Finite Group Databasebeta

← #14517021

Subgroups — #14517021

Order 1944.

681 conjugacy classes of subgroups; only the 46 normal subgroups are shown.

normal subgroups only

This group has 681 conjugacy classes of subgroups — too many to draw. Only its 46 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⋊#4183C211yesmaximal, characteristic, complemented
2C2×C3⋊#4175C211yesmaximal, characteristic, complemented
3C3×#66321C211yesmaximal, characteristic, complemented
4#10620147—31nomaximal
5#10619902—31nomaximal
6#10619551—33nomaximal
7C2×C3×AΣL(1,𝔽27)C2211yescharacteristic
8C3⋊#4183—21no—
9C3⋊#4175—21no—
10C2×C3⋊(C3⋊(C3⋊D3))D311yescharacteristic, complemented
11C2×C3×C3⋊(C3⋊D3)—31no—
12C33×Dic3—31no—
13C2×C3⋊AGL(1,ℤ/9)—61no—
14C2×C3⋊((C3⋊D3)⋊C3)—31no—
15C2×C3⋊((C3⋊D3)⋊C3)—31no—
16C3×#1084D311yescharacteristic, complemented
17C2×#4183—33no—
18C2×#4183—63no—
19C2×#4175—33no—
20#66321D313yescomplemented
21C3×AΣL(1,𝔽27)D411yescharacteristic, complemented, Sylow
22C4⋊(C3⋊(C3⋊D3))—91no—
23#6292—93no—
24#6292—91no—
25#6292—99no—
26#6292—91no—
27#6198—91no—
28C2×C34C2×D311yescharacteristic
29C3⋊(C3⋊(C3⋊D3))—21no—
30C3×C3⋊(C3⋊D3)—61no—
31C2×C3×3−1+2—21no—
32C2×C3×H(3,𝔽3)C2×D311yescharacteristic
33C3⋊AGL(1,ℤ/9)—62no—
34C3⋊((C3⋊D3)⋊C3)—61no—
35C3⋊((C3⋊D3)⋊C3)—61no—
36C2×AΣL(1,𝔽27)—23no—
37C2×AΣL(1,𝔽27)C2×D313yes—
38#4183—66no—
39#4183—63no—
40#4175—63no—
41C2×C3⋊(C3⋊D3)—31no—
42C2×C3⋊(C3⋊D3)—31no—
43C2×C3⋊(C3⋊D3)—31no—
44C2×C3⋊(C3⋊D3)—33no—
45C2×C3⋊(C3⋊D3)—91no—
46C2×C3⋊(C3⋊D3)—99no—
47C2×C3⋊(C3⋊D3)—181no—
48C2×C3×C3⋊D3—91no—
49C2×C3×C3⋊D3—99no—
50C2×C3×C3⋊D3—93no—
51C2×C3×C3⋊D3—91no—
52C33×C4—91no—
53C32×Dic3—39no—
54C32×Dic3—33no—
55C32×Dic3—31no—
56C32×Dic3—91no—
57C2×C3⋊D9—61no—
58C2×AGL(1,ℤ/9)—183no—
59C2×(C3⋊D3)⋊C3—91no—
60C2×(C3⋊D3)⋊C3—91no—
61C2×(C3⋊D3)⋊C3—181no—
62C2×(C3⋊D3)⋊C3—181no—
63#1084C3⋊D311yescharacteristic, complemented
64C34#6711yescharacteristic, complemented
65C3×3−1+2—21no—
66C3×H(3,𝔽3)D1211yescharacteristic, complemented
67AΣL(1,𝔽27)—23no—
68AΣL(1,𝔽27)D1213yescomplemented
69C4⋊(C3⋊D3)—271no—
70C4⋊(C3⋊D3)—273no—
71C4⋊(C3⋊D3)—279no—
72#626—271no—
73#626—273no—
74#626—279no—
75#626—271no—
76#626—273no—
77C2×C33—31no—
78C2×C33—39no—
79C2×C33—31no—
80C2×C33—61no—
81C2×C33D3211yescharacteristic
82C2×C33D3213yes—
83C3⋊(C3⋊D3)—61no—
84C3⋊(C3⋊D3)—61no—
85C3⋊(C3⋊D3)—61no—
86C3⋊(C3⋊D3)—63no—
87C3⋊(C3⋊D3)—181no—
88C3⋊(C3⋊D3)—182no—
89C3⋊(C3⋊D3)—189no—
90C3×C3⋊D3—181no—
91C3×C3⋊D3—189no—
92C3×C3⋊D3—181no—
93C3×C3⋊D3—183no—
94C2×3−1+2—23no—
95C2×3−1+2—121no—
96C2×H(3,𝔽3)—21no—
97C2×H(3,𝔽3)—61no—
98C2×H(3,𝔽3)C2×C3⋊D311yescharacteristic
99C2×C3×C9—61no—
100C3⋊D9—62no—
101AGL(1,ℤ/9)—186no—
102(C3⋊D3)⋊C3—182no—
103(C3⋊D3)⋊C3—182no—
104(C3⋊D3)⋊C3—181no—
105(C3⋊D3)⋊C3—181no—
106C2×C3⋊D3—99no—
107C2×C3⋊D3—93no—
108C2×C3⋊D3—91no—
109C2×C3⋊D3—91no—
110C2×C3⋊D3—91no—
111C2×C3⋊D3—91no—
112C2×C3⋊D3—181no—
113C2×C3⋊D3—181no—
114C2×C3⋊D3—273no—
115C2×C3⋊D3—279no—
116C2×C3⋊D3—273no—
117C2×C3⋊D3—273no—
118C2×C3⋊D3—279no—
