Finite Group Databasebeta

← D3×#447 #80000

Subgroups — D3×#447 #80000

Order 384.

1048 conjugacy classes of subgroups; only the 155 normal subgroups are shown.

normal subgroups only

This group has 1048 conjugacy classes of subgroups — too many to draw. Only its 155 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
1C22×D3×D4C211yesmaximal, characteristic, complemented
2C2×D3×D8C212yesmaximal, complemented
3D3×#121C211yesmaximal, characteristic, complemented
4C3×#447C211yesmaximal, characteristic, complemented
5#5217C211yesmaximal, characteristic, complemented
6#5156C212yesmaximal, complemented
7#5036C211yesmaximal, characteristic, complemented
8#4773C212yesmaximal, complemented
9D3×#102C212yesmaximal, complemented
10#4732C211yesmaximal, characteristic, complemented
11D3×C22⋊C8C211yesmaximal, characteristic, complemented
12C2×#447—31nomaximal, Sylow
13C24×D3—21no—
14C22×C3×D4C2211yescharacteristic, complemented
15C22×#67—21no—
16C2×D3×D4—28no—
17C2×D3×D4—21no—
18C2×D3×D4—21no—
19C2×D3×D4—21no—
20C2×D3×D4C2212yes—
21C2×D3×D4C2212yescomplemented
22C2×D3×D4C2211yescharacteristic, complemented
23C22×D12C2211yescharacteristic, complemented
24C22×C4×D3C2211yescharacteristic
25C2×C3×D8C2212yescomplemented
26C3×#121C2211yescharacteristic, complemented
27#939—21no—
28#938C2211yescharacteristic, complemented
29C2×#213C2212yescomplemented
30C2×#213C2212yescomplemented
31#930C2211yescharacteristic, complemented
32D3×D8—28no—
33C2×D24C2212yescomplemented
34C2×D3×C8C2212yescomplemented
35#895C2211yescharacteristic, complemented
36D3×C4⋊C4C2211yescharacteristic, complemented
37#884—21no—
38D3×C22⋊C4—21no—
39C3×#102C2212yescomplemented
40C3×C22⋊C8C2211yescharacteristic, complemented
41#832C2212yescomplemented
42#830C2211yescharacteristic, complemented
43#821C2212yescomplemented
44(C2×D3)⋊C8C2212yescomplemented
45#809C2212yescomplemented
46C23×D4—31no—
47C22×D8—32no—
48C2×#121—31no—
49#447—31no—
50#447—32no—
51#447—31no—
52#447—32no—
53#447—31no—
54#447D311yescharacteristic, direct product factor
55C2×#102—32no—
56C2×C22⋊C8—31no—
57C24×C3—21no—
58C23×D3—28no—
59C23×D3—21no—
60C23×D3—22no—
61C23×D3—22no—
62C23×D3—21no—
63C23×D3—44no—
64C23×D3—44no—
65C23×D3D411yescharacteristic
66C2×C3×D4—24no—
67C2×C3×D4—21no—
68C2×C3×D4—21no—
69C2×C3×D4C2312yes—
70C2×C3×D4C2311yescharacteristic, complemented
71C22×C3×C4C2311yescharacteristic
72C2×#67—28no—
73C2×#67—21no—
74C2×#67—21no—
75C2×#67—22no—
76C2×#67—22no—
77C2×#67—21no—
78C22×Dic3D411yescharacteristic
79D3×D4—28no—
80D3×D4—28no—
81D3×D4—24no—
82D3×D4—24no—
83D3×D4—24no—
84D3×D4—24no—
85D3×D4—44no—
86D3×D4D418yescomplemented
87C2×D12—21no—
88C2×D12—24no—
89C2×D12—21no—
90C2×D12C2312yes—
91C2×D12C2311yescharacteristic, complemented
92C2×C4×D3—24no—
93C2×C4×D3—21no—
94C2×C4×D3D411yescharacteristic
95C2×C4×D3D411yescharacteristic
96C2×C4×D3C2311yescharacteristic
97C2×C4×D3C2311yescharacteristic
98C3×D8—24no—
99C2×C3×C8C2312yescomplemented
100C3×C4⋊C4C2311yescharacteristic, complemented
101C3×C22⋊C4—21no—
102#217—21no—
103#213—24no—
104#213—24no—
105(C2×D3)⋊C4—21no—
106(C2×D3)⋊C4—21no—
107C4⋊Dic3C2311yescharacteristic, complemented
108Dic3⋊C4—21no—
109C2×C3⋊C8C2312yescomplemented
110D24—24no—
111D3×C8—24no—
112C25—61no—
113C22×D4—32no—
114C22×D4—32no—
115C22×D4—31no—
116C22×D4—31no—
117C22×D4—61no—
118C22×D4—61no—
119C22×D4—61no—
120C22×D4—68no—
121C22×D4—61no—
122C22×D4C2×D311yescharacteristic, complemented
123C23×C4—31no—
124C2×D8—32no—
125C2×D8—32no—
126C2×D8—32no—
127C2×D8—68no—
128C2×D8C2×D312yescomplemented
129C22×C8—32no—
130#121—31no—
131#121—31no—
132#121—31no—
133#121—61no—
134#121—61no—
135#121C2×D311yescharacteristic, complemented
136C2×C4⋊C4—31no—
137C2×C22⋊C4—61no—
138#102—32no—
139#102—32no—
140#102—32no—
141#102C2×D312yescomplemented
142C22⋊C8—31no—
143C22⋊C8—32no—
144C22⋊C8C2×D311yescharacteristic, complemented
145C23×C3—24no—
146C23×C3—22no—
147C23×C3—21no—
148C23×C3—42no—
149C23×C3—42no—
150C23×C3C2×D411yescharacteristic
151C22×D3—22no—
152C22×D3—22no—
153C22×D3—24no—
154C22×D3—28no—
155C22×D3—22no—
156C22×D3—28no—
157C22×D3—21no—
158C22×D3—44no—
159C22×D3—432no—
160C22×D3—42no—
161C22×D3—42no—
162C22×D3—44no—
163C22×D3—44no—
164C22×D3—44no—
165C22×D3—42no—
166C22×D3—42no—
