Finite Group Databasebeta

← D3×#534 #86307

Subgroups — D3×#534 #86307

Order 384.

1984 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D3×D4C212yesmaximal, complemented
2C3×#534C211yesmaximal, characteristic, complemented
3#5804C212yesmaximal, complemented
4#5653C214yesmaximal, complemented
5D3×#123C214yesmaximal, complemented
6#5605C214yesmaximal, complemented
7D3×#121C214yesmaximal, complemented
8#5589C214yesmaximal, complemented
9D3×#120C214yesmaximal, complemented
10#5493C211yesmaximal, characteristic, complemented
11C2×D3×C22⋊C4C211yesmaximal, characteristic, complemented
12C2×#534—31nomaximal, Sylow
13C24×D3C2211yescharacteristic
14C24×D3C2212yescomplemented
15C22×C3×D4C2212yescomplemented
16C22×#67C2212yescomplemented
17C22×#67C2212yescomplemented
18C2×D3×D4—216no—
19C2×D3×D4C2214yes—
20C2×D3×D4C2214yescomplemented
21C2×D3×D4C2214yescomplemented
22C2×D3×D4C2214yescomplemented
23C2×D3×D4C2214yescomplemented
24C22×D12C2212yescomplemented
25C22×C4×D3C2212yescomplemented
26C22×C4×D3C2212yescomplemented
27C3×#123C2214yescomplemented
28C3×#121C2214yescomplemented
29C3×#120C2214yescomplemented
30C2×C3×C22⋊C4C2211yescharacteristic, complemented
31#953C2214yescomplemented
32C2×#217C2211yescharacteristic, complemented
33#939C2218yescomplemented
34#938C2214yescomplemented
35#937C2218yescomplemented
36#937C2214yescomplemented
37#935C2214yescomplemented
38#930C2214yescomplemented
39#929C2214yescomplemented
40C2×(C2×D3)⋊C4C2212yescomplemented
41#895C2214yescomplemented
42#894C2218yescomplemented
43D3×C4⋊C4C2214yescomplemented
44#886C2214yescomplemented
45#884C2218yescomplemented
46#883C2218yescomplemented
47#882C2218yescomplemented
48#882C2214yescomplemented
49D3×C22⋊C4C2214yescomplemented
50D3×C22⋊C4C2218yescomplemented
51D3×C22⋊C4C2214yescomplemented
52C23×D4—32no—
53#534—32no—
54#534—34no—
55#534—34no—
56#534—34no—
57#534—31no—
58#534D311yescharacteristic, direct product factor
59C2×#123—34no—
60C2×#121—34no—
61C2×#120—34no—
62C22×C22⋊C4—31no—
63C24×C3C2311yescharacteristic
64C24×C3C2312yescomplemented
65C23×D3—28no—
66C23×D3—44no—
67C23×D3—48no—
68C23×D3D418yescomplemented
69C23×D3C2314yes—
70C23×D3C2312yes—
71C23×D3C2311yescharacteristic
72C23×D3C2312yes—
73C23×D3C2311yescharacteristic
74C23×D3C2312yescomplemented
75C23×D3C2314yescomplemented
76C2×C3×D4—28no—
77C2×C3×D4C2314yes—
78C2×C3×D4C2314yescomplemented
79C2×C3×D4C2314yescomplemented
80C22×C3×C4C2312yescomplemented
81C22×C3×C4C2312yescomplemented
82C2×#67—28no—
83C2×#67—28no—
84C2×#67C2314yes—
85C2×#67C2314yes—
86C2×#67C2314yescomplemented
87C2×#67C2314yescomplemented
88C2×#67C2318yescomplemented
89C22×Dic3C2312yescomplemented
90C22×Dic3C2312yescomplemented
91D3×D4—216no—
