Finite Group Databasebeta

← D3×#532 #86234

Subgroups — D3×#532 #86234

Order 384.

1728 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×#41C212yesmaximal, complemented
2C3×#532C211yesmaximal, characteristic, complemented
3#5832C212yesmaximal, complemented
4#5725C211yesmaximal, characteristic, complemented
5D3×C4⋊Q8C211yesmaximal, characteristic, complemented
6#5716C211yesmaximal, characteristic, complemented
7D3×#127C211yesmaximal, characteristic, complemented
8D3×#124C212yesmaximal, complemented
9#5668C212yesmaximal, complemented
10D3×#121C214yesmaximal, complemented
11#5596C214yesmaximal, complemented
12#5548C214yesmaximal, complemented
13C4×D3×D4C214yesmaximal, complemented
14#5477C211yesmaximal, characteristic, complemented
15C2×C42×D3C211yesmaximal, characteristic, complemented
16C2×#532—31nomaximal, Sylow
17C2×C3×#41C2212yescomplemented
18D3×#41—216no—
19C2×#239C2212yescomplemented
20C2×D3×Q8C2212yes—
21C2×#237C2212yescomplemented
22C2×#237C2214yescomplemented
23C2×D3×D4C2212yes—
24C2×D3×D4C2214yes—
25C2×D3×D4C2214yes—
26C2×#235C2212yescomplemented
27C2×#235C2214yescomplemented
28C22×C4×D3C2214yes—
29C22×C4×D3C2212yes—
30C22×C4×D3C2211yescharacteristic
31C3×C4⋊Q8C2211yescharacteristic, complemented
32C3×#127C2211yescharacteristic, complemented
33C3×#124C2212yescomplemented
34C3×#121C2214yescomplemented
35C3×C4×D4C2214yescomplemented
36C2×C3×C42C2211yescharacteristic, complemented
37#947C2212yescomplemented
38#944C2212yescomplemented
39#940C2212yescomplemented
40#940C2214yescomplemented
41#939C2218yescomplemented
42#938C2214yescomplemented
43#936C2212yescomplemented
44D4×Dic3C2214yescomplemented
45#930C2214yescomplemented
46C4×#67C2218yescomplemented
47C2×C4×Dic3C2211yescharacteristic, complemented
48C2×C4×Dic3C2212yescomplemented
49#895C2214yescomplemented
50#893C2214yescomplemented
51D3×C4⋊C4C2214yes—
52#888C2214yescomplemented
53#885C2218yescomplemented
54#884C2218yescomplemented
55#67⋊C4C2218yescomplemented
56D3×C22⋊C4C2218yes—
57#875C2212yescomplemented
58#874C2211yescharacteristic, complemented
59C4×D12C2214yescomplemented
60C42×D3C2211yescharacteristic
61C42×D3C2211yescharacteristic
62C42×D3C2212yes—
63C42×D3C2211yescharacteristic, complemented
64C42×D3C2211yescharacteristic, complemented
65C42×D3C2212yescomplemented
66#869C2211yescharacteristic, complemented
67C22×#41—32no—
68#532—32no—
69#532—31no—
70#532—31no—
71#532—32no—
72#532—34no—
73#532—34no—
74#532—31no—
75#532D311yescharacteristic, direct product factor
76C2×C4⋊Q8—31no—
77C2×#127—31no—
78C2×#124—32no—
79C2×#121—34no—
80C2×C4×D4—34no—
81C22×C42—31no—
82C23×D3C2314yes—
83C23×D3C2311yescharacteristic
84C3×#41—28no—
85C2×C3×Q8C2312yes—
86C2×C3×D4C2314yes—
87C2×C3×D4C2312yes—
88C2×C3×D4C2314yes—
89C22×C3×C4C2312yes—
90C22×C3×C4C2314yes—
91C22×C3×C4C2311yescharacteristic
92C2×#67C2318yes—
93C2×#67C2314yes—
94C2×#67C2314yes—
95C2×#67C2314yes—
96C22×Dic3C2314yes—
97C22×Dic3C2312yes—
98C22×Dic3C2311yescharacteristic
99#239—28no—
100D3×Q8—28no—
101#237—216no—
