Finite Group Databasebeta

← #19144107

Subgroups — #19144107

Order 5504.

494 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 494 conjugacy classes of subgroups — too many to draw. Only its 149 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×#13063351C211yesmaximal, characteristic
2C22×#10621883C211yesmaximal, characteristic, complemented
3#14583475C211yesmaximal, characteristic, complemented
4#14583114C214yesmaximal, complemented
5#14583104C214yesmaximal, complemented
6#14582926C211yesmaximal, characteristic, complemented
7#14582907C211yesmaximal, characteristic, complemented
8#14582893C211yesmaximal, characteristic, complemented
9C43×#518C211yesmaximal, characteristic, complemented
10C2×#10621898C2211yescharacteristic
11C22×Dic86C2211yescharacteristic
12#13063351—24no—
13C2×#10621883—24no—
14C2×#10621883C2212yes—
15C2×#10621883C2214yes—
16C2×#10621882C2212yes—
17C2×#10621877C2211yescharacteristic
18C22×C43⋊C8C2211yescharacteristic
19#13063325C2212yescomplemented
20#13063313C2212yescomplemented
21#13063309—22no—
22#13063305—22no—
23C4⋊(C43⋊C8)C2214yescomplemented
24#13063248C2212yescomplemented
25#13063248C2214yescomplemented
26#13063245C2212yescomplemented
27C22×D4×C43C2211yescharacteristic
28C4×D4×C43—22no—
29C4×D4×C43C2214yes—
30#117×C43C2211yescharacteristic
31#117×C43C2211yescharacteristic
32C2×C22⋊C4×C43—22no—
33C24×C43—21no—
34C2×D4×C43—21no—
35C2×D4×C43—22no—
36C2×D4×C43D414yes—
37C2×D4×C43C2312yes—
38C22×C4×C43—24no—
39C22×C4×C43C2311yescharacteristic
40C2×C22⋊D43—21no—
41C22×Dic43—21no—
42#10621898—22no—
43#10621898—22no—
44C2×D172C2311yescharacteristic
45C2×C4×D43—21no—
46C2×Dic86—22no—
47C2×Dic86—22no—
48C2×Dic86—21no—
49C2×Dic86C2312yes—
50C2×Dic86C2311yescharacteristic
51C4⋊C4×C43D412yes—
52C4⋊C4×C43C2312yes—
53C22⋊C4×C43—24no—
54C22⋊C4×C43—21no—
55C22⋊C4×C43D412yes—
56C42×C43—21no—
57C42×C43C2312yes—
58#10621883—28no—
59#10621883—24no—
60#10621882—24no—
61(C2×D43)⋊C4—24no—
62C4⋊Dic43—24no—
63#10621877—22no—
64C2×C43⋊C8—22no—
65C2×C43⋊C8C2312yes—
66C2×C43⋊C8C2312yes—
67C23×C43—22no—
68C23×C43—24no—
69C23×C43—82no—
70C23×C43C2×D411yescharacteristic
71C22×D43—21no—
72D4×C43—24no—
73D4×C43—22no—
74D4×C43C2×D414yes—
75C2×C4×C43—22no—
76C2×C4×C43—84no—
77C2×C4×C43C2×D412yes—
78C2×C4×C43C2×D414yes—
79C2×C4×C43C2×D411yescharacteristic
80C2×C4×C43#4112yes—
81C2×C4×C43C2411yescharacteristic
82C22⋊D43—42no—
83C2×Dic43—21no—
84C2×Dic43—22no—
85C2×Dic43—42no—
86D172—21no—
87D172—21no—
88C4×D43—42no—
89Dic86—22no—
90Dic86—21no—
91Dic86—22no—
92Dic86—21no—
93Dic86—42no—
94C43⋊C8—22no—
95C43⋊C8—22no—
96C22×C43—22no—
97C22×C43—24no—
98C22×C43—44no—
99C22×C43—84no—
100C22×C43#12112yes—
101C22×C43C22×D411yescharacteristic
102C2×D43—41no—
103C2×D43—42no—
104C4×C43—24no—
105C4×C43—42no—
106C4×C43#12112yes—
107C4×C43C22×D411yescharacteristic
108C4×C43C2×#4111yescharacteristic
109Dic43—42no—
110Dic43—41no—
111#3042—431nomaximal, Sylow
112C2×C43—22no—
