Finite Group Databasebeta

← C4⋊(C3⋊#4183) #14517736

Subgroups — C4⋊(C3⋊#4183) #14517736

Order 1944.

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

normal subgroups only

This group has 813 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⋊#4183C212yesmaximal, complemented
2C3×C4×AΣL(1,𝔽27)C211yesmaximal, characteristic, complemented
3C3×C4⋊(C3⋊(C3⋊D3))—31nomaximal
4C4⋊(C3⋊AGL(1,ℤ/9))—32nomaximal
5C4⋊(C3⋊((C3⋊D3)⋊C3))—31nomaximal
6C4⋊#4183—39nomaximal
7C2×C3×AΣL(1,𝔽27)C2211yescharacteristic
8C3⋊#4183—22no—
9C2×C3×C3⋊(C3⋊D3)—32no—
10C34×C4D311yescharacteristic, complemented
11C2×C3⋊AGL(1,ℤ/9)—34no—
12C2×C3⋊((C3⋊D3)⋊C3)—32no—
13C3×C4×3−1+2D312yescomplemented
14C3×C4×H(3,𝔽3)D311yescharacteristic, complemented
15C2×#4183—318no—
16C4×AΣL(1,𝔽27)D319yescomplemented
17C3×AΣL(1,𝔽27)D411yescharacteristic, complemented, Sylow
18C4⋊(C3⋊(C3⋊D3))—31no—
19C4⋊(C3⋊(C3⋊D3))—31no—
20C3×C4⋊(C3⋊D3)—99no—
21C3×C4⋊(C3⋊D3)—91no—
22C3×C4⋊(C3⋊D3)—93no—
23C4⋊(C3⋊D9)—32no—
24C4⋊AGL(1,ℤ/9)—96no—
25C4⋊((C3⋊D3)⋊C3)—93no—
26C2×C34C2×D311yescharacteristic
27C3×C3⋊(C3⋊D3)—62no—
28C2×C3×3−1+2C2×D312yes—
29C2×C3×H(3,𝔽3)C2×D311yescharacteristic
30C3⋊AGL(1,ℤ/9)—64no—
31C3⋊((C3⋊D3)⋊C3)—62no—
32C2×AΣL(1,𝔽27)C2×D319yes—
33#4183—618no—
34C2×C3⋊(C3⋊D3)—32no—
35C2×C3⋊(C3⋊D3)—32no—
36C2×C3×C3⋊D3—918no—
37C2×C3×C3⋊D3—96no—
38C2×C3×C3⋊D3—92no—
39C33×C4—31no—
40C33×C4—39no—
41C33×C4—31no—
42C33×C4—61no—
43C33×C4C3⋊D311yescharacteristic
44C33×C4C3⋊D313yescomplemented
45C2×C3⋊D9—34no—
46C2×AGL(1,ℤ/9)—912no—
47C2×(C3⋊D3)⋊C3—96no—
48C4×3−1+2—62no—
49C4×3−1+2C3⋊D316yescomplemented
50C4×H(3,𝔽3)—61no—
51C4×H(3,𝔽3)C3⋊D313yescomplemented
52C3×C4×C9—32no—
53C34D1211yescharacteristic, complemented
54C3×3−1+2D1212yescomplemented
55C3×H(3,𝔽3)D1211yescharacteristic, complemented
56AΣL(1,𝔽27)D1219yescomplemented
57C4⋊(C3⋊D3)—99no—
58C4⋊(C3⋊D3)—93no—
59C4⋊(C3⋊D3)—91no—
60C4⋊(C3⋊D3)—93no—
61C4⋊(C3⋊D3)—273no—
62C3×D12—279no—
63C3×D12—273no—
64C3×D12—271no—
65D36—96no—
66C2×C33—31no—
67C2×C33—39no—
68C2×C33—31no—
69C2×C33—61no—
70C2×C33C2×C3⋊D311yescharacteristic
71C2×C33C2×C3⋊D313yes—
72C3⋊(C3⋊D3)—62no—
73C3⋊(C3⋊D3)—62no—
74C3×C3⋊D3—1818no—
75C3×C3⋊D3—182no—
76C3×C3⋊D3—186no—
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—32no—
82C3⋊D9—64no—
83AGL(1,ℤ/9)—1812no—
84(C3⋊D3)⋊C3—186no—
85C2×C3⋊D3—918no—
86C2×C3⋊D3—96no—
87C2×C3⋊D3—92no—
88C2×C3⋊D3—96no—
89C2×C3⋊D3—276no—
90C2×C3×D3—2718no—
91C2×C3×D3—276no—
92C2×C3×D3—272no—
93C32×C4—21no—
94C32×C4—39no—
95C32×C4—33no—
96C32×C4—39no—
97C32×C4—33no—
98C32×C4—33no—
99C32×C4—69no—
100C32×C4—93no—
101C32×C4#27211yescharacteristic
102C32×C4C3⋊(C3⋊D3)11yescharacteristic
103C2×D9—912no—
104C4×C9—36no—
105C33—31no—
106C33—39no—
107C33—31no—
108C33—61no—
109C33C4⋊(C3⋊D3)11yescharacteristic
110C33C4⋊(C3⋊D3)13yescomplemented
1113−1+2—62no—
1123−1+2C4⋊(C3⋊D3)16yescomplemented
113H(3,𝔽3)—61no—
114H(3,𝔽3)C4⋊(C3⋊D3)13yescomplemented
115C3×C9—32no—
116C3×D4—811no—
117D12—279no—
118D12—273no—
119D12—271no—
120D12—813no—
121C2×C32—21no—
122C2×C32—39no—
123C2×C32—33no—
124C2×C32—39no—
125C2×C32—33no—
126C2×C32—33no—
127C2×C32—69no—
128C2×C32—93no—
129C2×C32C2×#27211yescharacteristic
130C2×C32C2×C3⋊(C3⋊D3)11yescharacteristic
131C3⋊D3—1818no—
132C3⋊D3—186no—
133C3⋊D3—182no—
134C3⋊D3—186no—
135C3⋊D3—546no—
136C3×D3—5418no—
137C3×D3—546no—
138C3×D3—542no—
139C2×C9—36no—
140D9—1812no—
141C22×C3—812no—
142C2×D3—2718no—
143C2×D3—276no—
144C2×D3—272no—
145C2×D3—816no—
146C3×C4—39no—
147C3×C4—31no—
148C3×C4—61no—
149C3×C4—93no—
150C3×C4#418313yescomplemented
151C3×C4C3⋊#27211yescharacteristic
152C32—21no—
153C32—39no—
154C32—39no—
155C32—33no—
156C32—33no—
157C32—33no—
158C32—69no—
159C32—93no—
160C32C4⋊#27211yescharacteristic
161C32C4⋊(C3⋊(C3⋊D3))11yescharacteristic
162C9—36no—
163D4—811noSylow
164C2×C3—39no—
165C2×C3—31no—
166C2×C3—61no—
167C2×C3—93no—
168C2×C3—1622no—
169C2×C3C2×#418313yes—
170C2×C3C2×C3⋊#27211yescharacteristic
171D3—5418no—
172D3—546no—
173D3—542no—
174D3—1626no—
175C22—812no—
176C4C3⋊#418311yescharacteristic, complemented
177C3—39no—
178C3—31no—
179C3—61no—
180C3—93no—
181C3C4⋊#418313yescomplemented
182C3C4⋊(C3⋊#272)11yescharacteristic
183C2—1622no—
184C2C2×C3⋊#418311yescharacteristic
subgroupG/H
centerC2C2×C3⋊#4183
commutator, cosocleC2×C3×AΣL(1,𝔽27)C22
FrattiniC2×C32C2×C3⋊(C3⋊D3)
FittingC3×C4×AΣL(1,𝔽27)C2
socleC2×C32C2×#272
hypercenterC4C3⋊#4183
hypocenterC3×AΣL(1,𝔽27)D4
LCSG ▷ C2×C3×AΣL(1,𝔽27) ▷ C3×AΣL(1,𝔽27)
UCSC1 ◁ C2 ◁ C4

