Finite Group Databasebeta

← #19146613

Subgroups — #19146613

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#14583587C211yesmaximal, characteristic, complemented
2D4×D172C211yesmaximal, characteristic
3#14583265C211yesmaximal, characteristic, complemented
4#14583225C211yesmaximal, characteristic, complemented
5#14583214C211yesmaximal, characteristic, complemented
6#14583146C211yesmaximal, characteristic, complemented
7#14583129C211yesmaximal, characteristic, complemented
8#14583100C211yesmaximal, characteristic, complemented
9#14583051C211yesmaximal, characteristic, complemented
10#14583051C211yesmaximal, characteristic, complemented
11#14582999C211yesmaximal, characteristic, complemented
12#14582969C211yesmaximal, characteristic, complemented
13#14582902C211yesmaximal, characteristic, complemented
14#102×D43C211yesmaximal, characteristic, complemented
15C43×#478C211yesmaximal, characteristic, complemented
16C22×D172—21no—
17C2×D4×D43C2211yescharacteristic
18C2×D4×D43C2211yescharacteristic
19C2×#10621873C2211yescharacteristic, complemented
20C2×#10621873C2211yescharacteristic, complemented
21C2×#10621883C2211yescharacteristic
22C2×#10621872C2211yescharacteristic, complemented
23C2×C8×D43C2211yescharacteristic, complemented
24#13063322C2211yescharacteristic
25#13063320—21no—
26#13063316—21no—
27#13063310—21no—
28#13063305C2211yescharacteristic, complemented
29#13063305C2211yescharacteristic, complemented
30#13063300C2211yescharacteristic
31#13063300C2211yescharacteristic
32#13063299—21no—
33#13063295—21no—
34#13063295—21no—
35C4×Dic86C2211yescharacteristic, complemented
36C4×D172C2211yescharacteristic
37#13063283—21no—
38#13063283C2211yescharacteristic, complemented
39C4⋊C4×D43C2211yescharacteristic, complemented
40#13063258C2211yescharacteristic, complemented
41#13063248C2211yescharacteristic, complemented
42#13063247C2211yescharacteristic, complemented
43#13063247C2211yescharacteristic, complemented
44#13063246C2211yescharacteristic
45#13063245C2211yescharacteristic, complemented
46#13063245C2211yescharacteristic, complemented
47#13063245C2211yescharacteristic, complemented
48#13063245C2211yescharacteristic, complemented
49(C2×D43)⋊C8C2211yescharacteristic, complemented
50(C2×D43)⋊C8C2211yescharacteristic, complemented
51#13063236C2211yescharacteristic, complemented
52#125×C43C2211yescharacteristic, complemented
53C4×D4×C43C2211yescharacteristic
54#107×C43C2211yescharacteristic, complemented
55#106×C43C2211yescharacteristic, complemented
56C4⋊C8×C43C2211yescharacteristic, complemented
57#102×C43C2211yescharacteristic
58#102×C43C2211yescharacteristic
59C23×D43—21no—
60C23×D43—21no—
61C2×D4×C43C2311yescharacteristic
62C22×C4×C43—21no—
63C2×C22⋊D43—21no—
64C2×C22⋊D43—21no—
65D4×D43—22no—
66D4×D43—22no—
67D4×D43—41no—
68D4×D43—41no—
69C2×D172—21no—
70C2×D172—21no—
71C2×D172—21no—
72C2×D172—21no—
73C2×D172—44no—
74C2×D172D411yescharacteristic
75C2×D172C2311yescharacteristic
76C2×D172C2311yescharacteristic
77C2×C4×D43—21no—
78C2×C4×D43C2311yescharacteristic
79C2×C4×D43C2311yescharacteristic
80C2×Dic86C2311yescharacteristic
81C2×C8×C43C2311yescharacteristic
82C2×C8×C43C2311yescharacteristic
83C4⋊C4×C43—21no—
84C4⋊C4×C43—21no—
85C4⋊C4×C43C2311yescharacteristic
86C4⋊C4×C43C2311yescharacteristic
87C4⋊C4×C43C2311yescharacteristic
88C22⋊C4×C43—21no—
89C42×C43C2311yescharacteristic
90#10621883—22no—
91(C2×D43)⋊C4—21no—
92(C2×D43)⋊C4—21no—
93(C2×D43)⋊C4—21no—
94(C2×D43)⋊C4—21no—
95(C2×D43)⋊C4—21no—
96(C2×D43)⋊C4D411yescharacteristic
97(C2×D43)⋊C4D411yescharacteristic
98C4⋊Dic43—21no—
99C4⋊Dic43—21no—
100C4⋊Dic43D411yescharacteristic
101C4⋊Dic43C2311yescharacteristic
102Dic43⋊C4—21no—
103Dic43⋊C4—21no—
104C4×Dic43—21no—
105C4×Dic43—21no—
106C2×C43⋊C8C2311yescharacteristic
107C2×C43⋊C8C2311yescharacteristic
108#10621873—41no—
109#10621873—41no—
110#10621872—41no—
111C8×D43—41no—
112C23×C43—21no—
113C22×D43—21no—
114C22×D43—21no—
115C22×D43—42no—
116C22×D43—42no—
117C22×D43—42no—
118C22×D43—42no—
119C22×D43—81no—
120C22×D43—81no—
121C22×D43C2×D411yescharacteristic
122C22×D43C2×D411yescharacteristic
123D4×C43—21no—
124D4×C43#4112yes—
125C2×C4×C43—21no—
126C2×C4×C43—21no—
127C2×C4×C43—21no—
128C2×C4×C43—42no—
129C2×C4×C43C2×D411yescharacteristic
130C2×C4×C43C2×D411yescharacteristic
131C2×C4×C43C2411yescharacteristic
132C22⋊D43—42no—
133C22⋊D43—42no—
134C2×Dic43—21no—
135C2×Dic43—21no—
