Finite Group Databasebeta

← #19144978

Subgroups — #19144978

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#14583455C211yesmaximal, characteristic, complemented
2#124×D43C211yesmaximal, characteristic
3#14583260C212yesmaximal, complemented
4#14583257C212yesmaximal, complemented
5#14583256C211yesmaximal, characteristic, complemented
6#14583254C211yesmaximal, characteristic, complemented
7#14583253C211yesmaximal, characteristic, complemented
8#14582906C212yesmaximal, complemented
9#14582902C212yesmaximal
10C4×#10621872C211yesmaximal, characteristic, complemented
11C43×#488C211yesmaximal, characteristic, complemented
12C2×Q8×D43C2211yescharacteristic
13C2×D4×D43C2211yescharacteristic
14C2×#10621872C2212yes—
15#13063324C2212yescomplemented
16#13063317C2211yescharacteristic, complemented
17#13063314C2211yescharacteristic
18#13063313C2211yescharacteristic
19#13063312C2211yescharacteristic
20#13063311—22no—
21#13063303—22no—
22#13063290—22no—
23#13063283C2212yes—
24C22⋊C4×D43—22no—
25C42×D43C2211yescharacteristic
26#13063250C2212yescomplemented
27#13063249C2212yescomplemented
28#13063248C2212yescomplemented
29#13063247C2212yes—
30#13063246C2212yes—
31#13063245C2212yes—
32#13063235C2212yescomplemented
33C4×C43⋊C8C2211yescharacteristic, complemented
34#125×C43C2211yescharacteristic, complemented
35#124×C43C2211yescharacteristic
36#103×C43C2212yescomplemented
37#102×C43C2212yes—
38C4×C8×C43C2211yescharacteristic, complemented
39C23×D43—21no—
40C2×Q8×C43C2311yescharacteristic
41C2×D4×C43C2311yescharacteristic
42C2×C22⋊D43—21no—
43Q8×D43—24no—
44D4×D43—24no—
45C2×D172C2311yescharacteristic
46C2×C4×D43—21no—
47C2×C4×D43D412yes—
48C2×C4×D43C2311yescharacteristic
49C2×Dic86—22no—
50C2×Dic86—21no—
51C2×Dic86C2311yescharacteristic
52C2×C8×C43C2312yes—
53C4⋊C4×C43—22no—
54C4⋊C4×C43C2312yes—
55C22⋊C4×C43—22no—
56C42×C43C2311yescharacteristic
57C22⋊Dic43—22no—
58(C2×D43)⋊C4—22no—
59(C2×D43)⋊C4—22no—
60(C2×D43)⋊C4—22no—
61C4⋊Dic43C2312yes—
62Dic43⋊C4—22no—
63Dic43⋊C4—22no—
64C4×Dic43—22no—
65C4×Dic43D412yes—
66C4×Dic43C2311yescharacteristic
67C2×C43⋊C8C2312yes—
68#10621872—24no—
69C23×C43—21no—
70C22×D43—21no—
71C22×D43—44no—
72C22×D43—42no—
73C22×D43C2×D411yescharacteristic
74Q8×C43—22no—
75D4×C43—22no—
76C2×C4×C43—22no—
77C2×C4×C43—21no—
78C2×C4×C43C2×D412yes—
79C2×C4×C43C2411yescharacteristic
80C22⋊D43—42no—
81C2×Dic43—22no—
82C2×Dic43—21no—
83C2×Dic43C2×D412yes—
84C2×Dic43C2×D411yescharacteristic
85D172—22no—
86C4×D43—42no—
87C4×D43—42no—
88C4×D43#4114yes—
89Dic86—22no—
90Dic86—44no—
91Dic86—42no—
92C8×C43—22no—
93C43⋊C8—22no—
94C22×C43—41no—
95C22×C43—42no—
96C22×C43C22×D411yescharacteristic
97C2×D43—22no—
98C2×D43—41no—
99C2×D43—42no—
100C2×D43—84no—
101C2×D43#12412yes—
102C4×C43—22no—
103C4×C43—41no—
104C4×C43—42no—
105C4×C43C2×#4112yes—
106Dic43—22no—
107Dic43—41no—
108Dic43—42no—
109Dic43#12412yes—
110#3140—431nomaximal, Sylow
111C2×C43—81no—
112C2×C43C2×#12411yescharacteristic
113C2×C43#57512yes—
