Finite Group Databasebeta

← D3×#469 #80862

Subgroups — D3×#469 #80862

Order 384.

596 conjugacy classes of subgroups; only the 135 normal subgroups are shown.

normal subgroups only

This group has 596 conjugacy classes of subgroups — too many to draw. Only its 135 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×D3×D8C211yesmaximal, characteristic, complemented
2C2×D3×M16C211yesmaximal, characteristic, complemented
3D3×#121C212yesmaximal, complemented
4C3×#469C211yesmaximal, characteristic, complemented
5#5159C211yesmaximal, characteristic, complemented
6#5135C211yesmaximal, characteristic, complemented
7#5039C212yesmaximal, complemented
8#4865C211yesmaximal, characteristic, complemented
9D3×#106C211yesmaximal, characteristic, complemented
10#4782C212yesmaximal, complemented
11D3×#102C212yesmaximal, complemented
12C2×#469—31nomaximal, Sylow
13C2×D3×D4—22no—
14C2×D3×D4C2212yes—
15C22×C4×D3C2211yescharacteristic
16C2×C3×D8C2211yescharacteristic, complemented
17C2×C3×M16C2211yescharacteristic, complemented
18C3×#121C2212yescomplemented
19#939—22no—
20#938C2212yescomplemented
21C2×#213C2212yescomplemented
22#930C2212yescomplemented
23C2×#208C2211yescharacteristic, complemented
24D3×D8—24no—
25D3×M16—24no—
26C2×D24C2211yescharacteristic, complemented
27C2×ΓL(1,𝔽25)C2211yescharacteristic, complemented
28C2×ΓL(1,𝔽25)C2211yescharacteristic, complemented
29C2×D3×C8C2211yescharacteristic
30C2×D3×C8C2211yescharacteristic
31#895C2212yescomplemented
32D3×C4⋊C4C2212yes—
33#884—22no—
34D3×C22⋊C4—22no—
35C3×#106C2211yescharacteristic, complemented
36C3×#102C2212yescomplemented
37#832C2212yescomplemented
38#821C2212yescomplemented
39#817C2211yescharacteristic, complemented
40#809C2212yescomplemented
41#808C2212yescomplemented
42C22×D8—31no—
43C22×M16—31no—
44C2×#121—32no—
45#469—31no—
46#469—31no—
47#469—32no—
48#469—31no—
49#469—32no—
50#469D311yescharacteristic, direct product factor
51C2×#106—31no—
52C2×#102—32no—
53C23×D3—22no—
54C23×D3D411yescharacteristic
55C2×C3×D4—22no—
56C2×C3×D4C2312yes—
57C22×C3×C4C2311yescharacteristic
58C2×#67—22no—
59C2×#67—22no—
60C2×#67—22no—
61C22×Dic3D411yescharacteristic
62D3×D4—24no—
63D3×D4—24no—
64D3×D4—48no—
65C2×D12—22no—
66C2×D12C2312yes—
67C2×C4×D3—22no—
68C2×C4×D3—22no—
69C2×C4×D3—22no—
70C2×C4×D3D411yescharacteristic
71C2×C4×D3D411yescharacteristic
72C2×C4×D3C2311yescharacteristic
73C2×C4×D3C2311yescharacteristic
74C3×D8—22no—
75C3×M16—22no—
76C2×C3×C8C2311yescharacteristic
77C2×C3×C8C2311yescharacteristic
78C3×C4⋊C4C2312yes—
79C3×C22⋊C4—22no—
80#217—22no—
81#213—24no—
82(C2×D3)⋊C4—22no—
83(C2×D3)⋊C4—22no—
84C4⋊Dic3C2312yes—
85Dic3⋊C4—22no—
86#208—22no—
87C2×C3⋊C8C2311yescharacteristic
88C2×C3⋊C8C2311yescharacteristic
89D24—22no—
90ΓL(1,𝔽25)—22no—
91ΓL(1,𝔽25)—22no—
92D3×C8—22no—
93D3×C8D414yescomplemented
94C22×D4—32no—
95C22×D4—62no—
96C23×C4—31no—
97C2×D8—32no—
98C2×D8—31no—
99C2×D8—64no—
100C2×D8C2×D311yescharacteristic, complemented
101C2×M16—31no—
102C2×M16—31no—
103C2×M16—31no—
104C2×M16—64no—
105C2×M16C2×D311yescharacteristic, complemented
106C22×C8—31no—
107C22×C8—31no—
108#121—32no—
109#121—32no—
110#121—32no—
111#121—62no—
112#121—62no—
113#121C2×D312yescomplemented
114C2×C4⋊C4—32no—
115C2×C22⋊C4—62no—
116#106—31no—
117#106—32no—
118#106C2×D311yescharacteristic, complemented
119#102—32no—
120#102—32no—
121#102—32no—
122#102C2×D312yescomplemented
