Finite Group Databasebeta

← #19146374

Subgroups — #19146374

Order 5504.

454 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14583714C211yesmaximal, characteristic, complemented
2#14583709C211yesmaximal, characteristic, complemented
3#14583707C211yesmaximal, characteristic, complemented
4#14583703C211yesmaximal, characteristic, complemented
5#14583281C211yesmaximal, characteristic, complemented
6#14583173C211yesmaximal, characteristic, complemented
7#14583167C211yesmaximal, characteristic, complemented
8#14583165C211yesmaximal, characteristic, complemented
9#14583160C211yesmaximal, characteristic, complemented
10#14583078C211yesmaximal, characteristic, complemented
11#14583076C211yesmaximal, characteristic, complemented
12#14583073C211yesmaximal, characteristic, complemented
13#14583013C211yesmaximal, characteristic, complemented
14#14583013C211yesmaximal, characteristic, complemented
15C43×#454C211yesmaximal, characteristic, complemented
16#13063372C2211yescharacteristic, complemented
17#13063371C2211yescharacteristic
18#13063370C2211yescharacteristic
19#13063358C2211yescharacteristic
20#13063356—21no—
21#13063356—21no—
22#13063356C2211yescharacteristic
23#13063356C2211yescharacteristic, complemented
24#13063355—21no—
25#13063355C2211yescharacteristic, complemented
26#13063354—21no—
27#13063353C2211yescharacteristic
28#13063352—21no—
29#13063350—21no—
30#13063350C2211yescharacteristic, complemented
31#13063349—21no—
32#13063349—21no—
33#13063346—21no—
34#13063345—21no—
35#13063345—21no—
36#13063345C2211yescharacteristic
37#13063345C2211yescharacteristic
38#13063344—21no—
39C2×#10621885—21no—
40C2×#10621885C2211yescharacteristic, complemented
41C2×#10621883C2211yescharacteristic, complemented
42C2×#10621884—21no—
43C2×#10621884C2211yescharacteristic, complemented
44SD16×D43—21no—
45C2×#10621882C2211yescharacteristic
46D8×D43—21no—
47#13063333C2211yescharacteristic
48#13063333C2211yescharacteristic, complemented
49#13063332C2211yescharacteristic, complemented
50#13063332C2211yescharacteristic, complemented
51#13063313C2211yescharacteristic, complemented
52#13063260C2211yescharacteristic, complemented
53#13063260C2211yescharacteristic, complemented
54#13063253C2211yescharacteristic
55#13063253C2211yescharacteristic, complemented
56#13063243C2211yescharacteristic, complemented
57#13063242C2211yescharacteristic, complemented
58#13063241C2211yescharacteristic, complemented
59C4×C43⋊C8C2211yescharacteristic, complemented
602−1+4×C43C2211yescharacteristic, complemented
61AGL(1,ℤ/8)×C43C2211yescharacteristic
62AGL(1,ℤ/8)×C43C2211yescharacteristic, complemented
63#124×C43C2211yescharacteristic, complemented
64#104×C43C2211yescharacteristic, complemented
65#104×C43C2211yescharacteristic, complemented
66#101×C43C2211yescharacteristic, complemented
67#41×C43—21no—
68#41×C43—21no—
69#41×C43—41no—
70#41×C43C2311yescharacteristic
71#41×C43C2311yescharacteristic
72C2×Q8×C43—21no—
73C2×Q8×C43—21no—
74C2×Q8×C43C2311yescharacteristic
75C2×D4×C43C2311yescharacteristic
76C2×C22⋊D43—41no—
77#10621902—21no—
78Q8×D43—21no—
79#10621900—21no—
80#10621900—21no—
81#10621900—21no—
82#10621900—41no—
83D4×D43—21no—
84D4×D43—21no—
85D4×D43—21no—
86D4×D43—41no—
87#10621898—21no—
88#10621898—21no—
89#10621898C2311yescharacteristic
90#10621898C2311yescharacteristic
91C2×D172—21no—
92C2×D172C2311yescharacteristic
93C2×Dic86—21no—
94C2×Dic86C2311yescharacteristic
95SD16×C43—21no—
96SD16×C43—21no—
97D8×C43—21no—
