Finite Group Databasebeta

← C2×C3×C52⋊#3862 #36348056

Subgroups — C2×C3×C52⋊#3862 #36348056

Order 22050.

192 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C52⋊#3862C211yesmaximal, characteristic, direct product factor, Hall
2C2×C52⋊#3862C313yesmaximal, direct product factor
3C2×C3×C52×C72C311yesmaximal, characteristic, complemented
4C52⋊#3862C2×C313yesdirect product factor
5C3×C52×C72C2×C311yescharacteristic, complemented
6C2×C3×C7⋊(C52⋊C3)—72nomaximal
7C2×C52×C72C3211yescharacteristic, complemented, Hall
8C3×C7⋊(C52⋊C3)—72no—
9C2×C3×C5×C72—32no—
10C52×C72C2×C3211yescharacteristic, complemented, Hall
11C2×C3×C52×C7—32no—
12C2×C3×C52×C7ΓL(1,𝔽8)12yescomplemented
13C2×C7⋊(C52⋊C3)—76no—
14C2×C3×#3862—251nomaximal, Hall
15C3×C5×C72—32no—
16C3×C52×C7—32no—
17C3×C52×C7C2×ΓL(1,𝔽8)12yescomplemented
18C7⋊(C52⋊C3)—76no—
19C2×C5×C72—32no—
20C2×C3×C52⋊C3—491noHall
21C3×#3862—251noHall
22C2×C52×C7—32no—
23C2×C52×C7C3×ΓL(1,𝔽8)12yescomplemented
24C2×C3×C72C52⋊C311yescharacteristic, complemented
25C2×#3862—253no—
26C5×C72—32no—
27C3×C52⋊C3—491noHall
28C2×C3×C5×C7—312no—
29C2×C3×C5×C7—34no—
30C52×C7—32no—
31C52×C7C2×C3×ΓL(1,𝔽8)12yescomplemented
32C2×C3×C52#386211yescharacteristic, complemented
33C2×C52⋊C3—493no—
34C3×C72C2×C52⋊C311yescharacteristic, complemented
35#3862—253no—
36C2×C3×ΓL(1,𝔽8)—1752no—
37C3×C5×C7—312no—
38C3×C5×C7—34no—
39C2×C72C3×C52⋊C311yescharacteristic, complemented, Hall
40C3×C52C2×#386211yescharacteristic, complemented
41C52⋊C3—493no—
42C2×C5×C7—312no—
43C2×C5×C7—34no—
44C3×ΓL(1,𝔽8)—1752no—
45C2×C52C3×#386211yescharacteristic, complemented, Hall
46C72C2×C3×C52⋊C311yescharacteristic, complemented, Sylow
47C2×C3×C7—32no—
48C2×C3×C7C7⋊(C52⋊C3)12yescomplemented
49C2×ΓL(1,𝔽8)—1756no—
50C5×C7—312no—
51C5×C7—34no—
52C2×C3×C5—32no—
53C52C2×C3×#386211yescharacteristic, complemented, Sylow
54C3×C7—32no—
55C3×C7C2×C7⋊(C52⋊C3)12yescomplemented
56ΓL(1,𝔽8)—1756no—
57C2×C32—12251noHall
58C3×C5—32no—
59C2×C7—32no—
60C2×C7C3×C7⋊(C52⋊C3)12yescomplemented
61C2×C5—32no—
62C32—12251noSylow
63C7—32no—
64C7C2×C3×C7⋊(C52⋊C3)12yescomplemented
65C2×C3—12253no—
66C2×C3C52⋊#386211yescharacteristic, direct product factor
67C5—32no—
68C3—12253no—
69C3C2×C52⋊#386211yescharacteristic, direct product factor
70C2C3×C52⋊#386211yescharacteristic, direct product factor, Sylow
subgroupG/H
center, hypercenterC2×C3C52⋊#3862
commutator, cosocle, hypocenterC52×C72C2×C32
FrattiniC1G
Fitting, socleC2×C3×C52×C72C3
LCSG ▷ C52×C72
UCSC1 ◁ C2×C3

Complements

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

NH ≅ G/Ntype
1. C3×C52⋊#3862C2direct (N × H)
2. C2×C52⋊#3862C3direct (N × H)
3. C2×C3×C52×C72C3semidirect
4. C52⋊#3862C2×C3direct (N × H)
5. C3×C52×C72C2×C3semidirect
7. C2×C52×C72C32semidirect
10. C52×C72C2×C32semidirect
12. C2×C3×C52×C7ΓL(1,𝔽8)semidirect
17. C3×C52×C7C2×ΓL(1,𝔽8)semidirect
23. C2×C52×C7C3×ΓL(1,𝔽8)semidirect
24. C2×C3×C72C52⋊C3semidirect
31. C52×C7C2×C3×ΓL(1,𝔽8)semidirect
32. C2×C3×C52#3862semidirect
34. C3×C72C2×C52⋊C3semidirect
39. C2×C72C3×C52⋊C3semidirect
40. C3×C52C2×#3862semidirect
45. C2×C52C3×#3862semidirect
46. C72C2×C3×C52⋊C3semidirect
48. C2×C3×C7C7⋊(C52⋊C3)semidirect
53. C52C2×C3×#3862semidirect
55. C3×C7C2×C7⋊(C52⋊C3)semidirect
60. C2×C7C3×C7⋊(C52⋊C3)semidirect
64. C7C2×C3×C7⋊(C52⋊C3)semidirect
66. C2×C3C52⋊#3862direct (N × H)
69. C3C2×C52⋊#3862direct (N × H)
70. C2C3×C52⋊#3862direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C52⋊#38622
C2×C52⋊#38623
C2×C3×C52×C723
C2×C3×C7⋊(C52⋊C3)7
C2×C3×#386225