Finite Group Databasebeta

← #21435860

Subgroups — #21435860

Order 7552.

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#16838213C211yesmaximal, characteristic, complemented
2#16838209C211yesmaximal, characteristic, complemented
3#16838205C211yesmaximal, characteristic, complemented
4#16837790C211yesmaximal, characteristic, complemented
5#16837670C211yesmaximal, characteristic, complemented
6#16837669C211yesmaximal, characteristic, complemented
7#16837665C211yesmaximal, characteristic, complemented
8#16837663C211yesmaximal, characteristic, complemented
9#16837580C211yesmaximal, characteristic, complemented
10#16837573C211yesmaximal, characteristic, complemented
11#16837570C211yesmaximal, characteristic, complemented
12#16837568C211yesmaximal, characteristic, complemented
13#16837524C211yesmaximal, characteristic, complemented
14#16837522C211yesmaximal, characteristic, complemented
15C59×#576C211yesmaximal, characteristic, complemented
16#14273774C2211yescharacteristic, complemented
17#14273773C2211yescharacteristic, complemented
18#14273759—21no—
19#14273757—21no—
20#14273757C2211yescharacteristic, complemented
21#14273757C2211yescharacteristic, complemented
22#14273753—21no—
23#14273753—21no—
24#14273753C2211yescharacteristic, complemented
25#14273753C2211yescharacteristic, complemented
26#14273752—21no—
27#14273752C2211yescharacteristic
28#14273752C2211yescharacteristic, complemented
29#14273751—21no—
30#14273748—21no—
31#14273747—21no—
32#14273747—21no—
33#14273747C2211yescharacteristic
34C2×#11745660C2211yescharacteristic, complemented
35C2×#11745670—21no—
36C2×#11745670C2211yescharacteristic, complemented
37SD16×D59—21no—
38C2×#11745669—21no—
39C2×#11745669C2211yescharacteristic, complemented
40#14273734C2211yescharacteristic, complemented
41#14273734C2211yescharacteristic, complemented
42#14273733C2211yescharacteristic, complemented
43#14273723C2211yescharacteristic, complemented
44#14273714C2211yescharacteristic, complemented
45#14273663C2211yescharacteristic, complemented
46#14273662C2211yescharacteristic, complemented
47#14273654C2211yescharacteristic, complemented
48#14273654C2211yescharacteristic, complemented
49#14273654C2211yescharacteristic, complemented
50#14273653C2211yescharacteristic, complemented
51#14273645C2211yescharacteristic, complemented
52#14273644C2211yescharacteristic, complemented
53#14273644C2211yescharacteristic, complemented
54#14273643C2211yescharacteristic, complemented
55#14273637C2211yescharacteristic, complemented
56H(5,𝔽2)×C59C2211yescharacteristic
57H(5,𝔽2)×C59C2211yescharacteristic, complemented
58AGL(1,ℤ/8)×C59—21no—
59AGL(1,ℤ/8)×C59—21no—
60AGL(1,ℤ/8)×C59C2211yescharacteristic
61AGL(1,ℤ/8)×C59C2211yescharacteristic, complemented
62#135×C59—21no—
63#135×C59C2211yescharacteristic
64C2×D8×C59—21no—
65C2×D8×C59C2211yescharacteristic, complemented
66#131×C59C2211yescharacteristic, complemented
67#41×C59—21no—
68#41×C59—21no—
69#41×C59—21no—
70#41×C59—21no—
71#41×C59C2311yescharacteristic
72#41×C59C2311yescharacteristic
73#41×C59C2311yescharacteristic
74C2×D4×C59—21no—
75C2×D4×C59—21no—
76C2×D4×C59—21no—
77C2×D4×C59—21no—
78C2×D4×C59—41no—
79C2×D4×C59—41no—
80C2×D4×C59C2311yescharacteristic
81C2×D4×C59C2311yescharacteristic
82C2×C22⋊D59—41no—
83#11745689—21no—
84Q8×D59—21no—
85#11745687—21no—
86#11745687—41no—
87D4×D59—21no—
88D4×D59—41no—
89#11745685—21no—
90#11745685—21no—
91#11745685C2311yescharacteristic
92C2×D236—21no—
93C2×D236C2311yescharacteristic
94C2×Dic118—21no—
95C2×Dic118C2311yescharacteristic
96Q16×C59D411yescharacteristic, complemented
97SD16×C59—21no—
98SD16×C59—21no—
99SD16×C59D411yescharacteristic, complemented
