Finite Group Databasebeta

← #489×D43 #19144921

Subgroups — #489×D43 #19144921

Order 5504.

436 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 436 conjugacy classes of subgroups — too many to draw. Only its 125 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
1C4⋊Q8×D43C211yesmaximal, characteristic, complemented
2#124×D43C211yesmaximal, characteristic
3#14583261C211yesmaximal, characteristic, complemented
4#14583260C212yesmaximal, complemented
5#14583259C211yesmaximal, characteristic, complemented
6#14583258C211yesmaximal, characteristic, complemented
7#14583257C212yesmaximal, complemented
8#103×D43C212yesmaximal, complemented
9#102×D43C212yesmaximal
10#97×D43C211yesmaximal, characteristic, complemented
11C43×#489C211yesmaximal, characteristic, complemented
12C2×Q8×D43—21no—
13C2×Q8×D43C2211yescharacteristic
14C2×D4×D43C2211yescharacteristic
15C2×C8×D43C2212yes—
16#13063325C2211yescharacteristic, complemented
17#13063324—21no—
18#13063324C2212yescomplemented
19#13063323—21no—
20#13063314C2211yescharacteristic
21#13063313C2211yescharacteristic
22#13063312C2211yescharacteristic
23#13063311—21no—
24#13063311—21no—
25C4⋊C4×D43—21no—
26C4⋊C4×D43C2212yes—
27C22⋊C4×D43—21no—
28C22⋊C4×D43—21no—
29C42×D43C2211yescharacteristic
30#13063250C2212yescomplemented
31#13063249C2212yescomplemented
32#13063248C2212yescomplemented
33#13063247C2212yes—
34#13063246C2212yes—
35#13063245C2212yes—
36#13063236C2211yescharacteristic, complemented
37#13063235C2212yescomplemented
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—
48Q8×D43—24no—
49Q8×D43—44no—
50D4×D43—24no—
51C2×D172C2311yescharacteristic
52C2×C4×D43—21no—
53C2×C4×D43—22no—
54C2×C4×D43D411yescharacteristic
55C2×C4×D43D411yescharacteristic
56C2×C4×D43C2311yescharacteristic
57C2×Dic86—21no—
58C2×Dic86—21no—
59C2×Dic86—22no—
60C2×Dic86C2311yescharacteristic
61C2×C8×C43C2312yes—
62C4⋊C4×C43—21no—
63C4⋊C4×C43C2312yes—
64C22⋊C4×C43—21no—
65C22⋊C4×C43—21no—
66C42×C43C2311yescharacteristic
67C22⋊Dic43—21no—
68C22⋊Dic43—21no—
69(C2×D43)⋊C4—21no—
70(C2×D43)⋊C4—21no—
71(C2×D43)⋊C4—21no—
72(C2×D43)⋊C4—21no—
73C4⋊Dic43—21no—
74C4⋊Dic43C2312yes—
75Dic43⋊C4—22no—
76Dic43⋊C4—22no—
77C4×Dic43D411yescharacteristic
78C4×Dic43D411yescharacteristic
79C4×Dic43C2311yescharacteristic
80C2×C43⋊C8C2312yes—
81C8×D43—24no—
82C23×C43—21no—
83C22×D43—21no—
84C22×D43—42no—
85C22×D43—42no—
86C22×D43—42no—
87C22×D43C2×D411yescharacteristic
88Q8×C43—22no—
89Q8×C43—42no—
90D4×C43—22no—
91C2×C4×C43—22no—
92C2×C4×C43—21no—
93C2×C4×C43C2×D411yescharacteristic
94C2×C4×C43C2×D411yescharacteristic
95C2×C4×C43C2411yescharacteristic
96C22⋊D43—42no—
97C2×Dic43—22no—
98C2×Dic43—21no—
99C2×Dic43C2×D411yescharacteristic
100C2×Dic43C2×D411yescharacteristic
101C2×Dic43C2×D411yescharacteristic
102D172—22no—
103C4×D43—22no—
104C4×D43—22no—
105C4×D43—42no—
106C4×D43—44no—
107C4×D43#4114yes—
108Dic86—22no—
109Dic86—44no—
110Dic86—42no—
111Dic86—42no—
112C8×C43—22no—
113C43⋊C8—22no—
114C22×C43—41no—
115C22×C43—41no—
116C22×C43—41no—
117C22×C43C22×D411yescharacteristic
118C2×D43—41no—
119C2×D43—41no—
120C2×D43—41no—
121C2×D43—84no—
122C2×D43#12412yes—
123C2×D43AGL(1,ℤ/8)12yes—
124C2×D43#13712yes—
125C4×C43—21no—
126C4×C43—21no—
127C4×C43—41no—
128C4×C43—42no—
129C4×C43C2×#4112yes—
130Dic43—21no—
131Dic43—21no—
132Dic43—41no—
133Dic43—42no—
134Dic43#12412yes—
135C2×#489—431nomaximal, Sylow
136C2×C43—81no—
137C2×C43C2×#12411yescharacteristic
138C2×C43C2×AGL(1,ℤ/8)11yescharacteristic
