Finite Group Databasebeta

← #19146616

Subgroups — #19146616

Order 5504.

450 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14583589C211yesmaximal, characteristic, complemented
2#14583263C211yesmaximal, characteristic, complemented
3#14583220C211yesmaximal, characteristic, complemented
4#14583210C211yesmaximal, characteristic, complemented
5#14583199C211yesmaximal, characteristic, complemented
6#14583143C211yesmaximal, characteristic, complemented
7#14583126C211yesmaximal, characteristic, complemented
8#14583096C211yesmaximal, characteristic, complemented
9#14583050C211yesmaximal, characteristic, complemented
10#14583050C211yesmaximal, characteristic, complemented
11#14582999C211yesmaximal, characteristic, complemented
12#14582971C211yesmaximal, characteristic, complemented
13#14582904C211yesmaximal, characteristic, complemented
14C2×#13063246C211yesmaximal, characteristic, complemented
15D42×C43C211yesmaximal, characteristic
16C2×#10621883C2211yescharacteristic
17C2×#10621883C2211yescharacteristic, complemented
18C2×#10621883C2211yescharacteristic, complemented
19C2×#10621877C2211yescharacteristic, complemented
20C22×C43⋊C8C2211yescharacteristic, complemented
21#13063318—21no—
22#13063317C2211yescharacteristic, complemented
23#13063315—21no—
24#13063306—21no—
25#13063304C2211yescharacteristic, complemented
26#13063304C2211yescharacteristic, complemented
27C4×Dic86C2211yescharacteristic, complemented
28#13063284C2211yescharacteristic, complemented
29#13063281—21no—
30C2×C4⋊Dic43C2211yescharacteristic, complemented
31#13063258C2211yescharacteristic, complemented
32#13063258C2211yescharacteristic, complemented
33#13063256C2211yescharacteristic, complemented
34C4⋊(C43⋊C8)C2211yescharacteristic, complemented
35#13063248C2211yescharacteristic, complemented
36#13063246C2211yescharacteristic
37#13063246C2211yescharacteristic
38#13063246C2211yescharacteristic
39#13063246C2211yescharacteristic, complemented
40#13063246C2211yescharacteristic, complemented
41#13063246C2211yescharacteristic, complemented
42#13063246C2211yescharacteristic, complemented
43#13063246C2211yescharacteristic, complemented
44#13063246C2211yescharacteristic, 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
79C22×Dic43—21no—
80C2×Dic86C2311yescharacteristic
81C4⋊C4×C43D411yescharacteristic
82C4⋊C4×C43C2311yescharacteristic
83C22⋊C4×C43—21no—
84C22⋊C4×C43—21no—
85C22⋊C4×C43—21no—
86C22⋊C4×C43D411yescharacteristic
87C22⋊C4×C43D411yescharacteristic
88C42×C43C2311yescharacteristic
89C22⋊Dic43—21no—
90C22⋊Dic43—21no—
91C22⋊Dic43—21no—
92#10621883—22no—
93#10621883—41no—
94#10621883—41no—
95C4⋊Dic43—21no—
96C4⋊Dic43C2311yescharacteristic
97C4⋊Dic43C2311yescharacteristic
98C4⋊Dic43C2311yescharacteristic
99Dic43⋊C4—21no—
100Dic43⋊C4—21no—
101Dic43⋊C4—21no—
102Dic43⋊C4—21no—
103Dic43⋊C4—21no—
104C4×Dic43—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
123D4×C43—22no—
124D4×C43—21no—
125D4×C43—21no—
126D4×C43—21no—
127D4×C43—21no—
128D4×C43—21no—
129D4×C43—42no—
130D4×C43—42no—
131D4×C43—42no—
132D4×C43—42no—
