Finite Group Databasebeta

← C4⋊#92303 #14517531

Subgroups — C4⋊#92303 #14517531

Order 1944.

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

normal subgroups only

This group has 417 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×#92303C212yesmaximal, complemented
2C4×C9⋊H(3,𝔽3)C211yesmaximal, characteristic, complemented
3C4⋊(C3⋊(C3⋊D9))C311yesmaximal, characteristic, complemented
4C4⋊(C3⋊AGL(1,ℤ/9))—31nomaximal
5C4⋊(C3⋊((C3⋊D3)⋊C3))—31nomaximal
6C4⋊#4169—32nomaximal
7C2×C9⋊H(3,𝔽3)C2211yescharacteristic
8#92303—22no—
9C2×C3⋊(C3⋊D9)C2×C312yescomplemented
10C2×C3⋊AGL(1,ℤ/9)—32no—
11C2×C3⋊((C3⋊D3)⋊C3)—32no—
12C3×C4×3−1+2—21no—
13C3×C4×3−1+2D311yescharacteristic, complemented
14C3×C4×H(3,𝔽3)D311yescharacteristic
15C32×C4×C9C2×C311yescharacteristic, complemented
16C2×#4169—34no—
17C4×C32⋊C9—21no—
18C4×C32⋊C9—22no—
19C4×C32⋊C9D312yescomplemented
20C9⋊H(3,𝔽3)D411yescharacteristic, complemented, Sylow
21C4⋊(C3⋊(C3⋊D3))—31no—
22C3×C4⋊(C3⋊D3)—91no—
23C4⋊(C3⋊D9)—31no—
24C4⋊(C3⋊D9)—32no—
25C4⋊(C3⋊D9)—93no—
26C4⋊AGL(1,ℤ/9)—93no—
27C4⋊((C3⋊D3)⋊C3)—93no—
28C2×C3×3−1+2—21no—
29C2×C3×3−1+2C2×D311yescharacteristic
30C2×C3×H(3,𝔽3)C2×D311yescharacteristic
31C2×C32×C9C22×C311yescharacteristic
32C3⋊(C3⋊D9)—22no—
33C3⋊AGL(1,ℤ/9)—62no—
34C3⋊((C3⋊D3)⋊C3)—62no—
35C2×C32⋊C9—21no—
36C2×C32⋊C9—22no—
37C2×C32⋊C9C2×D312yes—
38#4169—64no—
39C2×C3⋊(C3⋊D3)—32no—
40C2×C3×C3⋊D3—92no—
41C33×C4—21no—
42C33×C4C3×D311yescharacteristic
43C33×C4C3⋊D311yescharacteristic
44C2×C3⋊D9—32no—
45C2×C3⋊D9—34no—
46C2×C3⋊D9—96no—
47C2×AGL(1,ℤ/9)—96no—
48C2×(C3⋊D3)⋊C3—96no—
49C4×3−1+2—33no—
50C4×3−1+2—63no—
51C4×H(3,𝔽3)—33no—
52C3×C4×C9—21no—
53C3×C4×C9—22no—
54C3×C4×C9—33no—
55C3×C4×C9C3×D312yes—
56C3×C4×C9C3×D311yescharacteristic
57C3×3−1+2—21no—
58C3×3−1+2D1211yescharacteristic, complemented
59C3×H(3,𝔽3)D1211yescharacteristic
60C32×C9C3×D411yescharacteristic, complemented
61C32⋊C9—21no—
62C32⋊C9—22no—
63C32⋊C9D1212yescomplemented
64C4⋊(C3⋊D3)—91no—
65C4⋊(C3⋊D3)—93no—
66C4⋊(C3⋊D3)—271no—
67C4⋊(C3⋊D3)—272no—
68C3×D12—271no—
69C3×D12—271no—
70C3×D12—272no—
71D36—93no—
72D36—272no—
73C2×C33—21no—
74C2×C33C2×C3×D311yescharacteristic
75C2×C33C2×C3⋊D311yescharacteristic
76C3⋊(C3⋊D3)—62no—
77C3×C3⋊D3—182no—
78C2×3−1+2—33no—
79C2×3−1+2—63no—
80C2×H(3,𝔽3)—33no—
81C2×C3×C9—21no—
82C2×C3×C9—22no—
83C2×C3×C9—33no—
84C2×C3×C9C2×C3×D312yes—
85C2×C3×C9C2×C3×D311yescharacteristic
86C3⋊D9—62no—
87C3⋊D9—64no—
88C3⋊D9—186no—
89AGL(1,ℤ/9)—186no—
90(C3⋊D3)⋊C3—186no—
91C2×C3⋊D3—92no—
92C2×C3⋊D3—96no—
93C2×C3⋊D3—272no—
94C2×C3⋊D3—274no—
95C2×C3×D3—272no—
96C2×C3×D3—272no—
97C2×C3×D3—274no—
98C32×C4—31no—
99C32×C4—32no—
100C32×C4—31no—
101C32×C4—31no—
102C32×C4—32no—
103C32×C4—61no—
104C32×C4—61no—
105C32×C4—62no—
106C32×C4AGL(1,ℤ/9)13yescomplemented