92D3×D4—216no—
93D3×D4—216no—
94D3×D4—216no—
95D3×D4—48no—
96C2×D12—28no—
97C2×D12C2314yes—
98C2×D12C2314yescomplemented
99C2×D12C2314yescomplemented
100C2×C4×D3—28no—
101C2×C4×D3—44no—
102C2×C4×D3C2314yes—
103C2×C4×D3C2314yes—
104C2×C4×D3C2314yescomplemented
105C2×C4×D3C2314yescomplemented
106C3×C4⋊C4C2314yescomplemented
107C3×C22⋊C4C2314yescomplemented
108C3×C22⋊C4C2318yescomplemented
109#217C2314yescomplemented
110#217C2318yescomplemented
111(C2×D3)⋊C4C2318yescomplemented
112(C2×D3)⋊C4C2318yescomplemented
113(C2×D3)⋊C4C2318yescomplemented
114C4⋊Dic3C2314yescomplemented
115Dic3⋊C4C2318yescomplemented
116C25—31no—
117C25—32no—
118C22×D4—32no—
119C22×D4—32no—
120C22×D4—34no—
121C22×D4—34no—
122C22×D4—34no—
123C22×D4—34no—
124C22×D4—34no—
125C22×D4—32no—
126C22×D4—616no—
127C22×D4C2×D312yescomplemented
128C23×C4—32no—
129C23×C4—32no—
130#123—34no—
131#123—34no—
132#123—38no—
133#123—38no—
134#123—34no—
135#123C2×D314yescomplemented
136#121—34no—
137#121—38no—
138#121—34no—
139#121—34no—
140#121—38no—
141#121C2×D314yescomplemented
142#120—34no—
143#120—34no—
144#120—38no—
145#120—38no—
146#120—34no—
147#120C2×D314yescomplemented
148C2×C4⋊C4—34no—
149C2×C22⋊C4—31no—
150C2×C22⋊C4—32no—
151C2×C22⋊C4—34no—
152C2×C22⋊C4—34no—
153C2×C22⋊C4—38no—
154C2×C22⋊C4C2×D311yescharacteristic, complemented
155C23×C3—24no—
156C23×C3—42no—
157C23×C3—44no—
158C23×C3C2×D414yescomplemented
159C23×C3C2414yes—
160C23×C3C2412yes—
161C23×C3C2411yescharacteristic
162C22×D3—24no—
163C22×D3—28no—
164C22×D3—24no—
165C22×D3—28no—
166C22×D3—28no—
167C22×D3—216no—
168C22×D3—416no—
169C22×D3—44no—
170C22×D3—42no—
171C22×D3—48no—
172C22×D3—44no—
173C22×D3—432no—
174C22×D3C2×D418yes—
175C22×D3C2×D414yes—
176C22×D3C2×D418yescomplemented
177C22×D3C2×D414yescomplemented
178C22×D3C2414yes—
179C22×D3C2412yes—
180C22×D3C2411yescharacteristic
181C22×D3C2411yescharacteristic
182C3×D4—28no—
183C3×D4—28no—
184C3×D4—44no—
185C2×C3×C4—24no—
186C2×C3×C4—42no—
187C2×C3×C4C2414yes—
188C2×C3×C4C2414yes—
189#67—28no—
190#67—28no—
191#67—28no—
192#67—28no—
193#67—48no—
194C2×Dic3—24no—
195C2×Dic3—42no—
196C2×Dic3C2414yes—
197C2×Dic3C2414yes—
198D12—28no—
199D12—28no—
200D12—44no—
201C4×D3—28no—
202C4×D3—28no—
203C4×D3—28no—
204C4×D3—44no—
205C24—32no—
206C24—31no—
207C24—38no—
208C24—31no—
209C24—32no—
210C24—34no—
211C24—34no—
212C24—32no—
213C24—68no—
214C24—124no—
215C24—128no—
216C24C22×D311yescharacteristic
217C24C22×D312yescomplemented
218C2×D4—28no—
219C2×D4—34no—
220C2×D4—34no—
221C2×D4—34no—
222C2×D4—34no—
223C2×D4—38no—
224C2×D4—34no—
225C2×D4—34no—
226C2×D4—34no—
227C2×D4—68no—
228C2×D4—616no—
229C2×D4—616no—
230C2×D4—616no—
231C2×D4—616no—
232C2×D4—68no—
233C2×D4—68no—
