Finite Group Databasebeta

← C2×D32×3−1+2 #14519301

Subgroups — C2×D32×3−1+2 #14519301

Order 1944.

848 conjugacy classes of subgroups; only the 196 normal subgroups are shown.

normal subgroups only

This group has 848 conjugacy classes of subgroups — too many to draw. Only its 196 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⋊D3×3−1+2C211yesmaximal, characteristic, complemented
2C2×C3×D3×3−1+2C212yesmaximal, complemented
3D32×3−1+2C214yesmaximal, direct product factor
4C2×C32×D32C311yesmaximal, characteristic
5C22×D3×3−1+2—32nomaximal
6C2×D32×C9C313yesmaximal, complemented
7C2×C32×3−1+2C2211yescharacteristic, complemented
8C3⋊D3×3−1+2C2212yescomplemented
9C3×D3×3−1+2C2214yescomplemented
10C2×C32×C3⋊D3C2×C311yescharacteristic
11C2×C33×D3C2×C312yes—
12C32×D32C2×C314yes—
13C22×C3×3−1+2—32no—
14C2×C9×C3⋊D3C2×C313yescomplemented
15C2×D3×3−1+2—22no—
16C2×D3×3−1+2—26no—
17C2×D3×3−1+2—32no—
18C2×D3×3−1+2—38no—
19C2×D3×3−1+2—61no—
20C2×D3×3−1+2D312yesdirect product factor
21C2×C3×D3×C9C2×C316yescomplemented
22D32×C9C2×C3112yescomplemented
23C32×3−1+2C2311yescharacteristic, complemented, Sylow
24C22×C32×D3—32no—
25C2×C3×D32—31no—
26C2×C3×D32C3211yescharacteristic
27C23×3−1+2—91no—
28C22×D3×C9—36no—
29C2×C34C22×C311yescharacteristic
30C32×C3⋊D3C22×C312yes—
31C33×D3C22×C314yes—
32C2×C3×3−1+2—22no—
33C2×C3×3−1+2—21no—
34C2×C3×3−1+2—26no—
35C2×C3×3−1+2—34no—
36C2×C3×3−1+2—43no—
37C2×C3×3−1+2—41no—
38C2×C3×3−1+2C2×D312yescomplemented
39C2×C32×C9C22×C313yescomplemented
40C9×C3⋊D3C22×C316yescomplemented
41D3×3−1+2—24no—
42D3×3−1+2—212no—
43D3×3−1+2—34no—
44D3×3−1+2—62no—
45D3×3−1+2C2×D314yesdirect product factor
46C3×D3×C9C22×C3112yescomplemented
47C22×C33—32no—
48C2×C3×C3⋊D3—31no—
49C2×C3×C3⋊D3C2×C3211yescharacteristic
50C2×C32×D3—22no—
51C2×C32×D3—32no—
52C2×C32×D3—32no—
53C2×C32×D3—38no—
54C2×C32×D3—61no—
55C2×C32×D3—62no—
56C2×C32×D3C3×D312yes—
57C2×C32×D3C2×C3212yes—
58C3×D32—34no—
59C3×D32C2×C3214yes—
60C22×3−1+2—32no—
61C22×3−1+2—66no—
62C22×3−1+2—62no—
63C22×3−1+2—94no—
64C22×3−1+2—91no—
65C22×C3×C9—36no—
66C2×D3×C9—26no—
67C2×D3×C9—36no—
68C2×D3×C9—324no—
69C2×D3×C9—63no—
70C2×D3×C9C3×D316yescomplemented
71C34C23×C311yescharacteristic
72C3×3−1+2—22no—
73C3×3−1+2—21no—
74C3×3−1+2—26no—
75C3×3−1+2—43no—
76C3×3−1+2—41no—
77C3×3−1+2C22×D312yescomplemented
78C32×C9C23×C313yescomplemented
79C23×C32—91no—
80C22×C3×D3—32no—
81C22×C3×D3—92no—
82C2×D323−1+211yescharacteristic, direct product factor
83C23×C9—93no—
84C2×C33—21no—
85C2×C33—22no—
86C2×C33—31no—
87C2×C33—34no—
88C2×C33—41no—
89C2×C33—62no—
90C2×C33—121no—
91C2×C33C2×C3×D312yes—
92C2×C33C22×C3211yescharacteristic
93C3×C3⋊D3—32no—
94C3×C3⋊D3C22×C3212yes—
95C32×D3—24no—
96C32×D3—34no—
97C32×D3—34no—
98C32×D3—64no—
99C32×D3—62no—
100C32×D3C2×C3×D314yes—
101C32×D3C22×C3214yes—
102C2×3−1+2—22no—
103C2×3−1+2—26no—
104C2×3−1+2—34no—
105C2×3−1+2—46no—
106C2×3−1+2—46no—
107C2×3−1+2—41no—
108C2×3−1+2—43no—
109C2×3−1+2—612no—
110C2×3−1+2—64no—
111C2×3−1+2—92no—
112C2×3−1+2D3211yescharacteristic, direct product factor
113C2×C3×C9—26no—
114C2×C3×C9—23no—
115C2×C3×C9—312no—
116C2×C3×C9—43no—
117C2×C3×C9C2×C3×D316yescomplemented
118D3×C9—212no—
