Finite Group Databasebeta

← #481×D43 #19144491

Subgroups — #481×D43 #19144491

Order 5504.

512 conjugacy classes of subgroups; only the 135 normal subgroups are shown.

normal subgroups only

This group has 512 conjugacy classes of subgroups — too many to draw. Only its 135 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
1#121×D43C211yesmaximal, characteristic
2C2×C4⋊C4×D43C211yesmaximal, characteristic, complemented
3#14583219C212yesmaximal, complemented
4#14583218C211yesmaximal, characteristic, complemented
5#14583217C211yesmaximal, characteristic, complemented
6#14583216C212yesmaximal, complemented
7#14583215C211yesmaximal, characteristic, complemented
8#106×D43C212yesmaximal, complemented
9#102×D43C212yesmaximal, complemented
10C22⋊C8×D43C211yesmaximal, characteristic, complemented
11C43×#481C211yesmaximal, characteristic, complemented
12C2×D4×D43—21no—
13C2×D4×D43C2211yescharacteristic
14C22×C4×D43—21no—
15C22×C4×D43C2211yescharacteristic
16C2×C8×D43C2212yes—
17#13063300C2211yescharacteristic
18#13063299C2211yescharacteristic
19#13063298—21no—
20#13063297—21no—
21#13063296C2211yescharacteristic
22C2×C4⋊Dic43C2211yescharacteristic, complemented
23C2×Dic43⋊C4—21no—
24C4⋊C4×D43—21no—
25C4⋊C4×D43—21no—
26C4⋊C4×D43C2212yes—
27C4⋊C4×D43C2211yescharacteristic
28C4⋊C4×D43C2212yescomplemented
29C22⋊C4×D43—21no—
30#13063257C2212yescomplemented
31#13063256C2212yescomplemented
32#13063256C2212yescomplemented
33#13063247C2212yescomplemented
34#13063246C2212yescomplemented
35#13063245C2212yescomplemented
36C22⋊(C43⋊C8)C2211yescharacteristic, complemented
37(C2×D43)⋊C8C2212yescomplemented
38#121×C43C2211yescharacteristic
39C2×C4⋊C4×C43C2211yescharacteristic, complemented
40#106×C43C2212yescomplemented
41#102×C43C2212yescomplemented
42C22⋊C8×C43C2211yescharacteristic, complemented
43C23×D43—21no—
44C23×D43D411yescharacteristic
45C2×D4×C43—21no—
46C2×D4×C43C2311yescharacteristic
47C22×C4×C43—21no—
48C22×C4×C43C2311yescharacteristic
49C2×C22⋊D43—21no—
50C2×C22⋊D43—21no—
51C2×C22⋊D43—21no—
52C22×Dic43—21no—
53C22×Dic43D411yescharacteristic
54D4×D43—24no—
55D4×D43—44no—
56C2×D172—21no—
57C2×D172C2311yescharacteristic
58C2×C4×D43—24no—
59C2×C4×D43—21no—
60C2×C4×D43—22no—
61C2×C4×D43—22no—
62C2×C4×D43—44no—
63C2×C4×D43D411yescharacteristic
64C2×C4×D43D411yescharacteristic
65C2×C4×D43C2311yescharacteristic
66C2×C4×D43C2311yescharacteristic
67C2×C8×C43C2312yes—
68C4⋊C4×C43—21no—
69C4⋊C4×C43C2312yes—
70C4⋊C4×C43C2311yescharacteristic
71C22⋊C4×C43—21no—
72C22⋊Dic43—21no—
73(C2×D43)⋊C4—21no—
74(C2×D43)⋊C4—21no—
75C4⋊Dic43—21no—
76C4⋊Dic43C2312yes—
77C4⋊Dic43C2311yescharacteristic
78Dic43⋊C4—22no—
79Dic43⋊C4—22no—
80Dic43⋊C4—21no—
81C2×C43⋊C8C2312yes—
82C8×D43—24no—
