Finite Group Databasebeta

← #19143835

Subgroups — #19143835

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×#13063355C211yesmaximal, characteristic, complemented
3C2×#13063350C211yesmaximal, characteristic, complemented
4#14583059C214yesmaximal, complemented
5#14583042C214yesmaximal, complemented
6#14582907C211yesmaximal, characteristic, complemented
7#14582903C211yesmaximal, characteristic, complemented
8#14582863C211yesmaximal, characteristic, complemented
9C43×#525C211yesmaximal, characteristic, complemented
10C2×#10621898—22no—
11C2×#10621898—24no—
12C2×#10621898—24no—
13C2×#10621898C2214yes—
14C22×Dic86C2211yescharacteristic
15C22×D172C2211yescharacteristic
16C22×C22⋊D43—21no—
17C22×C4×D43—21no—
18#13063355—24no—
19#13063350—24no—
20C2×#10621885C2212yescomplemented
21C2×#10621883C2212yescomplemented
22C2×#10621884C2212yescomplemented
23C2×#10621882C2212yescomplemented
24C2×#10621877C2211yescharacteristic
25C2×#10621877C2211yescharacteristic
26#13063248C2214yescomplemented
27#13063245C2214yescomplemented
28C22⋊(C43⋊C8)C2214yescomplemented
29C2×#41×C43C2211yescharacteristic
30C23×C4×C43C2211yescharacteristic
31#123×C43—21no—
32C22⋊Q8×C43C2212yescomplemented
33#121×C43C2212yescomplemented
34#120×C43—21no—
35C4×D4×C43—22no—
36#117×C43C2211yescharacteristic
37C24×C43D411yescharacteristic
38C23×D43—21no—
39#41×C43—22no—
40#41×C43—22no—
41C2×Q8×C43C2311yescharacteristic
42C2×D4×C43—22no—
43C2×D4×C43—21no—
44C2×D4×C43C2311yescharacteristic
45C22×C4×C43—22no—
46C22×C4×C43—22no—
47C22×C4×C43—21no—
48C22×C4×C43D412yes—
49C22×C4×C43D411yescharacteristic
50C22×C4×C43C2312yes—
51C22×C4×C43C2311yescharacteristic
52C2×C22⋊D43—28no—
53C2×C22⋊D43—24no—
54C22×Dic43—21no—
55#10621898—216no—
56#10621898—28no—
57#10621898—28no—
58C2×D172—22no—
59C2×D172—21no—
60C2×D172D414yescomplemented
61C2×D172C2312yes—
62C2×C4×D43—28no—
63C2×C4×D43—24no—
64C2×Dic86—22no—
65C2×Dic86—21no—
66C2×Dic86D414yescomplemented
67C2×Dic86C2312yes—
68C4⋊C4×C43—22no—
69C4⋊C4×C43C2312yes—
70C22⋊C4×C43—22no—
71C22⋊C4×C43—21no—
72C22⋊C4×C43—22no—
73C42×C43—21no—
74#10621885—24no—
75#10621884—24no—
76#10621883—24no—
77#10621882—24no—
78#10621877—22no—
79#10621877—22no—
80C2×C43⋊C8C2312yes—
81C2×C43⋊C8C2312yes—
82C23×C43—22no—
83C23×C43—21no—
84C23×C43—42no—
85C23×C43C2×D412yes—
86C23×C43C2×D411yescharacteristic
87C22×D43—24no—
88C22×D43—22no—
89C22×D43—44no—
90Q8×C43—21no—
91Q8×C43—21no—
92D4×C43—21no—
93D4×C43—21no—
94D4×C43—44no—
95D4×C43—42no—
96C2×C4×C43—22no—
97C2×C4×C43—24no—
98C2×C4×C43—22no—
99C2×C4×C43—22no—
100C2×C4×C43—22no—
101C2×C4×C43—21no—
102C2×C4×C43—42no—
103C2×C4×C43C2×D412yes—
104C2×C4×C43C2×D412yes—
105C2×C4×C43C2×D412yes—
106C2×C4×C43C2×D411yescharacteristic
107C2×C4×C43C2411yescharacteristic
108C22⋊D43—216no—
109C2×Dic43—24no—
110C2×Dic43—22no—
111D172—24no—
112D172—22no—
113D172C2×D414yes—
114C4×D43—216no—
115Dic86—24no—
116Dic86—22no—
117Dic86C2×D414yes—
118C43⋊C8—22no—
119C43⋊C8—22no—
120C22×C43—22no—
121C22×C43—22no—
122C22×C43—22no—
123C22×C43—22no—
124C22×C43—44no—
125C22×C43—41no—
126C22×C43—42no—
127C22×C43#12012yes—
128C22×C43C22×D411yescharacteristic
129C2×D43—24no—
130C2×D43—48no—
131C2×D43—44no—
132C4×C43—22no—
133C4×C43—41no—
134C4×C43—42no—
135C4×C43#12012yes—
136C4×C43C22×D411yescharacteristic
137C4×C43C22×D411yescharacteristic
138Dic43—24no—
139#3005—431nomaximal, Sylow
140C2×C43—22no—
141C2×C43—42no—
142C2×C43—81no—
143C2×C43C2×#12011yescharacteristic
144C2×C43#57512yes—
