Finite Group Databasebeta

← #19143944

Subgroups — #19143944

Order 5504.

724 conjugacy classes of subgroups; only the 161 normal subgroups are shown.

normal subgroups only

This group has 724 conjugacy classes of subgroups — too many to draw. Only its 161 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#14583697C212yesmaximal, complemented
2#14583445C211yesmaximal, characteristic, complemented
3#14583082C212yesmaximal, complemented
4#14583077C212yesmaximal, complemented
5#14583072C212yesmaximal, complemented
6#14583067C212yesmaximal, complemented
7C2×#13063252C212yesmaximal, complemented
8#14582883C211yesmaximal, characteristic, complemented
9C43×#585C211yesmaximal, characteristic, complemented
10C2×#10621898C2211yescharacteristic, complemented
11#13063356—22no—
12#13063355C2214yescomplemented
13#13063351—22no—
14#13063350C2214yescomplemented
15#13063345—24no—
16C2×#10621877C2212yescomplemented
17#13063323C2211yescharacteristic, complemented
18#13063321C2211yescharacteristic, complemented
19#13063314C2211yescharacteristic, complemented
20#13063312C2211yescharacteristic, complemented
21#13063297—22no—
22C4×C22⋊D43—22no—
23C2×C4×Dic43C2211yescharacteristic, complemented
24#13063252C2214yescomplemented
25#13063252C2214yescomplemented
26#13063244C2212yescomplemented
27#13063242C2212yescomplemented
282−1+4×C43—22no—
292−1+4×C43C2212yes—
30H(5,𝔽2)×C43—22no—
31H(5,𝔽2)×C43—22no—
32H(5,𝔽2)×C43C2212yes—
33C2×#41×C43—24no—
34C2×#41×C43—22no—
35C2×#41×C43C2212yes—
36C2×#41×C43C2211yescharacteristic
37#41×C43—24no—
38#41×C43—28no—
39#41×C43—24no—
40#41×C43—24no—
41#41×C43—24no—
42#41×C43—22no—
43#41×C43—22no—
44#41×C43—24no—
45#41×C43—22no—
46#41×C43—22no—
47#41×C43D414yescomplemented
48#41×C43C2314yes—
49C2×Q8×C43—22no—
50C2×Q8×C43—24no—
51C2×Q8×C43D412yescomplemented
52C2×Q8×C43C2311yescharacteristic
53C2×D4×C43—22no—
54C2×D4×C43—28no—
55C2×D4×C43—24no—
56C2×D4×C43—24no—
57C2×D4×C43—22no—
58C2×D4×C43D412yes—
59C2×D4×C43D412yescomplemented
60C2×D4×C43C2311yescharacteristic
61C22×C4×C43—24no—
62C22×C4×C43—22no—
63C22×C4×C43D412yes—
64C22×C4×C43C2311yescharacteristic
65C2×C22⋊D43—22no—
66C2×C22⋊D43—21no—
67C22×Dic43—21no—
68#10621898—22no—
69#10621898—22no—
70C2×D172C2311yescharacteristic
71C2×C4×D43—21no—
72C2×Dic86C2311yescharacteristic
73C22⋊Dic43—22no—
74#10621885—24no—
75#10621884—24no—
76#10621883—24no—
77#10621882—24no—
78(C2×D43)⋊C4—22no—
79Dic43⋊C4—22no—
80C4×Dic43—21no—
81C4×Dic43C2311yescharacteristic
82C4×Dic43C2311yescharacteristic
83#10621877—22no—
84#10621877C2314yes—
85C2×C43⋊C8—22no—
86C23×C43—24no—
87C23×C43—22no—
88C23×C43C2×D412yes—
89C23×C43C2×D411yescharacteristic
90C22×D43—21no—
91Q8×C43—24no—
92Q8×C43—22no—
93Q8×C43—22no—
94Q8×C43C2×D414yes—
95D4×C43—28no—
96D4×C43—24no—
97D4×C43—24no—
98D4×C43—24no—
99D4×C43—24no—
100D4×C43—22no—
101D4×C43—22no—
102D4×C43C2×D414yes—
103C2×C4×C43—24no—
104C2×C4×C43—28no—
105C2×C4×C43—22no—
106C2×C4×C43—24no—
107C2×C4×C43—22no—
108C2×C4×C43—22no—
109C2×C4×C43—24no—
110C2×C4×C43C2×D412yes—
111C2×C4×C43C2×D411yescharacteristic
112C2×C4×C43C2×D412yes—
113C2×C4×C43C2×D412yes—
114C2×C4×C43C2411yescharacteristic
115C22⋊D43—44no—
116C22⋊D43—42no—
117C2×Dic43—21no—
118C2×Dic43—21no—
119C2×Dic43—21no—
120C2×Dic43—42no—
121D172—22no—
122C4×D43—41no—
123C4×D43—41no—
124Dic86—22no—
125C43⋊C8—24no—
126C22×C43—24no—
127C22×C43—22no—
128C22×C43—41no—
129C22×C43—42no—
130C22×C43—82no—
131C22×C43—84no—
132C22×C43#12012yes—
133C22×C43C22×D411yescharacteristic
134C2×D43—42no—
135C2×D43—41no—
136C4×C43—24no—
137C4×C43—22no—
138C4×C43#12011yescharacteristic
139C4×C43#12011yescharacteristic
140C4×C43C22×D412yes—
141Dic43—22no—
142Dic43—41no—
143Dic43—41no—
144#3018—431nomaximal, Sylow
145C2×C43—21no—
146C2×C43—22no—
147C2×C43—42no—
148C2×C43—44no—
149C2×C43C2×#12011yescharacteristic
