Finite Group Databasebeta

← #19145073

Subgroups — #19145073

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×#13063356C211yesmaximal, characteristic, complemented
2C2×#13063350C211yesmaximal, characteristic, complemented
3C2×#13063345C211yesmaximal, characteristic, complemented
4C22×#10621884C211yesmaximal, characteristic, complemented
5#14583468C211yesmaximal, characteristic, complemented
6#14583291C212yesmaximal, complemented
7#14583289C212yesmaximal, complemented
8#14583281C212yesmaximal, complemented
9#14583273C212yesmaximal, complemented
10#14582855C211yesmaximal, characteristic, complemented
11C43×#536C211yesmaximal, characteristic, complemented
12C2×#10621898C2211yescharacteristic
13C22×D172C2211yescharacteristic
14#13063356—24no—
15#13063350—24no—
16#13063345—24no—
17C2×#10621885C2211yescharacteristic, complemented
18C2×#10621885C2212yescomplemented
19C2×#10621883C2211yescharacteristic, complemented
20C2×#10621884—24no—
21C2×#10621884C2212yes—
22C2×#10621884C2212yes—
23C2×#10621884C2212yes—
24C2×#10621884C2211yescharacteristic, complemented
25C2×#10621884C2212yescomplemented
26C2×#10621882C2212yes—
27C2×#10621882C2211yescharacteristic, complemented
28C2×#10621877C2211yescharacteristic
29C22×C43⋊C8C2211yescharacteristic
30#13063322C2212yes—
31#13063313C2212yes—
32#13063300—22no—
33#13063295—22no—
34#13063236C2212yescomplemented
35C4×C43⋊C8C2212yescomplemented
36C2×#41×C43C2211yescharacteristic
37C22×Q8×C43C2211yescharacteristic
38C4⋊Q8×C43C2212yescomplemented
39#124×C43C2212yescomplemented
40#123×C43—22no—
41C22⋊Q8×C43—22no—
42#117×C43C2211yescharacteristic
43C23×D43—21no—
44#41×C43—22no—
45#41×C43—22no—
46C2×Q8×C43—21no—
47C2×Q8×C43—22no—
48C2×Q8×C43—22no—
49C2×Q8×C43C2312yes—
50C2×Q8×C43C2311yescharacteristic
51C2×D4×C43—21no—
52C2×D4×C43C2311yescharacteristic
53C22×C4×C43—21no—
54C22×C4×C43—21no—
55C22×C4×C43C2311yescharacteristic
56C2×C22⋊D43—21no—
57#10621898—22no—
58#10621898—22no—
59C2×D172—21no—
60C2×D172—24no—
61C2×D172—22no—
62C2×D172—22no—
63C2×D172C2312yes—
64C2×D172C2311yescharacteristic
65C2×C4×D43—21no—
66C2×Dic86C2311yescharacteristic
67C4⋊C4×C43—24no—
68C4⋊C4×C43D412yes—
69C22⋊C4×C43—24no—
70C22⋊C4×C43D412yes—
71C42×C43C2312yes—
72#10621885—22no—
73#10621885—24no—
74#10621884—24no—
75#10621884—24no—
76#10621884—24no—
77#10621884—22no—
78#10621884—24no—
79#10621883—22no—
80#10621882—24no—
81#10621882—22no—
82(C2×D43)⋊C4—24no—
83#10621877D414yescomplemented
84C2×C43⋊C8D414yescomplemented
85C2×C43⋊C8C2311yescharacteristic
86C2×C43⋊C8C2312yes—
87C2×C43⋊C8C2311yescharacteristic
88C23×C43—21no—
89C23×C43C2×D411yescharacteristic
90C22×D43—22no—
91C22×D43—21no—
92C22×D43—42no—
93C22×D43—82no—
94Q8×C43—22no—
95Q8×C43—21no—
96Q8×C43—22no—
97Q8×C43—21no—
98Q8×C43—42no—
99D4×C43—21no—
100D4×C43—21no—
101D4×C43—42no—
102C2×C4×C43—22no—
103C2×C4×C43—21no—
104C2×C4×C43—42no—
105C2×C4×C43—42no—
106C2×C4×C43C2×D412yes—
107C2×C4×C43C2×D412yes—
108C2×C4×C43C2×D414yes—
109C2×C4×C43C2×D411yescharacteristic
110C2×C4×C43C2411yescharacteristic
111C22⋊D43—42no—
112C2×Dic43—21no—
113D172—22no—
114D172—21no—
115D172—22no—
116D172—21no—
117D172—42no—
118D172—84no—
119C4×D43—42no—
120Dic86—21no—
121Dic86—21no—
122C43⋊C8C2×D412yes—
123C43⋊C8C2×D412yes—
124C43⋊C8C2×D414yes—
125C22×C43—22no—
126C22×C43—41no—
127C22×C43—42no—
128C22×C43#12712yes—
129C22×C43C22×D411yescharacteristic
130C2×D43—42no—
131C2×D43—41no—
132C2×D43—44no—
133C2×D43—42no—
134C2×D43—84no—
135C4×C43—24no—
136C4×C43—41no—
137C4×C43—42no—
138C4×C43#12712yes—
139C4×C43C22×D411yescharacteristic
