Finite Group Databasebeta

← #19145535

Subgroups — #19145535

Order 5504.

488 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 488 conjugacy classes of subgroups — too many to draw. Only its 123 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#14583453C211yesmaximal, characteristic, complemented
2#127×D43C211yesmaximal, characteristic
3#14583270C212yesmaximal, complemented
4#14583244C212yesmaximal, complemented
5#14583100C211yesmaximal, characteristic, complemented
6#14583099C211yesmaximal, characteristic, complemented
7#14583096C211yesmaximal, characteristic, complemented
8#14583051C212yesmaximal, complemented
9#14583048C212yesmaximal, complemented
10#14582951C211yesmaximal, characteristic, complemented
11C43×#460C211yesmaximal, characteristic, complemented
12C2×D4×D43—21no—
13C2×D4×D43—21no—
14C2×D4×D43C2212yes—
15C2×#10621873C2212yescomplemented
16C2×#10621883C2212yescomplemented
17C2×#10621884C2212yescomplemented
18#13063324C2211yescharacteristic, complemented
19#13063323C2211yescharacteristic, complemented
20#13063322C2211yescharacteristic
21#13063321—21no—
22#13063321—21no—
23#13063321C2212yes—
24#13063315—21no—
25#13063305C2211yescharacteristic
26#13063303—21no—
27#13063301C2211yescharacteristic
28C4×Dic86—21no—
29C4×Dic86C2211yescharacteristic, complemented
30#13063282—21no—
31C42×D43C2211yescharacteristic
32C4⋊(C43⋊C8)C2211yescharacteristic, complemented
33#13063247C2212yescomplemented
34#13063246C2212yescomplemented
35#13063245C2212yescomplemented
36(C2×D43)⋊C8C2212yes—
37C8×Dic43C2212yescomplemented
38C2×SD16×C43C2212yescomplemented
39#127×C43C2211yescharacteristic
40C4×Q8×C43C2211yescharacteristic, complemented
41C4⋊C8×C43C2211yescharacteristic, complemented
42#102×C43C2212yescomplemented
43C23×D43—22no—
44C2×Q8×C43C2311yescharacteristic
45C2×D4×C43—21no—
46C2×D4×C43—21no—
47C2×D4×C43C2312yes—
48C2×C22⋊D43—22no—
49C2×C22⋊D43—22no—
50C2×C22⋊D43—22no—
51D4×D43—42no—
52D4×D43—42no—
53D4×D43—44no—
54D4×D43—44no—
55C2×D172—21no—
56C2×D172—21no—
57C2×D172C2312yes—
58C2×C4×D43D411yescharacteristic
59C2×C4×D43D411yescharacteristic
60C2×C4×D43C2311yescharacteristic
61C2×Dic86—21no—
62C2×Dic86C2311yescharacteristic
63SD16×C43—42no—
64C2×C8×C43C2312yes—
65C4⋊C4×C43—21no—
66C4⋊C4×C43C2311yescharacteristic
67C42×C43—21no—
68C42×C43C2311yescharacteristic
69#10621884—42no—
70#10621883—42no—
71(C2×D43)⋊C4—21no—
72(C2×D43)⋊C4—21no—
73C4⋊Dic43—21no—
74C4⋊Dic43C2311yescharacteristic
75Dic43⋊C4—21no—
76Dic43⋊C4—21no—
77Dic43⋊C4—21no—
78Dic43⋊C4—21no—
79Dic43⋊C4—21no—
80C4×Dic43—21no—
81C4×Dic43D411yescharacteristic
82C4×Dic43D411yescharacteristic
83C4×Dic43C2311yescharacteristic
84C2×C43⋊C8C2312yes—
85#10621873—42no—
86C23×C43—22no—
87C22×D43—22no—
88C22×D43—44no—
89C22×D43—44no—
90C22×D43—44no—
91C22×D43C2×D411yescharacteristic
92Q8×C43—21no—
93Q8×C43—21no—
94D4×C43—22no—
95D4×C43—22no—
96D4×C43—42no—
97D4×C43—42no—
98C2×C4×C43—21no—
99C2×C4×C43—21no—
100C2×C4×C43C2×D411yescharacteristic
101C2×C4×C43C2×D411yescharacteristic
102C2×C4×C43C2411yescharacteristic
103C22⋊D43—44no—
104C22⋊D43—44no—
105C22⋊D43—44no—
106C2×Dic43—21no—
107C2×Dic43—21no—
108C2×Dic43C2×D411yescharacteristic
109C2×Dic43C2×D411yescharacteristic
110C2×Dic43C2×D411yescharacteristic
111D172—22no—
112D172—22no—
113D172—42no—
114D172—42no—
115C4×D43—21no—
116C4×D43—21no—
117C4×D43—22no—
118C4×D43SD1614yescomplemented
119Dic86—21no—
120Dic86—21no—
121Dic86—42no—
122C8×C43—22no—
123C43⋊C8—22no—
124C22×C43—42no—
125C22×C43—42no—
126C22×C43—42no—
127C22×C43C22×D411yescharacteristic
128C2×D43—21no—
129C2×D43—21no—
130C2×D43—42no—
131C2×D43—42no—
132C2×D43—42no—
133C2×D43—88no—
134C2×D43C2×SD1612yes—
135C4×C43—21no—
136C4×C43—41no—
137C4×C43—41no—
138C4×C43C2×SD1612yes—
139C4×C43H(5,𝔽2)11yescharacteristic
140C4×C43H(5,𝔽2)11yescharacteristic
141Dic43—21no—
142Dic43—41no—
143Dic43—41no—
144Dic43C2×SD1612yes—
145Dic43AGL(1,ℤ/8)12yes—
146#3208—431nomaximal, Sylow
147C2×C43—82no—
148C2×C43#53511yescharacteristic
