Finite Group Databasebeta

← #19146358

Subgroups — #19146358

Order 5504.

464 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14583711C211yesmaximal, characteristic, complemented
2#14583709C211yesmaximal, characteristic, complemented
3#14583703C211yesmaximal, characteristic, complemented
4#14583700C211yesmaximal, characteristic, complemented
5#14583287C211yesmaximal, characteristic, complemented
6#14583168C211yesmaximal, characteristic, complemented
7#14583163C211yesmaximal, characteristic, complemented
8#14583161C211yesmaximal, characteristic, complemented
9#14583079C211yesmaximal, characteristic, complemented
10#14583070C211yesmaximal, characteristic, complemented
11#14583069C211yesmaximal, characteristic, complemented
12#14583065C211yesmaximal, characteristic, complemented
13#14583020C211yesmaximal, characteristic, complemented
14#14583019C211yesmaximal, characteristic, complemented
15C43×#472C211yesmaximal, characteristic, complemented
16#13063372C2211yescharacteristic, complemented
17#13063371C2211yescharacteristic, complemented
18#13063370C2211yescharacteristic
19#13063370C2211yescharacteristic, complemented
20#13063358—21no—
21#13063358C2211yescharacteristic, complemented
22#13063358C2211yescharacteristic, complemented
23#13063354—21no—
24#13063353—21no—
25#13063353C2211yescharacteristic
26#13063353C2211yescharacteristic, complemented
27#13063352—21no—
28#13063351C2211yescharacteristic
29#13063351C2211yescharacteristic, complemented
30#13063349—21no—
31#13063349—21no—
32#13063349—21no—
33#13063349—21no—
34#13063347—21no—
35#13063347C2211yescharacteristic
36#13063346—21no—
37#13063345C2211yescharacteristic
38#13063344—21no—
39#13063344—21no—
40C2×#10621873—21no—
41C2×#10621873C2211yescharacteristic, complemented
42C2×#10621883C2211yescharacteristic, complemented
43SD16×D43—21no—
44C2×#10621882C2211yescharacteristic, complemented
45D8×D43—21no—
46D8×D43—21no—
47#13063333C2211yescharacteristic, complemented
48#13063333C2211yescharacteristic, complemented
49#13063331C2211yescharacteristic, complemented
50#13063321C2211yescharacteristic, complemented
51#13063312C2211yescharacteristic, complemented
52#13063260C2211yescharacteristic, complemented
53#13063252C2211yescharacteristic, complemented
54#13063251C2211yescharacteristic, complemented
55#13063251C2211yescharacteristic, complemented
56#13063251C2211yescharacteristic, complemented
57#13063243C2211yescharacteristic, complemented
58#13063241C2211yescharacteristic, complemented
59#13063235C2211yescharacteristic, complemented
60AGL(1,ℤ/8)×C43C2211yescharacteristic, complemented
61AGL(1,ℤ/8)×C43C2211yescharacteristic, complemented
62C2×D8×C43C2211yescharacteristic, complemented
63#131×C43C2211yescharacteristic, complemented
64#108×C43C2211yescharacteristic, complemented
65#100×C43C2211yescharacteristic, complemented
66#100×C43C2211yescharacteristic, complemented
67#41×C43C2311yescharacteristic
68C2×D4×C43C2311yescharacteristic
69C2×D4×C43C2311yescharacteristic
70C2×C22⋊D43—41no—
71C2×C22⋊D43—41no—
72C2×C22⋊D43—41no—
73#10621902—21no—
74Q8×D43—21no—
75#10621900—21no—
76#10621900—21no—
77#10621900—21no—
78#10621900—21no—
79#10621900—21no—
80#10621900—41no—
81D4×D43—21no—
82D4×D43—21no—
83D4×D43—21no—
84D4×D43—21no—
85D4×D43—21no—
86D4×D43—41no—
87#10621898—21no—
88#10621898—21no—
89#10621898C2311yescharacteristic
90#10621898C2311yescharacteristic
91#10621898C2311yescharacteristic
92C2×D172—21no—
93C2×D172C2311yescharacteristic
94C2×Dic86—21no—
95C2×Dic86C2311yescharacteristic
96SD16×C43—21no—
