Finite Group Databasebeta

← #19143820

Subgroups — #19143820

Order 5504.

994 conjugacy classes of subgroups; only the 153 normal subgroups are shown.

normal subgroups only

This group has 994 conjugacy classes of subgroups — too many to draw. Only its 153 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×#13063350C211yesmaximal, characteristic, complemented
3#14583406C211yesmaximal, characteristic, complemented
4#14583048C214yesmaximal, complemented
5#14583031C214yesmaximal, complemented
6#14582905C211yesmaximal, characteristic, complemented
7#14582904C211yesmaximal, characteristic, complemented
8#14582862C211yesmaximal, characteristic, complemented
9C2×AGL(1,ℤ/8)×C43C211yesmaximal, characteristic, complemented
10C24×D43—21no—
11C22×D172C2211yescharacteristic
12C22×C22⋊D43—21no—
13C2×D4×D43—24no—
14C2×D4×D43—24no—
15C2×D4×D43—22no—
16C2×D4×D43C2214yes—
17C22×C4×D43C2211yescharacteristic
18#13063350—24no—
19C2×#10621884C2212yescomplemented
20C2×#10621882C2212yescomplemented
21C2×#10621877C2211yescharacteristic, complemented
22#13063306—21no—
23#13063301C2212yescomplemented
24#13063296C2212yescomplemented
25#13063293—21no—
26C4×C22⋊D43—22no—
27#13063284C2211yescharacteristic, complemented
28#13063247C2214yescomplemented
29#13063246C2214yescomplemented
30(C2×D43)⋊C8C2214yescomplemented
31C2×#41×C43C2211yescharacteristic, complemented
32C22×D4×C43C2211yescharacteristic
33AGL(1,ℤ/8)×C43—24no—
34C2×SD16×C43C2212yescomplemented
35C2×D8×C43C2212yescomplemented
36C2×M16×C43C2211yescharacteristic, complemented
37C24×C43—21no—
38C23×D43—28no—
39C23×D43—21no—
40C23×D43—24no—
41C23×D43—48no—
42C23×D43D411yescharacteristic
43#41×C43—22no—
44#41×C43—22no—
45C2×Q8×C43C2311yescharacteristic, complemented
46C2×D4×C43—22no—
47C2×D4×C43—21no—
48C2×D4×C43—21no—
49C2×D4×C43D414yescomplemented
50C2×D4×C43C2312yes—
51C2×D4×C43C2311yescharacteristic, complemented
52C22×C4×C43—21no—
53C22×C4×C43C2311yescharacteristic
54C2×C22⋊D43—28no—
55C2×C22⋊D43—24no—
56C2×C22⋊D43—22no—
57C22×Dic43D411yescharacteristic
58D4×D43—216no—
59D4×D43—28no—
60D4×D43—28no—
61C2×D172—22no—
62C2×D172—21no—
63C2×D172D414yescomplemented
64C2×D172C2312yes—
65C2×C4×D43—22no—
66C2×C4×D43—22no—
67C2×C4×D43D412yes—
68C2×C4×D43C2312yes—
69SD16×C43—24no—
70D8×C43—24no—
71M16×C43—22no—
72C2×C8×C43C2312yescomplemented
73C22⋊Dic43—22no—
74C22⋊Dic43—21no—
75#10621884—24no—
76#10621882—24no—
77(C2×D43)⋊C4—22no—
78C4⋊Dic43C2312yescomplemented
79Dic43⋊C4—22no—
80C4×Dic43—21no—
81#10621877—22no—
82C2×C43⋊C8C2312yescomplemented
83C23×C43—24no—
84C23×C43—22no—
85C23×C43—21no—
86C23×C43—44no—
87C23×C43C2×D411yescharacteristic
88C22×D43—22no—
89C22×D43—24no—
90C22×D43—216no—