149C2×C43C22×SD1611yescharacteristic
150C2×C43C2×AGL(1,ℤ/8)11yescharacteristic
151D43—22no—
152D43—82no—
153#533—431no—
154C2×#127—431no—
155#492—432no—
156#486—432no—
157#460—431no—
158#460—431no—
159#460—431no—
160#460D4311yescharacteristic, complemented
161#450—432no—
162#450—432no—
163#431—431no—
164C43#320811yescharacteristic, complemented, Sylow
165C22×D4—432no—
166C22×D4—861no—
167C22×D4—861no—
168C2×SD16—432no—
169C2×SD16—432no—
170C2×SD16—432no—
171C2×SD16C2×D4312yescomplemented
172C4⋊Q8—431no—
173C4⋊Q8—431no—
174#127—432no—
175#127—431no—
176#127—861no—
177#127—861no—
178#127C2×D4311yescharacteristic
179#125—861no—
180C22⋊Q8—431no—
181C22⋊Q8—431no—
182C22⋊Q8—861no—
183C4×Q8—431no—
184C4×Q8—861no—
185C4×Q8C2×D4311yescharacteristic, complemented
186#117—861no—
187C2×C42—431no—
188C4⋊C8—431no—
189C4⋊C8C2×D4311yescharacteristic, complemented
190#102—432no—
191#102—432no—
192#102—432no—
193#102C2×D4312yescomplemented
194C22⋊C8—432no—
195C4×C8—432no—
196C24—862no—
197C2×Q8—431no—
198C2×Q8—861no—
199C2×Q8C22×D4311yescharacteristic
200C2×D4—21no—
201C2×D4—21no—
202C2×D4—432no—
203C2×D4—862no—
204C2×D4—862no—
205C2×D4—862no—
206C2×D4—861no—
207C2×D4—861no—
208C2×D4—1724no—
209C2×D4—1722no—
210C2×D4—1722no—
211C2×D4—1724no—
212C2×D4C22×D4312yes—
213C22×C4—431no—
214C22×C4—431no—
215C22×C4—431no—
216SD16—42no—
217SD16—1722no—
218SD16—1722no—
219SD16—1722no—
220C2×C8—432no—
221C2×C8C22×D4312yes—
222C4⋊C4—21no—
223C4⋊C4—431no—
224C4⋊C4—861no—
225C4⋊C4—861no—
226C4⋊C4—861no—
227C4⋊C4—861no—
228C4⋊C4—861no—
229C4⋊C4—861no—
230C4⋊C4C22×D4311yescharacteristic
231C22⋊C4—861no—
232C22⋊C4—861no—
233C42—21no—
234C42—431no—
235C42—431no—
236C42—431no—
237C42—861no—
238C42C22×D4311yescharacteristic
239C23—22no—
240C23—431no—
241C23—862no—
242C23—1724no—
243C23—1724no—
244C23—1724no—
245Q8—21no—
246Q8—21no—
247Q8—861no—
248Q8—861no—
249Q8—1722no—
250D4—22no—
251D4—22no—
252D4—42no—
253D4—42no—
254D4—862no—
255D4—862no—
256D4—1722no—
257D4—1724no—
258D4—1724no—
259D4—1724no—
260D4—1722no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—431no—
264C2×C4—431no—
265C2×C4—434no—
266C2×C4—431no—
267C2×C4—862no—
268C2×C4—861no—
269C2×C4—861no—
270C2×C4—861no—
271C2×C4—861no—
272C2×C4D4×D4311yescharacteristic
273C2×C4D4×D4311yescharacteristic
274C2×C4C23×D4311yescharacteristic
275C8—22no—
276C8—862no—
277C22—42no—
278C22—42no—
279C22—42no—
280C22—432no—
281C22—861no—
282C22—861no—
283C22—3448no—
284C22—1722no—
285C22—1722no—
286C22—1722no—
287C22C2×D4×D4311yescharacteristic
288C4—21no—
289C4—41no—
290C4—41no—
291C4—432no—
292C4—432no—
293C4—861no—
294C4—1721no—
295C4—1721no—
296C4SD16×D4312yes—
297C4#1306337011yescharacteristic
298C4#1306337111yescharacteristic
299C2—82no—
300C2—862no—
301C2—3442no—
302C2#1458346511yescharacteristic
303C2C2×SD16×D4311yescharacteristic
304C2AGL(1,ℤ/8)×D4311yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#460C2
socleC22×C43C22×D4
hypercenter#460D43
hypocenterC43#3208
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #460

Complements

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

NH ≅ G/Ntype
1. #14583453C2semidirect
3. #14583270C2semidirect
4. #14583244C2semidirect
5. #14583100C2semidirect
6. #14583099C2semidirect
7. #14583096C2semidirect
8. #14583051C2semidirect
9. #14583048C2semidirect
10. #14582951C2semidirect
11. C43×#460C2semidirect
15. C2×#10621873C22semidirect
16. C2×#10621883C22semidirect
17. C2×#10621884C22semidirect
18. #13063324C22semidirect
19. #13063323C22semidirect
29. C4×Dic86C22semidirect
32. C4⋊(C43⋊C8)C22semidirect
33. #13063247C22semidirect
34. #13063246C22semidirect
35. #13063245C22semidirect
37. C8×Dic43C22semidirect
38. C2×SD16×C43C22semidirect
40. C4×Q8×C43C22semidirect
41. C4⋊C8×C43C22semidirect
42. #102×C43C22semidirect
118. C4×D43SD16semidirect
160. #460D43semidirect
164. C43#3208semidirect
171. C2×SD16C2×D43semidirect
185. C4×Q8C2×D43semidirect
189. C4⋊C8C2×D43semidirect
193. #102C2×D43semidirect