Finite Group Databasebeta

← C4⋊(#4184⋊C3) #14517618

Subgroups — C4⋊(#4184⋊C3) #14517618

Order 1944.

362 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 362 conjugacy classes of subgroups — too many to draw. Only its 57 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×#4184⋊C3C212yesmaximal, complemented
2C4×#6910C211yesmaximal, characteristic, complemented
3C3×C4⋊AGL(1,ℤ/9)—32nomaximal
4C3×C4⋊AGL(1,ℤ/9)—31nomaximal
5C3×C4⋊((C3⋊D3)⋊C3)—31nomaximal
6C4⋊#4184C311yesmaximal, characteristic, complemented
7C2×#6910C2211yescharacteristic
8#4184⋊C3—22no—
9C2×C3×AGL(1,ℤ/9)—34no—
10C2×C3×AGL(1,ℤ/9)—32no—
11C2×C3×(C3⋊D3)⋊C3—32no—
12C3×C4×3−1+2D311yescharacteristic, complemented
13C3×C4×3−1+2D312yescomplemented
14C3×C4×H(3,𝔽3)D311yescharacteristic
15C2×#4184C2×C312yescomplemented
16C4×#731—22no—
17C4×#731—21no—
18C4×#731—21no—
19C4×#731C2×C311yescharacteristic, complemented
20#6910D411yescharacteristic, complemented, Sylow
21C3×C4⋊(C3⋊D3)—31no—
22C32×D12—91no—
23C4⋊AGL(1,ℤ/9)—32no—
24C4⋊AGL(1,ℤ/9)—32no—
25C4⋊AGL(1,ℤ/9)—32no—
26C4⋊AGL(1,ℤ/9)—31no—
27C4⋊AGL(1,ℤ/9)—32no—
28C4⋊((C3⋊D3)⋊C3)—32no—
29C4⋊((C3⋊D3)⋊C3)—31no—
30C3×D36—32no—
31C3×D36—31no—
32C2×C3×3−1+2C2×D311yescharacteristic
33C2×C3×3−1+2C2×D312yes—
34C2×C3×H(3,𝔽3)C2×D311yescharacteristic
35C3×AGL(1,ℤ/9)—64no—
36C3×AGL(1,ℤ/9)—62no—
37C3×(C3⋊D3)⋊C3—62no—
38C2×#731—22no—
39C2×#731—21no—
40C2×#731—21no—
41C2×#731C22×C311yescharacteristic
42#4184—22no—
43C2×C3×C3⋊D3—32no—
44C2×C32×D3—92no—
45C33×C4—31no—
46C33×C4C3⋊D311yescharacteristic
47C2×AGL(1,ℤ/9)—34no—
48C2×AGL(1,ℤ/9)—34no—
49C2×AGL(1,ℤ/9)—34no—
50C2×AGL(1,ℤ/9)—32no—
51C2×AGL(1,ℤ/9)—34no—
52C2×(C3⋊D3)⋊C3—34no—
53C2×(C3⋊D3)⋊C3—32no—
54C2×C3×D9—34no—
55C2×C3×D9—32no—
56C4×3−1+2—22no—
57C4×3−1+2—32no—
58C4×3−1+2—32no—
59C4×3−1+2—32no—
60C4×3−1+2—31no—
61C4×3−1+2C3×D312yescomplemented
62C4×H(3,𝔽3)—21no—
63C4×H(3,𝔽3)—32no—
64C4×H(3,𝔽3)C3×D311yescharacteristic
65C3×C4×C9—21no—
66C3×C4×C9—32no—
67C3×C4×C9C3×D311yescharacteristic, complemented
68C3×3−1+2D1211yescharacteristic, complemented
69C3×3−1+2D1212yescomplemented
70C3×H(3,𝔽3)D1211yescharacteristic
71#731—22no—
72#731—21no—
73#731—21no—
74#731C3×D411yescharacteristic, complemented
75C32×D4—271no—
76C4⋊(C3⋊D3)—31no—
77C3×D12—92no—
78C3×D12—91no—
79C3×D12—91no—
80C3×D12—271no—
81D36—32no—
82D36—31no—
83C2×C33—31no—
84C2×C33C2×C3⋊D311yescharacteristic
85C3×C3⋊D3—62no—
86C32×D3—182no—
87C2×3−1+2—22no—
88C2×3−1+2—32no—
89C2×3−1+2—32no—
90C2×3−1+2—32no—
91C2×3−1+2—31no—
92C2×3−1+2C2×C3×D312yes—
93C2×H(3,𝔽3)—21no—
94C2×H(3,𝔽3)—32no—
95C2×H(3,𝔽3)C2×C3×D311yescharacteristic
96C2×C3×C9—21no—
97C2×C3×C9—32no—
98C2×C3×C9C2×C3×D311yescharacteristic
99AGL(1,ℤ/9)—64no—
100AGL(1,ℤ/9)—64no—
101AGL(1,ℤ/9)—64no—
102AGL(1,ℤ/9)—62no—
103AGL(1,ℤ/9)—64no—
104(C3⋊D3)⋊C3—64no—
105(C3⋊D3)⋊C3—62no—
106C3×D9—64no—