97SD16×C43—21no—
98D8×C43—21no—
99D8×C43—21no—
100D8×C43—21no—
101D8×C43—21no—
102M16×C43—21no—
103M16×C43C2311yescharacteristic
104M16×C43C2311yescharacteristic
105M16×C43C2311yescharacteristic
106C2×C8×C43—21no—
107C2×C8×C43C2311yescharacteristic
108C22⋊Dic43—41no—
109#10621885D411yescharacteristic, complemented
110#10621884D411yescharacteristic, complemented
111#10621883—21no—
112#10621883—21no—
113#10621883—21no—
114#10621883—21no—
115#10621883D411yescharacteristic, complemented
116#10621882—21no—
117#10621882—21no—
118#10621882—21no—
119#10621882—21no—
120#10621882D411yescharacteristic, complemented
121C4×Dic43C2311yescharacteristic
122#10621877C2311yescharacteristic
123C2×C43⋊C8C2311yescharacteristic
124Dic172—21no—
125Dic172—21no—
126Dic172D411yescharacteristic, complemented
127D344—21no—
128D344—21no—
129D344D411yescharacteristic, complemented
130#10621873—21no—
131#10621873—21no—
132#10621873—21no—
133#10621873—21no—
134#10621873—21no—
135#10621873—21no—
136#10621873D411yescharacteristic, complemented
137#10621873D411yescharacteristic, complemented
138#10621872—21no—
139#10621872—21no—
140#10621872—21no—
141C8×D43—21no—
142C8×D43—21no—
143C8×D43—21no—
144C23×C43—21no—
145C23×C43—21no—
146C22×D43—21no—
147C22×D43—41no—
148C22×D43—41no—
149C22×D43—41no—
150Q8×C43C2×D411yescharacteristic
151D4×C43—21no—
152D4×C43—21no—
153D4×C43—21no—
154D4×C43—21no—
155D4×C43—21no—
156D4×C43C2×D411yescharacteristic
157C2×C4×C43—21no—
158C2×C4×C43C2411yescharacteristic
159C22⋊D43—21no—
160C22⋊D43—21no—
161C22⋊D43—21no—
162C22⋊D43—41no—
163C22⋊D43—41no—
164C22⋊D43—41no—
165C22⋊D43—41no—
166C22⋊D43—41no—
167C22⋊D43—41no—
168C22⋊D43—82no—
169C2×Dic43—21no—
170C2×Dic43—21no—
171C2×Dic43—41no—
172C2×Dic43—41no—
173C2×Dic43—41no—
174D172—21no—
175D172—21no—
176D172—41no—
177D172C2×D411yescharacteristic
178D172C2×D411yescharacteristic
179D172C2×D411yescharacteristic
180C4×D43—21no—
181C4×D43—21no—
182C4×D43—21no—
183C4×D43—41no—
184C4×D43—41no—
185Dic86—21no—
186Dic86—21no—
187Dic86—41no—
188Dic86C2×D411yescharacteristic
189Dic86C2×D411yescharacteristic
190Dic86C2×D411yescharacteristic
191C8×C43—21no—
192C8×C43—21no—
193C8×C43—21no—
194C8×C43C2×D411yescharacteristic
195C8×C43C2×D411yescharacteristic
196C43⋊C8—21no—
197C43⋊C8C2×D411yescharacteristic
198C43⋊C8C2×D411yescharacteristic
199C22×C43—21no—
200C22×C43—41no—
201C22×C43—41no—
202C22×C43—81no—
203C22×C43—81no—
204C22×C43H(5,𝔽2)11yescharacteristic
205C2×D43—21no—
206C2×D43—21no—
207C2×D43—21no—
208C2×D43—41no—
209C2×D43—81no—
210C2×D43—161no—
211C2×D43—161no—
212C2×D43—161no—
213C4×C43—21no—
214C4×C43C22×D411yescharacteristic
215C4×C43C22×D411yescharacteristic
216Dic43—21no—
217Dic43—21no—
218Dic43—21no—
219Dic43—41no—
220Dic43—41no—
221#3288—431nomaximal, Sylow
222C2×C43—21no—
223C2×C43—41no—
224C2×C43—81no—
225C2×C43—81no—
226C2×C43D4211yescharacteristic
227D43—41no—
228D43—41no—
229D43—41no—
230D43—81no—
231#577—431no—
232#577—431no—
233#576—431no—
234#576—431no—
235#496—431no—
236#472—431no—
237#472D4311yescharacteristic, complemented
238#471—431no—
239#471—431no—
240#455—431no—
241#454—431no—
242#453—431no—
243#453—431no—
244#444—431no—
245#444—431no—
246C43#328811yescharacteristic, complemented, Sylow
2472−1+4—431no—
248H(5,𝔽2)—431no—
249H(5,𝔽2)—431no—
250H(5,𝔽2)—431no—
251#137—431no—
252#137—431no—
253#137—861no—
254#137—861no—
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—
263AGL(1,ℤ/8)—861no—
264AGL(1,ℤ/8)—861no—
265AGL(1,ℤ/8)C2×D4311yescharacteristic, complemented
