Finite Group Databasebeta

← #19143861

Subgroups — #19143861

Order 5504.

784 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 784 conjugacy classes of subgroups — too many to draw. Only its 149 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×#13063371C211yesmaximal, characteristic, complemented
2C2×#13063351C211yesmaximal, characteristic, complemented
3C22×#10621882C211yesmaximal, characteristic, complemented
4#14583042C214yesmaximal, complemented
5#14583032C214yesmaximal, complemented
6#14582903C211yesmaximal, characteristic, complemented
7#14582893C211yesmaximal, characteristic, complemented
8#14582866C211yesmaximal, characteristic, complemented
9C43×#535C211yesmaximal, characteristic, complemented
10#13063371—24no—
11#13063371—24no—
12C2×#10621902—21no—
13C2×#10621898C2211yescharacteristic
14C2×#10621898C2212yescomplemented
15C22×D172C2211yescharacteristic
16C22×D172C2212yescomplemented
17C2×D4×D43—21no—
18C2×D4×D43—22no—
19#13063351—24no—
20C2×#10621883C2212yescomplemented
21C2×#10621882—24no—
22C2×#10621882C2214yescomplemented
23C2×#10621882C2212yescomplemented
24C2×#10621877C2211yescharacteristic, complemented
25C22×C43⋊C8C2211yescharacteristic, complemented
26#13063248C2212yescomplemented
27#13063245C2214yescomplemented
28#13063245C2212yescomplemented
29C22⋊(C43⋊C8)C2214yescomplemented
30C2×#41×C43C2211yescharacteristic
31C22×D4×C43C2211yescharacteristic, complemented
32#127×C43—21no—
33#124×C43—21no—
34#121×C43C2214yescomplemented
35#120×C43—22no—
36#117×C43C2211yescharacteristic, complemented
37C24×C43—21no—
38C23×D43—21no—
39C23×D43—22no—
40#41×C43—22no—
41#41×C43—22no—
42C2×Q8×C43D411yescharacteristic
43C2×D4×C43—21no—
44C2×D4×C43—24no—
45C2×D4×C43—22no—
46C2×D4×C43—22no—
47C2×D4×C43D412yes—
48C2×D4×C43D411yescharacteristic
49C2×D4×C43C2312yes—
50C22×C4×C43C2312yes—
51C22×C4×C43C2311yescharacteristic
52C2×C22⋊D43—21no—
53C2×C22⋊D43—22no—
54#10621902—28no—
55D4×D43—28no—
56D4×D43—216no—
57#10621898—22no—
58#10621898—24no—
59#10621898—24no—
60#10621898D414yescomplemented
61C2×D172—21no—
62C2×D172—22no—
63C2×D172—22no—
64C2×D172—24no—
65C2×D172—24no—
66C2×D172D414yescomplemented
67C2×D172C2312yes—
68C2×D172C2311yescharacteristic
69C2×C4×D43—21no—
70C2×C4×D43—22no—
71C2×Dic86C2311yescharacteristic
72C4⋊C4×C43C2312yes—
73C22⋊C4×C43—24no—
74C22⋊C4×C43—21no—
75C42×C43—21no—
76#10621883—24no—
77#10621882—28no—
78#10621882—24no—
79#10621877—22no—
80C2×C43⋊C8—22no—
81C2×C43⋊C8C2312yes—
82C2×C43⋊C8C2312yes—
83C23×C43—22no—
84C23×C43—42no—
85C23×C43—82no—
86C23×C43C2×D412yes—
87C23×C43C2×D411yescharacteristic
88C22×D43—21no—
89C22×D43—22no—
90C22×D43—28no—
91C22×D43—24no—
92C22×D43—82no—
93C22×D43—84no—
94Q8×C43—22no—
95D4×C43—24no—
96D4×C43—22no—
97D4×C43—22no—
98D4×C43—22no—
99D4×C43—42no—
100D4×C43—84no—
101C2×C4×C43—22no—
102C2×C4×C43—22no—
103C2×C4×C43—22no—
104C2×C4×C43C2×D412yes—
105C2×C4×C43C2×D412yes—
106C2×C4×C43C2×D412yes—
107C2×C4×C43C2×D411yescharacteristic
108C2×C4×C43C2411yescharacteristic
109C22⋊D43—28no—
110C22⋊D43—24no—
111C2×Dic43—21no—
112D172—28no—
113D172—24no—
114D172—21no—
115D172—22no—
116D172C2×D412yes—
117D172C2×D414yes—
118C4×D43—28no—
119C4×D43—24no—
120Dic86—21no—
121Dic86C2×D412yes—
122C43⋊C8—22no—
123C43⋊C8—22no—
124C22×C43—22no—
125C22×C43—22no—
126C22×C43—24no—
127C22×C43—42no—
128C22×C43—44no—
129C22×C43—84no—
130C22×C43#12012yes—
131C22×C43C22×D411yescharacteristic
132C2×D43—22no—
133C2×D43—24no—
134C2×D43—44no—
135C2×D43—42no—
136C2×D43—84no—
137C2×D43—88no—
138C4×C43—22no—
139C4×C43—42no—
140C4×C43#12012yes—
141C4×C43C22×D411yescharacteristic
142C4×C43C22×D411yescharacteristic
143Dic43—22no—
144#3008—431nomaximal, Sylow
145C2×C43—22no—
146C2×C43—42no—
147C2×C43—82no—
148C2×C43C2×#12011yescharacteristic
149C2×C43#57612yes—
150D43—44no—
151D43—42no—