150D43—81no—
151#585D4311yescharacteristic, complemented
152#575—432no—
153#532—431no—
154#456—432no—
155#455—432no—
156#454—432no—
157#453—432no—
158C2×#104—432no—
159#413—431no—
160C43#301811yescharacteristic, complemented, Sylow
1612−1+4—22no—
1622−1+4C2×D4312yes—
163H(5,𝔽2)—22no—
164H(5,𝔽2)—22no—
165H(5,𝔽2)C2×D4312yes—
166C2×#41—24no—
167C2×#41—22no—
168C2×#41—431no—
169C2×#41C2×D4312yes—
170C2×#41C2×D4311yescharacteristic
171#137—434no—
172#137—862no—
173AGL(1,ℤ/8)—434no—
174AGL(1,ℤ/8)—862no—
175#135—864no—
176C2×M16—432no—
177C4⋊Q8—431no—
178#127—431no—
179#124—431no—
180#124—431no—
181#121—862no—
182C4×D4—862no—
183C2×C42—431no—
184#104—434no—
185#104—434no—
186#101—432no—
187#100—432no—
188#41—24no—
189#41—28no—
190#41—24no—
191#41—24no—
192#41—24no—
193#41—22no—
194#41—22no—
195#41—24no—
196#41—22no—
197#41—22no—
198#41—862no—
199#41—862no—
200#41C22⋊D4314yescomplemented
201#41C22×D4314yes—
202C2×Q8—22no—
203C2×Q8—24no—
204C2×Q8—431no—
205C2×Q8C22⋊D4312yescomplemented
206C2×Q8C22×D4311yescharacteristic
207C2×D4—28no—
208C2×D4—22no—
209C2×D4—24no—
210C2×D4—22no—
211C2×D4—24no—
212C2×D4—431no—
213C2×D4—862no—
214C2×D4—861no—
215C2×D4C22⋊D4312yes—
216C2×D4C22⋊D4312yescomplemented
217C2×D4C22×D4311yescharacteristic
218C22×C4—24no—
219C22×C4—22no—
220C22×C4—861no—
221C22×C4—861no—
222C22×C4C22⋊D4312yes—
223C22×C4C22×D4311yescharacteristic
224Q16—864no—
225SD16—864no—
226SD16—864no—
227D8—864no—
228M16—434no—
229M16—862no—
230C2×C8—862no—
231C4⋊C4—862no—
232C22⋊C4—862no—
233C22⋊C4—862no—
234C42—431no—
235C42—431no—
236C42—861no—
237C23—24no—
238C23—22no—
239C23—861no—
240C23C2×C22⋊D4312yes—
241C23C2×C22⋊D4311yescharacteristic
242Q8—24no—
243Q8—22no—
244Q8—22no—
245Q8—862no—
246Q8C2×C22⋊D4314yes—
247D4—28no—
248D4—24no—
249D4—24no—
250D4—24no—
251D4—24no—
252D4—22no—
253D4—22no—
254D4—862no—
255D4—1724no—
256D4—1722no—
257D4C2×C22⋊D4314yes—
258C2×C4—24no—
259C2×C4—28no—
260C2×C4—22no—
261C2×C4—22no—
262C2×C4—24no—
263C2×C4—22no—
264C2×C4—24no—
265C2×C4—861no—
266C2×C4—861no—
267C2×C4—861no—
268C2×C4—1722no—
269C2×C4—1721no—
270C2×C4—1721no—
271C2×C4C2×C22⋊D4312yes—
272C2×C4C2×C22⋊D4311yescharacteristic
273C2×C4C2×C22⋊D4312yes—
274C2×C4C2×C22⋊D4312yes—
275C2×C4C23×D4311yescharacteristic
276C8—864no—
277C22—22no—
278C22—24no—
279C22—41no—
280C22—42no—
281C22—82no—
282C22—84no—
283C22—1722no—
284C22—1721no—
285C22#1306329412yes—
286C22C22×C22⋊D4311yescharacteristic
287C4—24no—
288C4—22no—
289C4—862no—
290C4—1721no—
291C4—1721no—
292C4#1306329411yescharacteristic
293C4#1306329411yescharacteristic
294C4C22×C22⋊D4312yes—
295C2—21no—
296C2—22no—
297C2—42no—
298C2—44no—
299C2—3441no—
300C2C2×#1306329411yescharacteristic
subgroupG/H
centerC4#13063294
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#585C2
socleC2×C43C2×#120
hypercenter#585D43
hypocenterC43#3018
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C4 ◁ C22×C4 ◁ #585

Complements

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

NH ≅ G/Ntype
1. #14583697C2semidirect
2. #14583445C2semidirect
3. #14583082C2semidirect
4. #14583077C2semidirect
5. #14583072C2semidirect
6. #14583067C2semidirect
7. C2×#13063252C2semidirect
8. #14582883C2semidirect
9. C43×#585C2semidirect
10. C2×#10621898C22semidirect
12. #13063355C22semidirect
14. #13063350C22semidirect
16. C2×#10621877C22semidirect
17. #13063323C22semidirect
18. #13063321C22semidirect
19. #13063314C22semidirect
20. #13063312C22semidirect
23. C2×C4×Dic43C22semidirect
24. #13063252C22semidirect
25. #13063252C22semidirect
26. #13063244C22semidirect
27. #13063242C22semidirect
47. #41×C43D4semidirect
51. C2×Q8×C43D4semidirect
59. C2×D4×C43D4semidirect
151. #585D43semidirect
160. C43#3018semidirect
200. #41C22⋊D43semidirect
205. C2×Q8C22⋊D43semidirect
216. C2×D4C22⋊D43semidirect