Finite Group Databasebeta

← #19146391

Subgroups — #19146391

Order 5504.

476 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 476 conjugacy classes of subgroups — too many to draw. Only its 117 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#14583703C212yesmaximal, complemented
2#14583702C212yesmaximal, complemented
3#14583275C211yesmaximal, characteristic, complemented
4#14583168C212yesmaximal, complemented
5#14583167C212yesmaximal, complemented
6#14583068C212yesmaximal, complemented
7#14583066C211yesmaximal, characteristic, complemented
8#14583013C212yesmaximal, complemented
9C43×#453C211yesmaximal, characteristic, complemented
10#13063371C2212yescomplemented
11#13063370C2211yescharacteristic, complemented
12#13063353C2212yescomplemented
13#13063352—22no—
14#13063351—22no—
15#13063351C2212yescomplemented
16#13063350—22no—
17#13063350C2212yescomplemented
18#13063349—22no—
19#13063346—22no—
20#13063345—22no—
21#13063345C2212yes—
22C2×#10621882—22no—
23C2×#10621882C2212yescomplemented
24C2×#10621882C2212yescomplemented
25D8×D43—22no—
26#13063333C2212yescomplemented
27#13063332C2212yescomplemented
28#13063322C2211yescharacteristic, complemented
29#13063260C2212yescomplemented
30#13063253C2212yescomplemented
31#13063242C2211yescharacteristic, complemented
32#13063241C2212yescomplemented
33C4×C43⋊C8C2211yescharacteristic, complemented
34H(5,𝔽2)×C43C2211yescharacteristic, complemented
35AGL(1,ℤ/8)×C43C2212yescomplemented
36#127×C43C2211yescharacteristic, complemented
37#104×C43C2212yescomplemented
38#100×C43C2211yescharacteristic, complemented
39#41×C43—22no—
40#41×C43C2312yes—
41C2×D4×C43—22no—
42C2×D4×C43—41no—
43C2×D4×C43—41no—
44C2×D4×C43C2311yescharacteristic
45C2×D4×C43C2311yescharacteristic
46C2×C22⋊D43—41no—
47#10621902—22no—
48#10621900—22no—
49D4×D43—22no—
50D4×D43—22no—
51D4×D43—42no—
52#10621898—22no—
53#10621898C2312yes—
54C2×D172—22no—
55C2×D172—41no—
56C2×D172C2312yes—
57SD16×C43—22no—
58D8×C43—22no—
59M16×C43C2312yes—
60C42×C43C2311yescharacteristic
61#10621885D412yescomplemented
62#10621884—22no—
63#10621884D412yescomplemented
64#10621883—22no—
65#10621883D412yescomplemented
66#10621882—22no—
67#10621882—22no—
68#10621882—22no—
69#10621882—22no—
70#10621882—22no—
71#10621882—22no—
72#10621882D412yescomplemented
73#10621877—22no—
74#10621877C2312yes—
75C2×C43⋊C8—22no—
76C2×C43⋊C8C2312yes—
77D344—22no—
78#10621873—22no—
79#10621872—22no—
80C8×D43—22no—
81C23×C43—21no—
82C23×C43—21no—
83C23×C43—41no—
84C22×D43—22no—
85C22×D43—41no—
86C22×D43—42no—
87Q8×C43C2×D412yes—
88D4×C43—22no—
89D4×C43—22no—
90D4×C43—22no—
91D4×C43—42no—
92D4×C43—82no—
93D4×C43C2×D412yes—
94C2×C4×C43—21no—
95C2×C4×C43—22no—
96C2×C4×C43—41no—
97C2×C4×C43C2411yescharacteristic
98C22⋊D43—22no—
99C22⋊D43—42no—
100C22⋊D43—42no—
101C2×Dic43—41no—
102D172—22no—
103D172—22no—
104D172—42no—
105D172—82no—
106D172C2×D412yes—
107C4×D43—22no—
108C4×D43—42no—
109Dic86C2×D412yes—
110C8×C43—22no—
111C43⋊C8—22no—
112C43⋊C8C2×D412yes—
113C43⋊C8C2×D412yes—
114C22×C43—22no—
115C22×C43—41no—
116C22×C43—41no—
117C22×C43—81no—
118C22×C43—81no—
119C22×C43—161no—
120C22×C43H(5,𝔽2)11yescharacteristic
121C2×D43—22no—
122C2×D43—42no—
123C2×D43—82no—
124C2×D43—161no—
125C2×D43—162no—
126C4×C43—22no—
127C4×C43—22no—
128C4×C43C22×D412yes—
129Dic43—22no—
130#3292—431nomaximal, Sylow
131C2×C43—21no—
132C2×C43—42no—
133C2×C43—81no—
134C2×C43—81no—
135C2×C43D4211yescharacteristic
136D43—42no—
137D43—82no—
138#576—432no—
139#576—432no—
140#493—431no—
141#472—432no—
142#472—432no—
143#453—431no—
144#453—432no—
145#453D4311yescharacteristic, complemented
146#443—432no—
147C43#329211yescharacteristic, complemented, Sylow
148H(5,𝔽2)—432no—
149H(5,𝔽2)—431no—
150H(5,𝔽2)C2×D4311yescharacteristic, complemented
151AGL(1,ℤ/8)—432no—
152AGL(1,ℤ/8)—432no—
153AGL(1,ℤ/8)—432no—
154AGL(1,ℤ/8)—862no—
155AGL(1,ℤ/8)—862no—
156AGL(1,ℤ/8)—862no—
157AGL(1,ℤ/8)—862no—
158AGL(1,ℤ/8)C2×D4312yescomplemented
159#135—432no—
160#135—862no—
161#135—862no—
162C2×D8—432no—
163C2×D8—432no—
164C2×D8—862no—
165C2×D8—862no—
166#131—432no—
167#131—432no—
168#127—431no—
169#127C2×D4311yescharacteristic, complemented
170#108—432no—
171#104—432no—
172#104C2×D4312yescomplemented
173#100—431no—
174#100—432no—
175#100C2×D4311yescharacteristic, complemented
176C4×C8—431no—
177#41—22no—
178#41—432no—
179#41—862no—
180#41—862no—
181#41—862no—
182#41C22×D4312yes—
183C2×D4—22no—
184C2×D4—41no—
185C2×D4—41no—
186C2×D4—432no—
187C2×D4—862no—
188C2×D4—862no—
189C2×D4—862no—
190C2×D4—1721no—
191C2×D4—1722no—
192C2×D4—1721no—
193C2×D4C22×D4311yescharacteristic
194C2×D4C22×D4311yescharacteristic
195Q16—432no—
196SD16—22no—
197SD16—432no—
198SD16—432no—
199SD16—862no—
200SD16—862no—
201SD16—862no—
202D8—22no—
203D8—432no—
204D8—862no—
205D8—862no—
206D8—862no—
207D8—862no—
208D8—862no—
209D8—862no—
210D8—862no—
211M16—432no—
212M16—862no—
213M16—862no—
214M16C22×D4312yes—
215C2×C8—432no—
216C2×C8—862no—
217C2×C8—862no—
218C42C22×D4311yescharacteristic
219C23—21no—
220C23—21no—
221C23—41no—
222C23—862no—
223C23—1722no—
224C23—1721no—
225Q8—432no—
226Q8D4×D4312yes—
227D4—22no—
228D4—22no—
229D4—22no—
230D4—42no—
231D4—82no—
232D4—432no—
233D4—862no—
234D4—862no—
235D4—862no—
236D4—3442no—
237D4—1722no—
238D4—1722no—
239D4—1722no—
240D4D4×D4312yes—
241C2×C4—21no—
242C2×C4—22no—
243C2×C4—41no—
244C2×C4—862no—
245C2×C4—1722no—
246C2×C4—1721no—
247C2×C4C23×D4311yescharacteristic
248C8—22no—
249C8—432no—
250C8—432no—
251C8—862no—
252C22—22no—
253C22—41no—
254C22—41no—
255C22—81no—
256C22—81no—
257C22—161no—
258C22—862no—
259C22—3442no—
260C22—1722no—
261C22—6882no—
262C22—6881no—
263C22#1306337011yescharacteristic
264C4—22no—
265C4—22no—
266C4—862no—
267C4C2×D4×D4312yes—
268C2—21no—
269C2—42no—
270C2—81no—
271C2—81no—
272C2—3442no—
273C2—1722no—
274C2#1458353111yescharacteristic
subgroupG/H
centerC2#14583531
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#453C2
socleC2×C43D42
hypercenter#453D43
hypocenterC43#3292
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C2×C4 ◁ #453