119D3×C9—312no—
120D3×C9—66no—
121D3×C9C2×C3×D3112yescomplemented
122C22×C32—32no—
123C22×C32—32no—
124C22×C32—62no—
125C22×C32—92no—
126C22×C32—94no—
127C22×C32—91no—
128C22×C32—182no—
129C2×C3⋊D3C2×3−1+211yescharacteristic, complemented
130C2×C3×D3—22no—
131C2×C3×D3—32no—
132C2×C3×D3—38no—
133C2×C3×D3—32no—
134C2×C3×D3—61no—
135C2×C3×D3—62no—
136C2×C3×D3—98no—
137C2×C3×D3—92no—
138C2×C3×D3—181no—
139C2×C3×D3C2×3−1+212yescomplemented
140C2×C3×D3C32×D312yes—
141D32C2×3−1+214yesdirect product factor
142C22×C9—36no—
143C22×C9—66no—
144C22×C9—912no—
145C22×C9—93no—
146C33—21no—
147C33—22no—
148C33—31no—
149C33—41no—
150C33—62no—
151C33—121no—
152C33C22×C3×D312yes—
153C33C23×C3211yescharacteristic
1543−1+2—22no—
1553−1+2—26no—
1563−1+2—46no—
1573−1+2—46no—
1583−1+2—41no—
1593−1+2—43no—
1603−1+2C2×D3211yescharacteristic, direct product factor
161C3×C9—26no—
162C3×C9—23no—
163C3×C9—43no—
164C3×C9C22×C3×D316yescomplemented
165C23×C3—91no—
166C23×C3—271no—
167C22×D3—32no—
168C2×C32—22no—
169C2×C32—21no—
170C2×C32—22no—
171C2×C32—34no—
172C2×C32—32no—
173C2×C32—34no—
174C2×C32—41no—
175C2×C32—41no—
176C2×C32—62no—
177C2×C32—61no—
178C2×C32—64no—
179C2×C32—62no—
180C2×C32—94no—
181C2×C32—92no—
182C2×C32—121no—
183C2×C32—122no—
184C2×C32—121no—
185C2×C32—122no—
186C2×C32—184no—
187C2×C32C22×3−1+211yescharacteristic, complemented
188C2×C32C3×D3211yescharacteristic
189C2×C32C2×C32×D312yes—
190C3⋊D3C22×3−1+212yescomplemented
191C3×D3—24no—
192C3×D3—34no—
193C3×D3—34no—
194C3×D3—62no—
195C3×D3—64no—
196C3×D3—94no—
197C3×D3—182no—
198C3×D3C22×3−1+214yescomplemented
199C3×D3C2×C32×D314yes—
200C2×C9—26no—
201C2×C9—312no—
202C2×C9—43no—
203C2×C9—612no—
204C2×C9—96no—
205C2×C9C3×D3213yescomplemented
206C22×C3—32no—
207C22×C3—32no—
208C22×C3—62no—
209C22×C3—92no—
210C22×C3—94no—
211C22×C3—91no—
212C22×C3—182no—
213C22×C3—271no—
214C22×C3—274no—
215C2×D3—32no—
216C2×D3—38no—
217C2×D3—61no—
218C2×D3D3×3−1+212yesdirect product factor
219C32—21no—
220C32—22no—
221C32—22no—
222C32—32no—
223C32—41no—
224C32—41no—
225C32—62no—
226C32—61no—
227C32—62no—
228C32—121no—
229C32—122no—
230C32—121no—
231C32—122no—
232C32C23×3−1+211yescharacteristic, complemented
233C32C2×C3×D3211yescharacteristic
234C32C22×C32×D312yes—
235C9—26no—
236C9—43no—
237C9C2×C3×D3213yescomplemented
238C23—91noSylow
239C2×C3—21no—
240C2×C3—22no—
241C2×C3—34no—
242C2×C3—34no—
243C2×C3—31no—
244C2×C3—41no—
245C2×C3—64no—
246C2×C3—62no—
247C2×C3—94no—
248C2×C3—92no—
249C2×C3—121no—
250C2×C3—184no—
251C2×C3—272no—
252C2×C3C2×D3×3−1+212yescomplemented
253C2×C3C32×D3211yescharacteristic
254D3—34no—
255D3—62no—
256D3C2×D3×3−1+214yesdirect product factor
257C22—32no—
258C22—94no—
259C22—91no—
260C3—21no—
261C3—22no—
262C3—31no—
263C3—41no—
264C3—62no—
265C3—121no—
266C3C22×D3×3−1+212yescomplemented
267C3C2×C32×D3211yescharacteristic
268C2—34no—
269C2—92no—
270C2D32×3−1+211yescharacteristic, direct product factor
subgroupG/H
centerC2×C3C32×D32
commutator, cosocleC33C23×C32
FrattiniC3C2×C32×D32
FittingC2×C32×3−1+2C22
socleC2×C33C22×C32
prime radicalC2×C32×D32C3
hypercenterC2×3−1+2D32
hypocenterC32C23×3−1+2
LCSG ▷ C33 ▷ C32
UCSC1 ◁ C2×C3 ◁ C2×3−1+2

