Finite Group Databasebeta

← #19144966

Subgroups — #19144966

Order 5504.

484 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 125 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#14583454C211yesmaximal, characteristic, complemented
2#127×D43C211yesmaximal, characteristic
3#14583262C214yesmaximal, complemented
4#14583247C211yesmaximal, characteristic, complemented
5#14583246C211yesmaximal, characteristic, complemented
6#14583245C211yesmaximal, characteristic, complemented
7#14582902C214yesmaximal, complemented
8C4×#10621872C211yesmaximal, characteristic, complemented
9C43×#486C211yesmaximal, characteristic, complemented
10C2×D4×D43—21no—
11C2×D4×D43—21no—
12C2×D4×D43C2212yes—
13C2×#10621872C2212yes—
14#13063325C2211yescharacteristic, complemented
15#13063322C2211yescharacteristic
16#13063321—21no—
17#13063321—21no—
18#13063321C2212yes—
19#13063316C2212yescomplemented
20#13063305—21no—
21#13063301—21no—
22Q8×Dic43—21no—
23#13063290—21no—
24#13063283C2212yes—
25C42×D43C2211yescharacteristic
26#13063247C2214yescomplemented
27#13063246C2214yescomplemented
28#13063245C2214yescomplemented
29#13063235C2212yescomplemented
30C4×C43⋊C8C2211yescharacteristic, complemented
31C4⋊Q8×C43C2211yescharacteristic, complemented
32#127×C43C2211yescharacteristic
33#102×C43C2214yescomplemented
34C4×C8×C43C2211yescharacteristic, complemented
35C23×D43—22no—
36C2×Q8×C43—21no—
37C2×D4×C43—21no—
38C2×D4×C43—21no—
39C2×D4×C43C2312yes—
40C2×C22⋊D43—22no—
41C2×C22⋊D43—22no—
42C2×C22⋊D43—22no—
43D4×D43—28no—
44D4×D43—44no—
45D4×D43—44no—
46C2×D172—21no—
47C2×D172—21no—
48C2×D172C2312yes—
49C2×C4×D43D411yescharacteristic
50C2×C4×D43D411yescharacteristic
51C2×C4×D43C2311yescharacteristic
52C2×Dic86—21no—
53C2×C8×C43C2312yes—
54C4⋊C4×C43—21no—
55C4⋊C4×C43C2312yes—
56C42×C43C2311yescharacteristic
57(C2×D43)⋊C4—22no—
58C4⋊Dic43—21no—
59C4⋊Dic43—22no—
60C4⋊Dic43C2312yes—
61Dic43⋊C4—22no—
62C4×Dic43—22no—
63C4×Dic43D411yescharacteristic
64C4×Dic43D411yescharacteristic
65C4×Dic43C2311yescharacteristic
66C2×C43⋊C8C2312yes—
67#10621872—24no—
68C23×C43—22no—
69C22×D43—22no—
70C22×D43—44no—
71C22×D43—44no—
72C22×D43—44no—
73C22×D43C2×D411yescharacteristic
74Q8×C43—42no—
75D4×C43—24no—
76D4×C43—42no—
77D4×C43—42no—
78C2×C4×C43—22no—
79C2×C4×C43C2×D411yescharacteristic
80C2×C4×C43C2×D411yescharacteristic
81C2×C4×C43C2411yescharacteristic
82C22⋊D43—44no—
83C22⋊D43—44no—
84C22⋊D43—44no—
85C2×Dic43—22no—
86C2×Dic43C2×D411yescharacteristic
87C2×Dic43C2×D411yescharacteristic
88C2×Dic43C2×D411yescharacteristic
89D172—24no—
90D172—42no—
91D172—42no—
92C4×D43—22no—
93C4×D43—22no—
94C4×D43#4114yes—
95Dic86—42no—
96C8×C43—22no—
97C43⋊C8—22no—
98C22×C43—42no—
99C22×C43—42no—
100C22×C43—42no—
101C22×C43C22×D411yescharacteristic
102C2×D43—21no—
103C2×D43—21no—
104C2×D43—42no—
105C2×D43—42no—
106C2×D43—42no—
107C2×D43—88no—
108C2×D43#12412yes—
109C4×C43—42no—
110C4×C43AGL(1,ℤ/8)12yes—
111C4×C43AGL(1,ℤ/8)12yes—
112C4×C43C2×#4112yes—
113Dic43—21no—
114Dic43—21no—
115Dic43—42no—
116Dic43#12412yes—
117#3138—431nomaximal, Sylow
118C2×C43—82no—
119C2×C43C2×#12411yescharacteristic
120C2×C43C2×AGL(1,ℤ/8)11yescharacteristic
