Finite Group Databasebeta

← D59×#1824 #28588472

Subgroups — D59×#1824 #28588472

Order 15104.

1878 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4⋊C4×D59C211yesmaximal, characteristic
2C2×C22⋊C8×D59C211yesmaximal, characteristic
3#380×D59C211yesmaximal, characteristic
4#21424187C211yesmaximal, characteristic, complemented
5#21424186C211yesmaximal, characteristic, complemented
6#21424185C214yesmaximal, complemented
7#21424184C211yesmaximal, characteristic, complemented
8#340×D59C214yesmaximal, complemented
9C59×#1824C211yesmaximal, characteristic, complemented
10C23×C4×D59—21no—
11C23×C4×D59C2211yescharacteristic
12C22×C8×D59C2212yes—
13C22×C4⋊Dic59C2211yescharacteristic
14C22×Dic59⋊C4—21no—
15C2×C4⋊C4×D59—21no—
16C2×C4⋊C4×D59—21no—
17C2×C4⋊C4×D59—24no—
18C2×C4⋊C4×D59C418yescomplemented
19C2×C4⋊C4×D59C2212yes—
20C2×C4⋊C4×D59C2212yes—
21C2×C4⋊C4×D59C2212yes—
22C2×C22⋊C4×D59—21no—
23C2×C22⋊(C59⋊C8)C2211yescharacteristic
24C2×(C2×D59)⋊C8C2212yes—
25C22⋊C8×D59—24no—
26#16837262C2211yescharacteristic
27#16837261—21no—
28#16837260—21no—
29#16837259C2212yes—
30#95×D59—21no—
31#16837165C2214yescomplemented
32#16837164C2214yescomplemented
33#16837164C2214yescomplemented
34C22×C4⋊C4×C59C2211yescharacteristic
35C2×C22⋊C8×C59C2211yescharacteristic
36C59×#380C2211yescharacteristic
37C59×#340C2214yescomplemented
38C24×D59D411yescharacteristic
39C23×Dic59—21no—
40C23×Dic59D411yescharacteristic
41C22×C4×D59—28no—
42C22×C4×D59—28no—
43C22×C4×D59—22no—
44C22×C4×D59—22no—
45C22×C4×D59—22no—
46C22×C4×D59—48no—
47C22×C4×D59C2×C414yes—
48C22×C4×D59D411yescharacteristic
49C22×C4×D59D411yescharacteristic
50C22×C4×D59D414yes—
51C22×C4×D59C2311yescharacteristic
52C22×C4×D59C2311yescharacteristic
53C22×C59⋊C8C2312yes—
54C2×C8×D59—24no—
55C2×C8×D59—28no—
56C2×C4⋊Dic59—21no—
57C2×C4⋊Dic59—22no—
58C2×C4⋊Dic59C2×C414yescomplemented
59C2×C4⋊Dic59C2312yes—
60C2×C4⋊Dic59C2312yes—
61C2×Dic59⋊C4—28no—
62C2×Dic59⋊C4—22no—
63C2×Dic59⋊C4—22no—
64C2×Dic59⋊C4—22no—
65C4⋊C4×D59—28no—
66C4⋊C4×D59—28no—
67C4⋊C4×D59—24no—
68C4⋊C4×D59—24no—
69C4⋊C4×D59—28no—
70C4⋊C4×D59C2×C418yes—
71C4⋊C4×D59C2×C418yescomplemented
72C2×C22⋊Dic59—21no—
73C2×(C2×D59)⋊C4—22no—
74C22⋊C4×D59—44no—
75C22⋊(C59⋊C8)—22no—
76(C2×D59)⋊C8—24no—
77C59⋊#95—21no—
78C59⋊#95—22no—
79C23×C4×C59—21no—
80C23×C4×C59C2311yescharacteristic
81C22×C8×C59C2312yes—
