Finite Group Databasebeta

← D59×#2237 #28743463

Subgroups — D59×#2237 #28743463

Order 15104.

586 conjugacy classes of subgroups.

The subgroup lattice has 506 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#467×D59C211yesmaximal, characteristic
2#427×D59C211yesmaximal, characteristic
3#21426307C211yesmaximal, characteristic, complemented
4#21426306C211yesmaximal, characteristic, complemented
5#21426305C211yesmaximal, characteristic, complemented
6#21426304C211yesmaximal, characteristic, complemented
7#21426303C211yesmaximal, characteristic, complemented
8#21426302C211yesmaximal, characteristic, complemented
9#21426301C211yesmaximal, characteristic, complemented
10#367×D59C211yesmaximal, characteristic, complemented
11#366×D59C211yesmaximal, characteristic, complemented
12#358×D59C211yesmaximal, characteristic, complemented
13#358×D59C211yesmaximal, characteristic, complemented
14C22⋊C16×D59C211yesmaximal, characteristic
15C59×#2237C211yesmaximal, characteristic, complemented
16C2×Q16×D59C2211yescharacteristic
17C22×C8×D59C2211yescharacteristic
18C22⋊Q8×D59—21no—
19#117×D59—21no—
20C2×C16×D59C2211yescharacteristic
21C2×C16×D59C2211yescharacteristic
22#16837644C2211yescharacteristic
23#16837643C2211yescharacteristic
24#16837642—21no—
25#16837641—21no—
26#16837640C2211yescharacteristic
27#16837440C2211yescharacteristic
28#16837439C2211yescharacteristic
29#16837439C2211yescharacteristic
30#16837438—21no—
31#16837437—21no—
32#107×D59C2211yescharacteristic
33#107×D59C2211yescharacteristic
34#107×D59C2211yescharacteristic
35#106×D59—21no—
36#103×D59—21no—
37#16837230C2211yescharacteristic, complemented
38#16837229C2211yescharacteristic, complemented
39#16837229C2211yescharacteristic, complemented
40#16837228C2211yescharacteristic, complemented
41#16837227C2211yescharacteristic, complemented
42#16837227C2211yescharacteristic, complemented
43#16837207C2211yescharacteristic, complemented
44#16837207C2211yescharacteristic, complemented
45#16837206C2211yescharacteristic, complemented
46#16837206C2211yescharacteristic, complemented
47#16837205C2211yescharacteristic, complemented
48#16837205C2211yescharacteristic, complemented
49C22⋊(C59⋊C16)C2211yescharacteristic
50(C2×D59)⋊C16C2211yescharacteristic
51(C2×D59)⋊C16C2211yescharacteristic
52C59×#467C2211yescharacteristic
53C59×#427C2211yescharacteristic
54C59×#367C2211yescharacteristic, complemented
55C59×#366C2211yescharacteristic, complemented
56C59×#358C2211yescharacteristic, complemented
57C59×#358C2211yescharacteristic, complemented
58C59×C22⋊C16C2211yescharacteristic
59C2×Q8×D59—21no—
60C22×C4×D59D411yescharacteristic
61C2×Dic236C2311yescharacteristic
62C2×#11745672—21no—
63Q16×D59—22no—
64Q16×D59—22no—
65C22×C59⋊C8D411yescharacteristic
66C2×C8×D59—22no—
67C2×C8×D59—22no—
68C2×C8×D59D411yescharacteristic
69C2×C8×D59D411yescharacteristic
70C2×C8×D59C2311yescharacteristic
71C2×C8×D59C2311yescharacteristic
72#14273707—21no—
73#14273706—21no—
74#14273705—41no—
75#14273704—41no—
76#14273703—21no—
77#14273686—21no—
78#14273685—21no—
79#14273685—21no—
80#14273684—41no—
81#14273683—41no—
82C4⋊C4×D59—21no—
83C4⋊C4×D59—21no—
84C4⋊C4×D59—21no—
85C4⋊C4×D59—41no—
86C22⋊C4×D59—41no—
87C22⋊C4×D59—41no—
88C42×D59—41no—
89C2×C59⋊C16C2311yescharacteristic
90C2×C59⋊C16C2311yescharacteristic
91C16×D59—22no—
92C16×D59—22no—
93#14273661C2311yescharacteristic
94#14273661C2311yescharacteristic
95#14273661C2311yescharacteristic
96#14273660—21no—
97#14273660—21no—
98#14273660—21no—
99#14273659—21no—
100#14273658—21no—
101#14273658—21no—
102#14273652—21no—
103#14273651—21no—
104#14273650—21no—
105C2×Q16×C59C2311yescharacteristic
106C22×C8×C59C2311yescharacteristic
107C22⋊Q8×C59—21no—
108#117×C59—21no—
109C2×C16×C59C2311yescharacteristic
110C2×C16×C59C2311yescharacteristic
111#107×C59C2311yescharacteristic
112#107×C59C2311yescharacteristic
113#107×C59C2311yescharacteristic
114#106×C59—21no—
115#103×C59—21no—
116C23×D59D811yescharacteristic
