Finite Group Databasebeta

← #19144536

Subgroups — #19144536

Order 5504.

462 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 462 conjugacy classes of subgroups — too many to draw. Only its 137 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
1C2×#13063299C211yesmaximal, characteristic
2C2×#13063284C211yesmaximal, characteristic, complemented
3#14583224C214yesmaximal, complemented
4#14583218C212yesmaximal, complemented
5#14583213C212yesmaximal, complemented
6#14582941C212yesmaximal, complemented
7#14582905C212yesmaximal, complemented
8C43×#407C211yesmaximal, characteristic, complemented
9C22×D172C2211yescharacteristic
10C22×C22⋊D43—21no—
11#13063299—21no—
12#13063299—21no—
13#13063299C2212yes—
14#13063299C2212yes—
15#13063284—21no—
16#13063284—21no—
17#13063284C2212yes—
18#13063284C2212yescomplemented
19C2×C4⋊Dic43C2211yescharacteristic
20C2×C4⋊Dic43C2211yescharacteristic, complemented
21C2×C4⋊Dic43C2211yescharacteristic, complemented
22C2×C22⋊Dic43—21no—
23C2×(C2×D43)⋊C4—21no—
24C2×C4×Dic43—21no—
25#13063259C2214yescomplemented
26#13063257C2214yescomplemented
27#13063247C2214yescomplemented
28#13063247C2214yescomplemented
29C23×C4×C43C2211yescharacteristic
30C2×M16×C43C2212yes—
31C22⋊C8×C43C2212yescomplemented
32C22⋊C8×C43C2212yescomplemented
33C24×C43D411yescharacteristic
34C23×D43—21no—
35C22×C4×C43—24no—
36C22×C4×C43D411yescharacteristic
37C22×C4×C43D411yescharacteristic
38C22×C4×C43D411yescharacteristic
39C22×C4×C43C2311yescharacteristic
40C22×C4×C43C2311yescharacteristic
41C22×C4×C43C2311yescharacteristic
42C2×C22⋊D43—22no—
43C2×C22⋊D43—22no—
44C2×C22⋊D43—44no—
45C22×Dic43—21no—
46C22×Dic43—21no—
47C22×Dic43—21no—
48C2×D172—21no—
49C2×D172—24no—
50C2×D172C2312yes—
51M16×C43—24no—
52C2×C8×C43C2314yes—
53C22⋊Dic43—22no—
54C22⋊Dic43—22no—
55(C2×D43)⋊C4—22no—
56(C2×D43)⋊C4—22no—
57C4⋊Dic43—21no—
58C4⋊Dic43—21no—
59C4⋊Dic43—21no—
60C4⋊Dic43C2312yes—
61C4⋊Dic43C2312yes—
62C4⋊Dic43C2312yes—
63C4×Dic43—22no—
64C4×Dic43—22no—
65C23×C43—22no—
66C23×C43—22no—
67C23×C43—41no—
68C23×C43C2×D411yescharacteristic
69C23×C43C2×D411yescharacteristic
70C23×C43C2×D411yescharacteristic
71C22×D43—22no—
72C22×D43—42no—
73C22×D43—42no—
74C22×D43—42no—
75C2×C4×C43—22no—
76C2×C4×C43—22no—
77C2×C4×C43—22no—
78C2×C4×C43—22no—
79C2×C4×C43—22no—
80C2×C4×C43C2×D411yescharacteristic
81C2×C4×C43C2×D411yescharacteristic
82C2×C4×C43C2×D411yescharacteristic
83C2×C4×C43#4114yes—
84C2×C4×C43C2411yescharacteristic
85C22⋊D43—44no—
86C22⋊D43—44no—
87C2×Dic43—22no—
88C2×Dic43—22no—
89C2×Dic43—22no—
90C2×Dic43—42no—
91C2×Dic43—42no—
92C2×Dic43—42no—
93D172—24no—
94D172—42no—
95C8×C43—24no—
96C22×C43—21no—
97C22×C43—21no—
98C22×C43—21no—
99C22×C43—21no—
100C22×C43—21no—
101C22×C43—21no—
102C22×C43—21no—
103C22×C43—44no—
104C22×C43#12312yes—
105C22×C43AGL(1,ℤ/8)12yes—
106C22×C43C22×D411yescharacteristic
107C2×D43—42no—
108C2×D43—42no—
109C2×D43—42no—
110C2×D43—84no—
111C4×C43—21no—
112C4×C43—21no—
113C4×C43#12312yes—
114C4×C43C2×#4112yes—
115Dic43—42no—
116Dic43—42no—
117Dic43—42no—
118#3094—431nomaximal, Sylow
119C2×C43—22no—
120C2×C43—22no—
121C2×C43—41no—
122C2×C43C2×#12311yescharacteristic
123C2×C43C2×AGL(1,ℤ/8)11yescharacteristic
124C2×C43#57511yescharacteristic
125D43—82no—