121C2×C43C2×AGL(1,ℤ/8)11yescharacteristic
122D43—22no—
123D43—82no—
124#533—431no—
125C2×#127—431no—
126#490—434no—
127#486—431no—
128#486—431no—
129#486—431no—
130#486D4311yescharacteristic, complemented
131#418—434no—
132C4×M16—431no—
133C43#313811yescharacteristic, complemented, Sylow
134C22×D4—432no—
135C22×D4—861no—
136C22×D4—861no—
137C2×M16—432no—
138C4⋊Q8—431no—
139C4⋊Q8C2×D4311yescharacteristic, complemented
140#127—432no—
141#127—431no—
142#127—861no—
143#127—861no—
144#127C2×D4311yescharacteristic
145#125—432no—
146C22⋊Q8—861no—
147C22⋊Q8—861no—
148C4×Q8—861no—
149C4×Q8—861no—
150#117—432no—
151C2×C42—431no—
152#102—434no—
153#102—434no—
154#102—434no—
155#102C2×D4314yescomplemented
156#97—432no—
157C4×C8—431no—
158C4×C8C2×D4311yescharacteristic, complemented
159C24—862no—
160C2×Q8—21no—
161C2×Q8—861no—
162C2×D4—21no—
163C2×D4—21no—
164C2×D4—432no—
165C2×D4—868no—
166C2×D4—862no—
167C2×D4—862no—
168C2×D4—862no—
169C2×D4—861no—
170C2×D4—861no—
171C2×D4—1724no—
172C2×D4—1724no—
173C2×D4C22×D4312yes—
174C22×C4—431no—
175C22×C4—431no—
176C22×C4—431no—
177M16—864no—
178C2×C8—432no—
179C2×C8C22×D4312yes—
180C4⋊C4—21no—
181C4⋊C4—432no—
182C4⋊C4—862no—
183C4⋊C4—862no—
184C4⋊C4—861no—
185C4⋊C4C22×D4312yes—
186C22⋊C4—862no—
187C42—431no—
188C42—431no—
189C42—431no—
190C42—862no—
191C42C22×D4311yescharacteristic
192C23—22no—
193C23—431no—
194C23—862no—
195C23—1724no—
196C23—1724no—
197C23—1724no—
198Q8—42no—
199Q8—1722no—
200D4—24no—
201D4—42no—
202D4—42no—
203D4—864no—
204D4—1724no—
205D4—1724no—
206D4—1724no—
207D4—1722no—
208D4—1722no—
209C2×C4—22no—
210C2×C4—431no—
211C2×C4—434no—
212C2×C4—431no—
213C2×C4—431no—
214C2×C4—862no—
215C2×C4—862no—
216C2×C4—862no—
217C2×C4D4×D4311yescharacteristic
218C2×C4D4×D4311yescharacteristic
219C2×C4C23×D4311yescharacteristic
220C8—22no—
221C8—862no—
222C22—42no—
223C22—42no—
224C22—42no—
225C22—432no—
226C22—861no—
227C22—861no—
228C22—3448no—
229C22—1722no—
230C22—1722no—
231C22—1722no—
232C22C2×D4×D4311yescharacteristic
233C4—42no—
234C4—432no—
235C4—861no—
236C4—861no—
237C4—1722no—
238C4#1306334912yes—
239C4#1306335212yes—
240C4#41×D4312yes—
241C2—82no—
242C2—862no—
243C2—3442no—
244C2#124×D4311yescharacteristic
245C2C2×#1306334911yescharacteristic
246C2C2×#1306335211yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#486C2
socleC22×C43C22×D4
hypercenter#486D43
hypocenterC43#3138
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #486

Complements

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

NH ≅ G/Ntype
1. #14583454C2semidirect
3. #14583262C2semidirect
4. #14583247C2semidirect
5. #14583246C2semidirect
6. #14583245C2semidirect
7. #14582902C2semidirect
8. C4×#10621872C2semidirect
9. C43×#486C2semidirect
14. #13063325C22semidirect
19. #13063316C22semidirect
26. #13063247C22semidirect
27. #13063246C22semidirect
28. #13063245C22semidirect
29. #13063235C22semidirect
30. C4×C43⋊C8C22semidirect
31. C4⋊Q8×C43C22semidirect
33. #102×C43C22semidirect
34. C4×C8×C43C22semidirect
130. #486D43semidirect
133. C43#3138semidirect
139. C4⋊Q8C2×D43semidirect
155. #102C2×D43semidirect
158. C4×C8C2×D43semidirect