Finite Group Databasebeta

← #447×D43 #19143768

Subgroups — #447×D43 #19143768

Order 5504.

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×D4×D43C211yesmaximal, characteristic, complemented
2C2×D8×D43C212yesmaximal, complemented
3#121×D43C211yesmaximal, characteristic, complemented
4#14583035C211yesmaximal, characteristic, complemented
5#14583034C212yesmaximal, complemented
6#14583033C211yesmaximal, characteristic, complemented
7#14583032C211yesmaximal, characteristic, complemented
8#14583031C212yesmaximal, complemented
9#102×D43C212yesmaximal, complemented
10C22⋊C8×D43C211yesmaximal, characteristic, complemented
11C43×#447C211yesmaximal, characteristic, complemented
12C24×D43—21no—
13C22×D172C2211yescharacteristic, complemented
14C22×C22⋊D43—21no—
15C2×D4×D43—28no—
16C2×D4×D43—21no—
17C2×D4×D43—21no—
18C2×D4×D43—21no—
19C2×D4×D43C2212yes—
20C2×D4×D43C2212yescomplemented
21C2×D4×D43C2211yescharacteristic, complemented
22C22×C4×D43C2211yescharacteristic
23C2×D344C2212yescomplemented
24C2×#10621882C2212yescomplemented
25C2×#10621882C2212yescomplemented
26D8×D43—28no—
27C2×C8×D43C2212yescomplemented
28#13063300C2211yescharacteristic, complemented
29#13063299C2211yescharacteristic, complemented
30#13063298—21no—
31#13063297—21no—
32#13063296C2211yescharacteristic, complemented
33C4⋊C4×D43C2211yescharacteristic, complemented
34C22⋊C4×D43—21no—
35#13063247C2212yescomplemented
36#13063246C2212yescomplemented
37#13063245C2212yescomplemented
38C22⋊(C43⋊C8)C2211yescharacteristic, complemented
39(C2×D43)⋊C8C2212yescomplemented
40C22×D4×C43C2211yescharacteristic, complemented
41C2×D8×C43C2212yescomplemented
42#121×C43C2211yescharacteristic, complemented
43#102×C43C2212yescomplemented
44C22⋊C8×C43C2211yescharacteristic, complemented
45C24×C43—21no—
46C23×D43—28no—
47C23×D43—21no—
48C23×D43—22no—
49C23×D43—22no—
50C23×D43—21no—
51C23×D43—44no—
52C23×D43—44no—
53C23×D43D411yescharacteristic
54C2×D4×C43—24no—
55C2×D4×C43—21no—
56C2×D4×C43—21no—
57C2×D4×C43C2312yes—
58C2×D4×C43C2311yescharacteristic, complemented
59C22×C4×C43C2311yescharacteristic
60C2×C22⋊D43—28no—
61C2×C22⋊D43—22no—
62C2×C22⋊D43—22no—
63C2×C22⋊D43—21no—
64C2×C22⋊D43—21no—
65C2×C22⋊D43—21no—
66C22×Dic43D411yescharacteristic
67D4×D43—28no—
68D4×D43—28no—
69D4×D43—24no—
70D4×D43—24no—
71D4×D43—24no—
72D4×D43—24no—
73D4×D43—44no—
74D4×D43D418yescomplemented
75C2×D172—21no—
76C2×D172—24no—
77C2×D172—21no—
78C2×D172C2312yes—
79C2×D172C2311yescharacteristic, complemented
80C2×C4×D43—24no—
81C2×C4×D43—21no—
82C2×C4×D43D411yescharacteristic
83C2×C4×D43D411yescharacteristic
84C2×C4×D43C2311yescharacteristic
85C2×C4×D43C2311yescharacteristic
86D8×C43—24no—
87C2×C8×C43C2312yescomplemented
88C4⋊C4×C43C2311yescharacteristic, complemented
89C22⋊C4×C43—21no—
90C22⋊Dic43—21no—
91#10621882—24no—
92#10621882—24no—
93(C2×D43)⋊C4—21no—
94(C2×D43)⋊C4—21no—
95C4⋊Dic43C2311yescharacteristic, complemented
96Dic43⋊C4—21no—
97C2×C43⋊C8C2312yescomplemented
98D344—24no—
99C8×D43—24no—
100C23×C43—24no—
101C23×C43—22no—
102C23×C43—21no—
103C23×C43—42no—
104C23×C43—42no—
105C23×C43C2×D411yescharacteristic
106C22×D43—22no—
107C22×D43—22no—
108C22×D43—24no—
109C22×D43—28no—
110C22×D43—22no—
111C22×D43—28no—
112C22×D43—21no—
113C22×D43—44no—
114C22×D43—432no—
115C22×D43—42no—
116C22×D43—42no—
117C22×D43—44no—
118C22×D43—44no—
119C22×D43—44no—
120C22×D43—42no—
121C22×D43—42no—
122C22×D43—42no—
123C22×D43D814yescomplemented
124C22×D43C2×D411yescharacteristic
125C22×D43C2×D411yescharacteristic
126D4×C43—24no—
127D4×C43—22no—
128D4×C43—22no—
129D4×C43—42no—
130D4×C43C2×D414yescomplemented
131C2×C4×C43—22no—
132C2×C4×C43—21no—
133C2×C4×C43C2×D411yescharacteristic
134C2×C4×C43C2411yescharacteristic
135C22⋊D43—28no—
136C22⋊D43—28no—
137C22⋊D43—42no—
138C22⋊D43—42no—
139C22⋊D43—42no—
140C2×Dic43—22no—
141C2×Dic43—21no—
142C2×Dic43C2×D411yescharacteristic
143C2×Dic43C2×D411yescharacteristic
144D172—24no—
145D172—22no—
146D172—22no—
147D172—42no—
148D172C2×D414yescomplemented
149C4×D43—22no—
150C4×D43—22no—
151C4×D43—22no—
152C4×D43—42no—
153C4×D43C2×D414yes—
154C8×C43—22no—
155C43⋊C8—22no—
156C22×C43—21no—
157C22×C43—21no—
158C22×C43—24no—
159C22×C43—48no—
160C22×C43—42no—
161C22×C43—42no—
162C22×C43—41no—
163C22×C43—41no—
164C22×C43—41no—
165C22×C43C2×D812yescomplemented
166C22×C43C22×D411yescharacteristic
167C2×D43—21no—
