Finite Group Databasebeta

← C4×C13⋊C3×C49⋊C3 #37524136

Subgroups — C4×C13⋊C3×C49⋊C3 #37524136

Order 22932.

108 conjugacy classes of subgroups; only the 42 normal subgroups are shown.

normal subgroups only

This group has 108 conjugacy classes of subgroups — too many to draw. Only its 42 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C13⋊C3×C49⋊C3C211yesmaximal, characteristic
2C4×#14274255C311yesmaximal, characteristic, complemented
3C4×#14274254C311yesmaximal, characteristic, complemented
4C4×C13×C49⋊C3C311yesmaximal, characteristic, complemented
5C4×C13⋊C3×C49C311yesmaximal, characteristic, complemented
6C13⋊C3×C49⋊C3C411yescharacteristic, direct product factor, Hall
7C2×#14274255C2×C311yescharacteristic
8C2×#14274254C2×C311yescharacteristic
9C2×C13×C49⋊C3C2×C311yescharacteristic
10C2×C13⋊C3×C49C2×C311yescharacteristic
11C4×ΓL(1,𝔽8)×C13⋊C3—71nomaximal
12C4×C13×C49C3211yescharacteristic, complemented, Hall
13#14274255C3×C411yescharacteristic, complemented
14#14274254C3×C411yescharacteristic, complemented
15C13⋊C3×C49C3×C411yescharacteristic, complemented
16C13×C49⋊C3C3×C411yescharacteristic, complemented
17C3×C4×C49⋊C3—131nomaximal, Hall
18C2×ΓL(1,𝔽8)×C13⋊C3—71no—
19C2×C13×C49C2×C3211yescharacteristic
20C4×#63271—71no—
21C4×#63270—71no—
22C4×C13×ΓL(1,𝔽8)—71no—
23C4×C7×C13⋊C3ΓL(1,𝔽8)11yescharacteristic
24C2×C3×C49⋊C3—131no—
25ΓL(1,𝔽8)×C13⋊C3—71no—
26C13×C49C32×C411yescharacteristic, complemented, Hall
27C3×C4×C49—131no—
28C4×C49⋊C3—131no—
29C4×C49⋊C3—131no—
30C4×C49⋊C3C13⋊C311yescharacteristic, direct product factor
31C2×#63271—71no—
32C2×#63270—71no—
33C2×C13×ΓL(1,𝔽8)—71no—
34C2×C7×C13⋊C3C2×ΓL(1,𝔽8)11yescharacteristic
35C3×C4×C13⋊C3—491noHall
36C3×C49⋊C3—131noHall
37C4×C7×C13C3×ΓL(1,𝔽8)11yescharacteristic
38C2×C3×C49—131no—
39C2×C49⋊C3—131no—
40C2×C49⋊C3—131no—
41C2×C49⋊C3C2×C13⋊C311yescharacteristic
42#63271—71no—
43#63270—71no—
44C7×C13⋊C3C4×ΓL(1,𝔽8)11yescharacteristic
45C13×ΓL(1,𝔽8)—71no—
46C3×C4×ΓL(1,𝔽8)—911no—
47C2×C3×C13⋊C3—491no—
48C4×C49C3×C13⋊C311yescharacteristic, complemented, Hall
49C2×C7×C13C2×C3×ΓL(1,𝔽8)11yescharacteristic
50C3×C4×C13—491no—
51C4×C13⋊C3—491no—
52C4×C13⋊C3—491no—
53C4×C13⋊C3C49⋊C311yescharacteristic, direct product factor
54C3×C49—131no—
55C49⋊C3—131no—
56C49⋊C3—131no—
57C49⋊C3C4×C13⋊C311yescharacteristic, direct product factor
58C2×C3×ΓL(1,𝔽8)—911no—
59C3×C13⋊C3—491noHall
60C2×C49C2×C3×C13⋊C311yescharacteristic
61C7×C13C3×C4×ΓL(1,𝔽8)11yescharacteristic
62C3×C4×C7—131no—
63C4×ΓL(1,𝔽8)—71no—
64C4×ΓL(1,𝔽8)—911no—
65C4×ΓL(1,𝔽8)—911no—
66C2×C3×C13—491no—
67C2×C13⋊C3—491no—
68C2×C13⋊C3—491no—
69C2×C13⋊C3C2×C49⋊C311yescharacteristic
70C3×ΓL(1,𝔽8)—911no—
71C4×C13C3×C49⋊C311yescharacteristic, complemented, Hall
72C49C3×C4×C13⋊C311yescharacteristic, complemented, Sylow
73C2×C3×C7—131no—
74C2×ΓL(1,𝔽8)—71no—
75C2×ΓL(1,𝔽8)—911no—
76C2×ΓL(1,𝔽8)—911no—
77C3×C13—491no—
78C13⋊C3—491no—
79C13⋊C3—491no—
80C13⋊C3C4×C49⋊C311yescharacteristic, direct product factor
81C32×C4—6371noHall
82C4×C7ΓL(1,𝔽8)×C13⋊C311yescharacteristic
83C2×C13C2×C3×C49⋊C311yescharacteristic
84C3×C7—131no—
85ΓL(1,𝔽8)—71no—
86ΓL(1,𝔽8)—911no—
87ΓL(1,𝔽8)—911no—
88C2×C32—6371no—
89C2×C7C2×ΓL(1,𝔽8)×C13⋊C311yescharacteristic
90C13C3×C4×C49⋊C311yescharacteristic, complemented, Sylow
91C3×C4—131no—
92C3×C4—491no—
93C3×C4—6371no—
94C3×C4—6371no—
95C32—6371noSylow
96C7C4×ΓL(1,𝔽8)×C13⋊C311yescharacteristic
97C2×C3—131no—
98C2×C3—491no—
99C2×C3—6371no—
100C2×C3—6371no—
101C4C13⋊C3×C49⋊C311yescharacteristic, direct product factor, Sylow
102C3—131no—
103C3—491no—
104C3—6371no—
105C3—6371no—
106C2C2×C13⋊C3×C49⋊C311yescharacteristic
subgroupG/H
center, hypercenterC4C13⋊C3×C49⋊C3
commutator, hypocenterC13×C49C32×C4
FrattiniC2×C7C2×ΓL(1,𝔽8)×C13⋊C3
FittingC4×C13×C49C32
socleC2×C7×C13C2×C3×ΓL(1,𝔽8)
prime radicalC2×C13⋊C3×C49⋊C3C2
cosocleC2×C13×C49C2×C32
LCSG ▷ C13×C49
UCSC1 ◁ C4

