Finite Group Databasebeta

← #14518803

Subgroups — #14518803

Order 1944.

1360 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 1360 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
1C2×C3⋊(C3⋊#272)C211yesmaximal, characteristic, complemented
2C2×C32×#272C211yesmaximal, characteristic, complemented
3H(3,𝔽3)×C3⋊Dic3C211yesmaximal, characteristic, complemented
4C3×#6291—34nomaximal
5#10619893—34nomaximal
6C2×C32×H(3,𝔽3)C2211yescharacteristic
7C3⋊(C3⋊#272)—21no—
8C32×#272—21no—
9C2×C3×C3⋊(C3⋊D3)—34no—
10C2×C33×D3—34no—
11C32×C3⋊Dic3D314yescomplemented
12C2×C3⋊#272—34no—
13C2×C3⋊#272—616no—
14C2×C3×#272D314yescomplemented
15Dic3×H(3,𝔽3)—34no—
16C32×H(3,𝔽3)D411yescharacteristic, complemented, Sylow
17C3×#638—91no—
18#6291—34no—
19C3×#626—916no—
20C4⋊#272—91no—
21C2×C34C2×D314yes—
22C3×C3⋊(C3⋊D3)—64no—
23C33×D3—64no—
24C2×C3×H(3,𝔽3)—216no—
25C2×C3×H(3,𝔽3)C2×D314yes—
26C3⋊#272—632no—
27C3⋊#272—64no—
28C3×#272—24no—
29C22×C33—91no—
30C2×C3⋊(C3⋊D3)—34no—
31C2×C3×C3⋊D3—916no—
32C2×C3×C3⋊D3—91no—
33C2×C3×C3⋊D3—1816no—
34C2×C32×D3—34no—
35C2×C32×D3—316no—
36C2×C32×D3—616no—
37C3×C3⋊Dic3—34no—
38C3×C3⋊Dic3C3⋊D311yescharacteristic
39C32×Dic3—316no—
40C2×#272—91no—
41C2×#272—1816no—
42C2×#272—1824no—
43C2×#272C3⋊D311yescharacteristic, complemented
44C4×H(3,𝔽3)—91no—
45C34D1214yescomplemented
46C3×H(3,𝔽3)—216no—
47C3×H(3,𝔽3)#6714yescomplemented
48#638—91no—
49C3×#67—274no—
50C3×D12—274no—
51#626—916no—
52C2×C33—216no—
53C2×C33—34no—
54C2×C33—616no—
55C2×C33—181no—
56C2×C33D32116yes—
57C2×C33C2×C3⋊D311yescharacteristic
58C3⋊(C3⋊D3)—64no—
59C3×C3⋊D3—1832no—
60C3×C3⋊D3—1816no—
61C3×C3⋊D3—181no—
62C32×D3—64no—
63C32×D3—632no—
64C32×D3—616no—
65C2×H(3,𝔽3)—224no—
66C2×H(3,𝔽3)—216no—
67C2×H(3,𝔽3)C2×C3⋊D311yescharacteristic
68#272—21no—
69#272—1848no—
70#272—1832no—
71#272—181no—
72C22×C32—91no—
73C22×C32—94no—
74C22×C32—184no—
75C2×C3⋊D3—91no—
76C2×C3⋊D3—916no—
77C2×C3⋊D3—1816no—
78C2×C3×D3—316no—
79C2×C3×D3—34no—
80C2×C3×D3—616no—
81C2×C3×D3—274no—
82C2×C3×D3—274no—
83C2×C3×D3—5416no—
84C32×C4—94no—
85C3⋊Dic3#27211yescharacteristic, complemented
86C3×Dic3—34no—
87C3×Dic3—916no—
88C33—216no—
89C33—34no—
90C33—616no—
91C33#626116yescomplemented
92C33C4⋊(C3⋊D3)11yescharacteristic
93H(3,𝔽3)—224no—
94H(3,𝔽3)—216no—
95H(3,𝔽3)#63811yescharacteristic, complemented
96C3×D4—811no—
97#67—274no—
98D12—274no—
99C2×C32—24no—
100C2×C32—216no—
101C2×C32—316no—
102C2×C32—616no—
103C2×C32—616no—
104C2×C32—1216no—
105C2×C32—188no—
106C2×C32—181no—
107C2×C32—184no—
108C2×C32C2×#27211yescharacteristic
109C2×C32D3×C3⋊D314yes—
110C2×C32D3×C3⋊D314yes—
111C3⋊D3—1816no—
112C3⋊D3—1832no—
113C3⋊D3—181no—
114C3×D3—616no—
115C3×D3—632no—
116C3×D3—64no—
117C3×D3—5432no—
118C3×D3—544no—
119C3×D3—544no—
120C22×C3—94no—
121C22×C3—91no—
122C22×C3—184no—
123C22×C3—811no—
124C2×D3—34no—
125C2×D3—274no—
126C2×D3—274no—
127C2×D3—5416no—
128C3×C4—91no—
129C3×C4—274no—
130Dic3—34no—
131C32—24no—
132C32—216no—
133C32—316no—
134C32—616no—
135C32—616no—
136C32—1216no—
137C32C4⋊#27211yescharacteristic, complemented
138C32#629114yescomplemented
139C32#629214yes—
140D4—811noSylow
141C2×C3—24no—
142C2×C3—34no—
143C2×C3—616no—
144C2×C3—188no—
145C2×C3—184no—
146C2×C3—181no—
147C2×C3—1621no—
148C2×C3D3×#27214yes—
149C2×C3C3⋊D3211yescharacteristic
150D3—64no—
151D3—544no—
152D3—5432no—
153D3—544no—
154C22—91no—
155C22—811no—
156C4—91no—
157C3—24no—
158C3—34no—
159C3—616no—
160C3#1061989314yescomplemented
161C3#1062015211yescharacteristic
162C2—181no—
163C2—1621no—
164C2C3⋊D3×#27211yescharacteristic
subgroupG/H
center, Frattini, hypercenterC2×C3C3⋊D32
commutator, Fitting, cosocleC2×C32×H(3,𝔽3)C22
socleC2×C33C2×C3⋊D3
hypocenterC32×H(3,𝔽3)D4
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
1. C2×C3⋊(C3⋊#272)C2semidirect
2. C2×C32×#272C2semidirect
3. H(3,𝔽3)×C3⋊Dic3C2semidirect
11. C32×C3⋊Dic3D3semidirect
14. C2×C3×#272D3semidirect
16. C32×H(3,𝔽3)D4semidirect
43. C2×#272C3⋊D3semidirect
45. C34D12semidirect
47. C3×H(3,𝔽3)#67semidirect
85. C3⋊Dic3#272semidirect
91. C33#626semidirect
95. H(3,𝔽3)#638semidirect
137. C32C4⋊#272semidirect
138. C32#6291semidirect
160. C3#10619893semidirect

Maximal subgroups

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

subgroupindex
C2×C3⋊(C3⋊#272)2
C2×C32×#2722
H(3,𝔽3)×C3⋊Dic32
C3×#62913
#106198933