Finite Group Databasebeta

← C61×#63103 #29566536

Subgroups — C61×#63103 #29566536

Order 15616.

59452 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C61×2−1+6C2128yesmaximal, complemented
2C61×H(7,𝔽2)C2136yesmaximal, complemented
3C2×C61×#585C2163yesmaximal, complemented
4C61×#585C221336yescomplemented
5C61×#585C2211008yescomplemented
6C2×2−1+4×C61C221378yescomplemented
7C2×H(5,𝔽2)×C61C221630yescomplemented
8C22×#41×C61C221315yescomplemented
92−1+4×C61C2312016yescomplemented
10H(5,𝔽2)×C61C2313360yescomplemented
11C2×#41×C61C2311260yescomplemented
12C2×#41×C61C2313780yescomplemented
13C22×Q8×C61C231315yescomplemented
14C22×D4×C61C231945yescomplemented
15C23×C4×C61C231135yescomplemented
16C24×C61C241135yes—
17#41×C61C241336yes—
18#41×C61C2415040yes—
19C2×Q8×C61C2411260yes—
20C2×D4×C61C2413780yes—
21C22×C4×C61C241315yes—
22C22×C4×C61C241945yes—
23C23×C61—8135no—
24C23×C61C251315yes—
25Q8×C61C251336yes—
26D4×C61C2511008yes—
27C2×C4×C61C251945yes—
28C2×C4×C61C25163yes—
29#63103C6111yesmaximal, characteristic, direct product factor, Sylow
30C22×C61—4315no—
31C22×C61C26163yes—
32C4×C61C26163yes—
33C4×C61C2611yescharacteristic
342−1+6C2×C61128yescomplemented
35H(7,𝔽2)C2×C61136yescomplemented
36C2×#585C2×C61163yescomplemented
37C2×C61—263no—
38C2×C61C2711yescharacteristic
39#585C22×C611336yescomplemented
40#585C22×C6111008yescomplemented
41C2×2−1+4C22×C611378yescomplemented
42C2×H(5,𝔽2)C22×C611630yescomplemented
43C22×#41C22×C611315yescomplemented
44C61#6310311yescharacteristic, direct product factor, Sylow
452−1+4C23×C6112016yescomplemented
46H(5,𝔽2)C23×C6113360yescomplemented
47C2×#41C23×C6111260yescomplemented
48C2×#41C23×C6113780yescomplemented
49C22×Q8C23×C611315yescomplemented
50C22×D4C23×C611945yescomplemented
51C23×C4C23×C611135yescomplemented
52C24C24×C611135yes—
53#41C24×C611336yes—
54#41C24×C6115040yes—
55C2×Q8C24×C6111260yes—
56C2×D4C24×C6113780yes—
57C22×C4C24×C611315yes—
58C22×C4C24×C611945yes—
59C23—8135no—
60C23C25×C611315yes—
61Q8C25×C611336yes—
62D4C25×C6111008yes—
63C2×C4C25×C61163yes—
64C2×C4C25×C611945yes—
65C22—4315no—
66C22C26×C61163yes—
67C4C26×C61163yes—
68C4C26×C6111yescharacteristic
69C2—263no—
70C2C27×C6111yescharacteristic
subgroupG/H
centerC4×C61C26
commutator, Frattini, cosocleC2C27×C61
socleC2×C61C27
LCSG ▷ C2 ▷ C1
UCSC1 ◁ C4×C61 ◁ G

Complements

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

NH ≅ G/Ntype
1. C61×2−1+6C2semidirect
2. C61×H(7,𝔽2)C2semidirect
3. C2×C61×#585C2semidirect
4. C61×#585C22semidirect
5. C61×#585C22semidirect
6. C2×2−1+4×C61C22semidirect
7. C2×H(5,𝔽2)×C61C22semidirect
8. C22×#41×C61C22semidirect
9. 2−1+4×C61C23semidirect
10. H(5,𝔽2)×C61C23semidirect
11. C2×#41×C61C23semidirect
12. C2×#41×C61C23semidirect
13. C22×Q8×C61C23semidirect
14. C22×D4×C61C23semidirect
15. C23×C4×C61C23semidirect
29. #63103C61direct (N × H)
34. 2−1+6C2×C61semidirect
35. H(7,𝔽2)C2×C61semidirect
36. C2×#585C2×C61semidirect
39. #585C22×C61semidirect
40. #585C22×C61semidirect
41. C2×2−1+4C22×C61semidirect
42. C2×H(5,𝔽2)C22×C61semidirect
43. C22×#41C22×C61semidirect
44. C61#63103direct (N × H)
45. 2−1+4C23×C61semidirect
46. H(5,𝔽2)C23×C61semidirect
47. C2×#41C23×C61semidirect
48. C2×#41C23×C61semidirect
49. C22×Q8C23×C61semidirect
50. C22×D4C23×C61semidirect
51. C23×C4C23×C61semidirect

Maximal subgroups

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

subgroupindex
C61×2−1+62
C61×H(7,𝔽2)2
C2×C61×#5852
#6310361