Finite Group Databasebeta

← #19144115

Subgroups — #19144115

Order 5504.

490 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 490 conjugacy classes of subgroups — too many to draw. Only its 133 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×#13063358C211yesmaximal, characteristic, complemented
2C22×#10621883C211yesmaximal, characteristic, complemented
3#14583466C211yesmaximal, characteristic
4#14583376C211yesmaximal, characteristic, complemented
5#14583120C214yesmaximal, complemented
6#14583098C214yesmaximal, complemented
7#14582927C211yesmaximal, characteristic, complemented
8#14582893C211yesmaximal, characteristic, complemented
9C43×#418C211yesmaximal, characteristic, complemented
10C2×#10621898C2211yescharacteristic
11C22×Dic86C2211yescharacteristic
12#13063358—24no—
13C2×Dic172C2212yescomplemented
14C2×#10621873C2212yescomplemented
15C2×#10621883—24no—
16C2×#10621883C2214yes—
17C22×C43⋊C8C2211yescharacteristic
18#13063321C2212yes—
19#13063312C2212yes—
20#13063296—22no—
21#13063294—22no—
22C4×Dic86—22no—
23#13063290C2214yescomplemented
24#13063284C2211yescharacteristic
25#13063281—22no—
26Dic43⋊C8C2214yescomplemented
27#13063248C2212yescomplemented
28#13063245C2212yescomplemented
29C22×D4×C43C2211yescharacteristic
30C2×M16×C43C2211yescharacteristic
31#117×C43C2211yescharacteristic
32#102×C43C2214yes—
33C24×C43—21no—
34C2×D4×C43—21no—
35C2×D4×C43—22no—
36C2×D4×C43—22no—
37C2×D4×C43C2312yes—
38C22×C4×C43C2311yescharacteristic
39C2×C22⋊D43—24no—
40C2×C22⋊D43—21no—
41C22×Dic43—21no—
42#10621898—22no—
43#10621898—22no—
44C2×D172C2311yescharacteristic
45C2×C4×D43—21no—
46C2×Dic86—21no—
47C2×Dic86—22no—
48C2×Dic86D414yescomplemented
49C2×Dic86C2311yescharacteristic
50C2×Dic86C2312yes—
51M16×C43—22no—
52C2×C8×C43C2312yes—
53C4⋊C4×C43C2312yes—
54C22⋊C4×C43—21no—
55C42×C43—21no—
56C22⋊Dic43—24no—
57C22⋊Dic43D412yes—
58#10621883—28no—
59C4⋊Dic43D412yes—
60Dic43⋊C4—24no—
61C4×Dic43—24no—
62C4×Dic43C2312yes—
63C2×C43⋊C8—22no—
64C2×C43⋊C8C2312yes—
65Dic172—24no—
66#10621873—24no—
67C23×C43—22no—
68C23×C43—42no—
69C23×C43—82no—
70C23×C43C2×D411yescharacteristic
71C22×D43—21no—
72D4×C43—22no—
73D4×C43—22no—
74D4×C43—42no—
75C2×C4×C43—22no—
76C2×C4×C43C2×D411yescharacteristic
77C2×C4×C43C2×D412yes—
78C2×C4×C43#4112yes—
79C2×C4×C43C2411yescharacteristic
80C22⋊D43—42no—
81C22⋊D43—84no—
82C2×Dic43—24no—
83C2×Dic43—22no—
84C2×Dic43—21no—
85C2×Dic43C2×D414yes—
86D172—21no—
87D172—21no—
88C4×D43—42no—
89Dic86—24no—
90Dic86—22no—
91Dic86—21no—
92Dic86—21no—
93Dic86C2×D414yes—
94C8×C43—22no—
95C43⋊C8—22no—
96C22×C43—22no—
97C22×C43—42no—
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—24no—
110Dic43—41no—
111#3043—431nomaximal, Sylow
112C2×C43—22no—
113C2×C43—82no—
114C2×C43C2×#12111yescharacteristic
115C2×C43#57712yes—
