Finite Group Databasebeta

← #19143834

Subgroups — #19143834

Order 5504.

758 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 758 conjugacy classes of subgroups — too many to draw. Only its 149 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
1C22×#10621900C211yesmaximal, characteristic, complemented
2C2×#13063355C211yesmaximal, characteristic, complemented
3#14583406C211yesmaximal, characteristic, complemented
4#14583058C214yesmaximal, complemented
5#14583041C214yesmaximal, complemented
6#14582909C211yesmaximal, characteristic, complemented
7#14582904C211yesmaximal, characteristic, complemented
8#14582862C211yesmaximal, characteristic, complemented
9C2×AGL(1,ℤ/8)×C43C211yesmaximal, characteristic, complemented
10C2×#10621900—24no—
11C2×#10621900—22no—
12C2×#10621900—24no—
13C2×#10621900C2214yes—
14C22×Dic86C2211yescharacteristic
15C22×C22⋊D43—21no—
16C23×Dic43—21no—
17C22×C4×D43C2211yescharacteristic
18#13063355—24no—
19C2×#10621885C2212yescomplemented
20C2×#10621883C2212yescomplemented
21C2×#10621877C2211yescharacteristic
22#13063306—21no—
23#13063301C2212yescomplemented
24#13063296C2212yescomplemented
25#13063293—21no—
26C4×C22⋊D43—22no—
27#13063284C2211yescharacteristic
28#13063250C2214yescomplemented
29#13063246C2214yescomplemented
30(C2×D43)⋊C8C2214yescomplemented
31C2×#41×C43C2211yescharacteristic
32C22×D4×C43C2211yescharacteristic
33AGL(1,ℤ/8)×C43—24no—
34C2×SD16×C43C2212yescomplemented
35C2×D8×C43C2212yescomplemented
36C2×M16×C43C2211yescharacteristic
37C24×C43—21no—
38C23×D43D411yescharacteristic
39#41×C43—22no—
40#41×C43—22no—
41C2×Q8×C43C2311yescharacteristic
42C2×D4×C43—22no—
43C2×D4×C43—21no—
44C2×D4×C43—21no—
45C2×D4×C43D414yescomplemented
46C2×D4×C43C2311yescharacteristic
47C2×D4×C43C2312yes—
48C22×C4×C43—21no—
49C22×C4×C43C2311yescharacteristic
50C2×C22⋊D43—28no—
51C2×C22⋊D43—24no—
52C2×C22⋊D43—22no—
53C22×Dic43—28no—
54C22×Dic43—24no—
55C22×Dic43—21no—
56C22×Dic43D411yescharacteristic
57#10621900—216no—
58#10621900—28no—
59#10621900—28no—
60C2×C4×D43—22no—
61C2×C4×D43—22no—
62C2×C4×D43D412yes—
63C2×C4×D43C2312yes—
64C2×Dic86—21no—
65C2×Dic86—22no—
66C2×Dic86D414yescomplemented
67C2×Dic86C2312yes—
68SD16×C43—24no—
69D8×C43—24no—
70M16×C43—22no—
71C2×C8×C43C2312yes—
72C22⋊Dic43—22no—
73C22⋊Dic43—21no—
74#10621885—24no—
75#10621883—24no—
76(C2×D43)⋊C4—22no—
77C4⋊Dic43C2312yes—
78Dic43⋊C4—22no—
79C4×Dic43—21no—
80#10621877—22no—
81C2×C43⋊C8C2312yes—
82C23×C43—24no—
83C23×C43—22no—
84C23×C43—21no—
85C23×C43—44no—
86C23×C43C2×D411yescharacteristic
87C22×D43—22no—
88C22×D43—42no—
89C22×D43C2×D412yes—
90Q8×C43—21no—
91Q8×C43—21no—
92D4×C43—24no—
93D4×C43—22no—
94D4×C43—21no—
95D4×C43—21no—
96D4×C43—42no—
97D4×C43C2×D414yes—
98C2×C4×C43—21no—
99C2×C4×C43—42no—
100C2×C4×C43C2×D411yescharacteristic
101C2×C4×C43C2×D412yes—
102C2×C4×C43C2×D412yes—
103C2×C4×C43C2411yescharacteristic
104C22⋊D43—216no—
105C22⋊D43—44no—
106C2×Dic43—216no—
107C2×Dic43—24no—
108C2×Dic43—22no—
109C2×Dic43—22no—
110C2×Dic43—22no—
111C2×Dic43C2×D412yes—
112C4×D43—24no—
113C4×D43—22no—
114C4×D43—22no—
115Dic86—24no—
116Dic86—22no—
117Dic86C2×D414yes—
118C8×C43—22no—
119C43⋊C8—22no—
120C22×C43—22no—
121C22×C43—24no—
122C22×C43—48no—
123C22×C43—44no—
124C22×C43—41no—
125C22×C43—42no—
126C22×C43#12012yes—
127C22×C43C22×D411yescharacteristic
128C2×D43—22no—
129C2×D43—22no—
130C2×D43—22no—
131C2×D43—44no—
132C4×C43—41no—
133C4×C43#12012yes—
134C4×C43C22×D411yescharacteristic
135C4×C43C22×D411yescharacteristic
136Dic43—24no—
137Dic43—22no—
138Dic43—42no—
139#3005—431nomaximal, Sylow
140C2×C43—22no—
141C2×C43—44no—
