Finite Group Databasebeta

← D59×#2084 #28617661

Subgroups — D59×#2084 #28617661

Order 15104.

1086 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#106×D59C212yesmaximal
2#389×D59C211yesmaximal, characteristic
3#384×D59C211yesmaximal, characteristic
4#21425576C212yesmaximal, complemented
5#21425575C212yesmaximal, complemented
6#21425574C211yesmaximal, characteristic, complemented
7#21425573C211yesmaximal, characteristic, complemented
8#21425572C211yesmaximal, characteristic, complemented
9#340×D59C212yesmaximal
10#336×D59C211yesmaximal, characteristic
11C59×#2084C211yesmaximal, characteristic, complemented
12C22×C8×D59C2212yes—
13C2×C4⋊C4×D59—21no—
14C2×C4⋊C4×D59—21no—
15C2×C4⋊C4×D59—21no—
16C2×C4⋊C4×D59C2212yes—
17C2×C4⋊C4×D59C2211yescharacteristic
18C2×C4⋊C4×D59C2211yescharacteristic
19C2×C42×D59C2211yescharacteristic
20C2×#14273659C2212yes—
21C2×#14273658C2212yes—
22C2×#14273658C2212yes—
23#106×D59—28no—
24#16837301C2211yescharacteristic
25#16837300C2211yescharacteristic
26#16837299—21no—
27#16837298C2211yescharacteristic
28#16837297—21no—
29#16837272C2211yescharacteristic
30#16837271—21no—
31#16837271—21no—
32#16837271C2212yes—
33#95×D59—21no—
34#16837165C2212yes—
35#16837164C2212yes—
36#16837164C2212yes—
37#16837157C2211yescharacteristic
38#16837156C2212yes—
39C2×#106×C59C2212yes—
40C59×#389C2211yescharacteristic
41C59×#384C2211yescharacteristic
42C59×#340C2212yes—
43C59×#336C2211yescharacteristic
44C22×C4×D59—21no—
45C22×C4×D59—21no—
46C22×C4×D59—22no—
47C22×C4×D59D411yescharacteristic
48C22×C4×D59D411yescharacteristic
49C22×C4×D59C2311yescharacteristic
50C22×C59⋊C8C2312yes—
51C2×C8×D59—24no—
52C2×C8×D59—24no—
53C2×C8×D59Q818yes—
54C2×C4⋊Dic59—21no—
55C2×C4⋊Dic59—21no—
56C2×C4⋊Dic59—21no—
57C2×C4⋊Dic59C2311yescharacteristic
58C2×C4⋊Dic59C2312yes—
59C2×C4⋊Dic59C2311yescharacteristic
60C2×Dic59⋊C4—21no—
61C2×Dic59⋊C4—21no—
62C2×Dic59⋊C4—22no—
63C2×Dic59⋊C4—22no—
64C2×Dic59⋊C4—22no—
65C2×Dic59⋊C4—21no—
66C2×Dic59⋊C4—21no—
67C4⋊C4×D59—22no—
68C4⋊C4×D59—24no—
69C4⋊C4×D59—24no—
70C4⋊C4×D59—24no—
71C4⋊C4×D59—44no—
72C4⋊C4×D59—44no—
73C4⋊C4×D59—44no—
74C4⋊C4×D59D414yes—
75C2×C4×Dic59D411yescharacteristic
76C2×C4×Dic59D411yescharacteristic
77C2×C4×Dic59C2311yescharacteristic
78C42×D59—24no—
79#14273659—24no—
80#14273658—24no—
81#14273658—24no—
82C59⋊#95—21no—
83C59⋊#95—21no—
84C59⋊#95—21no—
85C22×C8×C59C2312yes—
86C2×C4⋊C4×C59—21no—
87C2×C4⋊C4×C59—21no—
88C2×C4⋊C4×C59—21no—
89C2×C4⋊C4×C59C2311yescharacteristic
90C2×C4⋊C4×C59C2312yes—
91C2×C4⋊C4×C59C2311yescharacteristic
92C2×C42×C59C2311yescharacteristic
93#106×C59—24no—
94#95×C59—21no—
95C23×D59C2×D411yescharacteristic
96C22×C4×C59—21no—
97C22×C4×C59—21no—
98C22×C4×C59—22no—
