Finite Group Databasebeta

← #19145638

Subgroups — #19145638

Order 5504.

420 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 420 conjugacy classes of subgroups — too many to draw. Only its 109 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#14583503C211yesmaximal, characteristic, complemented
2#14583462C211yesmaximal, characteristic, complemented
3#14583286C211yesmaximal, characteristic, complemented
4#14583263C211yesmaximal, characteristic, complemented
5#14583254C211yesmaximal, characteristic, complemented
6#14583112C212yesmaximal, complemented
7#14583092C212yesmaximal, complemented
8#14583041C212yesmaximal, complemented
9#14583031C212yesmaximal, complemented
10#14582958C211yesmaximal, characteristic, complemented
11C43×#493C211yesmaximal, characteristic, complemented
12C2×#10621900C2211yescharacteristic
13C2×D4×D43C2211yescharacteristic
14C2×#10621883C2212yescomplemented
15C2×#10621882C2212yes—
16#13063321C2211yescharacteristic
17#13063317C2211yescharacteristic, complemented
18#13063313C2211yescharacteristic
19#13063312C2211yescharacteristic
20#13063306—22no—
21#13063297—22no—
22#13063297—22no—
23#13063296C2212yes—
24#13063293—22no—
25D4×Dic43C2212yescomplemented
26#13063282C2211yescharacteristic
27Dic43⋊C8C2212yescomplemented
28#13063250C2212yescomplemented
29#13063247C2212yes—
30#13063246C2212yes—
31#13063246C2212yescomplemented
32(C2×D43)⋊C8C2212yes—
33#13063236C2211yescharacteristic, complemented
34C2×D8×C43C2212yes—
35C2×D8×C43C2212yescomplemented
36#127×C43C2211yescharacteristic
37#127×C43C2211yescharacteristic, complemented
38C4×C8×C43C2211yescharacteristic, complemented
39C23×D43—21no—
40C2×D4×C43—22no—
41C2×D4×C43—22no—
42C2×D4×C43C2311yescharacteristic
43C2×D4×C43C2311yescharacteristic
44C2×D4×C43C2312yes—
45C2×C22⋊D43—21no—
46C2×C22⋊D43—22no—
47C2×C22⋊D43—21no—
48C2×C22⋊D43—22no—
49C22×Dic43—21no—
50C22×Dic43—22no—
51#10621900—42no—
52D4×D43—42no—
53C2×D172C2311yescharacteristic
54C2×C4×D43C2311yescharacteristic
55C2×Dic86C2311yescharacteristic
56D8×C43—42no—
57D8×C43—42no—
58C2×C8×C43C2312yes—
59C42×C43C2311yescharacteristic
60C22⋊Dic43—22no—
61C22⋊Dic43—22no—
62C22⋊Dic43—22no—
63#10621883—42no—
64#10621882—42no—
65(C2×D43)⋊C4—22no—
66(C2×D43)⋊C4D412yes—
67C4⋊Dic43C2312yes—
68Dic43⋊C4—22no—
69Dic43⋊C4D412yes—
70C4×Dic43C2311yescharacteristic
71C2×C43⋊C8C2312yes—
72C23×C43—22no—
73C23×C43—21no—
74C23×C43—21no—
75C22×D43—21no—
76C22×D43—42no—
77C22×D43—82no—
78C22×D43C2×D411yescharacteristic
79D4×C43—22no—
80D4×C43—22no—
81D4×C43—22no—
82D4×C43—22no—
83D4×C43—82no—
84D4×C43—82no—
85C2×C4×C43C2×D412yes—
86C2×C4×C43C2411yescharacteristic
87C22⋊D43—42no—
88C22⋊D43—42no—
89C22⋊D43—82no—
90C22⋊D43—82no—
91C2×Dic43—22no—
92C2×Dic43—21no—
93C2×Dic43—42no—
94C2×Dic43—82no—
95C2×Dic43C2×D412yes—
96C2×Dic43C2×D411yescharacteristic
97D172—22no—
98C4×D43—22no—
99Dic86—22no—
100C8×C43—22no—
101C43⋊C8—22no—
102C22×C43—41no—
103C22×C43—41no—
104C22×C43—42no—
105C22×C43—42no—
106C22×C43—42no—
107C22×C43—42no—
108C22×C43—42no—
109C22×C43C22×D411yescharacteristic
110C2×D43—21no—
111C2×D43—22no—
112C2×D43—41no—
113C2×D43—42no—
114C2×D43—84no—
115C4×C43—22no—
116C4×C43H(5,𝔽2)12yes—
117Dic43—21no—
118Dic43—22no—
119Dic43—41no—
120Dic43—42no—
121#3220—431nomaximal, Sylow
122C2×C43—81no—
