Finite Group Databasebeta

← #450×D43 #19143774

Subgroups — #450×D43 #19143774

Order 5504.

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

normal subgroups only

This group has 996 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
2C2×SD16×D43C212yesmaximal, complemented
3C22⋊Q8×D43C211yesmaximal, characteristic, complemented
4#14583052C211yesmaximal, characteristic, complemented
5#14583051C212yesmaximal, complemented
6#14583050C211yesmaximal, characteristic, complemented
7#14583049C211yesmaximal, characteristic, complemented
8#14583048C212yesmaximal, complemented
9#102×D43C212yesmaximal, complemented
10C22⋊C8×D43C211yesmaximal, characteristic, complemented
11C43×#450C211yesmaximal, characteristic, complemented
12C24×D43—21no—
13C2×Q8×D43C2211yescharacteristic, complemented
14C22×D172C2211yescharacteristic
15C22×C22⋊D43—21no—
16C2×D4×D43—28no—
17C2×D4×D43—21no—
18C2×D4×D43—21no—
19C2×D4×D43C2212yes—
20C2×D4×D43C2212yes—
21C22×C4×D43C2211yescharacteristic
22C2×#10621873C2212yescomplemented
23C2×#10621883C2212yescomplemented
24C2×#10621884C2212yescomplemented
25SD16×D43—28no—
26C2×C8×D43C2212yescomplemented
27#13063305C2211yescharacteristic, complemented
28#13063304C2211yescharacteristic, complemented
29#13063303—21no—
30#13063302—21no—
31#13063301C2211yescharacteristic, complemented
32C4⋊C4×D43—21no—
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
41C2×SD16×C43C2212yescomplemented
42C22⋊Q8×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—44no—
51C23×D43—44no—
52C23×D43D411yescharacteristic
53C2×Q8×C43C2311yescharacteristic, complemented
54C2×D4×C43—24no—
55C2×D4×C43—21no—
56C2×D4×C43C2312yes—
57C22×C4×C43C2311yescharacteristic
58C2×C22⋊D43—28no—
59C2×C22⋊D43—22no—
60C2×C22⋊D43—22no—
61C22×Dic43D411yescharacteristic
62Q8×D43—24no—
63D4×D43—28no—
64D4×D43—28no—
65D4×D43—24no—
66D4×D43—24no—
67D4×D43—24no—
68D4×D43D418yes—
69C2×D172—21no—
70C2×D172—24no—
71C2×D172C2312yes—
72C2×C4×D43—24no—
73C2×C4×D43—21no—
74C2×C4×D43—21no—
75C2×C4×D43D411yescharacteristic
76C2×C4×D43D411yescharacteristic
77C2×C4×D43C2311yescharacteristic
78C2×C4×D43C2311yescharacteristic
79C2×Dic86—21no—
80C2×Dic86C2311yescharacteristic, complemented
81SD16×C43—24no—
82C2×C8×C43C2312yescomplemented
83C4⋊C4×C43—21no—
84C4⋊C4×C43C2311yescharacteristic, complemented
85C22⋊C4×C43—21no—
86C22⋊Dic43—21no—
87#10621884—24no—
88#10621883—24no—
89(C2×D43)⋊C4—21no—
90(C2×D43)⋊C4—21no—
91C4⋊Dic43—21no—
92C4⋊Dic43C2311yescharacteristic, complemented
93Dic43⋊C4—21no—
94Dic43⋊C4—21no—
95Dic43⋊C4—21no—
96C2×C43⋊C8C2312yescomplemented
97#10621873—24no—
98C8×D43—24no—
99C23×C43—24no—
100C23×C43—22no—
101C23×C43—42no—
102C23×C43—42no—
103C23×C43C2×D411yescharacteristic
104C22×D43—22no—
105C22×D43—22no—
106C22×D43—24no—
107C22×D43—28no—
108C22×D43—22no—
109C22×D43—28no—
110C22×D43—44no—
111C22×D43—432no—
112C22×D43—42no—
113C22×D43—42no—
114C22×D43—44no—
115C22×D43—44no—
116C22×D43—44no—
117C22×D43SD1614yescomplemented
118C22×D43C2×D411yescharacteristic
119C22×D43C2×D411yescharacteristic
120Q8×C43—22no—
121D4×C43—24no—
122D4×C43—22no—
123D4×C43C2×D414yes—
124C2×C4×C43—22no—
125C2×C4×C43—21no—
126C2×C4×C43—21no—
127C2×C4×C43C2×D411yescharacteristic
128C2×C4×C43C2411yescharacteristic
129C22⋊D43—28no—
130C22⋊D43—28no—
131C2×Dic43—22no—
132C2×Dic43—21no—
133C2×Dic43—21no—
134C2×Dic43C2×D411yescharacteristic
135C2×Dic43C2×D411yescharacteristic
136D172—24no—
137D172—22no—
138D172C2×D414yes—
139C4×D43—22no—
140C4×D43—22no—
141C4×D43—22no—
142C4×D43—42no—
143C4×D43—42no—
144C4×D43C2×D414yes—
145Dic86—22no—
146Dic86—42no—
147C8×C43—22no—
148C43⋊C8—22no—
149C22×C43—21no—
150C22×C43—21no—
151C22×C43—24no—
152C22×C43—48no—
153C22×C43—42no—
154C22×C43—42no—
155C22×C43C2×SD1612yescomplemented
156C22×C43C22×D411yescharacteristic
157C2×D43—21no—
158C2×D43—21no—
159C2×D43—28no—
160C2×D43—24no—
161C2×D43—416no—
162C2×D43—48no—
163C2×D43—42no—
164C2×D43—42no—
165C2×D43—416no—
166C2×D43#12012yes—
