Finite Group Databasebeta

← #19146736

Subgroups — #19146736

Order 5504.

462 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14583595C211yesmaximal, characteristic, complemented
2#14583263C211yesmaximal, characteristic, complemented
3#14583220C211yesmaximal, characteristic, complemented
4#14583215C211yesmaximal, characteristic, complemented
5#14583199C211yesmaximal, characteristic, complemented
6#14583150C211yesmaximal, characteristic, complemented
7#14583133C211yesmaximal, characteristic, complemented
8#14583091C211yesmaximal, characteristic, complemented
9#14583033C211yesmaximal, characteristic, complemented
10#14583033C211yesmaximal, characteristic, complemented
11#14583009C211yesmaximal, characteristic, complemented
12#14582971C211yesmaximal, characteristic, complemented
13#14582904C211yesmaximal, characteristic, complemented
14C2×#13063246C211yesmaximal, characteristic, complemented
15D42×C43C211yesmaximal, characteristic, complemented
16C2×#10621882C2211yescharacteristic
17C2×#10621882C2211yescharacteristic, complemented
18C2×#10621882C2211yescharacteristic, complemented
19C2×#10621877C2211yescharacteristic, complemented
20C22×C43⋊C8C2211yescharacteristic, complemented
21#13063320—21no—
22#13063317C2211yescharacteristic, complemented
23#13063307—21no—
24#13063299C2211yescharacteristic, complemented
25#13063299C2211yescharacteristic, complemented
26#13063297—21no—
27C4×D172C2211yescharacteristic, complemented
28(C22⋊D43)⋊C4—21no—
29#13063284C2211yescharacteristic, complemented
30C2×C4⋊Dic43C2211yescharacteristic, complemented
31#13063258C2211yescharacteristic, complemented
32#13063256C2211yescharacteristic, complemented
33#13063256C2211yescharacteristic, complemented
34C4⋊(C43⋊C8)C2211yescharacteristic, complemented
35#13063246C2211yescharacteristic
36#13063246C2211yescharacteristic
37#13063246C2211yescharacteristic
38#13063246C2211yescharacteristic, complemented
39#13063246C2211yescharacteristic, complemented
40#13063246C2211yescharacteristic, complemented
41#13063246C2211yescharacteristic, complemented
42#13063246C2211yescharacteristic, complemented
43#13063246C2211yescharacteristic, complemented
44#13063245C2211yescharacteristic, complemented
45C22⋊(C43⋊C8)C2211yescharacteristic, complemented
46C22⋊(C43⋊C8)C2211yescharacteristic, complemented
47#13063236C2211yescharacteristic, complemented
48C22×D4×C43—21no—
49C22×D4×C43C2211yescharacteristic
50C22×D4×C43C2211yescharacteristic
51#127×C43C2211yescharacteristic
52#121×C43—21no—
53#121×C43C2211yescharacteristic
54#121×C43C2211yescharacteristic
55#120×C43—21no—
56#120×C43—21no—
57C4×D4×C43C2211yescharacteristic
58C4×D4×C43C2211yescharacteristic
59C24×C43—21no—
60C24×C43—21no—
61C2×D4×C43—21no—
62C2×D4×C43—21no—
63C2×D4×C43—21no—
64C2×D4×C43—21no—
65C2×D4×C43—21no—
66C2×D4×C43—21no—
67C2×D4×C43—22no—
68C2×D4×C43—22no—
69C2×D4×C43—41no—
70C2×D4×C43—41no—
71C2×D4×C43—44no—
72C2×D4×C43D411yescharacteristic
73C2×D4×C43C2311yescharacteristic
74C2×D4×C43C2311yescharacteristic
75C2×D4×C43C2311yescharacteristic
76C22×C4×C43—21no—
77C22×C4×C43C2311yescharacteristic
78C22×C4×C43C2311yescharacteristic
79C2×C22⋊D43—21no—
80C2×C22⋊D43—21no—
81C22×Dic43—21no—
82C2×D172C2311yescharacteristic
83C2×C4×D43—21no—
84C4⋊C4×C43D411yescharacteristic
85C4⋊C4×C43C2311yescharacteristic
86C22⋊C4×C43—21no—
87C22⋊C4×C43—21no—
88C22⋊C4×C43—21no—
89C22⋊C4×C43D411yescharacteristic
90C22⋊C4×C43D411yescharacteristic
91C42×C43C2311yescharacteristic
92C22⋊Dic43—21no—
93#10621882—22no—
94#10621882—41no—
95#10621882—41no—
96(C2×D43)⋊C4—21no—
97(C2×D43)⋊C4—21no—
98(C2×D43)⋊C4—21no—
99C4⋊Dic43—21no—
100C4⋊Dic43C2311yescharacteristic
101C4⋊Dic43C2311yescharacteristic
102C4⋊Dic43C2311yescharacteristic
103Dic43⋊C4—21no—
104Dic43⋊C4—21no—
105C4×Dic43—21no—
106#10621877—41no—
107C2×C43⋊C8—41no—
108C2×C43⋊C8C2311yescharacteristic
109C2×C43⋊C8C2311yescharacteristic
110C2×C43⋊C8C2311yescharacteristic
111C2×C43⋊C8C2311yescharacteristic
112C23×C43—21no—
113C23×C43—21no—
114C23×C43—21no—
115C23×C43—42no—
116C23×C43—42no—
117C23×C43—42no—
118C23×C43—42no—
119C23×C43—81no—
120C23×C43—81no—
121C23×C43C2×D411yescharacteristic
122C23×C43C2×D411yescharacteristic
123C22×D43—21no—
124D4×C43—22no—
125D4×C43—21no—
126D4×C43—21no—
127D4×C43—21no—
128D4×C43—21no—
129D4×C43—21no—
130D4×C43—42no—
131D4×C43—42no—
132D4×C43—42no—
133D4×C43—42no—
134D4×C43—42no—
135D4×C43—81no—
136D4×C43#4112yes—
137C2×C4×C43—21no—
138C2×C4×C43—21no—
139C2×C4×C43—21no—
140C2×C4×C43—21no—
141C2×C4×C43—21no—
142C2×C4×C43—42no—
143C2×C4×C43C2×D411yescharacteristic
144C2×C4×C43C2×D411yescharacteristic
145C2×C4×C43C2×D411yescharacteristic
146C2×C4×C43C2×D411yescharacteristic
147C2×C4×C43C2411yescharacteristic
148C22⋊D43—42no—
149C22⋊D43—81no—
150C2×Dic43—21no—
151C2×Dic43—21no—
152C2×Dic43—21no—