123C2×C43—81no—
124C2×C43—82no—
125C2×C43#53511yescharacteristic
126C2×C43#57612yes—
127D43—41no—
128D43—81no—
129#540—431no—
130#535—431no—
131#496—431no—
132#493D4311yescharacteristic, complemented
133#490—431no—
134#488—431no—
135#463—432no—
136#459—432no—
137#449—432no—
138#447—432no—
139#433—431no—
140C43#322011yescharacteristic, complemented, Sylow
141C2×#41—431no—
142C22×D4—431no—
143C2×SD16—432no—
144C2×D8—432no—
145C2×D8C2×D4312yes—
146C2×D8C2×D4312yescomplemented
147#127—431no—
148#127C2×D4311yescharacteristic
149#127C2×D4311yescharacteristic, complemented
150#125—431no—
151#124—431no—
152#124—431no—
153#123—862no—
154#121—432no—
155#121—862no—
156#121—862no—
157#120—862no—
158C4×D4—432no—
159#117—431no—
160C4⋊C8—432no—
161#103—432no—
162#102—432no—
163#102—432no—
164#102—432no—
165C22⋊C8—432no—
166#97—431no—
167C4×C8C2×D4311yescharacteristic, complemented
168C24—861no—
169#41—1722no—
170C2×Q8—431no—
171C2×D4—22no—
172C2×D4—22no—
173C2×D4—431no—
174C2×D4—862no—
175C2×D4—861no—
176C2×D4—862no—
177C2×D4—861no—
178C2×D4—1722no—
179C2×D4C22×D4311yescharacteristic
180C2×D4C22×D4311yescharacteristic
181C2×D4C22×D4312yes—
182C22×C4—431no—
183C22×C4—862no—
184C22×C4—861no—
185SD16—1722no—
186D8—42no—
187D8—42no—
188D8—1722no—
189C2×C8—432no—
190C2×C8C22×D4312yes—
191C4⋊C4—432no—
192C4⋊C4—432no—
193C4⋊C4—862no—
194C22⋊C4—432no—
195C22⋊C4—862no—
196C22⋊C4—862no—
197C22⋊C4—862no—
198C22⋊C4—862no—
199C42—431no—
200C42C22×D4311yescharacteristic
201C23—22no—
202C23—21no—
203C23—21no—
204C23—431no—
205C23—861no—
206C23—3442no—
207C23—1722no—
208Q8—862no—
209D4—22no—
210D4—22no—
211D4—22no—
212D4—22no—
213D4—82no—
214D4—82no—
215D4—862no—
216D4—3442no—
217D4—3442no—
218D4—1722no—
219D4—1722no—
220C2×C4—432no—
221C2×C4—431no—
222C2×C4—862no—
223C2×C4—861no—
224C2×C4—862no—
225C2×C4—3442no—
226C2×C4—1722no—
227C2×C4D4×D4312yes—
228C2×C4C23×D4311yescharacteristic
229C8—22no—
230C8—862no—
231C22—42no—
232C22—42no—
233C22—42no—
234C22—42no—
235C22—41no—
236C22—41no—
237C22—42no—
238C22—862no—
239C22—861no—
240C22—3444no—
241C22—1722no—
242C22—1721no—
243C22C2×D4×D4311yescharacteristic
244C4—22no—
245C4—862no—
246C4—861no—
247C4—1722no—
248C4—1721no—
249C4#1306337012yes—
250C2—81no—
251C2—82no—
252C2—81no—
253C2—3441no—
254C2—1721no—
255C2#1458346211yescharacteristic
256C2#1458370012yes—
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#493C2
socleC22×C43C22×D4
hypercenter#493D43
hypocenterC43#3220
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #493

Complements

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

NH ≅ G/Ntype
1. #14583503C2semidirect
2. #14583462C2semidirect
3. #14583286C2semidirect
4. #14583263C2semidirect
5. #14583254C2semidirect
6. #14583112C2semidirect
7. #14583092C2semidirect
8. #14583041C2semidirect
9. #14583031C2semidirect
10. #14582958C2semidirect
11. C43×#493C2semidirect
14. C2×#10621883C22semidirect
17. #13063317C22semidirect
25. D4×Dic43C22semidirect
27. Dic43⋊C8C22semidirect
28. #13063250C22semidirect
31. #13063246C22semidirect
33. #13063236C22semidirect
35. C2×D8×C43C22semidirect
37. #127×C43C22semidirect
38. C4×C8×C43C22semidirect
132. #493D43semidirect
140. C43#3220semidirect
146. C2×D8C2×D43semidirect
149. #127C2×D43semidirect
167. C4×C8C2×D43semidirect