Finite Group Databasebeta

← #19145394

Subgroups — #19145394

Order 5504.

514 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 514 conjugacy classes of subgroups — too many to draw. Only its 115 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×#13063300C211yesmaximal, characteristic, complemented
2#121×D43C211yesmaximal, characteristic, complemented
3#14583219C212yesmaximal, complemented
4#14583217C211yesmaximal, characteristic, complemented
5#14583153C212yesmaximal, complemented
6#14583151C212yesmaximal, complemented
7#14583035C211yesmaximal, characteristic, complemented
8#14583034C212yesmaximal, complemented
9#14583032C211yesmaximal, characteristic, complemented
10#14582861C211yesmaximal, characteristic, complemented
11C43×#481C211yesmaximal, characteristic, complemented
12C22×D172—21no—
13C22×D172C2211yescharacteristic, complemented
14C2×D4×D43—21no—
15C2×D4×D43C2211yescharacteristic, complemented
16C22×C4×D43C2211yescharacteristic
17C2×D344C2212yescomplemented
18C2×#10621882C2212yescomplemented
19C2×#10621872C2212yescomplemented
20#13063300—21no—
21#13063300—21no—
22#13063300C2212yes—
23#13063300C2211yescharacteristic, complemented
24#13063300C2212yescomplemented
25#13063299C2211yescharacteristic
26#13063298—21no—
27#13063297—21no—
28#13063296C2211yescharacteristic, complemented
29C4⋊C4×D43C2211yescharacteristic, complemented
30C2×(C2×D43)⋊C4—21no—
31C22⋊C4×D43—21no—
32#13063256C2212yescomplemented
33#13063247C2212yescomplemented
34#13063245C2212yescomplemented
35#13063245C2212yescomplemented
36C22⋊(C43⋊C8)C2211yescharacteristic, complemented
37(C2×D43)⋊C8C2212yescomplemented
38#121×C43C2211yescharacteristic
39C2×C4⋊C4×C43C2211yescharacteristic, complemented
40#106×C43C2212yescomplemented
41#102×C43C2212yescomplemented
42C22⋊C8×C43C2211yescharacteristic, complemented
43C23×D43—21no—
44C23×D43—21no—
45C23×D43D411yescharacteristic
46C2×D4×C43—21no—
47C2×D4×C43C2311yescharacteristic
48C22×C4×C43—21no—
49C22×C4×C43C2311yescharacteristic
50C2×C22⋊D43—21no—
51C2×C22⋊D43—21no—
52C2×C22⋊D43—21no—
53C22×Dic43D411yescharacteristic
54D4×D43—44no—
55D4×D43—42no—
56C2×D172—21no—
57C2×D172—21no—
58C2×D172—22no—
59C2×D172—22no—
60C2×D172—44no—
61C2×D172—42no—
62C2×D172C2311yescharacteristic
63C2×D172C2312yes—
64C2×C4×D43—21no—
65C2×C4×D43—42no—
66C2×C4×D43D411yescharacteristic
67C2×C4×D43D411yescharacteristic
68C2×C4×D43C2311yescharacteristic
69C2×C4×D43C2311yescharacteristic
70C2×C8×C43C2312yes—
71C4⋊C4×C43—21no—
72C4⋊C4×C43C2312yes—
73C4⋊C4×C43C2311yescharacteristic
74C22⋊C4×C43—21no—
75C22⋊Dic43—21no—
76#10621882—42no—
77(C2×D43)⋊C4—21no—
78(C2×D43)⋊C4—21no—
79(C2×D43)⋊C4—22no—
80(C2×D43)⋊C4—22no—
81C4⋊Dic43C2311yescharacteristic
82Dic43⋊C4—21no—
83C2×C43⋊C8C2312yes—
84D344—42no—
85#10621872—42no—
86C23×C43—21no—
87C23×C43C2×D411yescharacteristic