82C2×C4⋊C4×C59—21no—
83C2×C4⋊C4×C59—22no—
84C2×C4⋊C4×C59C2×C414yescomplemented
85C2×C4⋊C4×C59C2312yes—
86C2×C4⋊C4×C59C2312yes—
87C2×C22⋊C4×C59—21no—
88C22⋊C8×C59—22no—
89#95×C59—21no—
90C24×C59C2×D411yescharacteristic
91C23×D59—24no—
92C23×D59—24no—
93C23×D59C22⋊C414yes—
94C23×D59SD1614yes—
95C23×D59Q1614yes—
96C23×D59C2×D411yescharacteristic
97C23×D59C2×D411yescharacteristic
98C22×C4×C59—24no—
99C22×C4×C59—24no—
100C22×C4×C59—22no—
101C22×C4×C59—22no—
102C22×C4×C59—44no—
103C22×C4×C59C22×C412yes—
104C22×C4×C59C2×D411yescharacteristic
105C22×C4×C59C2×D412yes—
106C22×C4×C59C2411yescharacteristic
107C22×Dic59—24no—
108C22×Dic59—24no—
109C22×Dic59—22no—
110C22×Dic59—22no—
111C22×Dic59—44no—
112C22×Dic59C22⋊C414yes—
113C22×Dic59C2×D411yescharacteristic
114C22×Dic59C2×D411yescharacteristic
115C2×C4×D59—24no—
116C2×C4×D59—24no—
117C2×C4×D59—24no—
118C2×C4×D59—216no—
119C2×C4×D59—216no—
120C2×C4×D59—28no—
121C2×C4×D59—28no—
122C2×C4×D59—48no—
123C2×C4×D59—432no—
124C2×C4×D59—48no—
125C2×C4×D59—44no—
126C2×C4×D59—44no—
127C2×C4×D59—44no—
128C2×C4×D59C22⋊C414yes—
129C2×C4×D59C22⋊C414yes—
130C2×C4×D59C22×C412yes—
131C2×C4×D59C22×C412yes—
132C2×C4×D59C2×D412yes—
133C2×C4×D59C2×D412yes—
134C2×C4×D59#4118yes—
135C2×C8×C59—22no—
136C2×C8×C59—24no—
137C4⋊C4×C59—24no—
138C4⋊C4×C59—22no—
139C4⋊C4×C59—24no—
140C4⋊C4×C59C22×C414yes—
141C22⋊C4×C59—42no—
142C22⋊Dic59—42no—
143(C2×D59)⋊C4—44no—
144C4⋊Dic59—24no—
145C4⋊Dic59—22no—
146C4⋊Dic59—24no—
147C4⋊Dic59C22×C414yes—
148Dic59⋊C4—28no—
149Dic59⋊C4—28no—
150Dic59⋊C4—44no—
151C2×C59⋊C8—22no—
152C2×C59⋊C8—24no—
153C8×D59—48no—
154C23×C59—22no—
155C23×C59—22no—
156C23×C59C2×C22⋊C412yes—
157C23×C59C2×SD1612yes—
158C23×C59C2×Q1612yes—
159C23×C59C22×D411yescharacteristic
160C22×D59—22no—
161C22×D59—22no—
162C22×D59—28no—
163C22×D59—28no—
164C22×D59—216no—
165C22×D59—216no—
166C22×D59#103116yes—
167C22×D59C2×C22⋊C412yes—
168C22×D59C2×C22⋊C412yes—
169C22×D59#12314yes—
170C22×D59C2×SD1612yes—
171C22×D59C2×SD1612yes—
172C22×D59C2×Q1612yes—
173C22×D59C2×Q1612yes—
174C22×D59AGL(1,ℤ/8)14yes—
175C2×C4×C59—22no—
176C2×C4×C59—24no—
177C2×C4×C59—24no—
178C2×C4×C59—24no—
179C2×C4×C59—48no—
180C2×C4×C59—44no—
181C2×C4×C59—42no—
182C2×C4×C59—42no—
183C2×C4×C59—42no—
184C2×C4×C59C2×C22⋊C412yes—
185C2×C4×C59C23×C411yescharacteristic
186C2×C4×C59C22×D411yescharacteristic
187C2×C4×C59C2×#4114yes—
