Finite Group Databasebeta

← #19143824

Subgroups — #19143824

Order 5504.

994 conjugacy classes of subgroups; only the 153 normal subgroups are shown.

normal subgroups only

This group has 994 conjugacy classes of subgroups — too many to draw. Only its 153 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
1C22×D4×D43C211yesmaximal, characteristic, complemented
2C2×#13063353C211yesmaximal, characteristic, complemented
3C2×#13063351C211yesmaximal, characteristic, complemented
4#14583411C211yesmaximal, characteristic, complemented
5#14583051C214yesmaximal, complemented
6#14583034C214yesmaximal, complemented
7#14582903C211yesmaximal, characteristic, complemented
8#14582862C211yesmaximal, characteristic, complemented
9C43×#418C211yesmaximal, characteristic, complemented
10C24×D43—21no—
11C2×#10621898C2211yescharacteristic, complemented
12C22×D172C2211yescharacteristic
13C22×C22⋊D43—21no—
14C2×D4×D43—24no—
15C2×D4×D43—24no—
16C2×D4×D43—22no—
17C2×D4×D43C2214yes—
18C22×C4×D43C2211yescharacteristic
19#13063353—24no—
20#13063351—24no—
21C2×#10621873C2212yescomplemented
22C2×#10621883C2212yescomplemented
23C2×D344C2212yescomplemented
24C2×#10621882C2212yescomplemented
25C2×#10621877C2211yescharacteristic, complemented
26#13063309—21no—
27#13063305C2212yescomplemented
28#13063300C2212yescomplemented
29#13063295—21no—
30C4×D172—22no—
31#13063245C2214yescomplemented
32(C2×D43)⋊C8C2214yescomplemented
33C22×D4×C43C2211yescharacteristic
34C2×M16×C43C2211yescharacteristic, complemented
35#117×C43C2211yescharacteristic, complemented
36#102×C43C2214yescomplemented
37C24×C43—21no—
38C23×D43—28no—
39C23×D43—21no—
40C23×D43—24no—
41C23×D43—48no—
42C23×D43D411yescharacteristic
43C2×D4×C43—22no—
44C2×D4×C43—21no—
45C2×D4×C43D414yescomplemented
46C2×D4×C43C2312yes—
47C22×C4×C43C2311yescharacteristic
48C2×C22⋊D43—28no—
49C2×C22⋊D43—24no—
50C2×C22⋊D43—21no—
51C22×Dic43D411yescharacteristic
52D4×D43—216no—
53D4×D43—28no—
54D4×D43—28no—
55#10621898—22no—
56#10621898—22no—
57C2×D172—22no—
58C2×D172—21no—
59C2×D172—22no—
60C2×D172D414yescomplemented
61C2×D172C2312yes—
62C2×D172C2311yescharacteristic, complemented
63C2×C4×D43—22no—
64C2×C4×D43—22no—
65C2×C4×D43—21no—
66C2×C4×D43D412yes—
67C2×C4×D43C2312yes—
68C2×Dic86C2311yescharacteristic, complemented
69M16×C43—22no—
70C2×C8×C43C2312yescomplemented
71C4⋊C4×C43C2312yescomplemented
72C22⋊C4×C43—21no—
73C42×C43—21no—
74#10621883—24no—
75#10621882—24no—
76(C2×D43)⋊C4—22no—
77(C2×D43)⋊C4—22no—
78C4⋊Dic43—22no—
79#10621877—22no—
80C2×C43⋊C8C2312yescomplemented
81D344—24no—
82#10621873—24no—
83C23×C43—24no—
84C23×C43—22no—
85C23×C43—44no—
86C23×C43C2×D411yescharacteristic
87C22×D43—22no—
88C22×D43—24no—
89C22×D43—216no—
90C22×D43—24no—
91C22×D43—22no—
92C22×D43—21no—
93C22×D43—432no—
94C22×D43—48no—
95C22×D43—44no—
96C22×D43—48no—
97C22×D43C2×D412yes—
98D4×C43—24no—
99D4×C43—22no—
100D4×C43C2×D414yes—
101C2×C4×C43—22no—
102C2×C4×C43C2×D412yes—
103C2×C4×C43C2×D411yescharacteristic
104C2×C4×C43C2×D412yes—
105C2×C4×C43C2411yescharacteristic
106C22⋊D43—216no—
107C22⋊D43—42no—
108C2×Dic43—22no—
109C2×Dic43—21no—
110C2×Dic43C2×D412yes—
111D172—24no—
112D172—22no—
113D172—21no—
114D172—21no—
115D172—44no—
116D172C2×D414yes—
117C4×D43—24no—
118C4×D43—22no—
119C4×D43—22no—
120C4×D43—42no—
121Dic86—21no—
122Dic86—21no—
123C8×C43—22no—
124C43⋊C8—22no—
125C22×C43—22no—
126C22×C43—24no—
127C22×C43—48no—
128C22×C43—44no—
129C22×C43#12012yes—
