Finite Group Databasebeta

← D59×#2249 #28744084

Subgroups — D59×#2249 #28744084

Order 15104.

854 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×Q32×D59C211yesmaximal, characteristic, complemented
2C2×SD32×D59C212yesmaximal, complemented
3C2×D16×D59C211yesmaximal, characteristic
4#495×D59C212yesmaximal, complemented
5#21426358C211yesmaximal, characteristic, complemented
6#21426357C211yesmaximal, characteristic, complemented
7#21426356C212yesmaximal, complemented
8#21426355C212yesmaximal, complemented
9#21426354C211yesmaximal, characteristic, complemented
10C4×C16×D59C211yesmaximal, characteristic, complemented
11C59×#2249C211yesmaximal, characteristic, complemented
12C2×Q16×D59C2212yes—
13C2×SD16×D59—22no—
14C2×D8×D59C2212yes—
15#124×D59—22no—
16C2×Dic472C2211yescharacteristic, complemented
17C2×#14273673C2212yescomplemented
18Q32×D59—24no—
19C2×#14273672C2212yescomplemented
20C2×#14273671C2212yescomplemented
21C2×#14273670C2212yescomplemented
22SD32×D59—28no—
23C2×D944C2211yescharacteristic
24C2×#14273668C2212yes—
25D16×D59—24no—
26C2×C16×D59C2211yescharacteristic
27C2×C16×D59C2211yescharacteristic
28#16837787C2212yescomplemented
29#16837786C2212yescomplemented
30#16837785C2212yescomplemented
31#16837784—22no—
32#16837783—22no—
33C4×C8×D59C2211yescharacteristic
34C4×C59⋊C16C2211yescharacteristic, complemented
35C16×Dic59C2211yescharacteristic, complemented
36C16×Dic59C2211yescharacteristic, complemented
37C2×Q32×C59C2211yescharacteristic, complemented
38C2×SD32×C59C2212yescomplemented
39C2×D16×C59C2211yescharacteristic
40C59×#495C2212yescomplemented
41C4×C16×C59C2211yescharacteristic, complemented
42C2×Q8×D59—22no—
43C2×D4×D59—22no—
44C2×Dic236C2312yes—
45C2×#11745672—22no—
46Q16×D59—24no—
47Q16×D59—24no—
48C2×#11745660—22no—
49C2×#11745670—22no—
50C2×#11745671—22no—
51SD16×D59—48no—
52C2×D472C2312yes—
53C2×#11745669—22no—
54D8×D59—24no—
55D8×D59—24no—
56C2×C8×D59D411yescharacteristic
57C2×C8×D59C2311yescharacteristic
58#14273716—22no—
59#14273715—22no—
60#14273714—22no—
61#14273713—44no—
62C22⋊C4×D59—44no—
63C42×D59D411yescharacteristic
64Dic472—22no—
65#14273673—24no—
66#14273672—24no—
67#14273671—24no—
68#14273670—24no—
69D944—22no—
70#14273668—24no—
71C2×C59⋊C16C2311yescharacteristic
72C2×C59⋊C16C2311yescharacteristic
73C16×D59D414yes—
74C16×D59D414yes—
75C4×C59⋊C8D411yescharacteristic
76C8×Dic59D411yescharacteristic
77C8×Dic59C2311yescharacteristic
78C2×Q16×C59C2312yes—
79C2×SD16×C59—22no—
80C2×D8×C59C2312yes—
81#124×C59—22no—
82Q32×C59—22no—
83SD32×C59—24no—
84D16×C59—22no—
85C2×C16×C59C2311yescharacteristic
86C2×C16×C59C2311yescharacteristic
87C4×C8×C59C2311yescharacteristic
88C23×D59—42no—
89C2×Q8×C59—22no—
90C2×D4×C59—22no—
91C2×C22⋊D59—42no—
92Q8×D59—44no—
93Q8×D59—44no—
94D4×D59—44no—
95D4×D59—44no—
96C2×D236—22no—
97C2×C4×D59—42no—
98C2×C4×D59D812yes—
99C2×C4×D59C2×D411yescharacteristic
100C2×Dic118—22no—
101C2×Dic118—42no—
102Q16×C59—22no—
103Q16×C59—22no—
104SD16×C59—44no—
105D8×C59—22no—
106D8×C59—22no—
107C2×C8×C59C2×D411yescharacteristic
108C2×C8×C59C2411yescharacteristic
109C22⋊C4×C59—44no—
110C42×C59C2×D411yescharacteristic
111C22⋊Dic59—44no—
112#11745672—44no—
113#11745671—44no—
114#11745670—44no—
115#11745669—44no—
116(C2×D59)⋊C4—44no—
117(C2×D59)⋊C4—44no—
118C4×Dic59D812yes—
119C4×Dic59C2×D411yescharacteristic
120C2×C59⋊C8C2×D411yescharacteristic
121C2×C59⋊C8C2×D411yescharacteristic
122Dic236—22no—
123Dic236—22no—
124D472—22no—
125D472—22no—
126#11745660—44no—
127C8×D59D814yes—
128C8×D59C2×D412yes—
129C8×D59C2×D412yes—
130C16×C59C2×D412yes—
131C16×C59C2×D412yes—
132C59⋊C16C2×D412yes—
133C59⋊C16C2×D412yes—
134C23×C59—42no—
135C22×D59—42no—
136C22×D59—84no—
137C22×D59—88no—
138C22×D59C2×D811yescharacteristic
139Q8×C59—42no—
140Q8×C59—42no—
141D4×C59—42no—
142D4×C59—42no—
143C2×C4×C59—42no—
144C2×C4×C59C2×D812yes—
145C2×C4×C59C22×D411yescharacteristic
146C22⋊D59—84no—
147C2×Dic59—42no—
148C2×Dic59C2×D812yes—
149C2×Dic59C2×D811yescharacteristic
150D236—42no—
151D236—42no—
152C4×D59—24no—
153C4×D59—84no—
154C4×D59#12712yes—
155C4×D59C2×D812yes—
156Dic118—42no—
157Dic118—42no—
158Dic118—84no—
159C8×C59C2×D812yes—
160C8×C59C22×D411yescharacteristic
161C8×C59C22×D411yescharacteristic