167C2×D43C2×SD1612yes—
168C2×D43C2×SD1612yescomplemented
169C2×D43AGL(1,ℤ/8)12yes—
170C4×C43—21no—
171C4×C43—41no—
172C4×C43—41no—
173C4×C43C22×D412yes—
174Dic43—21no—
175Dic43—41no—
176Dic43—41no—
177Dic43#12012yes—
178C2×#450—431nomaximal, Sylow
179C2×C43—22no—
180C2×C43—44no—
181C2×C43C2×#12011yescharacteristic
182C2×C43C22×SD1611yescharacteristic
183C2×C43C2×AGL(1,ℤ/8)11yescharacteristic
184D43—22no—
185D43—44no—
186D43#45014yesdirect product factor
187C23×D4—431no—
188C22×SD16—432no—
189C2×C22⋊Q8—431no—
190#450—431no—
191#450—432no—
192#450—431no—
193#450—432no—
194#450—431no—
195#450D4311yescharacteristic, direct product factor
196C2×#102—432no—
197C2×C22⋊C8—431no—
198C43C2×#45011yescharacteristic, complemented, Sylow
199C25—861no—
200C22×Q8—431no—
201C22×D4—432no—
202C22×D4—432no—
203C22×D4—431no—
204C22×D4—861no—
205C22×D4—861no—
206C22×D4—861no—
207C22×D4—868no—
208C22×D4C2×D4311yescharacteristic
209C23×C4—431no—
210C2×SD16—432no—
211C2×SD16—432no—
212C2×SD16—432no—
213C2×SD16—868no—
214C2×SD16C2×D4312yescomplemented
215C22×C8—432no—
216C22⋊Q8—431no—
217C22⋊Q8—431no—
218C22⋊Q8—431no—
219C22⋊Q8—861no—
220C22⋊Q8—861no—
221C22⋊Q8C2×D4311yescharacteristic, complemented
222C2×C4⋊C4—431no—
223C2×C4⋊C4—861no—
224C2×C22⋊C4—861no—
225#102—432no—
226#102—432no—
227#102—432no—
228#102C2×D4312yescomplemented
229C22⋊C8—431no—
230C22⋊C8—432no—
231C22⋊C8C2×D4311yescharacteristic, complemented
232C24—21no—
233C24—431no—
234C24—862no—
235C24—862no—
236C24—868no—
237C24—861no—
238C24—1724no—
239C24—1724no—
240C2×Q8—431no—
241C2×Q8—861no—
242C2×Q8—864no—
243C2×Q8C22×D4311yescharacteristic, complemented
244C2×D4—24no—
245C2×D4—21no—
246C2×D4—438no—
247C2×D4—432no—
248C2×D4—864no—
249C2×D4—864no—
250C2×D4—862no—
251C2×D4—862no—
252C2×D4—864no—
253C2×D4—868no—
254C2×D4—868no—
255C2×D4—868no—
256C2×D4—864no—
257C2×D4—861no—
258C2×D4C22×D4312yes—
259C22×C4—431no—
260C22×C4—431no—
261C22×C4—431no—
262C22×C4—431no—
263C22×C4—431no—
264C22×C4—864no—
265C22×C4—861no—
266C22×C4—861no—
267C22×C4C22×D4311yescharacteristic
268SD16—24no—
269SD16—864no—
270SD16—864no—
271SD16—864no—
272C2×C8—432no—
273C2×C8—864no—
274C2×C8C22×D4312yescomplemented
275C4⋊C4—21no—
276C4⋊C4—431no—
277C4⋊C4—861no—
278C4⋊C4—861no—
279C4⋊C4—861no—
280C4⋊C4—861no—
281C4⋊C4C22×D4311yescharacteristic, complemented
282C22⋊C4—21no—
283C22⋊C4—861no—
284C22⋊C4—861no—
285C22⋊C4—861no—
286C23—24no—
287C23—22no—
288C23—42no—
289C23—42no—
290C23—431no—
291C23—434no—
292C23—431no—
293C23—862no—
294C23—862no—
295C23—868no—
296C23—864no—
297C23—868no—
298C23—862no—
299C23—1722no—
300C23—1724no—
301C23—1724no—
302C23—1724no—
303C23—17232no—
304C23—1724no—
305C23—1722no—
306C23D4×D4311yescharacteristic
307Q8—22no—
308Q8—862no—
309Q8—1722no—
310D4—24no—
311D4—22no—
312D4—434no—
313D4—864no—
314D4—868no—
315D4—868no—
316D4—862no—
317D4D4×D4314yes—
318C2×C4—22no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—431no—
322C2×C4—434no—
323C2×C4—431no—
324C2×C4—862no—
325C2×C4—862no—
326C2×C4—862no—
327C2×C4—862no—
328C2×C4—861no—
329C2×C4—861no—
330C2×C4—1722no—
331C2×C4—1722no—
332C2×C4D4×D4311yescharacteristic
333C2×C4C23×D4311yescharacteristic
334C8—22no—
335C8—862no—
336C22—21no—
337C22—21no—
338C22—24no—
339C22—48no—
340C22—42no—
341C22—42no—
342C22—432no—
343C22—432no—
344C22—432no—
345C22—432no—
346C22—868no—
347C22—861no—
348C22—861no—
349C22—864no—
350C22—1728no—
351C22—17216no—
352C22—17216no—
353C22—1722no—
354C22—1722no—
355C22SD16×D4312yescomplemented
356C22C2×D4×D4311yescharacteristic
357C4—21no—
358C4—41no—
359C4—41no—
360C4—432no—
361C4—861no—
362C4—1721no—
363C4—1721no—
364C4C2×D4×D4312yes—
365C2—22no—
366C2—44no—
367C2—434no—
368C2—862no—
369C2—1724no—
370C2#120×D4311yescharacteristic
371C2C2×SD16×D4311yescharacteristic
372C2AGL(1,ℤ/8)×D4311yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#450C2
socleC22×C43C22×D4
hypercenter#450D43
hypocenterC43C2×#450
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #450

