Finite Group Databasebeta

← #19145646

Subgroups — #19145646

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#14583505C211yesmaximal, characteristic, complemented
2#14583462C211yesmaximal, characteristic, complemented
3#14583288C211yesmaximal, characteristic, complemented
4#14583275C211yesmaximal, characteristic, complemented
5#14583256C211yesmaximal, characteristic, complemented
6#14583113C212yesmaximal, complemented
7#14583093C212yesmaximal, complemented
8#14583045C212yesmaximal, complemented
9#14583034C212yesmaximal, complemented
10#14582961C211yesmaximal, characteristic, complemented
11C43×#490C211yesmaximal, characteristic, complemented
12C2×#10621900C2211yescharacteristic
13C2×D4×D43C2211yescharacteristic
14C2×#10621873C2212yescomplemented
15C2×D344C2212yes—
16C2×#10621882C2212yes—
17C2×#10621882C2212yescomplemented
18#13063322C2211yescharacteristic, complemented
19#13063321C2211yescharacteristic
20#13063313C2211yescharacteristic
21#13063312C2211yescharacteristic
22#13063310—22no—
23#13063300—22no—
24#13063300C2212yes—
25#13063297—22no—
26#13063293—22no—
27#13063287C2212yescomplemented
28#13063282C2211yescharacteristic
29Dic43⋊C8C2212yescomplemented
30#13063248C2212yescomplemented
31#13063245C2212yes—
32(C2×D43)⋊C8C2212yes—
33C4×C43⋊C8C2211yescharacteristic, complemented
34#127×C43C2211yescharacteristic
35#125×C43C2211yescharacteristic, complemented
36#102×C43C2212yes—
37#102×C43C2212yescomplemented
38#97×C43C2211yescharacteristic, complemented
39C23×D43—21no—
40C2×D4×C43—22no—
41C2×D4×C43C2311yescharacteristic
42C2×D4×C43C2311yescharacteristic
43C2×C22⋊D43—21no—
44C2×C22⋊D43—22no—
45C2×C22⋊D43—21no—
46C22×Dic43—21no—
47#10621900—42no—
48D4×D43—42no—
49C2×D172—22no—
50C2×D172—22no—
51C2×D172C2311yescharacteristic
52C2×D172C2312yes—
53C2×C4×D43—22no—
54C2×C4×D43C2311yescharacteristic
55C2×Dic86C2311yescharacteristic
56C2×C8×C43C2312yes—
57C4⋊C4×C43—22no—
58C4⋊C4×C43C2312yes—
59C42×C43C2311yescharacteristic
60C22⋊Dic43—22no—
61#10621882—42no—
62#10621882—42no—
63(C2×D43)⋊C4—22no—
64(C2×D43)⋊C4—22no—
65(C2×D43)⋊C4—22no—
66(C2×D43)⋊C4D412yes—
67Dic43⋊C4D412yes—
68C4×Dic43C2311yescharacteristic
69C2×C43⋊C8C2312yes—
70D344—42no—
71#10621873—42no—
72C23×C43—21no—
73C23×C43—21no—
74C22×D43—22no—
75C22×D43—21no—
76C22×D43—42no—
77C22×D43—82no—
78C22×D43C2×D411yescharacteristic
79D4×C43—22no—
80D4×C43—22no—
81D4×C43—82no—
82C2×C4×C43—22no—
83C2×C4×C43C2×D412yes—
84C2×C4×C43C2411yescharacteristic
85C22⋊D43—42no—
86C22⋊D43—42no—
87C22⋊D43—82no—
88C2×Dic43—21no—
89C2×Dic43—42no—
90C2×Dic43C2×D412yes—
91C2×Dic43C2×D411yescharacteristic
92D172—22no—
93D172—22no—
94D172—22no—
95D172—82no—
96D172—82no—
97C4×D43—22no—
98C4×D43—82no—
99Dic86—22no—
100C8×C43—22no—
101C43⋊C8—22no—
102C22×C43—41no—
103C22×C43—41no—
104C22×C43—42no—
105C22×C43—42no—
106C22×C43C22×D411yescharacteristic
107C2×D43—21no—
108C2×D43—22no—
109C2×D43—41no—
110C2×D43—42no—
111C2×D43—42no—
112C2×D43—42no—
113C2×D43—42no—
114C2×D43—84no—
115C4×C43—22no—
116C4×C43—42no—
117C4×C43H(5,𝔽2)12yes—
118Dic43—21no—
