Finite Group Databasebeta

← C4⋊(C3⋊#4184) #14517739

Subgroups — C4⋊(C3⋊#4184) #14517739

Order 1944.

498 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 498 conjugacy classes of subgroups — too many to draw. Only its 105 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⋊#4184C212yesmaximal, complemented
2C3×C4×#731C211yesmaximal, characteristic, complemented
3C4⋊(C3⋊AGL(1,ℤ/9))—32nomaximal
4C4⋊(C3⋊((C3⋊D3)⋊C3))—31nomaximal
5C3×C4⋊(C3⋊D9)—31nomaximal
6C4⋊#4184—39nomaximal
7C2×C3×#731C2211yescharacteristic
8C3⋊#4184—22no—
9C2×C3⋊AGL(1,ℤ/9)—34no—
10C2×C3⋊((C3⋊D3)⋊C3)—32no—
11C2×C3×C3⋊D9—32no—
12C3×C4×3−1+2D312yescomplemented
13C3×C4×H(3,𝔽3)D311yescharacteristic
14C32×C4×C9D311yescharacteristic, complemented
15C2×#4184—318no—
16C4×#731D319yescomplemented
17C3×#731D411yescharacteristic, complemented, Sylow
18C4⋊(C3⋊(C3⋊D3))—31no—
19C3×C4⋊(C3⋊D3)—91no—
20C4⋊(C3⋊D9)—31no—
21C4⋊(C3⋊D9)—32no—
22C4⋊AGL(1,ℤ/9)—96no—
23C4⋊((C3⋊D3)⋊C3)—93no—
24C3×D36—93no—
25C2×C3×3−1+2C2×D312yes—
26C2×C3×H(3,𝔽3)C2×D311yescharacteristic
27C2×C32×C9C2×D311yescharacteristic
28C3⋊AGL(1,ℤ/9)—64no—
29C3⋊((C3⋊D3)⋊C3)—62no—
30C3×C3⋊D9—62no—
31C2×#731C2×D319yes—
32#4184—618no—
33C2×C3⋊(C3⋊D3)—32no—
34C2×C3×C3⋊D3—92no—
35C33×C4—31no—
36C33×C4C3⋊D311yescharacteristic
37C2×C3⋊D9—32no—
38C2×C3⋊D9—34no—
39C2×AGL(1,ℤ/9)—912no—
40C2×(C3⋊D3)⋊C3—96no—
41C2×C3×D9—96no—
42C4×3−1+2—62no—
43C4×3−1+2C3⋊D316yescomplemented
44C4×H(3,𝔽3)—61no—
45C4×H(3,𝔽3)C3⋊D313yes—
46C3×C4×C9—31no—
47C3×C4×C9—32no—
48C3×C4×C9—61no—
49C3×C4×C9C3⋊D313yescomplemented
50C3×3−1+2D1212yescomplemented
51C3×H(3,𝔽3)D1211yescharacteristic
52C32×C9D1211yescharacteristic, complemented
53#731D1219yescomplemented
54C4⋊(C3⋊D3)—91no—
55C4⋊(C3⋊D3)—93no—
56C4⋊(C3⋊D3)—273no—
57C3×D12—273no—
58C3×D12—271no—
59D36—93no—
60D36—96no—
61C2×C33—31no—
62C2×C33C2×C3⋊D311yescharacteristic
63C3⋊(C3⋊D3)—62no—
64C3×C3⋊D3—182no—
65C2×3−1+2—62no—
66C2×3−1+2C2×C3⋊D316yes—
67C2×H(3,𝔽3)—61no—
68C2×H(3,𝔽3)C2×C3⋊D313yes—
69C2×C3×C9—31no—
70C2×C3×C9—32no—
71C2×C3×C9—61no—
72C2×C3×C9C2×C3⋊D313yes—
73C3⋊D9—62no—
74C3⋊D9—64no—
75AGL(1,ℤ/9)—1812no—
76(C3⋊D3)⋊C3—186no—
77C3×D9—186no—
78C2×C3⋊D3—92no—
79C2×C3⋊D3—96no—
80C2×C3⋊D3—276no—
81C2×C3×D3—276no—
82C2×C3×D3—272no—
83C32×C4—21no—
84C32×C4—33no—
85C32×C4—33no—
86C32×C4—93no—
87C32×C4#27211yescharacteristic