167C22×D3—42no—
168C22×D3D814yescomplemented
169C22×D3C2×D411yescharacteristic
170C22×D3C2×D411yescharacteristic
171C3×D4—24no—
172C3×D4—22no—
173C3×D4—22no—
174C3×D4—42no—
175C3×D4C2×D414yescomplemented
176C2×C3×C4—22no—
177C2×C3×C4—21no—
178C2×C3×C4C2×D411yescharacteristic
179C2×C3×C4C2411yescharacteristic
180#67—28no—
181#67—28no—
182#67—42no—
183#67—42no—
184#67—42no—
185C2×Dic3—22no—
186C2×Dic3—21no—
187C2×Dic3C2×D411yescharacteristic
188C2×Dic3C2×D411yescharacteristic
189D12—24no—
190D12—22no—
191D12—22no—
192D12—42no—
193D12C2×D414yescomplemented
194C4×D3—22no—
195C4×D3—22no—
196C4×D3—22no—
197C4×D3—42no—
198C4×D3C2×D414yes—
199C3×C8—22no—
200C3⋊C8—22no—
201C24—21no—
202C24—31no—
203C24—62no—
204C24—62no—
205C24—61no—
206C24—68no—
207C24—61no—
208C24—124no—
209C24—124no—
210C2×D4—24no—
211C2×D4—21no—
212C2×D4—21no—
213C2×D4—38no—
214C2×D4—32no—
215C2×D4—31no—
216C2×D4—64no—
217C2×D4—61no—
218C2×D4—64no—
219C2×D4—64no—
220C2×D4—62no—
221C2×D4—62no—
222C2×D4—61no—
223C2×D4—64no—
224C2×D4—68no—
225C2×D4—68no—
226C2×D4—68no—
227C2×D4—64no—
228C2×D4—61no—
229C2×D4—61no—
230C2×D4—61no—
231C2×D4—124no—
232C2×D4C22×D312yes—
233C2×D4C22×D311yescharacteristic, complemented
234C22×C4—31no—
235C22×C4—31no—
236C22×C4—31no—
237C22×C4—31no—
238C22×C4—31no—
239C22×C4—64no—
240C22×C4—61no—
241C22×C4C22×D311yescharacteristic
242D8—24no—
243D8—64no—
244D8—64no—
245D8—64no—
246C2×C8—32no—
247C2×C8—64no—
248C2×C8C22×D312yescomplemented
249C4⋊C4—31no—
250C4⋊C4—61no—
251C4⋊C4C22×D311yescharacteristic, complemented
252C22⋊C4—21no—
253C22⋊C4—61no—
254C22⋊C4—61no—
255C22⋊C4—61no—
256C22×C3—21no—
257C22×C3—21no—
258C22×C3—24no—
259C22×C3—48no—
260C22×C3—42no—
261C22×C3—42no—
262C22×C3—41no—
263C22×C3—41no—
264C22×C3—41no—
265C22×C3C2×D812yescomplemented
266C22×C3C22×D411yescharacteristic
267C2×D3—21no—
268C2×D3—21no—
269C2×D3—28no—
270C2×D3—24no—
271C2×D3—416no—
272C2×D3—48no—
273C2×D3—42no—
274C2×D3—42no—
275C2×D3—416no—
276C2×D3—41no—
277C2×D3—41no—
278C2×D3—41no—
279C2×D3—84no—
280C2×D3#12012yes—
281C2×D3C2×D812yes—
282C2×D3C2×D812yescomplemented
283C2×D3AGL(1,ℤ/8)12yes—
284C3×C4—21no—
285C3×C4—41no—
286C3×C4C22×D412yes—
287Dic3—21no—
288Dic3—41no—
289Dic3#12012yes—
290C23—24no—
291C23—22no—
292C23—21no—
293C23—31no—
294C23—34no—
295C23—31no—
296C23—42no—
297C23—42no—
298C23—62no—
299C23—62no—
300C23—68no—
301C23—64no—
302C23—68no—
303C23—62no—
304C23—61no—
305C23—122no—
306C23—124no—
307C23—124no—
308C23—124no—
309C23—122no—
310C23—122no—
311C23—122no—
312C23—1232no—
313C23—124no—
314C23—122no—
315C23D3×D411yescharacteristic
316D4—24no—
317D4—22no—
318D4—22no—
319D4—34no—
320D4—42no—
321D4—64no—
322D4—68no—
323D4—68no—
324D4—62no—
325D4—62no—
326D4—122no—
327D4—122no—
328D4—122no—
329D4—122no—
330D4D3×D414yescomplemented
331C2×C4—22no—
332C2×C4—21no—
333C2×C4—31no—
334C2×C4—34no—
335C2×C4—31no—
336C2×C4—62no—
337C2×C4—62no—
338C2×C4—62no—
339C2×C4—62no—
340C2×C4—61no—
341C2×C4—122no—
342C2×C4D3×D411yescharacteristic
343C2×C4C23×D311yescharacteristic
344C8—22no—
345C8—62no—
346C2×C3—22no—
347C2×C3—44no—
348C2×C3—81no—
349C2×C3C2×#12011yescharacteristic
350C2×C3C22×D811yescharacteristic
351C2×C3C2×AGL(1,ℤ/8)11yescharacteristic
352D3—22no—
353D3—44no—
354D3—81no—
355D3#44714yesdirect product factor
356C22—21no—
357C22—21no—
358C22—24no—
359C22—32no—
360C22—32no—
361C22—32no—
362C22—32no—
363C22—48no—
364C22—42no—
365C22—42no—
366C22—41no—
367C22—41no—
368C22—41no—
369C22—68no—
370C22—61no—
371C22—61no—
372C22—64no—
373C22—128no—
374C22—1216no—
375C22—1216no—
376C22—122no—
377C22—122no—
378C22—121no—
379C22—121no—
380C22—121no—
381C22—244no—
382C22D3×D812yescomplemented
383C22C2×D3×D411yescharacteristic
384C4—21no—
385C4—32no—
386C4—41no—
387C4—61no—
388C4—121no—
389C4C2×D3×D412yes—
390C3C2×#44711yescharacteristic, complemented, Sylow
391C2—22no—
392C2—34no—
393C2—44no—
394C2—62no—
395C2—81no—
396C2—124no—
397C2—241no—
398C2D3×#12011yescharacteristic
399C2C2×D3×D811yescharacteristic
400C2D3×AGL(1,ℤ/8)11yescharacteristic
subgroupG/H
centerC22C2×D3×D4
commutator, cosocleC2×C3×C4C24
FrattiniC2×C4C23×D3
FittingC3×#447C2
socleC22×C3C22×D4
hypercenter#447D3
hypocenterC3C2×#447
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C22×C4 ◁ #447

