Finite Group Databasebeta

← #19146378

Subgroups — #19146378

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#14583711C211yesmaximal, characteristic, complemented
3#14583705C211yesmaximal, characteristic, complemented
4#14583703C211yesmaximal, characteristic, complemented
5#14583280C211yesmaximal, characteristic, complemented
6#14583173C211yesmaximal, characteristic, complemented
7#14583168C211yesmaximal, characteristic, complemented
8#14583163C211yesmaximal, characteristic, complemented
9#14583079C211yesmaximal, characteristic, complemented
10#14583075C211yesmaximal, characteristic, complemented
11#14583074C211yesmaximal, characteristic, complemented
12#14583070C211yesmaximal, characteristic, complemented
13#14583015C211yesmaximal, characteristic, complemented
14#14583014C211yesmaximal, characteristic, complemented
15C43×#471C211yesmaximal, characteristic, complemented
16#13063373C2211yescharacteristic, complemented
17#13063372C2211yescharacteristic, complemented
18#13063371C2211yescharacteristic
19#13063370C2211yescharacteristic
20#13063358—21no—
21#13063358C2211yescharacteristic
22#13063358C2211yescharacteristic, complemented
23#13063357—21no—
24#13063356C2211yescharacteristic
25#13063354—21no—
26#13063354—21no—
27#13063353—21no—
28#13063353C2211yescharacteristic
29#13063353C2211yescharacteristic, complemented
30#13063352—21no—
31#13063352—21no—
32#13063351C2211yescharacteristic, complemented
33#13063349—21no—
34#13063347—21no—
35#13063347C2211yescharacteristic
36#13063346—21no—
37#13063346—21no—
38#13063346—21no—
39#13063345C2211yescharacteristic
40C2×#10621885C2211yescharacteristic, complemented
41Q16×D43—21no—
42C2×#10621873—21no—
43C2×#10621873C2211yescharacteristic, complemented
44SD16×D43—21no—
45C2×#10621882C2211yescharacteristic
46D8×D43—21no—
47#13063333C2211yescharacteristic
48#13063333C2211yescharacteristic, complemented
49#13063331C2211yescharacteristic, complemented
50#13063314C2211yescharacteristic, complemented
51#13063312C2211yescharacteristic, complemented
52#13063260C2211yescharacteristic, complemented
53#13063252C2211yescharacteristic, complemented
54#13063251C2211yescharacteristic
55#13063251C2211yescharacteristic, complemented
56#13063251C2211yescharacteristic, complemented
57#13063243C2211yescharacteristic, complemented
58#13063241C2211yescharacteristic, complemented
59C8×Dic43C2211yescharacteristic, complemented
60#137×C43C2211yescharacteristic, complemented
61AGL(1,ℤ/8)×C43C2211yescharacteristic
62C2×SD16×C43C2211yescharacteristic, complemented
63#131×C43C2211yescharacteristic, complemented
64#108×C43C2211yescharacteristic, complemented
65#101×C43C2211yescharacteristic, complemented
66#100×C43C2211yescharacteristic, complemented
67#41×C43C2311yescharacteristic
68C2×Q8×C43C2311yescharacteristic
69C2×D4×C43C2311yescharacteristic
70C2×C22⋊D43—41no—
71#10621902—21no—
72#10621902—21no—
73#10621902—21no—
74Q8×D43—21no—
75Q8×D43—21no—
76Q8×D43—21no—
77#10621900—21no—
78#10621900—21no—
79#10621900—21no—
80#10621900—41no—
81D4×D43—21no—
82D4×D43—21no—
83D4×D43—21no—
84D4×D43—41no—
85#10621898—21no—
86#10621898—21no—
87#10621898—41no—
88#10621898C2311yescharacteristic
89#10621898C2311yescharacteristic
90#10621898C2311yescharacteristic
91C2×D172—21no—
92C2×D172C2311yescharacteristic
93C2×Dic86—21no—
94C2×Dic86C2311yescharacteristic
95Q16×C43—21no—
96SD16×C43—21no—
97SD16×C43—21no—
98SD16×C43—21no—
99SD16×C43—21no—
100D8×C43—21no—
101M16×C43—21no—
102M16×C43C2311yescharacteristic
103M16×C43C2311yescharacteristic
104M16×C43C2311yescharacteristic
105C2×C8×C43—21no—
106C2×C8×C43C2311yescharacteristic
107C22⋊Dic43—41no—
108#10621885—21no—
109#10621885—21no—
110#10621885—21no—
111#10621885D411yescharacteristic
112#10621884—21no—
113#10621884D411yescharacteristic
114#10621883—21no—
115#10621883D411yescharacteristic
116#10621882—21no—
117#10621882—21no—
118#10621882—21no—
119#10621882D411yescharacteristic
120(C2×D43)⋊C4—41no—
121C4×Dic43C2311yescharacteristic
122#10621877C2311yescharacteristic
123C2×C43⋊C8C2311yescharacteristic
124Dic172—21no—
125Dic172—21no—
126Dic172D411yescharacteristic
127D344—21no—
128D344—21no—
129D344D411yescharacteristic
130#10621873—21no—
131#10621873—21no—
132#10621873—21no—
133#10621873—21no—
134#10621873—21no—
135#10621873—21no—
136#10621873D411yescharacteristic
137#10621873D411yescharacteristic
138#10621872—21no—
139#10621872—21no—
140#10621872—21no—
141C8×D43—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×C43C2×D411yescharacteristic
151D4×C43—21no—
152D4×C43—21no—
153D4×C43—21no—
154D4×C43C2×D411yescharacteristic
155C2×C4×C43—21no—
156C2×C4×C43—21no—
157C2×C4×C43C2411yescharacteristic
158C22⋊D43—21no—
159C22⋊D43—21no—
160C22⋊D43—21no—
161C22⋊D43—41no—
162C22⋊D43—41no—
163C22⋊D43—41no—
164C22⋊D43—41no—
165C2×Dic43—21no—
166C2×Dic43—21no—
167C2×Dic43—41no—
168C2×Dic43—41no—