266AGL(1,ℤ/8)C2×D4311yescharacteristic, complemented
267#135—431no—
268#135—431no—
269#135—861no—
270#135—861no—
271#135—861no—
272#135—861no—
273C2×SD16—431no—
274C2×SD16—431no—
275C2×SD16—861no—
276C2×SD16—861no—
277C2×D8—431no—
278C2×D8—861no—
279C2×D8—861no—
280C2×D8C2×D4311yescharacteristic, complemented
281#131—431no—
282#131—431no—
283#131—431no—
284#131C2×D4311yescharacteristic, complemented
285#127—431no—
286#124—431no—
287#108—431no—
288#108C2×D4311yescharacteristic, complemented
289#104—431no—
290#104—431no—
291#104—431no—
292#104—431no—
293#101—431no—
294#100—431no—
295#100C2×D4311yescharacteristic, complemented
296#100C2×D4311yescharacteristic, complemented
297#97—431no—
298#41—431no—
299#41—431no—
300#41—431no—
301#41—861no—
302#41—861no—
303#41—861no—
304#41—861no—
305#41—861no—
306#41—861no—
307#41—861no—
308#41—861no—
309#41—1721no—
310#41C22×D4311yescharacteristic
311C2×Q8—431no—
312C2×Q8—861no—
313C2×Q8—861no—
314C2×D4—431no—
315C2×D4—861no—
316C2×D4—861no—
317C2×D4—861no—
318C2×D4—861no—
319C2×D4—861no—
320C2×D4—861no—
321C2×D4—1721no—
322C2×D4—1721no—
323C2×D4—1721no—
324C2×D4—1721no—
325C2×D4C22×D4311yescharacteristic
326C2×D4C22×D4311yescharacteristic
327Q16—431no—
328Q16—431no—
329Q16—861no—
330Q16—861no—
331SD16—21no—
332SD16—21no—
333SD16—431no—
334SD16—431no—
335SD16—431no—
336SD16—431no—
337SD16—861no—
338SD16—861no—
339SD16—861no—
340SD16—861no—
341SD16—861no—
342SD16—861no—
343SD16—861no—
344SD16—861no—
345SD16—861no—
346SD16—861no—
347D8—21no—
348D8—21no—
349D8—21no—
350D8—21no—
351D8—431no—
352D8—431no—
353D8—861no—
354D8—861no—
355D8—861no—
356D8—861no—
357D8—861no—
358D8—861no—
359M16—21no—
360M16—431no—
361M16—861no—
362M16—861no—
363M16—861no—
364M16C22×D4311yescharacteristic
365M16C22×D4311yescharacteristic
366M16C22×D4311yescharacteristic
367C2×C8—21no—
368C2×C8—431no—
369C2×C8—861no—
370C2×C8—861no—
371C2×C8—861no—
372C2×C8C22×D4311yescharacteristic
373C22⋊C4—1721no—
374C42—431no—
375C23—21no—
376C23—21no—
377C23—861no—
378C23—1721no—
379C23—1721no—
380C23—1721no—
381Q8—431no—
382Q8—431no—
383Q8—431no—
384Q8—861no—
385Q8—861no—
386Q8—1721no—
387Q8D4×D4311yescharacteristic
388D4—21no—
389D4—21no—
390D4—21no—
391D4—21no—
392D4—21no—
393D4—431no—
394D4—431no—
395D4—431no—
396D4—861no—
397D4—861no—
398D4—861no—
399D4—861no—
400D4—861no—
401D4—3442no—
402D4—1721no—
403D4—1721no—
404D4—1721no—
405D4—1721no—
406D4—1721no—
407D4—1721no—
408D4—1721no—
409D4D4×D4311yescharacteristic
410C2×C4—21no—
411C2×C4—861no—
412C2×C4—861no—
413C2×C4—861no—
414C2×C4—861no—
415C2×C4—861no—
416C2×C4—1721no—
417C2×C4—1721no—
418C2×C4—1721no—
419C2×C4—1721no—
420C2×C4—1721no—
421C2×C4C23×D4311yescharacteristic
422C8—21no—
423C8—21no—
424C8—21no—
425C8—431no—
426C8—431no—
427C8—861no—
428C8D4×D4311yescharacteristic
429C8D4×D4311yescharacteristic
430C22—21no—
431C22—41no—
432C22—41no—
433C22—81no—
434C22—81no—
435C22—861no—
436C22—861no—
437C22—861no—
438C22—3441no—
439C22—1721no—
440C22—6881no—
441C22—6881no—
442C22—6881no—
443C22#1306337111yescharacteristic
444C4—21no—
445C4—861no—
446C4—861no—
447C4—861no—
448C4—1721no—
449C4—1721no—
450C4C2×D4×D4311yescharacteristic
451C4C2×D4×D4311yescharacteristic
452C2—21no—
453C2—41no—
454C2—81no—
455C2—81no—
456C2—3441no—
457C2—1721no—
458C2—1721no—
459C2—1721no—
460C2#1458353311yescharacteristic
subgroupG/H
centerC2#14583533
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#472C2
socleC2×C43D42
hypercenter#472D43
hypocenterC43#3288
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C2×C4 ◁ #472

