Finite Group Databasebeta

← #19144104

Subgroups — #19144104

Order 5504.

494 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 494 conjugacy classes of subgroups — too many to draw. Only its 141 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
2#14583473C211yesmaximal, characteristic, complemented
3#14583374C211yesmaximal, characteristic, complemented
4#14583116C214yesmaximal, complemented
5#14583102C214yesmaximal, complemented
6#14582925C211yesmaximal, characteristic, complemented
7#14582908C211yesmaximal, characteristic, complemented
8#14582896C211yesmaximal, characteristic, complemented
9C22×SD16×C43C211yesmaximal, characteristic, complemented
10C2×#10621898C2211yescharacteristic
11#13063351—24no—
12C2×#10621883C2212yes—
13C2×#10621882C2212yes—
14C2×#10621877C2211yescharacteristic
15#13063323C2212yescomplemented
16#13063314C2212yescomplemented
17#13063308—22no—
18#13063301—22no—
19D4×Dic43—22no—
20D4×Dic43C2214yes—
21#13063284C2211yescharacteristic
22#13063284C2211yescharacteristic
23C2×C22⋊Dic43—22no—
24Dic43⋊C8C2214yescomplemented
25#13063250C2212yescomplemented
26#13063249C2214yescomplemented
27#13063247C2212yescomplemented
28C22×Q8×C43C2211yescharacteristic
29C22×D4×C43C2211yescharacteristic
30C2×SD16×C43—24no—
31C2×SD16×C43C2214yes—
32C22×C8×C43C2211yescharacteristic
33C24×C43—21no—
34C2×Q8×C43—21no—
35C2×Q8×C43—22no—
36C2×Q8×C43—22no—
37C2×Q8×C43C2312yes—
38C2×D4×C43—21no—
39C2×D4×C43—22no—
40C2×D4×C43D414yes—
41C2×D4×C43C2312yes—
42C22×C4×C43—21no—
43C22×C4×C43C2311yescharacteristic
44C2×C22⋊D43—21no—
45C22×Dic43—24no—
46#10621898—22no—
47#10621898—22no—
48C2×D172C2311yescharacteristic
49C2×C4×D43—21no—
50C2×Dic86C2311yescharacteristic
51SD16×C43—28no—
52C2×C8×C43—22no—
53C2×C8×C43C2312yes—
54C22⋊Dic43—24no—
55C22⋊Dic43—21no—
56C22⋊Dic43D412yes—
57#10621883—24no—
58#10621882—24no—
59(C2×D43)⋊C4—24no—
60C4⋊Dic43D412yes—
61C4⋊Dic43C2312yes—
62Dic43⋊C4—24no—
63C4×Dic43—21no—
64C4×Dic43C2312yes—
65#10621877—22no—
66C2×C43⋊C8C2312yes—
67C23×C43—22no—
68C23×C43—24no—
69C23×C43—82no—
70C23×C43C2×D411yescharacteristic
71C22×D43—21no—
72Q8×C43—22no—
73Q8×C43—22no—
74Q8×C43—42no—
75D4×C43—24no—
76D4×C43—22no—
77D4×C43C2×D414yes—
78C2×C4×C43—22no—
79C2×C4×C43—42no—
80C2×C4×C43C2×D411yescharacteristic
81C2×C4×C43C2×D412yes—
82C2×C4×C43#4112yes—
83C2×C4×C43C2411yescharacteristic
84C22⋊D43—42no—
85C2×Dic43—22no—
86C2×Dic43—21no—
87C2×Dic43—84no—
88C2×Dic43C2×D414yes—
89D172—21no—
90D172—21no—
91C4×D43—42no—
92Dic86—21no—
93Dic86—21no—
94C8×C43—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—42no—
105C4×C43#12112yes—
106C4×C43C22×D411yescharacteristic
107C4×C43C2×#4111yescharacteristic
108Dic43—24no—
109Dic43—41no—
110Dic43—42no—
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×SD16D4311yescharacteristic, complemented
