Finite Group Databasebeta

← C3×#88117 #11928355

Subgroups — C3×#88117 #11928355

Order 1248.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×Q8×D13C211yesmaximal, characteristic
2C3×C4⋊#261C211yesmaximal, characteristic
3C3×D13⋊C8C211yesmaximal, characteristic
4#88117C311yesmaximal, characteristic, direct product factor, Hall
5C2×C3×#261—21no—
6C3×Q8×C13C411yescharacteristic, complemented
7C3×C4×D13—21no—
8C3×C4×D13C2211yescharacteristic
9C3×Dic26—21no—
10C3×Dic26C411yescharacteristic, complemented
11C3×#1057—21no—
12Q8×D13C2×C311yescharacteristic
13C4⋊#261C2×C311yescharacteristic
14D13⋊C8C2×C311yescharacteristic
15C2×C3×D13D411yescharacteristic
16C3×#261—41no—
17C3×C4×C13—21no—
18C3×C4×C13C2×C411yescharacteristic
19C3×Dic13—21no—
20C3×Dic13D411yescharacteristic
21C2×#261—21no—
22Q8×C13C3×C411yescharacteristic, complemented
23C4×D13—21no—
24C4×D13C22×C311yescharacteristic
25Dic26—21no—
26Dic26C3×C411yescharacteristic, complemented
27#1057—21no—
28C3×#103—131nomaximal, Hall
29C2×C3×C13C22⋊C411yescharacteristic
30C3×D13SD1611yescharacteristic
31C3×D13Q1611yescharacteristic
32C2×D13C3×D411yescharacteristic
33#261—41no—
34C4×C13—21no—
35C4×C13C2×C3×C411yescharacteristic
36Dic13—21no—
37Dic13C3×D411yescharacteristic
38C2×C3×Q8—131no—
39C2×C3×C8—131no—
40C3×C4⋊C4—131no—
41C3×C13#10311yescharacteristic, complemented, Hall
42#103—131noSylow
43C2×C13C3×C22⋊C411yescharacteristic
44D13C3×SD1611yescharacteristic
45D13C3×Q1611yescharacteristic
46C3×Q8—131no—
47C3×Q8—261no—
48C3×Q8#26111yescharacteristic, complemented
49C2×C3×C4—131no—
50C2×C3×C4—261no—
51C2×C3×C4—261no—
52C3×C8—261no—
53C2×Q8—131no—
54C2×C8—131no—
55C4⋊C4—131no—
56C13C3×#10311yescharacteristic, complemented, Sylow
57C22×C3—131no—
58C3×C4—21no—
59C3×C4—131no—
60C3×C4—261no—
61C3×C4—521no—
62C3×C4C2×#26111yescharacteristic
63Q8—131no—
64Q8—261no—
65Q8C3×#26111yescharacteristic, complemented
66C2×C4—131no—
67C2×C4—261no—
68C2×C4—261no—
69C8—261no—
70C2×C3—131no—
71C2×C3—131no—
72C2×C3C22⋊#26111yescharacteristic
73C22—131no—
74C4—21no—
75C4—131no—
76C4—261no—
77C4—521no—
78C4C2×C3×#26111yescharacteristic
79C3#8811711yescharacteristic, direct product factor, Sylow
80C2—131no—
81C2—131no—
82C2C3×C22⋊#26111yescharacteristic
subgroupG/H
centerC2×C3C22⋊#261
commutatorC4×C13C2×C3×C4
FrattiniC4C2×C3×#261
FittingC3×Q8×C13C4
socleC2×C3×C13C22⋊C4
prime radicalC2×C3×D13D4
cosocleC4×D13C22×C3
hypercenterC3×Q8#261
hypocenterC13C3×#103
LCSG ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C3 ◁ C3×C4 ◁ C3×Q8

Complements

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

NH ≅ G/Ntype
4. #88117C3direct (N × H)
6. C3×Q8×C13C4semidirect
10. C3×Dic26C4semidirect
22. Q8×C13C3×C4semidirect
26. Dic26C3×C4semidirect
41. C3×C13#103semidirect
48. C3×Q8#261semidirect
56. C13C3×#103semidirect
65. Q8C3×#261semidirect
79. C3#88117direct (N × H)

Maximal subgroups

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

subgroupindex
C3×Q8×D132
C3×C4⋊#2612
C3×D13⋊C82
#881173
C3×#10313