117C2×Q8×C59—21no—
118C22×C4×C59C2×D411yescharacteristic
119C22×Dic59D811yescharacteristic
120Q8×D59—42no—
121Q8×D59—42no—
122C2×C4×D59—22no—
123C2×C4×D59—22no—
124C2×C4×D59—41no—
125C2×C4×D59—41no—
126C2×C4×D59—41no—
127C2×C4×D59—41no—
128C2×C4×D59D811yescharacteristic
129C2×C4×D59D811yescharacteristic
130C2×C4×D59C2×D411yescharacteristic
131C2×C4×D59C2×D411yescharacteristic
132C2×Dic118—21no—
133C2×Dic118—41no—
134Q16×C59—21no—
135Q16×C59—21no—
136C2×C8×C59—21no—
137C2×C8×C59—21no—
138C2×C8×C59C2×D411yescharacteristic
139C2×C8×C59C2411yescharacteristic
140C4⋊C4×C59—21no—
141C4⋊C4×C59—21no—
142C4⋊C4×C59—21no—
143C4⋊C4×C59—41no—
144C22⋊C4×C59—41no—
145C22⋊C4×C59—41no—
146C42×C59—41no—
147C22⋊Dic59—41no—
148C22⋊Dic59—41no—
149#11745672—42no—
150(C2×D59)⋊C4—41no—
151(C2×D59)⋊C4—41no—
152(C2×D59)⋊C4—41no—
153(C2×D59)⋊C4—41no—
154C4⋊Dic59—21no—
155C4⋊Dic59—21no—
156C4⋊Dic59—21no—
157C4⋊Dic59—41no—
158Dic59⋊C4—41no—
159Dic59⋊C4—41no—
160Dic59⋊C4—41no—
161Dic59⋊C4—41no—
162Dic59⋊C4—41no—
163C4×Dic59—41no—
164C4×Dic59—41no—
165C4×Dic59—41no—
166C2×C59⋊C8—22no—
167C2×C59⋊C8C2×D411yescharacteristic
168C2×C59⋊C8C2×D411yescharacteristic
169Dic236—21no—
170Dic236—21no—
171C8×D59—22no—
172C8×D59—21no—
173C8×D59—21no—
174C8×D59—22no—
175C8×D59#4112yes—
176C8×D59#4112yes—
177C16×C59—21no—
178C16×C59—21no—
179C59⋊C16—21no—
180C59⋊C16—21no—
181C23×C59C2×D811yescharacteristic
182C22×D59—22no—
183C22×D59—22no—
184C22×D59—22no—
185C22×D59C2×D811yescharacteristic
186C22×D59C2×D811yescharacteristic
187Q8×C59—41no—
188Q8×C59—41no—
189C2×C4×C59—21no—
190C2×C4×C59—21no—
191C2×C4×C59—41no—
192C2×C4×C59—41no—
193C2×C4×C59—41no—
194C2×C4×C59—41no—
195C2×C4×C59C2×D811yescharacteristic
196C2×C4×C59C22×D411yescharacteristic
197C2×Dic59—22no—
198C2×Dic59—41no—
199C2×Dic59—41no—
200C2×Dic59—41no—
201C2×Dic59—41no—
202C2×Dic59C2×D811yescharacteristic
203C2×Dic59C2×D811yescharacteristic
204C4×D59—22no—
205C4×D59—21no—
206C4×D59—21no—
207C4×D59—22no—
208C4×D59—82no—
209C4×D59—82no—
210C4×D59—82no—
211C4×D59—82no—
212C4×D59#12312yes—
213C4×D59#13712yes—
214Dic118—41no—
215Dic118—41no—
216Dic118—82no—
217C8×C59—21no—
218C8×C59C2×#4111yescharacteristic
219C8×C59C2×#4111yescharacteristic
220C59⋊C8—21no—
221C59⋊C8#12312yes—
222C2×#2237—591nomaximal, Sylow
223C22×C59—21no—
224C22×C59—21no—
225C22×C59—21no—
226C22×C59C22×D811yescharacteristic
227C2×D59—21no—
228C2×D59—21no—
229C2×D59—21no—
230C2×D59—44no—
231C2×D59#48012yes—
232C2×D59#50812yes—
233C2×D59#51012yes—
234C4×C59—21no—
235C4×C59—81no—
236C4×C59—81no—
237C4×C59—81no—
238C4×C59—81no—
239C4×C59C2×#12311yescharacteristic
240C4×C59C2×#13711yescharacteristic
241Dic59—21no—
242Dic59—81no—
243Dic59—81no—
244Dic59—81no—
245Dic59—81no—
246Dic59#48012yes—
247C2×#467—591no—
248C2×#427—591no—
249#2237—591no—
250#2237—591no—
251#2237—591no—
252#2237—591no—
253#2237—591no—
254#2237—591no—
255#2237—591no—
256#2237D5911yescharacteristic, direct product factor
257C2×#367—591no—
258C2×#366—591no—
259C2×#358—591no—
260C2×#358—591no—
261C2×C22⋊C16—591no—
262C2×C59—41no—
263C2×C59C2×#48011yescharacteristic
264C2×C59C2×#50811yescharacteristic
265C2×C59C2×#51011yescharacteristic
266D59—41no—
267D59#223714yesdirect product factor
268C22×Q16—591no—
269C23×C8—591no—
270C2×C22⋊Q8—1181no—
271C2×#117—1181no—
272C22×C16—591no—
273C22×C16—591no—
274#467—591no—
275#467—591no—
276#467—591no—
277#467—1181no—
278#467—1181no—
279#467C2×D5911yescharacteristic
280#427—591no—
281#427—591no—
282#427—591no—
283#427—1181no—
284#427—1181no—
285#427C2×D5911yescharacteristic
286C2×#107—591no—
287C2×#107—591no—
288C2×#107—591no—
289C2×#106—1181no—
290C2×#103—1181no—
291#367—591no—
292#367—591no—
293#367—591no—
294#367C2×D5911yescharacteristic, complemented
295#366—591no—
296#366—591no—
297#366—591no—
298#366C2×D5911yescharacteristic, complemented
299#358—591no—
300#358—591no—
301#358—591no—
302#358—591no—
303#358—591no—
304#358—591no—
305#358C2×D5911yescharacteristic, complemented
