Finite Group Databasebeta

← C3×#10619681 #14517698

Subgroups — C3×#10619681 #14517698

Order 1944.

400 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 60 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×#731C211yesmaximal, characteristic, complemented
2C2×C3×#4184C211yesmaximal, characteristic, complemented
3C3×#66331C211yesmaximal, characteristic, complemented
4C3×#611⋊C3—32nomaximal
5C3×#638⋊C3—31nomaximal
6C32×#611—31nomaximal
7#10619681C311yesmaximal, characteristic, direct product factor
8C2×C3×#731—21no—
9C2×C3×#731C2211yescharacteristic
10C3×#4184—21no—
11C22×C3×3−1+2D312yescomplemented
12C22×C3×H(3,𝔽3)D311yescharacteristic
13C22×C32×C9D311yescharacteristic, complemented
14C2×C3×AGL(1,ℤ/9)—32no—
15C2×C3×(C3⋊D3)⋊C3—31no—
16C2×C32×D9—31no—
17C3×3−1+2⋊C4—32no—
18C3×(C3⋊Dic3)⋊C3—31no—
19C32×Dic9—31no—
20C22×#731—22no—
21C22×#731—21no—
22C22×#731—21no—
23C22×#731C2×C311yescharacteristic, complemented
24C2×#4184C2×C311yescharacteristic, complemented
25#66331C2×C311yescharacteristic, complemented
26C3×#731D411yescharacteristic, complemented, Sylow
27C3×#638—31no—
28C32×#67—91no—
29#611⋊C3—34no—
30#611⋊C3—32no—
31#638⋊C3—32no—
32#638⋊C3—31no—
33C3×#611—31no—
34C3×#611—32no—
35C3×#611—32no—
36C3×#611—31no—
37C2×C3×3−1+2—22no—
38C2×C3×3−1+2C2×D312yes—
39C2×C3×H(3,𝔽3)—21no—
40C2×C3×H(3,𝔽3)C2×D311yescharacteristic
41C2×C32×C9—21no—
42C2×C32×C9C2×D311yescharacteristic
43C3×AGL(1,ℤ/9)—62no—
44C3×(C3⋊D3)⋊C3—61no—
45C32×D9—61no—
46C2×#731—24no—
47C2×#731—22no—
48C2×#731—22no—
49C2×#731—21no—
50C2×#731—22no—
51C2×#731—21no—
52C2×#731—21no—
53C2×#731C22×C311yescharacteristic
54#4184—21no—
55C22×C33—31no—
56C22×C33C3⋊D311yescharacteristic
57C2×C3×C3⋊D3—31no—
58C2×C32×D3—91no—
59C3×C3⋊Dic3—31no—
60C32×Dic3—91no—
61C22×3−1+2—22no—
62C22×3−1+2—34no—
63C22×3−1+2C3×D312yescomplemented
64C22×H(3,𝔽3)—21no—
65C22×H(3,𝔽3)—32no—
66C22×H(3,𝔽3)C3×D311yescharacteristic
67C22×C3×C9—21no—
68C22×C3×C9—31no—
69C22×C3×C9—32no—
70C22×C3×C9—32no—
71C22×C3×C9C3×D311yescharacteristic, complemented
72C2×AGL(1,ℤ/9)—34no—
73C2×AGL(1,ℤ/9)—32no—
74C2×(C3⋊D3)⋊C3—32no—
75C2×(C3⋊D3)⋊C3—31no—
76C2×C3×D9—31no—
77C2×C3×D9—32no—
78C2×C3×D9—32no—
79C2×C3×D9—31no—
803−1+2⋊C4—34no—
813−1+2⋊C4—32no—
82(C3⋊Dic3)⋊C3—32no—
83(C3⋊Dic3)⋊C3—31no—
84C3×Dic9—31no—
85C3×Dic9—32no—
86C3×Dic9—32no—
87C3×Dic9—31no—
88C3×3−1+2#6712yescomplemented
89C3×H(3,𝔽3)#6711yescharacteristic
90C32×C9#6711yescharacteristic, complemented
91#731—22no—
92#731—21no—
93#731—21no—
94#731C3×D411yescharacteristic, complemented
95C32×D4—271no—
96#638—31no—
97C3×#67—91no—
98C3×#67—92no—
99C3×#67—91no—
100C3×#67—271no—
101#611—31no—
102#611—32no—
103C2×C33—21no—
104C2×C33—31no—
105C2×C33—61no—
106C2×C33C2×C3⋊D311yescharacteristic
107C3×C3⋊D3—61no—
108C32×D3—181no—
109C2×3−1+2—24no—
110C2×3−1+2—22no—
111C2×3−1+2—22no—
112C2×3−1+2—34no—
113C2×3−1+2—64no—
114C2×3−1+2C2×C3×D312yes—
115C2×H(3,𝔽3)—22no—
116C2×H(3,𝔽3)—21no—
117C2×H(3,𝔽3)—21no—
118C2×H(3,𝔽3)—32no—
119C2×H(3,𝔽3)—62no—
120C2×H(3,𝔽3)C2×C3×D311yescharacteristic
121C2×C3×C9—22no—
122C2×C3×C9—21no—
123C2×C3×C9—21no—
124C2×C3×C9—31no—
125C2×C3×C9—32no—
126C2×C3×C9—32no—
127C2×C3×C9—61no—
128C2×C3×C9—62no—
129C2×C3×C9—62no—
130C2×C3×C9C2×C3×D311yescharacteristic
131AGL(1,ℤ/9)—64no—
132AGL(1,ℤ/9)—62no—
133(C3⋊D3)⋊C3—62no—
134(C3⋊D3)⋊C3—61no—
135C3×D9—61no—
136C3×D9—62no—
137C3×D9—62no—
138C3×D9—61no—
139C22×C32—31no—
140C22×C32—31no—
141C22×C32—61no—
142C22×C32—61no—
143C22×C32—91no—
144C22×C32—181no—
145C22×C32—271no—
