Finite Group Databasebeta

← C2×#376⋊C3 #73161

Subgroups — C2×#376⋊C3 #73161

Order 384.

175 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#376⋊C3C212yesmaximal, direct product factor
2C2×#95⋊C3C211yesmaximal, characteristic
3C2×#376C311yesmaximal, characteristic, complemented, Sylow
4C2×C4×A4—41nomaximal
5#95⋊C3C2211yescharacteristic
6C22×C42—31no—
7#376—32no—
8#376C2×C312yescomplemented
9C2×#95—31no—
10C2×#95C2×C311yescharacteristic
11C22×A4—41no—
12C4×A4—42no—
13C23×C4—31no—
14C23×C4—31no—
15C23×C4A411yescharacteristic
16C2×C42—32no—
17C2×C42—34no—
18C2×C42—32no—
19C2×C42—32no—
20C2×C42—32no—
21#95—32no—
22#95—31no—
23#95—32no—
24#95C22×C311yescharacteristic
25C2×A4—42no—
26C2×A4—41no—
27C2×C3×C4—161no—
28C24C2×A411yescharacteristic
29C22×C4—31no—
30C22×C4—31no—
31C22×C4—32no—
32C22×C4—32no—
33C22×C4—32no—
34C22×C4—32no—
35C22×C4—32no—
36C22×C4—31no—
37C22×C4—31no—
38C22×C4—32no—
39C22×C4—64no—
40C22×C4—62no—
41C22×C4—62no—
42C22×C4C2×A412yes—
43C42—34no—
44C42—34no—
45C42—34no—
46C42—34no—
47C22×C3—161no—
48A4—41no—
49C3×C4—162no—
50C23—31no—
51C23—32no—
52C23—31no—
53C23#41⋊C312yes—
54C23C22×A411yescharacteristic
55C2×C4—32no—
56C2×C4—31no—
57C2×C4—32no—
58C2×C4—32no—
59C2×C4—32no—
60C2×C4—32no—
61C2×C4—32no—
62C2×C4—34no—
63C2×C4—62no—
64C2×C4—62no—
65C2×C4—62no—
66C2×C4—64no—
67C2×C4—64no—
68C2×C4—64no—
69C2×C4—64no—
70C2×C4—62no—
71C2×C4C42⋊C311yescharacteristic
72C2×C3—162no—
73C2×C3—161no—
74C22—31no—
75C22—32no—
76C22—32no—
77C22—32no—
78C22—32no—
79C22—31no—
80C22—31no—
81C22C2×C42⋊C311yescharacteristic
82C22C2×#41⋊C311yescharacteristic
83C4—32no—
84C4—62no—
85C4—62no—
86C4—64no—
87C4C2×C42⋊C312yes—
88C3—161noSylow
89C2—31no—
90C2—31no—
91C2—32no—
92C2#376⋊C312yesdirect product factor
93C2C22×C42⋊C311yescharacteristic
subgroupG/H
center, hypercenterC2×C4C42⋊C3
commutator, cosocle, hypocenter#95C22×C3
FrattiniC23C22×A4
FittingC2×#376C3
socleC24C2×A4
prime radicalC2×#95⋊C3C2
LCSG ▷ #95
UCSC1 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
1. #376⋊C3C2direct (N × H)
3. C2×#376C3semidirect
8. #376C2×C3semidirect
92. C2#376⋊C3direct (N × H)

Maximal subgroups

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

subgroupindex
#376⋊C32
C2×#95⋊C32
C2×#3763
C2×C4×A44