88C22×D43—22no—
89C22×D43—22no—
90C22×D43—22no—
91C22×D43—21no—
92C22×D43—41no—
93C22×D43—42no—
94C22×D43—42no—
95C22×D43—42no—
96C22×D43—42no—
97C22×D43—42no—
98C22×D43—42no—
99C22×D43C2×D411yescharacteristic
100C22×D43C2×D411yescharacteristic
101D4×C43—22no—
102D4×C43—42no—
103C2×C4×C43—22no—
104C2×C4×C43—21no—
105C2×C4×C43—22no—
106C2×C4×C43—42no—
107C2×C4×C43C2×D411yescharacteristic
108C2×C4×C43C2411yescharacteristic
109C22⋊D43—42no—
110C22⋊D43—42no—
111C22⋊D43—42no—
112C2×Dic43—21no—
113C2×Dic43—41no—
114C2×Dic43C2×D411yescharacteristic
115C2×Dic43C2×D411yescharacteristic
116D172—22no—
117D172—22no—
118D172—22no—
119D172—42no—
120D172—44no—
121D172—42no—
122D172—44no—
123C4×D43—22no—
124C4×D43—22no—
125C4×D43—41no—
126C4×D43—41no—
127C4×D43—42no—
128C8×C43—22no—
129C43⋊C8—22no—
130C22×C43—21no—
131C22×C43—21no—
132C22×C43—41no—
133C22×C43—41no—
134C22×C43—41no—
135C22×C43AGL(1,ℤ/8)12yes—
136C22×C43C22×D411yescharacteristic
137C2×D43—21no—
138C2×D43—21no—
139C2×D43—21no—
140C2×D43—21no—
141C2×D43—21no—
142C2×D43—44no—
143C2×D43—42no—
144C2×D43—41no—
145C2×D43—41no—
146C2×D43—42no—
147C2×D43—42no—
148C2×D43—41no—
149C2×D43—84no—
150C2×D43—84no—
151C2×D43AGL(1,ℤ/8)12yes—
152C4×C43—21no—
153C4×C43—41no—
154C4×C43—42no—
155C4×C43H(5,𝔽2)12yes—
156Dic43—21no—
157Dic43—21no—
158Dic43—41no—
159#3192—431nomaximal, Sylow
160C2×C43—22no—
161C2×C43—81no—
162C2×C43#53411yescharacteristic
163C2×C43C2×AGL(1,ℤ/8)11yescharacteristic
164C2×C43C2×AGL(1,ℤ/8)11yescharacteristic
165D43—22no—
166D43—41no—
167D43—82no—
168D43—81no—
169C2×#121—431no—
170C2×#121—431no—
171#481—431no—
172#481—432no—
173#481D4311yescharacteristic, complemented
174#469—432no—
175#469—432no—
176#447—431no—
177#447—432no—
178#447—431no—
179#407—431no—
180C43#319211yescharacteristic, complemented, Sylow
181C22×D4—431no—
182C22×D4—431no—
183C22×D4—861no—
184C22×D4—861no—
185C23×C4—431no—
186C2×D8—432no—
187C2×D8—432no—
188C2×M16—432no—
189#121—431no—
190#121—431no—
191#121—432no—
192#121—431no—
193#121—432no—
194#121—861no—
195#121—861no—
196#121—861no—
197#121—861no—
198#121C2×D4311yescharacteristic
199C2×C4⋊C4—431no—
200C2×C4⋊C4C2×D4311yescharacteristic, complemented
201C2×C22⋊C4—861no—
202C2×C22⋊C4—861no—
203#106—432no—
204#106C2×D4312yescomplemented
205#102—432no—
206#102—432no—
207#102—432no—
208#102C2×D4312yescomplemented
209C22⋊C8—431no—
210C22⋊C8—432no—
211C22⋊C8C2×D4311yescharacteristic, complemented
212C24—431no—
213C24—861no—
214C24—861no—
215C2×D4—21no—
216C2×D4—432no—
217C2×D4—431no—
218C2×D4—861no—
219C2×D4—862no—
220C2×D4—862no—
221C2×D4—861no—
222C2×D4—861no—
223C2×D4—861no—
224C2×D4—861no—
225C2×D4—1722no—
226C2×D4—1724no—
227C2×D4—1722no—
228C2×D4—1724no—
229C2×D4C22×D4311yescharacteristic
230C22×C4—21no—
231C22×C4—431no—
232C22×C4—431no—
233C22×C4—431no—
234C22×C4—431no—
