Finite Group Databasebeta

← #14517022

Subgroups — #14517022

Order 1944.

489 conjugacy classes of subgroups; only the 42 normal subgroups are shown.

normal subgroups only

This group has 489 conjugacy classes of subgroups — too many to draw. Only its 42 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#10620156—31nomaximal
5#10619884—31nomaximal
6#10619551—33nomaximal
7C2×C3×AΣL(1,𝔽27)C2211yescharacteristic
8C3⋊#4183—21no—
9C3×#4175—21no—
10C2×C3×C3⋊(C3⋊D3)—31no—
11C2×C3×C3⋊(C3⋊D3)D311yescharacteristic, complemented
12C32×C3⋊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×#4175D313yescomplemented
20#66321—33no—
21C3×AΣL(1,𝔽27)D411yescharacteristic, complemented, Sylow
22#6295—91no—
23#6295—93no—
24#6292—91no—
25#6292—91no—
26#6291—91no—
27#6198—93no—
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—23no—
41C2×C3⋊(C3⋊D3)—31no—
42C2×C3⋊(C3⋊D3)—31no—
43C2×C3⋊(C3⋊D3)C3⋊D311yescharacteristic, complemented
44C2×C3×C3⋊D3—31no—
45C2×C3×C3⋊D3—91no—
46C2×C3×C3⋊D3—93no—
47C2×C3×C3⋊D3—93no—
48C2×C3×C3⋊D3—91no—
49C2×C3×C3⋊D3—91no—
50C2×C3×C3⋊D3—181no—
51C2×C3×C3⋊D3—183no—
52C2×C32×D3—91no—
53C3×C3⋊Dic3—33no—
54C3×C3⋊Dic3—31no—
55C3×C3⋊Dic3—91no—
56C32×Dic3—91no—
57C32×Dic3—91no—
58C32×Dic3—181no—
59C2×C3⋊D9—61no—
60C2×AGL(1,ℤ/9)—183no—
61C2×(C3⋊D3)⋊C3—33no—
62C2×(C3⋊D3)⋊C3—93no—
63#1084—33no—
64#1084—181no—
65C34#6711yescharacteristic, complemented
66C3×3−1+2—21no—
67C3×H(3,𝔽3)D1211yescharacteristic, complemented
68AΣL(1,𝔽27)—23no—
69AΣL(1,𝔽27)#6713yescomplemented
70#638—271no—
71C4⋊(C3⋊D3)—271no—
72#626—271no—
73#626—271no—
74#626—273no—
75#626—273no—
76#626—273no—
77#625—271no—
78C2×C33—21no—
79C2×C33—31no—
80C2×C33—33no—
81C2×C33—31no—
82C2×C33—61no—
83C2×C33—63no—
84C2×C33D3211yescharacteristic
85C2×C33C2×C3⋊D311yescharacteristic
86C3⋊(C3⋊D3)—21no—
87C3⋊(C3⋊D3)—61no—
88C3⋊(C3⋊D3)—61no—
89C3×C3⋊D3—61no—
90C3×C3⋊D3—181no—
91C3×C3⋊D3—182no—
92C3×C3⋊D3—183no—
93C3×C3⋊D3—186no—
94C3×C3⋊D3—181no—
95C3×C3⋊D3—181no—
96C3×C3⋊D3—183no—
97C32×D3—181no—
98C2×3−1+2—23no—
99C2×3−1+2—121no—
100C2×H(3,𝔽3)—61no—
101C2×H(3,𝔽3)D3213yes—
102C2×C3×C9—61no—
103C3⋊D9—62no—
104AGL(1,ℤ/9)—186no—
105(C3⋊D3)⋊C3—63no—
106(C3⋊D3)⋊C3—183no—
107C22×C32—271no—
108C2×C3⋊D3—31no—
109C2×C3⋊D3—91no—
110C2×C3⋊D3—91no—
111C2×C3⋊D3—93no—
112C2×C3⋊D3—93no—
113C2×C3⋊D3—91no—
114C2×C3⋊D3—93no—
115C2×C3⋊D3—183no—
116C2×C3⋊D3—181no—
117C2×C3⋊D3—271no—
118C2×C3⋊D3—541no—
119C2×C3×D3—93no—
120C2×C3×D3—91no—
121C2×C3×D3—271no—
122C2×C3×D3—273no—
123C2×C3×D3—271no—
124C2×C3×D3—273no—
125C2×C3×D3—271no—
126C2×C3×D3—541no—
127C2×C3×D3—543no—
128C32×C4—271no—
129C3⋊Dic3—31no—
130C3⋊Dic3—91no—
131C3×Dic3—93no—
132C3×Dic3—93no—
133C3×Dic3—91no—
134C3×Dic3—91no—