114D43—22no—
115D43—81no—
116#533—431no—
117C2×#124—431no—
118#489—432no—
119#489—432no—
120#488—431no—
121#488—431no—
122#488—431no—
123#488D4311yescharacteristic, complemented
124#419—432no—
125#418—432no—
126C4×M16—431no—
127C43#314011yescharacteristic, complemented, Sylow
128C22×Q8—431no—
129C22×D4—431no—
130C2×M16—432no—
131C4⋊Q8—432no—
132#125—431no—
133#125C2×D4311yescharacteristic, complemented
134#124—431no—
135#124—431no—
136#124—431no—
137#124—862no—
138#124C2×D4311yescharacteristic
139C22⋊Q8—862no—
140C4×Q8—862no—
141#117—432no—
142C2×C22⋊C4—862no—
143C2×C42—431no—
144#103—432no—
145#103—432no—
146#103—432no—
147#103C2×D4312yescomplemented
148#102—432no—
149#102—432no—
150#102—432no—
151#102C2×D4312yes—
152#97—432no—
153C4×C8—431no—
154C4×C8C2×D4311yescharacteristic, complemented
155C24—861no—
156C2×Q8—431no—
157C2×Q8—862no—
158C2×Q8—861no—
159C2×Q8—864no—
160C2×Q8C22×D4311yescharacteristic
161C2×D4—431no—
162C2×D4—864no—
163C2×D4—861no—
164C2×D4C22×D4311yescharacteristic
165C22×C4—431no—
166C22×C4—432no—
167C22×C4—861no—
168M16—864no—
169C2×C8—432no—
170C2×C8C22×D4312yes—
171C4⋊C4—22no—
172C4⋊C4—432no—
173C4⋊C4—862no—
174C4⋊C4—862no—
175C4⋊C4C22×D4312yes—
176C22⋊C4—22no—
177C22⋊C4—862no—
178C22⋊C4—862no—
179C22⋊C4—862no—
180C22⋊C4—862no—
181C42—432no—
182C42—431no—
183C42—862no—
184C42C22×D4311yescharacteristic
185C23—21no—
186C23—431no—
187C23—861no—
188C23—1722no—
189C23—1724no—
190Q8—22no—
191Q8—862no—
192Q8—1722no—
193Q8—1724no—
194D4—22no—
195D4—862no—
196D4—1722no—
197C2×C4—22no—
198C2×C4—21no—
199C2×C4—431no—
200C2×C4—434no—
201C2×C4—432no—
202C2×C4—862no—
203C2×C4—861no—
204C2×C4—1722no—
205C2×C4—1722no—
206C2×C4D4×D4312yes—
207C2×C4C23×D4311yescharacteristic
208C8—22no—
209C8—862no—
210C22—41no—
211C22—42no—
212C22—432no—
213C22—862no—
214C22—3444no—
215C22—1721no—
216C22—1722no—
217C22C2×D4×D4311yescharacteristic
218C4—22no—
219C4—41no—
220C4—42no—
221C4—432no—
222C4—862no—
223C4—1721no—
224C4—1722no—
225C4#41×D4312yes—
226C2—81no—
227C2—862no—
228C2—3441no—
229C2#124×D4311yescharacteristic
230C2#1458369612yes—
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#488C2
socleC22×C43C22×D4
hypercenter#488D43
hypocenterC43#3140
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #488

Complements

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

NH ≅ G/Ntype
1. #14583455C2semidirect
3. #14583260C2semidirect
4. #14583257C2semidirect
5. #14583256C2semidirect
6. #14583254C2semidirect
7. #14583253C2semidirect
8. #14582906C2semidirect
10. C4×#10621872C2semidirect
11. C43×#488C2semidirect
15. #13063324C22semidirect
16. #13063317C22semidirect
26. #13063250C22semidirect
27. #13063249C22semidirect
28. #13063248C22semidirect
32. #13063235C22semidirect
33. C4×C43⋊C8C22semidirect
34. #125×C43C22semidirect
36. #103×C43C22semidirect
38. C4×C8×C43C22semidirect
123. #488D43semidirect
127. C43#3140semidirect
133. #125C2×D43semidirect
147. #103C2×D43semidirect
154. C4×C8C2×D43semidirect