Finite Group Databasebeta

← #19143840

Subgroups — #19143840

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×#10621898C211yesmaximal, characteristic, complemented
2C2×#13063358C211yesmaximal, characteristic, complemented
3C2×#13063353C211yesmaximal, characteristic, complemented
4#14583410C211yesmaximal, characteristic, complemented
5#14583063C214yesmaximal, complemented
6#14583046C214yesmaximal, complemented
7#14582909C211yesmaximal, characteristic, complemented
8#14582905C211yesmaximal, characteristic, complemented
9C43×#407C211yesmaximal, characteristic, complemented
10C2×#10621898—22no—
11C2×#10621898—24no—
12C2×#10621898—24no—
13C2×#10621898C2214yes—
14C2×#10621898C2211yescharacteristic
15C22×Dic86C2211yescharacteristic
16C22×D172C2211yescharacteristic
17C22×C22⋊D43—21no—
18C22×C4×D43—21no—
19#13063358—24no—
20#13063353—24no—
21C2×Dic172C2212yescomplemented
22C2×#10621873C2212yescomplemented
23C2×#10621873C2212yescomplemented
24C2×D344C2212yescomplemented
25#13063308—21no—
26#13063304C2212yescomplemented
27#13063299C2212yescomplemented
28#13063294—21no—
29C4×C22⋊D43—22no—
30#13063284C2211yescharacteristic
31#13063250C2214yescomplemented
32#13063247C2214yescomplemented
33C23×C4×C43C2211yescharacteristic
34C2×M16×C43C2211yescharacteristic
35C2×M16×C43C2211yescharacteristic
36C22⋊C8×C43C2214yescomplemented
37C24×C43D411yescharacteristic
38C23×D43—21no—
39C22×C4×C43—22no—
40C22×C4×C43—22no—
41C22×C4×C43D412yes—
42C22×C4×C43D411yescharacteristic
43C22×C4×C43C2312yes—
44C22×C4×C43C2311yescharacteristic
45C2×C22⋊D43—28no—
46C2×C22⋊D43—24no—
47C2×C22⋊D43—22no—
48C2×C22⋊D43—21no—
49C22×Dic43—21no—
50#10621898—216no—
51#10621898—28no—
52#10621898—22no—
53#10621898—22no—
54#10621898—28no—
55C2×D172—22no—
56C2×D172—21no—
57C2×D172D414yescomplemented
58C2×D172C2311yescharacteristic
59C2×D172C2312yes—
60C2×C4×D43—28no—
61C2×C4×D43—24no—
62C2×C4×D43—21no—
63C2×Dic86—21no—
64C2×Dic86—22no—
65C2×Dic86D414yescomplemented
66C2×Dic86C2311yescharacteristic
67C2×Dic86C2312yes—
68M16×C43—22no—
69M16×C43—22no—
70C2×C8×C43C2312yes—
71C2×C8×C43C2312yes—
72C22⋊Dic43—21no—
73C22⋊Dic43—22no—
74(C2×D43)⋊C4—22no—
75C4⋊Dic43C2312yes—
76Dic43⋊C4—22no—
77C4×Dic43—21no—
78Dic172—24no—
79D344—24no—
80#10621873—24no—
81#10621873—24no—
82C23×C43—22no—
83C23×C43—42no—
84C23×C43C2×D412yes—
85C23×C43C2×D411yescharacteristic
86C22×D43—24no—
87C22×D43—22no—
88C22×D43—21no—
89C22×D43—44no—
90C2×C4×C43—22no—
91C2×C4×C43—24no—
92C2×C4×C43—22no—
93C2×C4×C43—22no—
94C2×C4×C43C2×D412yes—
95C2×C4×C43C2×D411yescharacteristic
96C2×C4×C43C2×D412yes—
97C2×C4×C43C2×D412yes—
98C2×C4×C43C2411yescharacteristic
99C22⋊D43—216no—
100C22⋊D43—44no—
101C22⋊D43—42no—
102C2×Dic43—24no—
103C2×Dic43—22no—
104C2×Dic43—22no—
105C2×Dic43—21no—
106D172—24no—
107D172—22no—
108D172—21no—
109D172—21no—
110D172C2×D414yes—
111C4×D43—216no—
112C4×D43—42no—
113Dic86—24no—
114Dic86—22no—
115Dic86—21no—
116Dic86—21no—
117Dic86C2×D414yes—
118C8×C43—22no—
119C8×C43—22no—
120C22×C43—22no—
121C22×C43—22no—
122C22×C43—22no—
123C22×C43—22no—
124C22×C43—44no—
125C22×C43#12012yes—
126C22×C43C22×D411yescharacteristic
127C2×D43—24no—
128C2×D43—48no—
129C2×D43—44no—
130C2×D43—41no—
131C2×D43—42no—
132C4×C43—22no—
133C4×C43#12012yes—
134C4×C43C22×D411yescharacteristic
135C4×C43C22×D411yescharacteristic
136Dic43—24no—
137Dic43—41no—
138Dic43—42no—
139#3005—431nomaximal, Sylow
140C2×C43—22no—
141C2×C43—42no—
142C2×C43C2×#12011yescharacteristic
