Finite Group Databasebeta

← AGL(1,𝔽7)×D235 #34089480

Subgroups — AGL(1,𝔽7)×D235 #34089480

Order 19740.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5⋊(ΓL(1,𝔽8)⋊D47)C211yesmaximal, characteristic, complemented
2ΓL(1,𝔽8)×D235C211yesmaximal, characteristic, complemented
3C5×AGL(1,𝔽7)×C47C211yesmaximal, characteristic, complemented
4D7×D235C311yesmaximal, characteristic, complemented, Hall
5C5×ΓL(1,𝔽8)×C47C2211yescharacteristic, complemented, Hall
6AGL(1,𝔽7)×D47—51nomaximal, Hall
7D1645C2×C311yescharacteristic, complemented
8C7×D235C2×C311yescharacteristic, complemented
9C5×D7×C47C2×C311yescharacteristic, complemented
10C2×C3×D235—71nomaximal, Hall
11ΓL(1,𝔽8)⋊D47—51no—
12AGL(1,𝔽7)×C47D511yescharacteristic, complemented
13ΓL(1,𝔽8)×D47—51no—
14C5×C7×C47C22×C311yescharacteristic, complemented, Hall
15C2×C3×C5×C47—71no—
16C3×D235—71no—
17C3×D235—141no—
18D7×D47—51noHall
19ΓL(1,𝔽8)×C47C2×D511yescharacteristic, complemented, Hall
20C2×D235—71noHall
21C3×C5×C47—141noHall
22D329—51no—
23C7×D47—51no—
24D7×C47C3×D511yescharacteristic, complemented
25C2×C3×D47—351noHall
26C2×C5×C47—71no—
27D235—71no—
28D235AGL(1,𝔽7)11yescharacteristic, direct product factor
29D5×AGL(1,𝔽7)—471nomaximal, Hall
30C7×C47C2×C3×D511yescharacteristic, complemented, Hall
31C2×C3×C47—71no—
32C3×D47—351no—
33C3×D47—701no—
34C5×C47C2×AGL(1,𝔽7)11yescharacteristic, complemented, Hall
35C5⋊AGL(1,𝔽7)—471no—
36D5×ΓL(1,𝔽8)—471no—
37C5×AGL(1,𝔽7)D4711yescharacteristic, complemented
38C2×D47—351noHall
39C3×C47—141noHall
40D5×D7—471noHall
41C5×ΓL(1,𝔽8)C2×D4711yescharacteristic, complemented, Hall
42C2×C47—71no—
43D47—51no—
44D47—351no—
45C2×AGL(1,𝔽7)—2351noHall
46D35—471no—
47C5×D7C3×D4711yescharacteristic, complemented
48C7×D5—471no—
49C2×C3×D5—3291noHall
50C47D5×AGL(1,𝔽7)11yescharacteristic, complemented, Sylow
51C2×ΓL(1,𝔽8)—2351no—
52AGL(1,𝔽7)—2351no—
53AGL(1,𝔽7)D23511yescharacteristic, direct product factor
54C5×C7C2×C3×D4711yescharacteristic, complemented, Hall
55C2×C3×C5—71no—
56C3×D5—3291no—
57C3×D5—3291no—
58C2×D7—2351noHall
59ΓL(1,𝔽8)C2×D23511yescharacteristic, complemented, Hall
60C2×D5—3291noHall
61C3×C5—71noHall
62C2×C7—2351no—
63D7—2351no—
64D7C3×D23511yescharacteristic, complemented
65C22×C3—16451noHall
66C2×C5—71no—
67D5—471no—
68D5—3291no—
69C7C2×C3×D23511yescharacteristic, complemented, Sylow
70C2×C3—71no—
71C2×C3—16451no—
72C2×C3—16451no—
73C5AGL(1,𝔽7)×D4711yescharacteristic, complemented, Sylow
74C22—16451noSylow
75C3—71noSylow
76C2—71no—
77C2—16451no—
78C2—2351no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC5×C7×C47C22×C3
LCSG ▷ C5×C7×C47
UCSC1

Complements

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

NH ≅ G/Ntype
1. C5⋊(ΓL(1,𝔽8)⋊D47)C2semidirect
2. ΓL(1,𝔽8)×D235C2semidirect
3. C5×AGL(1,𝔽7)×C47C2semidirect
4. D7×D235C3semidirect
5. C5×ΓL(1,𝔽8)×C47C22semidirect
7. D1645C2×C3semidirect
8. C7×D235C2×C3semidirect
9. C5×D7×C47C2×C3semidirect
12. AGL(1,𝔽7)×C47D5semidirect
14. C5×C7×C47C22×C3semidirect
19. ΓL(1,𝔽8)×C47C2×D5semidirect
24. D7×C47C3×D5semidirect
28. D235AGL(1,𝔽7)direct (N × H)
30. C7×C47C2×C3×D5semidirect
34. C5×C47C2×AGL(1,𝔽7)semidirect
37. C5×AGL(1,𝔽7)D47semidirect
41. C5×ΓL(1,𝔽8)C2×D47semidirect
47. C5×D7C3×D47semidirect
50. C47D5×AGL(1,𝔽7)semidirect
53. AGL(1,𝔽7)D235direct (N × H)
54. C5×C7C2×C3×D47semidirect
59. ΓL(1,𝔽8)C2×D235semidirect
64. D7C3×D235semidirect
69. C7C2×C3×D235semidirect
73. C5AGL(1,𝔽7)×D47semidirect

Maximal subgroups

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

subgroupindex
C5⋊(ΓL(1,𝔽8)⋊D47)2
ΓL(1,𝔽8)×D2352
C5×AGL(1,𝔽7)×C472
D7×D2353
AGL(1,𝔽7)×D475
C2×C3×D2357
D5×AGL(1,𝔽7)47