153C2×Dic43—81no—
154D172—21no—
155D172—21no—
156C4×D43—81no—
157C43⋊C8—21no—
158C43⋊C8—21no—
159C43⋊C8—21no—
160C43⋊C8—21no—
161C22×C43—21no—
162C22×C43—21no—
163C22×C43—22no—
164C22×C43—21no—
165C22×C43—21no—
166C22×C43—21no—
167C22×C43—41no—
168C22×C43—41no—
169C22×C43—41no—
170C22×C43—41no—
171C22×C43—41no—
172C22×C43—41no—
173C22×C43—41no—
174C22×C43—41no—
175C22×C43—84no—
176C22×C43—84no—
177C22×C43AGL(1,ℤ/8)12yes—
178C22×C43C22×D411yescharacteristic
179C2×D43—41no—
180C2×D43—41no—
181C2×D43—41no—
182C4×C43—21no—
183C4×C43—21no—
184C4×C43—21no—
185C4×C43—21no—
186C4×C43—41no—
187C4×C43C2×#4111yescharacteristic
188C4×C43H(5,𝔽2)11yescharacteristic
189Dic43—41no—
190Dic43—41no—
191Dic43—41no—
192#3318—431nomaximal, Sylow
193C2×C43—22no—
194C2×C43—41no—
195C2×C43—42no—
196C2×C43—81no—
197C2×C43—81no—
198C2×C43#54611yescharacteristic
199C2×C43C2×AGL(1,ℤ/8)11yescharacteristic
200C2×C43#57611yescharacteristic
201D43—81no—
202#553—431no—
203D42D4311yescharacteristic, complemented
204#490—431no—
205#482—431no—
206#481—431no—
207#478—431no—
208#469—431no—
209#466—431no—
210#459—431no—
211#447—431no—
212#447—431no—
213#442—431no—
214#435—431no—
215#418—431no—
216C2×#102—431no—
217C43#331811yescharacteristic, complemented, Sylow
218C22×D4—21no—
219C22×D4C2×D4311yescharacteristic
220C22×D4C2×D4311yescharacteristic
221C2×D8—431no—
222C2×D8—431no—
223C2×D8—431no—
224C2×M16—431no—
225C22×C8—431no—
226#127C2×D4311yescharacteristic
227#126—861no—
228#125—431no—
229#123—861no—
230#121—21no—
231#121—431no—
232#121—431no—
233#121—861no—
234#121C2×D4311yescharacteristic
235#121C2×D4311yescharacteristic
236#120—21no—
237#120—21no—
238C4×D4—431no—
239C4×D4—861no—
240C4×D4C2×D4311yescharacteristic
241C4×D4C2×D4311yescharacteristic
242#117—431no—
243C2×C4⋊C4—431no—
244#107—431no—
245#106—431no—
246#106—431no—
247C4⋊C8—431no—
248#102—431no—
249#102—431no—
250#102—431no—
251#102—431no—
252#102—431no—
253#102—431no—
254#102—431no—
255#102—431no—
256#102—431no—
257#102—431no—
258C22⋊C8—431no—
259C22⋊C8—431no—
260#97—431no—
261C24—21no—
262C24—21no—
263C2×D4—22no—
264C2×D4—22no—
265C2×D4—21no—
266C2×D4—21no—
267C2×D4—21no—
268C2×D4—21no—
269C2×D4—21no—
270C2×D4—21no—
271C2×D4—41no—
272C2×D4—41no—
273C2×D4—44no—
274C2×D4—431no—
275C2×D4—861no—
276C2×D4—861no—
277C2×D4C22⋊D4311yescharacteristic
278C2×D4C22×D4311yescharacteristic
279C2×D4C22×D4311yescharacteristic
280C2×D4C22×D4311yescharacteristic
281C22×C4—21no—
282C22×C4—861no—
283C22×C4—861no—
284C22×C4C22×D4311yescharacteristic
285C22×C4C22×D4311yescharacteristic
286D8—862no—
287D8—1721no—
288D8—1721no—
289M16—1721no—
290C2×C8—431no—
291C2×C8—431no—
292C2×C8—431no—
293C2×C8—431no—
294C2×C8—1721no—
295C4⋊C4—431no—
296C4⋊C4—431no—
297C4⋊C4—431no—
298C4⋊C4—861no—
299C4⋊C4—861no—
300C4⋊C4—861no—
301C4⋊C4C22⋊D4311yescharacteristic
302C4⋊C4C22×D4311yescharacteristic
303C22⋊C4—21no—
304C22⋊C4—21no—
305C22⋊C4—21no—
306C22⋊C4—861no—
307C22⋊C4—861no—
308C22⋊C4—861no—
309C22⋊C4—861no—
310C22⋊C4C22⋊D4311yescharacteristic
311C22⋊C4C22⋊D4311yescharacteristic
312C42—861no—
313C42C22×D4311yescharacteristic
314C23—21no—
315C23—21no—
316C23—21no—
317C23—42no—
318C23—42no—
319C23—42no—
320C23—42no—
321C23—81no—
322C23—81no—
323C23—861no—
324C23C2×C22⋊D4311yescharacteristic
325C23C2×C22⋊D4311yescharacteristic
326D4—22no—
327D4—21no—
328D4—21no—
329D4—21no—
330D4—21no—
331D4—21no—
332D4—42no—
333D4—42no—
334D4—42no—
335D4—42no—
336D4—42no—
337D4—81no—
338D4—861no—
339D4—861no—
340D4—3441no—
341D4—1722no—
342D4#1062190012yes—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—42no—
349C2×C4—861no—
350C2×C4—861no—
351C2×C4—861no—
352C2×C4—3441no—
353C2×C4—3441no—
354C2×C4C2×C22⋊D4311yescharacteristic
355C2×C4C2×C22⋊D4311yescharacteristic
356C2×C4C2×C22⋊D4311yescharacteristic
357C2×C4C2×C22⋊D4311yescharacteristic
358C2×C4C23×D4311yescharacteristic
359C8—861no—
360C8—861no—
361C8—861no—
362C8—861no—
363C22—21no—
364C22—21no—
365C22—21no—
366C22—21no—
367C22—21no—
368C22—22no—
369C22—41no—
370C22—41no—
371C22—41no—
372C22—41no—
373C22—41no—
374C22—41no—
375C22—41no—
376C22—41no—
377C22—84no—
378C22—84no—
379C22—1721no—
380C22—1721no—
381C22—1721no—
382C22#1306335112yes—
383C22C22×C22⋊D4311yescharacteristic
384C4—21no—
385C4—21no—
386C4—21no—
387C4—21no—
388C4—41no—
389C4—1721no—
390C4—1721no—
391C4—1721no—
392C4C2×#1062190011yescharacteristic
393C4#1306337011yescharacteristic
394C2—22no—
395C2—41no—
396C2—42no—
397C2—81no—
398C2—81no—
399C2—3441no—
400C2#1458354311yescharacteristic
401C2C2×#1306335111yescharacteristic
402C2#1458370211yescharacteristic
subgroupG/H
centerC22C22×C22⋊D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingD42×C43C2
socleC22×C43C22×D4
hypercenterD42D43
hypocenterC43#3318
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C4×D4 ◁ D42

