Finite Group Databasebeta

← C2×D3×#14274254 #37524263

Subgroups — C2×D3×#14274254 #37524263

Order 22932.

132 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 132 conjugacy classes of subgroups — too many to draw. Only its 49 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×C3×#14274254C211yesmaximal, characteristic, complemented
2D3×#14274254C212yesmaximal, direct product factor
3C2×D3×C13×C49C311yesmaximal, characteristic, complemented
4C22×#14274254—31nomaximal
5C3×#14274254C2211yescharacteristic, complemented, Hall
6D3×C13×C49C2×C312yescomplemented
7C2×#14274254—21no—
8C2×#14274254—32no—
9C2×#14274254D311yescharacteristic, direct product factor
10C2×C3×C13×C49C2×C311yescharacteristic, complemented
11C2×D3×#63270—71nomaximal
12C22×C13×C49—31noHall
13C3×C13×C49C22×C311yescharacteristic, complemented
14#14274254—21no—
15#14274254C2×D311yescharacteristic, direct product factor
16C2×D3×C49⋊C3—131nomaximal, Hall
17C2×C3×#63270—71no—
18D3×#63270—72no—
19C2×C13×C49—32no—
20C2×C13×C49C3×D311yescharacteristic, complemented
21C2×D3×C7×C13ΓL(1,𝔽8)11yescharacteristic
22C22×#63270—211no—
23C2×C3×C49⋊C3—131no—
24D3×C49⋊C3—132no—
25C3×#63270—71no—
26C13×C49C2×C3×D311yescharacteristic, complemented, Hall
27C2×D3×C49C13⋊C311yescharacteristic, complemented
28C22×C49⋊C3—391no—
29C2×C3×C7×C13C2×ΓL(1,𝔽8)11yescharacteristic
30D3×C7×C13C2×ΓL(1,𝔽8)12yes—
31C2×#63270—71no—
32C2×#63270—141no—
33C2×#63270—212no—
34C2×D3×C13⋊C3—491noHall
35C3×C49⋊C3—131noHall
36C22×C7×C13—31no—
37C2×C3×C49C2×C13⋊C311yescharacteristic, complemented
38D3×C49C2×C13⋊C312yescomplemented
39C2×C49⋊C3—131no—
40C2×C49⋊C3—261no—
41C2×C49⋊C3—392no—
42C3×C7×C13C22×ΓL(1,𝔽8)11yescharacteristic
43#63270—71no—
44#63270—141no—
45C2×D3×ΓL(1,𝔽8)—911no—
46C2×C3×C13⋊C3—491no—
47D3×C13⋊C3—492no—
48C22×C49—31noHall
49C2×C7×C13—32no—
50C2×C7×C13D3×ΓL(1,𝔽8)11yescharacteristic
51C2×D3×C13C49⋊C311yescharacteristic, complemented
52C22×C13⋊C3—1471no—
53C3×C49C22×C13⋊C311yescharacteristic, complemented
54C49⋊C3—131no—
55C49⋊C3—261no—
56C2×C3×ΓL(1,𝔽8)—911no—
57D3×ΓL(1,𝔽8)—912no—
58C3×C13⋊C3—491noHall
59C2×C49—32no—
60C2×C49D3×C13⋊C311yescharacteristic, complemented
61C7×C13C2×D3×ΓL(1,𝔽8)11yescharacteristic
62C2×D3×C7#6327011yescharacteristic
63C22×ΓL(1,𝔽8)—2731no—
64C2×C3×C13C2×C49⋊C311yescharacteristic, complemented
65D3×C13C2×C49⋊C312yescomplemented
66C2×C13⋊C3—491no—
67C2×C13⋊C3—981no—
68C2×C13⋊C3—1472no—
69C3×ΓL(1,𝔽8)—911no—
70C22×C13—31noHall
71C49C2×D3×C13⋊C311yescharacteristic, complemented, Sylow
72C2×C3×C7C2×#6327011yescharacteristic
73D3×C7C2×#6327012yes—
74C2×ΓL(1,𝔽8)—2732no—
75C2×ΓL(1,𝔽8)—911no—
76C2×ΓL(1,𝔽8)—1821no—
77C3×C13C22×C49⋊C311yescharacteristic, complemented
78C13⋊C3—491no—
79C13⋊C3—981no—
80C2×C3×D3—6371noHall
81C22×C7—31no—
82C2×C13—32no—
83C2×C13D3×C49⋊C311yescharacteristic, complemented
84C3×C7C22×#6327011yescharacteristic
85ΓL(1,𝔽8)—911no—
86ΓL(1,𝔽8)—1821no—
87C2×C32—6371no—
88C3×D3—6372no—
89C2×C7—32no—
90C2×C7D3×#6327011yescharacteristic
91C13C2×D3×C49⋊C311yescharacteristic, complemented, Sylow
92C22×C3—19111no—
93C2×D3#1427425411yescharacteristic, direct product factor
94C32—6371noSylow
95C7C2×D3×#6327011yescharacteristic
96C2×C3—19112no—
97C2×C3—6371no—
98C2×C3—12741no—
99C2×C3C2×#1427425411yescharacteristic, complemented
100D3C2×#1427425412yesdirect product factor
101C22—31noSylow
102C3—6371no—
103C3—12741no—
104C3C22×#1427425411yescharacteristic, complemented
105C2—32no—
106C2D3×#1427425411yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2D3×#14274254
commutator, cosocle, hypocenterC3×C13×C49C22×C3
FrattiniC7C2×D3×#63270
FittingC2×C3×C13×C49C2×C3
socleC2×C3×C7×C13C2×ΓL(1,𝔽8)
LCSG ▷ C3×C13×C49
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
1. C2×C3×#14274254C2semidirect
2. D3×#14274254C2direct (N × H)
3. C2×D3×C13×C49C3semidirect
5. C3×#14274254C22semidirect
6. D3×C13×C49C2×C3semidirect
9. C2×#14274254D3direct (N × H)
10. C2×C3×C13×C49C2×C3semidirect
13. C3×C13×C49C22×C3semidirect
15. #14274254C2×D3direct (N × H)
20. C2×C13×C49C3×D3semidirect
26. C13×C49C2×C3×D3semidirect
27. C2×D3×C49C13⋊C3semidirect
37. C2×C3×C49C2×C13⋊C3semidirect
38. D3×C49C2×C13⋊C3semidirect
51. C2×D3×C13C49⋊C3semidirect
53. C3×C49C22×C13⋊C3semidirect
60. C2×C49D3×C13⋊C3semidirect
64. C2×C3×C13C2×C49⋊C3semidirect
65. D3×C13C2×C49⋊C3semidirect
71. C49C2×D3×C13⋊C3semidirect
77. C3×C13C22×C49⋊C3semidirect
83. C2×C13D3×C49⋊C3semidirect
91. C13C2×D3×C49⋊C3semidirect
93. C2×D3#14274254direct (N × H)
99. C2×C3C2×#14274254semidirect
100. D3C2×#14274254direct (N × H)
104. C3C22×#14274254semidirect
106. C2D3×#14274254direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#142742542
D3×#142742542
C2×D3×C13×C493
C22×#142742543
C2×D3×#632707
C2×D3×C49⋊C313