139C2×C43C2×#13711yescharacteristic
140D43—81no—
141D43#48914yesdirect product factor
142C2×C4⋊Q8—431no—
143C2×#124—431no—
144#489—431no—
145#489—431no—
146#489—432no—
147#489—432no—
148#489—431no—
149#489D4311yescharacteristic, direct product factor
150C2×#103—432no—
151C2×#102—432no—
152C2×#97—431no—
153C43C2×#48911yescharacteristic, complemented, Sylow
154C22×Q8—431no—
155C22×Q8—861no—
156C22×D4—431no—
157C22×C8—432no—
158C4⋊Q8—432no—
159C4⋊Q8—431no—
160C4⋊Q8—861no—
161C4⋊Q8—861no—
162C4⋊Q8C2×D4311yescharacteristic, complemented
163#124—431no—
164#124—431no—
165#124—431no—
166#124—861no—
167#124—861no—
168#124C2×D4311yescharacteristic
169C2×C4⋊C4—432no—
170C2×C4⋊C4—861no—
171C2×C22⋊C4—861no—
172C2×C22⋊C4—861no—
173C2×C42—431no—
174#103—432no—
175#103—432no—
176#103—432no—
177#103C2×D4312yescomplemented
178#102—432no—
179#102—432no—
180#102—432no—
181#102C2×D4312yes—
182#97—432no—
183#97—431no—
184#97C2×D4311yescharacteristic, complemented
185C24—861no—
186C2×Q8—21no—
187C2×Q8—431no—
188C2×Q8—861no—
189C2×Q8—862no—
190C2×Q8—864no—
191C2×Q8—861no—
192C2×Q8—1724no—
193C2×Q8C22×D4311yescharacteristic
194C2×D4—431no—
195C2×D4—864no—
196C2×D4—861no—
197C2×D4C22×D4311yescharacteristic
198C22×C4—431no—
199C22×C4—431no—
200C22×C4—431no—
201C22×C4—861no—
202C22×C4—862no—
203C2×C8—432no—
204C2×C8—864no—
205C2×C8C22×D4312yes—
206C4⋊C4—21no—
207C4⋊C4—432no—
208C4⋊C4—862no—
209C4⋊C4—862no—
210C4⋊C4—861no—
211C4⋊C4C22×D4312yes—
212C22⋊C4—21no—
213C22⋊C4—21no—
214C22⋊C4—861no—
215C22⋊C4—861no—
216C22⋊C4—861no—
217C22⋊C4—861no—
218C22⋊C4—861no—
219C22⋊C4—861no—
220C42—431no—
221C42—431no—
222C42—431no—
223C42C22×D4311yescharacteristic
224C23—21no—
225C23—431no—
226C23—861no—
227C23—1722no—
228C23—1722no—
229C23—1722no—
230Q8—22no—
231Q8—42no—
232Q8—862no—
233Q8—1722no—
234Q8—1722no—
235Q8—1724no—
236D4—22no—
237D4—862no—
238D4—1722no—
239C2×C4—21no—
240C2×C4—22no—
241C2×C4—431no—
242C2×C4—434no—
243C2×C4—431no—
244C2×C4—431no—
245C2×C4—862no—
246C2×C4—862no—
247C2×C4—861no—
248C2×C4—862no—
249C2×C4—1722no—
250C2×C4—1724no—
251C2×C4D4×D4311yescharacteristic
252C2×C4D4×D4311yescharacteristic
253C2×C4C23×D4311yescharacteristic
254C8—22no—
255C8—862no—
256C22—41no—
257C22—41no—
258C22—41no—
259C22—432no—
260C22—432no—
261C22—432no—
262C22—3444no—
263C22—1721no—
264C22—1721no—
265C22—1721no—
266C22C2×D4×D4311yescharacteristic
267C4—21no—
268C4—21no—
269C4—41no—
270C4—42no—
271C4—432no—
272C4—861no—
273C4—861no—
274C4—1721no—
275C4—1722no—
276C4#41×D4312yes—
277C2—81no—
278C2—434no—
279C2—3441no—
280C2#124×D4311yescharacteristic
281C2AGL(1,ℤ/8)×D4311yescharacteristic
282C2#137×D4311yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#489C2
socleC22×C43C22×D4
hypercenter#489D43
hypocenterC43C2×#489
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. C4⋊Q8×D43C2semidirect
3. #14583261C2semidirect
4. #14583260C2semidirect
5. #14583259C2semidirect
6. #14583258C2semidirect
7. #14583257C2semidirect
8. #103×D43C2semidirect
10. #97×D43C2semidirect
11. C43×#489C2semidirect
16. #13063325C22semidirect
18. #13063324C22semidirect
30. #13063250C22semidirect
31. #13063249C22semidirect
32. #13063248C22semidirect
36. #13063236C22semidirect
37. #13063235C22semidirect
38. C4⋊Q8×C43C22semidirect
40. #103×C43C22semidirect
42. #97×C43C22semidirect
141. D43#489direct (N × H)
149. #489D43direct (N × H)
153. C43C2×#489semidirect
162. C4⋊Q8C2×D43semidirect
177. #103C2×D43semidirect
184. #97C2×D43semidirect