169D172—21no—
170D172—21no—
171D172—41no—
172D172—41no—
173D172C2×D411yescharacteristic
174D172C2×D411yescharacteristic
175D172C2×D411yescharacteristic
176C4×D43—21no—
177C4×D43—21no—
178C4×D43—21no—
179C4×D43—41no—
180C4×D43—41no—
181C4×D43—41no—
182C4×D43—41no—
183Dic86—21no—
184Dic86—21no—
185Dic86—41no—
186Dic86—41no—
187Dic86C2×D411yescharacteristic
188Dic86C2×D411yescharacteristic
189Dic86C2×D411yescharacteristic
190C8×C43—21no—
191C8×C43—21no—
192C8×C43—21no—
193C8×C43C2×D411yescharacteristic
194C8×C43C2×D411yescharacteristic
195C43⋊C8—21no—
196C43⋊C8C2×D411yescharacteristic
197C43⋊C8C2×D411yescharacteristic
198C22×C43—21no—
199C22×C43—41no—
200C22×C43—81no—
201C22×C43H(5,𝔽2)11yescharacteristic
202C2×D43—21no—
203C2×D43—21no—
204C2×D43—21no—
205C2×D43—41no—
206C2×D43—81no—
207C2×D43—161no—
208C2×D43—161no—
209C4×C43—21no—
210C4×C43—41no—
211C4×C43C22×D411yescharacteristic
212C4×C43C22×D411yescharacteristic
213Dic43—21no—
214Dic43—21no—
215Dic43—21no—
216Dic43—41no—
217Dic43—41no—
218#3290—431nomaximal, Sylow
219C2×C43—21no—
220C2×C43—41no—
221C2×C43—81no—
222C2×C43D4211yescharacteristic
223D43—41no—
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#471D4311yescharacteristic, complemented
236#455—431no—
237#455—431no—
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)—431no—
247#137—431no—
248#137—431no—
249#137—431no—
250#137—861no—
251#137—861no—
252#137—861no—
253#137—861no—
254#137C2×D4311yescharacteristic, complemented
255AGL(1,ℤ/8)—431no—
256AGL(1,ℤ/8)—431no—
257AGL(1,ℤ/8)—431no—
258AGL(1,ℤ/8)—861no—
259AGL(1,ℤ/8)—861no—
260AGL(1,ℤ/8)—861no—
261AGL(1,ℤ/8)—861no—
262AGL(1,ℤ/8)C2×D4311yescharacteristic
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—861no—
273C2×SD16—861no—
274C2×SD16C2×D4311yescharacteristic, complemented
275C2×D8—431no—
276C2×D8—861no—
277#131—431no—
278#131—431no—
279#131—431no—
280#131C2×D4311yescharacteristic, complemented
281#124—431no—
282#124—431no—
283#108—431no—
284#108C2×D4311yescharacteristic, complemented
285#104—431no—
286#104—431no—
287#104—431no—
288#104—431no—
289#101—431no—
290#101C2×D4311yescharacteristic, complemented
291#100—431no—
292#100C2×D4311yescharacteristic, complemented
293C4×C8—431no—
294#41—431no—
295#41—431no—
296#41—431no—
297#41—861no—
298#41—861no—
299#41—861no—
300#41—861no—
301#41—861no—
302#41—861no—
303#41—861no—
304#41—861no—
305#41—1721no—
306#41—1721no—
307#41C22×D4311yescharacteristic
308C2×Q8—431no—
309C2×Q8—861no—
310C2×Q8—861no—
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—21no—
323Q16—431no—
324Q16—431no—
325Q16—861no—
326Q16—861no—
327Q16—861no—
328Q16—861no—
329Q16—861no—
330SD16—21no—
331SD16—21no—
332SD16—21no—
333SD16—21no—
334SD16—431no—
335SD16—431no—
336SD16—431no—
337SD16—431no—
338SD16—861no—
339SD16—861no—
340SD16—861no—
341SD16—861no—
342SD16—861no—
343SD16—861no—
344SD16—861no—
345SD16—861no—
346D8—21no—
347D8—431no—
348D8—431no—
349D8—861no—
350D8—861no—
351D8—861no—
352D8—861no—
353D8—861no—
354M16—21no—
355M16—431no—
356M16—861no—
357M16—861no—
358M16—861no—
359M16C22×D4311yescharacteristic
360M16C22×D4311yescharacteristic
361M16C22×D4311yescharacteristic
362C2×C8—21no—
363C2×C8—431no—
364C2×C8—861no—
365C2×C8—861no—
366C2×C8—861no—
367C2×C8C22×D4311yescharacteristic
368C22⋊C4—1721no—
369C22⋊C4—1721no—
370C42—431no—
371C23—21no—
372C23—861no—
373C23—1721no—
374C23—1721no—
375Q8—21no—
376Q8—21no—
377Q8—431no—
378Q8—431no—
379Q8—431no—
380Q8—861no—
381Q8—861no—
382Q8—1721no—
383Q8—1721no—
384Q8D4×D4311yescharacteristic
385D4—21no—
386D4—21no—
387D4—21no—
388D4—431no—
389D4—431no—
390D4—431no—
391D4—861no—
392D4—861no—
393D4—861no—
394D4—861no—
395D4—861no—
396D4—1721no—
397D4—1721no—
398D4—1721no—
399D4—1721no—
400D4—1721no—
401D4—1721no—
402D4D4×D4311yescharacteristic
403C2×C4—21no—
404C2×C4—21no—
405C2×C4—861no—
406C2×C4—861no—
407C2×C4—861no—
408C2×C4—861no—
409C2×C4—861no—
410C2×C4—1721no—
411C2×C4—1721no—
412C2×C4—1721no—
413C2×C4—1721no—
414C2×C4—1721no—
415C2×C4—1721no—
416C2×C4C23×D4311yescharacteristic
417C8—21no—
418C8—21no—
419C8—21no—
420C8—431no—
421C8—431no—
422C8—861no—
423C8D4×D4311yescharacteristic
424C8D4×D4311yescharacteristic
425C22—21no—
426C22—41no—
427C22—81no—
428C22—861no—
429C22—861no—
430C22—861no—
431C22—3441no—
432C22—1721no—
433C22—6881no—
434C22—6881no—
435C22#1306337111yescharacteristic
436C4—21no—
437C4—41no—
438C4—861no—
439C4—861no—
440C4—861no—
441C4—1721no—
442C4—1721no—
443C4C2×D4×D4311yescharacteristic
444C4C2×D4×D4311yescharacteristic
445C2—21no—
446C2—41no—
447C2—81no—
448C2—3441no—
449C2—1721no—
450C2—1721no—
451C2—1721no—
452C2#1458353311yescharacteristic
subgroupG/H
centerC2#14583533
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#471C2
socleC2×C43D42
hypercenter#471D43
hypocenterC43#3290
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C2×C4 ◁ #471

