Finite Group Databasebeta

← C3×#13091645 #72243626

Subgroups — C3×#13091645 #72243626

Order 4374.

5347 conjugacy classes of subgroups; only the 668 normal subgroups are shown.

normal subgroups only

This group has 5347 conjugacy classes of subgroups — too many to draw. Only its 668 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
1C3×#10624930C211yesmaximal, characteristic, complemented, Sylow
2C3×#92392C311yesmaximal, characteristic, complemented
3C32×D3×H(3,𝔽3)—31nomaximal
4#13091645C3127yesmaximal, direct product factor
5C3×#92281C318yesmaximal, complemented
6C32×#4174C314yesmaximal, complemented
7C3×3−1+4—21no—
8C3×H(5,𝔽3)C2×C311yescharacteristic, complemented
9C33×H(3,𝔽3)D311yescharacteristic, complemented
10#10624930—227no—
11#10624930C2×C3127yescomplemented
12C3×#6909—28no—
13C3×#6909C2×C318yescomplemented
14C32×AΣL(1,𝔽27)—24no—
15C32×AΣL(1,𝔽27)C2×C314yescomplemented
16C34×D3—34no—
17C2×C32×H(3,𝔽3)—91no—
18#92392C3219yescomplemented
19C32×#272C3214yescomplemented
20C3×D3×H(3,𝔽3)—31no—
21C3×D3×H(3,𝔽3)—38no—
22C3×D3×H(3,𝔽3)—327no—
23C3×D3×H(3,𝔽3)—91no—
24#92281C32172yescomplemented
25C3×#4174C3211yescharacteristic, complemented
26C3×#4174C3218yescomplemented
27C3×#4174C32136yescomplemented
28C35C3×D314yescomplemented
293−1+4—227no—
303−1+4—618no—
31H(5,𝔽3)—29no—
32H(5,𝔽3)—69no—
33H(5,𝔽3)C2×C3219yescomplemented
34C3×#737—68no—
35C3×#737—61no—
36C32×3−1+2—28no—
37C32×3−1+2—24no—
38C32×H(3,𝔽3)—24no—
39C32×H(3,𝔽3)—31no—
40C32×H(3,𝔽3)—31no—
41C32×H(3,𝔽3)—69no—
42C32×H(3,𝔽3)—64no—
43C32×H(3,𝔽3)—64no—
44C32×H(3,𝔽3)C3×D311yescharacteristic
45C32×H(3,𝔽3)C3×D3127yescomplemented
46C32×H(3,𝔽3)C3×D318yescomplemented
47C32×H(3,𝔽3)C2×C3214yescomplemented
48#6909—2216no—
49#6909—272no—
50#6909C2×C32172yescomplemented
51C3×AΣL(1,𝔽27)—24no—
52C3×AΣL(1,𝔽27)—224no—
53C3×AΣL(1,𝔽27)—28no—
54C3×AΣL(1,𝔽27)—2108no—
55C3×AΣL(1,𝔽27)—236no—
56C3×AΣL(1,𝔽27)C2×C3211yescharacteristic
57C3×AΣL(1,𝔽27)C2×C32136yescomplemented
58C3×AΣL(1,𝔽27)C2×C3218yescomplemented
59C2×C34—94no—
60C33×D3—31no—
61C33×D3—38no—
62C33×D3—34no—
63C33×D3—336no—
64C33×D3—936no—
65C33×D3—94no—
66C2×C3×H(3,𝔽3)—98no—
67C2×C3×H(3,𝔽3)—927no—
68C2×C3×H(3,𝔽3)—91no—
69C3×#272C3311yescharacteristic
70C3×#272C33112yescomplemented
71D3×H(3,𝔽3)—39no—
72D3×H(3,𝔽3)—372no—
73D3×H(3,𝔽3)—99no—
74#4174C3313yescomplemented
75#4174C33124yescomplemented
76C34—34no—
77C34—34no—
78C34—64no—
79C34—612no—
80C34—64no—
81C34—936no—
82C34C32×D314yes—
83C34C32×D311yescharacteristic
84C34C32×D318yes—
85C34C32×D3136yescomplemented
86#737—6216no—
87#737—627no—
88C3×3−1+2—21no—
89C3×3−1+2—28no—
90C3×3−1+2—272no—
91C3×3−1+2—236no—
92C3×3−1+2—68no—
93C3×3−1+2—68no—
94C3×3−1+2—648no—
95C3×3−1+2—624no—
96C3×3−1+2—68no—
97C3×H(3,𝔽3)—24no—
98C3×H(3,𝔽3)—29no—
99C3×H(3,𝔽3)—24no—
100C3×H(3,𝔽3)—236no—
101C3×H(3,𝔽3)—212no—
102C3×H(3,𝔽3)—38no—
103C3×H(3,𝔽3)—327no—
104C3×H(3,𝔽3)—39no—
105C3×H(3,𝔽3)—6108no—
106C3×H(3,𝔽3)—672no—
107C3×H(3,𝔽3)—636no—
108C3×H(3,𝔽3)—624no—
109C3×H(3,𝔽3)—68no—