Complements

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

NH ≅ G/Ntype
1. C2×C3⋊#4183C2semidirect
2. C3×C4×AΣL(1,𝔽27)C2semidirect
10. C34×C4D3semidirect
13. C3×C4×3−1+2D3semidirect
14. C3×C4×H(3,𝔽3)D3semidirect
16. C4×AΣL(1,𝔽27)D3semidirect
17. C3×AΣL(1,𝔽27)D4semidirect
44. C33×C4C3⋊D3semidirect
49. C4×3−1+2C3⋊D3semidirect
51. C4×H(3,𝔽3)C3⋊D3semidirect
53. C34D12semidirect
54. C3×3−1+2D12semidirect
55. C3×H(3,𝔽3)D12semidirect
56. AΣL(1,𝔽27)D12semidirect
110. C33C4⋊(C3⋊D3)semidirect
112. 3−1+2C4⋊(C3⋊D3)semidirect
114. H(3,𝔽3)C4⋊(C3⋊D3)semidirect
150. C3×C4#4183semidirect
176. C4C3⋊#4183semidirect
181. C3C4⋊#4183semidirect

Maximal subgroups

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

subgroupindex
C2×C3⋊#41832
C3×C4×AΣL(1,𝔽27)2
C3×C4⋊(C3⋊(C3⋊D3))3
C4⋊(C3⋊AGL(1,ℤ/9))3
C4⋊(C3⋊((C3⋊D3)⋊C3))3
C4⋊#41833