Finite Group Databasebeta

← #2834⋊C3 #73208

Subgroups — #2834⋊C3 #73208

Order 384.

97 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#401⋊C3C212yesmaximal, complemented
2#399⋊C3C211yesmaximal, characteristic
3#2834C311yesmaximal, characteristic, complemented, Sylow
4C2×C4×A4—41nomaximal
5#95⋊C3C2211yescharacteristic
6#401C2×C312yescomplemented
7#399C2×C311yescharacteristic
8#398—32no—
9#397—31no—
10#385—31no—
11C22×A4—41no—
12C4×A4—42no—
13C23×C4A411yescharacteristic
14C2×C4⋊C4—31no—
15C2×C4⋊C4—31no—
16C2×C4⋊C4—32no—
17C2×C22⋊C4—31no—
18C2×C22⋊C4—31no—
19#95—32no—
20#95—31no—
21#95—32no—
22#95C22×C311yescharacteristic
23C2×A4—42no—
24C2×A4—41no—
25C2×C3×C4—161no—
26C24C2×A411yescharacteristic
27C22×C4—31no—
28C22×C4—32no—
29C22×C4—31no—
30C22×C4—121no—
31C22×C4C2×A412yes—
32C4⋊C4—122no—
33C4⋊C4—121no—
34C4⋊C4—121no—
35C22⋊C4—62no—
36C22⋊C4—121no—
37C22×C3—161no—
38A4—41no—
39C3×C4—162no—
40C23—61no—
41C23—61no—
42C23#41⋊C312yes—
43C23C22×A411yescharacteristic
44C2×C4—41no—
45C2×C4—62no—
46C2×C4—61no—
47C2×C4—61no—
48C2×C4—62no—
49C2×C4—62no—
50C2×C4—62no—
51C2×C4—62no—
52C2×C4—62no—
53C2×C4—121no—
54C2×C3—162no—
55C2×C3—161no—
56C22—31no—
57C22—31no—
58C22—41no—
59C22—62no—
60C22—121no—
61C22C2×#41⋊C311yescharacteristic
62C4—42no—
63C4—122no—
64C4—121no—
65C4—121no—
66C3—161noSylow
67C2—31no—
68C2—31no—
69C2—42no—
70C2#560⋊C311yescharacteristic
subgroupG/H
center, hypercenterC2#560⋊C3
commutator, cosocle, hypocenter#95C22×C3
Frattini, socleC23C22×A4
Fitting#2834C3
prime radical#399⋊C3C2
LCSG ▷ #95
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
1. #401⋊C3C2semidirect
3. #2834C3semidirect
6. #401C2×C3semidirect

Maximal subgroups

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

subgroupindex
#401⋊C32
#399⋊C32
#28343
C2×C4×A44