Finite Group Databasebeta

← C3×#88186 #11928827

Subgroups — C3×#88186 #11928827

Order 1248.

136 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 136 conjugacy classes of subgroups — too many to draw. Only its 58 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D4×C13C211yesmaximal, characteristic, complemented
2C3×#6127C211yesmaximal, characteristic, complemented
3C3×#6105C212yesmaximal, complemented
4C3×#6104C212yesmaximal, complemented
5C3×#6099C211yesmaximal, characteristic, complemented
6#88186C311yesmaximal, characteristic, direct product factor, Hall
7C23×C3×C13—21no—
8C3×D4×C13—21no—
9C3×D4×C13C2212yes—
10C2×C3×C4×C13C2211yescharacteristic
11C3×C22⋊D13—21no—
12C3×D52C2211yescharacteristic, complemented
13C3×C4×D13—21no—
14C3×Dic26C2211yescharacteristic, complemented
15C3×#1055C2212yescomplemented
16C2×D4×C13C2×C311yescharacteristic, complemented
17#6127C2×C311yescharacteristic, complemented
18#6105C2×C312yescomplemented
19#6104C2×C312yescomplemented
20#6099C2×C311yescharacteristic, complemented
21C22×C3×C13—22no—
22C22×C3×C13—42no—
23C22×C3×C13D411yescharacteristic
24C2×C3×D13—21no—
25C3×C4×C13D411yescharacteristic
26C3×C4×C13C2311yescharacteristic
27C3×Dic13—21no—
28C23×C13—21no—
29D4×C13—21no—
30D4×C13C22×C312yes—
31C2×C4×C13C22×C311yescharacteristic
32C22⋊D13—21no—
33D52C22×C311yescharacteristic, complemented
34C4×D13—21no—
35Dic26C22×C311yescharacteristic, complemented
36#1055C22×C312yescomplemented
37C3×AGL(1,ℤ/8)—131nomaximal, Hall
38C2×C3×C13—21no—
39C2×C3×C13—42no—
40C2×C3×C13C2×D411yescharacteristic
41C3×D13—41no—
42C22×C13—22no—
43C22×C13—42no—
44C22×C13C3×D411yescharacteristic
45C2×D13—21no—
46C4×C13C3×D411yescharacteristic
47C4×C13C23×C311yescharacteristic
48Dic13—21no—
49C3×#41—131no—
50C2×C3×D4D1311yescharacteristic, complemented
51C3×SD16—132no—
52C3×D8—132no—
53C3×M16—131no—
54C3×C13AGL(1,ℤ/8)11yescharacteristic, complemented, Hall
55AGL(1,ℤ/8)—131noSylow
56C2×C13—21no—
57C2×C13—42no—
58C2×C13C2×C3×D411yescharacteristic
59D13—41no—
60C23×C3—21no—
61C3×Q8—131no—
62C3×D4—21no—
63C3×D4—131no—
64C3×D4—261no—
65C3×D4C2×D1312yes—
66C2×C3×C4—261no—
67C2×C3×C4C2×D1311yescharacteristic
68C3×C8—132no—
69#41—131no—
70C2×D4C3×D1311yescharacteristic, complemented
71SD16—132no—
72D8—132no—
73M16—131no—
74C13C3×AGL(1,ℤ/8)11yescharacteristic, complemented, Sylow
75C22×C3—22no—
76C22×C3—42no—
77C22×C3—261no—
78C22×C3C22⋊D1311yescharacteristic
79C3×C4—261no—
80C3×C4C22⋊D1311yescharacteristic
81C3×C4C22×D1311yescharacteristic
82C23—21no—
83Q8—131no—
84D4—21no—
85D4—131no—
86D4—261no—
87D4C2×C3×D1312yes—
88C2×C4—261no—
89C2×C4C2×C3×D1311yescharacteristic
90C8—132no—
91C2×C3—21no—
92C2×C3—42no—
93C2×C3—521no—
94C2×C3C2×C22⋊D1311yescharacteristic
95C22—22no—
96C22—42no—
97C22—261no—
98C22C3×C22⋊D1311yescharacteristic
99C4—261no—
100C4C3×C22⋊D1311yescharacteristic
101C4C22×C3×D1311yescharacteristic
102C3#8818611yescharacteristic, direct product factor, Sylow
103C2—21no—
104C2—42no—
105C2—521no—
106C2C2×C3×C22⋊D1311yescharacteristic
subgroupG/H
centerC2×C3C2×C22⋊D13
commutator, cosocleC4×C13C23×C3
FrattiniC4C22×C3×D13
FittingC2×C3×D4×C13C2
socleC2×C3×C13C2×D4
hypercenterC2×C3×D4D13
hypocenterC13C3×AGL(1,ℤ/8)
LCSG ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C3 ◁ C2×C3×C4 ◁ C2×C3×D4

Complements

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

NH ≅ G/Ntype
1. C2×C3×D4×C13C2semidirect
2. C3×#6127C2semidirect
3. C3×#6105C2semidirect
4. C3×#6104C2semidirect
5. C3×#6099C2semidirect
6. #88186C3direct (N × H)
12. C3×D52C22semidirect
14. C3×Dic26C22semidirect
15. C3×#1055C22semidirect
16. C2×D4×C13C2×C3semidirect
17. #6127C2×C3semidirect
18. #6105C2×C3semidirect
19. #6104C2×C3semidirect
20. #6099C2×C3semidirect
33. D52C22×C3semidirect
35. Dic26C22×C3semidirect
36. #1055C22×C3semidirect
50. C2×C3×D4D13semidirect
54. C3×C13AGL(1,ℤ/8)semidirect
70. C2×D4C3×D13semidirect
74. C13C3×AGL(1,ℤ/8)semidirect
102. C3#88186direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×D4×C132
C3×#61272
C3×#61052
C3×#61042
C3×#60992
#881863
C3×AGL(1,ℤ/8)13