Finite Group Databasebeta

← C3×C19×AGL(1,ℤ/8) #14269814

Subgroups — C3×C19×AGL(1,ℤ/8) #14269814

Order 1824.

136 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 136 conjugacy classes of subgroups — too many to draw. Only its 80 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
1C3×#41×C19C211yesmaximal, characteristic, complemented
2C2×C3×D4×C19C211yesmaximal, characteristic, complemented
3C3×SD16×C19C212yesmaximal, complemented
4C3×D8×C19C212yesmaximal, complemented
5C3×M16×C19C211yesmaximal, characteristic, complemented
6C19×AGL(1,ℤ/8)C311yesmaximal, characteristic, direct product factor, Hall
7C23×C3×C19—21no—
8C3×Q8×C19C2211yescharacteristic, complemented
9C3×D4×C19—21no—
10C3×D4×C19—21no—
11C3×D4×C19C2212yes—
12C3×D4×C19C2211yescharacteristic, complemented
13C2×C3×C4×C19—21no—
14C2×C3×C4×C19C2211yescharacteristic
15C3×C8×C19C2212yescomplemented
16#41×C19C2×C311yescharacteristic, complemented
17C2×D4×C19C2×C311yescharacteristic, complemented
18SD16×C19C2×C312yescomplemented
19D8×C19C2×C312yescomplemented
20M16×C19C2×C311yescharacteristic, complemented
21C22×C3×C19—21no—
22C22×C3×C19—22no—
23C22×C3×C19—42no—
24C22×C3×C19D411yescharacteristic
25C3×C4×C19—21no—
26C3×C4×C19D411yescharacteristic
27C3×C4×C19C2311yescharacteristic
28C23×C19—21no—
29Q8×C19C22×C311yescharacteristic, complemented
30D4×C19—21no—
31D4×C19—21no—
32D4×C19C22×C312yes—
33D4×C19C22×C311yescharacteristic, complemented
34C2×C4×C19—21no—
35C2×C4×C19C22×C311yescharacteristic
36C8×C19C22×C312yescomplemented
37C2×C3×C19—21no—
38C2×C3×C19—41no—
39C2×C3×C19—42no—
40C2×C3×C19C2×D411yescharacteristic
41C3×AGL(1,ℤ/8)C1911yesmaximal, characteristic, direct product factor, Hall
42C22×C19—21no—
43C22×C19—22no—
44C22×C19—42no—
45C22×C19C3×D411yescharacteristic
46C4×C19—21no—
47C4×C19C3×D411yescharacteristic
48C4×C19C23×C311yescharacteristic
49C3×C19AGL(1,ℤ/8)11yescharacteristic, direct product factor, Hall
50C3×#41C2×C1911yescharacteristic, complemented
51C2×C3×D4C2×C1911yescharacteristic, complemented
52C3×SD16C2×C1912yescomplemented
53C3×D8C2×C1912yescomplemented
54C3×M16C2×C1911yescharacteristic, complemented
55C2×C19—21no—
56C2×C19—42no—
57C2×C19—41no—
58C2×C19C2×C3×D411yescharacteristic
59AGL(1,ℤ/8)C3×C1911yescharacteristic, direct product factor, Sylow
60C23×C3—21no—
61C3×Q8C22×C1911yescharacteristic, complemented
62C3×D4—21no—
63C3×D4—21no—
64C3×D4C22×C1912yes—
65C3×D4C22×C1911yescharacteristic, complemented
66C2×C3×C4—21no—
67C2×C3×C4C22×C1911yescharacteristic
68C3×C8C22×C1912yescomplemented
69C19C3×AGL(1,ℤ/8)11yescharacteristic, direct product factor, Sylow
70#41C2×C3×C1911yescharacteristic, complemented
71C2×D4C2×C3×C1911yescharacteristic, complemented
72SD16C2×C3×C1912yescomplemented
73D8C2×C3×C1912yescomplemented
74M16C2×C3×C1911yescharacteristic, complemented
75C22×C3—21no—
76C22×C3—22no—
77C22×C3—42no—
78C22×C3D4×C1911yescharacteristic
79C3×C4—21no—
80C3×C4D4×C1911yescharacteristic
81C3×C4C23×C1911yescharacteristic
82C23—21no—
83Q8C22×C3×C1911yescharacteristic, complemented
84D4—21no—
85D4—21no—
86D4C22×C3×C1912yes—
87D4C22×C3×C1911yescharacteristic, complemented
88C2×C4—21no—
89C2×C4C22×C3×C1911yescharacteristic
90C8C22×C3×C1912yescomplemented
91C2×C3—21no—
92C2×C3—42no—
93C2×C3—41no—
94C2×C3C2×D4×C1911yescharacteristic
95C22—21no—
96C22—22no—
97C22—42no—
98C22C3×D4×C1911yescharacteristic
99C4—21no—
100C4C3×D4×C1911yescharacteristic
101C4C23×C3×C1911yescharacteristic
102C3C19×AGL(1,ℤ/8)11yescharacteristic, direct product factor, Sylow
103C2—21no—
104C2—42no—
105C2—41no—
106C2C2×C3×D4×C1911yescharacteristic
subgroupG/H
center, socleC2×C3×C19C2×D4
commutator, Frattini, cosocleC4C23×C3×C19
LCSG ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C3×C19 ◁ C2×C3×C4×C19 ◁ G

Complements

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

NH ≅ G/Ntype
1. C3×#41×C19C2semidirect
2. C2×C3×D4×C19C2semidirect
3. C3×SD16×C19C2semidirect
4. C3×D8×C19C2semidirect
5. C3×M16×C19C2semidirect
6. C19×AGL(1,ℤ/8)C3direct (N × H)
8. C3×Q8×C19C22semidirect
12. C3×D4×C19C22semidirect
15. C3×C8×C19C22semidirect
16. #41×C19C2×C3semidirect
17. C2×D4×C19C2×C3semidirect
18. SD16×C19C2×C3semidirect
19. D8×C19C2×C3semidirect
20. M16×C19C2×C3semidirect
29. Q8×C19C22×C3semidirect
33. D4×C19C22×C3semidirect
36. C8×C19C22×C3semidirect
41. C3×AGL(1,ℤ/8)C19direct (N × H)
49. C3×C19AGL(1,ℤ/8)direct (N × H)
50. C3×#41C2×C19semidirect
51. C2×C3×D4C2×C19semidirect
52. C3×SD16C2×C19semidirect
53. C3×D8C2×C19semidirect
54. C3×M16C2×C19semidirect
59. AGL(1,ℤ/8)C3×C19direct (N × H)
61. C3×Q8C22×C19semidirect
65. C3×D4C22×C19semidirect
68. C3×C8C22×C19semidirect
69. C19C3×AGL(1,ℤ/8)direct (N × H)
70. #41C2×C3×C19semidirect
71. C2×D4C2×C3×C19semidirect
72. SD16C2×C3×C19semidirect
73. D8C2×C3×C19semidirect
74. M16C2×C3×C19semidirect
83. Q8C22×C3×C19semidirect
87. D4C22×C3×C19semidirect
90. C8C22×C3×C19semidirect
102. C3C19×AGL(1,ℤ/8)direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#41×C192
C2×C3×D4×C192
C3×SD16×C192
C3×D8×C192
C3×M16×C192
C19×AGL(1,ℤ/8)3
C3×AGL(1,ℤ/8)19