110C3×H(3,𝔽3)—64no—
111C3×H(3,𝔽3)—612no—
112C3×H(3,𝔽3)—64no—
113C3×H(3,𝔽3)—624no—
114C3×H(3,𝔽3)—64no—
115C3×H(3,𝔽3)—69no—
116C3×H(3,𝔽3)(C3⋊D3)⋊C311yescharacteristic
117C3×H(3,𝔽3)C32×D319yes—
118C3×H(3,𝔽3)C32×D3172yescomplemented
119C3×H(3,𝔽3)C2×C3311yescharacteristic
120C3×H(3,𝔽3)C2×C33112yescomplemented
121C32×C9—68no—
122C32×C9—64no—
123AΣL(1,𝔽27)—23no—
124AΣL(1,𝔽27)—236no—
125AΣL(1,𝔽27)—2216no—
126AΣL(1,𝔽27)—224no—
127AΣL(1,𝔽27)—272no—
128AΣL(1,𝔽27)C2×C3313yes—
129AΣL(1,𝔽27)C2×C33124yescomplemented
130C2×C33—91no—
131C2×C33—936no—
132C2×C33—98no—
133C2×C33—94no—
134C2×C33—2736no—
135C32×D3—39no—
136C32×D3—33no—
137C32×D3—31no—
138C32×D3—324no—
139C32×D3—312no—
140C32×D3—912no—
141C32×D3—9108no—
142C32×D3—924no—
143C32×D3—91no—
144C32×D3—912no—
145C32×D3—2712no—
146C2×H(3,𝔽3)—972no—
147C2×H(3,𝔽3)—99no—
148#272C3411yescharacteristic
149C33—24no—
150C33—212no—
151C33—31no—
152C33—39no—
153C33—336no—
154C33—38no—
155C33—31no—
156C33—312no—
157C33—61no—
158C33—68no—
159C33—636no—
160C33—636no—
161C33—64no—
162C33—612no—
163C33—912no—
164C33—936no—
165C33—9108no—
166C33—924no—
167C33—1836no—
168C33—18108no—
169C33—2712no—
170C33—5412no—
171C33C3×(C3⋊D3)⋊C314yes—
172C33C33×D311yescharacteristic
173C33C33×D3112yes—
174C33C33×D313yes—
175C33C33×D3124yes—
1763−1+2—23no—
1773−1+2—224no—
1783−1+2—62no—
1793−1+2—616no—
1803−1+2—672no—
1813−1+2—672no—
1823−1+2—672no—
183H(3,𝔽3)—236no—
184H(3,𝔽3)—21no—
185H(3,𝔽3)—212no—
186H(3,𝔽3)—372no—
187H(3,𝔽3)—672no—
188H(3,𝔽3)—61no—
189H(3,𝔽3)—612no—
190H(3,𝔽3)—636no—
191H(3,𝔽3)—624no—
192H(3,𝔽3)—68no—
193H(3,𝔽3)—636no—
194H(3,𝔽3)C3×(C3⋊D3)⋊C319yes—
195H(3,𝔽3)C2×C3411yescharacteristic
196C3×C9—672no—
197C3×C9—636no—
198C3×C9—68no—
199C3×C9—61no—
200C2×C32—93no—
201C2×C32—99no—
202C2×C32—91no—
203C2×C32—924no—
204C2×C32—912no—
205C2×C32—2712no—
206C2×C32—27108no—
207C2×C32—2724no—
208C3×D3—39no—
209C3×D3—33no—
210C3×D3—31no—
211C3×D3—912no—
212C3×D3—924no—
213C3×D3—91no—
214C3×D3—93no—
215C3×D3—2712no—
216C32—212no—
217C32—21no—
218C32—39no—
219C32—39no—
220C32—312no—
221C32—33no—
222C32—33no—
223C32—31no—
224C32—324no—
225C32—69no—
226C32—612no—
227C32—61no—
228C32—612no—
229C32—912no—
230C32—9108no—
231C32—924no—
232C32—924no—
233C32—93no—
234C32—1812no—
235C32—18108no—
236C32—1824no—
237C32—1812no—
238C32—2712no—
239C32—5412no—
240C32—5436no—
241C32C32×(C3⋊D3)⋊C3112yes—
242C32C32×(C3⋊D3)⋊C311yescharacteristic
243C32C34×D311yescharacteristic
244C9—624no—
245C9—63no—
246C2×C3—99no—
247C2×C3—93no—
248C2×C3—91no—
249C2×C3—2712no—
250C2×C3—2724no—
251D3—31no—
252D3—91no—
253C3—31no—
254C3—39no—
255C3—312no—
256C3—61no—
257C3—612no—
258C3—91no—
259C3—924no—
260C3—181no—
261C3—1812no—
262C3#1309164513yesdirect product factor
263C3C33×(C3⋊D3)⋊C311yescharacteristic
264C2—91noSylow
subgroupG/H
center, socleC32C32×(C3⋊D3)⋊C3
commutator, cosocle, hypocenterH(3,𝔽3)C2×C34
FrattiniC32C34×D3
FittingC3×#10624930C2
hypercenterC3×H(3,𝔽3)(C3⋊D3)⋊C3
LCSG ▷ H(3,𝔽3)
UCSC1 ◁ C32 ◁ C3×H(3,𝔽3)

