Finite Group Databasebeta

← #19143952

Subgroups — #19143952

Order 5504.

762 conjugacy classes of subgroups; only the 161 normal subgroups are shown.

normal subgroups only

This group has 762 conjugacy classes of subgroups — too many to draw. Only its 161 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#14583697C212yesmaximal, complemented
2#14583466C211yesmaximal, characteristic, complemented
3#14583077C214yesmaximal, complemented
4#14583067C214yesmaximal, complemented
5#14582916C212yesmaximal, complemented
6C2×#13063242C211yesmaximal, characteristic, complemented
7C2×H(5,𝔽2)×C43C211yesmaximal, characteristic, complemented
8C2×#10621898C2211yescharacteristic, complemented
9#13063356—22no—
10#13063355C2214yescomplemented
11#13063351—22no—
12#13063350C2214yescomplemented
13#13063345—24no—
14C2×#10621877C2212yescomplemented
15#13063321C2212yescomplemented
16#13063312C2212yescomplemented
17#13063296—22no—
18#13063294—22no—
19#13063284C2211yescharacteristic, complemented
20#13063252C2218yescomplemented
21#13063242C2214yescomplemented
22H(5,𝔽2)×C43—24no—
23H(5,𝔽2)×C43—22no—
24H(5,𝔽2)×C43C2214yes—
25C2×#41×C43—22no—
26C2×#41×C43C2212yes—
27C22×D4×C43—22no—
28C22×D4×C43—22no—
29C22×D4×C43C2211yescharacteristic
30C24×C43—22no—
31C24×C43D412yes—
32#41×C43—28no—
33#41×C43—28no—
34#41×C43—22no—
35#41×C43—22no—
36#41×C43D414yescomplemented
37#41×C43C2314yes—
38C2×Q8×C43D412yescomplemented
39C2×D4×C43—24no—
40C2×D4×C43—28no—
41C2×D4×C43—28no—
42C2×D4×C43—28no—
43C2×D4×C43—22no—
44C2×D4×C43—22no—
45C2×D4×C43—22no—
46C2×D4×C43—28no—
47C2×D4×C43D412yes—
48C2×D4×C43D412yescomplemented
49C2×D4×C43C2312yes—
50C22×C4×C43—22no—
51C22×C4×C43—22no—
52C22×C4×C43C2311yescharacteristic
53C2×C22⋊D43—21no—
54C2×C22⋊D43—24no—
55#10621898—22no—
56#10621898—22no—
57C2×D172C2311yescharacteristic, complemented
58C2×C4×D43—21no—
59C2×Dic86C2311yescharacteristic, complemented
60C22⋊Dic43—21no—
61C22⋊Dic43—24no—
62#10621885—24no—
63#10621884—24no—
64#10621883—24no—
65#10621882—24no—
66C4⋊Dic43—21no—
67C4×Dic43C2312yescomplemented
68#10621877—22no—
69#10621877C2314yescomplemented
70C2×C43⋊C8—22no—
71C23×C43—28no—
72C23×C43—22no—
73C23×C43—22no—
74C23×C43—22no—
75C23×C43—82no—
76C23×C43—84no—
77C23×C43C2×D414yes—
78C23×C43C2×D411yescharacteristic
79C22×D43—21no—
80Q8×C43—22no—
81Q8×C43C2×D414yes—
82D4×C43—216no—
83D4×C43—24no—
84D4×C43—24no—
85D4×C43—24no—
86D4×C43—22no—
87D4×C43—24no—
88D4×C43C2×D414yes—
89C2×C4×C43—28no—
90C2×C4×C43—22no—
91C2×C4×C43—24no—
92C2×C4×C43—24no—
93C2×C4×C43C2×D411yescharacteristic
94C2×C4×C43C2×D412yes—
95C2×C4×C43C2×D412yes—
96C2×C4×C43C2411yescharacteristic
97C22⋊D43—41no—
98C22⋊D43—41no—
99C22⋊D43—84no—
100C2×Dic43—22no—
101C2×Dic43—21no—
102D172—22no—
103C4×D43—42no—
104Dic86—22no—
105C43⋊C8—24no—
106C22×C43—24no—
107C22×C43—24no—
108C22×C43—41no—
109C22×C43—44no—
110C22×C43—44no—
111C22×C43—44no—
112C22×C43—82no—
113C22×C43—88no—
114C22×C43#12011yescharacteristic
115C22×C43#12011yescharacteristic
116C22×C43C22×D411yescharacteristic
117C2×D43—42no—
118C2×D43—41no—
119C4×C43—24no—
120C4×C43#12012yes—
121C4×C43C22×D412yes—
122Dic43—42no—
123Dic43—41no—
124#3019—431nomaximal, Sylow
125C2×C43—21no—
126C2×C43—21no—
127C2×C43—21no—
128C2×C43—44no—
129C2×C43—44no—
130C2×C43C2×#12011yescharacteristic
131D43—81no—
132C2×H(5,𝔽2)D4311yescharacteristic, complemented