168C2×D43—21no—
169C2×D43—28no—
170C2×D43—24no—
171C2×D43—416no—
172C2×D43—48no—
173C2×D43—42no—
174C2×D43—42no—
175C2×D43—416no—
176C2×D43—41no—
177C2×D43—41no—
178C2×D43—41no—
179C2×D43—84no—
180C2×D43#12012yes—
181C2×D43C2×D812yes—
182C2×D43C2×D812yescomplemented
183C2×D43AGL(1,ℤ/8)12yes—
184C4×C43—21no—
185C4×C43—41no—
186C4×C43C22×D412yes—
187Dic43—21no—
188Dic43—41no—
189Dic43#12012yes—
190C2×#447—431nomaximal, Sylow
191C2×C43—22no—
192C2×C43—44no—
193C2×C43—81no—
194C2×C43C2×#12011yescharacteristic
195C2×C43C22×D811yescharacteristic
196C2×C43C2×AGL(1,ℤ/8)11yescharacteristic
197D43—22no—
198D43—44no—
199D43—81no—
200D43#44714yesdirect product factor
201C23×D4—431no—
202C22×D8—432no—
203C2×#121—431no—
204#447—431no—
205#447—432no—
206#447—431no—
207#447—432no—
208#447—431no—
209#447D4311yescharacteristic, direct product factor
210C2×#102—432no—
211C2×C22⋊C8—431no—
212C43C2×#44711yescharacteristic, complemented, Sylow
213C25—861no—
214C22×D4—432no—
215C22×D4—432no—
216C22×D4—431no—
217C22×D4—431no—
218C22×D4—861no—
219C22×D4—861no—
220C22×D4—861no—
221C22×D4—868no—
222C22×D4—861no—
223C22×D4C2×D4311yescharacteristic, complemented
224C23×C4—431no—
225C2×D8—432no—
226C2×D8—432no—
227C2×D8—432no—
228C2×D8—868no—
229C2×D8C2×D4312yescomplemented
230C22×C8—432no—
231#121—431no—
232#121—431no—
233#121—431no—
234#121—861no—
235#121—861no—
236#121C2×D4311yescharacteristic, complemented
237C2×C4⋊C4—431no—
238C2×C22⋊C4—861no—
239#102—432no—
240#102—432no—
241#102—432no—
242#102C2×D4312yescomplemented
243C22⋊C8—431no—
244C22⋊C8—432no—
245C22⋊C8C2×D4311yescharacteristic, complemented
246C24—21no—
247C24—431no—
248C24—862no—
249C24—862no—
250C24—861no—
251C24—868no—
252C24—861no—
253C24—1724no—
254C24—1724no—
255C2×D4—24no—
256C2×D4—21no—
257C2×D4—21no—
258C2×D4—438no—
259C2×D4—432no—
260C2×D4—431no—
261C2×D4—864no—
262C2×D4—861no—
263C2×D4—864no—
264C2×D4—864no—
265C2×D4—862no—
266C2×D4—862no—
267C2×D4—861no—
268C2×D4—864no—
269C2×D4—868no—
270C2×D4—868no—
271C2×D4—868no—
272C2×D4—864no—
273C2×D4—861no—
274C2×D4—861no—
275C2×D4—861no—
276C2×D4—1724no—
277C2×D4C22×D4312yes—
278C2×D4C22×D4311yescharacteristic, complemented
279C22×C4—431no—
280C22×C4—431no—
281C22×C4—431no—
282C22×C4—431no—
283C22×C4—431no—
284C22×C4—864no—
285C22×C4—861no—
286C22×C4C22×D4311yescharacteristic
287D8—24no—
288D8—864no—
289D8—864no—
290D8—864no—
291C2×C8—432no—
292C2×C8—864no—
293C2×C8C22×D4312yescomplemented
294C4⋊C4—431no—
295C4⋊C4—861no—
296C4⋊C4C22×D4311yescharacteristic, complemented
297C22⋊C4—21no—
298C22⋊C4—861no—
299C22⋊C4—861no—
300C22⋊C4—861no—
301C23—24no—
302C23—22no—
303C23—21no—
304C23—42no—
305C23—42no—
306C23—431no—
307C23—434no—
308C23—431no—
309C23—862no—
310C23—862no—
311C23—868no—
312C23—864no—
313C23—868no—
314C23—862no—
315C23—861no—
316C23—1722no—
317C23—1722no—
318C23—1722no—
319C23—1722no—
320C23—1724no—
321C23—1724no—
322C23—1724no—
323C23—17232no—
324C23—1724no—
325C23—1722no—
326C23D4×D4311yescharacteristic
327D4—24no—
328D4—22no—
329D4—22no—
330D4—42no—
331D4—434no—
332D4—864no—
333D4—868no—
334D4—868no—
335D4—862no—
336D4—862no—
337D4—1722no—
338D4—1722no—
339D4—1722no—
340D4—1722no—
341D4D4×D4314yescomplemented
342C2×C4—22no—
343C2×C4—21no—
344C2×C4—431no—
345C2×C4—434no—
346C2×C4—431no—
347C2×C4—862no—
348C2×C4—862no—
349C2×C4—862no—
350C2×C4—862no—
351C2×C4—861no—
352C2×C4—1722no—
353C2×C4D4×D4311yescharacteristic
354C2×C4C23×D4311yescharacteristic
355C8—22no—
356C8—862no—
357C22—21no—
358C22—21no—
359C22—24no—
360C22—48no—
361C22—42no—
362C22—42no—
363C22—41no—
364C22—41no—
365C22—41no—
366C22—432no—
367C22—432no—
368C22—432no—
369C22—432no—
370C22—868no—
371C22—861no—
372C22—861no—
373C22—864no—
374C22—3444no—
375C22—1728no—
376C22—17216no—
377C22—17216no—
378C22—1721no—
379C22—1721no—
380C22—1721no—
381C22—1722no—
382C22—1722no—
383C22D8×D4312yescomplemented
384C22C2×D4×D4311yescharacteristic
385C4—21no—
386C4—41no—
387C4—432no—
388C4—861no—
389C4—1721no—
390C4C2×D4×D4312yes—
391C2—22no—
392C2—44no—
393C2—81no—
394C2—434no—
395C2—862no—
396C2—3441no—
397C2—1724no—
398C2#120×D4311yescharacteristic
399C2C2×D8×D4311yescharacteristic
400C2AGL(1,ℤ/8)×D4311yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#447C2
socleC22×C43C22×D4
hypercenter#447D43
hypocenterC43C2×#447
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #447

