Finite Group Databasebeta

← #19145354

Subgroups — #19145354

Order 5504.

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

normal subgroups only

This group has 468 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
1C2×#13063305C211yesmaximal, characteristic, complemented
2#121×D43C211yesmaximal, characteristic
3#14583231C212yesmaximal, complemented
4#14583217C211yesmaximal, characteristic, complemented
5#14583129C212yesmaximal, complemented
6#14583127C212yesmaximal, complemented
7#14583051C212yesmaximal, complemented
8#14583040C211yesmaximal, characteristic, complemented
9#14583037C211yesmaximal, characteristic, complemented
10C22⋊C8×D43C211yesmaximal, characteristic, complemented
11C43×#481C211yesmaximal, characteristic, complemented
12C22×Dic86C2211yescharacteristic, complemented
13C2×D4×D43—21no—
14C2×D4×D43C2211yescharacteristic
15C22×C4×D43C2211yescharacteristic
16C2×#10621873C2212yescomplemented
17C2×#10621883C2212yescomplemented
18C2×C8×D43C2212yescomplemented
19#13063305—21no—
20#13063305—21no—
21#13063305C2212yes—
22#13063305C2212yescomplemented
23#13063300C2211yescharacteristic
24#13063299C2211yescharacteristic
25#13063298—21no—
26#13063297—21no—
27#13063296C2211yescharacteristic
28C2×C4⋊Dic43—21no—
29C4⋊C4×D43C2211yescharacteristic
30C2×(C2×D43)⋊C4—21no—
31C22⋊C4×D43—21no—
32#13063256C2212yescomplemented
33#13063250C2212yescomplemented
34#13063248C2212yescomplemented
35#13063245C2212yescomplemented
36C22⋊(C43⋊C8)C2211yescharacteristic, complemented
37(C2×D43)⋊C8C2212yes—
38#121×C43C2211yescharacteristic
39C2×C4⋊C4×C43C2211yescharacteristic, complemented
40#106×C43C2212yescomplemented
41#102×C43C2212yescomplemented
42C22⋊C8×C43C2211yescharacteristic, complemented
43C23×D43—21no—
44C23×D43D411yescharacteristic
45C2×D4×C43—21no—
46C2×D4×C43C2311yescharacteristic
47C22×C4×C43—21no—
48C22×C4×C43C2311yescharacteristic
49C2×C22⋊D43—21no—
50C2×C22⋊D43—21no—
51C2×C22⋊D43—21no—
52C22×Dic43—21no—
53C22×Dic43D411yescharacteristic
54D4×D43—42no—
55D4×D43—44no—
56C2×D172—21no—
57C2×D172C2311yescharacteristic
58C2×C4×D43—21no—
59C2×C4×D43—42no—
60C2×C4×D43D411yescharacteristic
61C2×C4×D43D411yescharacteristic
62C2×C4×D43C2311yescharacteristic
63C2×C4×D43C2311yescharacteristic
64C2×Dic86—21no—
65C2×Dic86—42no—
66C2×Dic86C2312yes—
67C2×C8×C43C2312yes—
68C4⋊C4×C43—21no—
69C4⋊C4×C43C2312yes—
70C4⋊C4×C43C2311yescharacteristic
71C22⋊C4×C43—21no—
72C22⋊Dic43—21no—
73#10621883—42no—
74(C2×D43)⋊C4—21no—
75(C2×D43)⋊C4—21no—
76(C2×D43)⋊C4—22no—
77(C2×D43)⋊C4—22no—
78C4⋊Dic43—22no—
79C4⋊Dic43—22no—
80C4⋊Dic43C2311yescharacteristic
81Dic43⋊C4—21no—
82C2×C43⋊C8C2312yes—
83#10621873—42no—
84C8×D43—42no—
85C23×C43—21no—
