Finite Group Databasebeta

← #19146218

Subgroups — #19146218

Order 5504.

556 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 556 conjugacy classes of subgroups — too many to draw. Only its 125 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
1C2×#13063349C212yesmaximal, complemented
2#14583569C211yesmaximal, characteristic, complemented
3D4×D172C211yesmaximal, characteristic, complemented
4#14583275C211yesmaximal, characteristic, complemented
5#14583151C212yesmaximal, complemented
6#14583100C211yesmaximal, characteristic, complemented
7#14583045C212yesmaximal, complemented
8#14583031C212yesmaximal, complemented
9C4×#10621883C211yesmaximal, characteristic, complemented
10#14582976C211yesmaximal, characteristic, complemented
11C43×#459C211yesmaximal, characteristic, complemented
12C2×#10621900C2212yescomplemented
13C22×D172—21no—
14C2×D4×D43C2212yes—
15#13063349—28no—
16C2×#10621873C2212yescomplemented
17C2×#10621883C2211yescharacteristic
18C2×#10621882C2212yescomplemented
19C2×#10621882C2212yescomplemented
20C2×#10621872C2212yescomplemented
21#13063322C2211yescharacteristic
22#13063321—21no—
23#13063300C2212yes—
24#13063299—21no—
25#13063297—22no—
26#13063296C2212yescomplemented
27#13063295—22no—
28C4×Dic86C2211yescharacteristic, complemented
29C4×D172C2211yescharacteristic
30D4×Dic43—21no—
31#13063256C2211yescharacteristic, complemented
32#13063248C2211yescharacteristic, complemented
33#13063247C2212yescomplemented
34#13063246C2211yescharacteristic
35(C2×D43)⋊C8C2212yescomplemented
36C4×C43⋊C8C2211yescharacteristic, complemented
37C2×D8×C43C2212yes—
38#127×C43C2211yescharacteristic, complemented
39C4×D4×C43C2211yescharacteristic
40C4⋊C8×C43C2211yescharacteristic, complemented
41#102×C43C2212yescomplemented
42C23×D43—22no—
43C2×D4×C43—21no—
44C2×D4×C43—21no—
45C2×D4×C43C2312yes—
46C2×D4×C43C2311yescharacteristic
47C22×C4×C43—21no—
48C2×C22⋊D43—22no—
49C2×C22⋊D43—22no—
50C2×C22⋊D43—22no—
51C22×Dic43—22no—
52#10621900—24no—
53#10621900—42no—
54D4×D43—24no—
55D4×D43—42no—
56C2×D172—21no—
57C2×D172—21no—
58C2×D172—22no—
59C2×D172—44no—
60C2×D172D411yescharacteristic
61C2×D172C2312yes—
62C2×C4×D43C2312yes—
63C2×Dic86C2311yescharacteristic
64D8×C43—24no—
65C2×C8×C43C2312yes—
66C4⋊C4×C43C2311yescharacteristic
67C22⋊C4×C43—21no—
68C42×C43C2311yescharacteristic
69C22⋊Dic43—22no—
70#10621883D414yescomplemented
71#10621882—24no—
72#10621882—42no—
73(C2×D43)⋊C4—22no—
74(C2×D43)⋊C4D412yes—
75C4⋊Dic43D411yescharacteristic
76C4⋊Dic43C2311yescharacteristic
77Dic43⋊C4—21no—
78C4×Dic43—21no—
79C2×C43⋊C8C2311yescharacteristic
80C2×C43⋊C8C2311yescharacteristic
81#10621873—24no—
82#10621872—24no—
83C23×C43—21no—
84C23×C43—22no—
85C22×D43—22no—
86C22×D43—44no—
87C22×D43—44no—
88C22×D43—82no—
89C22×D43C2×D412yes—
90D4×C43—22no—
91D4×C43—21no—
92D4×C43—22no—
93D4×C43—42no—
94D4×C43—81no—
95D4×C43C2×D412yes—
96C2×C4×C43—21no—
97C2×C4×C43—42no—
98C2×C4×C43C2×D411yescharacteristic
99C2×C4×C43C2×D411yescharacteristic
100C2×C4×C43C2411yescharacteristic
101C22⋊D43—44no—
102C22⋊D43—44no—
103C22⋊D43—82no—
104C2×Dic43—21no—
105C2×Dic43—21no—
106C2×Dic43—44no—
107C2×Dic43C2×D412yes—
108D172—22no—
109D172—22no—
110D172—22no—
111D172—44no—
112D172—42no—
113D172—81no—
114C4×D43—22no—
115C4×D43—22no—
116Dic86—21no—
117Dic86C2×D412yescomplemented
118C8×C43—22no—
119C43⋊C8—21no—
120C43⋊C8C2×D412yescomplemented
121C22×C43—22no—
122C22×C43—41no—
123C22×C43—41no—
124C22×C43—42no—
125C22×C43—42no—
126C22×C43—42no—
127C22×C43C22×D411yescharacteristic
128C2×D43—22no—
129C2×D43—22no—
130C2×D43—22no—
131C2×D43—42no—
132C2×D43—42no—
133C2×D43—42no—
134C2×D43—88no—
135C4×C43—21no—
136C4×C43—41no—
137C4×C43AGL(1,ℤ/8)12yescomplemented
138C4×C43C22×D411yescharacteristic
139C4×C43H(5,𝔽2)11yescharacteristic
140Dic43—22no—
141Dic43—22no—
142Dic43—41no—
143#3274—431nomaximal, Sylow
144C2×C43—42no—
145C2×C43—82no—
146C2×C43D4211yescharacteristic
