Finite Group Databasebeta

← C2×2−1+4⋊C3 #5944

Subgroups — C2×2−1+4⋊C3 #5944

Order 192.

204 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
12−1+4⋊C3C214yesmaximal, direct product factor
2C2×#41⋊C3C211yesmaximal, characteristic, complemented
3C22×SL(2,𝔽3)C212yesmaximal, complemented
4C2×2−1+4C311yesmaximal, characteristic, complemented, Sylow
5C2×C3×D4—41nomaximal
6#41⋊C3C2212yescomplemented
7C2×SL(2,𝔽3)C2211yescharacteristic
8C2×SL(2,𝔽3)C2214yescomplemented
92−1+4—34no—
102−1+4C2×C314yescomplemented
11C2×#41—31no—
12C2×#41—32no—
13C2×#41C2×C311yescharacteristic, complemented
14C22×Q8—31no—
15C22×Q8C2×C312yescomplemented
16C23×C3—42no—
17C3×D4—44no—
18C2×C3×C4—41no—
19SL(2,𝔽3)C2311yescharacteristic
20#41—38no—
21#41—34no—
22#41—34no—
23#41—38no—
24#41—32no—
25#41C22×C312yescomplemented
26C2×Q8—34no—
27C2×Q8—34no—
28C2×Q8—31no—
29C2×Q8—32no—
30C2×Q8—34no—
31C2×Q8C22×C311yescharacteristic
32C2×Q8C22×C314yescomplemented
33C2×D4—31no—
34C2×D4—32no—
35C2×D4A411yescharacteristic
36C22×C4—32no—
37C22×C4—32no—
38C22×C4—31no—
39C22×C3—44no—
40C22×C3—41no—
41C22×C3—84no—
42C3×C4—42no—
43C23—31no—
44C23C2×A412yes—
45Q8—31no—
46Q8—34no—
47Q8—34no—
48Q8—34no—
49Q8C23×C311yescharacteristic
50D4—32no—
51D4—32no—
52D4—38no—
53D4C2×A414yes—
54C2×C4—38no—
55C2×C4—34no—
56C2×C4—34no—
57C2×C4—32no—
58C2×C4—31no—
59C2×C4—32no—
60C2×C4—32no—
61C2×C4C2×A411yescharacteristic
62C2×C3—42no—
63C2×C3—41no—
64C2×C3—84no—
65C22—24no—
66C22—32no—
67C22—62no—
68C22C22×A414yes—
69C22C22×A411yescharacteristic
70C4—34no—
71C4—31no—
72C4—31no—
73C4C22×A412yes—
74C3—41noSylow
75C2—24no—
76C2—62no—
77C22−1+4⋊C312yesdirect product factor
78C2C23×A411yescharacteristic
subgroupG/H
center, socleC22C22×A4
commutator, cosocle, hypocenterQ8C23×C3
FrattiniC2C23×A4
FittingC2×2−1+4C3
hypercenterC2×D4A4
LCSG ▷ Q8
UCSC1 ◁ C22 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
1. 2−1+4⋊C3C2direct (N × H)
2. C2×#41⋊C3C2semidirect
3. C22×SL(2,𝔽3)C2semidirect
4. C2×2−1+4C3semidirect
6. #41⋊C3C22semidirect
8. C2×SL(2,𝔽3)C22semidirect
10. 2−1+4C2×C3semidirect
13. C2×#41C2×C3semidirect
15. C22×Q8C2×C3semidirect
25. #41C22×C3semidirect
32. C2×Q8C22×C3semidirect
77. C22−1+4⋊C3direct (N × H)

Maximal subgroups

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

subgroupindex
2−1+4⋊C32
C2×#41⋊C32
C22×SL(2,𝔽3)2
C2×2−1+43
C2×C3×D44