100SD16×C59D411yescharacteristic, complemented
101D8×C59—21no—
102D8×C59—21no—
103D8×C59—21no—
104D8×C59—21no—
105D8×C59D411yescharacteristic, complemented
106M16×C59—21no—
107M16×C59C2311yescharacteristic
108C2×C8×C59—21no—
109C2×C8×C59C2311yescharacteristic
110C22⋊Dic59—41no—
111#11745672—21no—
112#11745672—21no—
113#11745672D411yescharacteristic, complemented
114#11745671—21no—
115#11745671—21no—
116#11745671D411yescharacteristic, complemented
117#11745670—21no—
118#11745670—21no—
119#11745670—21no—
120#11745670—21no—
121#11745670—21no—
122#11745670—21no—
123#11745670D411yescharacteristic, complemented
124#11745669—21no—
125#11745669—21no—
126#11745669—21no—
127#11745669—21no—
128#11745669—21no—
129#11745669—21no—
130#11745669D411yescharacteristic, complemented
131C4×Dic59C2311yescharacteristic
132#11745664—21no—
133#11745664—21no—
134#11745664C2311yescharacteristic
135#11745664C2311yescharacteristic
136#11745664C2311yescharacteristic
137C2×C59⋊C8—21no—
138C2×C59⋊C8—21no—
139C2×C59⋊C8C2311yescharacteristic
140#11745660—21no—
141#11745660—21no—
142#11745659—21no—
143C8×D59—21no—
144C23×C59—21no—
145C23×C59—21no—
146C23×C59—41no—
147C23×C59—41no—
148C22×D59—21no—
149C22×D59—41no—
150Q8×C59C2×D411yescharacteristic
151Q8×C59C2×D411yescharacteristic
152Q8×C59C2×D411yescharacteristic
153D4×C59—21no—
154D4×C59—21no—
155D4×C59—21no—
156D4×C59—21no—
157D4×C59—21no—
158D4×C59—21no—
159D4×C59—21no—
160D4×C59—41no—
161D4×C59—41no—
162D4×C59—41no—
163D4×C59—41no—
164D4×C59C2×D411yescharacteristic
165D4×C59C2×D411yescharacteristic
166D4×C59C2×D411yescharacteristic
167C2×C4×C59—21no—
168C2×C4×C59—21no—
169C2×C4×C59—21no—
170C2×C4×C59—41no—
171C2×C4×C59—41no—
172C2×C4×C59C2411yescharacteristic
173C22⋊D59—21no—
174C22⋊D59—41no—
175C22⋊D59—41no—
176C22⋊D59—82no—
177C2×Dic59—21no—
178C2×Dic59—21no—
179C2×Dic59—41no—
180D236—21no—
181D236—21no—
182D236—41no—
183D236C2×D411yescharacteristic
184C4×D59—21no—
185C4×D59—41no—
186C4×D59—41no—
187Dic118—21no—
188Dic118—21no—
189Dic118—41no—
190Dic118C2×D411yescharacteristic
191C8×C59—21no—
192C8×C59C2×D411yescharacteristic
193C8×C59C2×D411yescharacteristic
194C59⋊C8—21no—
195C59⋊C8—21no—
196C59⋊C8—21no—
197C59⋊C8C2×D411yescharacteristic
198C59⋊C8C2×D411yescharacteristic
199C22×C59—21no—
200C22×C59—21no—
201C22×C59—21no—
202C22×C59—41no—
203C22×C59—41no—
204C22×C59—81no—
205C22×C59—81no—
206C22×C59—161no—
207C22×C59—161no—
208C22×C59H(5,𝔽2)11yescharacteristic
209C2×D59—21no—
210C2×D59—41no—
211C2×D59—81no—
212C2×D59—161no—
213C4×C59—21no—
214C4×C59—21no—
215C4×C59—21no—
216C4×C59C22×D411yescharacteristic
217C4×C59C22×D411yescharacteristic
218Dic59—21no—
219Dic59—41no—
220Dic59—41no—
221#3288—591nomaximal, Sylow
222C2×C59—21no—
223C2×C59—41no—
224C2×C59—41no—
225C2×C59—41no—
226C2×C59—81no—
227C2×C59—81no—
228C2×C59D4211yescharacteristic
229D59—41no—
230D59—81no—
231#577—591no—
232#577—591no—
233#576—591no—
234#576D5911yescharacteristic, complemented
235#496—591no—
236#472—591no—
237#472—591no—
238#471—591no—
239#471—591no—
240#455—591no—
241#454—591no—
242#453—591no—
243#453—591no—
244#444—591no—
245#444—591no—
246C59#328811yescharacteristic, complemented, Sylow
2472−1+4—591no—
248H(5,𝔽2)—591no—
249H(5,𝔽2)C2×D5911yescharacteristic
250H(5,𝔽2)C2×D5911yescharacteristic, complemented
251#137—591no—
252#137—591no—
253#137—1181no—
254#137—1181no—
255AGL(1,ℤ/8)—21no—
256AGL(1,ℤ/8)—21no—
257AGL(1,ℤ/8)—591no—
258AGL(1,ℤ/8)—591no—
259AGL(1,ℤ/8)—591no—
260AGL(1,ℤ/8)—591no—
261AGL(1,ℤ/8)—1181no—
262AGL(1,ℤ/8)—1181no—
263AGL(1,ℤ/8)—1181no—
264AGL(1,ℤ/8)—1181no—
265AGL(1,ℤ/8)C2×D5911yescharacteristic
266AGL(1,ℤ/8)C2×D5911yescharacteristic, complemented