Complements

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

NH ≅ G/Ntype
1. C22×D4×D43C2semidirect
2. C2×D8×D43C2semidirect
3. #121×D43C2semidirect
4. #14583035C2semidirect
5. #14583034C2semidirect
6. #14583033C2semidirect
7. #14583032C2semidirect
8. #14583031C2semidirect
9. #102×D43C2semidirect
10. C22⋊C8×D43C2semidirect
11. C43×#447C2semidirect
13. C22×D172C22semidirect
20. C2×D4×D43C22semidirect
21. C2×D4×D43C22semidirect
23. C2×D344C22semidirect
24. C2×#10621882C22semidirect
25. C2×#10621882C22semidirect
27. C2×C8×D43C22semidirect
28. #13063300C22semidirect
29. #13063299C22semidirect
32. #13063296C22semidirect
33. C4⋊C4×D43C22semidirect
35. #13063247C22semidirect
36. #13063246C22semidirect
37. #13063245C22semidirect
38. C22⋊(C43⋊C8)C22semidirect
39. (C2×D43)⋊C8C22semidirect
40. C22×D4×C43C22semidirect
41. C2×D8×C43C22semidirect
42. #121×C43C22semidirect
43. #102×C43C22semidirect
44. C22⋊C8×C43C22semidirect
58. C2×D4×C43C23semidirect
74. D4×D43D4semidirect
79. C2×D172C23semidirect
87. C2×C8×C43C23semidirect
88. C4⋊C4×C43C23semidirect
95. C4⋊Dic43C23semidirect
97. C2×C43⋊C8C23semidirect
123. C22×D43D8semidirect
130. D4×C43C2×D4semidirect
148. D172C2×D4semidirect
165. C22×C43C2×D8semidirect
182. C2×D43C2×D8semidirect
200. D43#447direct (N × H)
209. #447D43direct (N × H)
212. C43C2×#447semidirect
223. C22×D4C2×D43semidirect
229. C2×D8C2×D43semidirect
236. #121C2×D43semidirect
242. #102C2×D43semidirect
245. C22⋊C8C2×D43semidirect
278. C2×D4C22×D43semidirect
293. C2×C8C22×D43semidirect
296. C4⋊C4C22×D43semidirect
341. D4D4×D43semidirect
383. C22D8×D43semidirect