135C3×Dic3—181no—
136C3×Dic3—183no—
137C3×Dic3—273no—
138C2×D9—183no—
139C33—21no—
140C33—31no—
141C33—33no—
142C33—31no—
143C33—61no—
144C33—63no—
145C33#62611yescharacteristic
146C33#63811yescharacteristic, complemented
1473−1+2—23no—
1483−1+2—121no—
149H(3,𝔽3)—61no—
150H(3,𝔽3)#62613yescomplemented
151C3×C9—61no—
152#67—811no—
153#67—811no—
154#67—813no—
155D12—811no—
156D12—813no—
157C2×C32—21no—
158C2×C32—31no—
159C2×C32—33no—
160C2×C32—31no—
161C2×C32—33no—
162C2×C32—33no—
163C2×C32—63no—
164C2×C32—61no—
165C2×C32—63no—
166C2×C32—63no—
167C2×C32—61no—
168C2×C32—91no—
169C2×C32—123no—
170C2×C32—181no—
171C2×C32—541no—
172C2×C32((C3⋊D3)⋊C3)⋊C211yescharacteristic
173C2×C32D3×C3⋊D311yescharacteristic
174C3⋊D3—61no—
175C3⋊D3—181no—
176C3⋊D3—181no—
177C3⋊D3—183no—
178C3⋊D3—186no—
179C3⋊D3—182no—
180C3⋊D3—181no—
181C3⋊D3—183no—
182C3⋊D3—183no—
183C3⋊D3—541no—
184C3⋊D3—542no—
185C3×D3—183no—
186C3×D3—181no—
187C3×D3—541no—
188C3×D3—543no—
189C3×D3—543no—
190C3×D3—541no—
191C3×D3—542no—
192C3×D3—546no—
193C3×D3—541no—
194C2×C9—63no—
195D9—186no—
196C22×C3—273no—
197C22×C3—271no—
198C22×C3—811no—
199C2×D3—91no—
200C2×D3—273no—
201C2×D3—271no—
202C2×D3—273no—
203C2×D3—271no—
204C2×D3—271no—
205C2×D3—541no—
206C2×D3—543no—
207C2×D3—813no—
208C3×C4—273no—
209C3×C4—271no—
210Dic3—91no—
211Dic3—91no—
212Dic3—181no—
213Dic3—273no—
214C32—21no—
215C32—33no—
216C32—31no—
217C32—31no—
218C32—33no—
219C32—33no—
220C32—61no—
221C32—63no—
222C32—63no—
223C32—63no—
224C32—61no—
225C32—91no—
226C32—123no—
227C32—181no—
228C32#620011yescharacteristic
229C32#629111yescharacteristic
230C9—63no—
231D4—2431noSylow
232C2×C3—21no—
233C2×C3—31no—
234C2×C3—33no—
235C2×C3—61no—
236C2×C3—63no—
237C2×C3—93no—
238C2×C3—543no—
239C2×C3—541no—
240C2×C3—1621no—
241C2×C3#4174⋊C211yescharacteristic
242C2×C3((C3⋊D3)⋊C3)⋊D311yescharacteristic
243D3—181no—
244D3—541no—
245D3—543no—
246D3—542no—
247D3—543no—
248D3—546no—
249D3—541no—
250D3—541no—
251D3—1623no—
252C22—271no—
253C22—811no—
254C4—271no—
255C3—21no—
256C3—33no—
257C3—31no—
258C3—63no—
259C3—61no—
260C3—93no—
261C3#1061955111yescharacteristic, complemented
262C3#1061988611yescharacteristic
263C2—541no—
264C2—1621no—
265C2#4175⋊D311yescharacteristic
subgroupG/H
center, hypercenterC2#4175⋊D3
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
11. C2×C3×C3⋊(C3⋊D3)D3semidirect
16. C3⋊#1084D3semidirect
19. C2×#4175D3semidirect
21. C3×AΣL(1,𝔽27)D4semidirect
43. C2×C3⋊(C3⋊D3)C3⋊D3semidirect
65. C34#67semidirect
67. C3×H(3,𝔽3)D12semidirect
69. AΣL(1,𝔽27)#67semidirect
146. C33#638semidirect
150. H(3,𝔽3)#626semidirect
261. 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
#106201563
#106198843
#106195513