306#358C2×D5911yescharacteristic, complemented
307C22⋊C16—591no—
308C22⋊C16—591no—
309C22⋊C16—591no—
310C22⋊C16C2×D5911yescharacteristic
311C59C2×#223711yescharacteristic, complemented, Sylow
312C22×Q8—1181no—
313C23×C4—591no—
314C2×Q16—591no—
315C2×Q16—1182no—
316C2×Q16—1182no—
317C2×Q16—1181no—
318C2×Q16C22×D5911yescharacteristic
319C22×C8—591no—
320C22×C8—591no—
321C22×C8—591no—
322C22×C8—591no—
323C22×C8—591no—
324C22×C8—1182no—
325C22×C8—1182no—
326C22×C8C22×D5911yescharacteristic
327C22⋊Q8—21no—
328C22⋊Q8—1181no—
329C22⋊Q8—1181no—
330C22⋊Q8—1181no—
331C22⋊Q8—2361no—
332C22⋊Q8—2361no—
333#117—21no—
334#117—1181no—
335#117—1181no—
336#117—1181no—
337#117—2361no—
338#117—2361no—
339C2×C4⋊C4—1181no—
340C2×C4⋊C4—1181no—
341C2×C4⋊C4—1181no—
342C2×C4⋊C4—2361no—
343C2×C22⋊C4—2361no—
344C2×C22⋊C4—2361no—
345C2×C42—2361no—
346C2×C16—591no—
347C2×C16—591no—
348C2×C16—1182no—
349C2×C16—1182no—
350C2×C16C22×D5911yescharacteristic
351C2×C16C22×D5911yescharacteristic
352#107—591no—
353#107—591no—
354#107—591no—
355#107—1181no—
356#107—1181no—
357#107—1181no—
358#107C22×D5911yescharacteristic
359#107C22×D5911yescharacteristic
360#107C22×D5911yescharacteristic
361#106—21no—
362#106—1181no—
363#106—1181no—
364#106—1181no—
365#103—21no—
366#103—1181no—
367#103—1181no—
368#103—1181no—
369C24—591no—
370C2×Q8—21no—
371C2×Q8—1181no—
372C2×Q8—2361no—
373C2×Q8—2362no—
374C2×Q8—2362no—
375C22×C4—591no—
376C22×C4—591no—
377C22×C4—591no—
378C22×C4—591no—
379C22×C4—591no—
380C22×C4—1182no—
381C22×C4—1182no—
382C22×C4—2361no—
383C22×C4—2361no—
384C22×C4—2361no—
385C22×C4—2361no—
386C22×C4D4×D5911yescharacteristic
387Q16—21no—
388Q16—21no—
389Q16—1181no—
390Q16—1181no—
391Q16—2362no—
392C2×C8—21no—
393C2×C8—21no—
394C2×C8—591no—
395C2×C8—592no—
396C2×C8—592no—
397C2×C8—591no—
398C2×C8—1182no—
399C2×C8—1182no—
400C2×C8—1182no—
401C2×C8—1181no—
402C2×C8—1181no—
403C2×C8D4×D5911yescharacteristic
404C2×C8C23×D5911yescharacteristic
405C4⋊C4—21no—
406C4⋊C4—21no—
407C4⋊C4—21no—
408C4⋊C4—41no—
409C4⋊C4—1181no—
410C4⋊C4—1181no—
411C4⋊C4—1181no—
412C4⋊C4—2361no—
413C4⋊C4—2361no—
414C4⋊C4—2361no—
415C4⋊C4—2361no—
416C4⋊C4—2361no—
417C4⋊C4—2361no—
418C22⋊C4—41no—
419C22⋊C4—41no—
420C22⋊C4—2361no—
421C22⋊C4—2361no—
422C22⋊C4—2361no—
423C22⋊C4—2361no—
424C22⋊C4—2361no—
425C22⋊C4—2361no—
426C42—41no—
427C42—2361no—
428C42—2361no—
429C42—2361no—
430C16—21no—
431C16—21no—
432C16—1181no—
433C16—1181no—
434C23—591no—
435C23—591no—
436C23—1182no—
437C23—1182no—
438C23—1182no—
439C23D8×D5911yescharacteristic
440Q8—41no—
441Q8—41no—
442Q8—4722no—
443Q8—2361no—
444Q8—2361no—
445C2×C4—21no—
446C2×C4—21no—
447C2×C4—41no—
448C2×C4—41no—
449C2×C4—41no—
450C2×C4—41no—
451C2×C4—591no—
452C2×C4—592no—
453C2×C4—592no—
454C2×C4—591no—
455C2×C4—1182no—
456C2×C4—1182no—
457C2×C4—1182no—
458C2×C4—1181no—
459C2×C4—1181no—
460C2×C4—4722no—
461C2×C4—4722no—
462C2×C4—4722no—
463C2×C4—4722no—
464C2×C4—2361no—
465C2×C4—2361no—
466C2×C4—2361no—
467C2×C4—2361no—
468C2×C4D8×D5911yescharacteristic
469C2×C4C2×D4×D5911yescharacteristic
470C8—21no—
471C8—592no—
472C8—1181no—
473C8#41×D5911yescharacteristic
474C8#41×D5911yescharacteristic
475C22—21no—
476C22—21no—
477C22—21no—
478C22—592no—
479C22—592no—
480C22—592no—
481C22—1181no—
482C22—1181no—
483C22—1181no—
484C22—2364no—
485C22C2×D8×D5911yescharacteristic
486C4—21no—
487C4—81no—
488C4—81no—
489C4—81no—
490C4—81no—
491C4—592no—
492C4—1181no—
493C4—4721no—
494C4—4721no—
495C4—4721no—
496C4—4721no—
497C4#123×D5911yescharacteristic
498C4#137×D5911yescharacteristic
499C2—41no—
500C2—594no—
501C2—2361no—
502C2#480×D5911yescharacteristic
503C2#508×D5911yescharacteristic
504C2#510×D5911yescharacteristic
subgroupG/H
centerC22C2×D8×D59
commutator, cosocleC2×C8×C59C24
FrattiniC2×C8C23×D59
FittingC59×#2237C2
socleC22×C59C22×D8
prime radicalC23×D59D8
hypercenter#2237D59
hypocenterC59C2×#2237
LCSG ▷ C2×C8×C59 ▷ C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2237

