Finite Group Databasebeta

← #21435876

Subgroups — #21435876

Order 7552.

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#16838217C211yesmaximal, characteristic, complemented
2#16838209C211yesmaximal, characteristic, complemented
3#16838205C211yesmaximal, characteristic, complemented
4#16837783C211yesmaximal, characteristic, complemented
5#16837675C211yesmaximal, characteristic, complemented
6#16837670C211yesmaximal, characteristic, complemented
7#16837665C211yesmaximal, characteristic, complemented
8#16837662C211yesmaximal, characteristic, complemented
9#16837580C211yesmaximal, characteristic, complemented
10#16837578C211yesmaximal, characteristic, complemented
11#16837575C211yesmaximal, characteristic, complemented
12#16837573C211yesmaximal, characteristic, complemented
13#16837519C211yesmaximal, characteristic, complemented
14#16837517C211yesmaximal, characteristic, complemented
15C59×#577C211yesmaximal, characteristic, complemented
16#14273774C2211yescharacteristic, complemented
17#14273773C2211yescharacteristic
18#14273759—21no—
19#14273758—21no—
20#14273758C2211yescharacteristic, complemented
21#14273757—21no—
22#14273757C2211yescharacteristic
23#14273757C2211yescharacteristic, complemented
24#14273753—21no—
25#14273753C2211yescharacteristic
26#14273752—21no—
27#14273752C2211yescharacteristic
28#14273752C2211yescharacteristic, complemented
29#14273751—21no—
30#14273748—21no—
31#14273747—21no—
32#14273747—21no—
33#14273747C2211yescharacteristic
34C2×#11745672—21no—
35C2×#11745672C2211yescharacteristic, complemented
36C2×#11745660C2211yescharacteristic, complemented
37SD16×D59—21no—
38C2×#11745669—21no—
39C2×#11745669C2211yescharacteristic
40#14273734C2211yescharacteristic
41#14273734C2211yescharacteristic, complemented
42#14273733C2211yescharacteristic, complemented
43#14273716C2211yescharacteristic, complemented
44#14273714C2211yescharacteristic, complemented
45#14273663C2211yescharacteristic, complemented
46#14273662C2211yescharacteristic, complemented
47#14273654C2211yescharacteristic
48#14273654C2211yescharacteristic, complemented
49#14273654C2211yescharacteristic, complemented
50#14273653C2211yescharacteristic, complemented
51#14273646C2211yescharacteristic, complemented
52#14273645C2211yescharacteristic, complemented
53#14273644C2211yescharacteristic, complemented
54#14273643C2211yescharacteristic, complemented
55C8×Dic59C2211yescharacteristic, complemented
562−1+4×C59C2211yescharacteristic, complemented
57H(5,𝔽2)×C59C2211yescharacteristic
58#137×C59—21no—
59#137×C59C2211yescharacteristic
60AGL(1,ℤ/8)×C59—21no—
61AGL(1,ℤ/8)×C59C2211yescharacteristic, complemented
62#135×C59—21no—
63#135×C59C2211yescharacteristic
64C2×SD16×C59—21no—
65C2×SD16×C59C2211yescharacteristic, complemented
66#131×C59C2211yescharacteristic, complemented
67#41×C59—21no—
68#41×C59—21no—
69#41×C59—21no—
70#41×C59—21no—
71#41×C59—41no—
72#41×C59C2311yescharacteristic
73#41×C59C2311yescharacteristic
74#41×C59C2311yescharacteristic
75C2×Q8×C59—21no—
76C2×Q8×C59—21no—
77C2×Q8×C59C2311yescharacteristic
78C2×D4×C59—21no—
79C2×D4×C59—21no—
80C2×D4×C59—41no—
81C2×D4×C59C2311yescharacteristic
82#11745689—21no—
83Q8×D59—21no—
84#11745687—21no—
85#11745687—41no—
86D4×D59—21no—
87D4×D59—41no—
88#11745685—21no—
89#11745685—21no—
90#11745685C2311yescharacteristic
91C2×D236—21no—
92C2×D236C2311yescharacteristic
93C2×Dic118—21no—
94C2×Dic118C2311yescharacteristic
95Q16×C59—21no—
