Finite Group Databasebeta

← D3×#465 #80655

Subgroups — D3×#465 #80655

Order 384.

564 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×SD16C211yesmaximal, characteristic, complemented
2C22×D3×C8C211yesmaximal, characteristic, complemented
3D3×C22⋊Q8C211yesmaximal, characteristic, complemented
4D3×#121C211yesmaximal, characteristic
5C3×#465C211yesmaximal, characteristic, complemented
6#5171C211yesmaximal, characteristic, complemented
7#5114C211yesmaximal, characteristic, complemented
8#5048C211yesmaximal, characteristic, complemented
9#5041C211yesmaximal, characteristic, complemented
10#4864C211yesmaximal, characteristic, complemented
11D3×#106C211yesmaximal, characteristic, complemented
12#4807C211yesmaximal, characteristic, complemented
13D3×#103C211yesmaximal, characteristic, complemented
14#4778C211yesmaximal, characteristic, complemented
15D3×#102C211yesmaximal, characteristic, complemented
16C2×#465—31nomaximal, Sylow
17C2×D3×Q8C2211yescharacteristic
18C2×D3×D4—21no—
19C2×D3×D4C2211yescharacteristic
20C22×C4×D3C2211yescharacteristic
21C2×C3×SD16C2211yescharacteristic, complemented
22C22×C3×C8C2211yescharacteristic, complemented
23C3×C22⋊Q8C2211yescharacteristic, complemented
24C3×#121C2211yescharacteristic
25#946C2211yescharacteristic, complemented
26C2×#215C2211yescharacteristic, complemented
27#939—21no—
28#938C2211yescharacteristic
29C2×#214C2211yescharacteristic, complemented
30#930C2211yescharacteristic
31#924C2211yescharacteristic, complemented
32C22×C3⋊C8C2211yescharacteristic, complemented
33D3×SD16—24no—
34C2×#204C2211yescharacteristic, complemented
35C2×D3×C8—24no—
36C2×D3×C8C2211yescharacteristic
37C2×D3×C8C2211yescharacteristic
38C2×D3×C8C2211yescharacteristic, complemented
39C2×D3×C8C2211yescharacteristic, complemented
40#897C2211yescharacteristic, complemented
41#896—21no—
42#895C2211yescharacteristic
43D3×C4⋊C4—21no—
44D3×C4⋊C4C2211yescharacteristic
45D3×C4⋊C4C2211yescharacteristic
46#884—21no—
47D3×C22⋊C4—21no—
48D3×C22⋊C4—21no—
49#878—21no—
50C3×#106C2211yescharacteristic, complemented
51C3×#103C2211yescharacteristic, complemented
52C3×#102C2211yescharacteristic, complemented
53#835C2211yescharacteristic, complemented
54#832C2211yescharacteristic, complemented
55#821C2211yescharacteristic, complemented
56#817C2211yescharacteristic, complemented
57#816C2211yescharacteristic, complemented
58#810C2211yescharacteristic, complemented
59#809C2211yescharacteristic, complemented
60#808C2211yescharacteristic, complemented
61#808C2211yescharacteristic, complemented
62C22×SD16—31no—
63C23×C8—31no—
64C2×C22⋊Q8—31no—
65C2×#121—31no—
66#465—31no—
67#465—31no—
68#465—31no—
69#465—31no—
70#465—31no—
71#465—31no—
72#465—31no—
73#465D311yescharacteristic, direct product factor
74C2×#106—31no—
75C2×#103—31no—
76C2×#102—31no—
77C23×D3—21no—
78C23×D3D411yescharacteristic
79C2×C3×Q8C2311yescharacteristic
80C2×C3×D4—21no—
81C2×C3×D4C2311yescharacteristic
82C22×C3×C4C2311yescharacteristic
83C2×#67—21no—
84C2×#67—21no—
85C2×#67—21no—
86C22×Dic3D411yescharacteristic
87D3×Q8—22no—
88D3×Q8—22no—
89D3×D4—22no—
90D3×D4—22no—
91D3×D4—44no—
92C2×D12—21no—
93C2×D12C2311yescharacteristic
