Finite Group Databasebeta

← #19146840

Subgroups — #19146840

Order 5504.

460 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 460 conjugacy classes of subgroups — too many to draw. Only its 115 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#14583614C211yesmaximal, characteristic, complemented
2#14583534C211yesmaximal, characteristic, complemented
3#14583245C211yesmaximal, characteristic, complemented
4#14583222C212yesmaximal, complemented
5#14583190C211yesmaximal, characteristic, complemented
6#14583149C212yesmaximal, complemented
7#14583031C212yesmaximal, complemented
8C4×#10621882C211yesmaximal, characteristic, complemented
9#14582976C211yesmaximal, characteristic, complemented
10#14582902C212yesmaximal, complemented
11C43×#459C211yesmaximal, characteristic, complemented
12C2×D4×D43—21no—
13C2×D4×D43C2212yes—
14C2×#10621882C2211yescharacteristic
15C2×#10621872C2212yescomplemented
16#13063325C2211yescharacteristic, complemented
17#13063311—22no—
18#13063299—21no—
19#13063296—21no—
20#13063296C2212yes—
21#13063296C2212yescomplemented
22#13063293—22no—
23C4×D172C2211yescharacteristic
24C4×D172C2211yescharacteristic
25#13063284—21no—
26#13063283C2212yescomplemented
27#13063258C2211yescharacteristic, complemented
28#13063257C2212yescomplemented
29#13063247C2212yes—
30#13063246C2211yescharacteristic, complemented
31#13063246C2212yescomplemented
32#13063246C2212yescomplemented
33#13063245C2211yescharacteristic
34(C2×D43)⋊C8C2212yescomplemented
35C4×C43⋊C8C2211yescharacteristic, complemented
36C2×D8×C43C2212yescomplemented
37#127×C43C2211yescharacteristic
38C4×D4×C43C2211yescharacteristic, complemented
39C4⋊C8×C43C2211yescharacteristic, complemented
40#102×C43C2212yescomplemented
41C23×D43—22no—
42C2×D4×C43—21no—
43C2×D4×C43—21no—
44C2×D4×C43C2312yes—
45C2×D4×C43C2311yescharacteristic
46C22×C4×C43—21no—
47C2×C22⋊D43—22no—
48C2×C22⋊D43—22no—
49C2×C22⋊D43—22no—
50D4×D43—24no—
51D4×D43—42no—
52D4×D43—44no—
53C2×D172D411yescharacteristic
54C2×D172C2311yescharacteristic
55C2×C4×D43—21no—
56C2×C4×D43C2312yes—
57C2×Dic86—21no—
58D8×C43—42no—
59C2×C8×C43C2312yes—
60C4⋊C4×C43C2311yescharacteristic
61C22⋊C4×C43—21no—
62C42×C43C2311yescharacteristic
63C22⋊Dic43—22no—
64C22⋊Dic43—22no—
65#10621882—22no—
66(C2×D43)⋊C4—21no—
67(C2×D43)⋊C4—22no—
68(C2×D43)⋊C4D412yes—
69C4⋊Dic43—21no—
70C4⋊Dic43D411yescharacteristic
71C4⋊Dic43C2312yes—
72C4⋊Dic43C2311yescharacteristic
73C4×Dic43—22no—
74C2×C43⋊C8C2311yescharacteristic
75C2×C43⋊C8C2311yescharacteristic
76#10621872—42no—
77C23×C43—21no—
78C23×C43—22no—
79C22×D43—21no—
80C22×D43—44no—
81C22×D43—44no—
82C22×D43—82no—
83C22×D43C2×D412yes—
84D4×C43—21no—
85D4×C43—22no—
86D4×C43—21no—
87D4×C43—22no—
88D4×C43—42no—
89D4×C43—81no—
90C2×C4×C43—21no—
91C2×C4×C43—42no—
92C2×C4×C43C2×D411yescharacteristic
93C2×C4×C43C2×D411yescharacteristic
94C2×C4×C43C2411yescharacteristic
95C22⋊D43—44no—
96C22⋊D43—44no—
97C22⋊D43—82no—
98C2×Dic43—22no—
99C2×Dic43—21no—
100C2×Dic43C2×D412yes—
101D172—22no—
102D172—21no—
103D172#4112yes—
104C4×D43—22no—
105C4×D43—22no—
106C4×D43—42no—
107Dic86—81no—
108C8×C43—22no—
109C43⋊C8—21no—
110C43⋊C8—21no—
111C22×C43—42no—
112C22×C43—41no—
113C22×C43—42no—
114C22×C43—41no—
115C22×C43—42no—
116C22×C43—41no—
117C22×C43C22×D411yescharacteristic
118C2×D43—22no—
119C2×D43—22no—
120C2×D43—22no—
121C2×D43—22no—
122C2×D43—41no—
123C2×D43—41no—
124C2×D43—88no—
125C4×C43—21no—
126C4×C43—41no—
127C4×C43AGL(1,ℤ/8)12yes—
128C4×C43C2×#4111yescharacteristic
129C4×C43H(5,𝔽2)11yescharacteristic
130Dic43—22no—
131Dic43—41no—
132Dic43—42no—
133#3325—431nomaximal, Sylow
134C2×C43—82no—
135C2×C43—81no—
