Finite Group Databasebeta

← #14518811

Subgroups — #14518811

Order 1944.

836 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 836 conjugacy classes of subgroups — too many to draw. Only its 100 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×#92392C211yesmaximal, characteristic
2#11758025C211yesmaximal, characteristic, complemented
3#11758013C211yesmaximal, characteristic, complemented
4Dic3×#272—34nomaximal
5D3×#1084—34nomaximal
6C2×H(5,𝔽3)C2211yescharacteristic
7#92392C412yescomplemented
8C2×C3×#272D314yes—
9C2×D3×H(3,𝔽3)—34no—
10C3⋊#1084—34no—
11C3⋊#1084—34no—
12C3⋊#1084—616no—
13C3×#1084D314yescomplemented
14Dic3×H(3,𝔽3)—34no—
15H(5,𝔽3)C2×C411yescharacteristic, complemented, Sylow
16C3×D3×Dic3—916no—
17C2×#1084—91no—
18C4×#272—91no—
19C2×C3×H(3,𝔽3)—216no—
20C2×C3×H(3,𝔽3)C2×D314yes—
21C2×C3×H(3,𝔽3)C2×D314yes—
22C3×#272Dic318yescomplemented
23D3×H(3,𝔽3)—38no—
24C2×C32×D3—316no—
25C3×C3⋊Dic3—916no—
26C3×C3⋊Dic3—1812no—
27C32×Dic3—316no—
28C22×H(3,𝔽3)—91no—
29C2×#272C3⋊D311yescharacteristic
30C4×H(3,𝔽3)—91no—
31#1084—91no—
32#1084—91no—
33#1084—1816no—
34#1084—1816no—
35#1084—1812no—
36#1084C3⋊D311yescharacteristic
37C3×H(3,𝔽3)—216no—
38C3×H(3,𝔽3)C4×D314yescomplemented
39C3×H(3,𝔽3)C2×Dic314yescomplemented
40C2×C3×Dic3—274no—
41C3×C4×D3—274no—
42D3×Dic3—916no—
43C2×C33—212no—
44C2×C33D32116yes—
45C32×D3—332no—
46C2×H(3,𝔽3)—212no—
47C2×H(3,𝔽3)—216no—
48C2×H(3,𝔽3)—216no—
49C2×H(3,𝔽3)—92no—
50C2×H(3,𝔽3)C2×C3⋊D311yescharacteristic
51C2×H(3,𝔽3)C2×C3⋊D311yescharacteristic
52#272C3⋊Dic312yescomplemented
53C22×C32—94no—
54C2×C3×D3—34no—
55C2×C3×D3—916no—
56C32×C4—94no—
57C3⋊Dic3—916no—
58C3⋊Dic3—1812no—
59C3×Dic3—34no—
60C3×Dic3—916no—
61C3×Dic3—274no—
62C3×Dic3—274no—
63C3×Dic3—5416no—
64C33—212no—
65C33D3×Dic3116yescomplemented
66H(3,𝔽3)—212no—
67H(3,𝔽3)—216no—
68H(3,𝔽3)—216no—
69H(3,𝔽3)C4×C3⋊D311yescharacteristic
70H(3,𝔽3)C2×C3⋊Dic311yescharacteristic
71C2×C3×C4—811no—
72C2×Dic3—274no—
73C4×D3—274no—
74C2×C32—216no—
75C2×C32—916no—
76C2×C32—98no—
77C2×C32—1812no—
78C2×C32D3×C3⋊D314yes—
79C2×C32D3×C3⋊D314yes—
80C3×D3—38no—
81C3×D3—932no—
82C22×C3—91no—
83C22×C3—274no—
84C2×D3—34no—
85C3×C4—91no—
86C3×C4—274no—
87C3×C4—811no—
88Dic3—34no—
89Dic3—274no—
90Dic3—274no—
91Dic3—5416no—
92C32—216no—
93C32—916no—
94C32—1812no—
95C32D3×C3⋊Dic314yes—
96C32Dic3×C3⋊D314yes—
97C2×C4—811noSylow
98C2×C3—34no—
99C2×C3—34no—
100C2×C3—616no—
101C2×C3—92no—
102C2×C3—278no—
103C2×C3C3⋊D3211yescharacteristic
104D3—38no—
105C22—91no—
106C4—91no—
107C4—811no—
108C3—34no—
109C3—34no—
110C3—616no—
111C3C3⋊D3×C3⋊Dic311yescharacteristic
112C2—92no—
113C2#1175808711yescharacteristic
subgroupG/H
center, Frattini, socle, hypercenterC2×C3C3⋊D32
commutator, hypocenterH(5,𝔽3)C2×C4
Fitting, cosocleC2×H(5,𝔽3)C22
prime radicalC2×#92392C2
LCSG ▷ H(5,𝔽3)
UCSC1 ◁ C2×C3

Complements

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

NH ≅ G/Ntype
2. #11758025C2semidirect
3. #11758013C2semidirect
7. #92392C4semidirect
13. C3×#1084D3semidirect
15. H(5,𝔽3)C2×C4semidirect
22. C3×#272Dic3semidirect
38. C3×H(3,𝔽3)C4×D3semidirect
39. C3×H(3,𝔽3)C2×Dic3semidirect
52. #272C3⋊Dic3semidirect
65. C33D3×Dic3semidirect

Maximal subgroups

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

subgroupindex
C2×#923922
#117580252
#117580132
Dic3×#2723
D3×#10843