99C22×C4×C59C2×D411yescharacteristic
100C22×C4×C59C2×D411yescharacteristic
101C22×C4×C59C2411yescharacteristic
102C22×Dic59—21no—
103C22×Dic59—21no—
104C22×Dic59—22no—
105C22×Dic59C2×D411yescharacteristic
106C22×Dic59C2×D411yescharacteristic
107C22×Dic59C2×D411yescharacteristic
108C2×C4×D59—22no—
109C2×C4×D59—22no—
110C2×C4×D59—22no—
111C2×C4×D59—22no—
112C2×C4×D59—24no—
113C2×C4×D59—42no—
114C2×C4×D59—42no—
115C2×C4×D59—44no—
116C2×C4×D59—42no—
117C2×C4×D59—44no—
118C2×C4×D59—42no—
119C2×C4×D59—44no—
120C2×C4×D59—42no—
121C2×C4×D59SD1614yes—
122C2×C4×D59SD1614yes—
123C2×C4×D59C2×D412yes—
124C2×C4×D59C2×Q814yes—
125C2×C4×D59#4114yes—
126C2×C4×D59#4112yes—
127C2×C8×C59—22no—
128C2×C8×C59—22no—
129C2×C8×C59C2×Q814yes—
130C4⋊C4×C59—21no—
131C4⋊C4×C59—22no—
132C4⋊C4×C59—22no—
133C4⋊C4×C59—22no—
134C4⋊C4×C59—42no—
135C4⋊C4×C59—42no—
136C4⋊C4×C59—42no—
137C4⋊C4×C59C2×D412yes—
138C42×C59—22no—
139C4⋊Dic59—21no—
140C4⋊Dic59—22no—
141C4⋊Dic59—22no—
142C4⋊Dic59—22no—
143C4⋊Dic59—42no—
144C4⋊Dic59—42no—
145C4⋊Dic59—42no—
146C4⋊Dic59C2×D412yes—
147Dic59⋊C4—24no—
148Dic59⋊C4—44no—
149Dic59⋊C4—42no—
150Dic59⋊C4—44no—
151Dic59⋊C4—42no—
152Dic59⋊C4—42no—
153Dic59⋊C4—44no—
154C4×Dic59—22no—
155C4×Dic59—22no—
156C4×Dic59—22no—
157C2×C59⋊C8—22no—
158C2×C59⋊C8—22no—
159C2×C59⋊C8C2×Q814yes—
160C8×D59—216no—
161C23×C59C22×D411yescharacteristic
162C22×D59#12112yes—
163C22×D59#12312yes—
164C22×D59C4⋊Q812yes—
165C22×D59C2×SD1612yes—
166C22×D59C2×SD1612yes—
167C22×D59AGL(1,ℤ/8)12yes—
168C22×D59#13712yes—
169C2×C4×C59—21no—
170C2×C4×C59—21no—
171C2×C4×C59—21no—
172C2×C4×C59—21no—
173C2×C4×C59—22no—
174C2×C4×C59—41no—
175C2×C4×C59—41no—
176C2×C4×C59—42no—
177C2×C4×C59—41no—
178C2×C4×C59—41no—
179C2×C4×C59—42no—
180C2×C4×C59—42no—
181C2×C4×C59—41no—
182C2×C4×C59C2×SD1612yes—
183C2×C4×C59C2×SD1612yes—
184C2×C4×C59C22×D411yescharacteristic
185C2×C4×C59C22×Q812yes—
186C2×C4×C59C2×#4112yes—
187C2×C4×C59C2×#4111yescharacteristic
188C2×Dic59—21no—
189C2×Dic59—21no—
190C2×Dic59—21no—
191C2×Dic59—21no—
192C2×Dic59—22no—
193C2×Dic59—41no—
194C2×Dic59—41no—
195C2×Dic59—42no—
196C2×Dic59—41no—
197C2×Dic59—41no—
198C2×Dic59—42no—
199C2×Dic59—42no—
200C2×Dic59—41no—
201C2×Dic59#12112yes—
202C2×Dic59#12312yes—
203C2×Dic59C4⋊Q812yes—
204C2×Dic59C2×SD1612yes—
205C2×Dic59C2×SD1612yes—
206C4×D59—28no—
207C4×D59—28no—
208C4×D59—48no—
209C4×D59—88no—
210C4×D59—84no—
211C4×D59C22⋊Q818yes—
212C4×D59#12518yes—
213C8×C59—24no—
214C59⋊C8—24no—
215C2×#2084—591nomaximal, Sylow
216C22×C59C2×#12111yescharacteristic
217C22×C59C2×#12311yescharacteristic
218C22×C59C2×C4⋊Q811yescharacteristic
219C22×C59C22×SD1611yescharacteristic
220C22×C59C22×SD1611yescharacteristic
221C22×C59C2×AGL(1,ℤ/8)11yescharacteristic