119Dic43—22no—
120Dic43—41no—
121#3220—431nomaximal, Sylow
122C2×C43—81no—
123C2×C43—81no—
124C2×C43#53511yescharacteristic
125C2×C43#57612yes—
126D43—41no—
127D43—82no—
128D43—81no—
129#540—431no—
130#535—431no—
131#496—431no—
132#493—431no—
133#490D4311yescharacteristic, complemented
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×D8—432no—
146C2×D8—432no—
147#127—431no—
148#127—431no—
149#127C2×D4311yescharacteristic
150#125C2×D4311yescharacteristic, complemented
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#102C2×D4312yes—
164#102C2×D4312yescomplemented
165C22⋊C8—432no—
166#97C2×D4311yescharacteristic, complemented
167C4×C8—431no—
168C24—861no—
169#41—1722no—
170C2×Q8—431no—
171C2×D4—22no—
172C2×D4—431no—
173C2×D4—432no—
174C2×D4—862no—
175C2×D4—862no—
176C2×D4—861no—
177C2×D4—861no—
178C2×D4—862no—
179C2×D4—1722no—
180C2×D4C22×D4311yescharacteristic
181C2×D4C22×D4311yescharacteristic
182C22×C4—431no—
183C22×C4—862no—
184C22×C4—861no—
185SD16—1722no—
186D8—1722no—
187D8—1722no—
188D8—1722no—
189C2×C8—432no—
190C2×C8C22×D4312yes—
191C4⋊C4—22no—
192C4⋊C4—432no—
193C4⋊C4C22×D4312yes—
194C22⋊C4—432no—
195C22⋊C4—862no—
196C22⋊C4—862no—
197C22⋊C4—862no—
198C22⋊C4—862no—
199C42—431no—
200C42C22×D4311yescharacteristic
201C23—21no—
202C23—21no—
203C23—431no—
204C23—862no—
205C23—861no—
206C23—3442no—
207C23—1722no—
208Q8—862no—
209D4—22no—
210D4—22no—
211D4—82no—
212D4—862no—
213D4—862no—
214D4—862no—
215D4—3442no—
216D4—3442no—
217D4—3442no—
218D4—1722no—
219D4—1722no—
220C2×C4—22no—
221C2×C4—432no—
222C2×C4—431no—
223C2×C4—862no—
224C2×C4—861no—
225C2×C4—3442no—
226C2×C4—1722no—
227C2×C4D4×D4312yes—
228C2×C4C23×D4311yescharacteristic
229C8—22no—
230C8—862no—
231C22—42no—
232C22—42no—
233C22—41no—
234C22—41no—
235C22—862no—
236C22—861no—
237C22—3444no—
238C22—1722no—
239C22—1722no—
240C22—1722no—
241C22—1721no—
242C22—1722no—
243C22C2×D4×D4311yescharacteristic
244C4—22no—
245C4—42no—
246C4—862no—
247C4—861no—
248C4—1721no—
249C4#1306337112yes—
250C2—81no—
251C2—81no—
252C2—3441no—
253C2—3442no—
254C2—1721no—
255C2#1458346711yescharacteristic
256C2#1458370312yes—
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#490C2
socleC22×C43C22×D4
hypercenter#490D43
hypocenterC43#3220
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #490

Complements

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

NH ≅ G/Ntype
1. #14583505C2semidirect
2. #14583462C2semidirect
3. #14583288C2semidirect
4. #14583275C2semidirect
5. #14583256C2semidirect
6. #14583113C2semidirect
7. #14583093C2semidirect
8. #14583045C2semidirect
9. #14583034C2semidirect
10. #14582961C2semidirect
11. C43×#490C2semidirect
14. C2×#10621873C22semidirect
17. C2×#10621882C22semidirect
18. #13063322C22semidirect
27. #13063287C22semidirect
29. Dic43⋊C8C22semidirect
30. #13063248C22semidirect
33. C4×C43⋊C8C22semidirect
35. #125×C43C22semidirect
37. #102×C43C22semidirect
38. #97×C43C22semidirect
133. #490D43semidirect
140. C43#3220semidirect
150. #125C2×D43semidirect
164. #102C2×D43semidirect
166. #97C2×D43semidirect