Finite Group Databasebeta

← C3×#10619642 #14517452

Subgroups — C3×#10619642 #14517452

Order 1944.

535 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 535 conjugacy classes of subgroups — too many to draw. Only its 66 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
1C22×C3×AΣL(1,𝔽27)C211yesmaximal, characteristic, complemented
2C2×C3×#4175C211yesmaximal, characteristic, complemented
3C3×#66322C211yesmaximal, characteristic, complemented
4C3×#6312C311yesmaximal, characteristic, complemented
5C3×#638⋊C3—31nomaximal
6#10619642C313yesmaximal, direct product factor
7C2×C3×AΣL(1,𝔽27)—21no—
8C2×C3×AΣL(1,𝔽27)C2211yescharacteristic
9C3×#4175—21no—
10C22×C34C2×C311yescharacteristic, complemented
11C2×C3×C3⋊(C3⋊D3)C2×C311yescharacteristic, complemented
12C3×C3⋊(C3⋊Dic3)C2×C311yescharacteristic, complemented
13C22×C3×3−1+2—21no—
14C22×C3×H(3,𝔽3)D311yescharacteristic, complemented
15C2×C3×(C3⋊D3)⋊C3—31no—
16C3×(C3⋊Dic3)⋊C3—31no—
17C22×AΣL(1,𝔽27)—23no—
18C22×AΣL(1,𝔽27)C2×C313yescomplemented
19C2×#4175C2×C313yescomplemented
20#66322C2×C313yescomplemented
21C3×AΣL(1,𝔽27)D411yescharacteristic, complemented, Sylow
22#6312C3211yescharacteristic, complemented
23C3×#638—31no—
24C3×#638—91no—
25C3×#638—93no—
26C32×#67—91no—
27#638⋊C3—33no—
28C2×C34—21no—
29C2×C34C22×C311yescharacteristic
30C3×C3⋊(C3⋊D3)—21no—
31C2×C3×3−1+2—22no—
32C2×C3×3−1+2—21no—
33C2×C3×H(3,𝔽3)—21no—
34C2×C3×H(3,𝔽3)C2×D311yescharacteristic
35C3×(C3⋊D3)⋊C3—61no—
36C2×AΣL(1,𝔽27)—26no—
37C2×AΣL(1,𝔽27)—23no—
38C2×AΣL(1,𝔽27)—23no—
39C2×AΣL(1,𝔽27)C22×C313yes—
40#4175—23no—
41C22×C33—21no—
42C22×C33—33no—
43C22×C33—31no—
44C22×C33—31no—
45C22×C33—61no—
46C22×C33—63no—
47C22×C33C3×D311yescharacteristic
48C22×C33C2×C3211yescharacteristic, complemented
49C2×C3⋊(C3⋊D3)C2×C3211yescharacteristic, complemented
50C2×C3×C3⋊D3—31no—
51C2×C3×C3⋊D3—91no—
52C2×C3×C3⋊D3—93no—
53C2×C32×D3—91no—
54C3⋊(C3⋊Dic3)C2×C3211yescharacteristic, complemented
55C3×C3⋊Dic3—31no—
56C3×C3⋊Dic3—91no—
57C3×C3⋊Dic3—93no—
58C32×Dic3—91no—
59C22×3−1+2—23no—
60C22×3−1+2—62no—
61C22×H(3,𝔽3)—61no—
62C22×H(3,𝔽3)C3×D313yescomplemented
63C22×C3×C9—61no—
64C2×(C3⋊D3)⋊C3—33no—
65(C3⋊Dic3)⋊C3—33no—
66C34C3×D411yescharacteristic, complemented
67C3×3−1+2—21no—
68C3×H(3,𝔽3)#6711yescharacteristic, complemented
69AΣL(1,𝔽27)—23no—
70AΣL(1,𝔽27)C3×D413yescomplemented
71C32×D4—271no—
72#638—31no—
73#638—91no—
74#638—93no—
75C3×#67—93no—
76C3×#67—91no—
77C3×#67—271no—
78C3×#67—273no—
79C2×C33—21no—
80C2×C33—22no—
81C2×C33—21no—
82C2×C33—21no—
83C2×C33—31no—
84C2×C33—33no—
85C2×C33—31no—
86C2×C33—61no—
87C2×C33—61no—
88C2×C33—62no—
89C2×C33—61no—
90C2×C33—63no—
91C2×C33—63no—
92C2×C33—66no—
93C2×C33C2×C3×D311yescharacteristic
94C2×C33C22×C3211yescharacteristic
95C3⋊(C3⋊D3)—21no—
96C3×C3⋊D3—61no—
97C3×C3⋊D3—181no—
98C3×C3⋊D3—183no—
99C32×D3—181no—
100C2×3−1+2—26no—
101C2×3−1+2—23no—
102C2×3−1+2—64no—
103C2×3−1+2—62no—
104C2×H(3,𝔽3)—23no—
105C2×H(3,𝔽3)—61no—
106C2×H(3,𝔽3)—62no—
107C2×H(3,𝔽3)C2×C3×D313yes—
108C2×C3×C9—62no—
109C2×C3×C9—61no—
110(C3⋊D3)⋊C3—63no—
111C22×C32—21no—
112C22×C32—31no—
113C22×C32—33no—
114C22×C32—31no—
115C22×C32—33no—