235C22×C4—431no—
236C22×C4—861no—
237C22×C4—1722no—
238C22×C4C22×D4311yescharacteristic
239D8—1722no—
240D8—1722no—
241M16—1722no—
242C2×C8—432no—
243C2×C8C22×D4312yes—
244C4⋊C4—21no—
245C4⋊C4—431no—
246C4⋊C4—861no—
247C4⋊C4C22×D4311yescharacteristic
248C4⋊C4C22×D4312yes—
249C22⋊C4—21no—
250C22⋊C4—861no—
251C22⋊C4—862no—
252C22⋊C4—862no—
253C22⋊C4—861no—
254C22⋊C4—861no—
255C23—21no—
256C23—431no—
257C23—431no—
258C23—862no—
259C23—862no—
260C23—862no—
261C23—861no—
262C23—1721no—
263C23—1722no—
264C23—1722no—
265C23—1722no—
266C23—1722no—
267C23—1722no—
268C23—1722no—
269C23D4×D4311yescharacteristic
270D4—22no—
271D4—42no—
272D4—862no—
273D4—862no—
274D4—862no—
275D4—1722no—
276D4—1724no—
277D4—1724no—
278D4—1722no—
279D4—1722no—
280D4—1722no—
281D4—1722no—
282C2×C4—22no—
283C2×C4—21no—
284C2×C4—22no—
285C2×C4—42no—
286C2×C4—431no—
287C2×C4—431no—
288C2×C4—862no—
289C2×C4—862no—
290C2×C4—861no—
291C2×C4—1721no—
292C2×C4—1721no—
293C2×C4—1722no—
294C2×C4—1721no—
295C2×C4D4×D4311yescharacteristic
296C2×C4C23×D4311yescharacteristic
297C8—22no—
298C8—862no—
299C22—21no—
300C22—21no—
301C22—41no—
302C22—41no—
303C22—41no—
304C22—432no—
305C22—861no—
306C22—861no—
307C22—861no—
308C22—861no—
309C22—861no—
310C22—3444no—
311C22—3444no—
312C22—1724no—
313C22—1722no—
314C22—1721no—
315C22—1721no—
316C22—1722no—
317C22—1722no—
318C22—1721no—
319C22#1306335212yes—
320C22C2×D4×D4311yescharacteristic
321C4—21no—
322C4—42no—
323C4—41no—
324C4—861no—
325C4—861no—
326C4—1721no—
327C4#1306337112yes—
328C2—22no—
329C2—81no—
330C2—862no—
331C2—3442no—
332C2—3441no—
333C2—1721no—
334C2#1458346011yescharacteristic
335C2AGL(1,ℤ/8)×D4311yescharacteristic
336C2C2×#1306335211yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#481C2
socleC22×C43C22×D4
hypercenter#481D43
hypocenterC43#3192
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×#13063300C2semidirect
2. #121×D43C2semidirect
3. #14583219C2semidirect
4. #14583217C2semidirect
5. #14583153C2semidirect
6. #14583151C2semidirect
7. #14583035C2semidirect
8. #14583034C2semidirect
9. #14583032C2semidirect
10. #14582861C2semidirect
11. C43×#481C2semidirect
13. C22×D172C22semidirect
15. C2×D4×D43C22semidirect
17. C2×D344C22semidirect
18. C2×#10621882C22semidirect
19. C2×#10621872C22semidirect
23. #13063300C22semidirect
24. #13063300C22semidirect
28. #13063296C22semidirect
29. C4⋊C4×D43C22semidirect
32. #13063256C22semidirect
33. #13063247C22semidirect
34. #13063245C22semidirect
35. #13063245C22semidirect
36. C22⋊(C43⋊C8)C22semidirect
37. (C2×D43)⋊C8C22semidirect
39. C2×C4⋊C4×C43C22semidirect
40. #106×C43C22semidirect
41. #102×C43C22semidirect
42. C22⋊C8×C43C22semidirect
173. #481D43semidirect
180. C43#3192semidirect
200. C2×C4⋊C4C2×D43semidirect
204. #106C2×D43semidirect
208. #102C2×D43semidirect
211. C22⋊C8C2×D43semidirect