143C2×C43#57512yes—
144D43—44no—
145D43—81no—
146C22×#41—431no—
147C2×#137—431no—
148C2×AGL(1,ℤ/8)—431no—
149#525—431no—
150#452—434no—
151#449—434no—
152#419—431no—
153#418—431no—
154#407D4311yescharacteristic, complemented
155C43#300511yescharacteristic, complemented, Sylow
156C2×#41—431no—
157C2×#41—434no—
158C2×#41—864no—
159C2×#41—864no—
160C2×#41—862no—
161C22×Q8—431no—
162C22×D4—431no—
163C22×D4—861no—
164C23×C4—861no—
165C23×C4C2×D4311yescharacteristic
166#137—864no—
167AGL(1,ℤ/8)—864no—
168C2×Q16—432no—
169C2×SD16—432no—
170C2×SD16—432no—
171C2×D8—432no—
172C2×M16C2×D4311yescharacteristic
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⋊C8C2×D4314yescomplemented
183C24—861no—
184C24D17211yescharacteristic
185#41—868no—
186#41—868no—
187#41—8616no—
188#41—862no—
189#41—862no—
190C2×Q8—434no—
191C2×Q8—432no—
192C2×Q8—431no—
193C2×Q8—861no—
194C2×Q8—862no—
195C2×D4—434no—
196C2×D4—432no—
197C2×D4—431no—
198C2×D4—868no—
199C2×D4—864no—
200C2×D4—862no—
201C2×D4—861no—
202C2×D4—861no—
203C2×D4—862no—
204C22×C4—22no—
205C22×C4—22no—
206C22×C4—868no—
207C22×C4—861no—
208C22×C4—864no—
209C22×C4—861no—
210C22×C4D17212yes—
211C22×C4D17211yescharacteristic
212C22×C4C22×D4312yes—
213C22×C4C22×D4311yescharacteristic
214Q16—864no—
215SD16—864no—
216SD16—864no—
217D8—864no—
218M16—22no—
219M16—22no—
220C2×C8C22×D4312yes—
221C2×C8C22×D4312yes—
222C4⋊C4—432no—
223C4⋊C4—862no—
224C22⋊C4—861no—
225C22⋊C4—862no—
226C22⋊C4—862no—
227C42—861no—
228C23—22no—
229C23—42no—
230C23—864no—
231C23—862no—
232C23—861no—
233C23—1724no—
234C23C2×D17212yes—
235C23C2×D17211yescharacteristic
236Q8—434no—
237Q8—864no—
238Q8—862no—
239Q8—861no—
240Q8—861no—
241D4—434no—
242D4—8616no—
243D4—864no—
244D4—862no—
245D4—861no—
246D4—861no—
247D4—1724no—
248D4—1722no—
249C2×C4—22no—
250C2×C4—24no—
251C2×C4—22no—
252C2×C4—22no—
253C2×C4—8616no—
254C2×C4—864no—
255C2×C4—862no—
256C2×C4—862no—
257C2×C4—861no—
258C2×C4—1722no—
259C2×C4C2×D17212yes—
260C2×C4C2×D17211yescharacteristic
261C2×C4D4×D4312yes—
262C2×C4D4×D4312yes—
263C2×C4C23×D4311yescharacteristic
264C8—22no—
265C8—22no—
266C22—22no—
267C22—22no—
268C22—22no—
269C22—22no—
270C22—44no—
271C22—864no—
272C22—1728no—
273C22—1721no—
274C22—1722no—
275C22—1724no—
276C22#1306329512yes—
277C22C22×D17211yescharacteristic
278C4—22no—
279C4—864no—
280C4—1721no—
281C4—1722no—
282C4#1306329512yes—
283C4C2×D4×D4311yescharacteristic
284C4C2×D4×D4311yescharacteristic
285C2—22no—
286C2—42no—
287C2—3441no—
288C2—1724no—
289C2C2×#1306329511yescharacteristic
290C2#1458369912yes—
subgroupG/H
centerC22C22×D172
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#407C2
socleC22×C43C22×D4
hypercenter#407D43
hypocenterC43#3005
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #407

Complements

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

NH ≅ G/Ntype
1. C22×#10621898C2semidirect
2. C2×#13063358C2semidirect
3. C2×#13063353C2semidirect
4. #14583410C2semidirect
5. #14583063C2semidirect
6. #14583046C2semidirect
7. #14582909C2semidirect
8. #14582905C2semidirect
9. C43×#407C2semidirect
21. C2×Dic172C22semidirect
22. C2×#10621873C22semidirect
23. C2×#10621873C22semidirect
24. C2×D344C22semidirect
26. #13063304C22semidirect
27. #13063299C22semidirect
31. #13063250C22semidirect
32. #13063247C22semidirect
36. C22⋊C8×C43C22semidirect
57. C2×D172D4semidirect
65. C2×Dic86D4semidirect
154. #407D43semidirect
155. C43#3005semidirect
182. C22⋊C8C2×D43semidirect