119#536—431no—
120#518—431no—
121#463—434no—
122#461—434no—
123#424—431no—
124#419—431no—
125#416—431no—
126C43#304211yescharacteristic, complemented, Sylow
127C2×#41—431no—
128C22×Q8C2×D4311yescharacteristic
129C22×D4C2×D4311yescharacteristic
130AGL(1,ℤ/8)—864no—
131C2×SD16—24no—
132C2×SD16—432no—
133C2×SD16C2×D4314yes—
134C2×D8—432no—
135C2×M16—431no—
136C22×C8C2×D4311yescharacteristic
137C4⋊Q8—432no—
138#124—432no—
139#123—862no—
140C22⋊Q8—862no—
141C4×D4—434no—
142C4×D4—862no—
143#117—431no—
144#117—431no—
145C2×C22⋊C4—862no—
146C4⋊C8—434no—
147#103—434no—
148#103—432no—
149#102—432no—
150C24—21no—
151#41—862no—
152#41—862no—
153C2×Q8—21no—
154C2×Q8—22no—
155C2×Q8—22no—
156C2×Q8—431no—
157C2×Q8C22×D4312yes—
158C2×D4—21no—
159C2×D4—22no—
160C2×D4—431no—
161C2×D4—861no—
162C2×D4C22⋊D4314yes—
163C2×D4C22×D4312yes—
164C22×C4—21no—
165C22×C4—864no—
166C22×C4—861no—
167C22×C4C22×D4311yescharacteristic
168SD16—28no—
169SD16—864no—
170D8—864no—
171M16—862no—
172C2×C8—22no—
173C2×C8—432no—
174C2×C8C22×D4312yes—
175C4⋊C4—432no—
176C4⋊C4—432no—
177C4⋊C4—864no—
178C22⋊C4—432no—
179C22⋊C4—864no—
180C22⋊C4—864no—
181C22⋊C4—861no—
182C42—432no—
183C42—861no—
184C23—22no—
185C23—24no—
186C23—82no—
187C23—861no—
188C23D4×D4311yescharacteristic
189Q8—22no—
190Q8—22no—
191Q8—42no—
192Q8—861no—
193Q8—861no—
194D4—24no—
195D4—22no—
196D4—861no—
197D4—861no—
198D4—1722no—
199D4C2×C22⋊D4314yes—
200C2×C4—22no—
201C2×C4—42no—
202C2×C4—434no—
203C2×C4—862no—
204C2×C4—861no—
205C2×C4—3444no—
206C2×C4—1722no—
207C2×C4D4×D4311yescharacteristic
208C2×C4#1062190012yes—
209C2×C4C2×C22⋊D4312yes—
210C2×C4C23×D4311yescharacteristic
211C8—22no—
212C8—862no—
213C22—22no—
214C22—24no—
215C22—44no—
216C22—84no—
217C22—1721no—
218C22—1722no—
219C22#1306329712yes—
220C22C2×D4×D4311yescharacteristic
221C4—42no—
222C4—864no—
223C4—1721no—
224C4—1722no—
225C4#1306329712yes—
226C4C22×C22⋊D4311yescharacteristic
227C4C2×#1062190011yescharacteristic
228C2—22no—
229C2—44no—
230C2—3441no—
231C2C2×#1306329711yescharacteristic
232C2#1458370512yes—
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC22×SD16×C43C2
socleC22×C43C22×D4
hypercenterC22×SD16D43
hypocenterC43#3042
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×SD16

Complements

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

NH ≅ G/Ntype
2. #14583473C2semidirect
3. #14583374C2semidirect
4. #14583116C2semidirect
5. #14583102C2semidirect
6. #14582925C2semidirect
7. #14582908C2semidirect
8. #14582896C2semidirect
9. C22×SD16×C43C2semidirect
15. #13063323C22semidirect
16. #13063314C22semidirect
24. Dic43⋊C8C22semidirect
25. #13063250C22semidirect
26. #13063249C22semidirect
27. #13063247C22semidirect
118. C22×SD16D43semidirect
126. C43#3042semidirect