Finite Group Databasebeta

← #19144980

Subgroups — #19144980

Order 5504.

400 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 117 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#14583454C211yesmaximal, characteristic, complemented
2#124×D43C211yesmaximal, characteristic
3#14583261C211yesmaximal, characteristic, complemented
4#14583259C211yesmaximal, characteristic, complemented
5#14583258C211yesmaximal, characteristic, complemented
6#14583255C212yesmaximal, complemented
7#14583252C212yesmaximal, complemented
8#14582906C212yesmaximal, complemented
9#14582902C212yesmaximal
10#14582851C211yesmaximal, characteristic, complemented
11C43×#489C211yesmaximal, characteristic, complemented
12C2×Q8×D43C2211yescharacteristic
13C2×D4×D43C2211yescharacteristic
14C2×#10621872C2212yes—
15#13063325C2211yescharacteristic, complemented
16#13063316C2212yescomplemented
17#13063314C2211yescharacteristic
18#13063313C2211yescharacteristic
19#13063312C2211yescharacteristic
20#13063311—21no—
21#13063311—21no—
22#13063305—21no—
23#13063301—21no—
24Q8×Dic43—21no—
25#13063290—21no—
26#13063283C2212yes—
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
37C8×Dic43C2212yescomplemented
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—
49D4×D43—24no—
50C2×D172C2311yescharacteristic
51C2×C4×D43—21no—
52C2×C4×D43D411yescharacteristic
53C2×C4×D43D411yescharacteristic
54C2×C4×D43C2311yescharacteristic
55C2×Dic86—21no—
56C2×Dic86—21no—
57C2×Dic86C2311yescharacteristic
58C2×C8×C43C2312yes—
59C4⋊C4×C43—21no—
60C4⋊C4×C43C2312yes—
61C22⋊C4×C43—21no—
62C22⋊C4×C43—21no—
63C42×C43C2311yescharacteristic
64C22⋊Dic43—21no—
65C22⋊Dic43—21no—
66(C2×D43)⋊C4—21no—
67(C2×D43)⋊C4—21no—
68(C2×D43)⋊C4—21no—
69(C2×D43)⋊C4—21no—
70(C2×D43)⋊C4—22no—
71C4⋊Dic43—21no—
72C4⋊Dic43—22no—
73C4⋊Dic43C2312yes—
74Dic43⋊C4—22no—
75C4×Dic43—22no—
76C4×Dic43D411yescharacteristic
77C4×Dic43D411yescharacteristic
78C4×Dic43C2311yescharacteristic
79C2×C43⋊C8C2312yes—
80#10621872—24no—
81C23×C43—21no—
82C22×D43—21no—
83C22×D43—42no—
84C22×D43—42no—
85C22×D43—42no—
86C22×D43C2×D411yescharacteristic
87Q8×C43—22no—
88Q8×C43—42no—
89D4×C43—22no—
90C2×C4×C43—22no—
91C2×C4×C43—21no—
92C2×C4×C43C2×D411yescharacteristic
93C2×C4×C43C2×D411yescharacteristic
94C2×C4×C43C2411yescharacteristic
95C22⋊D43—42no—
96C2×Dic43—22no—
97C2×Dic43—21no—
98C2×Dic43C2×D411yescharacteristic
99C2×Dic43C2×D411yescharacteristic
100C2×Dic43C2×D411yescharacteristic
101D172—22no—
102C4×D43—41no—
103C4×D43—41no—
104C4×D43—42no—
105C4×D43#4114yes—
106Dic86—22no—
107Dic86—42no—
108Dic86—42no—
109C8×C43—22no—
110C43⋊C8—22no—
111C22×C43—41no—
112C22×C43—41no—
113C22×C43—41no—
114C22×C43C22×D411yescharacteristic
115C2×D43—21no—
116C2×D43—21no—
117C2×D43—41no—
118C2×D43—41no—
119C2×D43—41no—
120C2×D43—84no—
121C2×D43#12412yes—
122C4×C43—21no—
123C4×C43—21no—
124C4×C43—41no—
125C4×C43—42no—
126C4×C43C2×#4112yes—
127Dic43—21no—
128Dic43—21no—
129Dic43—41no—
130Dic43—42no—
131Dic43#12412yes—
132#3140—431nomaximal, Sylow
133C2×C43—81no—
134C2×C43C2×#12411yescharacteristic
135C2×C43#57511yescharacteristic
136C2×C43#57511yescharacteristic
137D43—22no—
138D43—81no—
139#533—431no—
140C2×#124—431no—
141#489—431no—