126C2×#121—431no—
127C2×#117—431no—
128#482—434no—
129#481—432no—
130#480—432no—
131#428—432no—
132#418—432no—
133#407D4311yescharacteristic, complemented
134C43#309411yescharacteristic, complemented, Sylow
135C22×D4—431no—
136C22×D4—861no—
137C23×C4C2×D4311yescharacteristic
138C2×M16C2×D4312yes—
139#121—432no—
140#121—432no—
141#121—861no—
142#121—861no—
143#117—432no—
144#117—432no—
145#117—861no—
146#117—861no—
147C2×C4⋊C4—431no—
148C2×C4⋊C4—431no—
149C2×C4⋊C4—431no—
150C2×C22⋊C4—861no—
151C2×C22⋊C4—861no—
152C2×C42—861no—
153#107—434no—
154#106—434no—
155#102—434no—
156#102—434no—
157C22⋊C8C2×D4312yescomplemented
158C22⋊C8C2×D4312yescomplemented
159C24—861no—
160C24D17211yescharacteristic
161C2×D4—432no—
162C2×D4—862no—
163C2×D4—862no—
164C2×D4—861no—
165C2×D4—864no—
166C2×D4—1724no—
167C22×C4—24no—
168C22×C4—861no—
169C22×C4—861no—
170C22×C4—861no—
171C22×C4D17211yescharacteristic
172C22×C4D17211yescharacteristic
173C22×C4D17211yescharacteristic
174C22×C4C22×D4311yescharacteristic
175C22×C4C22×D4311yescharacteristic
176C22×C4C22×D4311yescharacteristic
177M16—24no—
178C2×C8C22×D4314yes—
179C4⋊C4—432no—
180C4⋊C4—432no—
181C4⋊C4—432no—
182C4⋊C4—861no—
183C4⋊C4—861no—
184C4⋊C4—861no—
185C22⋊C4—862no—
186C22⋊C4—862no—
187C22⋊C4—862no—
188C22⋊C4—862no—
189C42—862no—
190C42—862no—
191C23—22no—
192C23—22no—
193C23—41no—
194C23—862no—
195C23—1722no—
196C23—1722no—
197C23—1722no—
198C23C2×D17211yescharacteristic
199C23C2×D17211yescharacteristic
200C23C2×D17211yescharacteristic
201D4—864no—
202D4—1724no—
203D4—1724no—
204D4—1722no—
205C2×C4—22no—
206C2×C4—22no—
207C2×C4—22no—
208C2×C4—22no—
209C2×C4—22no—
210C2×C4—862no—
211C2×C4—862no—
212C2×C4—862no—
213C2×C4—1722no—
214C2×C4—1722no—
215C2×C4—1722no—
216C2×C4C2×D17211yescharacteristic
217C2×C4C2×D17211yescharacteristic
218C2×C4C2×D17211yescharacteristic
219C2×C4#1062190014yes—
220C2×C4C23×D4311yescharacteristic
221C8—24no—
222C22—21no—
223C22—21no—
224C22—21no—
225C22—21no—
226C22—21no—
227C22—21no—
228C22—21no—
229C22—44no—
230C22—3444no—
231C22—1722no—
232C22—1722no—
233C22—1722no—
234C22#1306330912yes—
235C22#1306335312yes—
236C22C22×D17211yescharacteristic
237C4—21no—
238C4—21no—
239C4—1722no—
240C4—1722no—
241C4—1722no—
242C4#1306330912yes—
243C4C2×#1062190012yes—
244C2—22no—
245C2—22no—
246C2—41no—
247C2—3442no—
248C2C2×#1306330911yescharacteristic
249C2C2×#1306335311yescharacteristic
250C2#1458369911yescharacteristic
subgroupG/H
centerC22C22×D172
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#407C2
socleC22×C43C22×D4
hypercenter#407D43
hypocenterC43#3094
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #407

Complements

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

NH ≅ G/Ntype
2. C2×#13063284C2semidirect
3. #14583224C2semidirect
4. #14583218C2semidirect
5. #14583213C2semidirect
6. #14582941C2semidirect
7. #14582905C2semidirect
8. C43×#407C2semidirect
18. #13063284C22semidirect
20. C2×C4⋊Dic43C22semidirect
21. C2×C4⋊Dic43C22semidirect
25. #13063259C22semidirect
26. #13063257C22semidirect
27. #13063247C22semidirect
28. #13063247C22semidirect
31. C22⋊C8×C43C22semidirect
32. C22⋊C8×C43C22semidirect
133. #407D43semidirect
134. C43#3094semidirect
157. C22⋊C8C2×D43semidirect
158. C22⋊C8C2×D43semidirect