107C32×C4C3×C3⋊D311yescharacteristic
108C2×D9—96no—
109C2×D9—274no—
110C4×C9—32no—
111C4×C9—61no—
112C4×C9—62no—
113C4×C9(C3⋊D3)⋊C313yescomplemented
114C33—21no—
115C33C3×D1211yescharacteristic
116C33C4⋊(C3⋊D3)11yescharacteristic
1173−1+2—33no—
1183−1+2—63no—
119H(3,𝔽3)—33no—
120C3×C9—21no—
121C3×C9—22no—
122C3×C9—33no—
123C3×C9C3×D1212yes—
124C3×C9C3×D1211yescharacteristic
125C3×D4—811no—
126D12—271no—
127D12—271no—
128D12—272no—
129D12—813no—
130C2×C32—31no—
131C2×C32—32no—
132C2×C32—31no—
133C2×C32—31no—
134C2×C32—32no—
135C2×C32—61no—
136C2×C32—61no—
137C2×C32—62no—
138C2×C32C2×AGL(1,ℤ/9)13yes—
139C2×C32C2×C3×C3⋊D311yescharacteristic
140C3⋊D3—182no—
141C3⋊D3—186no—
142C3⋊D3—542no—
143C3⋊D3—544no—
144C3×D3—542no—
145C3×D3—542no—
146C3×D3—544no—
147C2×C9—32no—
148C2×C9—61no—
149C2×C9—62no—
150C2×C9C2×(C3⋊D3)⋊C313yes—
151D9—186no—
152D9—544no—
153C22×C3—812no—
154C2×D3—272no—
155C2×D3—272no—
156C2×D3—274no—
157C2×D3—816no—
158C3×C4—33no—
159C3×C4—91no—
160C3×C4—181no—
161C3×C4C3⋊((C3⋊D3)⋊C3)11yescharacteristic
162C3×C4C3⋊AGL(1,ℤ/9)11yescharacteristic
163C3×C4#420712yes—
164C32—31no—
165C32—32no—
166C32—31no—
167C32—31no—
168C32—32no—
169C32—61no—
170C32—61no—
171C32—62no—
172C32C4⋊AGL(1,ℤ/9)13yescomplemented
173C32C3×C4⋊(C3⋊D3)11yescharacteristic
174C9—32no—
175C9—61no—
176C9—62no—
177C9C4⋊((C3⋊D3)⋊C3)13yescomplemented
178D4—811noSylow
179C2×C3—33no—
180C2×C3—91no—
181C2×C3—181no—
182C2×C3—1622no—
183C2×C3C2×C3⋊((C3⋊D3)⋊C3)11yescharacteristic
184C2×C3C2×C3⋊AGL(1,ℤ/9)11yescharacteristic
185C2×C3C2×#420712yes—
186D3—542no—
187D3—542no—
188D3—544no—
189D3—1626no—
190C22—812no—
191C4#9230311yescharacteristic, complemented
192C3—33no—
193C3—91no—
194C3—181no—
195C3C4⋊(C3⋊((C3⋊D3)⋊C3))11yescharacteristic
196C3C4⋊(C3⋊AGL(1,ℤ/9))11yescharacteristic
197C3C4⋊#420712yes—
198C2—1622no—
199C2C2×#9230311yescharacteristic
subgroupG/H
centerC2C2×#92303
commutator, cosocleC2×C32×C9C22×C3
Frattini, socleC2×C32C2×C3×C3⋊D3
FittingC4×C9⋊H(3,𝔽3)C2
hypercenterC4#92303
hypocenterC32×C9C3×D4
LCSG ▷ C2×C32×C9 ▷ C32×C9
UCSC1 ◁ C2 ◁ C4

Complements

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

NH ≅ G/Ntype
1. C2×#92303C2semidirect
2. C4×C9⋊H(3,𝔽3)C2semidirect
3. C4⋊(C3⋊(C3⋊D9))C3semidirect
9. C2×C3⋊(C3⋊D9)C2×C3semidirect
13. C3×C4×3−1+2D3semidirect
15. C32×C4×C9C2×C3semidirect
19. C4×C32⋊C9D3semidirect
20. C9⋊H(3,𝔽3)D4semidirect
58. C3×3−1+2D12semidirect
60. C32×C9C3×D4semidirect
63. C32⋊C9D12semidirect
106. C32×C4AGL(1,ℤ/9)semidirect
113. C4×C9(C3⋊D3)⋊C3semidirect
172. C32C4⋊AGL(1,ℤ/9)semidirect
177. C9C4⋊((C3⋊D3)⋊C3)semidirect
191. C4#92303semidirect

Maximal subgroups

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

subgroupindex
C2×#923032
C4×C9⋊H(3,𝔽3)2
C4⋊(C3⋊(C3⋊D9))3
C4⋊(C3⋊AGL(1,ℤ/9))3
C4⋊(C3⋊((C3⋊D3)⋊C3))3
C4⋊#41693