Complements

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

NH ≅ G/Ntype
1. C22×D3×D4C2semidirect
2. C2×D3×D8C2semidirect
3. D3×#121C2semidirect
4. C3×#447C2semidirect
5. #5217C2semidirect
6. #5156C2semidirect
7. #5036C2semidirect
8. #4773C2semidirect
9. D3×#102C2semidirect
10. #4732C2semidirect
11. D3×C22⋊C8C2semidirect
14. C22×C3×D4C22semidirect
21. C2×D3×D4C22semidirect
22. C2×D3×D4C22semidirect
23. C22×D12C22semidirect
25. C2×C3×D8C22semidirect
26. C3×#121C22semidirect
28. #938C22semidirect
29. C2×#213C22semidirect
30. C2×#213C22semidirect
31. #930C22semidirect
33. C2×D24C22semidirect
34. C2×D3×C8C22semidirect
35. #895C22semidirect
36. D3×C4⋊C4C22semidirect
39. C3×#102C22semidirect
40. C3×C22⋊C8C22semidirect
41. #832C22semidirect
42. #830C22semidirect
43. #821C22semidirect
44. (C2×D3)⋊C8C22semidirect
45. #809C22semidirect
54. #447D3direct (N × H)
70. C2×C3×D4C23semidirect
86. D3×D4D4semidirect
91. C2×D12C23semidirect
99. C2×C3×C8C23semidirect
100. C3×C4⋊C4C23semidirect
107. C4⋊Dic3C23semidirect
109. C2×C3⋊C8C23semidirect
122. C22×D4C2×D3semidirect
128. C2×D8C2×D3semidirect
135. #121C2×D3semidirect
141. #102C2×D3semidirect
144. C22⋊C8C2×D3semidirect
168. C22×D3D8semidirect
175. C3×D4C2×D4semidirect
193. D12C2×D4semidirect
233. C2×D4C22×D3semidirect
248. C2×C8C22×D3semidirect
251. C4⋊C4C22×D3semidirect
265. C22×C3C2×D8semidirect
282. C2×D3C2×D8semidirect
330. D4D3×D4semidirect
355. D3#447direct (N × H)
382. C22D3×D8semidirect
390. C3C2×#447semidirect

Maximal subgroups

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

subgroupindex
C22×D3×D42
C2×D3×D82
D3×#1212
C3×#4472
#52172
#51562
#50362
#47732
D3×#1022
#47322
D3×C22⋊C82
C2×#4473