96Q16×C59D411yescharacteristic
97SD16×C59—21no—
98SD16×C59—21no—
99SD16×C59—21no—
100SD16×C59—21no—
101SD16×C59D411yescharacteristic
102SD16×C59D411yescharacteristic
103D8×C59—21no—
104D8×C59D411yescharacteristic
105M16×C59—21no—
106M16×C59C2311yescharacteristic
107C2×C8×C59—21no—
108C2×C8×C59C2311yescharacteristic
109C22⋊Dic59—41no—
110#11745672—21no—
111#11745672—21no—
112#11745672—21no—
113#11745672—21no—
114#11745672—21no—
115#11745672D411yescharacteristic
116#11745671—21no—
117#11745671—21no—
118#11745671—21no—
119#11745671D411yescharacteristic
120#11745670—21no—
121#11745670—21no—
122#11745670—21no—
123#11745670D411yescharacteristic
124#11745669—21no—
125#11745669—21no—
126#11745669—21no—
127#11745669—21no—
128#11745669—21no—
129#11745669D411yescharacteristic
130(C2×D59)⋊C4—41no—
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—41no—
146C22×D59—21no—
147C22×D59—41no—
148Q8×C59—21no—
149Q8×C59—21no—
150Q8×C59—41no—
151Q8×C59C2×D411yescharacteristic
152Q8×C59C2×D411yescharacteristic
153Q8×C59C2×D411yescharacteristic
154D4×C59—21no—
155D4×C59—21no—
156D4×C59—21no—
157D4×C59—21no—
158D4×C59—21no—
159D4×C59—41no—
160D4×C59—41no—
161D4×C59—41no—
162D4×C59C2×D411yescharacteristic
163D4×C59C2×D411yescharacteristic
164D4×C59C2×D411yescharacteristic
165C2×C4×C59—21no—
166C2×C4×C59—21no—
167C2×C4×C59—21no—
168C2×C4×C59—21no—
169C2×C4×C59—41no—
170C2×C4×C59—41no—
171C2×C4×C59—41no—
172C2×C4×C59C2411yescharacteristic
173C22⋊D59—21no—
174C22⋊D59—41no—
175C22⋊D59—41no—
176C2×Dic59—21no—
177C2×Dic59—21no—
178C2×Dic59—41no—
179D236—21no—
180D236—21no—
181D236—41no—
182D236C2×D411yescharacteristic
183C4×D59—21no—
184C4×D59—41no—
185C4×D59—41no—
186Dic118—21no—
187Dic118—21no—
188Dic118—41no—
189Dic118C2×D411yescharacteristic
190C8×C59—21no—
191C8×C59C2×D411yescharacteristic
192C8×C59C2×D411yescharacteristic
193C59⋊C8—21no—
194C59⋊C8—21no—
195C59⋊C8—21no—
196C59⋊C8C2×D411yescharacteristic
197C59⋊C8C2×D411yescharacteristic
198C22×C59—21no—
199C22×C59—21no—
200C22×C59—21no—
201C22×C59—41no—
202C22×C59—81no—
203C22×C59—161no—
204C22×C59H(5,𝔽2)11yescharacteristic
205C2×D59—21no—
206C2×D59—41no—
207C2×D59—81no—
208C2×D59—161no—
209C4×C59—21no—
210C4×C59—21no—
211C4×C59—21no—
212C4×C59—41no—
213C4×C59C22×D411yescharacteristic
214C4×C59C22×D411yescharacteristic
215Dic59—21no—
216Dic59—41no—
217Dic59—41no—
218#3290—591nomaximal, Sylow
219C2×C59—21no—
220C2×C59—41no—
221C2×C59—41no—
222C2×C59—41no—
223C2×C59—81no—
224C2×C59D4211yescharacteristic
225D59—41no—
226D59—81no—
227#578—591no—
228#577—591no—
229#577D5911yescharacteristic, complemented
230#576—591no—
231#495—591no—
232#473—591no—
233#472—591no—
234#471—591no—
235#471—591no—
236#455—591no—
237#455—591no—
238#454—591no—
239#454—591no—
240#443—591no—
241#443—591no—
242C59#329011yescharacteristic, complemented, Sylow
2432−1+4—591no—
2442−1+4C2×D5911yescharacteristic, complemented
245H(5,𝔽2)—591no—
246H(5,𝔽2)C2×D5911yescharacteristic
247#137—21no—
248#137—591no—
249#137—591no—
250#137—591no—
251#137—1181no—
252#137—1181no—
253#137—1181no—
254#137C2×D5911yescharacteristic
255AGL(1,ℤ/8)—21no—
256AGL(1,ℤ/8)—591no—
257AGL(1,ℤ/8)—591no—
258AGL(1,ℤ/8)—591no—
259AGL(1,ℤ/8)—1181no—
260AGL(1,ℤ/8)—1181no—
261AGL(1,ℤ/8)—1181no—
262AGL(1,ℤ/8)C2×D5911yescharacteristic, complemented
263#135—21no—
264#135—591no—
265#135—1181no—
266#135—1181no—
267#135—1181no—
268#135C2×D5911yescharacteristic
269C2×Q16—591no—
270C2×Q16—1181no—