234C2×D4—128no—
235C2×D4C22×D314yes—
236C2×D4C22×D314yescomplemented
237C2×D4C22×D314yescomplemented
238C22×C4—32no—
239C22×C4—32no—
240C22×C4—34no—
241C22×C4—34no—
242C22×C4—34no—
243C22×C4—34no—
244C22×C4—68no—
245C22×C4—124no—
246C22×C4C22×D312yescomplemented
247C22×C4C22×D312yescomplemented
248C4⋊C4—38no—
249C4⋊C4—34no—
250C4⋊C4C22×D314yescomplemented
251C22⋊C4—34no—
252C22⋊C4—38no—
253C22⋊C4—38no—
254C22⋊C4—38no—
255C22⋊C4—38no—
256C22⋊C4C22×D314yescomplemented
257C22⋊C4C22×D318yescomplemented
258C22×C3—22no—
259C22×C3—24no—
260C22×C3—24no—
261C22×C3—28no—
262C22×C3—44no—
263C22×C3—48no—
264C22×C3C22×D414yes—
265C22×C3C22×D412yes—
266C22×C3C2511yescharacteristic
267C2×D3—22no—
268C2×D3—24no—
269C2×D3—216no—
270C2×D3—28no—
271C2×D3—24no—
272C2×D3—28no—
273C2×D3—44no—
274C2×D3—48no—
275C2×D3—416no—
276C2×D3—48no—
277C2×D3—416no—
278C2×D3C22×D414yes—
279C2×D3C22×D412yes—
280C2×D3C22×D412yes—
281C2×D3H(5,𝔽2)14yes—
282C3×C4—24no—
283C3×C4—24no—
284Dic3—24no—
285Dic3—24no—
286C23—24no—
287C23—31no—
288C23—38no—
289C23—34no—
290C23—32no—
291C23—31no—
292C23—34no—
293C23—38no—
294C23—34no—
295C23—42no—
296C23—44no—
297C23—64no—
298C23—68no—
299C23—68no—
300C23—68no—
301C23—616no—
302C23—64no—
303C23—122no—
304C23—124no—
305C23—124no—
306C23—128no—
307C23—1216no—
308C23—1232no—
309C23D3×D414yescomplemented
310C23C23×D314yes—
311C23C23×D312yes—
312C23C23×D311yescharacteristic
313D4—28no—
314D4—28no—
315D4—44no—
316D4—68no—
317D4—68no—
318D4—68no—
319D4—68no—
320D4—68no—
321D4—68no—
322D4—124no—
323D4—128no—
324C2×C4—24no—
325C2×C4—34no—
326C2×C4—34no—
327C2×C4—42no—
328C2×C4—68no—
329C2×C4—68no—
330C2×C4—68no—
331C2×C4—64no—
332C2×C4—124no—
333C2×C4—122no—
334C2×C4C23×D314yes—
335C2×C4C23×D314yes—
336C2×C3—24no—
337C2×C3—22no—
338C2×C3—44no—
339C2×C3C23×D411yescharacteristic
340C2×C3C2×H(5,𝔽2)12yes—
341D3—24no—
342D3—22no—
343D3—44no—
344D3#53414yesdirect product factor
345C22—22no—
346C22—24no—
347C22—24no—
348C22—28no—
349C22—32no—
350C22—34no—
351C22—34no—
352C22—32no—
353C22—44no—
354C22—48no—
355C22—616no—
356C22—68no—
357C22—62no—
358C22—64no—
359C22—64no—
360C22—68no—
361C22—128no—
362C22—124no—
363C22—128no—
364C22—1216no—
365C22—1216no—
366C22C2×D3×D414yes—
367C22C2×D3×D412yes—
368C22C24×D311yescharacteristic
369C4—24no—
370C4—24no—
371C4—64no—
372C4—64no—
373C3C2×#53411yescharacteristic, complemented, Sylow
374C2—24no—
375C2—22no—
376C2—34no—
377C2—44no—
378C2—64no—
379C2—62no—
380C2—124no—
381C2C22×D3×D411yescharacteristic
382C2D3×H(5,𝔽2)12yes—
subgroupG/H
center, FrattiniC22C24×D3
commutator, socle, cosocleC22×C3C25
FittingC3×#534C2
hypercenter#534D3
hypocenterC3C2×#534
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C22 ◁ #534