107C3×D9—62no—
108C22×C32—272no—
109C2×C3⋊D3—32no—
110C2×C3×D3—94no—
111C2×C3×D3—92no—
112C2×C3×D3—92no—
113C2×C3×D3—272no—
114C32×C4—31no—
115C32×C4—61no—
116C32×C4—91no—
117C32×C4—91no—
118C32×C4—181no—
119C32×C4#27212yes—
120C32×C4#27211yescharacteristic
121C32×C4C3×C3⋊D311yescharacteristic
122C2×D9—34no—
123C2×D9—32no—
124C4×C9—32no—
125C4×C9—31no—
126C4×C9—61no—
127C4×C9—62no—
128C33—31no—
129C33C4⋊(C3⋊D3)11yescharacteristic
1303−1+2—22no—
1313−1+2—32no—
1323−1+2—32no—
1333−1+2—32no—
1343−1+2—31no—
1353−1+2C3×D1212yescomplemented
136H(3,𝔽3)—21no—
137H(3,𝔽3)—32no—
138H(3,𝔽3)C3×D1211yescharacteristic
139C3×C9—21no—
140C3×C9—32no—
141C3×C9C3×D1211yescharacteristic, complemented
142C3×D4—271no—
143C3×D4—272no—
144C3×D4—271no—
145D12—91no—
146D12—271no—
147C2×C32—31no—
148C2×C32—61no—
149C2×C32—91no—
150C2×C32—91no—
151C2×C32—181no—
152C2×C32—542no—
153C2×C32C2×#27212yes—
154C2×C32C2×#27211yescharacteristic
155C2×C32C2×C3×C3⋊D311yescharacteristic
156C3⋊D3—62no—
157C3×D3—184no—
158C3×D3—182no—
159C3×D3—182no—
160C3×D3—542no—
161C2×C9—32no—
162C2×C9—31no—
163C2×C9—61no—
164C2×C9—62no—
165D9—64no—
166D9—62no—
167C22×C3—272no—
168C22×C3—274no—
169C22×C3—272no—
170C2×D3—92no—
171C2×D3—272no—
172C3×C4—31no—
173C3×C4—32no—
174C3×C4—31no—
175C3×C4—91no—
176C3×C4—181no—
177C3×C4C3×#27211yescharacteristic
178C32—31no—
179C32—61no—
180C32—91no—
181C32—91no—
182C32—181no—
183C32C4⋊#27212yes—
184C32C4⋊#27211yescharacteristic
185C32C3×C4⋊(C3⋊D3)11yescharacteristic
186C9—32no—
187C9—31no—
188C9—61no—
189C9—62no—
190D4—271noSylow
191C2×C3—31no—
192C2×C3—32no—
193C2×C3—31no—
194C2×C3—91no—
195C2×C3—181no—
196C2×C3—542no—
197C2×C3—544no—
198C2×C3—542no—
199C2×C3C2×C3×#27211yescharacteristic
200D3—182no—
201D3—542no—
202C22—272no—
203C4#4184⋊C311yescharacteristic, complemented
204C3—31no—
205C3—32no—
206C3—31no—
207C3—91no—
208C3—181no—
209C3C3×C4⋊#27211yescharacteristic
210C2—542no—
211C2C2×#4184⋊C311yescharacteristic
subgroupG/H
centerC2C2×#4184⋊C3
commutator, cosocleC2×#731C22×C3
FrattiniC2×C32C2×C3×C3⋊D3
FittingC4×#6910C2
socleC2×C3C2×C3×#272
hypercenterC4#4184⋊C3
hypocenter#731C3×D4
LCSG ▷ C2×#731 ▷ #731
UCSC1 ◁ C2 ◁ C4

Complements

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

NH ≅ G/Ntype
1. C2×#4184⋊C3C2semidirect
2. C4×#6910C2semidirect
6. C4⋊#4184C3semidirect
12. C3×C4×3−1+2D3semidirect
13. C3×C4×3−1+2D3semidirect
15. C2×#4184C2×C3semidirect
19. C4×#731C2×C3semidirect
20. #6910D4semidirect
61. C4×3−1+2C3×D3semidirect
67. C3×C4×C9C3×D3semidirect
68. C3×3−1+2D12semidirect
69. C3×3−1+2D12semidirect
74. #731C3×D4semidirect
135. 3−1+2C3×D12semidirect
141. C3×C9C3×D12semidirect
203. C4#4184⋊C3semidirect

Maximal subgroups

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

subgroupindex
C2×#4184⋊C32
C4×#69102
C3×C4⋊AGL(1,ℤ/9)3
C3×C4⋊((C3⋊D3)⋊C3)3
C4⋊#41843