83C23×C43—21no—
84C23×C43C2×D411yescharacteristic
85C22×D43—22no—
86C22×D43—22no—
87C22×D43—21no—
88C22×D43—42no—
89C22×D43—42no—
90C22×D43—42no—
91C22×D43SD1614yes—
92C22×D43C2×D411yescharacteristic
93C22×D43C2×D411yescharacteristic
94D4×C43—22no—
95D4×C43—42no—
96C2×C4×C43—22no—
97C2×C4×C43—22no—
98C2×C4×C43—21no—
99C2×C4×C43—42no—
100C2×C4×C43C2×D411yescharacteristic
101C2×C4×C43C2411yescharacteristic
102C22⋊D43—42no—
103C22⋊D43—42no—
104C22⋊D43—42no—
105C2×Dic43—22no—
106C2×Dic43—22no—
107C2×Dic43—21no—
108C2×Dic43—42no—
109C2×Dic43C2×D411yescharacteristic
110C2×Dic43C2×D411yescharacteristic
111D172—22no—
112D172—42no—
113C4×D43—22no—
114C4×D43—22no—
115C4×D43—22no—
116C4×D43—44no—
117C4×D43—42no—
118C4×D43—44no—
119C4×D43#4114yes—
120C8×C43—22no—
121C43⋊C8—22no—
122C22×C43—21no—
123C22×C43—21no—
124C22×C43—41no—
125C22×C43—41no—
126C22×C43—41no—
127C22×C43C2×SD1612yes—
128C22×C43C22×D411yescharacteristic
129C2×D43—21no—
130C2×D43—21no—
131C2×D43—28no—
132C2×D43—41no—
133C2×D43—41no—
134C2×D43—41no—
135C2×D43—84no—
136C2×D43#12312yes—
137C2×D43C2×SD1612yes—
138C2×D43C2×SD1612yes—
139C2×D43AGL(1,ℤ/8)12yes—
140C4×C43—21no—
141C4×C43—41no—
142C4×C43—42no—
143C4×C43C2×#4112yes—
144Dic43—21no—
145Dic43—41no—
146Dic43—42no—
147Dic43#12312yes—
148C2×#481—431nomaximal, Sylow
149C2×C43—22no—
150C2×C43—81no—
151C2×C43C2×#12311yescharacteristic
152C2×C43C22×SD1611yescharacteristic
153C2×C43C2×AGL(1,ℤ/8)11yescharacteristic
154D43—22no—
155D43—81no—
156D43#48114yesdirect product factor
157C2×#121—431no—
158C22×C4⋊C4—431no—
159#481—431no—
160#481—431no—
161#481—432no—
162#481—432no—
163#481—431no—
164#481D4311yescharacteristic, direct product factor
165C2×#106—432no—
166C2×#102—432no—
167C2×C22⋊C8—431no—
168C43C2×#48111yescharacteristic, complemented, Sylow
169C22×D4—431no—
170C22×D4—861no—
171C23×C4—431no—
172C23×C4—861no—
173C22×C8—432no—
174#121—431no—
175#121—431no—
176#121—431no—
177#121—861no—
178#121—861no—
179#121C2×D4311yescharacteristic
180C2×C4⋊C4—431no—
181C2×C4⋊C4—432no—
182C2×C4⋊C4—432no—
183C2×C4⋊C4—431no—
184C2×C4⋊C4—861no—
185C2×C4⋊C4—861no—
186C2×C4⋊C4—861no—
187C2×C4⋊C4C2×D4311yescharacteristic, complemented
188C2×C22⋊C4—861no—
189#106—432no—
190#106—432no—
191#106—432no—
192#106C2×D4312yescomplemented
193#102—432no—
194#102—432no—
195#102—432no—
196#102C2×D4312yescomplemented
197C22⋊C8—431no—
198C22⋊C8—432no—
199C22⋊C8C2×D4311yescharacteristic, complemented
200C24—431no—
201C24—861no—
202C2×D4—21no—
203C2×D4—431no—
204C2×D4—861no—
205C2×D4—864no—
206C2×D4—861no—
207C2×D4—861no—
208C2×D4—861no—
209C2×D4—1724no—
210C2×D4C22×D4311yescharacteristic
211C22×C4—21no—
212C22×C4—431no—
213C22×C4—431no—
214C22×C4—431no—
215C22×C4—431no—
216C22×C4—431no—