Complements

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

NH ≅ G/Ntype
3. #21426307C2semidirect
4. #21426306C2semidirect
5. #21426305C2semidirect
6. #21426304C2semidirect
7. #21426303C2semidirect
8. #21426302C2semidirect
9. #21426301C2semidirect
10. #367×D59C2semidirect
11. #366×D59C2semidirect
12. #358×D59C2semidirect
13. #358×D59C2semidirect
15. C59×#2237C2semidirect
37. #16837230C22semidirect
38. #16837229C22semidirect
39. #16837229C22semidirect
40. #16837228C22semidirect
41. #16837227C22semidirect
42. #16837227C22semidirect
43. #16837207C22semidirect
44. #16837207C22semidirect
45. #16837206C22semidirect
46. #16837206C22semidirect
47. #16837205C22semidirect
48. #16837205C22semidirect
54. C59×#367C22semidirect
55. C59×#366C22semidirect
56. C59×#358C22semidirect
57. C59×#358C22semidirect
256. #2237D59direct (N × H)
267. D59#2237direct (N × H)
294. #367C2×D59semidirect
298. #366C2×D59semidirect
305. #358C2×D59semidirect
306. #358C2×D59semidirect
311. C59C2×#2237semidirect

Maximal subgroups

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

subgroupindex
#467×D592
#427×D592
#214263072
#214263062
#214263052
#214263042
#214263032
#214263022
#214263012
#367×D592
#366×D592
#358×D592
C22⋊C16×D592
C59×#22372
C2×#223759