Complements

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

NH ≅ G/Ntype
1. #14583711C2semidirect
2. #14583709C2semidirect
3. #14583703C2semidirect
4. #14583700C2semidirect
5. #14583287C2semidirect
6. #14583168C2semidirect
7. #14583163C2semidirect
8. #14583161C2semidirect
9. #14583079C2semidirect
10. #14583070C2semidirect
11. #14583069C2semidirect
12. #14583065C2semidirect
13. #14583020C2semidirect
14. #14583019C2semidirect
15. C43×#472C2semidirect
16. #13063372C22semidirect
17. #13063371C22semidirect
19. #13063370C22semidirect
21. #13063358C22semidirect
22. #13063358C22semidirect
26. #13063353C22semidirect
29. #13063351C22semidirect
41. C2×#10621873C22semidirect
42. C2×#10621883C22semidirect
44. C2×#10621882C22semidirect
47. #13063333C22semidirect
48. #13063333C22semidirect
49. #13063331C22semidirect
50. #13063321C22semidirect
51. #13063312C22semidirect
52. #13063260C22semidirect
53. #13063252C22semidirect
54. #13063251C22semidirect
55. #13063251C22semidirect
56. #13063251C22semidirect
57. #13063243C22semidirect
58. #13063241C22semidirect
59. #13063235C22semidirect
60. AGL(1,ℤ/8)×C43C22semidirect
61. AGL(1,ℤ/8)×C43C22semidirect
62. C2×D8×C43C22semidirect
63. #131×C43C22semidirect
64. #108×C43C22semidirect
65. #100×C43C22semidirect
66. #100×C43C22semidirect
109. #10621885D4semidirect
110. #10621884D4semidirect
115. #10621883D4semidirect
120. #10621882D4semidirect
126. Dic172D4semidirect
129. D344D4semidirect
136. #10621873D4semidirect
137. #10621873D4semidirect
237. #472D43semidirect
246. C43#3288semidirect
265. AGL(1,ℤ/8)C2×D43semidirect
266. AGL(1,ℤ/8)C2×D43semidirect
280. C2×D8C2×D43semidirect
284. #131C2×D43semidirect
288. #108C2×D43semidirect
295. #100C2×D43semidirect
296. #100C2×D43semidirect