Finite Group Databasebeta

← #21433822

Subgroups — #21433822

Order 7552.

466 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16838198C211yesmaximal, characteristic, complemented
2C2×#14273751C211yesmaximal, characteristic, complemented
3AGL(1,ℤ/8)×D59C211yesmaximal, characteristic, complemented
4#16838167C211yesmaximal, characteristic, complemented
5#16837671C211yesmaximal, characteristic, complemented
6#16837670C211yesmaximal, characteristic, complemented
7#16837669C211yesmaximal, characteristic, complemented
8#16837666C211yesmaximal, characteristic, complemented
9#16837665C211yesmaximal, characteristic, complemented
10#16837664C211yesmaximal, characteristic, complemented
11#16837663C211yesmaximal, characteristic, complemented
12#16837449C211yesmaximal, characteristic, complemented
13#16837383C211yesmaximal, characteristic, complemented
14#100×D59C211yesmaximal, characteristic, complemented
15C59×#472C211yesmaximal, characteristic, complemented
16C2×#11745687C2211yescharacteristic
17#41×D59C2211yescharacteristic
18C2×D4×D59C2211yescharacteristic
19#14273760C2211yescharacteristic, complemented
20#14273757C2211yescharacteristic, complemented
21#14273756—21no—
22#14273755C2211yescharacteristic
23#14273754—21no—
24#14273753C2211yescharacteristic
25#14273753C2211yescharacteristic, complemented
26#14273752C2211yescharacteristic
27#14273751—21no—
28#14273751—21no—
29#14273751—21no—
30#14273751—21no—
31#14273751—21no—
32#14273751—21no—
33#14273748—21no—
34#14273746—21no—
35C2×#11745660C2211yescharacteristic, complemented
36C2×#11745670C2211yescharacteristic, complemented
37SD16×D59—21no—
38C2×#11745669C2211yescharacteristic, complemented
39D8×D59—21no—
40#14273735—21no—
41#14273735C2211yescharacteristic, complemented
42#14273734C2211yescharacteristic, complemented
43#14273733—21no—
44#14273733C2211yescharacteristic, complemented
45C2×#11745659—21no—
46C2×#11745659C2211yescharacteristic
47M16×D59—21no—
48M16×D59C2211yescharacteristic
49M16×D59C2211yescharacteristic
50M16×D59C2211yescharacteristic
51#14273663C2211yescharacteristic, complemented
52#14273662C2211yescharacteristic, complemented
53#14273662C2211yescharacteristic, complemented
54#14273645C2211yescharacteristic, complemented
55#14273645C2211yescharacteristic, complemented
56#14273644C2211yescharacteristic, complemented
57#14273644C2211yescharacteristic, complemented
58#14273643C2211yescharacteristic, complemented
59#14273643C2211yescharacteristic, complemented
60AGL(1,ℤ/8)×C59C2211yescharacteristic
61AGL(1,ℤ/8)×C59C2211yescharacteristic, complemented
62C2×D8×C59C2211yescharacteristic, complemented
63#131×C59C2211yescharacteristic, complemented
64#108×C59C2211yescharacteristic, complemented
65#100×C59C2211yescharacteristic, complemented
66#100×C59C2211yescharacteristic, complemented
67C23×D59—21no—
68#41×C59C2311yescharacteristic
69C2×D4×C59C2311yescharacteristic
70C2×D4×C59C2311yescharacteristic
71C2×C22⋊D59—21no—
72C2×C22⋊D59—21no—
73C22×Dic59—21no—
74#11745689D411yescharacteristic
75Q8×D59D411yescharacteristic
76#11745687—21no—
77#11745687—21no—
78#11745687—21no—
79#11745687—21no—
80#11745687—21no—
81#11745687D411yescharacteristic
82D4×D59—21no—
83D4×D59—21no—
84D4×D59—21no—
85D4×D59—21no—
86D4×D59—21no—
87D4×D59D411yescharacteristic
88#11745685—21no—
89#11745685C2311yescharacteristic
90C2×D236C2311yescharacteristic
91C2×C4×D59—21no—
92C2×C4×D59C2311yescharacteristic
93C2×Dic118C2311yescharacteristic
94SD16×C59—21no—
95SD16×C59—21no—
96D8×C59—21no—
97D8×C59—21no—