147C2×C43C2×AGL(1,ℤ/8)11yescharacteristic
148C2×C43#57611yescharacteristic
149D43—42no—
150D43—82no—
151C2×AGL(1,ℤ/8)—432no—
152#550—431no—
153D42—431no—
154#493—431no—
155#469—432no—
156#460—431no—
157#459D4311yescharacteristic, complemented
158#449—432no—
159#447—432no—
160C4×SD16—431no—
161#436—431no—
162C43#327411yescharacteristic, complemented, Sylow
163C2×#41—432no—
164C22×D4—432no—
165C22×D4—861no—
166AGL(1,ℤ/8)—868no—
167C2×SD16—431no—
168C2×SD16—432no—
169C2×D8—432no—
170C2×D8—432no—
171C2×D8C2×D4312yes—
172C2×M16—432no—
173#127—431no—
174#127—861no—
175#127C2×D4311yescharacteristic, complemented
176#121—432no—
177#121—432no—
178#121—862no—
179#121—861no—
180#120—862no—
181C4×Q8—431no—
182C4×D4—431no—
183C4×D4—861no—
184C4×D4C2×D4311yescharacteristic
185#106—431no—
186C4⋊C8C2×D4311yescharacteristic, complemented
187#103—431no—
188#102—431no—
189#102—432no—
190#102C2×D4312yescomplemented
191C22⋊C8—432no—
192C4×C8—431no—
193C24—862no—
194#41—864no—
195#41—1722no—
196C2×Q8—431no—
197C2×D4—21no—
198C2×D4—21no—
199C2×D4—431no—
200C2×D4—432no—
201C2×D4—862no—
202C2×D4—862no—
203C2×D4—864no—
204C2×D4—862no—
205C2×D4—862no—
206C2×D4—861no—
207C2×D4—861no—
208C2×D4—1724no—
209C2×D4—1722no—
210C2×D4C22×D4312yes—
211C2×D4C22×D4311yescharacteristic
212C22×C4—21no—
213C22×C4—432no—
214C22×C4—862no—
215SD16—434no—
216SD16—864no—
217D8—24no—
218D8—864no—
219D8—1722no—
220M16—864no—
221C2×C8—431no—
222C2×C8—431no—
223C2×C8C22×D4312yes—
224C4⋊C4—431no—
225C4⋊C4—431no—
226C4⋊C4—861no—
227C4⋊C4C22×D4311yescharacteristic
228C22⋊C4—21no—
229C22⋊C4—432no—
230C22⋊C4—862no—
231C22⋊C4—862no—
232C42—861no—
233C42C22×D4311yescharacteristic
234C23—21no—
235C23—22no—
236C23—432no—
237C23—862no—
238C23—3442no—
239C23—1724no—
240C23—1724no—
241Q8—432no—
242Q8—861no—
243D4—22no—
244D4—21no—
245D4—22no—
246D4—42no—
247D4—81no—
248D4—862no—
249D4—862no—
250D4—862no—
251D4—3441no—
252D4—3442no—
253D4—1724no—
254D4—1724no—
255D4—1724no—
256D4—1722no—
257D4D4×D4312yes—
258C2×C4—21no—
259C2×C4—42no—
260C2×C4—432no—
261C2×C4—861no—
262C2×C4—862no—
263C2×C4—862no—
264C2×C4—861no—
265C2×C4—1724no—
266C2×C4D4×D4311yescharacteristic
267C2×C4D4×D4311yescharacteristic
268C2×C4C23×D4311yescharacteristic
269C8—22no—
270C8—432no—
271C8—861no—
272C22—22no—
273C22—41no—
274C22—41no—
275C22—42no—
276C22—42no—
277C22—42no—
278C22—862no—
279C22—862no—
280C22—862no—
281C22—3448no—
282C22—1722no—
283C22—1722no—
284C22—1722no—
285C22C2×D4×D4311yescharacteristic
286C4—21no—
287C4—41no—
288C4—862no—
289C4—862no—
290C4—1721no—
291C4#1306334912yescomplemented
292C4C2×D4×D4311yescharacteristic
293C4#1306337111yescharacteristic
294C2—42no—
295C2—82no—
296C2—3442no—
297C2—1722no—
298C2#1458353311yescharacteristic
299C2C2×#1306334911yescharacteristic
300C2#1458370311yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#459C2
socleC22×C43C22×D4
hypercenter#459D43
hypocenterC43#3274
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. C2×#13063349C2semidirect
2. #14583569C2semidirect
3. D4×D172C2semidirect
4. #14583275C2semidirect
5. #14583151C2semidirect
6. #14583100C2semidirect
7. #14583045C2semidirect
8. #14583031C2semidirect
9. C4×#10621883C2semidirect
10. #14582976C2semidirect
11. C43×#459C2semidirect
12. C2×#10621900C22semidirect
16. C2×#10621873C22semidirect
18. C2×#10621882C22semidirect
19. C2×#10621882C22semidirect
20. C2×#10621872C22semidirect
26. #13063296C22semidirect
28. C4×Dic86C22semidirect
31. #13063256C22semidirect
32. #13063248C22semidirect
33. #13063247C22semidirect
35. (C2×D43)⋊C8C22semidirect
36. C4×C43⋊C8C22semidirect
38. #127×C43C22semidirect
40. C4⋊C8×C43C22semidirect
41. #102×C43C22semidirect
70. #10621883D4semidirect
117. Dic86C2×D4semidirect
120. C43⋊C8C2×D4semidirect
137. C4×C43AGL(1,ℤ/8)semidirect
157. #459D43semidirect
162. C43#3274semidirect
175. #127C2×D43semidirect
186. C4⋊C8C2×D43semidirect
190. #102C2×D43semidirect
291. C4#13063349semidirect