102#237—28no—
103D3×D4—216no—
104D3×D4—28no—
105D3×D4—216no—
106#235—28no—
107#235—216no—
108C2×D12C2314yes—
109C2×D12C2312yes—
110C2×D12C2314yes—
111C2×C4×D3—216no—
112C2×C4×D3—28no—
113C2×C4×D3D418yescomplemented
114C2×C4×D3C2312yes—
115C2×C4×D3C2312yes—
116C2×C4×D3C2312yes—
117C2×C4×D3C2314yes—
118C2×C4×D3C2314yes—
119C2×C4×D3C2314yes—
120C2×C4×D3C2311yescharacteristic
121C2×C4×D3C2311yescharacteristic
122C2×C4×D3C2311yescharacteristic
123C2×C4×D3C2311yescharacteristic
124C2×C4×D3C2312yes—
125C2×Dic6C2312yes—
126C2×Dic6C2314yes—
127C3×C4⋊C4C2314yes—
128C3×C22⋊C4C2318yes—
129C3×C42C2311yescharacteristic
130C3×C42C2312yes—
131C3×C42C2311yescharacteristic
132#217C2318yes—
133(C2×D3)⋊C4C2318yes—
134(C2×D3)⋊C4C2318yes—
135C4⋊Dic3C2314yes—
136Dic3⋊C4C2318yes—
137C4×Dic3C2312yes—
138C4×Dic3C2312yes—
139C4×Dic3C2312yes—
140C4×Dic3C2312yes—
141C4×Dic3C2312yes—
142C4×Dic3C2311yescharacteristic
143C4×Dic3C2311yescharacteristic
144C2×#41—32no—
145C2×#41—34no—
146C2×#41—32no—
147C2×#41—34no—
148C2×#41—32no—
149C2×#41—616no—
150C2×#41C2×D312yescomplemented
151C22×Q8—32no—
152C22×D4—34no—
153C22×D4—34no—
154C22×D4—32no—
155C23×C4—31no—
156C23×C4—34no—
157C23×C4—32no—
158C4⋊Q8—32no—
159C4⋊Q8—34no—
160C4⋊Q8—31no—
161C4⋊Q8C2×D311yescharacteristic, complemented
162#127—32no—
163#127—34no—
164#127—31no—
165#127C2×D311yescharacteristic, complemented
166#124—32no—
167#124—32no—
168#124—38no—
169#124—32no—
170#124C2×D312yescomplemented
171#121—34no—
172#121—38no—
173#121—34no—
174#121—34no—
175#121—38no—
176#121C2×D314yescomplemented
177C4×D4—34no—
178C4×D4—38no—
179C4×D4—34no—
180C4×D4—38no—
181C4×D4—34no—
182C4×D4C2×D314yescomplemented
183C2×C4⋊C4—34no—
184C2×C22⋊C4—38no—
185C2×C42—32no—
186C2×C42—31no—
187C2×C42—32no—
188C2×C42—31no—
189C2×C42—31no—
190C2×C42—31no—
191C2×C42—31no—
192C2×C42—32no—
193C2×C42C2×D311yescharacteristic, complemented
194C23×C3C2414yes—
195C23×C3C2411yescharacteristic
196C22×D3—24no—
197C22×D3—28no—
198C22×D3—216no—
199C22×D3C2×D414yes—
200C22×D3C2414yes—
201C22×D3C2411yescharacteristic
202C22×D3C2411yescharacteristic
203C3×Q8—24no—
204C3×D4—28no—
205C3×D4—24no—
206C3×D4—28no—
207C2×C3×C4—28no—
208C2×C3×C4—24no—
209C2×C3×C4C2×D414yescomplemented
210C2×C3×C4C2412yes—
211C2×C3×C4C2414yes—
212C2×C3×C4C2411yescharacteristic
213C2×C3×C4C2412yes—
214C2×C3×C4C2411yescharacteristic
215#67—28no—
216#67—28no—
217#67—28no—
218#67—216no—
219C2×Dic3—28no—
220C2×Dic3—24no—
221C2×Dic3C2×D414yescomplemented
222C2×Dic3C2412yes—
223C2×Dic3C2414yes—
224C2×Dic3C2411yescharacteristic
225C2×Dic3C2411yescharacteristic
226C2×Dic3C2412yes—
227D12—28no—
228D12—24no—
229D12—28no—
230C4×D3—28no—
231C4×D3—24no—
232C4×D3—28no—
233C4×D3—24no—
234C4×D3—28no—
235C4×D3—24no—
236C4×D3C2×D414yes—
237C4×D3C2×D414yes—
238C4×D3C2×D414yescomplemented
239C4×D3C2×D414yescomplemented
240C4×D3#4118yescomplemented
241Dic6—24no—
242Dic6—28no—
243C24—31no—
244C24—34no—
245#41—28no—
246#41—616no—
247#41—616no—
248#41—68no—
249#41—68no—
250#41—68no—
251C2×Q8—34no—
252C2×Q8—32no—