Complements

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

NH ≅ G/Ntype
1. #14583715C2semidirect
2. #14583711C2semidirect
3. #14583705C2semidirect
4. #14583703C2semidirect
5. #14583280C2semidirect
6. #14583173C2semidirect
7. #14583168C2semidirect
8. #14583163C2semidirect
9. #14583079C2semidirect
10. #14583075C2semidirect
11. #14583074C2semidirect
12. #14583070C2semidirect
13. #14583015C2semidirect
14. #14583014C2semidirect
15. C43×#471C2semidirect
16. #13063373C22semidirect
17. #13063372C22semidirect
22. #13063358C22semidirect
29. #13063353C22semidirect
32. #13063351C22semidirect
40. C2×#10621885C22semidirect
43. C2×#10621873C22semidirect
48. #13063333C22semidirect
49. #13063331C22semidirect
50. #13063314C22semidirect
51. #13063312C22semidirect
52. #13063260C22semidirect
53. #13063252C22semidirect
55. #13063251C22semidirect
56. #13063251C22semidirect
57. #13063243C22semidirect
58. #13063241C22semidirect
59. C8×Dic43C22semidirect
60. #137×C43C22semidirect
62. C2×SD16×C43C22semidirect
63. #131×C43C22semidirect
64. #108×C43C22semidirect
65. #101×C43C22semidirect
66. #100×C43C22semidirect
235. #471D43semidirect
242. C43#3290semidirect
254. #137C2×D43semidirect
274. C2×SD16C2×D43semidirect
280. #131C2×D43semidirect
284. #108C2×D43semidirect
290. #101C2×D43semidirect
292. #100C2×D43semidirect