98D8×C59—21no—
99D8×C59—21no—
100M16×C59—21no—
101M16×C59C2311yescharacteristic
102M16×C59C2311yescharacteristic
103M16×C59C2311yescharacteristic
104C2×C8×C59—21no—
105C2×C8×C59C2311yescharacteristic
106#11745672—21no—
107#11745671—21no—
108#11745670—21no—
109#11745670—21no—
110#11745670—21no—
111#11745670—21no—
112#11745670—21no—
113#11745669—21no—
114#11745669—21no—
115#11745669—21no—
116#11745669—21no—
117#11745669—21no—
118#11745664—21no—
119#11745664C2311yescharacteristic
120#11745664C2311yescharacteristic
121#11745664C2311yescharacteristic
122C2×C59⋊C8—21no—
123C2×C59⋊C8C2311yescharacteristic
124Dic236—21no—
125D472—21no—
126#11745660—21no—
127#11745660—21no—
128#11745660—21no—
129#11745660—21no—
130#11745659—21no—
131#11745659—21no—
132#11745659—21no—
133#11745659—21no—
134#11745659—21no—
135#11745659D411yescharacteristic
136#11745659D411yescharacteristic
137#11745659D411yescharacteristic
138#11745659D411yescharacteristic
139C8×D59—21no—
140C8×D59—21no—
141C8×D59—21no—
142C8×D59—21no—
143C8×D59—21no—
144C23×C59—21no—
145C23×C59—21no—
146C22×D59—21no—
147C22×D59—21no—
148C22×D59—41no—
149C22×D59—41no—
150C22×D59—82no—
151C22×D59#4111yescharacteristic
152Q8×C59C2×D411yescharacteristic
153D4×C59—21no—
154D4×C59—21no—
155D4×C59—21no—
156D4×C59—21no—
157D4×C59—21no—
158D4×C59C2×D411yescharacteristic
159C2×C4×C59—21no—
160C2×C4×C59C2411yescharacteristic
161C22⋊D59—21no—
162C22⋊D59—21no—
163C22⋊D59—21no—
164C22⋊D59—41no—
165C22⋊D59—41no—
166C22⋊D59—41no—
167C22⋊D59—41no—
168C2×Dic59—21no—
169C2×Dic59—21no—
170C2×Dic59—41no—
171C2×Dic59—41no—
172C2×Dic59#4111yescharacteristic
173D236—21no—
174D236—21no—
175D236—21no—
176D236C2×D411yescharacteristic
177C4×D59—21no—
178C4×D59—21no—
179C4×D59—21no—
180C4×D59C2×D411yescharacteristic
181C4×D59C2×D411yescharacteristic
182C4×D59C2×D411yescharacteristic
183C4×D59C2×D411yescharacteristic
184Dic118—21no—
185Dic118—21no—
186Dic118—21no—
187Dic118C2×D411yescharacteristic
188C8×C59—21no—
189C8×C59—21no—
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—41no—
200C22×C59—41no—
201C22×C59—81no—
202C22×C59—81no—
203C22×C59C2×#4111yescharacteristic
204C2×D59—21no—
205C2×D59—41no—
206C2×D59—41no—
207C2×D59—81no—
208C2×D59—82no—
209C2×D59—82no—
210C2×D59—81no—
211C2×D59#12111yescharacteristic
212C2×D59#12111yescharacteristic
213C4×C59—21no—
214C4×C59C22×D411yescharacteristic
215C4×C59C22×D411yescharacteristic
216Dic59—21no—
217Dic59—41no—
218Dic59#12111yescharacteristic
219Dic59#12111yescharacteristic
220#3068—591nomaximal, Sylow
221C2×C59—21no—
222C2×C59—41no—
223C2×C59—81no—
224C2×C59—81no—
225C2×C59C2×#12111yescharacteristic
226D59—21no—
227D59—21no—
228D59—41no—
229D59—81no—
230#575—591no—
231C2×AGL(1,ℤ/8)—591no—
232C2×AGL(1,ℤ/8)—591no—
233#568—591no—
234#472—591no—
235#472—591no—
236#472—591no—
237#472D5911yescharacteristic, complemented
238#471—591no—
239#471—591no—
240#471—591no—
241#471—591no—
242#430—591no—
243#413—591no—
244C2×#100—591no—
245C59#306811yescharacteristic, complemented, Sylow
246C2×#41—591no—
247C2×#41—591no—
248C22×D4—591no—
249#137—591no—
250#137—591no—
251#137—1181no—
252AGL(1,ℤ/8)—591no—
253AGL(1,ℤ/8)—591no—
254AGL(1,ℤ/8)—591no—
255AGL(1,ℤ/8)—591no—
256AGL(1,ℤ/8)—1181no—
257AGL(1,ℤ/8)—1181no—
258AGL(1,ℤ/8)—1181no—
259AGL(1,ℤ/8)—1181no—
260AGL(1,ℤ/8)—1181no—
261AGL(1,ℤ/8)—1181no—
262AGL(1,ℤ/8)—1181no—
263AGL(1,ℤ/8)C2×D5911yescharacteristic
264AGL(1,ℤ/8)C2×D5911yescharacteristic, complemented
265#135—1181no—
266#135—1181no—
267C2×SD16—591no—
268C2×SD16—591no—