Complements

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

NH ≅ G/Ntype
2. C2×SD16×D43C2semidirect
3. C22⋊Q8×D43C2semidirect
4. #14583052C2semidirect
5. #14583051C2semidirect
6. #14583050C2semidirect
7. #14583049C2semidirect
8. #14583048C2semidirect
9. #102×D43C2semidirect
10. C22⋊C8×D43C2semidirect
11. C43×#450C2semidirect
13. C2×Q8×D43C22semidirect
22. C2×#10621873C22semidirect
23. C2×#10621883C22semidirect
24. C2×#10621884C22semidirect
26. C2×C8×D43C22semidirect
27. #13063305C22semidirect
28. #13063304C22semidirect
31. #13063301C22semidirect
33. C4⋊C4×D43C22semidirect
35. #13063247C22semidirect
36. #13063246C22semidirect
37. #13063245C22semidirect
38. C22⋊(C43⋊C8)C22semidirect
39. (C2×D43)⋊C8C22semidirect
41. C2×SD16×C43C22semidirect
42. C22⋊Q8×C43C22semidirect
43. #102×C43C22semidirect
44. C22⋊C8×C43C22semidirect
53. C2×Q8×C43C23semidirect
80. C2×Dic86C23semidirect
82. C2×C8×C43C23semidirect
84. C4⋊C4×C43C23semidirect
92. C4⋊Dic43C23semidirect
96. C2×C43⋊C8C23semidirect
117. C22×D43SD16semidirect
155. C22×C43C2×SD16semidirect
168. C2×D43C2×SD16semidirect
186. D43#450direct (N × H)
195. #450D43direct (N × H)
198. C43C2×#450semidirect
214. C2×SD16C2×D43semidirect
221. C22⋊Q8C2×D43semidirect
228. #102C2×D43semidirect
231. C22⋊C8C2×D43semidirect
243. C2×Q8C22×D43semidirect
274. C2×C8C22×D43semidirect
281. C4⋊C4C22×D43semidirect
355. C22SD16×D43semidirect