119C2×C3⋊D3—549no—
120C2×C3×D3—271no—
121C2×C3×D3—279no—
122C2×C3×D3—273no—
123C2×C3×D3—273no—
124C2×C3×D3—271no—
125C32×C4—99no—
126C32×C4—93no—
127C32×C4—91no—
128C3×Dic3—39no—
129C3×Dic3—33no—
130C3×Dic3—31no—
131C3×Dic3—91no—
132C3×Dic3—93no—
133C2×D9—183no—
134C33—31no—
135C33—39no—
136C33—31no—
137C33—61no—
138C33#62611yescharacteristic
139C33#62613yescomplemented
1403−1+2—23no—
1413−1+2—121no—
142H(3,𝔽3)—21no—
143H(3,𝔽3)—61no—
144H(3,𝔽3)C4⋊(C3⋊D3)11yescharacteristic, complemented
145C3×C9—61no—
146#67—811no—
147#67—811no—
148D12—813no—
149D12—811no—
150D12—819no—
151C2×C32—21no—
152C2×C32—39no—
153C2×C32—33no—
154C2×C32—39no—
155C2×C32—33no—
156C2×C32—31no—
157C2×C32—69no—
158C2×C32—61no—
159C2×C32—93no—
160C2×C32((C3⋊D3)⋊C3)⋊C211yescharacteristic
161C2×C32D3×C3⋊D311yescharacteristic
162C3⋊D3—189no—
163C3⋊D3—183no—
164C3⋊D3—181no—
165C3⋊D3—181no—
166C3⋊D3—182no—
167C3⋊D3—181no—
168C3⋊D3—182no—
169C3⋊D3—181no—
170C3⋊D3—543no—
171C3⋊D3—543no—
172C3⋊D3—549no—
173C3⋊D3—543no—
174C3⋊D3—5418no—
175C3⋊D3—549no—
176C3×D3—541no—
177C3×D3—549no—
178C3×D3—543no—
179C3×D3—543no—
180C3×D3—541no—
181C2×C9—63no—
182D9—186no—
183C22×C3—811no—
184C22×C3—811no—
185C2×D3—279no—
186C2×D3—273no—
187C2×D3—273no—
188C2×D3—271no—
189C2×D3—271no—
190C2×D3—819no—
191C2×D3—811no—
192C2×D3—811no—
193C2×D3—1621no—
194C2×D3—1621no—
195C3×C4—99no—
196C3×C4—93no—
197C3×C4—91no—
198Dic3—31no—
199Dic3—91no—
200C32—21no—
201C32—39no—
202C32—39no—
203C32—33no—
204C32—33no—
205C32—31no—
206C32—69no—
207C32—61no—
208C32—93no—
209C32#620011yescharacteristic
210C32#629211yescharacteristic
211C9—63no—
212D4—2431noSylow
213C2×C3—31no—
214C2×C3—39no—
215C2×C3—61no—
216C2×C3—91no—
217C2×C3—181no—
218C2×C3—1621no—
219C2×C3—1621no—
220C2×C3#4174⋊C213yes—
221C2×C3((C3⋊D3)⋊C3)⋊D311yescharacteristic
222D3—549no—
223D3—543no—
224D3—543no—
225D3—541no—
226D3—541no—
227D3—1621no—
228D3—1629no—
229D3—1622no—
230D3—1621no—
231D3—1622no—
232C22—811no—
233C22—811no—
234C4—91no—
235C3—39no—
236C3—31no—
237C3—61no—
238C3—91no—
239C3—181no—
240C3#1061955113yescomplemented
241C3#1061988711yescharacteristic
242C2—1621no—
243C2—1621no—
244C2#1175773511yescharacteristic
subgroupG/H
center, hypercenterC2#11757735
commutator, Fitting, cosocleC2×C3×AΣL(1,𝔽27)C22
FrattiniC2×C32D3×C3⋊D3
socleC2×C32((C3⋊D3)⋊C3)⋊C2
hypocenterC3×AΣL(1,𝔽27)D4
LCSG ▷ C2×C3×AΣL(1,𝔽27) ▷ C3×AΣL(1,𝔽27)
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
1. C2×C3⋊#4183C2semidirect
2. C2×C3⋊#4175C2semidirect
3. C3×#66321C2semidirect
10. C2×C3⋊(C3⋊(C3⋊D3))D3semidirect
16. C3×#1084D3semidirect
20. #66321D3semidirect
21. C3×AΣL(1,𝔽27)D4semidirect
63. #1084C3⋊D3semidirect
64. C34#67semidirect
66. C3×H(3,𝔽3)D12semidirect
68. AΣL(1,𝔽27)D12semidirect
139. C33#626semidirect
144. H(3,𝔽3)C4⋊(C3⋊D3)semidirect
240. C3#10619551semidirect

Maximal subgroups

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

subgroupindex
C2×C3⋊#41832
C2×C3⋊#41752
C3×#663212
#106201473
#106199023
#106195513