217C22×C4—864no—
218C22×C4—861no—
219C22×C4—862no—
220C22×C4—862no—
221C22×C4—861no—
222C22×C4—1724no—
223C22×C4C22×D4311yescharacteristic
224C2×C8—432no—
225C2×C8—864no—
226C2×C8C22×D4312yes—
227C4⋊C4—21no—
228C4⋊C4—432no—
229C4⋊C4—431no—
230C4⋊C4—862no—
231C4⋊C4—862no—
232C4⋊C4—861no—
233C4⋊C4—861no—
234C4⋊C4C22×D4312yes—
235C4⋊C4C22×D4311yescharacteristic
236C22⋊C4—21no—
237C22⋊C4—861no—
238C22⋊C4—861no—
239C22⋊C4—861no—
240C23—21no—
241C23—431no—
242C23—434no—
243C23—431no—
244C23—862no—
245C23—862no—
246C23—861no—
247C23—1722no—
248C23—1722no—
249C23—1722no—
250C23D4×D4311yescharacteristic
251D4—22no—
252D4—42no—
253D4—862no—
254D4—1722no—
255D4—1722no—
256D4—1722no—
257D4—1722no—
258C2×C4—22no—
259C2×C4—21no—
260C2×C4—22no—
261C2×C4—42no—
262C2×C4—431no—
263C2×C4—434no—
264C2×C4—431no—
265C2×C4—862no—
266C2×C4—862no—
267C2×C4—862no—
268C2×C4—862no—
269C2×C4—861no—
270C2×C4—862no—
271C2×C4—1724no—
272C2×C4—1722no—
273C2×C4—1724no—
274C2×C4—1722no—
275C2×C4D4×D4311yescharacteristic
276C2×C4C23×D4311yescharacteristic
277C8—22no—
278C8—862no—
279C22—21no—
280C22—21no—
281C22—41no—
282C22—41no—
283C22—41no—
284C22—432no—
285C22—432no—
286C22—432no—
287C22—432no—
288C22—868no—
289C22—861no—
290C22—861no—
291C22—3444no—
292C22—1721no—
293C22—1721no—
294C22—1721no—
295C22SD16×D4312yes—
296C22C2×D4×D4311yescharacteristic
297C4—21no—
298C4—41no—
299C4—42no—
300C4—432no—
301C4—861no—
302C4—1721no—
303C4—1722no—
304C4#41×D4312yes—
305C2—22no—
306C2—81no—
307C2—434no—
308C2—862no—
309C2—3441no—
310C2#123×D4311yescharacteristic
311C2C2×SD16×D4311yescharacteristic
312C2AGL(1,ℤ/8)×D4311yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#481C2
socleC22×C43C22×D4
hypercenter#481D43
hypocenterC43C2×#481
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #481

Complements

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

NH ≅ G/Ntype
2. C2×C4⋊C4×D43C2semidirect
3. #14583219C2semidirect
4. #14583218C2semidirect
5. #14583217C2semidirect
6. #14583216C2semidirect
7. #14583215C2semidirect
8. #106×D43C2semidirect
9. #102×D43C2semidirect
10. C22⋊C8×D43C2semidirect
11. C43×#481C2semidirect
22. C2×C4⋊Dic43C22semidirect
28. C4⋊C4×D43C22semidirect
30. #13063257C22semidirect
31. #13063256C22semidirect
32. #13063256C22semidirect
33. #13063247C22semidirect
34. #13063246C22semidirect
35. #13063245C22semidirect
36. C22⋊(C43⋊C8)C22semidirect
37. (C2×D43)⋊C8C22semidirect
39. C2×C4⋊C4×C43C22semidirect
40. #106×C43C22semidirect
41. #102×C43C22semidirect
42. C22⋊C8×C43C22semidirect
156. D43#481direct (N × H)
164. #481D43direct (N × H)
168. C43C2×#481semidirect
187. C2×C4⋊C4C2×D43semidirect
192. #106C2×D43semidirect
196. #102C2×D43semidirect
199. C22⋊C8C2×D43semidirect