86C23×C43C2×D411yescharacteristic
87C22×D43—21no—
88C22×D43—41no—
89C22×D43—41no—
90C22×D43—42no—
91C22×D43—42no—
92C22×D43—42no—
93C22×D43SD1614yescomplemented
94C22×D43C2×D411yescharacteristic
95C22×D43C2×D411yescharacteristic
96D4×C43—22no—
97D4×C43—42no—
98C2×C4×C43—22no—
99C2×C4×C43—21no—
100C2×C4×C43—22no—
101C2×C4×C43—42no—
102C2×C4×C43C2×D411yescharacteristic
103C2×C4×C43C2411yescharacteristic
104C22⋊D43—42no—
105C22⋊D43—42no—
106C22⋊D43—42no—
107C2×Dic43—21no—
108C2×Dic43—22no—
109C2×Dic43—41no—
110C2×Dic43—42no—
111C2×Dic43C2×D411yescharacteristic
112C2×Dic43C2×D411yescharacteristic
113D172—22no—
114D172—42no—
115C4×D43—22no—
116C4×D43—22no—
117C4×D43—41no—
118C4×D43—41no—
119C4×D43—42no—
120Dic86—22no—
121Dic86—22no—
122Dic86—42no—
123C8×C43—22no—
124C43⋊C8—22no—
125C22×C43—21no—
126C22×C43—21no—
127C22×C43—41no—
128C22×C43—41no—
129C22×C43—41no—
130C22×C43C2×SD1612yes—
131C22×C43C22×D411yescharacteristic
132C2×D43—21no—
133C2×D43—21no—
134C2×D43—21no—
135C2×D43—21no—
136C2×D43—44no—
137C2×D43—41no—
138C2×D43—41no—
139C2×D43—41no—
140C2×D43—84no—
141C2×D43C2×SD1612yes—
142C2×D43C2×SD1612yes—
143C4×C43—21no—
144C4×C43—41no—
145C4×C43—42no—
146C4×C43H(5,𝔽2)12yes—
147Dic43—21no—
148Dic43—21no—
149Dic43—42no—
150Dic43—41no—
151#3187—431nomaximal, Sylow
152C2×C43—22no—
153C2×C43—81no—
154C2×C43#53411yescharacteristic
155C2×C43C22×SD1611yescharacteristic
156C2×C43#57511yescharacteristic
157D43—22no—
158D43—22no—
159D43—81no—
160C2×C22⋊Q8—431no—
161C2×#121—431no—
162#483—432no—
163#481—431no—
164#481D4311yescharacteristic, complemented
165#465—432no—
166#465—432no—
167#450—432no—
168#448—431no—
169#448—431no—
170C2×C22⋊C8—431no—
171C43#318711yescharacteristic, complemented, Sylow
172C22×Q8—431no—
173C22×D4—431no—
174C22×D4—861no—
175C23×C4—431no—
176C2×SD16—432no—
177C2×SD16—432no—
178C22×C8—432no—
179C22⋊Q8—432no—
180C22⋊Q8—432no—
181C22⋊Q8—861no—
182C22⋊Q8—861no—
183#121—431no—
184#121—431no—
185#121—431no—
186#121—861no—
187#121—861no—
188#121C2×D4311yescharacteristic
189C2×C4⋊C4—431no—
190C2×C4⋊C4—861no—
191C2×C4⋊C4C2×D4311yescharacteristic, complemented
192C2×C22⋊C4—861no—
193C2×C22⋊C4—861no—
194#106—432no—
195#106C2×D4312yescomplemented
196#103—432no—
197#103—432no—
198#102—432no—
199#102C2×D4312yescomplemented
200C22⋊C8—431no—
201C22⋊C8—432no—
202C22⋊C8C2×D4311yescharacteristic, complemented
203C24—431no—
204C24—861no—
205C2×Q8—432no—
206C2×Q8—861no—
207C2×Q8—1722no—
208C2×D4—21no—
209C2×D4—431no—
210C2×D4—861no—
211C2×D4—861no—
212C2×D4—861no—
213C2×D4—861no—
214C2×D4—1722no—
215C2×D4—1724no—
216C2×D4C22×D4311yescharacteristic
217C22×C4—21no—
218C22×C4—431no—
219C22×C4—431no—
220C22×C4—431no—
221C22×C4—431no—
222C22×C4—431no—
