Finite Group Databasebeta

← #19145409

Subgroups — #19145409

Order 5504.

466 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 466 conjugacy classes of subgroups — too many to draw. Only its 121 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#14583410C211yesmaximal, characteristic, complemented
2#14583229C211yesmaximal, characteristic, complemented
3#14583220C212yesmaximal, complemented
4#14583212C211yesmaximal, characteristic, complemented
5#14583150C212yesmaximal, complemented
6#14583143C212yesmaximal, complemented
7#14583050C211yesmaximal, characteristic, complemented
8#14583042C212yesmaximal, complemented
9#14583033C211yesmaximal, characteristic, complemented
10#14582863C211yesmaximal, characteristic, complemented
11C2×#121×C43C211yesmaximal, characteristic, complemented
12C2×#10621898C2211yescharacteristic, complemented
13C2×#10621883C2212yescomplemented
14C2×#10621882C2212yescomplemented
15C2×#10621877C2212yescomplemented
16#13063308—21no—
17#13063304C2211yescharacteristic
18#13063304C2211yescharacteristic, complemented
19#13063299C2211yescharacteristic
20#13063299C2211yescharacteristic, complemented
21#13063294—21no—
22C4×C22⋊D43—21no—
23C4×C22⋊D43—21no—
24#13063284C2211yescharacteristic, complemented
25#13063258C2212yescomplemented
26#13063256C2212yescomplemented
27#13063248C2212yescomplemented
28#13063246C2212yescomplemented
29#13063246C2212yescomplemented
30#13063245C2212yescomplemented
31C22⋊(C43⋊C8)C2211yescharacteristic
32C22⋊(C43⋊C8)C2211yescharacteristic
33C22⋊(C43⋊C8)C2212yescomplemented
34C22×D4×C43—21no—
35C22×D4×C43C2211yescharacteristic
36C23×C4×C43C2211yescharacteristic
37#121×C43—21no—
38#121×C43—21no—
39#121×C43C2212yes—
40#121×C43C2212yes—
41C2×C4⋊C4×C43C2211yescharacteristic
42C2×C22⋊C4×C43—21no—
43C24×C43—21no—
44C24×C43D411yescharacteristic
45C2×D4×C43—21no—
46C2×D4×C43—22no—
47C2×D4×C43—22no—
48C2×D4×C43—44no—
49C2×D4×C43—42no—
50C2×D4×C43C2312yes—
51C22×C4×C43—21no—
52C22×C4×C43—42no—
53C22×C4×C43D411yescharacteristic
54C22×C4×C43D411yescharacteristic
55C22×C4×C43D411yescharacteristic
56C22×C4×C43C2311yescharacteristic
57C22×C4×C43C2311yescharacteristic
58C22×C4×C43C2311yescharacteristic
59C2×C22⋊D43—21no—
60C2×C22⋊D43—21no—
61C2×C22⋊D43—21no—
62#10621898—42no—
63C2×D172C2311yescharacteristic
64C2×C4×D43—21no—
65C2×Dic86C2311yescharacteristic
66C4⋊C4×C43—21no—
67C4⋊C4×C43C2312yes—
68C22⋊C4×C43—22no—
69C22⋊C4×C43—22no—
70C22⋊Dic43—21no—
71C22⋊Dic43—21no—
72C22⋊Dic43—21no—
73#10621883—42no—
74#10621882—42no—
75(C2×D43)⋊C4—21no—
76(C2×D43)⋊C4—21no—
77C4⋊Dic43C2311yescharacteristic
78C4⋊Dic43C2311yescharacteristic
79Dic43⋊C4—21no—
80Dic43⋊C4—21no—
81C4×Dic43—21no—
82#10621877—42no—