Complements

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

NH ≅ G/Ntype
2. C4×#14274255C3semidirect
3. C4×#14274254C3semidirect
4. C4×C13×C49⋊C3C3semidirect
5. C4×C13⋊C3×C49C3semidirect
6. C13⋊C3×C49⋊C3C4direct (N × H)
12. C4×C13×C49C32semidirect
13. #14274255C3×C4semidirect
14. #14274254C3×C4semidirect
15. C13⋊C3×C49C3×C4semidirect
16. C13×C49⋊C3C3×C4semidirect
26. C13×C49C32×C4semidirect
30. C4×C49⋊C3C13⋊C3direct (N × H)
48. C4×C49C3×C13⋊C3semidirect
53. C4×C13⋊C3C49⋊C3direct (N × H)
57. C49⋊C3C4×C13⋊C3direct (N × H)
71. C4×C13C3×C49⋊C3semidirect
72. C49C3×C4×C13⋊C3semidirect
80. C13⋊C3C4×C49⋊C3direct (N × H)
90. C13C3×C4×C49⋊C3semidirect
101. C4C13⋊C3×C49⋊C3direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C13⋊C3×C49⋊C32
C4×#142742553
C4×#142742543
C4×C13×C49⋊C33
C4×C13⋊C3×C493
C4×ΓL(1,𝔽8)×C13⋊C37
C3×C4×C49⋊C313