Finite Group Databasebeta

← #19145583

Subgroups — #19145583

Order 5504.

444 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 444 conjugacy classes of subgroups — too many to draw. Only its 111 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#14583450C211yesmaximal, characteristic, complemented
2#124×D43C211yesmaximal, characteristic, complemented
3#14583289C211yesmaximal, characteristic, complemented
4#14583288C211yesmaximal, characteristic, complemented
5#14583261C211yesmaximal, characteristic, complemented
6#14583117C212yesmaximal, complemented
7#14583113C212yesmaximal, complemented
8#14583039C212yesmaximal, complemented
9#14583034C212yesmaximal, complemented
10#14582954C211yesmaximal, characteristic, complemented
11C43×#489C211yesmaximal, characteristic, complemented
12C2×#10621902—21no—
13C2×Q8×D43C2211yescharacteristic
14C2×D4×D43C2211yescharacteristic
15C2×#10621873C2212yescomplemented
16C2×#10621884C2212yescomplemented
17C2×D344C2212yes—
18C2×#10621882C2212yes—
19#13063322C2211yescharacteristic, complemented
20#13063314—21no—
21#13063314C2211yescharacteristic
22#13063313C2211yescharacteristic
23#13063312C2211yescharacteristic
24#13063311—21no—
25#13063311—21no—
26#13063300—21no—
27#13063300C2212yes—
28#13063287—21no—
29#13063287C2212yescomplemented
30C22⋊C4×D43—21no—
31C22⋊C4×D43—21no—
32C42×D43C2211yescharacteristic
33Dic43⋊C8C2212yescomplemented
34#13063248C2212yescomplemented
35#13063245C2212yes—
36(C2×D43)⋊C8C2212yes—
37#13063236C2211yescharacteristic, complemented
38C4⋊Q8×C43C2211yescharacteristic, complemented
39#124×C43C2211yescharacteristic
40#103×C43C2212yescomplemented
41#102×C43C2212yes—
42#97×C43C2211yescharacteristic, complemented
43C23×D43—21no—
44C2×Q8×C43—21no—
45C2×Q8×C43C2311yescharacteristic
46C2×D4×C43C2311yescharacteristic
47C2×C22⋊D43—21no—
48#10621902—44no—
49Q8×D43—42no—
50D4×D43—42no—
51C2×D172—21no—
52C2×D172—21no—
53C2×D172—22no—
54C2×D172C2311yescharacteristic
55C2×D172C2312yes—
56C2×C4×D43—22no—
57C2×C4×D43—21no—
58C2×C4×D43D411yescharacteristic
59C2×C4×D43D411yescharacteristic
60C2×C4×D43C2311yescharacteristic
61C2×Dic86—21no—
62C2×Dic86C2311yescharacteristic
63C2×C8×C43C2312yes—
64C4⋊C4×C43—21no—
65C4⋊C4×C43C2312yes—
66C22⋊C4×C43—21no—
67C22⋊C4×C43—21no—
68C42×C43C2311yescharacteristic
69C22⋊Dic43—21no—
70C22⋊Dic43—21no—
71#10621884—42no—
72#10621882—42no—
73(C2×D43)⋊C4—21no—
74(C2×D43)⋊C4—21no—
75(C2×D43)⋊C4—21no—
76(C2×D43)⋊C4—21no—
77(C2×D43)⋊C4—22no—
78(C2×D43)⋊C4—22no—
79C4×Dic43D411yescharacteristic
80C4×Dic43D411yescharacteristic
81C4×Dic43C2311yescharacteristic
82C2×C43⋊C8C2312yes—
83D344—42no—
84#10621873—42no—
85C23×C43—21no—
86C22×D43—21no—
87C22×D43—22no—
88C22×D43—42no—
89C22×D43—42no—
90C22×D43—42no—
91C22×D43C2×D411yescharacteristic
92Q8×C43—22no—
93Q8×C43—42no—
94D4×C43—22no—
95C2×C4×C43—21no—
96C2×C4×C43—22no—
97C2×C4×C43C2×D411yescharacteristic
98C2×C4×C43C2×D411yescharacteristic
99C2×C4×C43C2411yescharacteristic
100C22⋊D43—42no—
101C2×Dic43—21no—
102C2×Dic43C2×D411yescharacteristic
103C2×Dic43C2×D411yescharacteristic
104C2×Dic43C2×D411yescharacteristic
105D172—22no—
106D172—22no—
107D172—22no—
108D172—42no—
109D172—42no—
110D172—44no—
111C4×D43—22no—
112C4×D43—22no—
113C4×D43—41no—
114C4×D43—44no—
115C4×D43—42no—
116Dic86—22no—
117Dic86—42no—
118C8×C43—22no—
119C43⋊C8—22no—
120C22×C43—41no—
121C22×C43—41no—
122C22×C43—41no—
123C22×C43C22×D411yescharacteristic
124C2×D43—21no—
125C2×D43—21no—
126C2×D43—41no—
127C2×D43—42no—
128C2×D43—41no—
129C2×D43—42no—
130C2×D43—41no—
131C2×D43—42no—
132C2×D43—84no—
133C2×D43AGL(1,ℤ/8)12yes—
134C4×C43—21no—
135C4×C43—21no—
136C4×C43—41no—
137C4×C43—42no—
138C4×C43H(5,𝔽2)12yes—
139Dic43—21no—
140Dic43—21no—
141Dic43—21no—
142Dic43—41no—
143#3213—431nomaximal, Sylow