116C22×C32—33no—
117C22×C32—63no—
118C22×C32—61no—
119C22×C32—66no—
120C22×C32—63no—
121C22×C32—63no—
122C22×C32—61no—
123C22×C32—91no—
124C22×C32—181no—
125C22×C32—271no—
126C22×C32(C3⋊D3)⋊C311yescharacteristic
127C22×C32C32×D311yescharacteristic
128C2×C3⋊D3—31no—
129C2×C3⋊D3—91no—
130C2×C3⋊D3—93no—
131C2×C3×D3—93no—
132C2×C3×D3—91no—
133C2×C3×D3—271no—
134C2×C3×D3—273no—
135C32×C4—271no—
136C3⋊Dic3—31no—
137C3⋊Dic3—91no—
138C3⋊Dic3—93no—
139C3×Dic3—93no—
140C3×Dic3—91no—
141C3×Dic3—271no—
142C3×Dic3—273no—
143C22×C9—63no—
144C33—21no—
145C33—33no—
146C33—31no—
147C33—31no—
148C33—61no—
149C33—63no—
150C33C3×#6711yescharacteristic
151C33C32×D411yescharacteristic, complemented
1523−1+2—23no—
1533−1+2—62no—
154H(3,𝔽3)—61no—
155H(3,𝔽3)C3×#6713yescomplemented
156C3×C9—61no—
157C3×D4—273no—
158C3×D4—271no—
159#67—91no—
160#67—271no—
161#67—273no—
162C2×C32—21no—
163C2×C32—22no—
164C2×C32—21no—
165C2×C32—21no—
166C2×C32—31no—
167C2×C32—33no—
168C2×C32—31no—
169C2×C32—33no—
170C2×C32—33no—
171C2×C32—63no—
172C2×C32—61no—
173C2×C32—61no—
174C2×C32—61no—
175C2×C32—63no—
176C2×C32—62no—
177C2×C32—62no—
178C2×C32—66no—
179C2×C32—63no—
180C2×C32—66no—
181C2×C32—63no—
182C2×C32—63no—
183C2×C32—66no—
184C2×C32—612no—
185C2×C32—61no—
186C2×C32—63no—
187C2×C32—66no—
188C2×C32—91no—
189C2×C32—181no—
190C2×C32—181no—
191C2×C32—182no—
192C2×C32—541no—
193C2×C32C2×(C3⋊D3)⋊C311yescharacteristic
194C2×C32C2×C32×D311yescharacteristic
195C3⋊D3—61no—
196C3⋊D3—181no—
197C3⋊D3—183no—
198C3×D3—183no—
199C3×D3—181no—
200C3×D3—541no—
201C3×D3—543no—
202C2×C9—66no—
203C2×C9—63no—
204C22×C3—21no—
205C22×C3—33no—
206C22×C3—31no—
207C22×C3—61no—
208C22×C3—63no—
209C22×C3—93no—
210C22×C3—273no—
211C22×C3—271no—
212C22×C3#417511yescharacteristic, complemented
213C22×C3C3×(C3⋊D3)⋊C311yescharacteristic
214C2×D3—91no—
215C2×D3—271no—
216C2×D3—273no—
217C3×C4—273no—
218C3×C4—271no—
219Dic3—91no—
220Dic3—271no—
221Dic3—273no—
222C32—21no—
223C32—33no—
224C32—31no—
225C32—33no—
226C32—31no—
227C32—33no—
228C32—61no—
229C32—63no—
230C32—63no—
231C32—63no—
232C32—66no—
233C32—61no—
234C32—91no—
235C32—181no—
236C32#638⋊C311yescharacteristic
237C32C32×#6711yescharacteristic
238C9—63no—
239D4—271noSylow
240C2×C3—22no—
241C2×C3—21no—
242C2×C3—21no—
243C2×C3—21no—
244C2×C3—33no—
245C2×C3—31no—
246C2×C3—61no—
247C2×C3—63no—
248C2×C3—62no—
249C2×C3—66no—
250C2×C3—61no—
251C2×C3—63no—
252C2×C3—93no—
253C2×C3—183no—
254C2×C3—543no—
255C2×C3—541no—
256C2×C3C2×#417511yescharacteristic
257C2×C3C2×C3×(C3⋊D3)⋊C311yescharacteristic
258D3—181no—
259D3—541no—
260D3—543no—
261C22—271no—
262C22C3×#417511yescharacteristic, complemented
263C4—271no—
264C3—21no—
265C3—33no—
266C3—31no—
267C3—61no—
268C3—63no—
269C3—93no—
270C3#1061964211yescharacteristic, direct product factor
271C3C3×#638⋊C311yescharacteristic
272C2—21no—
273C2—541no—
274C2C2×C3×#417511yescharacteristic
subgroupG/H
centerC2×C3C2×#4175
commutator, cosocleC2×C33C22×C32
FrattiniC2×C32C2×C32×D3
FittingC22×C3×AΣL(1,𝔽27)C2
socleC2×C32C2×(C3⋊D3)⋊C3
hypercenterC22×C3#4175
hypocenterC33C32×D4
LCSG ▷ C2×C33 ▷ C33
UCSC1 ◁ C2×C3 ◁ C22×C3

