Finite Group Databasebeta

← C2×C79×2−1+6 #34174791

Subgroups — C2×C79×2−1+6 #34174791

Order 20224.

59186 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C79×2−1+6C2164yesmaximal, direct product factor
2C2×#585×C79C2136yesmaximal, complemented
3C22×2−1+4×C79C2127yesmaximal, complemented
4#585×C79C2211152yescomplemented
5C2×2−1+4×C79C221216yescomplemented
6C2×2−1+4×C79C221864yescomplemented
7C2×H(5,𝔽2)×C79C221120yescomplemented
8C22×#41×C79C221270yescomplemented
9C23×Q8×C79C22145yescomplemented
102−1+4×C79C2313456yescomplemented
11H(5,𝔽2)×C79C2311920yescomplemented
12C2×#41×C79C231720yes—
13C2×#41×C79C2314320yescomplemented
14C22×Q8×C79C231270yes—
15C22×Q8×C79C231720yescomplemented
16C22×D4×C79C231270yes—
17C23×C4×C79C231135yes—
18C24×C79C24145yes—
19#41×C79C2415760yes—
20C2×Q8×C79C241120yes—
21C2×Q8×C79C2412160yes—
22C2×D4×C79C241216yes—
23C2×D4×C79C2412160yes—
24C22×C4×C79C241270yes—
25C22×C4×C79C2411080yes—
26C23×C79—490no—
27C23×C79C25127yes—
28C23×C79C251180yes—
29Q8×C79C251480yes—
30D4×C79C251864yes—
31C2×C4×C79C2511080yes—
32C2×C4×C79C25136yes—
33C22×C79—254no—
34C22×C79—4180no—
35C22×C79C26154yes—
36C22×C79C2611yescharacteristic
37C4×C79C26172yes—
38C2×2−1+6C7911yesmaximal, characteristic, direct product factor, Sylow
39C2×C79—254no—
40C2×C792−1+612yesdirect product factor
41C2×C79C2711yescharacteristic
422−1+6C2×C79164yesdirect product factor
43C2×#585C2×C79136yescomplemented
44C22×2−1+4C2×C79127yescomplemented
45C79C2×2−1+611yescharacteristic, direct product factor, Sylow
46#585C22×C7911152yescomplemented
47C2×2−1+4C22×C791216yescomplemented
48C2×2−1+4C22×C791864yescomplemented
49C2×H(5,𝔽2)C22×C791120yescomplemented
50C22×#41C22×C791270yescomplemented
51C23×Q8C22×C79145yescomplemented
522−1+4C23×C7913456yescomplemented
53H(5,𝔽2)C23×C7911920yescomplemented
54C2×#41C23×C791720yes—
55C2×#41C23×C7914320yescomplemented
56C22×Q8C23×C791270yes—
57C22×Q8C23×C791720yescomplemented
58C22×D4C23×C791270yes—
59C23×C4C23×C791135yes—
60C24C24×C79145yes—
61#41C24×C7915760yes—
62C2×Q8C24×C791120yes—
63C2×Q8C24×C7912160yes—
64C2×D4C24×C791216yes—
65C2×D4C24×C7912160yes—
66C22×C4C24×C791270yes—
67C22×C4C24×C7911080yes—
68C23—490no—
69C23C25×C79127yes—
70C23C25×C791180yes—
71Q8C25×C791480yes—
72D4C25×C791864yes—
73C2×C4C25×C79136yes—
74C2×C4C25×C7911080yes—
75C22—254no—
76C22—4180no—
77C22C26×C79154yes—
78C22C26×C7911yescharacteristic
79C4C26×C79172yes—
80C2—254no—
81C2C79×2−1+612yesdirect product factor
82C2C27×C7911yescharacteristic
subgroupG/H
center, socleC22×C79C26
commutator, Frattini, cosocleC2C27×C79
LCSG ▷ C2 ▷ C1
UCSC1 ◁ C22×C79 ◁ G

Complements

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

NH ≅ G/Ntype
1. C79×2−1+6C2direct (N × H)
2. C2×#585×C79C2semidirect
3. C22×2−1+4×C79C2semidirect
4. #585×C79C22semidirect
5. C2×2−1+4×C79C22semidirect
6. C2×2−1+4×C79C22semidirect
7. C2×H(5,𝔽2)×C79C22semidirect
8. C22×#41×C79C22semidirect
9. C23×Q8×C79C22semidirect
10. 2−1+4×C79C23semidirect
11. H(5,𝔽2)×C79C23semidirect
13. C2×#41×C79C23semidirect
15. C22×Q8×C79C23semidirect
38. C2×2−1+6C79direct (N × H)
40. C2×C792−1+6direct (N × H)
42. 2−1+6C2×C79direct (N × H)
43. C2×#585C2×C79semidirect
44. C22×2−1+4C2×C79semidirect
45. C79C2×2−1+6direct (N × H)
46. #585C22×C79semidirect
47. C2×2−1+4C22×C79semidirect
48. C2×2−1+4C22×C79semidirect
49. C2×H(5,𝔽2)C22×C79semidirect
50. C22×#41C22×C79semidirect
51. C23×Q8C22×C79semidirect
52. 2−1+4C23×C79semidirect
53. H(5,𝔽2)C23×C79semidirect
55. C2×#41C23×C79semidirect
57. C22×Q8C23×C79semidirect
81. C2C79×2−1+6direct (N × H)

Maximal subgroups

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

subgroupindex
C79×2−1+62
C2×#585×C792
C22×2−1+4×C792
C2×2−1+679