152C2×H(5,𝔽2)—431no—
153C2×AGL(1,ℤ/8)—431no—
154C22×D8—431no—
155#535D4311yescharacteristic, complemented
156#449—434no—
157#447—434no—
158#418—431no—
159#416—431no—
160#408—431no—
161C43#300811yescharacteristic, complemented, Sylow
162H(5,𝔽2)—864no—
163H(5,𝔽2)—864no—
164C2×#41—431no—
165C2×#41—432no—
166C2×#41—861no—
167C2×#41C2×D4311yescharacteristic
168C22×D4—431no—
169C22×D4—432no—
170C22×D4—862no—
171C22×D4—861no—
172C22×D4C2×D4311yescharacteristic, complemented
173AGL(1,ℤ/8)—864no—
174C2×SD16—432no—
175C2×D8—434no—
176C2×D8—432no—
177C2×D8—864no—
178C2×M16—431no—
179C22×C8—431no—
180#127—21no—
181#124—21no—
182#121C2×D4314yescomplemented
183#120—22no—
184#117C2×D4311yescharacteristic, complemented
185#103—432no—
186#102—432no—
187#102—434no—
188C22⋊C8—434no—
189C24—21no—
190C24—862no—
191C24—861no—
192#41—22no—
193#41—22no—
194#41—434no—
195#41—864no—
196#41—864no—
197#41—868no—
198#41—862no—
199C2×Q8—431no—
200C2×Q8C22⋊D4311yescharacteristic
201C2×D4—24no—
202C2×D4—22no—
203C2×D4—22no—
204C2×D4—21no—
205C2×D4—434no—
206C2×D4—432no—
207C2×D4—431no—
208C2×D4—864no—
209C2×D4—864no—
210C2×D4—8616no—
211C2×D4—868no—
212C2×D4—862no—
213C2×D4—861no—
214C2×D4—862no—
215C2×D4—862no—
216C2×D4—861no—
217C2×D4C22⋊D4312yes—
218C2×D4C22⋊D4311yescharacteristic
219C2×D4C22×D4312yes—
220C22×C4—862no—
221C22×C4—861no—
222C22×C4C22×D4312yes—
223C22×C4C22×D4311yescharacteristic
224SD16—864no—
225D8—868no—
226D8—864no—
227M16—862no—
228C2×C8—432no—
229C2×C8—432no—
230C2×C8—862no—
231C4⋊C4C22×D4312yes—
232C22⋊C4—21no—
233C22⋊C4—24no—
234C42—21no—
235C23—22no—
236C23—42no—
237C23—82no—
238C23—868no—
239C23—864no—
240C23—862no—
241C23—861no—
242C23—3442no—
243C23—3444no—
244C23C2×C22⋊D4312yes—
245C23C2×C22⋊D4311yescharacteristic
246Q8—22no—
247Q8—432no—
248Q8—861no—
249D4—24no—
250D4—22no—
251D4—22no—
252D4—22no—
253D4—42no—
254D4—84no—
255D4—434no—
256D4—432no—
257D4—868no—
258D4—868no—
259D4—864no—
260D4—864no—
261D4—861no—
262D4—862no—
263C2×C4—22no—
264C2×C4—22no—
265C2×C4—22no—
266C2×C4—868no—
267C2×C4—861no—
268C2×C4—864no—
269C2×C4D4×D4312yes—
270C2×C4D4×D4312yes—
271C2×C4C2×C22⋊D4312yes—
272C2×C4C2×C22⋊D4311yescharacteristic
273C2×C4C23×D4311yescharacteristic
274C8—862no—
275C8—862no—
276C22—22no—
277C22—22no—
278C22—24no—
279C22—42no—
280C22—44no—
281C22—84no—
282C22—864no—
283C22—862no—
284C22—3444no—
285C22—3448no—
286C22—1724no—
287C22—1722no—
288C22#1306329312yes—
289C22C22×C22⋊D4311yescharacteristic
290C4—22no—
291C4—42no—
292C4—862no—
293C4#1306329312yes—
294C4C2×D4×D4311yescharacteristic
295C4C2×D4×D4311yescharacteristic
296C2—22no—
297C2—42no—
298C2—82no—
299C2—1724no—
300C2—1722no—
301C2C2×#1306329311yescharacteristic
302C2#1458370212yes—
subgroupG/H
centerC22C22×C22⋊D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#535C2
socleC22×C43C22×D4
hypercenter#535D43
hypocenterC43#3008
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×#41 ◁ #535

Complements

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

NH ≅ G/Ntype
1. C2×#13063371C2semidirect
2. C2×#13063351C2semidirect
3. C22×#10621882C2semidirect
4. #14583042C2semidirect
5. #14583032C2semidirect
6. #14582903C2semidirect
7. #14582893C2semidirect
8. #14582866C2semidirect
9. C43×#535C2semidirect
14. C2×#10621898C22semidirect
16. C22×D172C22semidirect
20. C2×#10621883C22semidirect
22. C2×#10621882C22semidirect
23. C2×#10621882C22semidirect
24. C2×#10621877C22semidirect
25. C22×C43⋊C8C22semidirect
26. #13063248C22semidirect
27. #13063245C22semidirect
28. #13063245C22semidirect
29. C22⋊(C43⋊C8)C22semidirect
31. C22×D4×C43C22semidirect
34. #121×C43C22semidirect
36. #117×C43C22semidirect
60. #10621898D4semidirect
66. C2×D172D4semidirect
155. #535D43semidirect
161. C43#3008semidirect
172. C22×D4C2×D43semidirect
182. #121C2×D43semidirect
184. #117C2×D43semidirect