271C2×SD16—21no—
272C2×SD16—591no—
273C2×SD16—1181no—
274C2×SD16C2×D5911yescharacteristic, complemented
275C2×D8—591no—
276C2×D8—1181no—
277#131—591no—
278#131—591no—
279#131—591no—
280#131C2×D5911yescharacteristic, complemented
281#124—591no—
282#124—591no—
283#108—591no—
284#108—591no—
285#104—591no—
286#104—591no—
287#104—591no—
288#104—591no—
289#101—591no—
290#101—591no—
291#100—591no—
292#100—591no—
293C4×C8—591no—
294#41—21no—
295#41—21no—
296#41—21no—
297#41—21no—
298#41—41no—
299#41—591no—
300#41—1181no—
301#41—1181no—
302#41—1181no—
303#41—1181no—
304#41—2361no—
305#41C22×D5911yescharacteristic
306#41C22×D5911yescharacteristic
307#41C22×D5911yescharacteristic
308C2×Q8—21no—
309C2×Q8—21no—
310C2×Q8—591no—
311C2×Q8—1181no—
312C2×Q8—1181no—
313C2×Q8C22×D5911yescharacteristic
314C2×D4—21no—
315C2×D4—21no—
316C2×D4—41no—
317C2×D4—591no—
318C2×D4—1181no—
319C2×D4—1181no—
320C2×D4—2361no—
321C2×D4C22×D5911yescharacteristic
322Q16—21no—
323Q16—591no—
324Q16—1181no—
325Q16—1181no—
326Q16—1181no—
327Q16—1181no—
328Q16—1181no—
329Q16C22⋊D5911yescharacteristic
330SD16—21no—
331SD16—21no—
332SD16—21no—
333SD16—21no—
334SD16—591no—
335SD16—591no—
336SD16—1181no—
337SD16—1181no—
338SD16—1181no—
339SD16—1181no—
340SD16—1181no—
341SD16—1181no—
342SD16—1181no—
343SD16—1181no—
344SD16C22⋊D5911yescharacteristic
345SD16C22⋊D5911yescharacteristic
346D8—21no—
347D8—591no—
348D8—1181no—
349D8—1181no—
350D8—1181no—
351D8—1181no—
352D8—1181no—
353D8C22⋊D5911yescharacteristic
354M16—21no—
355M16—591no—
356M16—591no—
357M16—591no—
358M16—1181no—
359M16—1181no—
360M16—1181no—
361M16C22×D5911yescharacteristic
362C2×C8—21no—
363C2×C8—591no—
364C2×C8—1181no—
365C2×C8—1181no—
366C2×C8—1181no—
367C2×C8C22×D5911yescharacteristic
368C22⋊C4—2361no—
369C22⋊C4—2361no—
370C42—591no—
371C23—21no—
372C23—41no—
373C23—1181no—
374C23—2361no—
375Q8—21no—
376Q8—21no—
377Q8—41no—
378Q8—591no—
379Q8—1181no—
380Q8—1181no—
381Q8—2361no—
382Q8D4×D5911yescharacteristic
383Q8C2×C22⋊D5911yescharacteristic
384Q8C2×C22⋊D5911yescharacteristic
385D4—21no—
386D4—21no—
387D4—21no—
388D4—21no—
389D4—21no—
390D4—41no—
391D4—41no—
392D4—41no—
393D4—591no—
394D4—1181no—
395D4—1181no—
396D4—1181no—
397D4—2361no—
398D4—2361no—
399D4—2361no—
400D4D4×D5911yescharacteristic
401D4C2×C22⋊D5911yescharacteristic
402D4C2×C22⋊D5911yescharacteristic
403C2×C4—21no—
404C2×C4—21no—
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—41no—
408C2×C4—41no—
409C2×C4—41no—
410C2×C4—1181no—
411C2×C4—1181no—
412C2×C4—1181no—
413C2×C4—2361no—
414C2×C4—2361no—
415C2×C4—2361no—
416C2×C4C23×D5911yescharacteristic
417C8—21no—
418C8—591no—
419C8—591no—
420C8—1181no—
421C8—1181no—
422C8—1181no—
423C8C2×C22⋊D5911yescharacteristic
424C8C2×C22⋊D5911yescharacteristic
425C22—21no—
426C22—21no—
427C22—21no—
428C22—41no—
429C22—81no—
430C22—161no—
431C22—1181no—
432C22—9441no—
433C22—4721no—
434C22—2361no—
435C22#1427377211yescharacteristic
436C4—21no—
437C4—21no—
438C4—21no—
439C4—41no—
440C4—1181no—
441C4—2361no—
442C4—2361no—
443C4C2×D4×D5911yescharacteristic
444C4C22×C22⋊D5911yescharacteristic
445C2—21no—
446C2—41no—
447C2—41no—
448C2—41no—
449C2—81no—
450C2—4721no—
451C2—2361no—
452C2D4×C22⋊D5911yescharacteristic
subgroupG/H
centerC2D4×C22⋊D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#577C2
socleC2×C59D42
hypercenter#577D59
hypocenterC59#3290
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2 ◁ C2×C4 ◁ #577