162C59⋊C8#12712yes—
163C59⋊C8C2×D812yes—
164C2×#2249—591nomaximal, Sylow
165C22×C59—82no—
166C22×C59—84no—
167C22×C59C22×D811yescharacteristic
168C2×D59—82no—
169C2×D59—84no—
170C2×D59—168no—
171C2×D59#49312yes—
172C2×D59#50814yes—
173C4×C59—22no—
174C4×C59—82no—
175C4×C59C2×#12711yescharacteristic
176C4×C59C22×D811yescharacteristic
177Dic59—22no—
178Dic59—82no—
179Dic59#49312yes—
180C22×Q32—591no—
181C22×SD32—592no—
182C22×D16—591no—
183C2×#495—592no—
184#2249—591no—
185#2249—592no—
186#2249—591no—
187#2249—592no—
188#2249—591no—
189#2249D5911yescharacteristic, direct product factor
190C2×C4×C16—591no—
191C2×C59—162no—
192C2×C59C2×#49311yescharacteristic
193C2×C59C2×#50812yes—
194D59—162no—
195D59#224914yesdirect product factor
196C22×Q16—592no—
197C22×SD16—1182no—
198C22×D8—592no—
199C2×#124—1182no—
200C2×Q32—592no—
201C2×Q32—591no—
202C2×Q32—1184no—
203C2×Q32C2×D5911yescharacteristic, complemented
204C2×SD32—592no—
205C2×SD32—592no—
206C2×SD32—592no—
207C2×SD32—1188no—
208C2×SD32C2×D5912yescomplemented
209C2×D16—592no—
210C2×D16—591no—
211C2×D16—1184no—
212C2×D16C2×D5911yescharacteristic
213C22×C16—591no—
214C22×C16—591no—
215#495—592no—
216#495—592no—
217#495—592no—
218#495—1182no—
219#495—1182no—
220#495C2×D5912yescomplemented
221C2×C4×C8—591no—
222C4×C16—591no—
223C4×C16—591no—
224C4×C16—591no—
225C4×C16C2×D5911yescharacteristic, complemented
226C59C2×#224911yescharacteristic, complemented, Sylow
227C22×Q8—1182no—
228C22×D4—1182no—
229C2×Q16—592no—
230C2×Q16—1184no—
231C2×Q16—1184no—
232C2×Q16—1182no—
233C2×Q16C22×D5912yes—
234C2×SD16—22no—
235C2×SD16—1182no—
236C2×SD16—1182no—
237C2×SD16—1182no—
238C2×SD16—2368no—
239C2×D8—592no—
240C2×D8—1184no—
241C2×D8—1184no—
242C2×D8—1182no—
243C2×D8C22×D5912yes—
244C22×C8—591no—
245C22×C8—591no—
246#124—22no—
247#124—1182no—
248#124—1182no—
249#124—1182no—
250#124—2364no—
251C2×C22⋊C4—2364no—
252C2×C42—591no—
253Q32—22no—
254Q32—1184no—
255Q32—1182no—
256SD32—24no—
257SD32—1184no—
258SD32—1184no—
259SD32—1184no—
260D16—22no—
261D16—1184no—
262D16—1182no—
263C2×C16—591no—
264C2×C16—591no—
265C2×C16—594no—
266C2×C16—594no—
267C2×C16C22×D5911yescharacteristic
268C2×C16C22×D5911yescharacteristic
269C4×C8—591no—
270C4×C8—591no—
271C4×C8—591no—
272C4×C8C22×D5911yescharacteristic
273C24—2362no—
274C2×Q8—22no—
275C2×Q8—1182no—
276C2×Q8—2362no—
277C2×Q8—2364no—
278C2×Q8—2364no—
279C2×D4—22no—
280C2×D4—1182no—
281C2×D4—2364no—
282C2×D4—2364no—
283C2×D4—2362no—
284C22×C4—591no—
285C22×C4—592no—
286C22×C4—2362no—
287Q16—22no—
288Q16—22no—
289Q16—1182no—
290Q16—1182no—
291Q16—2364no—
292SD16—44no—
293SD16—2364no—
294SD16—2364no—
295SD16—2364no—
296D8—22no—
297D8—22no—
298D8—1182no—
299D8—1182no—
300D8—2364no—
301C2×C8—591no—
302C2×C8—591no—
303C2×C8—594no—
304C2×C8—592no—
305C2×C8—592no—
306C2×C8D4×D5911yescharacteristic
307C2×C8C23×D5911yescharacteristic
308C22⋊C4—44no—
309C22⋊C4—2364no—
310C22⋊C4—2364no—
311C22⋊C4—2364no—
312C42—592no—
313C42—591no—
314C42D4×D5911yescharacteristic
315C16—592no—
316C16—592no—
317C16D4×D5912yes—
318C16D4×D5912yes—
319C23—42no—
320C23—591no—
321C23—4724no—
322C23—4728no—
323C23—2362no—
324Q8—42no—
325Q8—42no—
326Q8—4724no—
327Q8—2362no—
328Q8—2362no—
329D4—42no—
330D4—42no—
331D4—4724no—
332D4—2362no—
333D4—2362no—
334C2×C4—42no—
335C2×C4—591no—
336C2×C4—592no—
337C2×C4—592no—
338C2×C4—592no—
339C2×C4—1184no—
340C2×C4—4724no—
341C2×C4—2362no—
342C2×C4D8×D5912yes—
343C2×C4C2×D4×D5911yescharacteristic
344C8—592no—
345C8—592no—
346C8D8×D5912yes—
347C8C2×D4×D5911yescharacteristic
348C8C2×D4×D5911yescharacteristic
349C22—84no—
350C22—82no—
351C22—594no—
352C22—592no—
353C22—9448no—
354C22—4724no—
355C22—4722no—
356C22C2×D8×D5911yescharacteristic
357C4—22no—
358C4—82no—
359C4—592no—
360C4—1182no—
361C4—4722no—
362C4#127×D5911yescharacteristic
363C4C2×D8×D5911yescharacteristic
364C2—162no—
365C2—594no—
366C2—9442no—
367C2#493×D5911yescharacteristic
368C2#508×D5912yes—
subgroupG/H
centerC22C2×D8×D59
commutator, cosocleC2×C8×C59C24
FrattiniC2×C8C23×D59
FittingC59×#2249C2
socleC22×C59C22×D8
prime radicalC2×D16×D59C2
hypercenter#2249D59
hypocenterC59C2×#2249
LCSG ▷ C2×C8×C59 ▷ C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2249

