Finite Group Databasebeta

← C79×#63103 #34174792

Subgroups — C79×#63103 #34174792

Order 20224.

59452 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C79×2−1+6C2128yesmaximal, complemented
2C79×H(7,𝔽2)C2136yesmaximal, complemented
3C2×#585×C79C2163yesmaximal, complemented
4#585×C79C221336yescomplemented
5#585×C79C2211008yescomplemented
6C2×2−1+4×C79C221378yescomplemented
7C2×H(5,𝔽2)×C79C221630yescomplemented
8C22×#41×C79C221315yescomplemented
92−1+4×C79C2312016yescomplemented
10H(5,𝔽2)×C79C2313360yescomplemented
11C2×#41×C79C2311260yescomplemented
12C2×#41×C79C2313780yescomplemented
13C22×Q8×C79C231315yescomplemented
14C22×D4×C79C231945yescomplemented
15C23×C4×C79C231135yescomplemented
16C24×C79C241135yes—
17#41×C79C241336yes—
18#41×C79C2415040yes—
19C2×Q8×C79C2411260yes—
20C2×D4×C79C2413780yes—
21C22×C4×C79C241315yes—
22C22×C4×C79C241945yes—
23C23×C79—8135no—
24C23×C79C251315yes—
25Q8×C79C251336yes—
26D4×C79C2511008yes—
27C2×C4×C79C251945yes—
28C2×C4×C79C25163yes—
29C22×C79—4315no—
30C22×C79C26163yes—
31C4×C79C26163yes—
32C4×C79C2611yescharacteristic
33#63103C7911yesmaximal, characteristic, direct product factor, Sylow
34C2×C79—263no—
35C2×C79C2711yescharacteristic
362−1+6C2×C79128yescomplemented
37H(7,𝔽2)C2×C79136yescomplemented
38C2×#585C2×C79163yescomplemented
39C79#6310311yescharacteristic, direct product factor, Sylow
40#585C22×C791336yescomplemented
41#585C22×C7911008yescomplemented
42C2×2−1+4C22×C791378yescomplemented
43C2×H(5,𝔽2)C22×C791630yescomplemented
44C22×#41C22×C791315yescomplemented
452−1+4C23×C7912016yescomplemented
46H(5,𝔽2)C23×C7913360yescomplemented
47C2×#41C23×C7911260yescomplemented
48C2×#41C23×C7913780yescomplemented
49C22×Q8C23×C791315yescomplemented
50C22×D4C23×C791945yescomplemented
51C23×C4C23×C791135yescomplemented
52C24C24×C791135yes—
53#41C24×C791336yes—
54#41C24×C7915040yes—
55C2×Q8C24×C7911260yes—
56C2×D4C24×C7913780yes—
57C22×C4C24×C791315yes—
58C22×C4C24×C791945yes—
59C23—8135no—
60C23C25×C791315yes—
61Q8C25×C791336yes—
62D4C25×C7911008yes—
63C2×C4C25×C79163yes—
64C2×C4C25×C791945yes—
65C22—4315no—
66C22C26×C79163yes—
67C4C26×C7911yescharacteristic
68C4C26×C79163yes—
69C2—263no—
70C2C27×C7911yescharacteristic
subgroupG/H
centerC4×C79C26
commutator, Frattini, cosocleC2C27×C79
socleC2×C79C27
LCSG ▷ C2 ▷ C1
UCSC1 ◁ C4×C79 ◁ G

Complements

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

NH ≅ G/Ntype
1. C79×2−1+6C2semidirect
2. C79×H(7,𝔽2)C2semidirect
3. C2×#585×C79C2semidirect
4. #585×C79C22semidirect
5. #585×C79C22semidirect
6. C2×2−1+4×C79C22semidirect
7. C2×H(5,𝔽2)×C79C22semidirect
8. C22×#41×C79C22semidirect
9. 2−1+4×C79C23semidirect
10. H(5,𝔽2)×C79C23semidirect
11. C2×#41×C79C23semidirect
12. C2×#41×C79C23semidirect
13. C22×Q8×C79C23semidirect
14. C22×D4×C79C23semidirect
15. C23×C4×C79C23semidirect
33. #63103C79direct (N × H)
36. 2−1+6C2×C79semidirect
37. H(7,𝔽2)C2×C79semidirect
38. C2×#585C2×C79semidirect
39. C79#63103direct (N × H)
40. #585C22×C79semidirect
41. #585C22×C79semidirect
42. C2×2−1+4C22×C79semidirect
43. C2×H(5,𝔽2)C22×C79semidirect
44. C22×#41C22×C79semidirect
45. 2−1+4C23×C79semidirect
46. H(5,𝔽2)C23×C79semidirect
47. C2×#41C23×C79semidirect
48. C2×#41C23×C79semidirect
49. C22×Q8C23×C79semidirect
50. C22×D4C23×C79semidirect
51. C23×C4C23×C79semidirect

Maximal subgroups

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

subgroupindex
C79×2−1+62
C79×H(7,𝔽2)2
C2×#585×C792
#6310379