Finite Group Databasebeta

← #14518802

Subgroups — #14518802

Order 1944.

1120 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 1120 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⋊D3×H(3,𝔽3)C211yesmaximal, characteristic, complemented
2C2×C32×#272C211yesmaximal, characteristic, complemented
3C3⋊(C3⋊#1084)C211yesmaximal, characteristic, complemented
4C3×#6290—34nomaximal
5#10619891—34nomaximal
6C2×C32×H(3,𝔽3)C2211yescharacteristic
7C3⋊D3×H(3,𝔽3)—21no—
8C32×#272—21no—
9C2×C32×C3⋊D3D314yescomplemented
10C2×C33×D3—34no—
11C3×C3⋊(C3⋊Dic3)—34no—
12C2×C3×#272D314yescomplemented
13C2×D3×H(3,𝔽3)—34no—
14C3⋊#1084—34no—
15C3⋊#1084—616no—
16C32×H(3,𝔽3)D411yescharacteristic, complemented, Sylow
17C3×#638—91no—
18#6290—34no—
19C3×#625—916no—
20#6235—91no—
21C2×C34C2×D314yes—
22C32×C3⋊D3—24no—
23C33×D3—64no—
24C2×C3×H(3,𝔽3)—216no—
25C2×C3×H(3,𝔽3)C2×D314yes—
26C3×#272—24no—
27D3×H(3,𝔽3)—64no—
28C22×C33—91no—
29C2×C3×C3⋊D3—34no—
30C2×C3×C3⋊D3C3⋊D311yescharacteristic
31C2×C32×D3—34no—
32C2×C32×D3—316no—
33C2×C32×D3—316no—
34C2×C32×D3—616no—
35C3⋊(C3⋊Dic3)—34no—
36C3×C3⋊Dic3—916no—
37C3×C3⋊Dic3—91no—
38C3×C3⋊Dic3—1816no—
39C22×H(3,𝔽3)—91no—
40C2×#272C3⋊D311yescharacteristic, complemented
41#1084—91no—
42#1084—1816no—
43#1084—1824no—
44C34#6714yescomplemented
45C3×H(3,𝔽3)—216no—
46C3×H(3,𝔽3)#6714yescomplemented
47#638—91no—
48C3×#67—274no—
49C3×#67—274no—
50#625—916no—
51C2×C33—216no—
52C2×C33—34no—
53C2×C33—616no—
54C2×C33—181no—
55C2×C33D32116yes—
56C2×C33C2×C3⋊D311yescharacteristic
57C3×C3⋊D3—21no—
58C3×C3⋊D3—64no—
59C32×D3—64no—
60C32×D3—632no—
61C32×D3—616no—
62C32×D3—616no—
63C2×H(3,𝔽3)—224no—
64C2×H(3,𝔽3)—216no—
65C2×H(3,𝔽3)—181no—
66C2×H(3,𝔽3)C2×C3⋊D311yescharacteristic
67#272—21no—
68C22×C32—91no—
69C22×C32—94no—
70C22×C32—94no—
71C22×C32—184no—
72C2×C3⋊D3#27211yescharacteristic, complemented
73C2×C3×D3—316no—
74C2×C3×D3—34no—
75C2×C3×D3—34no—
76C2×C3×D3—616no—
77C2×C3×D3—916no—
78C3⋊Dic3—91no—
79C3⋊Dic3—916no—
80C3⋊Dic3—1816no—
81C3×Dic3—274no—
82C3×Dic3—274no—
83C3×Dic3—5416no—
84C33—216no—
85C33—34no—
86C33—616no—
87C33#625116yescomplemented
88C33#63811yescharacteristic
89H(3,𝔽3)—224no—
90H(3,𝔽3)—216no—
91H(3,𝔽3)#63811yescharacteristic, complemented
92C3×D4—811no—
93#67—274no—
94#67—274no—
95C2×C32—24no—
96C2×C32—216no—
97C2×C32—316no—
98C2×C32—616no—
99C2×C32—616no—
100C2×C32—1216no—
101C2×C32—188no—
102C2×C32—181no—
103C2×C32—184no—
104C2×C32—184no—
105C2×C32C2×#27211yescharacteristic
106C2×C32D3×C3⋊D314yes—
107C2×C32D3×C3⋊D314yes—
108C3⋊D3—21no—
109C3×D3—616no—
110C3×D3—632no—
111C3×D3—64no—
112C3×D3—64no—
113C3×D3—1816no—
114C22×C3—94no—
115C22×C3—91no—
116C22×C3—91no—
117C22×C3—184no—
118C22×C3—274no—
119C2×D3—34no—
120C2×D3—34no—
121C3×C4—811no—
122Dic3—274no—
123Dic3—274no—
124Dic3—5416no—
125C32—24no—
126C32—216no—
127C32—316no—
128C32—616no—
129C32—616no—
130C32—1216no—
131C32#623511yescharacteristic, complemented
132C32#629014yes—
133C32#629014yescomplemented
134D4—811noSylow
135C2×C3—24no—
136C2×C3—34no—
137C2×C3—616no—
138C2×C3—188no—
139C2×C3—184no—
140C2×C3—181no—
141C2×C3—181no—
142C2×C3—544no—
143C2×C3D3×#27214yes—
144C2×C3C3⋊D3211yescharacteristic
145D3—64no—
146D3—64no—
147C22—91no—
148C22—91no—
149C4—811no—
150C3—24no—
151C3—34no—
152C3—616no—
153C3#1061989114yescomplemented
154C3#1062015111yescharacteristic
155C2—181no—
156C2—181no—
157C2C3⋊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⋊D3×H(3,𝔽3)C2semidirect
2. C2×C32×#272C2semidirect
3. C3⋊(C3⋊#1084)C2semidirect
9. C2×C32×C3⋊D3D3semidirect
12. C2×C3×#272D3semidirect
16. C32×H(3,𝔽3)D4semidirect
40. C2×#272C3⋊D3semidirect
44. C34#67semidirect
46. C3×H(3,𝔽3)#67semidirect
72. C2×C3⋊D3#272semidirect
87. C33#625semidirect
91. H(3,𝔽3)#638semidirect
131. C32#6235semidirect
133. C32#6290semidirect
153. C3#10619891semidirect

Maximal subgroups

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

subgroupindex
C2×C3⋊D3×H(3,𝔽3)2
C2×C32×#2722
C3⋊(C3⋊#1084)2
C3×#62903
#106198913