Finite Group Databasebeta

← #19145067

Subgroups — #19145067

Order 5504.

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

normal subgroups only

This group has 564 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×#13063355C211yesmaximal, characteristic, complemented
2C2×#13063351C211yesmaximal, characteristic, complemented
3C2×#13063345C211yesmaximal, characteristic, complemented
4C22×#10621883C211yesmaximal, characteristic, complemented
5#14583475C211yesmaximal, characteristic, complemented
6#14583294C212yesmaximal, complemented
7#14583286C212yesmaximal, complemented
8#14583281C212yesmaximal, complemented
9#14583271C212yesmaximal, complemented
10#14582855C211yesmaximal, characteristic, complemented
11C43×#535C211yesmaximal, characteristic, complemented
12C2×#10621898C2211yescharacteristic
13C22×Dic86C2211yescharacteristic
14#13063355—24no—
15#13063351—24no—
16#13063345—24no—
17C2×#10621885C2211yescharacteristic, complemented
18C2×#10621885C2212yescomplemented
19C2×#10621883—24no—
20C2×#10621883C2212yes—
21C2×#10621883C2212yes—
22C2×#10621883C2212yes—
23C2×#10621883C2211yescharacteristic, complemented
24C2×#10621883C2212yescomplemented
25C2×#10621884C2211yescharacteristic, complemented
26C2×#10621882C2212yes—
27C2×#10621882C2211yescharacteristic, complemented
28C2×#10621877C2211yescharacteristic
29C22×C43⋊C8C2211yescharacteristic
30#13063325C2212yescomplemented
31#13063313C2212yescomplemented
32#13063309—22no—
33#13063305—22no—
34#13063236C2212yescomplemented
35C4×C43⋊C8C2212yescomplemented
36C2×#41×C43C2211yescharacteristic
37C22×D4×C43C2211yescharacteristic
38#127×C43C2212yes—
39#124×C43C2212yes—
40#121×C43—22no—
41#120×C43—22no—
42#117×C43C2211yescharacteristic
43C24×C43—21no—
44#41×C43—22no—
45#41×C43—22no—
46C2×Q8×C43C2311yescharacteristic
47C2×D4×C43—21no—
48C2×D4×C43—24no—
49C2×D4×C43—21no—
50C2×D4×C43—22no—
51C2×D4×C43—22no—
52C2×D4×C43C2312yes—
53C2×D4×C43C2311yescharacteristic
54C22×C4×C43—21no—
55C22×C4×C43C2311yescharacteristic
56C2×C22⋊D43—21no—
57C22×Dic43—21no—
58#10621898—22no—
59#10621898—22no—
60C2×D172C2311yescharacteristic
61C2×C4×D43—21no—
62C2×Dic86—22no—
63C2×Dic86—22no—
64C2×Dic86—21no—
65C2×Dic86C2312yes—
66C2×Dic86C2311yescharacteristic
67C4⋊C4×C43D412yes—
68C22⋊C4×C43—24no—
69C22⋊C4×C43D412yes—
70C42×C43C2312yes—
71#10621885—22no—
72#10621885—24no—
73#10621884—22no—
74#10621883—24no—
75#10621883—24no—
76#10621883—24no—
77#10621883—22no—
78#10621883—24no—
79#10621882—24no—
80#10621882—22no—
81(C2×D43)⋊C4—24no—
82C4⋊Dic43—24no—
83#10621877D414yescomplemented
84C2×C43⋊C8D414yescomplemented
85C2×C43⋊C8C2311yescharacteristic
86C2×C43⋊C8C2312yes—
87C2×C43⋊C8C2311yescharacteristic
88C23×C43—22no—
89C23×C43—21no—
90C23×C43—42no—
91C23×C43—82no—
92C23×C43C2×D411yescharacteristic
93C22×D43—21no—
94Q8×C43—21no—
95Q8×C43—21no—
96D4×C43—22no—
97D4×C43—21no—
98D4×C43—22no—
99D4×C43—21no—
100D4×C43—42no—
101D4×C43—42no—
102D4×C43—84no—
103C2×C4×C43—21no—
104C2×C4×C43—42no—
105C2×C4×C43C2×D412yes—
106C2×C4×C43C2×D412yes—
107C2×C4×C43C2×D414yes—
108C2×C4×C43C2×D411yescharacteristic
109C2×C4×C43C2411yescharacteristic
110C22⋊D43—42no—
111C2×Dic43—21no—
112C2×Dic43—22no—
113C2×Dic43—42no—
114D172—21no—
115D172—21no—
116C4×D43—42no—
117Dic86—22no—
118Dic86—21no—
119Dic86—22no—
120Dic86—21no—
121Dic86—42no—
122C43⋊C8C2×D412yes—
123C43⋊C8C2×D412yes—
124C43⋊C8C2×D414yes—
125C22×C43—22no—
126C22×C43—42no—
127C22×C43—41no—
128C22×C43—44no—
129C22×C43—42no—
130C22×C43—84no—
131C22×C43#12712yes—
132C22×C43C22×D411yescharacteristic
133C2×D43—41no—
134C2×D43—42no—
135C4×C43—24no—
136C4×C43—41no—
137C4×C43#12712yes—
138C4×C43C22×D411yescharacteristic
139C4×C43C22×D411yescharacteristic
140Dic43—42no—
141Dic43—41no—
142#3154—431nomaximal, Sylow
