Finite Group Databasebeta

← #2823⋊C3 #73206

Subgroups — #2823⋊C3 #73206

Order 384.

116 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#126⋊C3C212yesmaximal, complemented
2#384⋊C3C211yesmaximal, characteristic, complemented
3#2823C311yesmaximal, characteristic, complemented, Sylow
4D4×A4—41nomaximal
5#126⋊C3—22no—
6C2×C42⋊C3C2211yescharacteristic
7C2×#126C2×C312yescomplemented
8#398—31no—
9#396—32no—
10#394—31no—
11#384C2×C311yescharacteristic, complemented
12C22×A4—42no—
13C4×A4—41no—
14C42⋊C3D411yescharacteristic, complemented
15C22×D4A411yescharacteristic
16#126—22no—
17#126—62no—
18C2×C4⋊C4—32no—
19C2×C4⋊C4—31no—
20C2×C4⋊C4—31no—
21C2×C4⋊C4—31no—
22C2×C22⋊C4—32no—
23C2×C22⋊C4—32no—
24C2×C42C22×C311yescharacteristic
25#95—31no—
26#95—31no—
27C2×A4—41no—
28C2×A4—82no—
29C3×D4—161no—
30C24C2×A412yes—
31C2×D4—121no—
32C22×C4—31no—
33C22×C4—32no—
34C22×C4—31no—
35C22×C4C2×A411yescharacteristic
36C4⋊C4—62no—
37C4⋊C4—62no—
38C4⋊C4—121no—
39C4⋊C4—121no—
40C4⋊C4—121no—
41C22⋊C4—62no—
42C22⋊C4—62no—
43C22⋊C4—122no—
44C42—31no—
45C42C3×D411yescharacteristic, complemented
46C22×C3—162no—
47A4—41no—
48C3×C4—161no—
49C23—22no—
50C23—62no—
51C23—62no—
52C23C22×A411yescharacteristic
53D4—41no—
54D4—121no—
55C2×C4—31no—
56C2×C4—31no—
57C2×C4—61no—
58C2×C4—61no—
59C2×C4—61no—
60C2×C4—62no—
61C2×C4—62no—
62C2×C4—61no—
63C2×C4—62no—
64C2×C4—62no—
65C2×C3—161no—
66C2×C3—322no—
67C22—31no—
68C22—31no—
69C22—42no—
70C22—122no—
71C22—122no—
72C22D4×A411yescharacteristic
73C4—41no—
74C4—61no—
75C4—61no—
76C4—122no—
77C4—121no—
78C3—161noSylow
79C2—31no—
80C2—31no—
81C2—82no—
82C2#560⋊C311yescharacteristic
subgroupG/H
center, hypercenterC2#560⋊C3
commutator, cosocleC2×C42C22×C3
Frattini, socleC23C22×A4
Fitting#2823C3
hypocenterC42C3×D4
LCSG ▷ C2×C42 ▷ C42
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
1. C2×#126⋊C3C2semidirect
2. #384⋊C3C2semidirect
3. #2823C3semidirect
7. C2×#126C2×C3semidirect
11. #384C2×C3semidirect
14. C42⋊C3D4semidirect
45. C42C3×D4semidirect

Maximal subgroups

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

subgroupindex
C2×#126⋊C32
#384⋊C32
#28233
D4×A44