98D8×C43—21no—
99M16×C43C2311yescharacteristic
100M16×C43C2311yescharacteristic
101C22⋊C4×C43—41no—
102C42×C43C2311yescharacteristic
103#10621885—21no—
104#10621885—21no—
105#10621885—21no—
106#10621885—21no—
107#10621885—21no—
108#10621885D411yescharacteristic
109#10621885D411yescharacteristic
110#10621884—21no—
111#10621884—21no—
112#10621884—21no—
113#10621884—21no—
114#10621884—21no—
115#10621884D411yescharacteristic
116#10621884D411yescharacteristic
117#10621883—21no—
118#10621883—21no—
119#10621883—21no—
120#10621883D411yescharacteristic
121#10621883D411yescharacteristic
122#10621882—21no—
123#10621882—21no—
124#10621882—21no—
125#10621882D411yescharacteristic
126#10621882D411yescharacteristic
127(C2×D43)⋊C4—41no—
128#10621877—21no—
129#10621877—21no—
130#10621877C2311yescharacteristic
131#10621877C2311yescharacteristic
132C2×C43⋊C8—21no—
133C2×C43⋊C8—21no—
134C2×C43⋊C8C2311yescharacteristic
135C2×C43⋊C8C2311yescharacteristic
136Dic172—21no—
137D344—21no—
138#10621873—21no—
139#10621873—21no—
140#10621872—21no—
141#10621872—21no—
142C8×D43—21no—
143C8×D43—21no—
144C23×C43—21no—
145C22×D43—21no—
146C22×D43—41no—
147C22×D43—41no—
148Q8×C43—21no—
149Q8×C43—21no—
150Q8×C43—41no—
151Q8×C43C2×D411yescharacteristic
152Q8×C43C2×D411yescharacteristic
153D4×C43—21no—
154D4×C43—21no—
155D4×C43—21no—
156D4×C43—21no—
157D4×C43—41no—
158D4×C43C2×D411yescharacteristic
159D4×C43C2×D411yescharacteristic
160C2×C4×C43—21no—
161C2×C4×C43—21no—
162C2×C4×C43—21no—
163C2×C4×C43—21no—
164C2×C4×C43—41no—
165C2×C4×C43—41no—
166C2×C4×C43C2411yescharacteristic
167C22⋊D43—21no—
168C22⋊D43—21no—
169C22⋊D43—41no—
170C22⋊D43—41no—
171C22⋊D43—41no—
172C22⋊D43—41no—
173C2×Dic43—21no—
174C2×Dic43—41no—
175C2×Dic43—41no—
176D172—21no—
177D172—21no—
178D172—41no—
179D172C2×D411yescharacteristic
180D172C2×D411yescharacteristic
181C4×D43—21no—
182C4×D43—21no—
183C4×D43—41no—
184C4×D43—41no—
185Dic86—21no—
186Dic86—21no—
187Dic86—41no—
188Dic86C2×D411yescharacteristic
189Dic86C2×D411yescharacteristic
190C8×C43—21no—
191C8×C43—21no—
192C43⋊C8—21no—
193C43⋊C8—21no—
194C43⋊C8C2×D411yescharacteristic
195C43⋊C8C2×D411yescharacteristic
196C43⋊C8C2×D411yescharacteristic
197C43⋊C8C2×D411yescharacteristic
198C22×C43—21no—
199C22×C43—21no—
200C22×C43—41no—
201C22×C43—81no—
202C22×C43H(5,𝔽2)11yescharacteristic
203C2×D43—21no—
204C2×D43—21no—
205C2×D43—41no—
206C2×D43—81no—
207C2×D43—161no—
208C2×D43—161no—
209C4×C43—21no—
210C4×C43—21no—
211C4×C43—41no—
212C4×C43—41no—
213C4×C43C22×D411yescharacteristic
214C4×C43C22×D411yescharacteristic
215Dic43—21no—
216Dic43—21no—
217Dic43—41no—
218#3290—431nomaximal, Sylow
219C2×C43—21no—
220C2×C43—41no—
221C2×C43—41no—
222C2×C43—81no—
223C2×C43D4211yescharacteristic
224D43—41no—
225D43—41no—
226D43—81no—
227#578—431no—
228#577—431no—
229#577—431no—
230#576—431no—
231#495—431no—
232#473—431no—
233#472—431no—
234#471—431no—
235#471—431no—
236#455—431no—
237#455—431no—
238#454—431no—
239#454D4311yescharacteristic, complemented
240#443—431no—
241#443—431no—
242C43#329011yescharacteristic, complemented, Sylow
2432−1+4—431no—
2442−1+4C2×D4311yescharacteristic, complemented
245H(5,𝔽2)—431no—
246H(5,𝔽2)—431no—
247#137—431no—
248#137—431no—
249#137—431no—
250#137—431no—
251#137—861no—
252#137—861no—
253#137—861no—
254#137—861no—
255AGL(1,ℤ/8)—431no—
256AGL(1,ℤ/8)—431no—
257AGL(1,ℤ/8)—861no—
258AGL(1,ℤ/8)—861no—
259AGL(1,ℤ/8)—861no—
260AGL(1,ℤ/8)—861no—
261AGL(1,ℤ/8)C2×D4311yescharacteristic
