Finite Group Databasebeta

← C31×#63103 #21519862

Subgroups — C31×#63103 #21519862

Order 7936.

59452 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×2−1+6C2128yesmaximal, complemented
2C31×H(7,𝔽2)C2136yesmaximal, complemented
3C2×C31×#585C2163yesmaximal, complemented
4C31×#585C221336yescomplemented
5C31×#585C2211008yescomplemented
6C2×C31×2−1+4C221378yescomplemented
7C2×C31×H(5,𝔽2)C221630yescomplemented
8C22×#41×C31C221315yescomplemented
9C31×2−1+4C2312016yescomplemented
10C31×H(5,𝔽2)C2313360yescomplemented
11C2×#41×C31C2311260yescomplemented
12C2×#41×C31C2313780yescomplemented
13C22×Q8×C31C231315yescomplemented
14C22×D4×C31C231945yescomplemented
15C23×C4×C31C231135yescomplemented
16C24×C31C241135yes—
17#41×C31C241336yes—
18#41×C31C2415040yes—
19C2×Q8×C31C2411260yes—
20C2×D4×C31C2413780yes—
21C22×C4×C31C241315yes—
22C22×C4×C31C241945yes—
23#63103C3111yesmaximal, characteristic, direct product factor, Sylow
24C23×C31—8135no—
25C23×C31C251315yes—
26Q8×C31C251336yes—
27D4×C31C2511008yes—
28C2×C4×C31C251945yes—
29C2×C4×C31C25163yes—
302−1+6C2×C31128yescomplemented
31H(7,𝔽2)C2×C31136yescomplemented
32C2×#585C2×C31163yescomplemented
33C22×C31—4315no—
34C22×C31C26163yes—
35C4×C31C26163yes—
36C4×C31C2611yescharacteristic
37#585C22×C311336yescomplemented
38#585C22×C3111008yescomplemented
39C2×2−1+4C22×C311378yescomplemented
40C2×H(5,𝔽2)C22×C311630yescomplemented
41C22×#41C22×C311315yescomplemented
42C2×C31—263no—
43C2×C31C2711yescharacteristic
442−1+4C23×C3112016yescomplemented
45H(5,𝔽2)C23×C3113360yescomplemented
46C2×#41C23×C3111260yescomplemented
47C2×#41C23×C3113780yescomplemented
48C22×Q8C23×C311315yescomplemented
49C22×D4C23×C311945yescomplemented
50C23×C4C23×C311135yescomplemented
51C31#6310311yescharacteristic, direct product factor, Sylow
52C24C24×C311135yes—
53#41C24×C311336yes—
54#41C24×C3115040yes—
55C2×Q8C24×C3111260yes—
56C2×D4C24×C3113780yes—
57C22×C4C24×C311315yes—
58C22×C4C24×C311945yes—
59C23—8135no—
60C23C25×C311315yes—
61Q8C25×C311336yes—
62D4C25×C3111008yes—
63C2×C4C25×C31163yes—
64C2×C4C25×C311945yes—
65C22—4315no—
66C22C26×C31163yes—
67C4C26×C3111yescharacteristic
68C4C26×C31163yes—
69C2—263no—
70C2C27×C3111yescharacteristic
subgroupG/H
centerC4×C31C26
commutator, Frattini, cosocleC2C27×C31
socleC2×C31C27
LCSG ▷ C2 ▷ C1
UCSC1 ◁ C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C31×2−1+6C2semidirect
2. C31×H(7,𝔽2)C2semidirect
3. C2×C31×#585C2semidirect
4. C31×#585C22semidirect
5. C31×#585C22semidirect
6. C2×C31×2−1+4C22semidirect
7. C2×C31×H(5,𝔽2)C22semidirect
8. C22×#41×C31C22semidirect
9. C31×2−1+4C23semidirect
10. C31×H(5,𝔽2)C23semidirect
11. C2×#41×C31C23semidirect
12. C2×#41×C31C23semidirect
13. C22×Q8×C31C23semidirect
14. C22×D4×C31C23semidirect
15. C23×C4×C31C23semidirect
23. #63103C31direct (N × H)
30. 2−1+6C2×C31semidirect
31. H(7,𝔽2)C2×C31semidirect
32. C2×#585C2×C31semidirect
37. #585C22×C31semidirect
38. #585C22×C31semidirect
39. C2×2−1+4C22×C31semidirect
40. C2×H(5,𝔽2)C22×C31semidirect
41. C22×#41C22×C31semidirect
44. 2−1+4C23×C31semidirect
45. H(5,𝔽2)C23×C31semidirect
46. C2×#41C23×C31semidirect
47. C2×#41C23×C31semidirect
48. C22×Q8C23×C31semidirect
49. C22×D4C23×C31semidirect
50. C23×C4C23×C31semidirect
51. C31#63103direct (N × H)

Maximal subgroups

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

subgroupindex
C31×2−1+62
C31×H(7,𝔽2)2
C2×C31×#5852
#6310331