267#135—21no—
268#135—591no—
269#135—1181no—
270#135—1181no—
271#135—1181no—
272#135C2×D5911yescharacteristic
273C2×SD16—591no—
274C2×SD16—591no—
275C2×SD16—1181no—
276C2×SD16—1181no—
277C2×D8—21no—
278C2×D8—591no—
279C2×D8—1181no—
280C2×D8C2×D5911yescharacteristic, complemented
281#131—591no—
282#131—591no—
283#131—591no—
284#131C2×D5911yescharacteristic, complemented
285#127—591no—
286#124—591no—
287#108—591no—
288#108—591no—
289#104—591no—
290#104—591no—
291#104—591no—
292#104—591no—
293#101—591no—
294#100—591no—
295#100—591no—
296#100—591no—
297#97—591no—
298#41—21no—
299#41—21no—
300#41—21no—
301#41—21no—
302#41—591no—
303#41—1181no—
304#41—1181no—
305#41—1181no—
306#41—1181no—
307#41—2361no—
308#41C22×D5911yescharacteristic
309#41C22×D5911yescharacteristic
310#41C22×D5911yescharacteristic
311C2×Q8—591no—
312C2×Q8—1181no—
313C2×Q8—1181no—
314C2×D4—21no—
315C2×D4—21no—
316C2×D4—21no—
317C2×D4—21no—
318C2×D4—41no—
319C2×D4—41no—
320C2×D4—591no—
321C2×D4—1181no—
322C2×D4—1181no—
323C2×D4—2361no—
324C2×D4—2361no—
325C2×D4C22×D5911yescharacteristic
326C2×D4C22×D5911yescharacteristic
327Q16—591no—
328Q16—1181no—
329Q16—1181no—
330Q16C22⋊D5911yescharacteristic, complemented
331SD16—21no—
332SD16—21no—
333SD16—591no—
334SD16—591no—
335SD16—1181no—
336SD16—1181no—
337SD16—1181no—
338SD16—1181no—
339SD16—1181no—
340SD16—1181no—
341SD16—1181no—
342SD16—1181no—
343SD16—1181no—
344SD16—1181no—
345SD16C22⋊D5911yescharacteristic, complemented
346SD16C22⋊D5911yescharacteristic, complemented
347D8—21no—
348D8—21no—
349D8—21no—
350D8—21no—
351D8—591no—
352D8—1181no—
353D8—1181no—
354D8—1181no—
355D8—1181no—
356D8—1181no—
357D8—1181no—
358D8C22⋊D5911yescharacteristic, complemented
359M16—21no—
360M16—591no—
361M16—591no—
362M16—591no—
363M16—1181no—
364M16—1181no—
365M16—1181no—
366M16C22×D5911yescharacteristic
367C2×C8—21no—
368C2×C8—591no—
369C2×C8—1181no—
370C2×C8—1181no—
371C2×C8—1181no—
372C2×C8C22×D5911yescharacteristic
373C22⋊C4—2361no—
374C42—591no—
375C23—21no—
376C23—21no—
377C23—41no—
378C23—41no—
379C23—1181no—
380C23—2361no—
381Q8—591no—
382Q8—1181no—
383Q8—1181no—
384Q8—2361no—
385Q8D4×D5911yescharacteristic
386Q8C2×C22⋊D5911yescharacteristic
387Q8C2×C22⋊D5911yescharacteristic
388D4—21no—
389D4—21no—
390D4—21no—
391D4—21no—
392D4—21no—
393D4—21no—
394D4—21no—
395D4—41no—
396D4—41no—
397D4—41no—
398D4—41no—
399D4—591no—
400D4—1181no—
401D4—1181no—
402D4—1181no—
403D4—4722no—
404D4—2361no—
405D4—2361no—
406D4—2361no—
407D4D4×D5911yescharacteristic
408D4C2×C22⋊D5911yescharacteristic
409D4C2×C22⋊D5911yescharacteristic
410C2×C4—21no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—41no—
414C2×C4—41no—
415C2×C4—1181no—
416C2×C4—1181no—
417C2×C4—1181no—
418C2×C4—2361no—
419C2×C4—2361no—
420C2×C4—2361no—
421C2×C4C23×D5911yescharacteristic
422C8—21no—
423C8—591no—
424C8—591no—
425C8—1181no—
426C8—1181no—
427C8—1181no—
428C8C2×C22⋊D5911yescharacteristic
429C8C2×C22⋊D5911yescharacteristic
430C22—21no—
431C22—21no—
432C22—21no—
433C22—41no—
434C22—41no—
435C22—81no—
436C22—81no—
437C22—161no—
438C22—161no—
439C22—1181no—
440C22—9441no—
441C22—4721no—
442C22—2361no—
443C22#1427377211yescharacteristic
444C4—21no—
445C4—21no—
446C4—21no—
447C4—1181no—
448C4—2361no—
449C4—2361no—
450C4C2×D4×D5911yescharacteristic
451C4C22×C22⋊D5911yescharacteristic
452C2—21no—
453C2—41no—
454C2—41no—
455C2—41no—
456C2—81no—
457C2—81no—
458C2—4721no—
459C2—2361no—
460C2D4×C22⋊D5911yescharacteristic
subgroupG/H
centerC2D4×C22⋊D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#576C2
socleC2×C59D42
hypercenter#576D59
hypocenterC59#3288
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2 ◁ C2×C4 ◁ #576