262AGL(1,ℤ/8)C2×D4311yescharacteristic, complemented
263#135—431no—
264#135—431no—
265#135—861no—
266#135—861no—
267#135—861no—
268#135—861no—
269C2×Q16—431no—
270C2×Q16—861no—
271C2×SD16—431no—
272C2×SD16—431no—
273C2×SD16—861no—
274C2×SD16—861no—
275C2×D8—431no—
276C2×D8—861no—
277#131—431no—
278#131—431no—
279#131—431no—
280#131—431no—
281#124—431no—
282#124C2×D4311yescharacteristic, complemented
283#108—431no—
284#108—431no—
285#104—431no—
286#104—431no—
287#104C2×D4311yescharacteristic, complemented
288#104C2×D4311yescharacteristic, complemented
289#101—431no—
290#101C2×D4311yescharacteristic, complemented
291#100—431no—
292#100—431no—
293C4×C8—431no—
294#41—21no—
295#41—21no—
296#41—41no—
297#41—431no—
298#41—431no—
299#41—861no—
300#41—861no—
301#41—861no—
302#41—861no—
303#41—861no—
304#41—861no—
305#41—1721no—
306#41C22×D4311yescharacteristic
307#41C22×D4311yescharacteristic
308C2×Q8—21no—
309C2×Q8—21no—
310C2×Q8—431no—
311C2×Q8—861no—
312C2×Q8—861no—
313C2×Q8C22×D4311yescharacteristic
314C2×D4—431no—
315C2×D4—861no—
316C2×D4—861no—
317C2×D4—861no—
318C2×D4—861no—
319C2×D4—1721no—
320C2×D4—1721no—
321C2×D4C22×D4311yescharacteristic
322Q16—431no—
323Q16—431no—
324Q16—861no—
325Q16—861no—
326Q16—861no—
327Q16—861no—
328Q16—861no—
329Q16—861no—
330SD16—21no—
331SD16—21no—
332SD16—431no—
333SD16—431no—
334SD16—431no—
335SD16—431no—
336SD16—861no—
337SD16—861no—
338SD16—861no—
339SD16—861no—
340SD16—861no—
341SD16—861no—
342SD16—861no—
343SD16—861no—
344SD16—861no—
345SD16—861no—
346D8—21no—
347D8—21no—
348D8—431no—
349D8—431no—
350D8—861no—
351D8—861no—
352D8—861no—
353D8—861no—
354M16—431no—
355M16—431no—
356M16—861no—
357M16—861no—
358M16—861no—
359M16—861no—
360M16C22×D4311yescharacteristic
361M16C22×D4311yescharacteristic
362C2×C8—431no—
363C2×C8—431no—
364C2×C8—861no—
365C2×C8—861no—
366C2×C8—861no—
367C2×C8—861no—
368C22⋊C4—41no—
369C22⋊C4—1721no—
370C42C22×D4311yescharacteristic
371C23—21no—
372C23—861no—
373C23—1721no—
374C23—1721no—
375Q8—21no—
376Q8—21no—
377Q8—41no—
378Q8—431no—
379Q8—431no—
380Q8—861no—
381Q8—861no—
382Q8—1721no—
383Q8D4×D4311yescharacteristic
384Q8D4×D4311yescharacteristic
385D4—21no—
386D4—21no—
387D4—21no—
388D4—21no—
389D4—41no—
390D4—431no—
391D4—431no—
392D4—861no—
393D4—861no—
394D4—861no—
395D4—861no—
396D4—1721no—
397D4—1721no—
398D4—1721no—
399D4—1721no—
400D4—1721no—
401D4D4×D4311yescharacteristic
402D4D4×D4311yescharacteristic
403C2×C4—21no—
404C2×C4—21no—
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—41no—
408C2×C4—41no—
409C2×C4—861no—
410C2×C4—861no—
411C2×C4—861no—
412C2×C4—1721no—
413C2×C4—1721no—
414C2×C4—1721no—
415C2×C4—1721no—
416C2×C4C23×D4311yescharacteristic
417C8—21no—
418C8—21no—
419C8—431no—
420C8—431no—
421C8—431no—
422C8—431no—
423C8—861no—
424C8—861no—
425C22—21no—
426C22—21no—
427C22—41no—
428C22—81no—
429C22—861no—
430C22—861no—
431C22—3441no—
432C22—1721no—
433C22—6881no—
434C22—6881no—
435C22#1306337011yescharacteristic
436C4—21no—
437C4—21no—
438C4—41no—
439C4—41no—
440C4—861no—
441C4—861no—
442C4—1721no—
443C4C2×D4×D4311yescharacteristic
444C4C2×D4×D4311yescharacteristic
445C2—21no—
446C2—41no—
447C2—41no—
448C2—81no—
449C2—3441no—
450C2—1721no—
451C2—1721no—
452C2#1458353111yescharacteristic
subgroupG/H
centerC2#14583531
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#454C2
socleC2×C43D42
hypercenter#454D43
hypocenterC43#3290
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C2×C4 ◁ #454