145D43—44no—
146C22×#41—431no—
147C2×#137—431no—
148C2×AGL(1,ℤ/8)—431no—
149#525D4311yescharacteristic, complemented
150#452—434no—
151#449—434no—
152#419—431no—
153#418—431no—
154#407—431no—
155C43#300511yescharacteristic, complemented, Sylow
156C2×#41—434no—
157C2×#41—864no—
158C2×#41—864no—
159C2×#41—862no—
160C2×#41C2×D4311yescharacteristic
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×M16—431no—
173C2×M16—431no—
174#123—21no—
175C22⋊Q8C2×D4312yescomplemented
176#121C2×D4312yescomplemented
177#120—21no—
178C4×D4—22no—
179#117C2×D4311yescharacteristic
180#103—434no—
181#102—434no—
182C22⋊C8—434no—
183C24—861no—
184C24C22⋊D4311yescharacteristic
185#41—22no—
186#41—22no—
187#41—868no—
188#41—868no—
189#41—8616no—
190C2×Q8—434no—
191C2×Q8—432no—
192C2×Q8—862no—
193C2×Q8—861no—
194C2×Q8C22×D4311yescharacteristic
195C2×D4—22no—
196C2×D4—21no—
197C2×D4—434no—
198C2×D4—432no—
199C2×D4—868no—
200C2×D4—864no—
201C2×D4—862no—
202C2×D4—861no—
203C2×D4C22×D4311yescharacteristic
204C22×C4—22no—
205C22×C4—22no—
206C22×C4—21no—
207C22×C4—868no—
208C22×C4—861no—
209C22×C4—864no—
210C22×C4C22⋊D4312yes—
211C22×C4C22⋊D4311yescharacteristic
212C22×C4C22×D4312yes—
213C22×C4C22×D4311yescharacteristic
214Q16—864no—
215SD16—864no—
216SD16—864no—
217D8—864no—
218M16—862no—
219M16—862no—
220C2×C8—432no—
221C2×C8—432no—
222C4⋊C4—22no—
223C4⋊C4C22×D4312yes—
224C22⋊C4—21no—
225C22⋊C4—22no—
226C22⋊C4—22no—
227C42—21no—
228C23—22no—
229C23—21no—
230C23—42no—
231C23—864no—
232C23—862no—
233C23—1724no—
234C23C2×C22⋊D4312yes—
235C23C2×C22⋊D4311yescharacteristic
236Q8—21no—
237Q8—21no—
238Q8—434no—
239Q8—864no—
240Q8—862no—
241D4—21no—
242D4—21no—
243D4—44no—
244D4—42no—
245D4—434no—
246D4—8616no—
247D4—864no—
248D4—862no—
249C2×C4—22no—
250C2×C4—24no—
251C2×C4—22no—
252C2×C4—22no—
253C2×C4—22no—
254C2×C4—21no—
255C2×C4—42no—
256C2×C4—8616no—
257C2×C4—864no—
258C2×C4—862no—
259C2×C4D4×D4312yes—
260C2×C4D4×D4312yes—
261C2×C4C2×C22⋊D4312yes—
262C2×C4C2×C22⋊D4311yescharacteristic
263C2×C4C23×D4311yescharacteristic
264C8—862no—
265C8—862no—
266C22—22no—
267C22—22no—
268C22—22no—
269C22—22no—
270C22—44no—
271C22—41no—
272C22—42no—
273C22—864no—
274C22—1728no—
275C22—1724no—
276C22#1306329312yes—
277C22C22×C22⋊D4311yescharacteristic
278C4—22no—
279C4—41no—
280C4—42no—
281C4—864no—
282C4#1306329312yes—
283C4C2×D4×D4311yescharacteristic
284C4C2×D4×D4311yescharacteristic
285C2—22no—
286C2—42no—
287C2—81no—
288C2—1724no—
289C2C2×#1306329311yescharacteristic
290C2#1458369712yes—
subgroupG/H
centerC22C22×C22⋊D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#525C2
socleC22×C43C22×D4
hypercenter#525D43
hypocenterC43#3005
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #525

Complements

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

NH ≅ G/Ntype
1. C22×#10621898C2semidirect
2. C2×#13063355C2semidirect
3. C2×#13063350C2semidirect
4. #14583059C2semidirect
5. #14583042C2semidirect
6. #14582907C2semidirect
7. #14582903C2semidirect
8. #14582863C2semidirect
9. C43×#525C2semidirect
20. C2×#10621885C22semidirect
21. C2×#10621883C22semidirect
22. C2×#10621884C22semidirect
23. C2×#10621882C22semidirect
26. #13063248C22semidirect
27. #13063245C22semidirect
28. C22⋊(C43⋊C8)C22semidirect
32. C22⋊Q8×C43C22semidirect
33. #121×C43C22semidirect
60. C2×D172D4semidirect
66. C2×Dic86D4semidirect
149. #525D43semidirect
155. C43#3005semidirect
175. C22⋊Q8C2×D43semidirect
176. #121C2×D43semidirect