Finite Group Databasebeta

← #19146609

Subgroups — #19146609

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#14583583C211yesmaximal, characteristic, complemented
2D4×C22⋊D43C211yesmaximal, characteristic
3#14583262C211yesmaximal, characteristic, complemented
4#14583224C211yesmaximal, characteristic, complemented
5#14583211C211yesmaximal, characteristic, complemented
6#14583201C211yesmaximal, characteristic, complemented
7#14583147C211yesmaximal, characteristic, complemented
8#14583125C211yesmaximal, characteristic, complemented
9#14583097C211yesmaximal, characteristic, complemented
10#14583048C211yesmaximal, characteristic, complemented
11#14583000C211yesmaximal, characteristic, complemented
12#14582973C211yesmaximal, characteristic, complemented
13#14582904C211yesmaximal, characteristic, complemented
14#102×D43C211yesmaximal, characteristic, complemented
15C43×#450C211yesmaximal, characteristic, complemented
16C22×C22⋊D43—21no—
17C2×D4×D43C2211yescharacteristic
18C2×#10621884C2211yescharacteristic, complemented
19C2×#10621877C2211yescharacteristic, complemented
20C2×C8×D43C2211yescharacteristic, complemented
21#13063321C2211yescharacteristic
22#13063318—21no—
23#13063316C2211yescharacteristic, complemented
24#13063315—21no—
25#13063307—21no—
26#13063301C2211yescharacteristic, complemented
27#13063299C2211yescharacteristic
28#13063297—21no—
29#13063296C2211yescharacteristic
30#13063294—21no—
31#13063293—21no—
32Q8×Dic43C2211yescharacteristic, complemented
33D4×Dic43C2211yescharacteristic
34C4×C22⋊D43C2211yescharacteristic
35#13063284C2211yescharacteristic, complemented
36#13063283—21no—
37C4⋊C4×D43C2211yescharacteristic, complemented
38#13063259C2211yescharacteristic, complemented
39#13063258C2211yescharacteristic, complemented
40#13063257C2211yescharacteristic, complemented
41Dic43⋊C8C2211yescharacteristic, complemented
42#13063249C2211yescharacteristic, complemented
43#13063247C2211yescharacteristic, complemented
44#13063247C2211yescharacteristic, complemented
45#13063246C2211yescharacteristic
46#13063246C2211yescharacteristic
47#13063246C2211yescharacteristic, complemented
48#13063246C2211yescharacteristic, complemented
49#13063245C2211yescharacteristic, complemented
50(C2×D43)⋊C8C2211yescharacteristic, complemented
51#13063235C2211yescharacteristic, complemented
52C22×D4×C43C2211yescharacteristic
53C2×SD16×C43C2211yescharacteristic
54C2×SD16×C43C2211yescharacteristic, complemented
55C22⋊Q8×C43C2211yescharacteristic, complemented
56#102×C43C2211yescharacteristic
57#102×C43C2211yescharacteristic, complemented
58C22⋊C8×C43C2211yescharacteristic, complemented
59C24×C43—21no—
60C23×D43—21no—
61C2×Q8×C43C2311yescharacteristic
62C2×D4×C43—21no—
63C2×D4×C43—22no—
64C2×D4×C43—41no—
65C2×D4×C43C2311yescharacteristic
66C2×D4×C43C2311yescharacteristic
67C22×C4×C43C2311yescharacteristic
68C2×C22⋊D43—21no—
69C2×C22⋊D43—21no—
70C2×C22⋊D43—21no—
71C2×C22⋊D43—21no—
72C2×C22⋊D43—21no—
73C2×C22⋊D43—44no—
74C2×C22⋊D43D411yescharacteristic
75C22×Dic43—21no—
76D4×D43—22no—
77D4×D43—41no—
78C2×D172C2311yescharacteristic
79C2×C4×D43—21no—
80C2×C4×D43C2311yescharacteristic
81SD16×C43—22no—
82SD16×C43—41no—
83C2×C8×C43C2311yescharacteristic
84C2×C8×C43C2311yescharacteristic
85C4⋊C4×C43—21no—
86C4⋊C4×C43C2311yescharacteristic
87C22⋊C4×C43—21no—
88C22⋊Dic43—21no—
89C22⋊Dic43—21no—
90C22⋊Dic43—21no—
91C22⋊Dic43D411yescharacteristic
92#10621884—41no—
93(C2×D43)⋊C4—21no—
94(C2×D43)⋊C4—21no—
95(C2×D43)⋊C4D411yescharacteristic
96C4⋊Dic43—21no—
97C4⋊Dic43—21no—
98C4⋊Dic43C2311yescharacteristic
99C4⋊Dic43C2311yescharacteristic
100C4⋊Dic43C2311yescharacteristic
101Dic43⋊C4—21no—
102Dic43⋊C4—21no—
103Dic43⋊C4—21no—
104Dic43⋊C4D411yescharacteristic
105C4×Dic43—21no—
106C4×Dic43—21no—
107C4×Dic43C2311yescharacteristic
108#10621877—41no—
109C2×C43⋊C8C2311yescharacteristic
110C2×C43⋊C8C2311yescharacteristic
111C8×D43—41no—
112C23×C43—21no—
113C23×C43—21no—
114C23×C43—42no—
115C23×C43—42no—
116C23×C43—81no—
117C23×C43C2×D411yescharacteristic
118C22×D43—21no—
119C22×D43—42no—
120C22×D43—42no—
121C22×D43—81no—
122C22×D43C2×D411yescharacteristic
123Q8×C43—21no—
124Q8×C43—21no—
125D4×C43—21no—
126D4×C43—21no—
127D4×C43—21no—
128D4×C43—42no—
129D4×C43#4112yes—
130C2×C4×C43—21no—
131C2×C4×C43—21no—
132C2×C4×C43—21no—
133C2×C4×C43—21no—
134C2×C4×C43C2×D411yescharacteristic
135C2×C4×C43C2411yescharacteristic
136C22⋊D43—22no—
137C22⋊D43—42no—
138C22⋊D43—42no—
139C22⋊D43—42no—
140C22⋊D43—42no—
141C22⋊D43—81no—