Complements

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

NH ≅ G/Ntype
1. #14583703C2semidirect
2. #14583702C2semidirect
3. #14583275C2semidirect
4. #14583168C2semidirect
5. #14583167C2semidirect
6. #14583068C2semidirect
7. #14583066C2semidirect
8. #14583013C2semidirect
9. C43×#453C2semidirect
10. #13063371C22semidirect
11. #13063370C22semidirect
12. #13063353C22semidirect
15. #13063351C22semidirect
17. #13063350C22semidirect
23. C2×#10621882C22semidirect
24. C2×#10621882C22semidirect
26. #13063333C22semidirect
27. #13063332C22semidirect
28. #13063322C22semidirect
29. #13063260C22semidirect
30. #13063253C22semidirect
31. #13063242C22semidirect
32. #13063241C22semidirect
33. C4×C43⋊C8C22semidirect
34. H(5,𝔽2)×C43C22semidirect
35. AGL(1,ℤ/8)×C43C22semidirect
36. #127×C43C22semidirect
37. #104×C43C22semidirect
38. #100×C43C22semidirect
61. #10621885D4semidirect
63. #10621884D4semidirect
65. #10621883D4semidirect
72. #10621882D4semidirect
145. #453D43semidirect
147. C43#3292semidirect
150. H(5,𝔽2)C2×D43semidirect
158. AGL(1,ℤ/8)C2×D43semidirect
169. #127C2×D43semidirect
172. #104C2×D43semidirect
175. #100C2×D43semidirect