Finite Group Databasebeta

← #14519200

Subgroups — #14519200

Order 1944.

559 conjugacy classes of subgroups; only the 56 normal subgroups are shown.

normal subgroups only

This group has 559 conjugacy classes of subgroups — too many to draw. Only its 56 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
1C22⋊H(5,𝔽3)C211yesmaximal, characteristic, complemented
2C3×#6258C314yesmaximal, complemented
3S4×H(3,𝔽3)—33nomaximal
4#67×H(3,𝔽3)—31nomaximal
5#92392—41nomaximal
6C22×C3×H(3,𝔽3)D311yescharacteristic, complemented
7C2×D3×H(3,𝔽3)—31no—
8C3×C22⋊H(3,𝔽3)—24no—
9C3×C22⋊H(3,𝔽3)C2×C314yescomplemented
10A4×H(3,𝔽3)—212no—
11A4×H(3,𝔽3)D313yescomplemented
12Dic3×H(3,𝔽3)—31no—
13H(5,𝔽3)—41noSylow
14C32×S4—312no—
15C32×#67—34no—
16#6258C3211yescharacteristic, complemented
17D4×H(3,𝔽3)—91no—
18C2×C3×H(3,𝔽3)—31no—
19C3×#272—44no—
20D3×H(3,𝔽3)—61no—
21D3×H(3,𝔽3)—123no—
22C22×C33C3×D314yescomplemented
23C2×C32×D3—34no—
24C32×A4—212no—
25C32×A4C3×D3112yescomplemented
26C32×Dic3—34no—
27C22×H(3,𝔽3)—24no—
28C22×H(3,𝔽3)—91no—
29C22×H(3,𝔽3)C3⋊D311yescharacteristic
30C22⋊H(3,𝔽3)—212no—
31C22⋊H(3,𝔽3)—24no—
32C22⋊H(3,𝔽3)—212no—
33C22⋊H(3,𝔽3)—212no—
34C22⋊H(3,𝔽3)C2×C3211yescharacteristic
35C4×H(3,𝔽3)—91no—
36C3×H(3,𝔽3)—44no—
37C3×H(3,𝔽3)—43no—
38C3×H(3,𝔽3)—812no—
39C3×H(3,𝔽3)—84no—
40C3×H(3,𝔽3)S411yescharacteristic, complemented
41C3×S4—33no—
42C3×S4—912no—
43C32×D4—94no—
44C3×#67—31no—
45C3×#67—94no—
46C2×C33—34no—
47C32×D3—64no—
48C32×D3—1212no—
49C2×H(3,𝔽3)—31no—
50C2×H(3,𝔽3)—64no—
51C2×H(3,𝔽3)—181no—
52#272—41no—
53C22×C32—24no—
54C22×C32—94no—
55C22×C32—94no—
56C22×C32C32×D311yescharacteristic
57C22×C32C3×C3⋊D314yes—
58C2×C3×D3—31no—
59C2×C3×D3—94no—
60C3×A4—212no—
61C3×A4—912no—
62C3×A4—1812no—
63C3×A4C32×D313yes—
64C32×C4—94no—
65C3×Dic3—31no—
66C3×Dic3—94no—
67C33—412no—
68C33—812no—
69C33C3×S414yescomplemented
70H(3,𝔽3)—24no—
71H(3,𝔽3)—41no—
72H(3,𝔽3)—812no—
73H(3,𝔽3)—812no—
74H(3,𝔽3)—84no—
75H(3,𝔽3)—812no—
76H(3,𝔽3)C3⋊S411yescharacteristic
77S4—33no—
78C3×D4—91no—
79C3×D4—274no—
80#67—31no—
81C2×C32—31no—
82C2×C32—34no—
83C2×C32—64no—
84C2×C32—94no—
85C2×C32—184no—
86C2×C32—184no—
87C3×D3—61no—
88C3×D3—123no—
89C3×D3—184no—
90C3×D3—3612no—
91C22×C3—31no—
92C22×C3—34no—
93C22×C3—64no—
94C22×C3—91no—
95C22×C3—274no—
96C22×C3C32×C3⋊D311yescharacteristic
97C2×D3—31no—
98A4—33no—
99A4—612no—
100C3×C4—91no—
101C3×C4—274no—
102Dic3—31no—
103C32—24no—
104C32—43no—
105C32—812no—
106C32—94no—
107C32—3612no—
108C32—7212no—
109C32C32×S411yescharacteristic
110C32C3×C3⋊S414yes—
111D4—91noSylow
112C2×C3—31no—
113C2×C3—31no—
114C2×C3—61no—
115C2×C3—94no—
116C2×C3—184no—
117C2×C3—181no—
118C2×C3—544no—
119D3—61no—
120D3—123no—
121C22—91no—
122C22#9239211yescharacteristic, complemented
123C4—91no—
124C3—31no—
125C3—34no—
126C3—64no—
127C3—123no—
128C3—2412no—
129C3C32×C3⋊S411yescharacteristic
130C2—31no—
131C2—181no—
subgroupG/H
center, FrattiniC3C32×C3⋊S4
commutator, cosocle, hypocenterC22⋊H(3,𝔽3)C2×C32
FittingC22×C3×H(3,𝔽3)D3
socleC22×C3C32×C3⋊D3
hypercenterH(3,𝔽3)C3⋊S4
LCSG ▷ C22⋊H(3,𝔽3)
UCSC1 ◁ C3 ◁ H(3,𝔽3)

Complements

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

NH ≅ G/Ntype
1. C22⋊H(5,𝔽3)C2semidirect
2. C3×#6258C3semidirect
6. C22×C3×H(3,𝔽3)D3semidirect
9. C3×C22⋊H(3,𝔽3)C2×C3semidirect
11. A4×H(3,𝔽3)D3semidirect
16. #6258C32semidirect
22. C22×C33C3×D3semidirect
25. C32×A4C3×D3semidirect
40. C3×H(3,𝔽3)S4semidirect
69. C33C3×S4semidirect
122. C22#92392semidirect

Maximal subgroups

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

subgroupindex
C22⋊H(5,𝔽3)2
C3×#62583
S4×H(3,𝔽3)3
#67×H(3,𝔽3)3
#923924