Finite Group Databasebeta

← #19144108

Subgroups — #19144108

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×#13063353C211yesmaximal, characteristic
2C22×#10621873C211yesmaximal, characteristic, complemented
3#14583475C211yesmaximal, characteristic, complemented
4#14583373C211yesmaximal, characteristic, complemented
5#14583115C214yesmaximal, complemented
6#14583105C214yesmaximal, complemented
7#14582909C211yesmaximal, characteristic, complemented
8#14582896C211yesmaximal, characteristic, complemented
9C43×#424C211yesmaximal, characteristic, complemented
10C2×#10621898C2211yescharacteristic
11C22×Dic86C2211yescharacteristic
12C22×D172C2211yescharacteristic
13#13063353—24no—
14C2×#10621873—24no—
15C2×#10621873C2212yes—
16C2×#10621873C2214yes—
17C2×D344C2212yes—
18#13063325C2212yescomplemented
19#13063313C2212yescomplemented
20#13063309—22no—
21#13063305—22no—
22C4×D172C2214yes—
23#13063287—22no—
24#13063284C2211yescharacteristic
25C22⋊C4×D43—22no—
26#13063250C2212yescomplemented
27#13063250C2214yescomplemented
28#13063247C2212yescomplemented
29C2×M16×C43C2211yescharacteristic
30C22×C8×C43C2211yescharacteristic
31#117×C43C2211yescharacteristic
32C4⋊C8×C43C2214yescomplemented
33C23×D43—21no—
34C22×C4×C43C2311yescharacteristic
35C2×C22⋊D43—21no—
36C22×Dic43—21no—
37#10621898—22no—
38#10621898—22no—
39C2×D172—21no—
40C2×D172—22no—
41C2×D172D414yes—
42C2×D172C2311yescharacteristic
43C2×D172C2312yes—
44C2×C4×D43—21no—
45C2×C4×D43—24no—
46C2×Dic86—22no—
47C2×Dic86—22no—
48C2×Dic86—21no—
49C2×Dic86C2312yes—
50C2×Dic86C2311yescharacteristic
51M16×C43—22no—
52C2×C8×C43—22no—
53C2×C8×C43C2312yes—
54C2×C8×C43C2312yes—
55C4⋊C4×C43D412yes—
56C22⋊C4×C43D412yes—
57C42×C43C2312yes—
58C22⋊Dic43—21no—
59(C2×D43)⋊C4—24no—
60(C2×D43)⋊C4—24no—
61C4⋊Dic43—24no—
62C4⋊Dic43C2312yes—
63C4×Dic43—21no—
64D344—24no—
65#10621873—28no—
66#10621873—24no—
67C23×C43C2×D411yescharacteristic
68C22×D43—22no—
69C22×D43—24no—
70C22×D43—21no—
71C22×D43—82no—
72C2×C4×C43C2×D414yes—
73C2×C4×C43C2×D411yescharacteristic
74C2×C4×C43C2×D412yes—
75C2×C4×C43#4112yes—
76C2×C4×C43C2411yescharacteristic
77C22⋊D43—42no—
78C2×Dic43—22no—
79C2×Dic43—21no—
80C2×Dic43—22no—
81C2×Dic43—42no—
82D172—24no—
83D172—21no—
84D172—22no—
85D172—21no—
86D172C2×D414yes—
87C4×D43—42no—
88C4×D43—84no—
89Dic86—22no—
90Dic86—21no—
91Dic86—22no—
92Dic86—21no—
93Dic86—42no—
94C8×C43—22no—
95C8×C43—22no—
96C22×C43—22no—
97C22×C43#12112yes—
98C22×C43C22×D411yescharacteristic
99C2×D43—24no—
100C2×D43—44no—
101C2×D43—41no—
102C2×D43—42no—
103C2×D43—84no—
104C4×C43—24no—
105C4×C43#12112yes—
106C4×C43C22×D411yescharacteristic
107C4×C43C2×#4111yescharacteristic
108Dic43—42no—
109Dic43—41no—
110Dic43—42no—
111#3042—431nomaximal, Sylow
112C2×C43—22no—
113C2×C43C2×#12111yescharacteristic
114C2×C43#57712yes—
115D43—44no—