83C2×C43⋊C8C2312yes—
84C2×C43⋊C8C2312yes—
85C23×C43—22no—
86C23×C43—22no—
87C23×C43—41no—
88C23×C43—41no—
89C23×C43—42no—
90C23×C43—42no—
91C23×C43—42no—
92C23×C43C2×D411yescharacteristic
93C23×C43C2×D411yescharacteristic
94C23×C43C2×D411yescharacteristic
95C22×D43—21no—
96D4×C43—22no—
97D4×C43—22no—
98D4×C43—42no—
99D4×C43—44no—
100D4×C43—44no—
101C2×C4×C43—22no—
102C2×C4×C43—22no—
103C2×C4×C43—22no—
104C2×C4×C43—22no—
105C2×C4×C43—41no—
106C2×C4×C43—41no—
107C2×C4×C43—41no—
108C2×C4×C43—42no—
109C2×C4×C43C2×D411yescharacteristic
110C2×C4×C43C2×D411yescharacteristic
111C2×C4×C43C2×D411yescharacteristic
112C2×C4×C43C2411yescharacteristic
113C22⋊D43—42no—
114C22⋊D43—42no—
115C22⋊D43—42no—
116C2×Dic43—21no—
117C2×Dic43—21no—
118C2×Dic43—21no—
119D172—22no—
120C4×D43—42no—
121Dic86—22no—
122C43⋊C8—22no—
123C43⋊C8—22no—
124C22×C43—21no—
125C22×C43—21no—
126C22×C43—21no—
127C22×C43—21no—
128C22×C43—21no—
129C22×C43—21no—
130C22×C43—21no—
131C22×C43—21no—
132C22×C43—44no—
133C22×C43—42no—
134C22×C43—42no—
135C22×C43—42no—
136C22×C43—84no—
137C22×C43AGL(1,ℤ/8)12yes—
138C22×C43C22×D411yescharacteristic
139C2×D43—41no—
140C2×D43—41no—
141C2×D43—41no—
142C4×C43—21no—
143C4×C43—21no—
144C4×C43—21no—
145C4×C43—42no—
146C4×C43H(5,𝔽2)12yes—
147Dic43—41no—
148Dic43—41no—
149Dic43—41no—
150#3194—431nomaximal, Sylow
151C2×C43—22no—
152C2×C43—41no—
153C2×C43—41no—
154C2×C43—82no—
155C2×C43#53411yescharacteristic
156C2×C43C2×AGL(1,ℤ/8)11yescharacteristic
157C2×C43#57511yescharacteristic
158D43—81no—
159#525—431no—
160C2×#121D4311yescharacteristic, complemented
161#483—431no—
162#482—432no—
163#480—431no—
164#469—432no—
165#468—432no—
166#450—431no—
167#449—432no—
168#447—431no—
169#407—431no—
170C43#319411yescharacteristic, complemented, Sylow
171C2×#41—431no—
172C22×D4—21no—
173C22×D4C2×D4311yescharacteristic
174C23×C4C2×D4311yescharacteristic
175C2×SD16—432no—
176C2×D8—432no—
177C2×M16—432no—
178#123—861no—
179C22⋊Q8—431no—
180C22⋊Q8—431no—
181#121—21no—
182#121—21no—
183#121—431no—
184#121—431no—
185#121C2×D4312yes—
186#121C2×D4312yes—
187#120—861no—
188C4×D4—861no—
189C4×D4—861no—
190#117—431no—
191C2×C4⋊C4C2×D4311yescharacteristic
192C2×C22⋊C4—21no—
193#107—432no—
194#106—432no—
195#103—432no—
196#102—432no—
197#102—432no—
198#102—432no—
199C22⋊C8—431no—
200C22⋊C8—431no—
201C22⋊C8—432no—
202C24—21no—
203C24C22⋊D4311yescharacteristic
204#41—1722no—
205C2×Q8—431no—
206C2×D4—22no—
207C2×D4—22no—
208C2×D4—21no—
209C2×D4—42no—
210C2×D4—44no—
211C2×D4—431no—
212C2×D4—861no—
213C2×D4—861no—
214C2×D4—861no—
215C2×D4C22×D4312yes—
216C22×C4—21no—
217C22×C4—42no—
218C22×C4—861no—
219C22×C4C22⋊D4311yescharacteristic