188C2×Dic59—22no—
189C2×Dic59—28no—
190C2×Dic59—24no—
191C2×Dic59—48no—
192C2×Dic59—44no—
193C2×Dic59—42no—
194C2×Dic59—42no—
195C2×Dic59—42no—
196C2×Dic59C2×C22⋊C412yes—
197C2×Dic59C2×C22⋊C412yes—
198C2×Dic59#12314yes—
199C4×D59—28no—
200C4×D59—24no—
201C4×D59—24no—
202C4×D59—28no—
203C4×D59—416no—
204C4×D59—416no—
205C4×D59—88no—
206C4×D59#11718yes—
207C4×D59#12318yes—
208C8×C59—42no—
209C59⋊C8—42no—
210C2×#1824—591nomaximal, Sylow
211C22×C59—24no—
212C22×C59—24no—
213C22×C59—22no—
214C22×C59—22no—
215C22×C59C2×#10314yes—
216C22×C59C22×C22⋊C411yescharacteristic
217C22×C59C2×#12312yes—
218C22×C59C22×SD1611yescharacteristic
219C22×C59C22×Q1611yescharacteristic
220C22×C59C2×AGL(1,ℤ/8)12yes—
221C2×D59—24no—
222C2×D59—24no—
223C2×D59—22no—
224C2×D59—22no—
225C2×D59—232no—
226C2×D59#38114yes—
227C2×D59C2×#10314yes—
228C2×D59C2×#10314yes—
229C2×D59#41814yes—
230C2×D59#48118yes—
231C2×D59#48418yes—
232C4×C59—22no—
233C4×C59—44no—
234C4×C59—82no—
235C4×C59C2×#11712yes—
236C4×C59C2×#12312yes—
237Dic59—22no—
238Dic59—44no—
239Dic59—82no—
240Dic59#38114yes—
241C23×C4⋊C4—591no—
242C22×C22⋊C8—591no—
243C2×#380—591no—
244#1824—591no—
245#1824—591no—
246#1824—594no—
247#1824—591no—
248#1824D5911yescharacteristic, direct product factor
249C2×#340—594no—
250C2×C59—24no—
251C2×C59C2×#38111yescharacteristic
252C2×C59C22×#10311yescharacteristic
253C2×C59C2×#41811yescharacteristic
254C2×C59C2×#48112yes—
255C2×C59C2×#48412yes—
256D59—24no—
257D59#182418yesdirect product factor
258C24×C4—591no—
259C24×C4—1181no—
260C23×C8—592no—
261C22×C4⋊C4—591no—
262C22×C4⋊C4—598no—
263C22×C4⋊C4—592no—
264C22×C4⋊C4—592no—
265C22×C4⋊C4—592no—
266C22×C4⋊C4—1181no—
267C22×C4⋊C4—1181no—
268C22×C4⋊C4—1184no—
269C22×C4⋊C4—1181no—
270C22×C4⋊C4C2×D5911yescharacteristic
271C22×C22⋊C4—1181no—
272C2×C22⋊C8—591no—
273C2×C22⋊C8—592no—
274C2×C22⋊C8—1184no—
275C2×C22⋊C8C2×D5911yescharacteristic
276#380—591no—
277#380—592no—
278#380—1181no—
279#380—1181no—
280#380C2×D5911yescharacteristic
281C2×#95—1181no—
282#340—594no—
283#340—594no—
284#340—594no—
285#340C2×D5914yescomplemented
286C59C2×#182411yescharacteristic, complemented, Sylow
287C25—591no—
288C23×C4—21no—
289C23×C4—591no—
290C23×C4—591no—
291C23×C4—594no—
292C23×C4—591no—
293C23×C4—591no—
294C23×C4—594no—
295C23×C4—591no—
296C23×C4—1188no—
297C23×C4—1188no—
298C23×C4—1182no—