269C2×SD16—1181no—
270C2×D8—591no—
271C2×D8—1181no—
272C2×D8C2×D5911yescharacteristic, complemented
273#131—591no—
274#131—591no—
275#131—591no—
276#131—1181no—
277#131—1181no—
278#131C2×D5911yescharacteristic, complemented
279C2×M16—591no—
280C2×M16—591no—
281C2×M16—591no—
282C2×M16—591no—
283C2×M16—1181no—
284C2×M16—1181no—
285#108—591no—
286#108—591no—
287#108—591no—
288#108C2×D5911yescharacteristic, complemented
289#101—591no—
290#101—591no—
291#100—591no—
292#100—591no—
293#100—591no—
294#100—591no—
295#100C2×D5911yescharacteristic, complemented
296#100C2×D5911yescharacteristic, complemented
297C24—1181no—
298#41—591no—
299#41—591no—
300#41—591no—
301#41—1181no—
302#41—1181no—
303#41—1181no—
304#41—1181no—
305#41—1181no—
306#41—1181no—
307#41C22×D5911yescharacteristic
308C2×Q8—591no—
309C2×Q8—591no—
310C2×D4—591no—
311C2×D4—591no—
312C2×D4—1181no—
313C2×D4—1181no—
314C2×D4—1181no—
315C2×D4—1181no—
316C2×D4—1181no—
317C2×D4—1181no—
318C2×D4—1181no—
319C2×D4C22×D5911yescharacteristic
320C2×D4C22×D5911yescharacteristic
321C22×C4—591no—
322C22×C4—1181no—
323C22×C4—1181no—
324Q16—1181no—
325Q16—1181no—
326SD16—21no—
327SD16—21no—
328SD16—1181no—
329SD16—1181no—
330SD16—1181no—
331SD16—1181no—
332SD16—1181no—
333SD16—1181no—
334SD16—1181no—
335SD16—1181no—
336SD16—1181no—
337SD16—1181no—
338D8—21no—
339D8—21no—
340D8—21no—
341D8—21no—
342D8—1181no—
343D8—1181no—
344D8—1181no—
345D8—1181no—
346D8—1181no—
347D8—1181no—
348M16—21no—
349M16—591no—
350M16—591no—
351M16—591no—
352M16—591no—
353M16—591no—
354M16—591no—
355M16—591no—
356M16—1181no—
357M16—1181no—
358M16—1181no—
359M16—1181no—
360M16—1181no—
361M16—1181no—
362M16C22×D5911yescharacteristic
363M16C22×D5911yescharacteristic
364M16C22×D5911yescharacteristic
365C2×C8—21no—
366C2×C8—591no—
367C2×C8—1181no—
368C2×C8—1181no—
369C2×C8—1181no—
370C2×C8—1181no—
371C2×C8—1181no—
372C2×C8—1181no—
373C2×C8C22×D5911yescharacteristic
374C23—21no—
375C23—21no—
376C23—591no—
377C23—1181no—
378C23—1181no—
379C23—4722no—
380C23—2361no—
381C23—2361no—
382Q8—591no—
383Q8—1181no—
384Q8—1181no—
385Q8—1181no—
386Q8D4×D5911yescharacteristic
387D4—21no—
388D4—21no—
389D4—21no—
390D4—21no—
391D4—21no—
392D4—591no—
393D4—1181no—
394D4—1181no—
395D4—1181no—
396D4—1181no—
397D4—1181no—
398D4—1181no—
399D4—2361no—
400D4—2361no—
401D4—2361no—
402D4—2361no—
403D4D4×D5911yescharacteristic
404C2×C4—21no—
405C2×C4—591no—
406C2×C4—591no—
407C2×C4—591no—
408C2×C4—591no—
409C2×C4—591no—
410C2×C4—1181no—
411C2×C4—1181no—
412C2×C4—1181no—
413C2×C4—1181no—
414C2×C4—1181no—
415C2×C4—2361no—
416C2×C4—2361no—
417C2×C4C23×D5911yescharacteristic
418C8—21no—
419C8—21no—
420C8—21no—
421C8—591no—
422C8—591no—
423C8—1181no—
424C8—1181no—
425C8—1181no—
426C8D4×D5911yescharacteristic
427C8D4×D5911yescharacteristic
428C22—21no—
429C22—41no—
430C22—41no—
431C22—81no—
432C22—81no—
433C22—591no—
434C22—591no—
435C22—1181no—
436C22—4721no—
437C22—4721no—
438C22—4722no—
439C22—4722no—
440C22—2361no—
441C22—2361no—
442C22#41×D5911yescharacteristic
443C4—21no—
444C4—591no—
445C4—591no—
446C4—1181no—
447C4—2361no—
448C4C2×D4×D5911yescharacteristic
449C4C2×D4×D5911yescharacteristic
450C2—21no—
451C2—41no—
452C2—81no—
453C2—81no—
454C2—1181no—
455C2—1181no—
456C2—4721no—
457C2—2361no—
458C2#121×D5911yescharacteristic
subgroupG/H
centerC2#121×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#472C2
socleC2×C59C2×#121
hypercenter#472D59
hypocenterC59#3068
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2 ◁ C2×C4 ◁ #472

