Finite Group Databasebeta

← #19146836

Subgroups — #19146836

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#14583615C211yesmaximal, characteristic, complemented
2#14583534C211yesmaximal, characteristic, complemented
3#14583221C212yesmaximal, complemented
4#14583186C211yesmaximal, characteristic, complemented
5#14583151C212yesmaximal, complemented
6#14583091C211yesmaximal, characteristic, complemented
7#14583034C212yesmaximal, complemented
8C4×D344C211yesmaximal, characteristic, complemented
9#14582978C211yesmaximal, characteristic, complemented
10#14582902C212yesmaximal, complemented
11C43×#486C211yesmaximal, characteristic, complemented
12C2×D4×D43—21no—
13C2×D4×D43C2212yes—
14C2×D344C2211yescharacteristic
15C2×#10621882C2212yescomplemented
16C2×#10621872C2212yescomplemented
17#13063314—22no—
18#13063300—21no—
19#13063300C2212yescomplemented
20#13063296—21no—
21#13063296C2212yes—
22#13063293—22no—
23C4×D172C2211yescharacteristic
24C4×D172C2211yescharacteristic
25C4×D172C2211yescharacteristic, complemented
26#13063283—21no—
27#13063283C2212yescomplemented
28#13063259C2211yescharacteristic, complemented
29#13063256C2212yescomplemented
30C4⋊(C43⋊C8)C2211yescharacteristic, complemented
31#13063247C2211yescharacteristic
32#13063247C2211yescharacteristic, complemented
33#13063246C2212yescomplemented
34#13063245C2212yes—
35(C2×D43)⋊C8C2212yescomplemented
36C4⋊Q8×C43C2211yescharacteristic, complemented
37#127×C43C2211yescharacteristic
38#102×C43C2212yescomplemented
39#102×C43C2212yescomplemented
40C4×C8×C43C2211yescharacteristic, complemented
41C23×D43—22no—
42C2×Q8×C43—21no—
43C2×D4×C43—21no—
44C2×D4×C43—21no—
45C2×D4×C43C2312yes—
46C2×C22⋊D43—22no—
47C2×C22⋊D43—22no—
48D4×D43—24no—
49D4×D43—42no—
50D4×D43—44no—
51C2×D172—22no—
52C2×D172D411yescharacteristic
53C2×D172C2311yescharacteristic
54C2×D172C2311yescharacteristic
55C2×C4×D43—21no—
56C2×C4×D43—21no—
57C2×C4×D43C2312yes—
58C2×C8×C43C2311yescharacteristic
59C2×C8×C43C2311yescharacteristic
60C4⋊C4×C43—21no—
61C4⋊C4×C43C2312yes—
62C42×C43C2311yescharacteristic
63C22⋊Dic43—22no—
64#10621882—42no—
65(C2×D43)⋊C4—21no—
66(C2×D43)⋊C4—21no—
67(C2×D43)⋊C4—22no—
68(C2×D43)⋊C4—22no—
69(C2×D43)⋊C4D412yes—
70C4⋊Dic43D411yescharacteristic
71C4⋊Dic43C2311yescharacteristic
72C4⋊Dic43C2311yescharacteristic
73C4×Dic43—22no—
74C2×C43⋊C8C2312yes—
75D344—22no—
76#10621872—42no—
77C23×C43—22no—
78C22×D43—21no—
79C22×D43—21no—
80C22×D43—44no—
81C22×D43—44no—
82C22×D43—82no—
83C22×D43C2×D412yes—
84Q8×C43—81no—
85D4×C43—22no—
86D4×C43—22no—
87D4×C43—42no—
88D4×C43—81no—
89C2×C4×C43—22no—
90C2×C4×C43C2×D411yescharacteristic
91C2×C4×C43C2×D411yescharacteristic
92C2×C4×C43C2411yescharacteristic
93C22⋊D43—44no—
94C22⋊D43—44no—
95C2×Dic43—21no—
96C2×Dic43—21no—
97C2×Dic43C2×D412yes—
98D172—22no—
99D172—21no—
100D172—21no—
101D172—21no—
102D172—82no—
103D172#4112yes—
104C4×D43—22no—
105C4×D43—22no—
106C4×D43—42no—
107C4×D43—42no—
108C8×C43—21no—
109C8×C43—21no—
110C43⋊C8—22no—
111C22×C43—42no—
112C22×C43—42no—
113C22×C43—42no—
114C22×C43C22×D411yescharacteristic
115C2×D43—22no—
116C2×D43—22no—
117C2×D43—22no—
118C2×D43—22no—
119C2×D43—41no—
120C2×D43—41no—
121C2×D43—41no—
122C2×D43—41no—
123C2×D43—41no—
124C2×D43—88no—
125C4×C43—21no—
126C4×C43—42no—
127C4×C43AGL(1,ℤ/8)12yes—
128C4×C43C2×#4111yescharacteristic
129C4×C43H(5,𝔽2)11yescharacteristic
130Dic43—22no—
131Dic43—41no—
132Dic43—41no—
133#3325—431nomaximal, Sylow
134C2×C43—82no—
135C2×C43#54611yescharacteristic
136C2×C43C2×AGL(1,ℤ/8)11yescharacteristic
137C2×C43#57611yescharacteristic