123C23×C3—22no—
124C23×C3C2×D411yescharacteristic
125C22×D3—22no—
126C22×D3—24no—
127C22×D3—22no—
128C22×D3—44no—
129C22×D3—44no—
130C22×D3—44no—
131C22×D3C2×D411yescharacteristic
132C22×D3C2×D411yescharacteristic
133C3×D4—22no—
134C3×D4—22no—
135C3×D4—44no—
136C2×C3×C4—21no—
137C2×C3×C4—21no—
138C2×C3×C4—22no—
139C2×C3×C4C2×D411yescharacteristic
140C2×C3×C4C2411yescharacteristic
141#67—44no—
142#67—44no—
143#67—44no—
144C2×Dic3—22no—
145C2×Dic3—22no—
146C2×Dic3C2×D411yescharacteristic
147C2×Dic3C2×D411yescharacteristic
148D12—22no—
149D12—22no—
150D12—44no—
151C4×D3—22no—
152C4×D3—21no—
153C4×D3—21no—
154C4×D3—22no—
155C4×D3—44no—
156C4×D3C2×D412yes—
157C4×D3#4112yes—
158C3×C8—21no—
159C3×C8C2×D412yescomplemented
160C3⋊C8—21no—
161C3⋊C8C2×D412yescomplemented
162C24—31no—
163C24—62no—
164C2×D4—22no—
165C2×D4—32no—
166C2×D4—62no—
167C2×D4—64no—
168C2×D4—64no—
169C2×D4—62no—
170C2×D4—62no—
171C2×D4—62no—
172C2×D4—128no—
173C2×D4C22×D312yes—
174C22×C4—31no—
175C22×C4—31no—
176C22×C4—31no—
177C22×C4—31no—
178C22×C4—31no—
179C22×C4—62no—
180C22×C4—62no—
181C22×C4—62no—
182C22×C4C22×D311yescharacteristic
183D8—22no—
184D8—64no—
185D8—62no—
186M16—22no—
187M16—62no—
188M16—62no—
189M16—62no—
190C2×C8—31no—
191C2×C8—34no—
192C2×C8—31no—
193C2×C8—62no—
194C2×C8C22×D311yescharacteristic
195C2×C8C22×D311yescharacteristic
196C4⋊C4—32no—
197C4⋊C4—62no—
198C4⋊C4C22×D312yes—
199C22⋊C4—22no—
200C22⋊C4—62no—
201C22⋊C4—62no—
202C22⋊C4—62no—
203C22×C3—21no—
204C22×C3—22no—
205C22×C3—42no—
206C22×C3—42no—
207C22×C3—42no—
208C22×C3C22×D411yescharacteristic
209C2×D3—21no—
210C2×D3—22no—
211C2×D3—44no—
212C2×D3—42no—
213C2×D3—42no—
214C2×D3—42no—
215C2×D3—88no—
216C2×D3#12112yes—
217C2×D3AGL(1,ℤ/8)14yes—
218C3×C4—21no—
219C3×C4—42no—
220C3×C4C22×D411yescharacteristic
221C3×C4C2×#4111yescharacteristic
222Dic3—21no—
223Dic3—42no—
224Dic3#12112yes—
225C23—22no—
226C23—31no—
227C23—31no—
228C23—62no—
229C23—64no—
230C23—62no—
231C23—124no—
232C23—124no—
233C23—124no—
234C23D3×D411yescharacteristic
235D4—22no—
236D4—22no—
237D4—44no—
238D4—62no—
239D4—62no—
240D4—124no—
241D4—124no—
242D4—124no—
243D4—124no—
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—22no—
247C2×C4—31no—
248C2×C4—32no—
249C2×C4—32no—
250C2×C4—31no—
251C2×C4—62no—
252C2×C4—62no—
253C2×C4—62no—
254C2×C4—61no—
255C2×C4—61no—
256C2×C4—62no—
257C2×C4—124no—
258C2×C4D3×D411yescharacteristic
259C2×C4C23×D311yescharacteristic
260C8—21no—
261C8—32no—
262C8—61no—
263C8D3×D412yescomplemented
264C2×C3—41no—
265C2×C3—82no—
266C2×C3C2×#12111yescharacteristic
267C2×C3C2×AGL(1,ℤ/8)12yes—
268D3—41no—
269D3—82no—
270D3#46914yesdirect product factor
271C22—22no—
272C22—21no—
273C22—34no—
274C22—32no—
275C22—42no—
276C22—42no—
277C22—42no—
278C22—62no—
279C22—61no—
280C22—124no—
281C22—122no—
282C22—122no—
283C22—122no—
284C22—248no—
285C22C2×D3×D411yescharacteristic
286C4—21no—
287C4—32no—
288C4—42no—
289C4—61no—
290C4—122no—
291C4C2×D3×D411yescharacteristic
292C4D3×#4111yescharacteristic
293C3C2×#46911yescharacteristic, complemented, Sylow
294C2—34no—
295C2—41no—
296C2—82no—
297C2—121no—
298C2—242no—
299C2D3×#12111yescharacteristic
300C2D3×AGL(1,ℤ/8)12yes—
subgroupG/H
centerC22C2×D3×D4
commutator, cosocleC2×C3×C4C24
FrattiniC2×C4C23×D3
FittingC3×#469C2
socleC22×C3C22×D4
hypercenter#469D3
hypocenterC3C2×#469
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C22×C4 ◁ #469

