Finite Group Databasebeta

← #19146379

Subgroups — #19146379

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#14583715C211yesmaximal, characteristic, complemented
2#14583710C211yesmaximal, characteristic, complemented
3#14583708C211yesmaximal, characteristic, complemented
4#14583702C211yesmaximal, characteristic, complemented
5#14583281C211yesmaximal, characteristic, complemented
6#14583172C211yesmaximal, characteristic, complemented
7#14583168C211yesmaximal, characteristic, complemented
8#14583164C211yesmaximal, characteristic, complemented
9#14583161C211yesmaximal, characteristic, complemented
10#14583078C211yesmaximal, characteristic, complemented
11#14583073C211yesmaximal, characteristic, complemented
12#14583071C211yesmaximal, characteristic, complemented
13#14583013C211yesmaximal, characteristic, complemented
14#14583013C211yesmaximal, characteristic, complemented
15C43×#455C211yesmaximal, characteristic, complemented
16#13063373C2211yescharacteristic, complemented
17#13063372C2211yescharacteristic, complemented
18#13063371C2211yescharacteristic
19#13063358C2211yescharacteristic, complemented
20#13063357—21no—
21#13063357—21no—
22#13063355—21no—
23#13063355C2211yescharacteristic
24#13063354—21no—
25#13063353C2211yescharacteristic, complemented
26#13063352—21no—
27#13063351—21no—
28#13063351—21no—
29#13063351C2211yescharacteristic
30#13063351C2211yescharacteristic, complemented
31#13063350—21no—
32#13063350C2211yescharacteristic
33#13063348—21no—
34#13063346—21no—
35#13063345—21no—
36#13063345—21no—
37#13063345C2211yescharacteristic
38#13063345C2211yescharacteristic
39C2×#10621885C2211yescharacteristic, complemented
40Q16×D43—21no—
41C2×#10621883—21no—
42C2×#10621883C2211yescharacteristic, complemented
43C2×#10621884C2211yescharacteristic, complemented
44SD16×D43—21no—
45C2×#10621882—21no—
46C2×#10621882C2211yescharacteristic
47#13063333C2211yescharacteristic, complemented
48#13063333C2211yescharacteristic, complemented
49#13063332C2211yescharacteristic
50#13063332C2211yescharacteristic, complemented
51#13063313C2211yescharacteristic, complemented
52#13063260C2211yescharacteristic, complemented
53#13063260C2211yescharacteristic, complemented
54#13063253C2211yescharacteristic, complemented
55#13063253C2211yescharacteristic, complemented
56#13063244C2211yescharacteristic, complemented
57#13063243C2211yescharacteristic, complemented
58#13063241C2211yescharacteristic, complemented
59C4×C43⋊C8C2211yescharacteristic, complemented
60H(5,𝔽2)×C43C2211yescharacteristic
61#137×C43C2211yescharacteristic
62#137×C43C2211yescharacteristic, complemented
63#124×C43C2211yescharacteristic, complemented
64#104×C43C2211yescharacteristic
65#104×C43C2211yescharacteristic, complemented
66#100×C43C2211yescharacteristic, complemented
67#41×C43—21no—
68#41×C43—21no—
69#41×C43C2311yescharacteristic
70#41×C43C2311yescharacteristic
71C2×Q8×C43C2311yescharacteristic
72C2×D4×C43—21no—
73C2×D4×C43—21no—
74C2×D4×C43—41no—
75C2×D4×C43C2311yescharacteristic
76#10621902—21no—
77#10621902—21no—
78#10621902—21no—
79Q8×D43—21no—
80Q8×D43—21no—
81Q8×D43—21no—
82#10621900—21no—
83#10621900—41no—
84D4×D43—21no—
85D4×D43—41no—
86#10621898—21no—
87#10621898—21no—
88#10621898—41no—
89#10621898C2311yescharacteristic
90#10621898C2311yescharacteristic
91C2×D172—21no—
92C2×D172C2311yescharacteristic
93C2×Dic86—21no—
94C2×Dic86C2311yescharacteristic
95Q16×C43—21no—
96Q16×C43—21no—
97SD16×C43—21no—
98SD16×C43—21no—
99M16×C43C2311yescharacteristic
100M16×C43C2311yescharacteristic
101C22⋊C4×C43—41no—
102C42×C43C2311yescharacteristic
103#10621885—21no—
104#10621885—21no—
105#10621885—21no—
106#10621885D411yescharacteristic
107#10621885D411yescharacteristic
108#10621884—21no—
109#10621884—21no—
110#10621884—21no—
111#10621884D411yescharacteristic
112#10621884D411yescharacteristic
113#10621883—21no—
114#10621883—21no—
115#10621883—21no—
116#10621883—21no—
117#10621883—21no—
118#10621883D411yescharacteristic
119#10621883D411yescharacteristic
120#10621882—21no—
121#10621882—21no—
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—
145C23×C43—41no—
146C22×D43—21no—
147C22×D43—41no—
148Q8×C43—21no—
149Q8×C43—21no—
150Q8×C43C2×D411yescharacteristic
151Q8×C43C2×D411yescharacteristic
152D4×C43—21no—
153D4×C43—21no—
154D4×C43—21no—
155D4×C43—21no—
156D4×C43—41no—
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×C43C2411yescharacteristic
166C22⋊D43—21no—
167C22⋊D43—21no—
168C22⋊D43—41no—
169C22⋊D43—41no—
170C2×Dic43—21no—
171C2×Dic43—41no—
172D172—21no—
173D172—21no—
174D172—41no—
175D172—41no—
176D172C2×D411yescharacteristic
177D172C2×D411yescharacteristic
178C4×D43—21no—
179C4×D43—21no—
180C4×D43—41no—
181C4×D43—41no—
182C4×D43—41no—
183C4×D43—41no—
184Dic86—21no—
185Dic86—21no—
186Dic86—41no—
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×C43—161no—
203C22×C43H(5,𝔽2)11yescharacteristic
204C2×D43—21no—
205C2×D43—21no—
206C2×D43—41no—
207C2×D43—81no—
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#455D4311yescharacteristic, complemented
238#454—431no—
239#454—431no—
240#443—431no—
241#443—431no—
242C43#329011yescharacteristic, complemented, Sylow
2432−1+4—431no—
2442−1+4—431no—
245H(5,𝔽2)—431no—
246H(5,𝔽2)C2×D4311yescharacteristic
247#137—431no—
248#137—431no—
249#137—861no—
250#137—861no—
251#137—861no—
252#137—861no—
253#137C2×D4311yescharacteristic
254#137C2×D4311yescharacteristic, complemented
255AGL(1,ℤ/8)—431no—
256AGL(1,ℤ/8)—431no—
257AGL(1,ℤ/8)—431no—
258AGL(1,ℤ/8)—431no—
259AGL(1,ℤ/8)—861no—
260AGL(1,ℤ/8)—861no—
261AGL(1,ℤ/8)—861no—
262AGL(1,ℤ/8)—861no—
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
288#104C2×D4311yescharacteristic, complemented
289#101—431no—
290#101—431no—
291#100—431no—
292#100C2×D4311yescharacteristic, complemented
293C4×C8—431no—
294#41—21no—
295#41—21no—
296#41—431no—
297#41—431no—
298#41—861no—
299#41—861no—
300#41—861no—
301#41—861no—
302#41—861no—
303#41—861no—
304#41—1721no—
305#41—1721no—
306#41C22×D4311yescharacteristic
307#41C22×D4311yescharacteristic
308C2×Q8—431no—
309C2×Q8—861no—
310C2×Q8—861no—
311C2×Q8—861no—
312C2×Q8—861no—
313C2×Q8C22×D4311yescharacteristic
314C2×D4—21no—
315C2×D4—21no—
316C2×D4—41no—
317C2×D4—431no—
318C2×D4—861no—
319C2×D4—861no—
320C2×D4—1721no—
321C2×D4C22×D4311yescharacteristic
322Q16—21no—
323Q16—21no—
324Q16—431no—
325Q16—431no—
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—431no—
347D8—431no—
348D8—861no—
349D8—861no—
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—41no—
373C23—861no—
374C23—1721no—
375Q8—21no—
376Q8—21no—
377Q8—431no—
378Q8—431no—
379Q8—861no—
380Q8—861no—
381Q8—1721no—
382Q8—1721no—
383Q8D4×D4311yescharacteristic
384Q8D4×D4311yescharacteristic
385D4—21no—
386D4—21no—
387D4—21no—
388D4—21no—
389D4—41no—
390D4—41no—
391D4—431no—
392D4—431no—
393D4—861no—
394D4—861no—
395D4—861no—
396D4—861no—
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—861no—
409C2×C4—861no—
410C2×C4—861no—
411C2×C4—1721no—
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—161no—
430C22—861no—
431C22—861no—
432C22—3441no—
433C22—1721no—
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×#455C2
socleC2×C43D42
hypercenter#455D43
hypocenterC43#3290
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C2×C4 ◁ #455

