Finite Group Databasebeta

← #19144992

Subgroups — #19144992

Order 5504.

392 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 392 conjugacy classes of subgroups — too many to draw. Only its 117 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
1#14583448C211yesmaximal, characteristic
2#125×D43C211yesmaximal, characteristic, complemented
3#14583266C212yesmaximal, complemented
4#14583262C212yesmaximal, complemented
5#14583256C211yesmaximal, characteristic, complemented
6#14583254C211yesmaximal, characteristic, complemented
7#14583253C211yesmaximal, characteristic, complemented
8#14582899C212yesmaximal, complemented
9#14582897C212yesmaximal, complemented
10C4×#10621872C211yesmaximal, characteristic, complemented
11C43×#488C211yesmaximal, characteristic, complemented
12C2×#10621902C2211yescharacteristic
13C2×#10621900C2211yescharacteristic
14C2×#10621872C2212yes—
15#13063323C2211yescharacteristic
16#13063321C2211yescharacteristic
17#13063317C2211yescharacteristic
18#13063316C2212yes—
19#13063315—22no—
20#13063313C2211yescharacteristic
21#13063298—22no—
22(C22⋊D43)⋊C4—22no—
23C4⋊C4×D43—22no—
24C4⋊C4×D43C2212yes—
25C42×D43C2211yescharacteristic
26#13063250C2212yes—
27#13063249C2212yes—
28#13063248C2212yes—
29#13063247C2212yes—
30#13063246C2212yes—
31#13063245C2212yes—
32#13063235C2212yes—
33C4×C43⋊C8C2211yescharacteristic
34#125×C43C2211yescharacteristic
35#124×C43C2211yescharacteristic
36#103×C43C2212yes—
37#102×C43C2212yes—
38C4×C8×C43C2211yescharacteristic
39C2×Q8×C43C2311yescharacteristic
40C2×D4×C43C2311yescharacteristic
41C2×C22⋊D43—22no—
42C2×C22⋊D43—21no—
43C22×Dic43—21no—
44#10621902—24no—
45#10621900—24no—
46C2×D172—21no—
47C2×D172C2311yescharacteristic
48C2×C4×D43—21no—
49C2×C4×D43—22no—
50C2×C4×D43D412yes—
51C2×C4×D43C2311yescharacteristic
52C2×Dic86C2311yescharacteristic
53C2×C8×C43C2312yes—
54C4⋊C4×C43—22no—
55C4⋊C4×C43C2312yes—
56C22⋊C4×C43—22no—
57C42×C43C2311yescharacteristic
58(C2×D43)⋊C4—22no—
59C4⋊Dic43—22no—
60C4⋊Dic43C2312yes—
61Dic43⋊C4—22no—
62Dic43⋊C4—22no—
63Dic43⋊C4—22no—
64Dic43⋊C4—22no—
65C4×Dic43D412yes—
66C4×Dic43C2311yescharacteristic
67C2×C43⋊C8C2312yes—
68#10621872—24no—
69C23×C43—21no—
70C22×D43—21no—
71C22×D43C2×D411yescharacteristic
72Q8×C43—22no—
73D4×C43—22no—
74C2×C4×C43—22no—
75C2×C4×C43—21no—
76C2×C4×C43C2×D412yes—
77C2×C4×C43C2411yescharacteristic
78C22⋊D43—44no—
79C22⋊D43—42no—
80C2×Dic43—22no—
81C2×Dic43—21no—
82C2×Dic43—42no—
83C2×Dic43C2×D412yes—
84C2×Dic43C2×D411yescharacteristic
85D172—22no—
86D172—42no—
87C4×D43—42no—
88C4×D43—44no—
89C4×D43—42no—
90C4×D43#4114yes—
91Dic86—22no—
92C8×C43—22no—
93C43⋊C8—22no—
94C22×C43—41no—
95C22×C43—42no—
96C22×C43C22×D411yescharacteristic
97C2×D43—22no—
98C2×D43—41no—
99C2×D43—42no—
100C2×D43#12412yes—
101C4×C43—22no—
102C4×C43—41no—