Complements

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

NH ≅ G/Ntype
1. C2×D3×D8C2semidirect
2. C2×D3×M16C2semidirect
3. D3×#121C2semidirect
4. C3×#469C2semidirect
5. #5159C2semidirect
6. #5135C2semidirect
7. #5039C2semidirect
8. #4865C2semidirect
9. D3×#106C2semidirect
10. #4782C2semidirect
11. D3×#102C2semidirect
16. C2×C3×D8C22semidirect
17. C2×C3×M16C22semidirect
18. C3×#121C22semidirect
20. #938C22semidirect
21. C2×#213C22semidirect
22. #930C22semidirect
23. C2×#208C22semidirect
26. C2×D24C22semidirect
27. C2×ΓL(1,𝔽25)C22semidirect
28. C2×ΓL(1,𝔽25)C22semidirect
31. #895C22semidirect
35. C3×#106C22semidirect
36. C3×#102C22semidirect
37. #832C22semidirect
38. #821C22semidirect
39. #817C22semidirect
40. #809C22semidirect
41. #808C22semidirect
50. #469D3direct (N × H)
93. D3×C8D4semidirect
100. C2×D8C2×D3semidirect
105. C2×M16C2×D3semidirect
113. #121C2×D3semidirect
118. #106C2×D3semidirect
122. #102C2×D3semidirect
159. C3×C8C2×D4semidirect
161. C3⋊C8C2×D4semidirect
263. C8D3×D4semidirect
270. D3#469direct (N × H)
293. C3C2×#469semidirect

Maximal subgroups

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

subgroupindex
C2×D3×D82
C2×D3×M162
D3×#1212
C3×#4692
#51592
#51352
#50392
#48652
D3×#1062
#47822
D3×#1022
C2×#4693