130C22×C43C22×D411yescharacteristic
131C2×D43—28no—
132C2×D43—22no—
133C2×D43—22no—
134C2×D43—24no—
135C2×D43—432no—
136C2×D43—48no—
137C2×D43—44no—
138C2×D43—41no—
139C2×D43—42no—
140C2×D43AGL(1,ℤ/8)14yescomplemented
141C4×C43—42no—
142C4×C43#12012yes—
143C4×C43C22×D411yescharacteristic
144C4×C43C22×D411yescharacteristic
145Dic43—22no—
146Dic43—41no—
147#3003—431nomaximal, Sylow
148C2×C43—22no—
149C2×C43—44no—
150C2×C43C2×#12011yescharacteristic
151C2×C43C2×AGL(1,ℤ/8)12yes—
152D43—24no—
153D43—44no—
154D43—81no—
155C23×D4—431no—
156C2×AGL(1,ℤ/8)—431no—
157C2×AGL(1,ℤ/8)—431no—
158#525—431no—
159#450—434no—
160#447—434no—
161#418—431no—
162#418D4311yescharacteristic, complemented
163#407—431no—
164C43#300311yescharacteristic, complemented, Sylow
165C25—861no—
166C2×#41—431no—
167C22×D4—434no—
168C22×D4—431no—
169C22×D4—862no—
170C22×D4—861no—
171C22×D4—864no—
172C22×D4—864no—
173C22×D4C2×D4311yescharacteristic
174C23×C4—431no—
175AGL(1,ℤ/8)—864no—
176AGL(1,ℤ/8)—864no—
177C2×SD16—432no—
178C2×SD16—432no—
179C2×D8—432no—
180C2×D8—432no—
181C2×M16—431no—
182C2×M16C2×D4311yescharacteristic, complemented
183#123—861no—
184C22⋊Q8—432no—
185#121—432no—
186#120—861no—
187C4×D4—862no—
188#117C2×D4311yescharacteristic, complemented
189#102—434no—
190#102C2×D4314yescomplemented
191C22⋊C8—434no—
192C24—21no—
193C24—431no—
194C24—864no—
195C24—868no—
196C24—861no—
197C24—1728no—
198#41—862no—
199#41—862no—
200C2×Q8—431no—
201C2×D4—21no—
202C2×D4—22no—
203C2×D4—434no—
204C2×D4—432no—
205C2×D4—431no—
206C2×D4—862no—
207C2×D4—864no—
208C2×D4—868no—
209C2×D4—8616no—
210C2×D4—868no—
211C2×D4—868no—
212C2×D4—861no—
213C2×D4—862no—
214C2×D4—861no—
215C2×D4D17214yescomplemented
216C2×D4C22×D4312yes—
217C22×C4—431no—
218C22×C4—432no—
219C22×C4—432no—
220C22×C4—862no—
221C22×C4—862no—
222C22×C4—861no—
223C22×C4C22×D4311yescharacteristic
224SD16—864no—
225SD16—864no—
226D8—864no—
227D8—864no—
228M16—22no—
229M16—862no—
230C2×C8—432no—
231C2×C8C22×D4312yescomplemented
232C4⋊C4—862no—
233C4⋊C4C22×D4312yescomplemented
234C22⋊C4—21no—
235C22⋊C4—862no—
236C22⋊C4—862no—
237C42—21no—
238C23—24no—
239C23—22no—
240C23—44no—
241C23—432no—
242C23—864no—
243C23—8616no—
244C23—862no—
245C23—864no—
246C23—862no—
247C23—861no—
248C23—1724no—
249C23—1728no—
250C23—17232no—
251C23—1728no—
252C23D4×D4311yescharacteristic
253Q8—861no—
254Q8—861no—
255D4—24no—
256D4—22no—
257D4—434no—
258D4—8616no—
259D4—864no—
260D4—861no—
261D4—862no—
262D4—861no—
263D4—1724no—
264D4—1722no—
265D4C2×D17214yes—
266C2×C4—22no—
267C2×C4—432no—
268C2×C4—862no—
269C2×C4—864no—
270C2×C4—862no—
271C2×C4—862no—
272C2×C4—861no—
273C2×C4—1722no—
274C2×C4C2×D17212yes—
275C2×C4D4×D4311yescharacteristic
276C2×C4D4×D4312yes—
277C2×C4C23×D4311yescharacteristic
278C8—22no—
279C8—862no—
280C22—22no—
281C22—24no—
282C22—48no—
283C22—44no—
284C22—434no—
285C22—868no—
286C22—862no—
287C22—862no—
288C22—864no—
289C22—1728no—
290C22—17232no—
291C22—1721no—
292C22—1722no—
293C22—1724no—
294C22#1306329512yes—
295C22C2×D4×D4311yescharacteristic
296C4—42no—
297C4—862no—
298C4—1721no—
299C4#1306329512yes—
300C4C2×D4×D4311yescharacteristic
301C4C22×D17211yescharacteristic
302C2—22no—
303C2—44no—
304C2—864no—
305C2—3441no—
306C2—1724no—
307C2C2×#1306329511yescharacteristic
308C2AGL(1,ℤ/8)×D4312yes—
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#418C2
socleC22×C43C22×D4
hypercenter#418D43
hypocenterC43#3003
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #418