142#489—431no—
143#489—431no—
144#489D4311yescharacteristic, complemented
145#488—432no—
146#488—432no—
147#419—432no—
148#418—432no—
149C4×M16—431no—
150C43#314011yescharacteristic, complemented, Sylow
151C22×Q8—431no—
152C22×D4—431no—
153C2×M16—432no—
154C4⋊Q8—431no—
155C4⋊Q8C2×D4311yescharacteristic, complemented
156#125—432no—
157#124—431no—
158#124—431no—
159#124—431no—
160#124—861no—
161#124—861no—
162#124C2×D4311yescharacteristic
163C22⋊Q8—861no—
164C22⋊Q8—861no—
165C4×Q8—861no—
166C4×Q8—861no—
167#117—432no—
168C2×C22⋊C4—861no—
169C2×C22⋊C4—861no—
170C2×C42—431no—
171#103—432no—
172#103—432no—
173#103—432no—
174#103C2×D4312yescomplemented
175#102—432no—
176#102—432no—
177#102—432no—
178#102C2×D4312yes—
179#97—431no—
180#97C2×D4311yescharacteristic, complemented
181C4×C8—432no—
182C24—861no—
183C2×Q8—21no—
184C2×Q8—431no—
185C2×Q8—861no—
186C2×Q8—864no—
187C2×Q8—861no—
188C2×Q8C22×D4311yescharacteristic
189C2×D4—431no—
190C2×D4—864no—
191C2×D4—861no—
192C2×D4C22×D4311yescharacteristic
193C22×C4—431no—
194C22×C4—431no—
195C22×C4—431no—
196C22×C4—861no—
197M16—864no—
198C2×C8—432no—
199C2×C8C22×D4312yes—
200C4⋊C4—21no—
201C4⋊C4—432no—
202C4⋊C4—862no—
203C4⋊C4—862no—
204C4⋊C4—861no—
205C4⋊C4C22×D4312yes—
206C22⋊C4—21no—
207C22⋊C4—21no—
208C22⋊C4—861no—
209C22⋊C4—861no—
210C22⋊C4—862no—
211C22⋊C4—861no—
212C22⋊C4—861no—
213C22⋊C4—861no—
214C22⋊C4—861no—
215C42—431no—
216C42—431no—
217C42—431no—
218C42—862no—
219C42C22×D4311yescharacteristic
220C23—21no—
221C23—431no—
222C23—861no—
223C23—1722no—
224C23—1722no—
225C23—1722no—
226Q8—22no—
227Q8—42no—
228Q8—862no—
229Q8—1722no—
230Q8—1722no—
231D4—22no—
232D4—862no—
233D4—1722no—
234C2×C4—22no—
235C2×C4—21no—
236C2×C4—431no—
237C2×C4—434no—
238C2×C4—431no—
239C2×C4—431no—
240C2×C4—862no—
241C2×C4—861no—
242C2×C4—1721no—
243C2×C4—1721no—
244C2×C4—1722no—
245C2×C4D4×D4311yescharacteristic
246C2×C4D4×D4311yescharacteristic
247C2×C4C23×D4311yescharacteristic
248C8—22no—
249C8—862no—
250C22—41no—
251C22—41no—
252C22—41no—
253C22—432no—
254C22—861no—
255C22—861no—
256C22—3444no—
257C22—1721no—
258C22—1721no—
259C22—1721no—
260C22C2×D4×D4311yescharacteristic
261C4—21no—
262C4—21no—
263C4—41no—
264C4—42no—
265C4—432no—
266C4—861no—
267C4—861no—
268C4—1721no—
269C4—1722no—
270C4#41×D4312yes—
271C2—81no—
272C2—862no—
273C2—3441no—
274C2#124×D4311yescharacteristic
275C2#1458369511yescharacteristic
276C2#1458369811yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#489C2
socleC22×C43C22×D4
hypercenter#489D43
hypocenterC43#3140
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. #14583454C2semidirect
3. #14583261C2semidirect
4. #14583259C2semidirect
5. #14583258C2semidirect
6. #14583255C2semidirect
7. #14583252C2semidirect
8. #14582906C2semidirect
10. #14582851C2semidirect
11. C43×#489C2semidirect
15. #13063325C22semidirect
16. #13063316C22semidirect
30. #13063250C22semidirect
31. #13063249C22semidirect
32. #13063248C22semidirect
36. #13063236C22semidirect
37. C8×Dic43C22semidirect
38. C4⋊Q8×C43C22semidirect
40. #103×C43C22semidirect
42. #97×C43C22semidirect
144. #489D43semidirect
150. C43#3140semidirect
155. C4⋊Q8C2×D43semidirect
174. #103C2×D43semidirect
180. #97C2×D43semidirect