Finite Group Databasebeta

← C3×#6189⋊C3 #14518632

Subgroups — C3×#6189⋊C3 #14518632

Order 1944.

454 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 454 conjugacy classes of subgroups — too many to draw. Only its 94 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×C3⋊(3−1+2⋊C4)C211yesmaximal, characteristic
2C3×Dic3×3−1+2C211yesmaximal, characteristic
3C32×3−1+2⋊C4C211yesmaximal, characteristic
4C32×#627—31nomaximal
5C3×3−1+2⋊Q8—31nomaximal
6#6189⋊C3C313yesmaximal, direct product factor
7C3×#6189C311yesmaximal, characteristic, complemented
8C2×C32×3−1+2C2211yescharacteristic
9C32×C3⋊Dic3—31no—
10C33×Dic3—31no—
11C33×Dic3D311yescharacteristic
12C3×C4×3−1+2—31no—
13C3⋊(3−1+2⋊C4)C2×C313yes—
14C3×C3⋊Dic9C2×C311yescharacteristic
15Dic3×3−1+2—23no—
16Dic3×3−1+2C2×C313yes—
17C3×3−1+2⋊C4—23no—
18C3×3−1+2⋊C4—21no—
19C3×3−1+2⋊C4—31no—
20C3×3−1+2⋊C4—61no—
21C3×3−1+2⋊C4D311yescharacteristic
22C3×3−1+2⋊C4C2×C313yes—
23C3×C9×Dic3—21no—
24C3×C9×Dic3C2×C311yescharacteristic
25C32×Dic9C2×C311yescharacteristic
26C32×3−1+2Q811yescharacteristic, complemented, Sylow
27C32×Dic6—91no—
28C32×Dic6—91no—
29C3×#627—31no—
30C3×#627—33no—
313−1+2⋊Q8—33no—
32C3×Dic18—31no—
33#6189C3211yescharacteristic, complemented
34C2×C34C2×D311yescharacteristic
35C2×C3×3−1+2—23no—
36C2×C3×3−1+2—21no—
37C2×C3×3−1+2—23no—
38C2×C3×3−1+2—21no—
39C2×C3×3−1+2—41no—
40C2×C3×3−1+2—43no—
41C2×C3×3−1+2C2×D311yescharacteristic
42C2×C3×3−1+2C22×C313yes—
43C2×C32×C9—21no—
44C2×C32×C9C22×C311yescharacteristic
45C33×C4—31no—
46C33×C4—91no—
47C3×C3⋊Dic3—31no—
48C3×C3⋊Dic3—33no—
49C32×Dic3—31no—
50C32×Dic3—31no—
51C32×Dic3—31no—
52C32×Dic3—33no—
53C32×Dic3—61no—
54C32×Dic3—63no—
55C32×Dic3—61no—
56C32×Dic3—91no—
57C32×Dic3—91no—
58C32×Dic3—181no—
59C32×Dic3C3×D311yescharacteristic
60C32×Dic3C3×D313yes—
61C4×3−1+2—33no—
62C4×3−1+2—63no—
63C3×C4×C9—31no—
64C3×C4×C9—61no—
65C3⋊Dic9C2×C3211yescharacteristic
663−1+2⋊C4—23no—
673−1+2⋊C4—33no—
683−1+2⋊C4—63no—
693−1+2⋊C4C3×D313yes—
70C9×Dic3—23no—
71C9×Dic3—21no—
72C9×Dic3C2×C3211yescharacteristic
73C3×Dic9—21no—
74C3×Dic9—31no—
75C3×Dic9—61no—
76C3×Dic9C3×D311yescharacteristic
77C3×Dic9C2×C3211yescharacteristic
78C34Dic611yescharacteristic
79C3×3−1+2—23no—
80C3×3−1+2—21no—
81C3×3−1+2—23no—
82C3×3−1+2—21no—
83C3×3−1+2—41no—
84C3×3−1+2—43no—
85C3×3−1+2Dic611yescharacteristic, complemented
86C3×3−1+2C3×Q813yescomplemented
87C32×C9—21no—
88C32×C9C3×Q811yescharacteristic, complemented
89C32×Q8—271no—
90C3×Dic6—91no—
91C3×Dic6—93no—
92C3×Dic6—93no—
93C3×Dic6—91no—
94#627—31no—
95Dic18—31no—
96C2×C33—23no—
97C2×C33—21no—
98C2×C33—31no—
99C2×C33—61no—
100C2×C33—61no—
101C2×C33—121no—
102C2×C33D3211yescharacteristic
103C2×C33C2×C3×D311yescharacteristic
104C2×C33C2×C3×D313yes—
105C2×3−1+2—23no—
106C2×3−1+2—23no—
107C2×3−1+2—23no—
108C2×3−1+2—43no—
109C2×3−1+2—46no—
110C2×3−1+2—43no—
111C2×3−1+2—43no—
112C2×3−1+2C2×C3×D313yes—
113C2×C3×C9—21no—
114C2×C3×C9—21no—
115C2×C3×C9—23no—
116C2×C3×C9—21no—
117C2×C3×C9—21no—
118C2×C3×C9—41no—
119C2×C3×C9—43no—
120C2×C3×C9—41no—
121C2×C3×C9C2×C3×D311yescharacteristic
122C2×C3×C9C22×C3211yescharacteristic
123C32×C4—31no—
124C32×C4—33no—
125C32×C4—91no—
126C32×C4—91no—
127C32×C4—93no—
128C32×C4—91no—
129C32×C4—181no—
130C32×C4—183no—
131C32×C4—181no—
132C32×C4—271no—
133C3⋊Dic3—31no—
134C3×Dic3—21no—
135C3×Dic3—31no—
136C3×Dic3—33no—
137C3×Dic3—31no—
138C3×Dic3—33no—
139C3×Dic3—61no—
140C3×Dic3—63no—