116D43—81no—
117C2×AGL(1,ℤ/8)—431no—
118C22×SD16—431no—
119#536—431no—
120#518—431no—
121#463—434no—
122#461—434no—
123#424D4311yescharacteristic, complemented
124#419—431no—
125#416—431no—
126C43#304211yescharacteristic, complemented, Sylow
127C2×#41—431no—
128C22×Q8—431no—
129C22×D4—431no—
130AGL(1,ℤ/8)—864no—
131C2×SD16—434no—
132C2×SD16—432no—
133C2×SD16—864no—
134C2×D8—432no—
135C2×M16C2×D4311yescharacteristic
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#117C2×D4311yescharacteristic
145C2×C22⋊C4—862no—
146C4⋊C8C2×D4314yescomplemented
147#103—432no—
148#103—434no—
149#102—432no—
150C24—861no—
151#41—862no—
152#41—862no—
153C2×Q8—432no—
154C2×Q8—431no—
155C2×Q8—861no—
156C2×Q8—862no—
157C2×Q8—862no—
158C2×D4—434no—
159C2×D4—432no—
160C2×D4—431no—
161C2×D4—861no—
162C2×D4—861no—
163C2×D4—862no—
164C22×C4—861no—
165C22×C4—864no—
166C22×C4—861no—
167C22×C4C22×D4311yescharacteristic
168SD16—868no—
169SD16—864no—
170D8—864no—
171M16—22no—
172C2×C8—22no—
173C2×C8C22×D4312yes—
174C2×C8C22×D4312yes—
175C4⋊C4—432no—
176C4⋊C4—864no—
177C4⋊C4D17212yes—
178C22⋊C4—861no—
179C22⋊C4—864no—
180C22⋊C4—864no—
181C22⋊C4D17212yes—
182C42—861no—
183C42C22×D4312yes—
184C23—864no—
185C23—862no—
186C23—861no—
187C23—3442no—
188C23C2×D17211yescharacteristic
189Q8—862no—
190Q8—861no—
191Q8—862no—
192Q8—861no—
193Q8—1722no—
194D4—434no—
195D4—864no—
196D4—861no—
197D4—862no—
198D4—861no—
199D4—1722no—
200C2×C4—862no—
201C2×C4—862no—
202C2×C4—861no—
203C2×C4—3444no—
204C2×C4—1722no—
205C2×C4—1722no—
206C2×C4C2×D17214yes—
207C2×C4C2×D17211yescharacteristic
208C2×C4D4×D4312yes—
209C2×C4#1062190212yes—
210C2×C4C23×D4311yescharacteristic
211C8—22no—
212C8—22no—
213C22—22no—
214C22—864no—
215C22—3444no—
216C22—1721no—
217C22—1722no—
218C22—1724no—
219C22#1306330012yes—
220C22C22×D17211yescharacteristic
221C4—24no—
222C4—1721no—
223C4—1722no—
224C4—1722no—
225C4#1306330012yes—
226C4C2×D4×D4311yescharacteristic
227C4C2×#1062190211yescharacteristic
228C2—22no—
229C2—3441no—
230C2—1724no—
231C2C2×#1306330011yescharacteristic
232C2#1458371112yes—
subgroupG/H
centerC22C22×D172
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#424C2
socleC22×C43C22×D4
hypercenter#424D43
hypocenterC43#3042
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ #117 ◁ #424

Complements

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

NH ≅ G/Ntype
2. C22×#10621873C2semidirect
3. #14583475C2semidirect
4. #14583373C2semidirect
5. #14583115C2semidirect
6. #14583105C2semidirect
7. #14582909C2semidirect
8. #14582896C2semidirect
9. C43×#424C2semidirect
18. #13063325C22semidirect
19. #13063313C22semidirect
26. #13063250C22semidirect
27. #13063250C22semidirect
28. #13063247C22semidirect
32. C4⋊C8×C43C22semidirect
123. #424D43semidirect
126. C43#3042semidirect
146. C4⋊C8C2×D43semidirect