Complements

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

NH ≅ G/Ntype
1. #14583715C2semidirect
2. #14583710C2semidirect
3. #14583708C2semidirect
4. #14583702C2semidirect
5. #14583281C2semidirect
6. #14583172C2semidirect
7. #14583168C2semidirect
8. #14583164C2semidirect
9. #14583161C2semidirect
10. #14583078C2semidirect
11. #14583073C2semidirect
12. #14583071C2semidirect
13. #14583013C2semidirect
14. #14583013C2semidirect
15. C43×#455C2semidirect
16. #13063373C22semidirect
17. #13063372C22semidirect
19. #13063358C22semidirect
25. #13063353C22semidirect
30. #13063351C22semidirect
39. C2×#10621885C22semidirect
42. C2×#10621883C22semidirect
43. C2×#10621884C22semidirect
47. #13063333C22semidirect
48. #13063333C22semidirect
50. #13063332C22semidirect
51. #13063313C22semidirect
52. #13063260C22semidirect
53. #13063260C22semidirect
54. #13063253C22semidirect
55. #13063253C22semidirect
56. #13063244C22semidirect
57. #13063243C22semidirect
58. #13063241C22semidirect
59. C4×C43⋊C8C22semidirect
62. #137×C43C22semidirect
63. #124×C43C22semidirect
65. #104×C43C22semidirect
66. #100×C43C22semidirect
237. #455D43semidirect
242. C43#3290semidirect
254. #137C2×D43semidirect
282. #124C2×D43semidirect
288. #104C2×D43semidirect
292. #100C2×D43semidirect