3×C4—21no—
17C22×C3×C4—21no—
18C22×C3×C4—42no—
19C22×C3×C4—41no—
20C22×C3×C4D411yescharacteristic
21C22×C3×C4D411yescharacteristic
22C2×C3×C8—41no—
23C2×C3×C8—41no—
24C3×C4⋊C4—42no—
25C3×C22⋊C4—21no—
26C3×C22⋊C4—41no—
27C3×C22⋊C4C812yescomplemented
28C23×C4C3×C411yescharacteristic
29C2×C4⋊C4—21no—
30C2×C22⋊C4C3×C411yescharacteristic
31C2×C22⋊C4C22×C311yescharacteristic
32C22⋊C8—21no—
33C22⋊C8—21no—
34#95—21no—
35C23×C3—21no—
36C23×C3—21no—
37C23×C3—41no—
38C23×C3—41no—
39C23×C3C22⋊C411yescharacteristic
40C23×C3C2×C811yescharacteristic
41C23×C3M1611yescharacteristic
42C2×C3×C4—22no—
43C2×C3×C4—22no—
44C2×C3×C4—21no—
45C2×C3×C4—21no—
46C2×C3×C4—41no—
47C2×C3×C4—41no—
48C2×C3×C4—41no—
49C2×C3×C4—42no—
50C2×C3×C4—41no—
51C2×C3×C4—41no—
52C2×C3×C4—41no—
53C2×C3×C4—42no—
54C3×C8—81no—
55C3×C8—81no—
56C24C2×C3×C411yescharacteristic
57C22×C4—21no—
58C22×C4—21no—
59C22×C4—42no—
60C22×C4—41no—
61C22×C4C3×D411yescharacteristic
62C22×C4C3×D411yescharacteristic
63C2×C8—41no—
64C2×C8—41no—
65C4⋊C4—42no—
66C22⋊C4—21no—
67C22⋊C4—41no—
68C22⋊C4C3×C812yescomplemented
69C22×C3—21no—
70C22×C3—21no—
71C22×C3—21no—
72C22×C3—21no—
73C22×C3—41no—
74C22×C3—41no—
75C22×C3—42no—
76C22×C3—41no—
77C22×C3—41no—
78C22×C3C22⋊C811yescharacteristic
79C22×C3#9911yescharacteristic
80C22×C3#10111yescharacteristic
81C3×C4—42no—
82C3×C4—41no—
83C3×C4—42no—
84C3×C4—41no—
85C23—21no—
86C23—21no—
87C23—41no—
88C23—41no—
89C23C3×C22⋊C411yescharacteristic
90C23C2×C3×C811yescharacteristic
91C23C3×M1611yescharacteristic
92C2×C4—22no—
93C2×C4—22no—
94C2×C4—21no—
95C2×C4—21no—
96C2×C4—41no—
97C2×C4—41no—
98C2×C4—41no—
99C2×C4—42no—
100C2×C4—41no—
101C2×C4—41no—
102C2×C4—41no—
103C2×C4—42no—
104C8—81no—
105C8—81no—
106C2×C3—21no—
107C2×C3—21no—
108C2×C3—41no—
109C2×C3—41no—
110C2×C3#32411yescharacteristic
111C2×C3AΣL(1,𝔽16)11yescharacteristic
112C2×C3#35211yescharacteristic
113C22—21no—
114C22—21no—
115C22—21no—
116C22—21no—
117C22—41no—
118C22—41no—
119C22—42no—
120C22—41no—
121C22—41no—
122C22C3×C22⋊C811yescharacteristic
123C22C3×#9911yescharacteristic
124C22C3×#10111yescharacteristic
125C4—42no—
126C4—41no—
127C4—42no—
128C4—41no—
129C3#132611yescharacteristic, direct product factor, Sylow
130C2—21no—
131C2—21no—
132C2—41no—
133C2—41no—
134C2C3×#32411yescharacteristic
135C2C3×AΣL(1,𝔽16)11yescharacteristic
136C2C3×#35211yescharacteristic
subgroupG/H
center, socleC22×C3#99
commutatorC23C2×C3×C8
Frattini, cosocleC2×C22⋊C4C22×C3
prime radicalC24×C3C2×C4
LCSG ▷ C23 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C3 ◁ C23×C3 ◁ C2×C3×C22⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
4. #1326C3direct (N × H)
27. C3×C22⋊C4C8semidirect
68. C22⋊C4C3×C8semidirect
129. C3#1326direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#3852
C3×#3232
#13263