Finite Group Databasebeta

← C4×C3⋊#4184 #14517738

Subgroups — C4×C3⋊#4184 #14517738

Order 1944.

498 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 498 conjugacy classes of subgroups — too many to draw. Only its 107 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⋊#4184C211yesmaximal, characteristic
2C3×C4×#731C211yesmaximal, characteristic, complemented
3C3⋊#66331C211yesmaximal, characteristic, complemented
4C4×C3⋊AGL(1,ℤ/9)—32nomaximal
5C4×C3⋊((C3⋊D3)⋊C3)—31nomaximal
6C3×C4×C3⋊D9—31nomaximal
7C4×#4184—39nomaximal
8C2×C3×#731C2211yescharacteristic
9C3⋊#4184C412yesdirect product factor
10C2×C3⋊AGL(1,ℤ/9)—32no—
11C2×C3⋊((C3⋊D3)⋊C3)—31no—
12C2×C3×C3⋊D9—31no—
13C3×C4×3−1+2D312yescomplemented
14C3×C4×H(3,𝔽3)D311yescharacteristic
15C32×C4×C9D311yescharacteristic, complemented
16C3⋊(3−1+2⋊C4)—32no—
17C3⋊((C3⋊Dic3)⋊C3)—31no—
18C3×C3⋊Dic9—31no—
19C2×#4184—39no—
20C4×#731D319yescomplemented
21#66331—39no—
22C3×#731C2×C411yescharacteristic, complemented, Sylow
23C4×C3⋊(C3⋊D3)—31no—
24C3×C4×C3⋊D3—91no—
25C4×C3⋊D9—31no—
26C4×C3⋊D9—32no—
27C4×AGL(1,ℤ/9)—96no—
28C4×(C3⋊D3)⋊C3—93no—
29C3×C4×D9—93no—
30C2×C3×3−1+2C2×D312yes—
31C2×C3×H(3,𝔽3)C2×D311yescharacteristic
32C2×C32×C9C2×D311yescharacteristic
33C3⋊AGL(1,ℤ/9)—34no—
34C3⋊((C3⋊D3)⋊C3)—32no—
35C3×C3⋊D9—32no—
36C2×#731C2×D319yes—
37#4184—318no—
38C2×C3⋊(C3⋊D3)—31no—
39C2×C3×C3⋊D3—91no—
40C33×C4—31no—
41C33×C4C3⋊D311yescharacteristic
42C3⋊(C3⋊Dic3)—31no—
43C3×C3⋊Dic3—91no—
44C2×C3⋊D9—31no—
45C2×C3⋊D9—32no—
46C2×AGL(1,ℤ/9)—96no—
47C2×(C3⋊D3)⋊C3—93no—
48C2×C3×D9—93no—
49C4×3−1+2—62no—
50C4×3−1+2C3⋊D316yescomplemented
51C4×H(3,𝔽3)—61no—
52C4×H(3,𝔽3)C3⋊D313yes—
53C3×C4×C9—31no—
54C3×C4×C9—32no—
55C3×C4×C9—61no—
56C3×C4×C9C3⋊D313yescomplemented
57C3⋊Dic9—31no—
58C3⋊Dic9—32no—
593−1+2⋊C4—96no—
60(C3⋊Dic3)⋊C3—93no—
61C3×Dic9—93no—
62C3×3−1+2C4×D312yescomplemented
63C3×H(3,𝔽3)C4×D311yescharacteristic
64C32×C9C4×D311yescharacteristic, complemented
65#731C4×D319yescomplemented
66C4×C3⋊D3—91no—
67C4×C3⋊D3—93no—
68C4×C3⋊D3—273no—
69C3×C4×D3—273no—
70C3×C4×D3—271no—
71C4×D9—93no—
72C4×D9—96no—
73C2×C33—31no—
74C2×C33C2×C3⋊D311yescharacteristic
75C3⋊(C3⋊D3)—32no—
76C3×C3⋊D3—92no—
77C2×3−1+2—62no—
78C2×3−1+2C2×C3⋊D316yes—
79C2×H(3,𝔽3)—61no—
80C2×H(3,𝔽3)C2×C3⋊D313yes—
81C2×C3×C9—31no—
82C2×C3×C9—32no—
83C2×C3×C9—61no—
84C2×C3×C9C2×C3⋊D313yes—
85C3⋊D9—32no—
86C3⋊D9—34no—
87AGL(1,ℤ/9)—912no—
88(C3⋊D3)⋊C3—96no—
89C3×D9—96no—
90C2×C3⋊D3—91no—
91C2×C3⋊D3—93no—
92C2×C3⋊D3—273no—
93C2×C3×D3—273no—
94C2×C3×D3—271no—
95C32×C4—21no—