138D43—42no—
139D43—42no—
140D43—81no—
141#555—431no—
142D42—431no—
143#486D4311yescharacteristic, complemented
144#482—432no—
145#476—431no—
146#469—432no—
147#459—431no—
148#447—432no—
149C4×D8—431no—
150#436—431no—
151#418—432no—
152C43#332511yescharacteristic, complemented, Sylow
153C22×D4—432no—
154C22×D4—861no—
155C2×D8—432no—
156C2×D8—431no—
157C2×M16—432no—
158C4⋊Q8C2×D4311yescharacteristic, complemented
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×D4—431no—
169#117—432no—
170#117—861no—
171#107—431no—
172#106—432no—
173C4⋊C8—431no—
174#102—432no—
175#102—431no—
176#102—431no—
177#102—432no—
178#102C2×D4312yescomplemented
179#102C2×D4312yescomplemented
180C22⋊C8—432no—
181C4×C8C2×D4311yescharacteristic, complemented
182C24—862no—
183C2×Q8—21no—
184C2×D4—21no—
185C2×D4—21no—
186C2×D4—431no—
187C2×D4—431no—
188C2×D4—431no—
189C2×D4—862no—
190C2×D4—862no—
191C2×D4—864no—
192C2×D4—862no—
193C2×D4—1722no—
194C2×D4—1724no—
195C2×D4C22×D4312yes—
196C22×C4—432no—
197C22×C4—861no—
198C22×C4—861no—
199D8—862no—
200D8—1722no—
201M16—1722no—
202C2×C8—432no—
203C2×C8C22×D4311yescharacteristic
204C2×C8C22×D4311yescharacteristic
205C4⋊C4—21no—
206C4⋊C4—431no—
207C4⋊C4—431no—
208C4⋊C4—431no—
209C4⋊C4C22×D4312yes—
210C22⋊C4—432no—
211C22⋊C4—862no—
212C22⋊C4—862no—
213C22⋊C4—862no—
214C22⋊C4—861no—
215C22⋊C4—861no—
216C42—862no—
217C42C22×D4311yescharacteristic
218C23—22no—
219C23—432no—
220C23—861no—
221C23—861no—
222C23—3442no—
223C23—1724no—
224C23—1724no—
225Q8—81no—
226D4—22no—
227D4—22no—
228D4—42no—
229D4—81no—
230D4—432no—
231D4—862no—
232D4—861no—
233D4—861no—
234D4—861no—
235D4—3442no—
236D4—1724no—
237D4—1724no—
238C2×C4—22no—
239C2×C4—432no—
240C2×C4—862no—
241C2×C4—862no—
242C2×C4—861no—
243C2×C4—861no—
244C2×C4—1722no—
245C2×C4—1722no—
246C2×C4D4×D4311yescharacteristic
247C2×C4D4×D4311yescharacteristic
248C2×C4C23×D4311yescharacteristic
249C8—21no—
250C8—21no—
251C8—862no—
252C22—42no—
253C22—42no—
254C22—42no—
255C22—862no—
256C22—862no—
257C22—862no—
258C22—862no—
259C22—3448no—
260C22—1721no—
261C22—1721no—
262C22—1721no—
263C22—1721no—
264C22—1721no—
265C22C2×D4×D4311yescharacteristic
266C4—21no—
267C4—42no—
268C4—862no—
269C4—1721no—
270C4—1721no—
271C4#1306335212yes—
272C4#41×D4311yescharacteristic
273C4#1306337111yescharacteristic
274C2—82no—
275C2—3441no—
276C2—1722no—
277C2—1722no—
278C2#1458354211yescharacteristic
279C2C2×#1306335211yescharacteristic
280C2#1458370011yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#486C2
socleC22×C43C22×D4
hypercenter#486D43
hypocenterC43#3325
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #486

Complements

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

NH ≅ G/Ntype
1. #14583615C2semidirect
2. #14583534C2semidirect
3. #14583221C2semidirect
4. #14583186C2semidirect
5. #14583151C2semidirect
6. #14583091C2semidirect
7. #14583034C2semidirect
8. C4×D344C2semidirect
9. #14582978C2semidirect
10. #14582902C2semidirect
11. C43×#486C2semidirect
15. C2×#10621882C22semidirect
16. C2×#10621872C22semidirect
19. #13063300C22semidirect
25. C4×D172C22semidirect
27. #13063283C22semidirect
28. #13063259C22semidirect
29. #13063256C22semidirect
30. C4⋊(C43⋊C8)C22semidirect
32. #13063247C22semidirect
33. #13063246C22semidirect
35. (C2×D43)⋊C8C22semidirect
36. C4⋊Q8×C43C22semidirect
38. #102×C43C22semidirect
39. #102×C43C22semidirect
40. C4×C8×C43C22semidirect
143. #486D43semidirect
152. C43#3325semidirect
158. C4⋊Q8C2×D43semidirect
178. #102C2×D43semidirect
179. #102C2×D43semidirect
181. C4×C8C2×D43semidirect