136C2×C43#54611yescharacteristic
137C2×C43C2×AGL(1,ℤ/8)11yescharacteristic
138C2×C43#57611yescharacteristic
139D43—42no—
140D43—42no—
141#555—431no—
142D42—431no—
143#486—431no—
144#482—432no—
145#476—431no—
146#469—432no—
147#459D4311yescharacteristic, complemented
148#447—432no—
149C4×D8—431no—
150#436—431no—
151#418—432no—
152C43#332511yescharacteristic, complemented, Sylow
153C22×D4—432no—
154C22×D4—861no—
155C2×D8—431no—
156C2×D8C2×D4312yescomplemented
157C2×M16—432no—
158C4⋊Q8—431no—
159#127C2×D4311yescharacteristic
160#124—862no—
161#121—432no—
162#121—432no—
163#121—861no—
164#121—861no—
165#120—862no—
166C4×D4—431no—
167C4×D4—431no—
168C4×D4C2×D4311yescharacteristic, complemented
169#117—432no—
170#117—861no—
171#107—431no—
172#106—432no—
173C4⋊C8C2×D4311yescharacteristic, complemented
174#102—432no—
175#102—431no—
176#102—432no—
177#102—432no—
178#102—431no—
179#102C2×D4312yescomplemented
180C22⋊C8—432no—
181C4×C8—431no—
182C24—862no—
183C2×Q8—861no—
184C2×D4—21no—
185C2×D4—21no—
186C2×D4—431no—
187C2×D4—431no—
188C2×D4—862no—
189C2×D4—864no—
190C2×D4—862no—
191C2×D4—862no—
192C2×D4—1722no—
193C2×D4—1724no—
194C2×D4C22×D4312yes—
195C2×D4C22×D4311yescharacteristic
196C22×C4—21no—
197C22×C4—432no—
198C22×C4—861no—
199D8—42no—
200D8—862no—
201M16—1722no—
202C2×C8—431no—
203C2×C8—431no—
204C2×C8C22×D4312yes—
205C4⋊C4—431no—
206C4⋊C4—432no—
207C4⋊C4—431no—
208C4⋊C4—861no—
209C4⋊C4C22×D4311yescharacteristic
210C22⋊C4—21no—
211C22⋊C4—432no—
212C22⋊C4—862no—
213C22⋊C4—862no—
214C22⋊C4—862no—
215C22⋊C4—861no—
216C42—862no—
217C42C22×D4311yescharacteristic
218C23—21no—
219C23—22no—
220C23—432no—
221C23—861no—
222C23—3442no—
223C23—1724no—
224C23—1724no—
225Q8—3441no—
226D4—21no—
227D4—22no—
228D4—21no—
229D4—22no—
230D4—42no—
231D4—81no—
232D4—432no—
233D4—862no—
234D4—861no—
235D4—3442no—
236D4—1724no—
237D4—1724no—
238C2×C4—21no—
239C2×C4—42no—
240C2×C4—432no—
241C2×C4—862no—
242C2×C4—862no—
243C2×C4—862no—
244C2×C4—861no—
245C2×C4—1722no—
246C2×C4D4×D4311yescharacteristic
247C2×C4D4×D4311yescharacteristic
248C2×C4C23×D4311yescharacteristic
249C8—22no—
250C8—861no—
251C8—861no—
252C22—41no—
253C22—42no—
254C22—42no—
255C22—41no—
256C22—42no—
257C22—41no—
258C22—862no—
259C22—862no—
260C22—862no—
261C22—862no—
262C22—3448no—
263C22—1721no—
264C22—1721no—
265C22C2×D4×D4311yescharacteristic
266C4—21no—
267C4—41no—
268C4—862no—
269C4—1721no—
270C4—1722no—
271C4#1306334912yes—
272C4#41×D4311yescharacteristic
273C4#1306337011yescharacteristic
274C2—82no—
275C2—81no—
276C2—1722no—
277C2—1722no—
278C2#1458354611yescharacteristic
279C2C2×#1306334911yescharacteristic
280C2#1458370311yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#459C2
socleC22×C43C22×D4
hypercenter#459D43
hypocenterC43#3325
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. #14583614C2semidirect
2. #14583534C2semidirect
3. #14583245C2semidirect
4. #14583222C2semidirect
5. #14583190C2semidirect
6. #14583149C2semidirect
7. #14583031C2semidirect
8. C4×#10621882C2semidirect
9. #14582976C2semidirect
10. #14582902C2semidirect
11. C43×#459C2semidirect
15. C2×#10621872C22semidirect
16. #13063325C22semidirect
21. #13063296C22semidirect
26. #13063283C22semidirect
27. #13063258C22semidirect
28. #13063257C22semidirect
30. #13063246C22semidirect
31. #13063246C22semidirect
32. #13063246C22semidirect
34. (C2×D43)⋊C8C22semidirect
35. C4×C43⋊C8C22semidirect
36. C2×D8×C43C22semidirect
38. C4×D4×C43C22semidirect
39. C4⋊C8×C43C22semidirect
40. #102×C43C22semidirect
147. #459D43semidirect
152. C43#3325semidirect
156. C2×D8C2×D43semidirect
168. C4×D4C2×D43semidirect
173. C4⋊C8C2×D43semidirect
179. #102C2×D43semidirect