Complements

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

NH ≅ G/Ntype
1. #16838198C2semidirect
2. C2×#14273751C2semidirect
3. AGL(1,ℤ/8)×D59C2semidirect
4. #16838167C2semidirect
5. #16837671C2semidirect
6. #16837670C2semidirect
7. #16837669C2semidirect
8. #16837666C2semidirect
9. #16837665C2semidirect
10. #16837664C2semidirect
11. #16837663C2semidirect
12. #16837449C2semidirect
13. #16837383C2semidirect
14. #100×D59C2semidirect
15. C59×#472C2semidirect
19. #14273760C22semidirect
20. #14273757C22semidirect
25. #14273753C22semidirect
35. C2×#11745660C22semidirect
36. C2×#11745670C22semidirect
38. C2×#11745669C22semidirect
41. #14273735C22semidirect
42. #14273734C22semidirect
44. #14273733C22semidirect
51. #14273663C22semidirect
52. #14273662C22semidirect
53. #14273662C22semidirect
54. #14273645C22semidirect
55. #14273645C22semidirect
56. #14273644C22semidirect
57. #14273644C22semidirect
58. #14273643C22semidirect
59. #14273643C22semidirect
61. AGL(1,ℤ/8)×C59C22semidirect
62. C2×D8×C59C22semidirect
63. #131×C59C22semidirect
64. #108×C59C22semidirect
65. #100×C59C22semidirect
66. #100×C59C22semidirect
237. #472D59semidirect
245. C59#3068semidirect
264. AGL(1,ℤ/8)C2×D59semidirect
272. C2×D8C2×D59semidirect
278. #131C2×D59semidirect
288. #108C2×D59semidirect
295. #100C2×D59semidirect
296. #100C2×D59semidirect