Finite Group Databasebeta

← C4×#4177⋊C3 #14517389

Subgroups — C4×#4177⋊C3 #14517389

Order 1944.

284 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 75 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×#4177⋊C3C211yesmaximal, characteristic
2C4×#6910C211yesmaximal, characteristic, complemented
3#66324⋊C3C211yesmaximal, characteristic, complemented
4C4×C3⋊AGL(1,ℤ/9)C311yesmaximal, characteristic, complemented
5C3×C4×(C3⋊D3)⋊C3—31nomaximal
6C4×#4177C313yesmaximal, complemented
7C2×#6910C2211yescharacteristic
8#4177⋊C3C412yesdirect product factor
9C2×C3⋊AGL(1,ℤ/9)C2×C311yescharacteristic
10C2×C3×(C3⋊D3)⋊C3—31no—
11C3×C4×3−1+2—21no—
12C3×C4×3−1+2C2×C311yescharacteristic, complemented
13C3×C4×H(3,𝔽3)D311yescharacteristic
14C3⋊(3−1+2⋊C4)C2×C311yescharacteristic, complemented
15C3×(C3⋊Dic3)⋊C3—31no—
16C2×#4177C2×C313yes—
17C4×#731—23no—
18C4×#731C2×C313yescomplemented
19#66324C2×C313yescomplemented
20#6910C2×C411yescharacteristic, complemented, Sylow
21C3×C4×C3⋊D3—31no—
22C32×C4×D3—91no—
23C4×C3⋊D9C3211yescharacteristic, complemented
24C4×AGL(1,ℤ/9)—91no—
25C4×(C3⋊D3)⋊C3—33no—
26C2×C3×3−1+2—21no—
27C2×C3×3−1+2C22×C311yescharacteristic
28C2×C3×H(3,𝔽3)C2×D311yescharacteristic
29C3⋊AGL(1,ℤ/9)C3×C412yescomplemented
30C3×(C3⋊D3)⋊C3—32no—
31C2×#731—23no—
32C2×#731C22×C313yes—
33#4177C3×C416yescomplemented
34C2×C3×C3⋊D3—31no—
35C2×C32×D3—91no—
36C33×C4—31no—
37C33×C4C3×D311yescharacteristic
38C3×C3⋊Dic3—31no—
39C32×Dic3—91no—
40C2×C3⋊D9C2×C3211yescharacteristic
41C2×AGL(1,ℤ/9)—91no—
42C2×(C3⋊D3)⋊C3—33no—
43C4×3−1+2—23no—
44C4×3−1+2—31no—
45C4×3−1+2—61no—
46C4×3−1+2—61no—
47C4×3−1+2—61no—
48C4×H(3,𝔽3)—61no—
49C4×H(3,𝔽3)C3×D313yes—
50C3×C4×C9—21no—
51C3×C4×C9—61no—
52C3×C4×C9C2×C3211yescharacteristic, complemented
53C3⋊Dic9C2×C3211yescharacteristic, complemented
543−1+2⋊C4—91no—
55(C3⋊Dic3)⋊C3—33no—
56C3×3−1+2—21no—
57C3×3−1+2C2×C3×C411yescharacteristic, complemented
58C3×H(3,𝔽3)C4×D311yescharacteristic
59#731—23no—
60#731C2×C3×C413yescomplemented
61C2×C32×C4—271no—
62C4×C3⋊D3—31no—
63C3×C4×D3—93no—
64C3×C4×D3—91no—
65C3×C4×D3—271no—
66C4×D9—91no—
67C2×C33—31no—
68C2×C33C2×C3×D311yescharacteristic
69C3×C3⋊D3—32no—
70C32×D3—92no—
71C2×3−1+2—23no—
72C2×3−1+2—31no—
73C2×3−1+2—61no—
74C2×3−1+2—61no—
75C2×3−1+2—61no—
76C2×H(3,𝔽3)—61no—
77C2×H(3,𝔽3)C2×C3×D313yes—
78C2×C3×C9—21no—
79C2×C3×C9—61no—
80C2×C3×C9C22×C3211yescharacteristic
81C3⋊D9C32×C412yescomplemented
82AGL(1,ℤ/9)—92no—
83(C3⋊D3)⋊C3—36no—
84C22×C32—271no—
85C2×C3⋊D3—31no—
86C2×C3×D3—93no—
87C2×C3×D3—91no—
88C2×C3×D3—271no—
89C32×C4—21no—
90C32×C4—33no—
91C32×C4—91no—
92C32×C4—91no—
93C32×C4—181no—
94C32×C4—271no—
