Finite Group Databasebeta

← #14518805

Subgroups — #14518805

Order 1944.

908 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 908 conjugacy classes of subgroups — too many to draw. Only its 99 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
1C3⋊(C3⋊#1084)C211yesmaximal, characteristic
2H(3,𝔽3)×C3⋊Dic3C211yesmaximal, characteristic
3C32×#1084C211yesmaximal, characteristic
4C3×#6293—34nomaximal
5#10619894—34nomaximal
6C2×C32×H(3,𝔽3)C2211yescharacteristic
7C3×C3⋊(C3⋊Dic3)—34no—
8C32×C3⋊Dic3D314yes—
9C33×Dic3—34no—
10C3⋊#1084—34no—
11C3⋊#1084—616no—
12C3×#1084D314yes—
13Dic3×H(3,𝔽3)—34no—
14C32×H(3,𝔽3)Q811yescharacteristic, complemented, Sylow
15C3×#634—91no—
16#6293—34no—
17C3×#627—916no—
18#6229—91no—
19C2×C34C2×D314yes—
20C2×C3×H(3,𝔽3)—216no—
21C2×C3×H(3,𝔽3)C2×D314yes—
22C33×C4—91no—
23C3⋊(C3⋊Dic3)—34no—
24C3×C3⋊Dic3—34no—
25C3×C3⋊Dic3—916no—
26C3×C3⋊Dic3—91no—
27C3×C3⋊Dic3—1816no—
28C3×C3⋊Dic3C3⋊D311yescharacteristic
29C32×Dic3—34no—
30C32×Dic3—316no—
31C32×Dic3—316no—
32C32×Dic3—616no—
33C4×H(3,𝔽3)—91no—
34#1084—91no—
35#1084—1816no—
36#1084—1824no—
37#1084C3⋊D311yescharacteristic
38C34Dic614yescomplemented
39C3×H(3,𝔽3)—216no—
40C3×H(3,𝔽3)Dic614yescomplemented
41#634—91no—
42C3×Dic6—274no—
43C3×Dic6—274no—
44#627—916no—
45C2×C33—216no—
46C2×C33—34no—
47C2×C33—616no—
48C2×C33D32116yes—
49C2×C33C2×C3⋊D311yescharacteristic
50C2×H(3,𝔽3)—224no—
51C2×H(3,𝔽3)—216no—
52C2×H(3,𝔽3)C2×C3⋊D311yescharacteristic
53C32×C4—91no—
54C32×C4—94no—
55C32×C4—94no—
56C32×C4—184no—
57C3⋊Dic3—91no—
58C3⋊Dic3—916no—
59C3⋊Dic3—1816no—
60C3⋊Dic3#27211yescharacteristic
61C3×Dic3—316no—
62C3×Dic3—34no—
63C3×Dic3—34no—
64C3×Dic3—616no—
65C3×Dic3—916no—
66C3×Dic3—274no—
67C3×Dic3—274no—
68C3×Dic3—5416no—
69C33—216no—
70C33—34no—
71C33—616no—
72C33#627116yescomplemented
73C33#63411yescharacteristic
74H(3,𝔽3)—224no—
75H(3,𝔽3)—216no—
76H(3,𝔽3)#63411yescharacteristic, complemented
77C3×Q8—811no—
78Dic6—274no—
79Dic6—274no—
80C2×C32—24no—
81C2×C32—216no—
82C2×C32—316no—
83C2×C32—616no—
84C2×C32—616no—
85C2×C32—1216no—
86C2×C32C2×#27211yescharacteristic
87C2×C32D3×C3⋊D314yes—
88C2×C32D3×C3⋊D314yes—
89C3×C4—94no—
90C3×C4—91no—
91C3×C4—91no—
92C3×C4—184no—
93C3×C4—274no—
94C3×C4—811no—
95Dic3—34no—
96Dic3—34no—
97Dic3—274no—
98Dic3—274no—
99Dic3—5416no—
100C32—24no—
101C32—216no—
102C32—316no—
103C32—616no—
104C32—616no—
105C32—1216no—
106C32#622911yescharacteristic, complemented
107C32#629314yes—
108C32#629314yescomplemented
109Q8—811noSylow
110C2×C3—24no—
111C2×C3—34no—
112C2×C3—616no—
113C2×C3D3×#27214yes—
114C2×C3C3⋊D3211yescharacteristic
115C4—91no—
116C4—91no—
117C4—811no—
118C3—24no—
119C3—34no—
120C3—616no—
121C3#1061989414yescomplemented
122C3#1062015311yescharacteristic
123C2C3⋊D3×#27211yescharacteristic
subgroupG/H
center, Frattini, hypercenterC2×C3C3⋊D32
commutator, Fitting, prime radical, cosocleC2×C32×H(3,𝔽3)C22
socleC2×C33C2×C3⋊D3
hypocenterC32×H(3,𝔽3)Q8
LCSG ▷ C2×C32×H(3,𝔽3) ▷ C32×H(3,𝔽3)
UCSC1 ◁ C2×C3

Complements

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

NH ≅ G/Ntype
14. C32×H(3,𝔽3)Q8semidirect
38. C34Dic6semidirect
40. C3×H(3,𝔽3)Dic6semidirect
72. C33#627semidirect
76. H(3,𝔽3)#634semidirect
106. C32#6229semidirect
108. C32#6293semidirect
121. C3#10619894semidirect

Maximal subgroups

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

subgroupindex
C3⋊(C3⋊#1084)2
H(3,𝔽3)×C3⋊Dic32
C32×#10842
C3×#62933
#106198943