113C2×C43—44no—
114C2×C43C2×#12111yescharacteristic
115C2×C43#57712yes—
116D43—81no—
117C2×AGL(1,ℤ/8)—431no—
118C22×SD16—431no—
119#536—431no—
120#518D4311yescharacteristic, complemented
121#463—434no—
122#461—434no—
123#424—431no—
124#419—431no—
125#416—431no—
126C43#304211yescharacteristic, complemented, Sylow
127C2×#41—431no—
128C22×Q8—431no—
129C22×D4C2×D4311yescharacteristic
130AGL(1,ℤ/8)—864no—
131C2×SD16—434no—
132C2×SD16—432no—
133C2×SD16—864no—
134C2×D8—432no—
135C2×M16—431no—
136C22×C8—431no—
137C4⋊Q8—432no—
138#124—432no—
139#123—862no—
140C22⋊Q8—862no—
141C4×D4—22no—
142C4×D4C2×D4314yes—
143#117C2×D4311yescharacteristic
144#117C2×D4311yescharacteristic
145C2×C22⋊C4—22no—
146C4⋊C8—434no—
147#103—432no—
148#103—434no—
149#102—432no—
150C24—21no—
151#41—862no—
152#41—862no—
153C2×Q8—432no—
154C2×Q8—431no—
155C2×Q8—861no—
156C2×Q8—862no—
157C2×Q8—862no—
158C2×D4—22no—
159C2×D4—21no—
160C2×D4—431no—
161C2×D4—861no—
162C2×D4D17214yes—
163C2×D4C22×D4312yes—
164C22×C4—24no—
165C22×C4—861no—
166C22×C4—861no—
167C22×C4C22×D4311yescharacteristic
168SD16—868no—
169SD16—864no—
170D8—864no—
171M16—862no—
172C2×C8—432no—
173C2×C8—432no—
174C2×C8—862no—
175C4⋊C4—864no—
176C4⋊C4C22⋊D4312yes—
177C4⋊C4C22×D4312yes—
178C22⋊C4—21no—
179C22⋊C4—24no—
180C22⋊C4—864no—
181C22⋊C4C22⋊D4312yes—
182C42—21no—
183C42C22×D4312yes—
184C23—22no—
185C23—24no—
186C23—82no—
187C23—861no—
188C23C2×C22⋊D4311yescharacteristic
189Q8—862no—
190Q8—861no—
191Q8—862no—
192Q8—861no—
193Q8—1722no—
194D4—24no—
195D4—22no—
196D4—861no—
197D4—861no—
198D4—1722no—
199D4C2×D17214yes—
200C2×C4—22no—
201C2×C4—84no—
202C2×C4—862no—
203C2×C4—861no—
204C2×C4—1722no—
205C2×C4—1722no—
206C2×C4C2×D17212yes—
207C2×C4#1062189812yes—
208C2×C4C2×C22⋊D4314yes—
209C2×C4C2×C22⋊D4311yescharacteristic
210C2×C4C23×D4311yescharacteristic
211C8—862no—
212C8—862no—
213C22—22no—
214C22—24no—
215C22—44no—
216C22—84no—
217C22—1721no—
218C22—1722no—
219C22#1306329912yes—
220C22C22×C22⋊D4311yescharacteristic
221C4—24no—
222C4—42no—
223C4—1721no—
224C4—1722no—
225C4#1306329912yes—
226C4C22×D17211yescharacteristic
227C4C2×#1062189811yescharacteristic
228C2—22no—
229C2—44no—
230C2—3441no—
231C2C2×#1306329911yescharacteristic
232C2#1458371012yes—
subgroupG/H
centerC22C22×C22⋊D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#518C2
socleC22×C43C22×D4
hypercenter#518D43
hypocenterC43#3042
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ #117 ◁ #518

Complements

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

NH ≅ G/Ntype
2. C22×#10621883C2semidirect
3. #14583475C2semidirect
4. #14583114C2semidirect
5. #14583104C2semidirect
6. #14582926C2semidirect
7. #14582907C2semidirect
8. #14582893C2semidirect
9. C43×#518C2semidirect
19. #13063325C22semidirect
20. #13063313C22semidirect
23. C4⋊(C43⋊C8)C22semidirect
24. #13063248C22semidirect
25. #13063248C22semidirect
26. #13063245C22semidirect
120. #518D43semidirect
126. C43#3042semidirect