299C23×C4—1182no—
300C23×C4—1182no—
301C23×C4—1181no—
302C23×C4—2368no—
303C23×C4C22×D5911yescharacteristic
304C22×C8—592no—
305C22×C8—1184no—
306C22×C8—1188no—
307C22×C8C22×D5912yes—
308C2×C4⋊C4—21no—
309C2×C4⋊C4—22no—
310C2×C4⋊C4—594no—
311C2×C4⋊C4—592no—
312C2×C4⋊C4—598no—
313C2×C4⋊C4—598no—
314C2×C4⋊C4—592no—
315C2×C4⋊C4—1188no—
316C2×C4⋊C4—1188no—
317C2×C4⋊C4—1184no—
318C2×C4⋊C4—1184no—
319C2×C4⋊C4—1188no—
320C2×C4⋊C4—1188no—
321C2×C4⋊C4—1182no—
322C2×C4⋊C4—1182no—
323C2×C4⋊C4—1181no—
324C2×C4⋊C4—1182no—
325C2×C4⋊C4—1182no—
326C2×C4⋊C4C4×D5914yescomplemented
327C2×C4⋊C4C22×D5912yes—
328C2×C4⋊C4C22×D5912yes—
329C2×C22⋊C4—21no—
330C2×C22⋊C4—1182no—
331C2×C22⋊C4—1181no—
332C2×C22⋊C4—2364no—
333C22⋊C8—22no—
334C22⋊C8—1184no—
335C22⋊C8—1182no—
336#95—21no—
337#95—1182no—
338#95—1181no—
339C24—591no—
340C24—594no—
341C24—594no—
342C24—594no—
343C24—591no—
344C24—1184no—
345C24—1184no—
346C24D4×D5911yescharacteristic
347C22×C4—24no—
348C22×C4—24no—
349C22×C4—22no—
350C22×C4—22no—
351C22×C4—44no—
352C22×C4—591no—
353C22×C4—592no—
354C22×C4—592no—
355C22×C4—598no—
356C22×C4—594no—
357C22×C4—591no—
358C22×C4—594no—
359C22×C4—594no—
360C22×C4—592no—
361C22×C4—592no—
362C22×C4—1184no—
363C22×C4—11816no—
364C22×C4—11816no—
365C22×C4—1184no—
366C22×C4—1188no—
367C22×C4—1188no—
368C22×C4—1184no—
369C22×C4—1184no—
370C22×C4—1184no—
371C22×C4—1182no—
372C22×C4—1182no—
373C22×C4—2364no—
374C22×C4—2364no—
375C22×C4—2364no—
376C22×C4—2368no—
377C22×C4—23632no—
378C22×C4—2368no—
379C22×C4—2364no—
380C22×C4C2×C4×D5912yes—
381C22×C4D4×D5911yescharacteristic
382C22×C4D4×D5912yes—
383C22×C4C23×D5911yescharacteristic
384C2×C8—22no—
385C2×C8—24no—
386C2×C8—1182no—
387C2×C8—1184no—
388C2×C8—2368no—
389C4⋊C4—24no—
390C4⋊C4—22no—
391C4⋊C4—24no—
392C4⋊C4—594no—
393C4⋊C4—1188no—
394C4⋊C4—1188no—
395C4⋊C4—1184no—
396C4⋊C4—1182no—
397C4⋊C4—1184no—
398C4⋊C4—2364no—
399C4⋊C4C2×C4×D5914yes—
400C22⋊C4—42no—
401C22⋊C4—2364no—
402C22⋊C4—2362no—
403C23—22no—
404C23—22no—
405C23—594no—
406C23—592no—
407C23—592no—
408C23—594no—
409C23—592no—
410C23—5916no—
411C23—592no—
412C23—592no—
413C23—592no—
414C23—1188no—
415C23—1188no—
416C23—11816no—
417C23—11816no—
418C23—1182no—
419C23—1182no—
420C23C22⋊C4×D5912yes—
421C23SD16×D5912yes—
422C23Q16×D5912yes—
423C23C2×D4×D5911yescharacteristic
424C2×C4—22no—
425C2×C4—24no—
426C2×C4—24no—
427C2×C4—24no—
