Finite Group Databasebeta

← #71509

Subgroups — #71509

Order 384.

112 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#508C211yesmaximal, characteristic, complemented
2C2×D48C211yesmaximal, characteristic, complemented
3#4521C212yesmaximal, complemented
4#4519C212yesmaximal, complemented
5#4499C211yesmaximal, characteristic, complemented
6#2263—31nomaximal, Sylow
7C3×#135—21no—
8C2×D24—21no—
9C3×Q32C2211yescharacteristic, complemented
10C3×SD32—21no—
11C3×D16C2211yescharacteristic, complemented
12C2×C3×C16C2211yescharacteristic
13D48—21no—
14D48C2212yes—
15C3⋊C32C2212yescomplemented
16#508D311yescharacteristic, complemented
17C2×D16—31no—
18SD64—32no—
19D32—32no—
20M64—31no—
21C3×#41—41no—
22C2×D12—41no—
23C3×Q16—21no—
24C3×SD16—41no—
25C3×D8—21no—
26C2×C3×C8D411yescharacteristic
27D24—22no—
28D24—41no—
29C3×C16D411yescharacteristic
30C3×C16C2311yescharacteristic
31#135—21no—
32C2×D8—61no—
33Q32C2×D311yescharacteristic, complemented
34SD32—21no—
35D16—32no—
36D16—61no—
37D16C2×D311yescharacteristic, complemented
38C2×C16C2×D311yescharacteristic
39C32—32no—
40C22×D3—81no—
41C3×Q8—41no—
42C3×D4—41no—
43C3×D4—81no—
44C2×C3×C4—81no—
45C2×C3×C4D811yescharacteristic
46D12—42no—
47D12—81no—
48C3×C8D811yescharacteristic
49C3×C8C2×D411yescharacteristic
50#41—41no—
51C2×D4—121no—
52Q16—21no—
53SD16—41no—
54D8—21no—
55D8—62no—
56D8—121no—
57C2×C8#6711yescharacteristic
58C16#6711yescharacteristic
59C16C22×D311yescharacteristic
60C22×C3—81no—
61C22×C3D1611yescharacteristic
62C2×D3—82no—
63C2×D3—162no—
64C3×C4—81no—
65C3×C4D1611yescharacteristic
66C3×C4C2×D811yescharacteristic
67C23—241no—
68Q8—41no—
69D4—41no—
70D4—81no—
71D4—122no—
72D4—241no—
73C2×C4—81no—
74C2×C4#21311yescharacteristic
75C8#21311yescharacteristic
76C8C2×#6711yescharacteristic
77C2×C3—21no—
78C2×C3—161no—
79C2×C3C2×D1611yescharacteristic
80D3—162no—
81C22—81no—
82C22—242no—
83C22—482no—
84C22#82611yescharacteristic
85C4—81no—
86C4#82611yescharacteristic
87C4C2×#21311yescharacteristic
88C3#226311yescharacteristic, complemented, Sylow
89C2—21no—
90C2—161no—
91C2—482no—
92C2C2×#82611yescharacteristic
subgroupG/H
centerC2C2×#826
commutator, cosocleC3×C16C23
FrattiniC16C22×D3
FittingC3×#508C2
socleC2×C3C2×D16
hypercenter#508D3
hypocenterC3#2263
LCSG ▷ C3×C16 ▷ C3×C8 ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16 ◁ #508

Complements

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

NH ≅ G/Ntype
1. C3×#508C2semidirect
2. C2×D48C2semidirect
3. #4521C2semidirect
4. #4519C2semidirect
5. #4499C2semidirect
9. C3×Q32C22semidirect
11. C3×D16C22semidirect
15. C3⋊C32C22semidirect
16. #508D3semidirect
33. Q32C2×D3semidirect
37. D16C2×D3semidirect
88. C3#2263semidirect

Maximal subgroups

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

subgroupindex
C3×#5082
C2×D482
#45212
#45192
#44992
#22633