88C32×C4C3⋊(C3⋊D3)11yescharacteristic
89C2×D9—96no—
90C2×D9—912no—
91C4×C9—33no—
92C4×C9—36no—
93C33—31no—
94C33C4⋊(C3⋊D3)11yescharacteristic
953−1+2—62no—
963−1+2C4⋊(C3⋊D3)16yescomplemented
97H(3,𝔽3)—61no—
98H(3,𝔽3)C4⋊(C3⋊D3)13yes—
99C3×C9—31no—
100C3×C9—32no—
101C3×C9—61no—
102C3×C9C4⋊(C3⋊D3)13yescomplemented
103C3×D4—811no—
104D12—273no—
105D12—271no—
106D12—813no—
107C2×C32—21no—
108C2×C32—33no—
109C2×C32—33no—
110C2×C32—93no—
111C2×C32C2×#27211yescharacteristic
112C2×C32C2×C3⋊(C3⋊D3)11yescharacteristic
113C3⋊D3—182no—
114C3⋊D3—186no—
115C3⋊D3—546no—
116C3×D3—546no—
117C3×D3—542no—
118C2×C9—33no—
119C2×C9—36no—
120D9—186no—
121D9—1812no—
122C22×C3—812no—
123C2×D3—276no—
124C2×D3—272no—
125C2×D3—816no—
126C3×C4—31no—
127C3×C4—61no—
128C3×C4—93no—
129C3×C4#418413yescomplemented
130C3×C4C3⋊#27211yescharacteristic
131C32—21no—
132C32—33no—
133C32—33no—
134C32—93no—
135C32C4⋊#27211yescharacteristic
136C32C4⋊(C3⋊(C3⋊D3))11yescharacteristic
137C9—33no—
138C9—36no—
139D4—811noSylow
140C2×C3—31no—
141C2×C3—61no—
142C2×C3—93no—
143C2×C3—1622no—
144C2×C3C2×#418413yes—
145C2×C3C2×C3⋊#27211yescharacteristic
146D3—546no—
147D3—542no—
148D3—1626no—
149C22—812no—
150C4C3⋊#418411yescharacteristic, complemented
151C3—31no—
152C3—61no—
153C3—93no—
154C3C4⋊#418413yescomplemented
155C3C4⋊(C3⋊#272)11yescharacteristic
156C2—1622no—
157C2C2×C3⋊#418411yescharacteristic
subgroupG/H
centerC2C2×C3⋊#4184
commutator, cosocleC2×C3×#731C22
FrattiniC2×C32C2×C3⋊(C3⋊D3)
FittingC3×C4×#731C2
socleC2×C32C2×#272
hypercenterC4C3⋊#4184
hypocenterC3×#731D4
LCSG ▷ C2×C3×#731 ▷ C3×#731
UCSC1 ◁ C2 ◁ C4

Complements

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

NH ≅ G/Ntype
1. C2×C3⋊#4184C2semidirect
2. C3×C4×#731C2semidirect
12. C3×C4×3−1+2D3semidirect
14. C32×C4×C9D3semidirect
16. C4×#731D3semidirect
17. C3×#731D4semidirect
43. C4×3−1+2C3⋊D3semidirect
49. C3×C4×C9C3⋊D3semidirect
50. C3×3−1+2D12semidirect
52. C32×C9D12semidirect
53. #731D12semidirect
96. 3−1+2C4⋊(C3⋊D3)semidirect
102. C3×C9C4⋊(C3⋊D3)semidirect
129. C3×C4#4184semidirect
150. C4C3⋊#4184semidirect
154. C3C4⋊#4184semidirect

Maximal subgroups

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

subgroupindex
C2×C3⋊#41842
C3×C4×#7312
C4⋊(C3⋊AGL(1,ℤ/9))3
C4⋊(C3⋊((C3⋊D3)⋊C3))3
C3×C4⋊(C3⋊D9)3
C4⋊#41843