96C32×C4—33no—
97C32×C4—33no—
98C32×C4—93no—
99C32×C4#27211yescharacteristic
100C32×C4C3⋊(C3⋊D3)11yescharacteristic
101C3⋊Dic3—91no—
102C3⋊Dic3—93no—
103C3⋊Dic3—273no—
104C3×Dic3—273no—
105C3×Dic3—271no—
106C2×D9—93no—
107C2×D9—96no—
108C4×C9—33no—
109C4×C9—36no—
110Dic9—93no—
111Dic9—96no—
112C33—31no—
113C33C4×C3⋊D311yescharacteristic
1143−1+2—62no—
1153−1+2C4×C3⋊D316yescomplemented
116H(3,𝔽3)—61no—
117H(3,𝔽3)C4×C3⋊D313yes—
118C3×C9—31no—
119C3×C9—32no—
120C3×C9—61no—
121C3×C9C4×C3⋊D313yescomplemented
122C2×C3×C4—811no—
123C4×D3—273no—
124C4×D3—271no—
125C4×D3—813no—
126C2×C32—21no—
127C2×C32—33no—
128C2×C32—33no—
129C2×C32—93no—
130C2×C32C2×#27211yescharacteristic
131C2×C32C2×C3⋊(C3⋊D3)11yescharacteristic
132C3⋊D3—92no—
133C3⋊D3—96no—
134C3⋊D3—276no—
135C3×D3—276no—
136C3×D3—272no—
137C2×C9—33no—
138C2×C9—36no—
139D9—96no—
140D9—912no—
141C22×C3—811no—
142C2×D3—273no—
143C2×D3—271no—
144C2×D3—813no—
145C3×C4—31no—
146C3×C4—61no—
147C3×C4—93no—
148C3×C4—811no—
149C3×C4#418413yescomplemented
150C3×C4C3⋊#27211yescharacteristic
151Dic3—273no—
152Dic3—271no—
153Dic3—813no—
154C32—21no—
155C32—33no—
156C32—33no—
157C32—93no—
158C32C4×#27211yescharacteristic
159C32C4×C3⋊(C3⋊D3)11yescharacteristic
160C9—33no—
161C9—36no—
162C2×C4—811noSylow
163C2×C3—31no—
164C2×C3—61no—
165C2×C3—93no—
166C2×C3—812no—
167C2×C3C2×#418413yes—
168C2×C3C2×C3⋊#27211yescharacteristic
169D3—276no—
170D3—272no—
171D3—816no—
172C22—811no—
173C4—811no—
174C4C3⋊#418411yescharacteristic, direct product factor
175C3—31no—
176C3—61no—
177C3—93no—
178C3C4×#418413yescomplemented
179C3C4×C3⋊#27211yescharacteristic
180C2—812no—
181C2C2×C3⋊#418411yescharacteristic
subgroupG/H
center, hypercenterC4C3⋊#4184
commutator, hypocenterC3×#731C2×C4
FrattiniC2×C32C2×C3⋊(C3⋊D3)
FittingC3×C4×#731C2
socleC2×C32C2×#272
prime radicalC2×C3⋊#4184C2
cosocleC2×C3×#731C22
LCSG ▷ C3×#731
UCSC1 ◁ C4

Complements

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

NH ≅ G/Ntype
2. C3×C4×#731C2semidirect
3. C3⋊#66331C2semidirect
9. C3⋊#4184C4direct (N × H)
13. C3×C4×3−1+2D3semidirect
15. C32×C4×C9D3semidirect
20. C4×#731D3semidirect
22. C3×#731C2×C4semidirect
50. C4×3−1+2C3⋊D3semidirect
56. C3×C4×C9C3⋊D3semidirect
62. C3×3−1+2C4×D3semidirect
64. C32×C9C4×D3semidirect
65. #731C4×D3semidirect
115. 3−1+2C4×C3⋊D3semidirect
121. C3×C9C4×C3⋊D3semidirect
149. C3×C4#4184semidirect
174. C4C3⋊#4184direct (N × H)
178. 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
C3⋊#663312
C4×C3⋊AGL(1,ℤ/9)3
C4×C3⋊((C3⋊D3)⋊C3)3
C3×C4×C3⋊D93
C4×#41843