141C3×Dic3—93no—
142C3×Dic3—91no—
143C3×Dic3—91no—
144C3×Dic3—93no—
145C3×Dic3—181no—
146C3×Dic3—183no—
147C3×Dic3AGL(1,ℤ/9)11yescharacteristic
148C3×Dic3C32×D311yescharacteristic
149C4×C9—31no—
150C4×C9—61no—
151C4×C9—63no—
152Dic9—31no—
153Dic9—61no—
154Dic9C32×D311yescharacteristic
155C33—23no—
156C33—21no—
157C33—31no—
158C33—61no—
159C33—61no—
160C33—121no—
161C33#62711yescharacteristic
162C33C3×Dic611yescharacteristic
163C33C3×Dic613yes—
1643−1+2—23no—
1653−1+2—23no—
1663−1+2—23no—
1673−1+2—43no—
1683−1+2—46no—
1693−1+2—43no—
1703−1+2—43no—
1713−1+2C3×Dic613yescomplemented
172C3×C9—21no—
173C3×C9—21no—
174C3×C9—23no—
175C3×C9—21no—
176C3×C9—21no—
177C3×C9—41no—
178C3×C9—43no—
179C3×C9—41no—
180C3×C9C3×Dic611yescharacteristic, complemented
181C3×C9C32×Q811yescharacteristic, complemented
182C3×Q8—271no—
183C3×Q8—273no—
184Dic6—91no—
185Dic6—91no—
186C2×C32—21no—
187C2×C32—21no—
188C2×C32—21no—
189C2×C32—23no—
190C2×C32—31no—
191C2×C32—33no—
192C2×C32—41no—
193C2×C32—61no—
194C2×C32—63no—
195C2×C32—63no—
196C2×C32—61no—
197C2×C32—121no—
198C2×C32—123no—
199C2×C32C2×AGL(1,ℤ/9)11yescharacteristic
200C2×C32C3×D3211yescharacteristic
201C2×C32C3×D3213yes—
202C2×C32C2×C32×D311yescharacteristic
203C2×C9—23no—
204C2×C9—21no—
205C2×C9—21no—
206C2×C9—41no—
207C2×C9—43no—
208C2×C9C2×C32×D311yescharacteristic
209C3×C4—31no—
210C3×C4—31no—
211C3×C4—61no—
212C3×C4—93no—
213C3×C4—93no—
214C3×C4—91no—
215C3×C4—91no—
216C3×C4—181no—
217C3×C4—183no—
218C3×C4—273no—
219C3×C4—271no—
220Dic3—31no—
221Dic3—91no—
222Dic3—91no—
223Dic3—181no—
224Dic3C3×AGL(1,ℤ/9)11yescharacteristic
225C32—21no—
226C32—21no—
227C32—21no—
228C32—23no—
229C32—31no—
230C32—33no—
231C32—41no—
232C32—61no—
233C32—63no—
234C32—63no—
235C32—61no—
236C32—121no—
237C32—123no—
238C323−1+2⋊Q811yescharacteristic, complemented
239C32C3×#62711yescharacteristic
240C32C3×#62713yes—
241C32C32×Dic611yescharacteristic
242C9—23no—
243C9—21no—
244C9—21no—
245C9—41no—
246C9—43no—
247C9C32×Dic611yescharacteristic, complemented
248Q8—271noSylow
249C2×C3—21no—
250C2×C3—21no—
251C2×C3—21no—
252C2×C3—33no—
253C2×C3—41no—
254C2×C3—63no—
255C2×C3D3×AGL(1,ℤ/9)11yescharacteristic
256C2×C3C2×C3×AGL(1,ℤ/9)11yescharacteristic
257C2×C3C32×D3211yescharacteristic
258C4—31no—
259C4—91no—
260C4—271no—
261C3—21no—
262C3—21no—
263C3—21no—
264C3—33no—
265C3—41no—
266C3—63no—
267C3#6189⋊C311yescharacteristic, direct product factor
268C3C3×3−1+2⋊Q811yescharacteristic, complemented
269C3C32×#62711yescharacteristic
270C2C3×D3×AGL(1,ℤ/9)11yescharacteristic
subgroupG/H
center, hypercenterC2×C3D3×AGL(1,ℤ/9)
commutator, cosocleC2×C3×C9C22×C32
FrattiniC2×C3C32×D32
FittingC2×C32×3−1+2C22
socleC2×C33C2×C3×D3
prime radicalC2×C34C2×D3
hypocenterC3×C9C32×Q8
LCSG ▷ C2×C3×C9 ▷ C3×C9
UCSC1 ◁ C2×C3

Complements

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

NH ≅ G/Ntype
6. #6189⋊C3C3direct (N × H)
7. C3×#6189C3semidirect
26. C32×3−1+2Q8semidirect
33. #6189C32semidirect
85. C3×3−1+2Dic6semidirect
86. C3×3−1+2C3×Q8semidirect
88. C32×C9C3×Q8semidirect
171. 3−1+2C3×Dic6semidirect
180. C3×C9C3×Dic6semidirect
181. C3×C9C32×Q8semidirect
238. C323−1+2⋊Q8semidirect
247. C9C32×Dic6semidirect
267. C3#6189⋊C3direct (N × H)
268. C3C3×3−1+2⋊Q8semidirect

Maximal subgroups

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

subgroupindex
C3×C3⋊(3−1+2⋊C4)2
C3×Dic3×3−1+22
C32×3−1+2⋊C42
C32×#6273
C3×3−1+2⋊Q83
#6189⋊C33
C3×#61893