Finite Group Databasebeta

← C3⋊#21439563 #37524813

Subgroups — C3⋊#21439563 #37524813

Order 22932.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C13×#3862C211yesmaximal, characteristic
2C7×Dic273—31nomaximal
3#21439563—33nomaximal
4C3×C13×#3862C411yescharacteristic, complemented, Hall
5C2×C13×#3862D313yes—
6C2×C3×C72×C13D311yescharacteristic
7C7×Dic91—91noHall
8C3×C72×C13Dic311yescharacteristic, complemented
9C13×#3862Dic313yescomplemented
10C3⋊#10596868—131nomaximal, Hall
11C2×C3×C13×ΓL(1,𝔽8)—141no—
12C2×C72×C13C3⋊D311yescharacteristic
13Dic273—31no—
14C7×Dic39—211no—
15C2×C3×#3862D1311yescharacteristic
16C3×C13×ΓL(1,𝔽8)—141no—
17C72×C13C3⋊Dic311yescharacteristic, complemented, Hall
18C7×Dic21—391no—
19#10596868—393no—
20C2×C3×C7×C13—21no—
21C2×C3×C7×C13—31no—
22C2×C3×C7×C13—31no—
23C2×C13×ΓL(1,𝔽8)—143no—
24C3⋊Dic39—491nomaximal, Hall
25C3×#3862Dic1311yescharacteristic, complemented, Hall
26Dic91—91no—
27C7×Dic13—631no—
28C2×C3×C72D3911yescharacteristic
29C2×#3862D3913yes—
30C3×C7×C13—21no—
31C3×C7×C13—31no—
32C3×C7×C13—31no—
33C13×ΓL(1,𝔽8)—143no—
34C2×C32×C13—981no—
35C7×Dic7—1171noHall
36C2×C7×C13—21no—
37C2×C7×C13—31no—
38C2×C7×C13—61no—
39Dic39—211no—
40Dic39—1473no—
41C3×C72Dic3911yescharacteristic, complemented
42#3862Dic3913yescomplemented
43C2×C3×ΓL(1,𝔽8)—141no—
44C32×C13—981noHall
45C2×C72C3⋊D3911yescharacteristic
46C7×C13—21no—
47C7×C13—31no—
48C7×C13—61no—
49Dic21—391no—
50C7×Dic3—2731no—
51C2×C3×C13—983no—
52C2×C3×C13#6441811yescharacteristic
53C3×ΓL(1,𝔽8)—141no—
54Dic13—631noHall
55C72C3⋊Dic3911yescharacteristic, complemented, Sylow
56C2×C3×C7—21no—
57C2×C3×C7—61no—
58C2×C3×C7—61no—
59C2×ΓL(1,𝔽8)—143no—
60C3×C13—983no—
61C3×C13#1059686811yescharacteristic, complemented
62C3⋊Dic3—6371noHall
63C4×C7—8191no—
64Dic7—1171no—
65C2×C13C3⋊#6441811yescharacteristic
66C3×C7—21no—
67C3×C7—61no—
68C3×C7—61no—
69ΓL(1,𝔽8)—143no—
70C2×C32—981no—
71C2×C7—21no—
72C2×C7—61no—
73C2×C7—61no—
74C13C3⋊#1059686811yescharacteristic, complemented, Sylow
75Dic3—2731no—
76Dic3—19113no—
77C32—981noSylow
78C7—21no—
79C7—61no—
80C7—61no—
81C2×C3—983no—
82C2×C3C13⋊#6441811yescharacteristic
83C4—8191noSylow
84C3—983no—
85C3#2143956311yescharacteristic, complemented
86C2C3⋊(C13⋊#64418)11yescharacteristic
subgroupG/H
center, Frattini, hypercenterC2C3⋊(C13⋊#64418)
commutator, hypocenterC3×C13×#3862C4
Fitting, socleC2×C3×C72×C13D3
prime radical, cosocleC2×C3×C13×#3862C2
LCSG ▷ C3×C13×#3862
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
4. C3×C13×#3862C4semidirect
8. C3×C72×C13Dic3semidirect
9. C13×#3862Dic3semidirect
17. C72×C13C3⋊Dic3semidirect
25. C3×#3862Dic13semidirect
41. C3×C72Dic39semidirect
42. #3862Dic39semidirect
55. C72C3⋊Dic39semidirect
61. C3×C13#10596868semidirect
74. C13C3⋊#10596868semidirect
85. C3#21439563semidirect

Maximal subgroups

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

subgroupindex
C2×C3×C13×#38622
C7×Dic2733
#214395633
C3⋊#1059686813
C3⋊Dic3949