Finite Group Databasebeta

← C3⋊#26043023 #46856049

Subgroups — C3⋊#26043023 #46856049

Order 35028.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#15668588C211yesmaximal, characteristic
2#26043023—31nomaximal
3Dic2919C311yesmaximal, characteristic, complemented
4C3×#15668588C411yescharacteristic, complemented, Hall
5C2×#15668588—21no—
6C2×#15668588D311yescharacteristic
7C2×C3×C7×C139C2×C311yescharacteristic
8C3⋊((C139⋊C3)⋊C4)—71nomaximal, Hall
9Dic973—31noHall
10C3×C7×C139C3×C411yescharacteristic, complemented
11#15668588—21no—
12#15668588Dic311yescharacteristic, complemented
13C2×C3×C139⋊C3—71no—
14C2×C7×C139C3×D311yescharacteristic
15Dic417—71no—
16(C139⋊C3)⋊C4—211no—
17C3×C139⋊C3—71noHall
18C7×C139C3×Dic311yescharacteristic, complemented, Hall
19C2×C3×C139AGL(1,𝔽7)11yescharacteristic
20C2×C139⋊C3—71no—
21C2×C139⋊C3—141no—
22Dic139—211noHall
23C3×C139ΓL(1,𝔽8)⋊C411yescharacteristic, complemented
24C139⋊C3—71no—
25C139⋊C3—141no—
26C2×C139C3⋊AGL(1,𝔽7)11yescharacteristic
27C3⋊(ΓL(1,𝔽8)⋊C4)—1391nomaximal, Hall
28C139C3⋊(ΓL(1,𝔽8)⋊C4)11yescharacteristic, complemented, Sylow
29C2×C3×ΓL(1,𝔽8)—1391no—
30Dic21—1391no—
31ΓL(1,𝔽8)⋊C4—4171no—
32C3×ΓL(1,𝔽8)—1391noHall
33C2×C3×C7D139⋊C311yescharacteristic
34C2×ΓL(1,𝔽8)—2781no—
35C2×ΓL(1,𝔽8)—1391no—
36C3×Dic3—9731noHall
37Dic7—4171noHall
38C3×C7(C139⋊C3)⋊C411yescharacteristic, complemented
39ΓL(1,𝔽8)—2781no—
40ΓL(1,𝔽8)—1391no—
41C2×C32—9731no—
42C2×C7C3⋊(D139⋊C3)11yescharacteristic
43C3×C4—29191no—
44Dic3—9731no—
45C32—9731noSylow
46C7C3⋊((C139⋊C3)⋊C4)11yescharacteristic, complemented, Sylow
47C2×C3—19461no—
48C2×C3—9731no—
49C2×C3#1915425411yescharacteristic
50C4—29191noSylow
51C3—19461no—
52C3—9731no—
53C3#2604302311yescharacteristic, complemented
54C2C3⋊#1915425411yescharacteristic
subgroupG/H
center, Frattini, hypercenterC2C3⋊#19154254
commutator, hypocenterC3×C7×C139C3×C4
Fitting, socle, cosocleC2×C3×C7×C139C2×C3
prime radicalC2×C3×#15668588C2
LCSG ▷ C3×C7×C139
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
3. Dic2919C3semidirect
4. C3×#15668588C4semidirect
10. C3×C7×C139C3×C4semidirect
12. #15668588Dic3semidirect
18. C7×C139C3×Dic3semidirect
23. C3×C139ΓL(1,𝔽8)⋊C4semidirect
28. C139C3⋊(ΓL(1,𝔽8)⋊C4)semidirect
38. C3×C7(C139⋊C3)⋊C4semidirect
46. C7C3⋊((C139⋊C3)⋊C4)semidirect
53. C3#26043023semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#156685882
#260430233
Dic29193
C3⋊((C139⋊C3)⋊C4)7
C3⋊(ΓL(1,𝔽8)⋊C4)139