253C2×Q8—68no—
254C2×Q8C22×D312yes—
255C2×D4—38no—
256C2×D4—34no—
257C2×D4—34no—
258C2×D4—34no—
259C2×D4—34no—
260C2×D4—34no—
261C2×D4—32no—
262C2×D4—68no—
263C2×D4—616no—
264C2×D4—616no—
265C2×D4C22×D314yes—
266C2×D4C22×D314yes—
267C2×D4C22×D312yes—
268C22×C4—31no—
269C22×C4—38no—
270C22×C4—32no—
271C22×C4—31no—
272C22×C4—31no—
273C22×C4—31no—
274C22×C4—31no—
275C22×C4—32no—
276C22×C4—34no—
277C22×C4—32no—
278C22×C4—32no—
279C22×C4—32no—
280C22×C4—34no—
281C22×C4—34no—
282C22×C4—34no—
283C22×C4—616no—
284C22×C4—68no—
285C22×C4C22×D312yes—
286C22×C4C22×D314yes—
287C22×C4C22×D311yescharacteristic
288C4⋊C4—38no—
289C4⋊C4—34no—
290C4⋊C4C22×D314yes—
291C22⋊C4—38no—
292C22⋊C4—38no—
293C22⋊C4—38no—
294C22⋊C4C22×D318yes—
295C42—32no—
296C42—32no—
297C42—32no—
298C42—31no—
299C42—31no—
300C42—32no—
301C42—32no—
302C42C22×D311yescharacteristic
303C42C22×D311yescharacteristic
304C42C22×D312yes—
305C22×C3—22no—
306C22×C3—24no—
307C22×C3—28no—
308C22×C3C22×D412yes—
309C22×C3C2511yescharacteristic
310C2×D3—22no—
311C2×D3—28no—
312C2×D3—24no—
313C2×D3—28no—
314C2×D3—416no—
315C2×D3C22×D412yes—
316C2×D3C22×D412yes—
317C2×D3C2×#4114yes—
318C3×C4—24no—
319C3×C4—22no—
320C3×C4C22×D412yes—
321C3×C4C22×D412yes—
322C3×C4C2×#4114yescomplemented
323Dic3—24no—
324Dic3—22no—
325Dic3C22×D412yes—
326Dic3C22×D412yes—
327Dic3C2×#4114yescomplemented
328C23—31no—
329C23—34no—
330C23—31no—
331C23—34no—
332C23—64no—
333C23—68no—
334C23—616no—
335C23C23×D314yes—
336C23C23×D311yescharacteristic
337Q8—24no—
338Q8—68no—
339Q8—64no—
340D4—28no—
341D4—24no—
342D4—28no—
343D4—68no—
344D4—68no—
345D4—616no—
346D4—68no—
347D4—68no—
348D4—64no—
349D4—68no—
350C2×C4—28no—
351C2×C4—24no—
352C2×C4—34no—
353C2×C4—32no—
354C2×C4—31no—
355C2×C4—31no—
356C2×C4—34no—
357C2×C4—34no—
358C2×C4—34no—
359C2×C4—34no—
360C2×C4—38no—
361C2×C4—32no—
362C2×C4—34no—
363C2×C4—68no—
364C2×C4—64no—
365C2×C4—68no—
366C2×C4—64no—
367C2×C4—68no—
368C2×C4—64no—
369C2×C4—68no—
370C2×C4—64no—
371C2×C4D3×D414yescomplemented
372C2×C4C23×D312yes—
373C2×C4C23×D314yes—
374C2×C4C23×D311yescharacteristic
375C2×C4C23×D312yes—
376C2×C4C23×D311yescharacteristic
377C2×C3—22no—
378C2×C3—44no—
379C2×C3C23×D411yescharacteristic
380C2×C3C22×#4112yes—
381D3—22no—
382D3—44no—
383D3#53214yesdirect product factor
384C22—22no—
385C22—24no—
386C22—28no—
387C22—32no—
388C22—34no—
389C22—32no—
390C22—68no—
391C22—62no—
392C22—64no—
393C22—68no—
394C22—1216no—
395C22C2×D3×D412yes—
396C22C24×D311yescharacteristic
397C4—24no—
398C4—22no—
399C4—32no—
400C4—32no—
401C4—34no—
402C4—64no—
403C4—62no—
404C4C2×D3×D412yes—
405C4C2×D3×D412yes—
406C4D3×#4114yescomplemented
407C3C2×#53211yescharacteristic, complemented, Sylow
408C2—22no—
409C2—34no—
410C2—44no—
411C2—62no—
412C2—124no—
413C2C22×D3×D411yescharacteristic
414C2C2×D3×#4112yes—
subgroupG/H
centerC2×C4C23×D3
commutator, socle, cosocleC22×C3C25
FrattiniC22C24×D3
FittingC3×#532C2
hypercenter#532D3
hypocenterC3C2×#532
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C2×C4 ◁ #532