142C2×Dic43—21no—
143C2×Dic43—21no—
144C2×Dic43—21no—
145C2×Dic43—42no—
146C2×Dic43C2×D411yescharacteristic
147C2×Dic43C2×D411yescharacteristic
148C2×Dic43C2×D411yescharacteristic
149D172—21no—
150D172—21no—
151C4×D43—21no—
152C4×D43—21no—
153C4×D43—42no—
154C8×C43—21no—
155C8×C43—21no—
156C43⋊C8—21no—
157C43⋊C8—21no—
158C22×C43—22no—
159C22×C43—21no—
160C22×C43—21no—
161C22×C43—21no—
162C22×C43—41no—
163C22×C43—41no—
164C22×C43—41no—
165C22×C43—41no—
166C22×C43—41no—
167C22×C43—84no—
168C22×C43C22×D411yescharacteristic
169C2×D43—21no—
170C2×D43—21no—
171C2×D43—41no—
172C2×D43—41no—
173C2×D43—41no—
174C2×D43—84no—
175C2×D43AGL(1,ℤ/8)12yes—
176C4×C43—21no—
177C4×C43—41no—
178C4×C43—41no—
179C4×C43C2×#4111yescharacteristic
180C4×C43H(5,𝔽2)11yescharacteristic
181Dic43—21no—
182Dic43—21no—
183Dic43—21no—
184Dic43—41no—
185Dic43—41no—
186Dic43—41no—
187#3310—431nomaximal, Sylow
188C2×C43—42no—
189C2×C43—41no—
190C2×C43—81no—
191C2×C43#54611yescharacteristic
192C2×C43C2×AGL(1,ℤ/8)11yescharacteristic
193C2×C43#57711yescharacteristic
194D43—22no—
195D43—81no—
196#552—431no—
197D42—431no—
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#450D4311yescharacteristic, complemented
207#440—431no—
208#435—431no—
209#418—431no—
210C2×#102—431no—
211C43#331011yescharacteristic, complemented, Sylow
212C22×D4—431no—
213C22×D4—861no—
214C22×D4C2×D4311yescharacteristic
215C2×SD16—431no—
216C2×SD16C2×D4311yescharacteristic
217C2×SD16C2×D4311yescharacteristic, complemented
218C2×M16—431no—
219C22×C8—431no—
220#127—431no—
221#126—861no—
222#125—431no—
223#125—861no—
224#123—861no—
225C22⋊Q8—431no—
226C22⋊Q8C2×D4311yescharacteristic, complemented
227#121—431no—
228#121—431no—
229#121—861no—
230#120—861no—
231#120—861no—
232C4×Q8—431no—
233C4×D4—431no—
234C4×D4—431no—
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#102C2×D4311yescharacteristic
251#102C2×D4311yescharacteristic, complemented
252C22⋊C8—431no—
253C22⋊C8C2×D4311yescharacteristic, complemented
254#97—431no—
255C24—21no—
256C24—861no—
257C2×Q8C22×D4311yescharacteristic
258C2×D4—22no—
259C2×D4—21no—
260C2×D4—41no—
261C2×D4—431no—
262C2×D4—431no—
263C2×D4—861no—
264C2×D4—861no—
265C2×D4—861no—
266C2×D4—862no—
267C2×D4—861no—
268C2×D4—861no—
269C2×D4—1721no—
270C2×D4—1724no—
271C2×D4C22×D4311yescharacteristic
272C2×D4C22×D4311yescharacteristic
273C22×C4—431no—
274C22×C4—861no—
275C22×C4—861no—
276C22×C4C22×D4311yescharacteristic
277SD16—22no—
278SD16—41no—
279SD16—1721no—
280M16—1721no—
281C2×C8—431no—
282C2×C8—431no—
283C2×C8—1721no—
284C2×C8C22×D4311yescharacteristic
285C2×C8C22×D4311yescharacteristic
286C4⋊C4—21no—
287C4⋊C4—431no—
288C4⋊C4—431no—
289C4⋊C4—431no—
290C4⋊C4—431no—
291C4⋊C4—861no—
292C4⋊C4—861no—
293C4⋊C4—861no—
294C4⋊C4—861no—
295C4⋊C4—861no—
296C4⋊C4C22×D4311yescharacteristic
297C22⋊C4—21no—
298C22⋊C4—431no—
299C22⋊C4—431no—
300C22⋊C4—861no—
301C22⋊C4—861no—
302C22⋊C4—861no—
303C22⋊C4—861no—
304C22⋊C4—861no—
305C42—431no—
306C42—861no—
307C42—861no—
308C23—21no—
309C23—21no—
310C23—42no—
311C23—42no—
312C23—81no—
313C23—431no—
314C23—861no—
315C23—3441no—
316C23—1722no—
317C23—1722no—
318C23D4×D4311yescharacteristic
319Q8—21no—
320Q8—21no—
321D4—21no—
322D4—21no—
323D4—21no—
324D4—42no—
325D4—862no—
326D4—861no—
327D4—861no—
328D4—3441no—
329D4—1722no—
330D4—1722no—
331D4—1722no—
332D4—1722no—
333D4#1062190012yes—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—431no—
339C2×C4—431no—
340C2×C4—431no—
341C2×C4—861no—
342C2×C4—861no—
343C2×C4—861no—
344C2×C4—861no—
345C2×C4—861no—
346C2×C4—1722no—
347C2×C4—1722no—
348C2×C4D4×D4311yescharacteristic
349C2×C4C23×D4311yescharacteristic
350C8—21no—
351C8—21no—
352C8—861no—
353C8—861no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—22no—
358C22—41no—
359C22—41no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22—84no—
364C22—432no—
365C22—861no—
366C22—861no—
367C22—3444no—
368C22—1721no—
369C22—1721no—
370C22—1721no—
371C22C2×D4×D4311yescharacteristic
372C4—21no—
373C4—41no—
374C4—41no—
375C4—861no—
376C4—861no—
377C4—861no—
378C4—1721no—
379C4—1721no—
380C4—1721no—
381C4C2×#1062190011yescharacteristic
382C4#1306337011yescharacteristic
383C2—41no—
384C2—42no—
385C2—81no—
386C2—862no—
387C2—3441no—
388C2#1458353611yescharacteristic
389C2AGL(1,ℤ/8)×D4311yescharacteristic
390C2#1458370511yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#450C2
socleC22×C43C22×D4
hypercenter#450D43
hypocenterC43#3310
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #450