Complements

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

NH ≅ G/Ntype
1. #16838217C2semidirect
2. #16838209C2semidirect
3. #16838205C2semidirect
4. #16837783C2semidirect
5. #16837675C2semidirect
6. #16837670C2semidirect
7. #16837665C2semidirect
8. #16837662C2semidirect
9. #16837580C2semidirect
10. #16837578C2semidirect
11. #16837575C2semidirect
12. #16837573C2semidirect
13. #16837519C2semidirect
14. #16837517C2semidirect
15. C59×#577C2semidirect
16. #14273774C22semidirect
20. #14273758C22semidirect
23. #14273757C22semidirect
28. #14273752C22semidirect
35. C2×#11745672C22semidirect
36. C2×#11745660C22semidirect
41. #14273734C22semidirect
42. #14273733C22semidirect
43. #14273716C22semidirect
44. #14273714C22semidirect
45. #14273663C22semidirect
46. #14273662C22semidirect
48. #14273654C22semidirect
49. #14273654C22semidirect
50. #14273653C22semidirect
51. #14273646C22semidirect
52. #14273645C22semidirect
53. #14273644C22semidirect
54. #14273643C22semidirect
55. C8×Dic59C22semidirect
56. 2−1+4×C59C22semidirect
61. AGL(1,ℤ/8)×C59C22semidirect
65. C2×SD16×C59C22semidirect
66. #131×C59C22semidirect
229. #577D59semidirect
242. C59#3290semidirect
244. 2−1+4C2×D59semidirect
262. AGL(1,ℤ/8)C2×D59semidirect
274. C2×SD16C2×D59semidirect
280. #131C2×D59semidirect