Finite Group Databasebeta

← C2×#383⋊C3 #73169

Subgroups — C2×#383⋊C3 #73169

Order 384.

144 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C42⋊C3C211yesmaximal, characteristic
2#383⋊C3C212yesmaximal, direct product factor
3C2×#383C311yesmaximal, characteristic, complemented, Sylow
4C2×C4×A4—41nomaximal
5C2×C42⋊C3C412yescomplemented
6C2×C42⋊C3C2211yescharacteristic
7C22×C42C2×C311yescharacteristic
8#383—32no—
9#383C2×C312yescomplemented
10C2×#95—31no—
11C2×#95—31no—
12C22×A4—41no—
13C4×A4—42no—
14C42⋊C3C2×C411yescharacteristic, complemented
15C23×C4—31no—
16C23×C4—31no—
17C23×C4A411yescharacteristic
18C2×C42—31no—
19C2×C42—32no—
20C2×C42C3×C412yescomplemented
21C2×C42C22×C311yescharacteristic
22#95—32no—
23#95—32no—
24#95—32no—
25#95—32no—
26C2×A4—42no—
27C2×A4—41no—
28C2×C3×C4—161no—
29C24C2×A411yescharacteristic
30C22×C4—32no—
31C22×C4—32no—
32C22×C4—31no—
33C22×C4—31no—
34C22×C4—32no—
35C22×C4—61no—
36C22×C4—62no—
37C22×C4—61no—
38C22×C4—61no—
39C22×C4—64no—
40C22×C4—61no—
41C22×C4—61no—
42C22×C4—61no—
43C22×C4C2×A412yes—
44C42—32no—
45C42—31no—
46C42—32no—
47C42C2×C3×C411yescharacteristic, complemented
48C22×C3—161no—
49A4—41no—
50C3×C4—162no—
51C23—32no—
52C23—31no—
53C23—31no—
54C23C4×A412yes—
55C23C22×A411yescharacteristic
56C2×C4—31no—
57C2×C4—32no—
58C2×C4—31no—
59C2×C4—41no—
60C2×C4—62no—
61C2×C4—61no—
62C2×C4—61no—
63C2×C4—62no—
64C2×C4—62no—
65C2×C4—62no—
66C2×C4—62no—
67C2×C4—61no—
68C2×C4—61no—
69C2×C4—64no—
70C2×C4—62no—
71C2×C4—121no—
72C2×C4—122no—
73C2×C4—122no—
74C2×C3—162no—
75C2×C3—161no—
76C22—31no—
77C22—32no—
78C22—32no—
79C22—32no—
80C22—32no—
81C22—31no—
82C22—31no—
83C22#126⋊C311yescharacteristic
84C22C2×C4×A411yescharacteristic
85C4—42no—
86C4—61no—
87C4—62no—
88C4—61no—
89C4—122no—
90C3—161noSylow
91C2—31no—
92C2—31no—
93C2—32no—
94C2#383⋊C312yesdirect product factor
95C2C2×#126⋊C311yescharacteristic
subgroupG/H
center, hypercenterC22#126⋊C3
commutator, hypocenterC42C2×C3×C4
FrattiniC23C22×A4
FittingC2×#383C3
socleC24C2×A4
prime radicalC22×C42⋊C3C2
cosocleC2×C42C22×C3
LCSG ▷ C42
UCSC1 ◁ C22

Complements

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

NH ≅ G/Ntype
2. #383⋊C3C2direct (N × H)
3. C2×#383C3semidirect
5. C2×C42⋊C3C4semidirect
9. #383C2×C3semidirect
14. C42⋊C3C2×C4semidirect
20. C2×C42C3×C4semidirect
47. C42C2×C3×C4semidirect
94. C2#383⋊C3direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C42⋊C32
#383⋊C32
C2×#3833
C2×C4×A44