Complements

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

NH ≅ G/Ntype
1. C2×C3⋊D3×3−1+2C2semidirect
2. C2×C3×D3×3−1+2C2semidirect
3. D32×3−1+2C2direct (N × H)
6. C2×D32×C9C3semidirect
7. C2×C32×3−1+2C22semidirect
8. C3⋊D3×3−1+2C22semidirect
9. C3×D3×3−1+2C22semidirect
14. C2×C9×C3⋊D3C2×C3semidirect
20. C2×D3×3−1+2D3direct (N × H)
21. C2×C3×D3×C9C2×C3semidirect
22. D32×C9C2×C3semidirect
23. C32×3−1+2C23semidirect
38. C2×C3×3−1+2C2×D3semidirect
39. C2×C32×C9C22×C3semidirect
40. C9×C3⋊D3C22×C3semidirect
45. D3×3−1+2C2×D3direct (N × H)
46. C3×D3×C9C22×C3semidirect
70. C2×D3×C9C3×D3semidirect
77. C3×3−1+2C22×D3semidirect
78. C32×C9C23×C3semidirect
82. C2×D323−1+2direct (N × H)
112. C2×3−1+2D32direct (N × H)
117. C2×C3×C9C2×C3×D3semidirect
121. D3×C9C2×C3×D3semidirect
129. C2×C3⋊D3C2×3−1+2semidirect
139. C2×C3×D3C2×3−1+2semidirect
141. D32C2×3−1+2direct (N × H)
160. 3−1+2C2×D32direct (N × H)
164. C3×C9C22×C3×D3semidirect
187. C2×C32C22×3−1+2semidirect
190. C3⋊D3C22×3−1+2semidirect
198. C3×D3C22×3−1+2semidirect
205. C2×C9C3×D32semidirect
218. C2×D3D3×3−1+2direct (N × H)
232. C32C23×3−1+2semidirect
237. C9C2×C3×D32semidirect
252. C2×C3C2×D3×3−1+2semidirect
256. D3C2×D3×3−1+2direct (N × H)
266. C3C22×D3×3−1+2semidirect
270. C2D32×3−1+2direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3⋊D3×3−1+22
C2×C3×D3×3−1+22
D32×3−1+22
C2×C32×D323
C22×D3×3−1+23
C2×D32×C93