Complements

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

NH ≅ G/Ntype
1. C22×C3×AΣL(1,𝔽27)C2semidirect
2. C2×C3×#4175C2semidirect
3. C3×#66322C2semidirect
4. C3×#6312C3semidirect
6. #10619642C3direct (N × H)
10. C22×C34C2×C3semidirect
11. C2×C3×C3⋊(C3⋊D3)C2×C3semidirect
12. C3×C3⋊(C3⋊Dic3)C2×C3semidirect
14. C22×C3×H(3,𝔽3)D3semidirect
18. C22×AΣL(1,𝔽27)C2×C3semidirect
19. C2×#4175C2×C3semidirect
20. #66322C2×C3semidirect
21. C3×AΣL(1,𝔽27)D4semidirect
22. #6312C32semidirect
48. C22×C33C2×C32semidirect
49. C2×C3⋊(C3⋊D3)C2×C32semidirect
54. C3⋊(C3⋊Dic3)C2×C32semidirect
62. C22×H(3,𝔽3)C3×D3semidirect
66. C34C3×D4semidirect
68. C3×H(3,𝔽3)#67semidirect
70. AΣL(1,𝔽27)C3×D4semidirect
151. C33C32×D4semidirect
155. H(3,𝔽3)C3×#67semidirect
212. C22×C3#4175semidirect
262. C22C3×#4175semidirect
270. C3#10619642direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×AΣL(1,𝔽27)2
C2×C3×#41752
C3×#663222
C3×#63123
C3×#638⋊C33
#106196423