95C32×C4(C3⋊D3)⋊C311yescharacteristic
96C32×C4C32×D311yescharacteristic
97C3⋊Dic3—31no—
98C3×Dic3—93no—
99C3×Dic3—91no—
100C3×Dic3—271no—
101C2×D9—91no—
102C4×C9—31no—
103C4×C9—61no—
104C4×C9—63no—
105Dic9—91no—
106C33—31no—
107C33C3×C4×D311yescharacteristic
1083−1+2—23no—
1093−1+2—31no—
1103−1+2—61no—
1113−1+2—61no—
1123−1+2—61no—
113H(3,𝔽3)—61no—
114H(3,𝔽3)C3×C4×D313yes—
115C3×C9—21no—
116C3×C9—61no—
117C3×C9C2×C32×C411yescharacteristic, complemented
118C2×C3×C4—271no—
119C2×C3×C4—273no—
120C4×D3—91no—
121C4×D3—271no—
122C2×C32—21no—
123C2×C32—33no—
124C2×C32—91no—
125C2×C32—91no—
126C2×C32—181no—
127C2×C32—272no—
128C2×C32C2×(C3⋊D3)⋊C311yescharacteristic
129C2×C32C2×C32×D311yescharacteristic
130C3⋊D3—32no—
131C3×D3—96no—
132C3×D3—92no—
133C3×D3—272no—
134C2×C9—31no—
135C2×C9—61no—
136C2×C9—63no—
137D9—92no—
138C22×C3—271no—
139C22×C3—273no—
140C2×D3—91no—
141C2×D3—271no—
142C3×C4—31no—
143C3×C4—31no—
144C3×C4—61no—
145C3×C4—93no—
146C3×C4—271no—
147C3×C4—273no—
148C3×C4C3×(C3⋊D3)⋊C311yescharacteristic
149Dic3—91no—
150Dic3—271no—
151C32—21no—
152C32—33no—
153C32—91no—
154C32—91no—
155C32—181no—
156C32C4×(C3⋊D3)⋊C311yescharacteristic
157C32C32×C4×D311yescharacteristic
158C9—31no—
159C9—61no—
160C9—63no—
161C2×C4—271noSylow
162C2×C3—31no—
163C2×C3—31no—
164C2×C3—61no—
165C2×C3—93no—
166C2×C3—272no—
167C2×C3—276no—
168C2×C3C2×C3×(C3⋊D3)⋊C311yescharacteristic
169D3—92no—
170D3—272no—
171C22—271no—
172C4—271no—
173C4#4177⋊C311yescharacteristic, direct product factor
174C3—31no—
175C3—31no—
176C3—61no—
177C3—93no—
178C3C3×C4×(C3⋊D3)⋊C311yescharacteristic
179C2—272no—
180C2C2×#4177⋊C311yescharacteristic
subgroupG/H
center, hypercenterC4#4177⋊C3
commutator, hypocenterC3×C9C2×C32×C4
FrattiniC2×C32C2×C32×D3
FittingC4×#6910C2
socleC2×C3C2×C3×(C3⋊D3)⋊C3
prime radicalC2×#4177⋊C3C2
cosocleC2×C3×C9C22×C32
LCSG ▷ C3×C9
UCSC1 ◁ C4

Complements

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

NH ≅ G/Ntype
2. C4×#6910C2semidirect
3. #66324⋊C3C2semidirect
4. C4×C3⋊AGL(1,ℤ/9)C3semidirect
6. C4×#4177C3semidirect
8. #4177⋊C3C4direct (N × H)
12. C3×C4×3−1+2C2×C3semidirect
14. C3⋊(3−1+2⋊C4)C2×C3semidirect
18. C4×#731C2×C3semidirect
19. #66324C2×C3semidirect
20. #6910C2×C4semidirect
23. C4×C3⋊D9C32semidirect
29. C3⋊AGL(1,ℤ/9)C3×C4semidirect
33. #4177C3×C4semidirect
52. C3×C4×C9C2×C32semidirect
53. C3⋊Dic9C2×C32semidirect
57. C3×3−1+2C2×C3×C4semidirect
60. #731C2×C3×C4semidirect
81. C3⋊D9C32×C4semidirect
117. C3×C9C2×C32×C4semidirect
173. C4#4177⋊C3direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#4177⋊C32
C4×#69102
#66324⋊C32
C4×C3⋊AGL(1,ℤ/9)3
C3×C4×(C3⋊D3)⋊C33
C4×#41773