Complements

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

NH ≅ G/Ntype
1. #14583595C2semidirect
2. #14583263C2semidirect
3. #14583220C2semidirect
4. #14583215C2semidirect
5. #14583199C2semidirect
6. #14583150C2semidirect
7. #14583133C2semidirect
8. #14583091C2semidirect
9. #14583033C2semidirect
10. #14583033C2semidirect
11. #14583009C2semidirect
12. #14582971C2semidirect
13. #14582904C2semidirect
14. C2×#13063246C2semidirect
15. D42×C43C2semidirect
17. C2×#10621882C22semidirect
18. C2×#10621882C22semidirect
19. C2×#10621877C22semidirect
20. C22×C43⋊C8C22semidirect
22. #13063317C22semidirect
24. #13063299C22semidirect
25. #13063299C22semidirect
27. C4×D172C22semidirect
29. #13063284C22semidirect
30. C2×C4⋊Dic43C22semidirect
31. #13063258C22semidirect
32. #13063256C22semidirect
33. #13063256C22semidirect
34. C4⋊(C43⋊C8)C22semidirect
38. #13063246C22semidirect
39. #13063246C22semidirect
40. #13063246C22semidirect
41. #13063246C22semidirect
42. #13063246C22semidirect
43. #13063246C22semidirect
44. #13063245C22semidirect
45. C22⋊(C43⋊C8)C22semidirect
46. C22⋊(C43⋊C8)C22semidirect
47. #13063236C22semidirect
203. D42D43semidirect
217. C43#3318semidirect