Complements

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

NH ≅ G/Ntype
1. #14583714C2semidirect
2. #14583709C2semidirect
3. #14583707C2semidirect
4. #14583703C2semidirect
5. #14583281C2semidirect
6. #14583173C2semidirect
7. #14583167C2semidirect
8. #14583165C2semidirect
9. #14583160C2semidirect
10. #14583078C2semidirect
11. #14583076C2semidirect
12. #14583073C2semidirect
13. #14583013C2semidirect
14. #14583013C2semidirect
15. C43×#454C2semidirect
16. #13063372C22semidirect
23. #13063356C22semidirect
25. #13063355C22semidirect
30. #13063350C22semidirect
40. C2×#10621885C22semidirect
41. C2×#10621883C22semidirect
43. C2×#10621884C22semidirect
48. #13063333C22semidirect
49. #13063332C22semidirect
50. #13063332C22semidirect
51. #13063313C22semidirect
52. #13063260C22semidirect
53. #13063260C22semidirect
55. #13063253C22semidirect
56. #13063243C22semidirect
57. #13063242C22semidirect
58. #13063241C22semidirect
59. C4×C43⋊C8C22semidirect
60. 2−1+4×C43C22semidirect
62. AGL(1,ℤ/8)×C43C22semidirect
63. #124×C43C22semidirect
64. #104×C43C22semidirect
65. #104×C43C22semidirect
66. #101×C43C22semidirect
239. #454D43semidirect
242. C43#3290semidirect
244. 2−1+4C2×D43semidirect
262. AGL(1,ℤ/8)C2×D43semidirect
282. #124C2×D43semidirect
287. #104C2×D43semidirect
288. #104C2×D43semidirect
290. #101C2×D43semidirect