Complements

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

NH ≅ G/Ntype
1. #14583583C2semidirect
3. #14583262C2semidirect
4. #14583224C2semidirect
5. #14583211C2semidirect
6. #14583201C2semidirect
7. #14583147C2semidirect
8. #14583125C2semidirect
9. #14583097C2semidirect
10. #14583048C2semidirect
11. #14583000C2semidirect
12. #14582973C2semidirect
13. #14582904C2semidirect
14. #102×D43C2semidirect
15. C43×#450C2semidirect
18. C2×#10621884C22semidirect
19. C2×#10621877C22semidirect
20. C2×C8×D43C22semidirect
23. #13063316C22semidirect
26. #13063301C22semidirect
32. Q8×Dic43C22semidirect
35. #13063284C22semidirect
37. C4⋊C4×D43C22semidirect
38. #13063259C22semidirect
39. #13063258C22semidirect
40. #13063257C22semidirect
41. Dic43⋊C8C22semidirect
42. #13063249C22semidirect
43. #13063247C22semidirect
44. #13063247C22semidirect
47. #13063246C22semidirect
48. #13063246C22semidirect
49. #13063245C22semidirect
50. (C2×D43)⋊C8C22semidirect
51. #13063235C22semidirect
54. C2×SD16×C43C22semidirect
55. C22⋊Q8×C43C22semidirect
57. #102×C43C22semidirect
58. C22⋊C8×C43C22semidirect
206. #450D43semidirect
211. C43#3310semidirect
217. C2×SD16C2×D43semidirect
226. C22⋊Q8C2×D43semidirect
251. #102C2×D43semidirect
253. C22⋊C8C2×D43semidirect