91C22×D43—24no—
92C22×D43—22no—
93C22×D43—432no—
94C22×D43—48no—
95C22×D43—44no—
96C22×D43—48no—
97C22×D43C2×D412yes—
98Q8×C43—21no—
99Q8×C43—21no—
100D4×C43—24no—
101D4×C43—22no—
102D4×C43—21no—
103D4×C43—21no—
104D4×C43—42no—
105D4×C43C2×D414yes—
106C2×C4×C43—21no—
107C2×C4×C43—42no—
108C2×C4×C43C2×D411yescharacteristic
109C2×C4×C43C2×D412yes—
110C2×C4×C43C2×D412yes—
111C2×C4×C43C2411yescharacteristic
112C22⋊D43—216no—
113C22⋊D43—44no—
114C2×Dic43—22no—
115C2×Dic43—22no—
116C2×Dic43C2×D412yes—
117D172—24no—
118D172—22no—
119D172C2×D414yes—
120C4×D43—24no—
121C4×D43—22no—
122C4×D43—22no—
123C8×C43—22no—
124C43⋊C8—22no—
125C22×C43—22no—
126C22×C43—24no—
127C22×C43—48no—
128C22×C43—44no—
129C22×C43—41no—
130C22×C43—42no—
131C22×C43#12012yes—
132C22×C43C22×D411yescharacteristic
133C2×D43—28no—
134C2×D43—22no—
135C2×D43—22no—
136C2×D43—24no—
137C2×D43—432no—
138C2×D43—48no—
139C2×D43—44no—
140C2×D43AGL(1,ℤ/8)14yescomplemented
141C4×C43—41no—
142C4×C43#12012yes—
143C4×C43C22×D411yescharacteristic
144C4×C43C22×D411yescharacteristic
145Dic43—22no—
146Dic43—42no—
147#3003—431nomaximal, Sylow
148C2×C43—22no—
149C2×C43—44no—
150C2×C43—81no—
151C2×C43C2×#12011yescharacteristic
152C2×C43C2×AGL(1,ℤ/8)12yes—
153D43—24no—
154D43—44no—
155C23×D4—431no—
156C2×AGL(1,ℤ/8)—431no—
157C2×AGL(1,ℤ/8)D4311yescharacteristic, complemented
158#525—431no—
159#450—434no—
160#447—434no—
161#418—431no—
162#418—431no—
163#407—431no—
164C43#300311yescharacteristic, complemented, Sylow
165C25—861no—
166C2×#41C2×D4311yescharacteristic, complemented
167C22×D4—434no—
168C22×D4—431no—
169C22×D4—862no—
170C22×D4—861no—
171C22×D4—864no—
172C22×D4—864no—
173C22×D4C2×D4311yescharacteristic
174C23×C4—431no—
175AGL(1,ℤ/8)—24no—
176AGL(1,ℤ/8)—864no—
177C2×SD16—432no—
178C2×SD16C2×D4312yescomplemented
179C2×D8—432no—
180C2×D8C2×D4312yescomplemented
181C2×M16—431no—
182C2×M16C2×D4311yescharacteristic, complemented
183#123—861no—
184C22⋊Q8—432no—
185#121—432no—
186#120—861no—
187C4×D4—862no—
188#117—431no—
189#102—434no—
190#102—434no—
191C22⋊C8—434no—
192C24—21no—
193C24—431no—
194C24—864no—
195C24—868no—
196C24—861no—
197C24—1728no—
198#41—22no—
199#41—22no—
200C2×Q8C22×D4311yescharacteristic, complemented
201C2×D4—21no—
202C2×D4—21no—
203C2×D4—22no—
204C2×D4—434no—
205C2×D4—432no—
206C2×D4—864no—
207C2×D4—868no—
208C2×D4—8616no—
209C2×D4—868no—
210C2×D4—868no—
211C2×D4—862no—
212C2×D4—861no—
213C2×D4—862no—
214C2×D4C22⋊D4314yescomplemented
215C2×D4C22×D4312yes—
216C2×D4C22×D4311yescharacteristic, complemented
217C22×C4—21no—
218C22×C4—431no—
219C22×C4—432no—
220C22×C4—432no—
221C22×C4—862no—
222C22×C4—862no—
223C22×C4C22×D4311yescharacteristic
224SD16—24no—
225SD16—864no—