Complements

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

NH ≅ G/Ntype
1. C2×D3×#41C2semidirect
2. C3×#532C2semidirect
3. #5832C2semidirect
4. #5725C2semidirect
5. D3×C4⋊Q8C2semidirect
6. #5716C2semidirect
7. D3×#127C2semidirect
8. D3×#124C2semidirect
9. #5668C2semidirect
10. D3×#121C2semidirect
11. #5596C2semidirect
12. #5548C2semidirect
13. C4×D3×D4C2semidirect
14. #5477C2semidirect
15. C2×C42×D3C2semidirect
17. C2×C3×#41C22semidirect
19. C2×#239C22semidirect
21. C2×#237C22semidirect
22. C2×#237C22semidirect
26. C2×#235C22semidirect
27. C2×#235C22semidirect
31. C3×C4⋊Q8C22semidirect
32. C3×#127C22semidirect
33. C3×#124C22semidirect
34. C3×#121C22semidirect
35. C3×C4×D4C22semidirect
36. C2×C3×C42C22semidirect
37. #947C22semidirect
38. #944C22semidirect
39. #940C22semidirect
40. #940C22semidirect
41. #939C22semidirect
42. #938C22semidirect
43. #936C22semidirect
44. D4×Dic3C22semidirect
45. #930C22semidirect
46. C4×#67C22semidirect
47. C2×C4×Dic3C22semidirect
48. C2×C4×Dic3C22semidirect
49. #895C22semidirect
50. #893C22semidirect
52. #888C22semidirect
53. #885C22semidirect
54. #884C22semidirect
55. #67⋊C4C22semidirect
57. #875C22semidirect
58. #874C22semidirect
59. C4×D12C22semidirect
63. C42×D3C22semidirect
64. C42×D3C22semidirect
65. C42×D3C22semidirect
66. #869C22semidirect
75. #532D3direct (N × H)
113. C2×C4×D3D4semidirect
150. C2×#41C2×D3semidirect
161. C4⋊Q8C2×D3semidirect
165. #127C2×D3semidirect
170. #124C2×D3semidirect
176. #121C2×D3semidirect
182. C4×D4C2×D3semidirect
193. C2×C42C2×D3semidirect
209. C2×C3×C4C2×D4semidirect
221. C2×Dic3C2×D4semidirect
238. C4×D3C2×D4semidirect
239. C4×D3C2×D4semidirect
240. C4×D3#41semidirect
322. C3×C4C2×#41semidirect
327. Dic3C2×#41semidirect
371. C2×C4D3×D4semidirect
383. D3#532direct (N × H)
406. C4D3×#41semidirect
407. C3C2×#532semidirect

Maximal subgroups

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

subgroupindex
C2×D3×#412
C3×#5322
#58322
#57252
D3×C4⋊Q82
#57162
D3×#1272
D3×#1242
#56682
D3×#1212
#55962
#55482
C4×D3×D42
#54772
C2×C42×D32
C2×#5323