140C4×C43C22×D411yescharacteristic
141Dic43—41no—
142#3154—431nomaximal, Sylow
143C2×C43—22no—
144C2×C43—81no—
145C2×C43C2×#12711yescharacteristic
146C2×C43#57712yes—
147D43—81no—
148D43—82no—
149C2×#137—431no—
150C2×AGL(1,ℤ/8)—431no—
151C2×#135—431no—
152C22×SD16—431no—
153#536D4311yescharacteristic, complemented
154#535—431no—
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×Q8C2×D4311yescharacteristic
164C22×D4—431no—
165#137—864no—
166AGL(1,ℤ/8)—864no—
167#135—864no—
168C2×Q16—431no—
169C2×Q16—432no—
170C2×SD16—432no—
171C2×SD16—432no—
172C2×SD16—431no—
173C2×SD16—432no—
174C2×SD16—432no—
175C2×SD16—431no—
176C2×SD16—864no—
177C2×D8—431no—
178C2×D8—432no—
179C2×M16—431no—
180C22×C8—431no—
181C4⋊Q8C2×D4312yescomplemented
182#127—432no—
183#124—432no—
184#124C2×D4312yescomplemented
185#123—22no—
186C22⋊Q8—22no—
187#121—862no—
188#120—862no—
189#117C2×D4311yescharacteristic
190#97—432no—
191C4×C8—432no—
192C24—861no—
193#41—22no—
194#41—22no—
195#41—862no—
196#41—862no—
197C2×Q8—21no—
198C2×Q8—22no—
199C2×Q8—22no—
200C2×Q8—431no—
201C2×Q8C22×D4312yes—
202C2×Q8C22×D4311yescharacteristic
203C2×D4—21no—
204C2×D4—432no—
205C2×D4—431no—
206C2×D4—861no—
207C2×D4—862no—
208C2×D4—862no—
209C2×D4—864no—
210C2×D4—861no—
211C2×D4C22×D4311yescharacteristic
212C22×C4—21no—
213C22×C4—21no—
214C22×C4—861no—
215C22×C4C22×D4311yescharacteristic
216Q16—862no—
217Q16—864no—
218SD16—862no—
219SD16—864no—
220SD16—864no—
221SD16—862no—
222SD16—864no—
223SD16—864no—
224D8—862no—
225D8—864no—
226M16—434no—
227C2×C8—434no—
228C2×C8—431no—
229C2×C8—432no—
230C2×C8—431no—
231C4⋊C4—24no—
232C4⋊C4C22⋊D4312yes—
233C22⋊C4—24no—
234C22⋊C4—864no—
235C22⋊C4C22⋊D4312yes—
236C42C22×D4312yes—
237C23—21no—
238C23—862no—
239C23—861no—
240C23—3442no—
241C23—1722no—
242C23C2×C22⋊D4311yescharacteristic
243Q8—22no—
244Q8—21no—
245Q8—22no—
246Q8—21no—
247Q8—42no—
248Q8—861no—
249Q8—861no—
250D4—21no—
251D4—21no—
252D4—42no—
253D4—862no—
254D4—861no—
255D4—862no—
256D4—861no—
257D4—3444no—
258D4—1722no—
259D4—1722no—
260C2×C4—22no—
261C2×C4—21no—
262C2×C4—42no—
263C2×C4—42no—
264C2×C4—861no—
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—3444no—
278C22—1721no—
279C22—1722no—
280C22—1722no—
281C22—1724no—
282C22#1306332112yes—
283C22C22×C22⋊D4311yescharacteristic
284C4—24no—
285C4—41no—
286C4—42no—
287C4—1721no—
288C4#1306332112yes—
289C4C2×D4×D4311yescharacteristic
290C4C2×D4×D4311yescharacteristic
291C2—22no—
292C2—81no—
293C2—3442no—
294C2—3441no—
295C2C2×#1306332111yescharacteristic
296C2#1458370712yes—
subgroupG/H
centerC22C22×C22⋊D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#536C2
socleC22×C43C22×D4
hypercenter#536D43
hypocenterC43#3154
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ #117 ◁ #536

Complements

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

NH ≅ G/Ntype
1. C2×#13063356C2semidirect
2. C2×#13063350C2semidirect
3. C2×#13063345C2semidirect
4. C22×#10621884C2semidirect
5. #14583468C2semidirect
6. #14583291C2semidirect
7. #14583289C2semidirect
8. #14583281C2semidirect
9. #14583273C2semidirect
10. #14582855C2semidirect
11. C43×#536C2semidirect
17. C2×#10621885C22semidirect
18. C2×#10621885C22semidirect
19. C2×#10621883C22semidirect
24. C2×#10621884C22semidirect
25. C2×#10621884C22semidirect
27. C2×#10621882C22semidirect
34. #13063236C22semidirect
35. C4×C43⋊C8C22semidirect
38. C4⋊Q8×C43C22semidirect
39. #124×C43C22semidirect
83. #10621877D4semidirect
84. C2×C43⋊C8D4semidirect
153. #536D43semidirect
160. C43#3154semidirect
181. C4⋊Q8C2×D43semidirect
184. #124C2×D43semidirect