223C22×C4—861no—
224C22×C4—861no—
225C22×C4—1722no—
226C22×C4C22×D4311yescharacteristic
227SD16—1722no—
228SD16—1722no—
229C2×C8—432no—
230C2×C8—1722no—
231C2×C8C22×D4312yes—
232C4⋊C4—21no—
233C4⋊C4—431no—
234C4⋊C4—861no—
235C4⋊C4—862no—
236C4⋊C4—862no—
237C4⋊C4C22×D4312yes—
238C4⋊C4C22×D4311yescharacteristic
239C22⋊C4—21no—
240C22⋊C4—861no—
241C22⋊C4—862no—
242C22⋊C4—862no—
243C22⋊C4—861no—
244C22⋊C4—861no—
245C23—21no—
246C23—431no—
247C23—431no—
248C23—434no—
249C23—861no—
250C23—1721no—
251C23—1721no—
252C23—1722no—
253C23—1722no—
254C23—1722no—
255C23D4×D4311yescharacteristic
256Q8—862no—
257Q8—862no—
258Q8—1722no—
259D4—22no—
260D4—42no—
261D4—862no—
262D4—1722no—
263D4—1722no—
264D4—1722no—
265D4—1722no—
266C2×C4—22no—
267C2×C4—21no—
268C2×C4—22no—
269C2×C4—42no—
270C2×C4—431no—
271C2×C4—431no—
272C2×C4—862no—
273C2×C4—862no—
274C2×C4—861no—
275C2×C4—862no—
276C2×C4—1721no—
277C2×C4—1721no—
278C2×C4—1722no—
279C2×C4—1721no—
280C2×C4—1722no—
281C2×C4D4×D4311yescharacteristic
282C2×C4C23×D4311yescharacteristic
283C8—22no—
284C8—862no—
285C22—21no—
286C22—21no—
287C22—41no—
288C22—41no—
289C22—41no—
290C22—432no—
291C22—432no—
292C22—861no—
293C22—861no—
294C22—861no—
295C22—861no—
296C22—3444no—
297C22—1724no—
298C22—1721no—
299C22—1721no—
300C22—1721no—
301C22SD16×D4312yes—
302C22C2×D4×D4311yescharacteristic
303C4—21no—
304C4—41no—
305C4—42no—
306C4—861no—
307C4—861no—
308C4—1721no—
309C4—1722no—
310C4#1306337112yes—
311C2—22no—
312C2—81no—
313C2—862no—
314C2—862no—
315C2—3441no—
316C2#1458346011yescharacteristic
317C2C2×SD16×D4311yescharacteristic
318C2#1458369511yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#481C2
socleC22×C43C22×D4
hypercenter#481D43
hypocenterC43#3187
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #481

Complements

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

NH ≅ G/Ntype
1. C2×#13063305C2semidirect
3. #14583231C2semidirect
4. #14583217C2semidirect
5. #14583129C2semidirect
6. #14583127C2semidirect
7. #14583051C2semidirect
8. #14583040C2semidirect
9. #14583037C2semidirect
10. C22⋊C8×D43C2semidirect
11. C43×#481C2semidirect
12. C22×Dic86C22semidirect
16. C2×#10621873C22semidirect
17. C2×#10621883C22semidirect
18. C2×C8×D43C22semidirect
22. #13063305C22semidirect
32. #13063256C22semidirect
33. #13063250C22semidirect
34. #13063248C22semidirect
35. #13063245C22semidirect
36. C22⋊(C43⋊C8)C22semidirect
39. C2×C4⋊C4×C43C22semidirect
40. #106×C43C22semidirect
41. #102×C43C22semidirect
42. C22⋊C8×C43C22semidirect
93. C22×D43SD16semidirect
164. #481D43semidirect
171. C43#3187semidirect
191. C2×C4⋊C4C2×D43semidirect
195. #106C2×D43semidirect
199. #102C2×D43semidirect
202. C22⋊C8C2×D43semidirect