133#575—432no—
134#535—431no—
135#455—434no—
136#453—434no—
137#421—432no—
138C2×#100—431no—
139C43#301911yescharacteristic, complemented, Sylow
140H(5,𝔽2)—24no—
141H(5,𝔽2)—22no—
142H(5,𝔽2)C2×D4314yes—
143C2×#41—22no—
144C2×#41—431no—
145C2×#41C2×D4312yes—
146C22×D4—22no—
147C22×D4—22no—
148C22×D4C2×D4311yescharacteristic
149#137—434no—
150#137—862no—
151AGL(1,ℤ/8)—434no—
152AGL(1,ℤ/8)—862no—
153#135—864no—
154C2×M16—432no—
155#127—432no—
156#124—432no—
157#121—862no—
158#120—862no—
159#117—431no—
160#104—438no—
161#100—434no—
162C24—22no—
163C24C22⋊D4312yes—
164#41—28no—
165#41—28no—
166#41—22no—
167#41—22no—
168#41—862no—
169#41—862no—
170#41C22⋊D4314yescomplemented
171#41C22×D4314yes—
172C2×Q8—431no—
173C2×Q8C22⋊D4312yescomplemented
174C2×D4—24no—
175C2×D4—28no—
176C2×D4—28no—
177C2×D4—22no—
178C2×D4—28no—
179C2×D4—28no—
180C2×D4—22no—
181C2×D4—22no—
182C2×D4—431no—
183C2×D4—864no—
184C2×D4—861no—
185C2×D4C22⋊D4312yes—
186C2×D4C22⋊D4312yescomplemented
187C2×D4C22×D4312yes—
188C22×C4—22no—
189C22×C4—22no—
190C22×C4—861no—
191C22×C4C22×D4311yescharacteristic
192Q16—864no—
193SD16—864no—
194SD16—864no—
195D8—864no—
196M16—434no—
197M16—862no—
198C2×C8—862no—
199C4⋊C4—861no—
200C22⋊C4—861no—
201C22⋊C4—864no—
202C42—432no—
203C23—28no—
204C23—22no—
205C23—22no—
206C23—22no—
207C23—82no—
208C23—84no—
209C23—861no—
210C23C2×C22⋊D4314yes—
211C23C2×C22⋊D4311yescharacteristic
212Q8—22no—
213Q8—862no—
214Q8C2×C22⋊D4314yes—
215D4—216no—
216D4—24no—
217D4—24no—
218D4—24no—
219D4—22no—
220D4—24no—
221D4—862no—
222D4—3444no—
223D4—1721no—
224D4—1721no—
225D4C2×C22⋊D4314yes—
226C2×C4—28no—
227C2×C4—22no—
228C2×C4—24no—
229C2×C4—24no—
230C2×C4—862no—
231C2×C4—861no—
232C2×C4—1722no—
233C2×C4C2×C22⋊D4311yescharacteristic
234C2×C4C2×C22⋊D4312yes—
235C2×C4C2×C22⋊D4312yes—
236C2×C4C23×D4311yescharacteristic
237C8—864no—
238C22—24no—
239C22—24no—
240C22—41no—
241C22—44no—
242C22—44no—
243C22—44no—
244C22—82no—
245C22—88no—
246C22—1722no—
247C22—1721no—
248C22#1306329411yescharacteristic
249C22#1306329411yescharacteristic
250C22C22×C22⋊D4311yescharacteristic
251C4—24no—
252C4—1722no—
253C4—1721no—
254C4#1306329412yes—
255C4C22×C22⋊D4312yes—
256C2—21no—
257C2—21no—
258C2—21no—
259C2—44no—
260C2—44no—
261C2—3441no—
262C2C2×#1306329411yescharacteristic
subgroupG/H
centerC2C2×#13063294
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC2×H(5,𝔽2)×C43C2
socleC2×C43C2×#120
hypercenterC2×H(5,𝔽2)D43
hypocenterC43#3019
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×H(5,𝔽2)

Complements

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

NH ≅ G/Ntype
1. #14583697C2semidirect
2. #14583466C2semidirect
3. #14583077C2semidirect
4. #14583067C2semidirect
5. #14582916C2semidirect
6. C2×#13063242C2semidirect
7. C2×H(5,𝔽2)×C43C2semidirect
8. C2×#10621898C22semidirect
10. #13063355C22semidirect
12. #13063350C22semidirect
14. C2×#10621877C22semidirect
15. #13063321C22semidirect
16. #13063312C22semidirect
19. #13063284C22semidirect
20. #13063252C22semidirect
21. #13063242C22semidirect
36. #41×C43D4semidirect
38. C2×Q8×C43D4semidirect
48. C2×D4×C43D4semidirect
57. C2×D172C23semidirect
59. C2×Dic86C23semidirect
67. C4×Dic43C23semidirect
69. #10621877C23semidirect
132. C2×H(5,𝔽2)D43semidirect
139. C43#3019semidirect
170. #41C22⋊D43semidirect
173. C2×Q8C22⋊D43semidirect
186. C2×D4C22⋊D43semidirect