Complements

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

NH ≅ G/Ntype
1. C3×#10624930C2semidirect
2. C3×#92392C3semidirect
4. #13091645C3direct (N × H)
5. C3×#92281C3semidirect
6. C32×#4174C3semidirect
8. C3×H(5,𝔽3)C2×C3semidirect
9. C33×H(3,𝔽3)D3semidirect
11. #10624930C2×C3semidirect
13. C3×#6909C2×C3semidirect
15. C32×AΣL(1,𝔽27)C2×C3semidirect
18. #92392C32semidirect
19. C32×#272C32semidirect
24. #92281C32semidirect
25. C3×#4174C32semidirect
26. C3×#4174C32semidirect
27. C3×#4174C32semidirect
28. C35C3×D3semidirect
33. H(5,𝔽3)C2×C32semidirect
45. C32×H(3,𝔽3)C3×D3semidirect
46. C32×H(3,𝔽3)C3×D3semidirect
47. C32×H(3,𝔽3)C2×C32semidirect
50. #6909C2×C32semidirect
57. C3×AΣL(1,𝔽27)C2×C32semidirect
58. C3×AΣL(1,𝔽27)C2×C32semidirect
70. C3×#272C33semidirect
74. #4174C33semidirect
75. #4174C33semidirect
85. C34C32×D3semidirect
118. C3×H(3,𝔽3)C32×D3semidirect
120. C3×H(3,𝔽3)C2×C33semidirect
129. AΣL(1,𝔽27)C2×C33semidirect
262. C3#13091645direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#106249302
C3×#923923
C32×D3×H(3,𝔽3)3
#130916453
C3×#922813
C32×#41743