Finite Group Databasebeta

← ΓL(1,𝔽8)×D157⋊C3 #34089957

Subgroups — ΓL(1,𝔽8)×D157⋊C3 #34089957

Order 19782.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1ΓL(1,𝔽8)×C157⋊C3C211yesmaximal, characteristic, complemented, Hall
2#20268646C311yesmaximal, characteristic, complemented
3#20268645C311yesmaximal, characteristic, complemented
4ΓL(1,𝔽8)×D157C311yesmaximal, characteristic, complemented
5C7×D157⋊C3C311yesmaximal, characteristic, complemented
6#15693074C2×C311yescharacteristic, complemented
7#15693073C2×C311yescharacteristic, complemented
8C7×C157⋊C3C2×C311yescharacteristic, complemented
9ΓL(1,𝔽8)×C157C2×C311yescharacteristic, complemented
10C3×D157⋊C3—71nomaximal, Hall
11C7×D157C3211yescharacteristic, complemented, Hall
12C3×C157⋊C3—71noHall
13C7×C157C2×C3211yescharacteristic, complemented, Hall
14C3×D157—71no—
15D157⋊C3—71no—
16D157⋊C3—71no—
17D157⋊C3ΓL(1,𝔽8)11yescharacteristic, direct product factor
18C3×C157—71no—
19C157⋊C3—71no—
20C157⋊C3—71no—
21C157⋊C3C2×ΓL(1,𝔽8)11yescharacteristic, complemented
22D157C3×ΓL(1,𝔽8)11yescharacteristic, complemented, Hall
23C157C2×C3×ΓL(1,𝔽8)11yescharacteristic, complemented, Sylow
24C2×C3×ΓL(1,𝔽8)—1571nomaximal, Hall
25C3×ΓL(1,𝔽8)—1571noHall
26C2×C3×C7—1571no—
27C2×ΓL(1,𝔽8)—1571no—
28C2×ΓL(1,𝔽8)—1571no—
29C2×ΓL(1,𝔽8)—4711no—
30C3×C7—1571no—
31ΓL(1,𝔽8)—1571no—
32ΓL(1,𝔽8)—1571no—
33ΓL(1,𝔽8)D157⋊C311yescharacteristic, direct product factor
34C2×C32—10991noHall
35C2×C7—4711noHall
36C32—10991noSylow
37C7C3×D157⋊C311yescharacteristic, complemented, Sylow
38C2×C3—10991no—
39C2×C3—10991no—
40C2×C3—1571no—
41C2×C3—32971no—
42C3—71no—
43C3—10991no—
44C3—10991no—
45C3—1571no—
46C2—4711noSylow
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC7×C157C2×C32
LCSG ▷ C7×C157
UCSC1

Complements

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

NH ≅ G/Ntype
1. ΓL(1,𝔽8)×C157⋊C3C2semidirect
2. #20268646C3semidirect
3. #20268645C3semidirect
4. ΓL(1,𝔽8)×D157C3semidirect
5. C7×D157⋊C3C3semidirect
6. #15693074C2×C3semidirect
7. #15693073C2×C3semidirect
8. C7×C157⋊C3C2×C3semidirect
9. ΓL(1,𝔽8)×C157C2×C3semidirect
11. C7×D157C32semidirect
13. C7×C157C2×C32semidirect
17. D157⋊C3ΓL(1,𝔽8)direct (N × H)
21. C157⋊C3C2×ΓL(1,𝔽8)semidirect
22. D157C3×ΓL(1,𝔽8)semidirect
23. C157C2×C3×ΓL(1,𝔽8)semidirect
33. ΓL(1,𝔽8)D157⋊C3direct (N × H)
37. C7C3×D157⋊C3semidirect

Maximal subgroups

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

subgroupindex
ΓL(1,𝔽8)×C157⋊C32
#202686463
#202686453
ΓL(1,𝔽8)×D1573
C7×D157⋊C33
C3×D157⋊C37
C2×C3×ΓL(1,𝔽8)157