Finite Group Databasebeta

← #520⋊C3 #5440

Subgroups — #520⋊C3 #5440

Order 192.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#41⋊C3C211yesmaximal, characteristic
2C4×SL(2,𝔽3)C212yesmaximal, complemented
3#520C311yesmaximal, characteristic, complemented, Sylow
4#41⋊C3C412yescomplemented
5C2×SL(2,𝔽3)C2211yescharacteristic
6C3×C4⋊C4—41nomaximal
7C2×#41C2×C311yescharacteristic
8C4×Q8C2×C312yes—
9C4×D4—32no—
10#117—31no—
11C2×C4⋊C4—31no—
12C2×C3×C4—41no—
13C2×C3×C4—42no—
14SL(2,𝔽3)C2×C411yescharacteristic, complemented
15#41—32no—
16#41C3×C412yescomplemented
17C2×Q8C22×C311yescharacteristic
18C2×D4—31no—
19C22×C4—31no—
20C22×C4—32no—
21C4⋊C4—32no—
22C4⋊C4—31no—
23C4⋊C4A411yescharacteristic
24C22⋊C4—32no—
25C42—32no—
26C22×C3—41no—
27C3×C4—42no—
28C3×C4—82no—
29C23—31no—
30Q8—31no—
31Q8C2×C3×C411yescharacteristic
32D4—32no—
33D4—32no—
34C2×C4—31no—
35C2×C4—32no—
36C2×C4—32no—
37C2×C4—32no—
38C2×C4—122no—
39C2×C4C2×A412yes—
40C2×C4C2×A411yescharacteristic
41C2×C3—41no—
42C2×C3—41no—
43C2×C3—41no—
44C22—32no—
45C22—61no—
46C22—61no—
47C22C22×A411yescharacteristic
48C4—22no—
49C4—31no—
50C4—31no—
51C4—62no—
52C4C4×A412yes—
53C3—41noSylow
54C2—62no—
55C2C2×C4×A411yescharacteristic
56C2#99411yescharacteristic
57C22−1+4⋊C311yescharacteristic
subgroupG/H
center, Frattini, socleC22C22×A4
commutator, hypocenterQ8C2×C3×C4
Fitting#520C3
prime radicalC2×#41⋊C3C2
cosocleC2×Q8C22×C3
hypercenterC4⋊C4A4
LCSG ▷ Q8
UCSC1 ◁ C22 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C4×SL(2,𝔽3)C2semidirect
3. #520C3semidirect
4. #41⋊C3C4semidirect
14. SL(2,𝔽3)C2×C4semidirect
16. #41C3×C4semidirect

Maximal subgroups

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

subgroupindex
C2×#41⋊C32
C4×SL(2,𝔽3)2
#5203
C3×C4⋊C44