226D8—24no—
227D8—864no—
228M16—22no—
229M16—862no—
230C2×C8—432no—
231C2×C8C22×D4312yescomplemented
232C4⋊C4—432no—
233C4⋊C4—862no—
234C22⋊C4—862no—
235C22⋊C4—862no—
236C22⋊C4—861no—
237C42—861no—
238C23—24no—
239C23—22no—
240C23—21no—
241C23—44no—
242C23—432no—
243C23—864no—
244C23—8616no—
245C23—862no—
246C23—864no—
247C23—862no—
248C23—1724no—
249C23—1728no—
250C23—17232no—
251C23—1728no—
252C23D4×D4311yescharacteristic
253Q8—21no—
254Q8—21no—
255D4—24no—
256D4—22no—
257D4—21no—
258D4—21no—
259D4—42no—
260D4—434no—
261D4—8616no—
262D4—864no—
263D4—862no—
264D4—1724no—
265D4C2×C22⋊D4314yes—
266C2×C4—21no—
267C2×C4—42no—
268C2×C4—432no—
269C2×C4—862no—
270C2×C4—864no—
271C2×C4—862no—
272C2×C4—862no—
273C2×C4—862no—
274C2×C4D4×D4311yescharacteristic
275C2×C4D4×D4312yes—
276C2×C4C2×C22⋊D4312yes—
277C2×C4C23×D4311yescharacteristic
278C8—22no—
279C8—862no—
280C22—22no—
281C22—24no—
282C22—48no—
283C22—44no—
284C22—41no—
285C22—42no—
286C22—434no—
287C22—868no—
288C22—862no—
289C22—862no—
290C22—864no—
291C22—1728no—
292C22—17232no—
293C22—1724no—
294C22#1306329312yes—
295C22C2×D4×D4311yescharacteristic
296C4—41no—
297C4—862no—
298C4—1722no—
299C4#1306329312yes—
300C4C2×D4×D4311yescharacteristic
301C4C22×C22⋊D4311yescharacteristic
302C2—22no—
303C2—44no—
304C2—81no—
305C2—864no—
306C2—1724no—
307C2C2×#1306329311yescharacteristic
308C2AGL(1,ℤ/8)×D4312yes—
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC2×AGL(1,ℤ/8)×C43C2
socleC22×C43C22×D4
hypercenterC2×AGL(1,ℤ/8)D43
hypocenterC43#3003
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. C22×D4×D43C2semidirect
2. C2×#13063350C2semidirect
3. #14583406C2semidirect
4. #14583048C2semidirect
5. #14583031C2semidirect
6. #14582905C2semidirect
7. #14582904C2semidirect
8. #14582862C2semidirect
9. C2×AGL(1,ℤ/8)×C43C2semidirect
19. C2×#10621884C22semidirect
20. C2×#10621882C22semidirect
21. C2×#10621877C22semidirect
23. #13063301C22semidirect
24. #13063296C22semidirect
27. #13063284C22semidirect
28. #13063247C22semidirect
29. #13063246C22semidirect
30. (C2×D43)⋊C8C22semidirect
31. C2×#41×C43C22semidirect
34. C2×SD16×C43C22semidirect
35. C2×D8×C43C22semidirect
36. C2×M16×C43C22semidirect
45. C2×Q8×C43C23semidirect
49. C2×D4×C43D4semidirect
51. C2×D4×C43C23semidirect
63. C2×D172D4semidirect
72. C2×C8×C43C23semidirect
78. C4⋊Dic43C23semidirect
82. C2×C43⋊C8C23semidirect
140. C2×D43AGL(1,ℤ/8)semidirect
157. C2×AGL(1,ℤ/8)D43semidirect
164. C43#3003semidirect
166. C2×#41C2×D43semidirect
178. C2×SD16C2×D43semidirect
180. C2×D8C2×D43semidirect
182. C2×M16C2×D43semidirect
200. C2×Q8C22×D43semidirect
214. C2×D4C22⋊D43semidirect
216. C2×D4C22×D43semidirect
231. C2×C8C22×D43semidirect