220C22×C4C22⋊D4311yescharacteristic
221C22×C4C22⋊D4311yescharacteristic
222C22×C4C22×D4311yescharacteristic
223C22×C4C22×D4311yescharacteristic
224C22×C4C22×D4311yescharacteristic
225SD16—1722no—
226D8—1722no—
227M16—1722no—
228C2×C8—432no—
229C2×C8—432no—
230C4⋊C4—21no—
231C4⋊C4—431no—
232C4⋊C4—431no—
233C4⋊C4—861no—
234C4⋊C4—861no—
235C4⋊C4C22×D4312yes—
236C22⋊C4—22no—
237C22⋊C4—22no—
238C22⋊C4—861no—
239C22⋊C4—861no—
240C22⋊C4—861no—
241C22⋊C4—861no—
242C22⋊C4—861no—
243C42—861no—
244C23—22no—
245C23—22no—
246C23—41no—
247C23—41no—
248C23—42no—
249C23—42no—
250C23—42no—
251C23—861no—
252C23C2×C22⋊D4311yescharacteristic
253C23C2×C22⋊D4311yescharacteristic
254C23C2×C22⋊D4311yescharacteristic
255Q8—862no—
256D4—22no—
257D4—22no—
258D4—42no—
259D4—44no—
260D4—44no—
261D4—862no—
262D4—1722no—
263D4—1722no—
264D4—1722no—
265C2×C4—22no—
266C2×C4—22no—
267C2×C4—22no—
268C2×C4—22no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—42no—
273C2×C4—861no—
274C2×C4—861no—
275C2×C4—861no—
276C2×C4—1722no—
277C2×C4C2×C22⋊D4311yescharacteristic
278C2×C4C2×C22⋊D4311yescharacteristic
279C2×C4C2×C22⋊D4311yescharacteristic
280C2×C4C23×D4311yescharacteristic
281C8—862no—
282C8—862no—
283C22—21no—
284C22—21no—
285C22—21no—
286C22—21no—
287C22—21no—
288C22—21no—
289C22—21no—
290C22—21no—
291C22—44no—
292C22—42no—
293C22—42no—
294C22—42no—
295C22—84no—
296C22—1721no—
297C22—1721no—
298C22—1721no—
299C22#1306335112yes—
300C22C22×C22⋊D4311yescharacteristic
301C4—21no—
302C4—21no—
303C4—21no—
304C4—42no—
305C4—1721no—
306C4—1721no—
307C4—1721no—
308C4#1306337012yes—
309C2—22no—
310C2—41no—
311C2—41no—
312C2—82no—
313C2—3441no—
314C2#1458345811yescharacteristic
315C2C2×#1306335111yescharacteristic
316C2#1458369711yescharacteristic
subgroupG/H
centerC22C22×C22⋊D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC2×#121×C43C2
socleC22×C43C22×D4
hypercenterC2×#121D43
hypocenterC43#3194
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
1. #14583410C2semidirect
2. #14583229C2semidirect
3. #14583220C2semidirect
4. #14583212C2semidirect
5. #14583150C2semidirect
6. #14583143C2semidirect
7. #14583050C2semidirect
8. #14583042C2semidirect
9. #14583033C2semidirect
10. #14582863C2semidirect
11. C2×#121×C43C2semidirect
12. C2×#10621898C22semidirect
13. C2×#10621883C22semidirect
14. C2×#10621882C22semidirect
15. C2×#10621877C22semidirect
18. #13063304C22semidirect
20. #13063299C22semidirect
24. #13063284C22semidirect
25. #13063258C22semidirect
26. #13063256C22semidirect
27. #13063248C22semidirect
28. #13063246C22semidirect
29. #13063246C22semidirect
30. #13063245C22semidirect
33. C22⋊(C43⋊C8)C22semidirect
160. C2×#121D43semidirect
170. C43#3194semidirect