94C2×C4×D3—22no—
95C2×C4×D3—22no—
96C2×C4×D3—21no—
97C2×C4×D3—21no—
98C2×C4×D3—21no—
99C2×C4×D3D411yescharacteristic
100C2×C4×D3D411yescharacteristic
101C2×C4×D3C2311yescharacteristic
102C2×C4×D3C2311yescharacteristic
103C2×Dic6—21no—
104C2×Dic6C2311yescharacteristic
105C3×SD16—22no—
106C2×C3×C8—22no—
107C2×C3×C8C2311yescharacteristic
108C2×C3×C8C2311yescharacteristic
109C3×C4⋊C4—21no—
110C3×C4⋊C4C2311yescharacteristic
111C3×C4⋊C4C2311yescharacteristic
112C3×C22⋊C4—21no—
113C3×C22⋊C4—21no—
114#217—21no—
115#217—21no—
116#215—22no—
117#214—22no—
118(C2×D3)⋊C4—21no—
119(C2×D3)⋊C4—21no—
120(C2×D3)⋊C4—21no—
121(C2×D3)⋊C4—21no—
122C4⋊Dic3—21no—
123C4⋊Dic3C2311yescharacteristic
124C4⋊Dic3C2311yescharacteristic
125Dic3⋊C4—21no—
126Dic3⋊C4—21no—
127Dic3⋊C4—21no—
128Dic3⋊C4—21no—
129C2×C3⋊C8—22no—
130C2×C3⋊C8C2311yescharacteristic
131C2×C3⋊C8C2311yescharacteristic
132#204—22no—
133D3×C8—22no—
134D3×C8—22no—
135D3×C8—22no—
136D3×C8D414yescomplemented
137C22×Q8—31no—
138C22×D4—31no—
139C22×D4—61no—
140C23×C4—31no—
141C2×SD16—31no—
142C2×SD16—31no—
143C2×SD16—31no—
144C2×SD16—64no—
145C2×SD16C2×D311yescharacteristic, complemented
146C22×C8—31no—
147C22×C8—31no—
148C22×C8—31no—
149C22×C8—31no—
150C22×C8—31no—
151C22×C8—64no—
152C22×C8C2×D311yescharacteristic, complemented
153C22⋊Q8—31no—
154C22⋊Q8—31no—
155C22⋊Q8—31no—
156C22⋊Q8—61no—
157C22⋊Q8—61no—
158C22⋊Q8C2×D311yescharacteristic, complemented
159#121—31no—
160#121—31no—
161#121—31no—
162#121—61no—
163#121—61no—
164#121C2×D311yescharacteristic
165C2×C4⋊C4—31no—
166C2×C4⋊C4—31no—
167C2×C4⋊C4—61no—
168C2×C22⋊C4—61no—
169C2×C22⋊C4—61no—
170#106—31no—
171#106—31no—
172#106—31no—
173#106C2×D311yescharacteristic, complemented
174#103—31no—
175#103—31no—
176#103—31no—
177#103C2×D311yescharacteristic, complemented
178#102—31no—
179#102—31no—
180#102—31no—
181#102C2×D311yescharacteristic, complemented
182C23×C3—21no—
183C23×C3C2×D411yescharacteristic
184C22×D3—22no—
185C22×D3—22no—
186C22×D3—21no—
187C22×D3—42no—
188C22×D3—42no—
189C22×D3—42no—
190C22×D3SD1614yescomplemented
191C22×D3C2×D411yescharacteristic
192C22×D3C2×D411yescharacteristic
193C3×Q8—21no—
194C3×Q8—21no—
195C3×D4—21no—
196C3×D4—21no—
197C3×D4—42no—
198C2×C3×C4—21no—
199C2×C3×C4—21no—
200C2×C3×C4—21no—
201C2×C3×C4—21no—
202C2×C3×C4—21no—
203C2×C3×C4C2×D411yescharacteristic
204C2×C3×C4C2411yescharacteristic
205#67—42no—
206#67—42no—
207#67—42no—
208C2×Dic3—22no—
209C2×Dic3—21no—
210C2×Dic3—21no—
211C2×Dic3—21no—
212C2×Dic3C2×D411yescharacteristic
213C2×Dic3C2×D411yescharacteristic
214D12—21no—
215D12—21no—
216D12—42no—
217C4×D3—22no—
218C4×D3—21no—
219C4×D3—21no—
220C4×D3—22no—
221C4×D3—42no—
222C4×D3—42no—
223C4×D3—42no—
224C4×D3C2×D412yes—
225C4×D3#4112yes—
226Dic6—21no—
227Dic6—21no—
228Dic6—42no—
229C3×C8—21no—
230C3×C8C2×D412yescomplemented
231C3⋊C8—21no—
232C3⋊C8C2×D412yescomplemented
233C24—31no—
234C24—61no—
235C2×Q8—31no—
236C2×Q8—61no—
237C2×Q8—62no—
238C2×Q8—62no—
239C2×Q8C22×D311yescharacteristic
240C2×D4—21no—
241C2×D4—31no—
242C2×D4—61no—
243C2×D4—62no—
244C2×D4—62no—
245C2×D4—61no—
246C2×D4—61no—
247C2×D4—61no—
248C2×D4—124no—
249C2×D4C22×D311yescharacteristic
250C22×C4—31no—