116D43—81no—
117C2×#137—431no—
118C22×SD16—431no—
119#535—431no—
120#519—431no—
121#464—434no—
122#460—434no—
123#424—431no—
124#418D4311yescharacteristic, complemented
125#416—431no—
126C43#304311yescharacteristic, complemented, Sylow
127C2×#41—431no—
128C22×Q8—431no—
129C22×D4C2×D4311yescharacteristic
130#137—864no—
131C2×Q16—432no—
132C2×SD16—434no—
133C2×SD16—432no—
134C2×SD16—864no—
135C2×M16C2×D4311yescharacteristic
136C22×C8—431no—
137#127—432no—
138#124—432no—
139#121—862no—
140#120—862no—
141C4×Q8—434no—
142C4×Q8—862no—
143#117—431no—
144#117—862no—
145#117C2×D4311yescharacteristic
146C4⋊C8—434no—
147#103—432no—
148#102—432no—
149#102C2×D4314yes—
150C24—21no—
151#41—862no—
152#41—862no—
153C2×Q8—434no—
154C2×Q8—432no—
155C2×Q8—431no—
156C2×Q8—862no—
157C2×Q8—861no—
158C2×D4—22no—
159C2×D4—22no—
160C2×D4—21no—
161C2×D4—431no—
162C2×D4—864no—
163C2×D4—861no—
164C2×D4C22×D4312yes—
165C22×C4—861no—
166C22×C4—861no—
167C22×C4C22×D4311yescharacteristic
168Q16—864no—
169SD16—864no—
170SD16—868no—
171M16—22no—
172C2×C8—432no—
173C2×C8—862no—
174C2×C8C22×D4312yes—
175C4⋊C4—432no—
176C4⋊C4—864no—
177C4⋊C4C22×D4312yes—
178C22⋊C4—21no—
179C22⋊C4—432no—
180C22⋊C4—864no—
181C42—21no—
182C42—432no—
183C42—864no—
184C23—22no—
185C23—42no—
186C23—82no—
187C23—861no—
188C23D4×D4311yescharacteristic
189Q8—434no—
190Q8—864no—
191Q8—862no—
192Q8—861no—
193Q8—861no—
194D4—22no—
195D4—22no—
196D4—42no—
197D4—861no—
198D4—861no—
199D4—3444no—
200D4—1722no—
201C2×C4—22no—
202C2×C4—434no—
203C2×C4—864no—
204C2×C4—862no—
205C2×C4—861no—
206C2×C4—1722no—
207C2×C4#1062189812yes—
208C2×C4D4×D4311yescharacteristic
209C2×C4D4×D4312yes—
210C2×C4C23×D4311yescharacteristic
211C8—22no—
212C8—862no—
213C22—22no—
214C22—42no—
215C22—44no—
216C22—84no—
217C22—1721no—
218C22—1722no—
219C22#1306329812yes—
220C22C2×D4×D4311yescharacteristic
221C4—42no—
222C4—864no—
223C4—864no—
224C4—1721no—
225C4#1306329812yes—
226C4C2×D4×D4311yescharacteristic
227C4C2×#1062189811yescharacteristic
228C2—22no—
229C2—82no—
230C2—3441no—
231C2C2×#1306329811yescharacteristic
232C2#1458370912yes—
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#418C2
socleC22×C43C22×D4
hypercenter#418D43
hypocenterC43#3043
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #418

Complements

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

NH ≅ G/Ntype
1. C2×#13063358C2semidirect
2. C22×#10621883C2semidirect
4. #14583376C2semidirect
5. #14583120C2semidirect
6. #14583098C2semidirect
7. #14582927C2semidirect
8. #14582893C2semidirect
9. C43×#418C2semidirect
13. C2×Dic172C22semidirect
14. C2×#10621873C22semidirect
23. #13063290C22semidirect
26. Dic43⋊C8C22semidirect
27. #13063248C22semidirect
28. #13063245C22semidirect
48. C2×Dic86D4semidirect
124. #418D43semidirect
126. C43#3043semidirect