Complements

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

NH ≅ G/Ntype
1. C22×D3×D4C2semidirect
2. C3×#534C2semidirect
3. #5804C2semidirect
4. #5653C2semidirect
5. D3×#123C2semidirect
6. #5605C2semidirect
7. D3×#121C2semidirect
8. #5589C2semidirect
9. D3×#120C2semidirect
10. #5493C2semidirect
11. C2×D3×C22⋊C4C2semidirect
14. C24×D3C22semidirect
15. C22×C3×D4C22semidirect
16. C22×#67C22semidirect
17. C22×#67C22semidirect
20. C2×D3×D4C22semidirect
21. C2×D3×D4C22semidirect
22. C2×D3×D4C22semidirect
23. C2×D3×D4C22semidirect
24. C22×D12C22semidirect
25. C22×C4×D3C22semidirect
26. C22×C4×D3C22semidirect
27. C3×#123C22semidirect
28. C3×#121C22semidirect
29. C3×#120C22semidirect
30. C2×C3×C22⋊C4C22semidirect
31. #953C22semidirect
32. C2×#217C22semidirect
33. #939C22semidirect
34. #938C22semidirect
35. #937C22semidirect
36. #937C22semidirect
37. #935C22semidirect
38. #930C22semidirect
39. #929C22semidirect
40. C2×(C2×D3)⋊C4C22semidirect
41. #895C22semidirect
42. #894C22semidirect
43. D3×C4⋊C4C22semidirect
44. #886C22semidirect
45. #884C22semidirect
46. #883C22semidirect
47. #882C22semidirect
48. #882C22semidirect
49. D3×C22⋊C4C22semidirect
50. D3×C22⋊C4C22semidirect
51. D3×C22⋊C4C22semidirect
58. #534D3direct (N × H)
64. C24×C3C23semidirect
68. C23×D3D4semidirect
74. C23×D3C23semidirect
75. C23×D3C23semidirect
78. C2×C3×D4C23semidirect
79. C2×C3×D4C23semidirect
80. C22×C3×C4C23semidirect
81. C22×C3×C4C23semidirect
86. C2×#67C23semidirect
87. C2×#67C23semidirect
88. C2×#67C23semidirect
89. C22×Dic3C23semidirect
90. C22×Dic3C23semidirect
98. C2×D12C23semidirect
99. C2×D12C23semidirect
104. C2×C4×D3C23semidirect
105. C2×C4×D3C23semidirect
106. C3×C4⋊C4C23semidirect
107. C3×C22⋊C4C23semidirect
108. C3×C22⋊C4C23semidirect
109. #217C23semidirect
110. #217C23semidirect
111. (C2×D3)⋊C4C23semidirect
112. (C2×D3)⋊C4C23semidirect
113. (C2×D3)⋊C4C23semidirect
114. C4⋊Dic3C23semidirect
115. Dic3⋊C4C23semidirect
127. C22×D4C2×D3semidirect
135. #123C2×D3semidirect
141. #121C2×D3semidirect
147. #120C2×D3semidirect
154. C2×C22⋊C4C2×D3semidirect
158. C23×C3C2×D4semidirect
176. C22×D3C2×D4semidirect
177. C22×D3C2×D4semidirect
217. C24C22×D3semidirect
236. C2×D4C22×D3semidirect
237. C2×D4C22×D3semidirect
246. C22×C4C22×D3semidirect
247. C22×C4C22×D3semidirect
250. C4⋊C4C22×D3semidirect
256. C22⋊C4C22×D3semidirect
257. C22⋊C4C22×D3semidirect
309. C23D3×D4semidirect
344. D3#534direct (N × H)
373. C3C2×#534semidirect

Maximal subgroups

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

subgroupindex
C22×D3×D42
C3×#5342
#58042
#56532
D3×#1232
#56052
D3×#1212
#55892
D3×#1202
#54932
C2×D3×C22⋊C42
C2×#5343