Finite Group Databasebeta

← #884

Subgroups — #884

Order 96.

94 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#67C211yesmaximal, characteristic, complemented
2C2×#67C211yesmaximal, characteristic, complemented
3C2×D12C211yesmaximal, characteristic, complemented
4C2×C4×D3C211yesmaximal, characteristic, complemented
5C3×C22⋊C4C211yesmaximal, characteristic, complemented
6(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
7Dic3⋊C4C211yesmaximal, characteristic, complemented
8#121—31nomaximal, Sylow
9C23×C3C2211yescharacteristic
10C22×D3C2211yescharacteristic
11C22×D3C2211yescharacteristic
12C2×C3×C4C2211yescharacteristic
13C2×C3×C4C2211yescharacteristic
14#67—22no—
15#67—22no—
16C2×Dic3C2211yescharacteristic
17C2×Dic3C2211yescharacteristic
18D12—22no—
19C4×D3—22no—
20C2×D4—31no—
21C2×D4—31no—
22C2×D4—31no—
23C22×C4—31no—
24C4⋊C4—31no—
25C22⋊C4—31no—
26C22⋊C4D311yescharacteristic, complemented
27C22×C3—21no—
28C22×C3—21no—
29C22×C3—21no—
30C22×C3C2311yescharacteristic
31C2×D3—21no—
32C2×D3—21no—
33C2×D3—21no—
34C2×D3—21no—
35C2×D3—21no—
36C2×D3D412yescomplemented
37C3×C4—21no—
38C3×C4—21no—
39Dic3—21no—
40Dic3D412yescomplemented
41C23—31no—
42C23—31no—
43C23C2×D311yescharacteristic
44D4—62no—
45D4—62no—
46D4—62no—
47C2×C4—31no—
48C2×C4—31no—
49C2×C4—62no—
50C2×C4C2×D311yescharacteristic
51C2×C4C2×D311yescharacteristic
52C2×C3—41no—
53C2×C3C2×D411yescharacteristic
54C2×C3C2×D411yescharacteristic
55C2×C3#4111yescharacteristic
56D3—22no—
57D3—41no—
58C22—21no—
59C22—21no—
60C22—21no—
61C22—32no—
62C22—61no—
63C22—61no—
64C22—61no—
65C22—61no—
66C22—61no—
67C22C22×D311yescharacteristic
68C4—21no—
69C4—21no—
70C4—32no—
71C4—61no—
72C3#12111yescharacteristic, complemented, Sylow
73C2—41no—
74C2—62no—
75C2—121no—
76C2#23511yescharacteristic
77C2D3×D411yescharacteristic
78C2D3×D411yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3
commutator, socle, cosocleC22×C3C23
FittingC3×C22⋊C4C2
hypercenterC22⋊C4D3
hypocenterC3#121
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C22 ◁ C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#67C2semidirect
2. C2×#67C2semidirect
3. C2×D12C2semidirect
4. C2×C4×D3C2semidirect
5. C3×C22⋊C4C2semidirect
6. (C2×D3)⋊C4C2semidirect
7. Dic3⋊C4C2semidirect
26. C22⋊C4D3semidirect
36. C2×D3D4semidirect
40. Dic3D4semidirect
72. C3#121semidirect

Maximal subgroups

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

subgroupindex
C2×#672
C2×D122
C2×C4×D32
C3×C22⋊C42
(C2×D3)⋊C42
Dic3⋊C42
#1213