103C4×C43—42no—
104C4×C43C2×#4112yes—
105Dic43—22no—
106Dic43—41no—
107Dic43—42no—
108Dic43#12412yes—
109#3142—431nomaximal, Sylow
110C2×C43—81no—
111C2×C43C2×#12411yescharacteristic
112C2×C43#57512yes—
113D43—22no—
114D43—81no—
115#532—431no—
116C2×#125—431no—
117#491—432no—
118#490—432no—
119#488—431no—
120#488—431no—
121#488—431no—
122#488D4311yescharacteristic, complemented
123#417—432no—
124#417—432no—
125C4×M16—431no—
126C43#314211yescharacteristic, complemented, Sylow
127C2×#41—431no—
128C2×#41—431no—
129C2×M16—432no—
130C4⋊Q8—431no—
131#127—431no—
132#125—432no—
133#125—431no—
134#125—862no—
135#125C2×D4311yescharacteristic
136#124—431no—
137#124C2×D4311yescharacteristic
138#121—862no—
139C4×D4—862no—
140C2×C4⋊C4—432no—
141C2×C4⋊C4—862no—
142C2×C42—431no—
143#103—432no—
144#103—432no—
145#103—432no—
146#103C2×D4312yes—
147#102—432no—
148#102—432no—
149#102—432no—
150#102C2×D4312yes—
151#97—432no—
152C4×C8—431no—
153C4×C8C2×D4311yescharacteristic
154#41—864no—
155#41—864no—
156C2×Q8—431no—
157C2×Q8C22×D4311yescharacteristic
158C2×D4—431no—
159C2×D4—861no—
160C2×D4—862no—
161C2×D4—861no—
162C2×D4C22×D4311yescharacteristic
163C22×C4—431no—
164C22×C4—432no—
165C22×C4—861no—
166C22×C4—862no—
167C22×C4—861no—
168M16—864no—
169C2×C8—432no—
170C2×C8C22×D4312yes—
171C4⋊C4—22no—
172C4⋊C4—432no—
173C4⋊C4—862no—
174C4⋊C4—862no—
175C4⋊C4—862no—
176C4⋊C4—862no—
177C4⋊C4—862no—
178C4⋊C4C22×D4312yes—
179C22⋊C4—22no—
180C22⋊C4—862no—
181C42—432no—
182C42—431no—
183C42C22×D4311yescharacteristic
184C23—21no—
185C23—431no—
186C23—861no—
187Q8—22no—
188Q8—862no—
189D4—22no—
190D4—862no—
191D4—1722no—
192D4—1724no—
193D4—1722no—
194C2×C4—21no—
195C2×C4—22no—
196C2×C4—431no—
197C2×C4—434no—
198C2×C4—432no—
199C2×C4—861no—
200C2×C4—862no—
201C2×C4—1722no—
202C2×C4—1722no—
203C2×C4—1724no—
204C2×C4—1722no—
205C2×C4D4×D4312yes—
206C2×C4C23×D4311yescharacteristic
207C8—22no—
208C8—862no—
209C22—41no—
210C22—42no—
211C22—432no—
212C22—862no—
213C22—1721no—
214C22—1722no—
215C22C2×D4×D4311yescharacteristic
216C4—22no—
217C4—41no—
218C4—42no—
219C4—432no—
220C4—862no—
221C4—1721no—
222C4—1722no—
223C4#41×D4312yes—
224C2—81no—
225C2—862no—
226C2—3441no—
227C2#124×D4311yescharacteristic
228C2#1458369612yes—
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#488C2
socleC22×C43C22×D4
hypercenter#488D43
hypocenterC43#3142
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #488

Complements

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

NH ≅ G/Ntype
2. #125×D43C2semidirect
3. #14583266C2semidirect
4. #14583262C2semidirect
5. #14583256C2semidirect
6. #14583254C2semidirect
7. #14583253C2semidirect
8. #14582899C2semidirect
9. #14582897C2semidirect
10. C4×#10621872C2semidirect
11. C43×#488C2semidirect
122. #488D43semidirect
126. C43#3142semidirect