251C22×C4—31no—
252C22×C4—31no—
253C22×C4—31no—
254C22×C4—31no—
255C22×C4—62no—
256C22×C4—62no—
257C22×C4—61no—
258C22×C4—61no—
259C22×C4—61no—
260C22×C4C22×D311yescharacteristic
261SD16—22no—
262SD16—62no—
263SD16—62no—
264SD16—62no—
265C2×C8—22no—
266C2×C8—31no—
267C2×C8—34no—
268C2×C8—31no—
269C2×C8—62no—
270C2×C8—62no—
271C2×C8—62no—
272C2×C8—62no—
273C2×C8C22×D311yescharacteristic
274C2×C8C22×D311yescharacteristic
275C4⋊C4—21no—
276C4⋊C4—31no—
277C4⋊C4—31no—
278C4⋊C4—61no—
279C4⋊C4—61no—
280C4⋊C4—61no—
281C4⋊C4—61no—
282C4⋊C4—61no—
283C4⋊C4C22×D311yescharacteristic
284C4⋊C4C22×D311yescharacteristic
285C22⋊C4—21no—
286C22⋊C4—21no—
287C22⋊C4—61no—
288C22⋊C4—61no—
289C22⋊C4—61no—
290C22⋊C4—61no—
291C22⋊C4—61no—
292C22⋊C4—61no—
293C22×C3—21no—
294C22×C3—21no—
295C22×C3—41no—
296C22×C3—41no—
297C22×C3—41no—
298C22×C3C2×SD1612yescomplemented
299C22×C3C22×D411yescharacteristic
300C2×D3—21no—
301C2×D3—21no—
302C2×D3—28no—
303C2×D3—41no—
304C2×D3—41no—
305C2×D3—41no—
306C2×D3—84no—
307C2×D3#12112yes—
308C2×D3C2×SD1612yes—
309C2×D3C2×SD1612yescomplemented
310C2×D3#13512yes—
311C3×C4—21no—
312C3×C4—41no—
313C3×C4—41no—
314C3×C4—41no—
315C3×C4C22×D411yescharacteristic
316C3×C4C2×#4111yescharacteristic
317Dic3—21no—
318Dic3—41no—
319Dic3—41no—
320Dic3—41no—
321Dic3#12112yes—
322C23—21no—
323C23—31no—
324C23—34no—
325C23—31no—
326C23—62no—
327C23—62no—
328C23—61no—
329C23—122no—
330C23—122no—
331C23—122no—
332C23D3×D411yescharacteristic
333Q8—21no—
334Q8—21no—
335Q8—61no—
336Q8—61no—
337Q8—122no—
338D4—21no—
339D4—21no—
340D4—42no—
341D4—61no—
342D4—61no—
343D4—122no—
344D4—122no—
345D4—122no—
346D4—122no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—31no—
353C2×C4—32no—
354C2×C4—32no—
355C2×C4—31no—
356C2×C4—62no—
357C2×C4—62no—
358C2×C4—62no—
359C2×C4—61no—
360C2×C4—61no—
361C2×C4—61no—
362C2×C4—61no—
363C2×C4—61no—
364C2×C4—122no—
365C2×C4—122no—
366C2×C4—122no—
367C2×C4D3×D411yescharacteristic
368C2×C4C23×D311yescharacteristic
369C8—21no—
370C8—32no—
371C8—61no—
372C8D3×D412yescomplemented
373C2×C3—22no—
374C2×C3—81no—
375C2×C3C2×#12111yescharacteristic
376C2×C3C22×SD1611yescharacteristic
377C2×C3C2×#13511yescharacteristic
378D3—22no—
379D3—81no—
380D3#46514yesdirect product factor
381C22—21no—
382C22—21no—
383C22—32no—
384C22—32no—
385C22—32no—
386C22—32no—
387C22—41no—
388C22—41no—
389C22—41no—
390C22—68no—
391C22—61no—
392C22—61no—
393C22—121no—
394C22—121no—
395C22—121no—
396C22—244no—
397C22D3×SD1612yescomplemented
398C22C2×D3×D411yescharacteristic
399C4—21no—
400C4—32no—
401C4—41no—
402C4—41no—
403C4—41no—
404C4—61no—
405C4—121no—
406C4—121no—
407C4—121no—
408C4C2×D3×D411yescharacteristic
409C4D3×#4111yescharacteristic
410C3C2×#46511yescharacteristic, complemented, Sylow
411C2—22no—
412C2—34no—
413C2—62no—
414C2—81no—
415C2—241no—
416C2D3×#12111yescharacteristic
417C2C2×D3×SD1611yescharacteristic
418C2D3×#13511yescharacteristic
subgroupG/H
centerC22C2×D3×D4
commutator, cosocleC2×C3×C4C24
FrattiniC2×C4C23×D3
FittingC3×#465C2
socleC22×C3C22×D4
prime radicalD3×#121C2
hypercenter#465D3
hypocenterC3C2×#465
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C22×C4 ◁ #465