136C2×Dic43C2×D411yescharacteristic
137C2×Dic43C2×D411yescharacteristic
138D172—22no—
139D172—21no—
140D172—21no—
141D172—21no—
142D172—21no—
143D172—42no—
144D172—42no—
145D172—42no—
146D172—81no—
147C4×D43—21no—
148C4×D43—21no—
149C4×D43—21no—
150C4×D43—21no—
151C4×D43—42no—
152Dic86—21no—
153Dic86—21no—
154C8×C43—21no—
155C8×C43—21no—
156C43⋊C8—21no—
157C43⋊C8—21no—
158C22×C43—22no—
159C22×C43—41no—
160C22×C43—41no—
161C22×C43C22×D411yescharacteristic
162C2×D43—21no—
163C2×D43—21no—
164C2×D43—21no—
165C2×D43—21no—
166C2×D43—21no—
167C2×D43—41no—
168C2×D43—41no—
169C2×D43—41no—
170C2×D43—41no—
171C2×D43—41no—
172C2×D43—41no—
173C2×D43—84no—
174C2×D43—84no—
175C2×D43AGL(1,ℤ/8)12yes—
176C4×C43—21no—
177C4×C43—21no—
178C4×C43—41no—
179C4×C43—41no—
180C4×C43—41no—
181C4×C43C2×#4111yescharacteristic
182C4×C43H(5,𝔽2)11yescharacteristic
183Dic43—21no—
184Dic43—21no—
185Dic43—41no—
186Dic43—41no—
187#3310—431nomaximal, Sylow
188C2×C43—42no—
189C2×C43#54611yescharacteristic
190C2×C43C2×AGL(1,ℤ/8)11yescharacteristic
191C2×C43#57711yescharacteristic
192D43—22no—
193D43—41no—
194D43—81no—
195D43—81no—
196#552—431no—
197D42—431no—
198#490—431no—
199#482—431no—
200#480—431no—
201#478D4311yescharacteristic, complemented
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—431no—
213C22×D4—431no—
214C22×D4—861no—
215C2×SD16—431no—
216C2×SD16—431no—
217C2×SD16—431no—
218C2×M16—431no—
219C22×C8—431no—
220#127—431no—
221#126—861no—
222#125—861no—
223#125C2×D4311yescharacteristic, complemented
224#123—861no—
225C22⋊Q8—431no—
226C22⋊Q8—431no—
227#121—431no—
228#121—431no—
229#121—861no—
230#120—861no—
231#120—861no—
232C4×Q8—431no—
233C4×D4—431no—
234C4×D4C2×D4311yescharacteristic
235#117—431no—
236#117—861no—
237C2×C4⋊C4—431no—
238#107—431no—
239#107C2×D4311yescharacteristic, complemented
240#106C2×D4311yescharacteristic, complemented
241C4⋊C8C2×D4311yescharacteristic, complemented
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
252C22⋊C8—431no—
253C22⋊C8—431no—
254#97—431no—
255C24—861no—
256C24—861no—
257C2×Q8—431no—
258C2×D4—431no—
259C2×D4—431no—
260C2×D4—431no—
261C2×D4—861no—
262C2×D4—861no—
263C2×D4—861no—
264C2×D4—861no—
265C2×D4—862no—
266C2×D4—862no—
267C2×D4—861no—
268C2×D4—861no—
269C2×D4—1724no—
270C2×D4—1721no—
271C2×D4—1721no—
272C2×D4C22×D4311yescharacteristic
273C22×C4—21no—
274C22×C4—431no—
275C22×C4—431no—
276C22×C4—861no—
277SD16—862no—
278SD16—1721no—
279SD16—1721no—
280M16—1721no—
281C2×C8—431no—
282C2×C8—431no—
283C2×C8—1721no—
284C2×C8C22×D4311yescharacteristic
285C2×C8C22×D4311yescharacteristic
286C4⋊C4—21no—
287C4⋊C4—21no—
288C4⋊C4—431no—
289C4⋊C4—431no—
290C4⋊C4—861no—
291C4⋊C4—861no—
292C4⋊C4—861no—
293C4⋊C4—861no—
294C4⋊C4C22×D4311yescharacteristic
295C4⋊C4C22×D4311yescharacteristic
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—861no—
306C42—861no—
307C42C22×D4311yescharacteristic
308C23—21no—
309C23—431no—
310C23—431no—
311C23—861no—
312C23—861no—
313C23—3441no—
314C23—3441no—
315C23—1722no—
316C23—1722no—
317C23—1722no—
318C23—1722no—
319Q8—861no—
320Q8—861no—
321D4—21no—
322D4—862no—
323D4—861no—
324D4—861no—
325D4—861no—
326D4—861no—
327D4—3441no—
328D4—1722no—
329D4—1722no—
330D4—1722no—
331D4—1722no—
332D4—1722no—
333D4#1062190212yes—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—42no—
338C2×C4—431no—
339C2×C4—431no—
340C2×C4—861no—
341C2×C4—861no—
342C2×C4—861no—
343C2×C4—861no—
344C2×C4—861no—
345C2×C4—861no—
346C2×C4—1722no—
347C2×C4D4×D4311yescharacteristic
348C2×C4D4×D4311yescharacteristic
349C2×C4C23×D4311yescharacteristic
350C8—21no—
351C8—21no—
352C8—861no—
353C8—861no—
354C22—22no—
355C22—41no—
356C22—41no—
357C22—432no—
358C22—861no—
359C22—861no—
360C22—861no—
361C22—861no—
362C22—861no—
363C22—3444no—
364C22—3444no—
365C22—1721no—
366C22—1721no—
367C22—1721no—
368C22—1721no—
369C22—1721no—
370C22—1721no—
371C22C2×D4×D4311yescharacteristic
372C4—21no—
373C4—21no—
374C4—41no—
375C4—41no—
376C4—41no—
377C4—861no—
378C4—861no—
379C4—1721no—
380C4—1721no—
381C4C2×#1062190211yescharacteristic
382C4#1306337111yescharacteristic
383C2—42no—
384C2—862no—
385C2—3441no—
386C2—3441no—
387C2—1721no—
388C2#1458354011yescharacteristic
389C2AGL(1,ℤ/8)×D4311yescharacteristic
390C2#1458370611yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#478C2
socleC22×C43C22×D4
hypercenter#478D43
hypocenterC43#3310
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #478

