Finite Group Databasebeta

← C23×C3×C7×C8 #13061985

Subgroups — C23×C3×C7×C8 #13061985

Order 1344.

676 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C3×C4×C7C211yesmaximal, characteristic
2C22×C3×C7×C8C2114yesmaximal, direct product factor
3C23×C7×C8C311yesmaximal, characteristic, direct product factor, Hall
4C24×C3×C7C411yescharacteristic
5C22×C3×C4×C7C417yes—
6C22×C3×C4×C7C2217yes—
7C2×C3×C7×C8C22128yesdirect product factor
8C23×C4×C7C2×C311yescharacteristic
9C22×C7×C8C2×C3114yesdirect product factor
10C23×C3×C8C711yesmaximal, characteristic, direct product factor, Hall
11C23×C3×C7C818yesdirect product factor
12C23×C3×C7C2×C417yes—
13C2×C3×C4×C7C2×C4121yes—
14C2×C3×C4×C7C2317yes—
15C3×C7×C8C2318yesdirect product factor
16C24×C7C3×C411yescharacteristic
17C22×C4×C7C3×C417yes—
18C22×C4×C7C22×C317yes—
19C2×C7×C8C22×C3128yesdirect product factor
20C23×C3×C4C2×C711yescharacteristic
21C22×C3×C8C2×C7114yesdirect product factor
22C22×C3×C7C2×C8128yesdirect product factor
23C22×C3×C7C22×C417yes—
24C3×C4×C7C22×C417yes—
25C3×C4×C7C2411yescharacteristic
26C23×C8C3×C711yescharacteristic, direct product factor, Sylow
27C23×C7C3×C818yesdirect product factor
28C23×C7C2×C3×C417yes—
29C2×C4×C7C2×C3×C4121yes—
30C2×C4×C7C23×C317yes—
31C7×C8C23×C318yesdirect product factor
32C24×C3C4×C711yescharacteristic
33C22×C3×C4C4×C717yes—
34C22×C3×C4C22×C717yes—
35C2×C3×C8C22×C7128yesdirect product factor
36C2×C3×C7C22×C8114yesdirect product factor
37C2×C3×C7C23×C411yescharacteristic
38C23×C4C2×C3×C711yescharacteristic
39C22×C8C2×C3×C7114yesdirect product factor
40C22×C7C2×C3×C8128yesdirect product factor
41C22×C7C22×C3×C417yes—
42C4×C7C22×C3×C417yes—
43C4×C7C24×C311yescharacteristic
44C23×C3C7×C818yesdirect product factor
45C23×C3C2×C4×C717yes—
46C2×C3×C4C2×C4×C7121yes—
47C2×C3×C4C23×C717yes—
48C3×C8C23×C718yesdirect product factor
49C3×C7C23×C811yescharacteristic, direct product factor, Hall
50C24C3×C4×C711yescharacteristic
51C22×C4C3×C4×C717yes—
52C22×C4C22×C3×C717yes—
53C2×C8C22×C3×C7128yesdirect product factor
54C2×C7C22×C3×C8114yesdirect product factor
55C2×C7C23×C3×C411yescharacteristic
56C22×C3C2×C7×C8128yesdirect product factor
57C22×C3C22×C4×C717yes—
58C3×C4C22×C4×C717yes—
59C3×C4C24×C711yescharacteristic
60C23C3×C7×C818yesdirect product factor
61C23C2×C3×C4×C717yes—
62C2×C4C2×C3×C4×C7121yes—
63C2×C4C23×C3×C717yes—
64C8C23×C3×C718yesdirect product factor
65C7C23×C3×C811yescharacteristic, direct product factor, Sylow
66C2×C3C22×C7×C8114yesdirect product factor
67C2×C3C23×C4×C711yescharacteristic
68C22C2×C3×C7×C8128yesdirect product factor
69C22C22×C3×C4×C717yes—
70C4C22×C3×C4×C717yes—
71C4C24×C3×C711yescharacteristic
72C3C23×C7×C811yescharacteristic, direct product factor, Sylow
73C2C22×C3×C7×C8114yesdirect product factor
74C2C23×C3×C4×C711yescharacteristic
subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC4C24×C3×C7
socle, prime radicalC24×C3×C7C4
LCSG ▷ C1
UCSC1 ◁ G

Complements

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

NH ≅ G/Ntype
2. C22×C3×C7×C8C2direct (N × H)
3. C23×C7×C8C3direct (N × H)
7. C2×C3×C7×C8C22direct (N × H)
9. C22×C7×C8C2×C3direct (N × H)
10. C23×C3×C8C7direct (N × H)
11. C23×C3×C7C8direct (N × H)
15. C3×C7×C8C23direct (N × H)
19. C2×C7×C8C22×C3direct (N × H)
21. C22×C3×C8C2×C7direct (N × H)
22. C22×C3×C7C2×C8direct (N × H)
26. C23×C8C3×C7direct (N × H)
27. C23×C7C3×C8direct (N × H)
31. C7×C8C23×C3direct (N × H)
35. C2×C3×C8C22×C7direct (N × H)
36. C2×C3×C7C22×C8direct (N × H)
39. C22×C8C2×C3×C7direct (N × H)
40. C22×C7C2×C3×C8direct (N × H)
44. C23×C3C7×C8direct (N × H)
48. C3×C8C23×C7direct (N × H)
49. C3×C7C23×C8direct (N × H)
53. C2×C8C22×C3×C7direct (N × H)
54. C2×C7C22×C3×C8direct (N × H)
56. C22×C3C2×C7×C8direct (N × H)
60. C23C3×C7×C8direct (N × H)
64. C8C23×C3×C7direct (N × H)
65. C7C23×C3×C8direct (N × H)
66. C2×C3C22×C7×C8direct (N × H)
68. C22C2×C3×C7×C8direct (N × H)
72. C3C23×C7×C8direct (N × H)
73. C2C22×C3×C7×C8direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C3×C4×C72
C22×C3×C7×C82
C23×C7×C83
C23×C3×C87