143C2×C43—22no—
144C2×C43—81no—
145C2×C43—82no—
146C2×C43C2×#12711yescharacteristic
147C2×C43#57712yes—
148D43—81no—
149C2×#137—431no—
150C2×AGL(1,ℤ/8)—431no—
151C2×#135—431no—
152C22×SD16—431no—
153#536—431no—
154#535D4311yescharacteristic, complemented
155#497—432no—
156#496—432no—
157#495—432no—
158#492—432no—
159#405—431no—
160C43#315411yescharacteristic, complemented, Sylow
161C2×#41—431no—
162C2×#41C2×D4311yescharacteristic
163C22×Q8—431no—
164C22×D4C2×D4311yescharacteristic
165#137—864no—
166AGL(1,ℤ/8)—864no—
167#135—864no—
168C2×Q16—431no—
169C2×Q16—432no—
170C2×SD16—431no—
171C2×SD16—432no—
172C2×SD16—432no—
173C2×SD16—431no—
174C2×SD16—432no—
175C2×SD16—432no—
176C2×SD16—864no—
177C2×D8—431no—
178C2×D8—432no—
179C2×M16—431no—
180C22×C8—431no—
181C4⋊Q8—432no—
182#127C2×D4312yes—
183#124—432no—
184#124C2×D4312yes—
185#123—862no—
186C22⋊Q8—862no—
187#121—22no—
188#120—22no—
189#117C2×D4311yescharacteristic
190#97—432no—
191C4×C8—432no—
192C24—21no—
193#41—22no—
194#41—22no—
195#41—862no—
196#41—862no—
197C2×Q8—432no—
198C2×Q8—431no—
199C2×Q8—861no—
200C2×Q8—862no—
201C2×Q8—862no—
202C2×Q8C22×D4311yescharacteristic
203C2×D4—21no—
204C2×D4—22no—
205C2×D4—22no—
206C2×D4—21no—
207C2×D4—24no—
208C2×D4—431no—
209C2×D4—861no—
210C2×D4C22×D4312yes—
211C2×D4C22×D4311yescharacteristic
212C22×C4—21no—
213C22×C4—861no—
214C22×C4—861no—
215C22×C4C22×D4311yescharacteristic
216Q16—862no—
217Q16—864no—
218SD16—864no—
219SD16—864no—
220SD16—862no—
221SD16—864no—
222SD16—864no—
223SD16—862no—
224D8—862no—
225D8—864no—
226M16—434no—
227C2×C8—434no—
228C2×C8—431no—
229C2×C8—432no—
230C2×C8—431no—
231C4⋊C4—864no—
232C4⋊C4C22⋊D4312yes—
233C22⋊C4—24no—
234C22⋊C4—864no—
235C22⋊C4C22⋊D4312yes—
236C42C22×D4312yes—
237C23—22no—
238C23—21no—
239C23—42no—
240C23—82no—
241C23—861no—
242C23C2×C22⋊D4311yescharacteristic
243Q8—21no—
244Q8—21no—
245Q8—862no—
246Q8—861no—
247Q8—862no—
248Q8—861no—
249Q8—1722no—
250D4—22no—
251D4—21no—
252D4—22no—
253D4—21no—
254D4—42no—
255D4—42no—
256D4—84no—
257D4—861no—
258D4—861no—
259D4—1722no—
260C2×C4—21no—
261C2×C4—42no—
262C2×C4—862no—
263C2×C4—861no—
264C2×C4—1722no—
265C2×C4—1722no—
266C2×C4D4×D4312yes—
267C2×C4D4×D4312yes—
268C2×C4C2×C22⋊D4314yes—
269C2×C4C2×C22⋊D4311yescharacteristic
270C2×C4C23×D4311yescharacteristic
271C8—432no—
272C8—432no—
273C8—434no—
274C22—22no—
275C22—41no—
276C22—42no—
277C22—42no—
278C22—44no—
279C22—84no—
280C22—1721no—
281C22—1722no—
282C22#1306332112yes—
283C22C22×C22⋊D4311yescharacteristic
284C4—24no—
285C4—41no—
286C4—1721no—
287C4—1722no—
288C4#1306332112yes—
289C4C2×D4×D4311yescharacteristic
290C4C2×D4×D4311yescharacteristic
291C2—22no—
292C2—82no—
293C2—81no—
294C2—3441no—
295C2C2×#1306332111yescharacteristic
296C2#1458371012yes—
subgroupG/H
centerC22C22×C22⋊D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#535C2
socleC22×C43C22×D4
hypercenter#535D43
hypocenterC43#3154
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ #117 ◁ #535

Complements

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

NH ≅ G/Ntype
1. C2×#13063355C2semidirect
2. C2×#13063351C2semidirect
3. C2×#13063345C2semidirect
4. C22×#10621883C2semidirect
5. #14583475C2semidirect
6. #14583294C2semidirect
7. #14583286C2semidirect
8. #14583281C2semidirect
9. #14583271C2semidirect
10. #14582855C2semidirect
11. C43×#535C2semidirect
17. C2×#10621885C22semidirect
18. C2×#10621885C22semidirect
23. C2×#10621883C22semidirect
24. C2×#10621883C22semidirect
25. C2×#10621884C22semidirect
27. C2×#10621882C22semidirect
30. #13063325C22semidirect
31. #13063313C22semidirect
34. #13063236C22semidirect
35. C4×C43⋊C8C22semidirect
83. #10621877D4semidirect
84. C2×C43⋊C8D4semidirect
154. #535D43semidirect
160. C43#3154semidirect