Complements

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

NH ≅ G/Ntype
1. #14583587C2semidirect
3. #14583265C2semidirect
4. #14583225C2semidirect
5. #14583214C2semidirect
6. #14583146C2semidirect
7. #14583129C2semidirect
8. #14583100C2semidirect
9. #14583051C2semidirect
10. #14583051C2semidirect
11. #14582999C2semidirect
12. #14582969C2semidirect
13. #14582902C2semidirect
14. #102×D43C2semidirect
15. C43×#478C2semidirect
19. C2×#10621873C22semidirect
20. C2×#10621873C22semidirect
22. C2×#10621872C22semidirect
23. C2×C8×D43C22semidirect
28. #13063305C22semidirect
29. #13063305C22semidirect
35. C4×Dic86C22semidirect
38. #13063283C22semidirect
39. C4⋊C4×D43C22semidirect
40. #13063258C22semidirect
41. #13063248C22semidirect
42. #13063247C22semidirect
43. #13063247C22semidirect
45. #13063245C22semidirect
46. #13063245C22semidirect
47. #13063245C22semidirect
48. #13063245C22semidirect
49. (C2×D43)⋊C8C22semidirect
50. (C2×D43)⋊C8C22semidirect
51. #13063236C22semidirect
52. #125×C43C22semidirect
54. #107×C43C22semidirect
55. #106×C43C22semidirect
56. C4⋊C8×C43C22semidirect
201. #478D43semidirect
211. C43#3310semidirect
223. #125C2×D43semidirect
239. #107C2×D43semidirect
240. #106C2×D43semidirect
241. C4⋊C8C2×D43semidirect