Complements

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

NH ≅ G/Ntype
1. C2×Q32×D59C2semidirect
2. C2×SD32×D59C2semidirect
4. #495×D59C2semidirect
5. #21426358C2semidirect
6. #21426357C2semidirect
7. #21426356C2semidirect
8. #21426355C2semidirect
9. #21426354C2semidirect
10. C4×C16×D59C2semidirect
11. C59×#2249C2semidirect
16. C2×Dic472C22semidirect
17. C2×#14273673C22semidirect
19. C2×#14273672C22semidirect
20. C2×#14273671C22semidirect
21. C2×#14273670C22semidirect
28. #16837787C22semidirect
29. #16837786C22semidirect
30. #16837785C22semidirect
34. C4×C59⋊C16C22semidirect
35. C16×Dic59C22semidirect
36. C16×Dic59C22semidirect
37. C2×Q32×C59C22semidirect
38. C2×SD32×C59C22semidirect
40. C59×#495C22semidirect
41. C4×C16×C59C22semidirect
189. #2249D59direct (N × H)
195. D59#2249direct (N × H)
203. C2×Q32C2×D59semidirect
208. C2×SD32C2×D59semidirect
220. #495C2×D59semidirect
225. C4×C16C2×D59semidirect
226. C59C2×#2249semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×Q32×D592
C2×SD32×D592
C2×D16×D592
#495×D592
#214263582
#214263572
#214263562
#214263552
#214263542
C4×C16×D592
C59×#22492
C2×#224959