133D4×C43—42no—
134D4×C43—81no—
135D4×C43#4112yes—
136C2×C4×C43—21no—
137C2×C4×C43—21no—
138C2×C4×C43—21no—
139C2×C4×C43—21no—
140C2×C4×C43—21no—
141C2×C4×C43—42no—
142C2×C4×C43C2×D411yescharacteristic
143C2×C4×C43C2×D411yescharacteristic
144C2×C4×C43C2×D411yescharacteristic
145C2×C4×C43C2×D411yescharacteristic
146C2×C4×C43C2411yescharacteristic
147C2×Dic43—21no—
148C2×Dic43—21no—
149C2×Dic43—21no—
150C2×Dic43—21no—
151C2×Dic43—42no—
152Dic86—21no—
153Dic86—21no—
154C43⋊C8—21no—
155C43⋊C8—21no—
156C43⋊C8—21no—
157C43⋊C8—21no—
158C22×C43—21no—
159C22×C43—21no—
160C22×C43—22no—
161C22×C43—21no—
162C22×C43—21no—
163C22×C43—21no—
164C22×C43—41no—
165C22×C43—41no—
166C22×C43—41no—
167C22×C43—41no—
168C22×C43—41no—
169C22×C43—41no—
170C22×C43—41no—
171C22×C43—41no—
172C22×C43—84no—
173C22×C43—84no—
174C22×C43AGL(1,ℤ/8)12yes—
175C22×C43C22×D411yescharacteristic
176C4×C43—21no—
177C4×C43—21no—
178C4×C43—21no—
179C4×C43—21no—
180C4×C43—41no—
181C4×C43C2×#4111yescharacteristic
182C4×C43H(5,𝔽2)11yescharacteristic
183Dic43—41no—
184Dic43—41no—
185Dic43—41no—
186Dic43—41no—
187#3310—431nomaximal, Sylow
188C2×C43—22no—
189C2×C43—41no—
190C2×C43—42no—
191C2×C43—81no—
192C2×C43—81no—
193C2×C43#54611yescharacteristic
194C2×C43C2×AGL(1,ℤ/8)11yescharacteristic
195C2×C43#57711yescharacteristic
196#552—431no—
197D42D4311yescharacteristic
198#490—431no—
199#482—431no—
200#480—431no—
201#478—431no—
202#468—431no—
203#465—431no—
204#460—431no—
205#450—431no—
206#450—431no—
207#440—431no—
208#435—431no—
209#418—431no—
210C2×#102—431no—
211C43#331011yescharacteristic, complemented, Sylow
212C22×D4—21no—
213C22×D4C2×D4311yescharacteristic
214C22×D4C2×D4311yescharacteristic
215C2×SD16—431no—
216C2×SD16—431no—
217C2×SD16—431no—
218C2×M16—431no—
219C22×C8—431no—
220#127C2×D4311yescharacteristic
221#126—861no—
222#125—431no—
223#125—861no—
224#123—861no—
225C22⋊Q8—431no—
226C22⋊Q8—431no—
227#121—21no—
228#121C2×D4311yescharacteristic
229#121C2×D4311yescharacteristic
230#120—21no—
231#120—21no—
232C4×Q8—431no—
233C4×D4C2×D4311yescharacteristic
234C4×D4C2×D4311yescharacteristic
235#117—431no—
236#117—861no—
237C2×C4⋊C4—431no—
238#107—431no—
239#107—431no—
240#106—431no—
241C4⋊C8—431no—
242#103—431no—
243#102—431no—
244#102—431no—
245#102—431no—
246#102—431no—
247#102—431no—
248#102—431no—
249#102—431no—
250#102—431no—
251#102—431no—
252C22⋊C8—431no—
253C22⋊C8—431no—
254#97—431no—
255C24—21no—
256C24—21no—
257C2×Q8—431no—
258C2×D4—22no—
259C2×D4—22no—
260C2×D4—21no—
261C2×D4—21no—
262C2×D4—21no—
263C2×D4—21no—
264C2×D4—21no—
265C2×D4—21no—
266C2×D4—41no—
267C2×D4—41no—
268C2×D4—44no—
269C2×D4C22⋊D4311yescharacteristic
270C2×D4C22×D4311yescharacteristic
271C2×D4C22×D4311yescharacteristic
272C2×D4C22×D4311yescharacteristic
273C22×C4—21no—
274C22×C4—861no—
275C22×C4C22×D4311yescharacteristic
276C22×C4C22×D4311yescharacteristic
277SD16—862no—
278SD16—1721no—
279SD16—1721no—
280M16—1721no—
281C2×C8—431no—
282C2×C8—431no—
283C2×C8—431no—
284C2×C8—431no—
285C2×C8—1721no—
286C4⋊C4—431no—
287C4⋊C4—431no—
288C4⋊C4—431no—