Complements

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

NH ≅ G/Ntype
1. C2×D3×SD16C2semidirect
2. C22×D3×C8C2semidirect
3. D3×C22⋊Q8C2semidirect
5. C3×#465C2semidirect
6. #5171C2semidirect
7. #5114C2semidirect
8. #5048C2semidirect
9. #5041C2semidirect
10. #4864C2semidirect
11. D3×#106C2semidirect
12. #4807C2semidirect
13. D3×#103C2semidirect
14. #4778C2semidirect
15. D3×#102C2semidirect
21. C2×C3×SD16C22semidirect
22. C22×C3×C8C22semidirect
23. C3×C22⋊Q8C22semidirect
25. #946C22semidirect
26. C2×#215C22semidirect
29. C2×#214C22semidirect
31. #924C22semidirect
32. C22×C3⋊C8C22semidirect
34. C2×#204C22semidirect
38. C2×D3×C8C22semidirect
39. C2×D3×C8C22semidirect
40. #897C22semidirect
50. C3×#106C22semidirect
51. C3×#103C22semidirect
52. C3×#102C22semidirect
53. #835C22semidirect
54. #832C22semidirect
55. #821C22semidirect
56. #817C22semidirect
57. #816C22semidirect
58. #810C22semidirect
59. #809C22semidirect
60. #808C22semidirect
61. #808C22semidirect
73. #465D3direct (N × H)
136. D3×C8D4semidirect
145. C2×SD16C2×D3semidirect
152. C22×C8C2×D3semidirect
158. C22⋊Q8C2×D3semidirect
173. #106C2×D3semidirect
177. #103C2×D3semidirect
181. #102C2×D3semidirect
190. C22×D3SD16semidirect
230. C3×C8C2×D4semidirect
232. C3⋊C8C2×D4semidirect
298. C22×C3C2×SD16semidirect
309. C2×D3C2×SD16semidirect
372. C8D3×D4semidirect
380. D3#465direct (N × H)
397. C22D3×SD16semidirect
410. C3C2×#465semidirect

Maximal subgroups

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

subgroupindex
C2×D3×SD162
C22×D3×C82
D3×C22⋊Q82
D3×#1212
C3×#4652
#51712
#51142
#50482
#50412
#48642
D3×#1062
#48072
D3×#1032
#47782
D3×#1022
C2×#4653