Complements

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

NH ≅ G/Ntype
1. #16838213C2semidirect
2. #16838209C2semidirect
3. #16838205C2semidirect
4. #16837790C2semidirect
5. #16837670C2semidirect
6. #16837669C2semidirect
7. #16837665C2semidirect
8. #16837663C2semidirect
9. #16837580C2semidirect
10. #16837573C2semidirect
11. #16837570C2semidirect
12. #16837568C2semidirect
13. #16837524C2semidirect
14. #16837522C2semidirect
15. C59×#576C2semidirect
16. #14273774C22semidirect
17. #14273773C22semidirect
20. #14273757C22semidirect
21. #14273757C22semidirect
24. #14273753C22semidirect
25. #14273753C22semidirect
28. #14273752C22semidirect
34. C2×#11745660C22semidirect
36. C2×#11745670C22semidirect
39. C2×#11745669C22semidirect
40. #14273734C22semidirect
41. #14273734C22semidirect
42. #14273733C22semidirect
43. #14273723C22semidirect
44. #14273714C22semidirect
45. #14273663C22semidirect
46. #14273662C22semidirect
47. #14273654C22semidirect
48. #14273654C22semidirect
49. #14273654C22semidirect
50. #14273653C22semidirect
51. #14273645C22semidirect
52. #14273644C22semidirect
53. #14273644C22semidirect
54. #14273643C22semidirect
55. #14273637C22semidirect
57. H(5,𝔽2)×C59C22semidirect
61. AGL(1,ℤ/8)×C59C22semidirect
65. C2×D8×C59C22semidirect
66. #131×C59C22semidirect
96. Q16×C59D4semidirect
99. SD16×C59D4semidirect
100. SD16×C59D4semidirect
105. D8×C59D4semidirect
113. #11745672D4semidirect
116. #11745671D4semidirect
123. #11745670D4semidirect
130. #11745669D4semidirect
234. #576D59semidirect
246. C59#3288semidirect
250. H(5,𝔽2)C2×D59semidirect
266. AGL(1,ℤ/8)C2×D59semidirect
280. C2×D8C2×D59semidirect
284. #131C2×D59semidirect
330. Q16C22⋊D59semidirect
345. SD16C22⋊D59semidirect
346. SD16C22⋊D59semidirect
358. D8C22⋊D59semidirect