144C2×C43—81no—
145C2×C43#53511yescharacteristic
146C2×C43C2×AGL(1,ℤ/8)11yescharacteristic
147C2×C43#57511yescharacteristic
148D43—22no—
149D43—82no—
150D43—81no—
151#532—431no—
152C2×#124—431no—
153#496—431no—
154#496—431no—
155#489—431no—
156#489D4311yescharacteristic, complemented
157#463—432no—
158#463—432no—
159#448—432no—
160#447—432no—
161#432—431no—
162C43#321311yescharacteristic, complemented, Sylow
163C2×#41—861no—
164C22×Q8—431no—
165C22×D4—431no—
166C2×SD16—432no—
167C2×SD16—432no—
168C2×D8—432no—
169C2×D8—432no—
170C4⋊Q8C2×D4311yescharacteristic, complemented
171#127—431no—
172#124—431no—
173#124—431no—
174#124—431no—
175#124—861no—
176#124—861no—
177#124—861no—
178#124C2×D4311yescharacteristic
179#121—432no—
180#121—861no—
181C4×D4—432no—
182C4×D4—861no—
183C2×C22⋊C4—861no—
184C2×C22⋊C4—861no—
185C2×C42—431no—
186C4⋊C8—432no—
187#103—432no—
188#103C2×D4312yescomplemented
189#102—432no—
190#102C2×D4312yes—
191C22⋊C8—432no—
192#97—431no—
193#97C2×D4311yescharacteristic, complemented
194C24—861no—
195#41—1724no—
196C2×Q8—21no—
197C2×Q8—431no—
198C2×Q8—861no—
199C2×Q8—1722no—
200C2×Q8C22×D4311yescharacteristic
201C2×D4—431no—
202C2×D4—432no—
203C2×D4—862no—
204C2×D4—861no—
205C2×D4—861no—
206C2×D4—861no—
207C2×D4—1722no—
208C2×D4C22×D4311yescharacteristic
209C22×C4—431no—
210C22×C4—431no—
211C22×C4—431no—
212C22×C4—862no—
213C22×C4—861no—
214SD16—1722no—
215SD16—1722no—
216D8—1722no—
217D8—1722no—
218C2×C8—432no—
219C2×C8C22×D4312yes—
220C4⋊C4—21no—
221C4⋊C4C22×D4312yes—
222C22⋊C4—21no—
223C22⋊C4—21no—
224C22⋊C4—861no—
225C22⋊C4—861no—
226C22⋊C4—862no—
227C22⋊C4—862no—
228C22⋊C4—861no—
229C22⋊C4—861no—
230C22⋊C4—861no—
231C22⋊C4—861no—
232C42—431no—
233C42—431no—
234C42—431no—
235C42C22×D4311yescharacteristic
236C23—21no—
237C23—431no—
238C23—861no—
239C23—862no—
240C23—1722no—
241C23—1722no—
242C23—1722no—
243Q8—22no—
244Q8—42no—
245Q8—862no—
246Q8—1722no—
247D4—22no—
248D4—862no—
249D4—862no—
250D4—862no—
251D4—1722no—
252D4—1722no—
253D4—1724no—
254D4—1722no—
255C2×C4—21no—
256C2×C4—22no—
257C2×C4—431no—
258C2×C4—431no—
259C2×C4—431no—
260C2×C4—862no—
261C2×C4—862no—
262C2×C4—861no—
263C2×C4—1721no—
264C2×C4—1724no—
265C2×C4—1722no—
266C2×C4D4×D4311yescharacteristic
267C2×C4D4×D4311yescharacteristic
268C2×C4C23×D4311yescharacteristic
269C8—22no—
270C8—862no—
271C22—41no—
272C22—41no—
273C22—41no—
274C22—432no—
275C22—861no—
276C22—861no—
277C22—3444no—
278C22—1722no—
279C22—1721no—
280C22—1722no—
281C22—1721no—
282C22—1721no—
283C22—1722no—
284C22C2×D4×D4311yescharacteristic
285C4—21no—
286C4—21no—
287C4—42no—
288C4—41no—
289C4—861no—
290C4—861no—
291C4—861no—
292C4—1721no—
293C4#1306337112yes—
294C2—81no—
295C2—862no—
296C2—3441no—
297C2—3442no—
298C2#1458346711yescharacteristic
299C2AGL(1,ℤ/8)×D4311yescharacteristic
300C2#1458369811yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#489C2
socleC22×C43C22×D4
hypercenter#489D43
hypocenterC43#3213
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #489

Complements

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

NH ≅ G/Ntype
1. #14583450C2semidirect
2. #124×D43C2semidirect
3. #14583289C2semidirect
4. #14583288C2semidirect
5. #14583261C2semidirect
6. #14583117C2semidirect
7. #14583113C2semidirect
8. #14583039C2semidirect
9. #14583034C2semidirect
10. #14582954C2semidirect
11. C43×#489C2semidirect
15. C2×#10621873C22semidirect
16. C2×#10621884C22semidirect
19. #13063322C22semidirect
29. #13063287C22semidirect
33. Dic43⋊C8C22semidirect
34. #13063248C22semidirect
37. #13063236C22semidirect
38. C4⋊Q8×C43C22semidirect
40. #103×C43C22semidirect
42. #97×C43C22semidirect
156. #489D43semidirect
162. C43#3213semidirect
170. C4⋊Q8C2×D43semidirect
188. #103C2×D43semidirect
193. #97C2×D43semidirect