428C2×C4—48no—
429C2×C4—44no—
430C2×C4—42no—
431C2×C4—42no—
432C2×C4—42no—
433C2×C4—594no—
434C2×C4—592no—
435C2×C4—598no—
436C2×C4—598no—
437C2×C4—592no—
438C2×C4—1188no—
439C2×C4—1188no—
440C2×C4—1188no—
441C2×C4—1182no—
442C2×C4—1184no—
443C2×C4—1184no—
444C2×C4—1184no—
445C2×C4—4728no—
446C2×C4—23616no—
447C2×C4—23616no—
448C2×C4—2362no—
449C2×C4—2362no—
450C2×C4—2362no—
451C2×C4—2368no—
452C2×C4—2364no—
453C2×C4C22⋊C4×D5912yes—
454C2×C4C22×C4×D5911yescharacteristic
455C2×C4C2×D4×D5911yescharacteristic
456C2×C4#41×D5914yes—
457C8—42no—
458C8—2362no—
459C22—22no—
460C22—22no—
461C22—24no—
462C22—24no—
463C22—594no—
464C22—594no—
465C22—594no—
466C22—598no—
467C22—598no—
468C22—594no—
469C22—11832no—
470C22—1182no—
471C22—1182no—
472C22—1184no—
473C22—1184no—
474C22#103×D5914yes—
475C22C2×C22⋊C4×D5911yescharacteristic
476C22#123×D5912yes—
477C22C2×SD16×D5911yescharacteristic
478C22C2×Q16×D5911yescharacteristic
479C22AGL(1,ℤ/8)×D5912yes—
480C4—22no—
481C4—44no—
482C4—82no—
483C4—594no—
484C4—1182no—
485C4—4722no—
486C4—2364no—
487C4#117×D5912yes—
488C4#123×D5912yes—
489C2—24no—
490C2—598no—
491C2—1184no—
492C2#381×D5911yescharacteristic
493C2C2×#103×D5911yescharacteristic
494C2#418×D5911yescharacteristic
495C2#481×D5912yes—
496C2#484×D5912yes—
subgroupG/H
centerC23C2×D4×D59
commutatorC2×C4×C59C23×C4
FrattiniC22×C4C23×D59
FittingC59×#1824C2
socleC23×C59C22×D4
prime radicalC24×D59D4
cosocleC22×C4×C59C24
hypercenter#1824D59
hypocenterC59C2×#1824
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1824

Complements

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

NH ≅ G/Ntype
4. #21424187C2semidirect
5. #21424186C2semidirect
6. #21424185C2semidirect
7. #21424184C2semidirect
8. #340×D59C2semidirect
9. C59×#1824C2semidirect
18. C2×C4⋊C4×D59C4semidirect
31. #16837165C22semidirect
32. #16837164C22semidirect
33. #16837164C22semidirect
37. C59×#340C22semidirect
58. C2×C4⋊Dic59C2×C4semidirect
71. C4⋊C4×D59C2×C4semidirect
84. C2×C4⋊C4×C59C2×C4semidirect
248. #1824D59direct (N × H)
257. D59#1824direct (N × H)
285. #340C2×D59semidirect
286. C59C2×#1824semidirect
326. C2×C4⋊C4C4×D59semidirect

Maximal subgroups

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

subgroupindex
C22×C4⋊C4×D592
C2×C22⋊C8×D592
#380×D592
#214241872
#214241862
#214241852
#214241842
#340×D592
C59×#18242
C2×#182459