Finite Group Databasebeta

← C3⋊#24922588 #44544743

Subgroups — C3⋊#24922588 #44544743

Order 32004.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#14581887C211yesmaximal, characteristic
2#24922588—31nomaximal
3Dic2667C311yesmaximal, characteristic, complemented
4C3×#14581887C411yescharacteristic, complemented, Hall
5C2×#14581887—21no—
6C2×#14581887D311yescharacteristic
7C2×C3×C7×C127C2×C311yescharacteristic
8C3⋊((C127⋊C3)⋊C4)—71nomaximal, Hall
9Dic889—31noHall
10C3×C7×C127C3×C411yescharacteristic, complemented
11#14581887—21no—
12#14581887Dic311yescharacteristic, complemented
13C2×C3×C127⋊C3—71no—
14C2×C7×C127C3×D311yescharacteristic
15Dic381—71no—
16(C127⋊C3)⋊C4—211no—
17C3×C127⋊C3—71noHall
18C7×C127C3×Dic311yescharacteristic, complemented, Hall
19C2×C3×C127AGL(1,𝔽7)11yescharacteristic
20C2×C127⋊C3—71no—
21C2×C127⋊C3—141no—
22Dic127—211noHall
23C3×C127ΓL(1,𝔽8)⋊C411yescharacteristic, complemented
24C127⋊C3—71no—
25C127⋊C3—141no—
26C2×C127C3⋊AGL(1,𝔽7)11yescharacteristic
27C3⋊(ΓL(1,𝔽8)⋊C4)—1271nomaximal, Hall
28C127C3⋊(ΓL(1,𝔽8)⋊C4)11yescharacteristic, complemented, Sylow
29C2×C3×ΓL(1,𝔽8)—1271no—
30Dic21—1271no—
31ΓL(1,𝔽8)⋊C4—3811no—
32C3×ΓL(1,𝔽8)—1271noHall
33C2×C3×C7D127⋊C311yescharacteristic
34C2×ΓL(1,𝔽8)—1271no—
35C2×ΓL(1,𝔽8)—2541no—
36C3×Dic3—8891noHall
37Dic7—3811noHall
38C3×C7(C127⋊C3)⋊C411yescharacteristic, complemented
39ΓL(1,𝔽8)—1271no—
40ΓL(1,𝔽8)—2541no—
41C2×C32—8891no—
42C2×C7C3⋊(D127⋊C3)11yescharacteristic
43C3×C4—26671no—
44Dic3—8891no—
45C32—8891noSylow
46C7C3⋊((C127⋊C3)⋊C4)11yescharacteristic, complemented, Sylow
47C2×C3—8891no—
48C2×C3—17781no—
49C2×C3#1912863311yescharacteristic
50C4—26671noSylow
51C3—8891no—
52C3—17781no—
53C3#2492258811yescharacteristic, complemented
54C2C3⋊#1912863311yescharacteristic
subgroupG/H
center, Frattini, hypercenterC2C3⋊#19128633
commutator, hypocenterC3×C7×C127C3×C4
Fitting, socle, cosocleC2×C3×C7×C127C2×C3
prime radicalC2×C3×#14581887C2
LCSG ▷ C3×C7×C127
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
3. Dic2667C3semidirect
4. C3×#14581887C4semidirect
10. C3×C7×C127C3×C4semidirect
12. #14581887Dic3semidirect
18. C7×C127C3×Dic3semidirect
23. C3×C127ΓL(1,𝔽8)⋊C4semidirect
28. C127C3⋊(ΓL(1,𝔽8)⋊C4)semidirect
38. C3×C7(C127⋊C3)⋊C4semidirect
46. C7C3⋊((C127⋊C3)⋊C4)semidirect
53. C3#24922588semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#145818872
#249225883
Dic26673
C3⋊((C127⋊C3)⋊C4)7
C3⋊(ΓL(1,𝔽8)⋊C4)127