146C22×C32#27211yescharacteristic
147C22×C32#27212yes—
148C22×C32C3×C3⋊D311yescharacteristic
149C2×C3⋊D3—31no—
150C2×C3×D3—91no—
151C2×C3×D3—92no—
152C2×C3×D3—91no—
153C2×C3×D3—271no—
154C32×C4—271no—
155C3⋊Dic3—31no—
156C3×Dic3—91no—
157C3×Dic3—92no—
158C3×Dic3—91no—
159C3×Dic3—271no—
160C22×C9—31no—
161C22×C9—32no—
162C22×C9—61no—
163C22×C9—62no—
164C2×D9—31no—
165C2×D9—32no—
166Dic9—31no—
167Dic9—32no—
168C33—31no—
169C33#63811yescharacteristic
1703−1+2—22no—
1713−1+2—34no—
1723−1+2C3×#6712yescomplemented
173H(3,𝔽3)—21no—
174H(3,𝔽3)—32no—
175H(3,𝔽3)C3×#6711yescharacteristic
176C3×C9—21no—
177C3×C9—31no—
178C3×C9—32no—
179C3×C9—32no—
180C3×C9C3×#6711yescharacteristic, complemented
181C3×D4—272no—
182C3×D4—271no—
183C3×D4—271no—
184#67—91no—
185#67—271no—
186C2×C32—21no—
187C2×C32—22no—
188C2×C32—21no—
189C2×C32—31no—
190C2×C32—31no—
191C2×C32—61no—
192C2×C32—61no—
193C2×C32—62no—
194C2×C32—61no—
195C2×C32—62no—
196C2×C32—61no—
197C2×C32—91no—
198C2×C32—181no—
199C2×C32—181no—
200C2×C32—182no—
201C2×C32—541no—
202C2×C32C2×#27211yescharacteristic
203C2×C32C2×#27212yes—
204C2×C32C2×C3×C3⋊D311yescharacteristic
205C3⋊D3—61no—
206C3×D3—181no—
207C3×D3—182no—
208C3×D3—181no—
209C3×D3—541no—
210C2×C9—31no—
211C2×C9—32no—
212C2×C9—61no—
213C2×C9—62no—
214C2×C9—62no—
215C2×C9—64no—
216C2×C9—61no—
217C2×C9—62no—
218D9—61no—
219D9—62no—
220C22×C3—21no—
221C22×C3—32no—
222C22×C3—31no—
223C22×C3—91no—
224C22×C3—181no—
225C22×C3—272no—
226C22×C3—271no—
227C22×C3—271no—
228C22×C3#418411yescharacteristic, complemented
229C22×C3C3×#27211yescharacteristic
230C2×D3—91no—
231C2×D3—271no—
232C3×C4—272no—
233C3×C4—271no—
234C3×C4—271no—
235Dic3—91no—
236Dic3—271no—
237C32—31no—
238C32—31no—
239C32—61no—
240C32—61no—
241C32—91no—
242C32—181no—
243C32#623511yescharacteristic
244C32#623512yes—
245C32C3×#63811yescharacteristic
246C9—31no—
247C9—32no—
248C9—61no—
249C9—62no—
250D4—271noSylow
251C2×C3—22no—
252C2×C3—21no—
253C2×C3—21no—
254C2×C3—21no—
255C2×C3—32no—
256C2×C3—31no—
257C2×C3—62no—
258C2×C3—61no—
259C2×C3—91no—
260C2×C3—181no—
261C2×C3—182no—
262C2×C3—181no—
263C2×C3—542no—
264C2×C3—541no—
265C2×C3—541no—
266C2×C3C2×#418411yescharacteristic
267C2×C3C2×C3×#27211yescharacteristic
268D3—181no—
269D3—541no—
270C22—271no—
271C22C3×#418411yescharacteristic, complemented
272C4—271no—
273C3—21no—
274C3—32no—
275C3—31no—
276C3—91no—
277C3—181no—
278C3#1061968111yescharacteristic, direct product factor
279C3C3×#623511yescharacteristic
280C2—21no—
281C2—541no—
282C2C2×C3×#418411yescharacteristic
subgroupG/H
centerC2×C3C2×#4184
commutator, cosocleC2×#731C22×C3
FrattiniC2×C32C2×C3×C3⋊D3
FittingC22×C3×#731C2
socleC2×C32C2×#272
hypercenterC22×C3#4184
hypocenter#731C3×D4
LCSG ▷ C2×#731 ▷ #731
UCSC1 ◁ C2×C3 ◁ C22×C3

Complements

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

NH ≅ G/Ntype
1. C22×C3×#731C2semidirect
2. C2×C3×#4184C2semidirect
3. C3×#66331C2semidirect
7. #10619681C3direct (N × H)
11. C22×C3×3−1+2D3semidirect
13. C22×C32×C9D3semidirect
23. C22×#731C2×C3semidirect
24. C2×#4184C2×C3semidirect
25. #66331C2×C3semidirect
26. C3×#731D4semidirect
63. C22×3−1+2C3×D3semidirect
71. C22×C3×C9C3×D3semidirect
88. C3×3−1+2#67semidirect
90. C32×C9#67semidirect
94. #731C3×D4semidirect
172. 3−1+2C3×#67semidirect
180. C3×C9C3×#67semidirect
228. C22×C3#4184semidirect
271. C22C3×#4184semidirect
278. C3#10619681direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×#7312
C2×C3×#41842
C3×#663312
C3×#611⋊C33
C3×#638⋊C33
C32×#6113
#106196813