Complements

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

NH ≅ G/Ntype
1. C22×D4×D43C2semidirect
2. C2×#13063353C2semidirect
3. C2×#13063351C2semidirect
4. #14583411C2semidirect
5. #14583051C2semidirect
6. #14583034C2semidirect
7. #14582903C2semidirect
8. #14582862C2semidirect
9. C43×#418C2semidirect
11. C2×#10621898C22semidirect
21. C2×#10621873C22semidirect
22. C2×#10621883C22semidirect
23. C2×D344C22semidirect
24. C2×#10621882C22semidirect
25. C2×#10621877C22semidirect
27. #13063305C22semidirect
28. #13063300C22semidirect
31. #13063245C22semidirect
32. (C2×D43)⋊C8C22semidirect
34. C2×M16×C43C22semidirect
35. #117×C43C22semidirect
36. #102×C43C22semidirect
45. C2×D4×C43D4semidirect
60. C2×D172D4semidirect
62. C2×D172C23semidirect
68. C2×Dic86C23semidirect
70. C2×C8×C43C23semidirect
71. C4⋊C4×C43C23semidirect
80. C2×C43⋊C8C23semidirect
140. C2×D43AGL(1,ℤ/8)semidirect
162. #418D43semidirect
164. C43#3003semidirect
182. C2×M16C2×D43semidirect
188. #117C2×D43semidirect
190. #102C2×D43semidirect
215. C2×D4D172semidirect
231. C2×C8C22×D43semidirect
233. C4⋊C4C22×D43semidirect