142C2×C43—81no—
143C2×C43C2×#12011yescharacteristic
144C2×C43#57512yes—
145D43—42no—
146C22×#41—431no—
147C2×#137—431no—
148C2×AGL(1,ℤ/8)D4311yescharacteristic, complemented
149#525—431no—
150#452—434no—
151#449—434no—
152#419—431no—
153#418—431no—
154#407—431no—
155C43#300511yescharacteristic, complemented, Sylow
156C2×#41—434no—
157C2×#41—862no—
158C2×#41—864no—
159C2×#41—864no—
160C2×#41C2×D4311yescharacteristic
161C22×Q8—431no—
162C22×D4—861no—
163C22×D4C2×D4311yescharacteristic
164C23×C4—431no—
165C23×C4—861no—
166#137—864no—
167AGL(1,ℤ/8)—24no—
168C2×Q16—432no—
169C2×SD16—432no—
170C2×SD16C2×D4312yescomplemented
171C2×D8C2×D4312yescomplemented
172C2×M16—431no—
173C2×M16C2×D4311yescharacteristic
174#123—861no—
175C22⋊Q8—432no—
176#121—432no—
177#120—861no—
178C4×D4—862no—
179#117—431no—
180#103—434no—
181#102—434no—
182C22⋊C8—434no—
183C24—21no—
184C24—431no—
185#41—22no—
186#41—22no—
187#41—868no—
188#41—8616no—
189#41—868no—
190C2×Q8—434no—
191C2×Q8—432no—
192C2×Q8—861no—
193C2×Q8—862no—
194C2×Q8C22×D4311yescharacteristic
195C2×D4—21no—
196C2×D4—21no—
197C2×D4—22no—
198C2×D4—864no—
199C2×D4—868no—
200C2×D4—862no—
201C2×D4C22⋊D4314yescomplemented
202C2×D4C22×D4311yescharacteristic
203C2×D4C22×D4312yes—
204C22×C4—21no—
205C22×C4—431no—
206C22×C4—432no—
207C22×C4—432no—
208C22×C4—864no—
209C22×C4—868no—
210C22×C4—861no—
211C22×C4—862no—
212C22×C4—862no—
213C22×C4C22×D4311yescharacteristic
214Q16—864no—
215SD16—24no—
216SD16—864no—
217D8—24no—
218M16—22no—
219M16—862no—
220C2×C8—432no—
221C2×C8C22×D4312yes—
222C4⋊C4—432no—
223C4⋊C4—862no—
224C22⋊C4—862no—
225C22⋊C4—862no—
226C22⋊C4—861no—
227C42—861no—
228C23—24no—
229C23—22no—
230C23—21no—
231C23—44no—
232C23—432no—
233C23—862no—
234C23—1722no—
235C23D4×D4311yescharacteristic
236Q8—21no—
237Q8—21no—
238Q8—434no—
239Q8—864no—
240Q8—862no—
241D4—24no—
242D4—22no—
243D4—21no—
244D4—21no—
245D4—42no—
246D4—8616no—
247D4—1724no—
248D4C2×C22⋊D4314yes—
249C2×C4—21no—
250C2×C4—42no—
251C2×C4—432no—
252C2×C4—8616no—
253C2×C4—862no—
254C2×C4—864no—
255C2×C4—862no—
256C2×C4—864no—
257C2×C4—862no—
258C2×C4—862no—
259C2×C4—862no—
260C2×C4D4×D4311yescharacteristic
261C2×C4D4×D4312yes—
262C2×C4C2×C22⋊D4312yes—
263C2×C4C23×D4311yescharacteristic
264C8—22no—
265C8—862no—
266C22—22no—
267C22—24no—
268C22—48no—
269C22—44no—
270C22—41no—
271C22—42no—
272C22—862no—
273C22—862no—
274C22—862no—
275C22—1724no—
276C22#1306329312yes—
277C22C2×D4×D4311yescharacteristic
278C4—41no—
279C4—862no—
280C4—864no—
281C4—1722no—
282C4#1306329312yes—
283C4C2×D4×D4311yescharacteristic
284C4C22×C22⋊D4311yescharacteristic
285C2—22no—
286C2—44no—
287C2—81no—
288C2—1722no—
289C2C2×#1306329311yescharacteristic
290C2#1458369512yes—
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC2×AGL(1,ℤ/8)×C43C2
socleC22×C43C22×D4
hypercenterC2×AGL(1,ℤ/8)D43
hypocenterC43#3005
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. C22×#10621900C2semidirect
2. C2×#13063355C2semidirect
3. #14583406C2semidirect
4. #14583058C2semidirect
5. #14583041C2semidirect
6. #14582909C2semidirect
7. #14582904C2semidirect
8. #14582862C2semidirect
9. C2×AGL(1,ℤ/8)×C43C2semidirect
19. C2×#10621885C22semidirect
20. C2×#10621883C22semidirect
23. #13063301C22semidirect
24. #13063296C22semidirect
28. #13063250C22semidirect
29. #13063246C22semidirect
30. (C2×D43)⋊C8C22semidirect
34. C2×SD16×C43C22semidirect
35. C2×D8×C43C22semidirect
45. C2×D4×C43D4semidirect
66. C2×Dic86D4semidirect
148. C2×AGL(1,ℤ/8)D43semidirect
155. C43#3005semidirect
170. C2×SD16C2×D43semidirect
171. C2×D8C2×D43semidirect
201. C2×D4C22⋊D43semidirect