289C4⋊C4—861no—
290C4⋊C4—861no—
291C4⋊C4—861no—
292C4⋊C4—861no—
293C4⋊C4—861no—
294C4⋊C4—861no—
295C4⋊C4C22⋊D4311yescharacteristic
296C4⋊C4C22×D4311yescharacteristic
297C22⋊C4—21no—
298C22⋊C4—21no—
299C22⋊C4—21no—
300C22⋊C4—861no—
301C22⋊C4—861no—
302C22⋊C4—861no—
303C22⋊C4C22⋊D4311yescharacteristic
304C22⋊C4C22⋊D4311yescharacteristic
305C42—861no—
306C42—861no—
307C42C22×D4311yescharacteristic
308C23—21no—
309C23—21no—
310C23—21no—
311C23—42no—
312C23—42no—
313C23—42no—
314C23—42no—
315C23—81no—
316C23—81no—
317C23C2×C22⋊D4311yescharacteristic
318C23C2×C22⋊D4311yescharacteristic
319Q8—861no—
320Q8—861no—
321D4—22no—
322D4—21no—
323D4—21no—
324D4—21no—
325D4—21no—
326D4—21no—
327D4—42no—
328D4—42no—
329D4—42no—
330D4—42no—
331D4—42no—
332D4—81no—
333D4#1062190012yes—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—42no—
340C2×C4—861no—
341C2×C4—861no—
342C2×C4—861no—
343C2×C4—861no—
344C2×C4—1722no—
345C2×C4C2×C22⋊D4311yescharacteristic
346C2×C4C2×C22⋊D4311yescharacteristic
347C2×C4C2×C22⋊D4311yescharacteristic
348C2×C4C2×C22⋊D4311yescharacteristic
349C2×C4C23×D4311yescharacteristic
350C8—861no—
351C8—861no—
352C8—861no—
353C8—861no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—21no—
358C22—21no—
359C22—22no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22—41no—
364C22—41no—
365C22—41no—
366C22—41no—
367C22—41no—
368C22—84no—
369C22—84no—
370C22#1306335112yes—
371C22C22×C22⋊D4311yescharacteristic
372C4—21no—
373C4—21no—
374C4—21no—
375C4—21no—
376C4—41no—
377C4—1721no—
378C4—1721no—
379C4—1721no—
380C4—1721no—
381C4C2×#1062190011yescharacteristic
382C4#1306337011yescharacteristic
383C2—22no—
384C2—41no—
385C2—42no—
386C2—81no—
387C2—81no—
388C2#1458354311yescharacteristic
389C2C2×#1306335111yescharacteristic
390C2#1458371011yescharacteristic
subgroupG/H
centerC22C22×C22⋊D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingD42×C43C2
socleC22×C43C22×D4
hypercenterD42D43
hypocenterC43#3310
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. #14583589C2semidirect
2. #14583263C2semidirect
3. #14583220C2semidirect
4. #14583210C2semidirect
5. #14583199C2semidirect
6. #14583143C2semidirect
7. #14583126C2semidirect
8. #14583096C2semidirect
9. #14583050C2semidirect
10. #14583050C2semidirect
11. #14582999C2semidirect
12. #14582971C2semidirect
13. #14582904C2semidirect
14. C2×#13063246C2semidirect
17. C2×#10621883C22semidirect
18. C2×#10621883C22semidirect
19. C2×#10621877C22semidirect
20. C22×C43⋊C8C22semidirect
22. #13063317C22semidirect
25. #13063304C22semidirect
26. #13063304C22semidirect
27. C4×Dic86C22semidirect
28. #13063284C22semidirect
30. C2×C4⋊Dic43C22semidirect
31. #13063258C22semidirect
32. #13063258C22semidirect
33. #13063256C22semidirect
34. C4⋊(C43⋊C8)C22semidirect
35. #13063248C22semidirect
39. #13063246C22semidirect
40. #13063246C22semidirect
41. #13063246C22semidirect
42. #13063246C22semidirect
43. #13063246C22semidirect
44. #13063246C22semidirect
45. C22⋊(C43⋊C8)C22semidirect
46. C22⋊(C43⋊C8)C22semidirect
47. #13063236C22semidirect
211. C43#3310semidirect