222C22×C59C2×#13711yescharacteristic
223C2×D59#39814yes—
224C2×D59#46014yes—
225C2×D59#46114yes—
226C2×D59#48114yes—
227C2×D59#48314yes—
228C2×D59#49814yes—
229C2×D59#50114yes—
230C4×C59—22no—
231C4×C59—22no—
232C4×C59—42no—
233C4×C59—81no—
234C4×C59—82no—
235C4×C59C2×C22⋊Q812yes—
236C4×C59C2×#12512yes—
237Dic59—22no—
238Dic59—22no—
239Dic59—42no—
240Dic59—81no—
241Dic59—82no—
242Dic59#39814yes—
243C22×#106—592no—
244C2×#389—591no—
245C2×#384—591no—
246#2084—592no—
247#2084—591no—
248#2084—591no—
249#2084—592no—
250#2084—591no—
251#2084D5911yescharacteristic, direct product factor
252C2×#340—592no—
253C2×#336—591no—
254C2×C59C2×#39811yescharacteristic
255C2×C59C2×#46111yescharacteristic
256C2×C59C2×#46011yescharacteristic
257C2×C59C2×#48311yescharacteristic
258C2×C59C2×#48111yescharacteristic
259C2×C59C2×#49811yescharacteristic
260C2×C59C2×#50111yescharacteristic
261D59#208418yesdirect product factor
262C23×C8—592no—
263C22×C4⋊C4—591no—
264C22×C4⋊C4—592no—
265C22×C4⋊C4—591no—
266C22×C4⋊C4—1181no—
267C22×C4⋊C4—1181no—
268C22×C4⋊C4—1181no—
269C22×C42—591no—
270C2×#106—592no—
271C2×#106—592no—
272C2×#106—592no—
273C2×#106—1188no—
274C2×#106C2×D5912yes—
275#389—591no—
276#389—591no—
277#389—591no—
278#389—1181no—
279#389—1181no—
280#389C2×D5911yescharacteristic
281#384—592no—
282#384—591no—
283#384—1181no—
284#384—1181no—
285#384C2×D5911yescharacteristic
286C2×#95—1181no—
287#340—592no—
288#340—592no—
289#340—592no—
290#340C2×D5912yes—
291#336—592no—
292#336—591no—
293#336C2×D5911yescharacteristic
294C59C2×#208411yescharacteristic, complemented, Sylow
295C23×C4—591no—
296C23×C4—591no—
297C23×C4—591no—
298C23×C4—1181no—
299C23×C4—1182no—
300C23×C4—1181no—
301C22×C8—592no—
302C22×C8—598no—
303C22×C8—1184no—
304C22×C8—1184no—
305C22×C8C22×D5912yes—
306C2×C4⋊C4—21no—
307C2×C4⋊C4—21no—
308C2×C4⋊C4—21no—
309C2×C4⋊C4—591no—
310C2×C4⋊C4—594no—
311C2×C4⋊C4—591no—
312C2×C4⋊C4—592no—
313C2×C4⋊C4—1182no—
314C2×C4⋊C4—1184no—
315C2×C4⋊C4—1184no—
316C2×C4⋊C4—1184no—
317C2×C4⋊C4—1181no—
318C2×C4⋊C4—1182no—
319C2×C4⋊C4—1181no—
320C2×C4⋊C4—1182no—
321C2×C4⋊C4—1182no—
322C2×C4⋊C4—1181no—
323C2×C4⋊C4—1181no—
324C2×C4⋊C4—1181no—
325C2×C4⋊C4—1181no—
326C2×C4⋊C4—1181no—
327C2×C4⋊C4—2364no—
328C2×C4⋊C4—2364no—
329C2×C4⋊C4—2364no—
330C2×C4⋊C4C22×D5911yescharacteristic
331C2×C4⋊C4C22×D5912yes—
332C2×C4⋊C4C22×D5911yescharacteristic
333C2×C42—591no—
334C2×C42—591no—
335C2×C42—591no—
336C2×C42—1184no—
337C2×C42C22×D5911yescharacteristic
338#106—24no—
339#106—1184no—
340#106—1184no—
341#106—1184no—
342#95—21no—
343#95—1181no—
344#95—1181no—
345#95—1181no—
346C24—591no—
347C22×C4—21no—
348C22×C4—21no—
349C22×C4—22no—
350C22×C4—591no—
351C22×C4—592no—
352C22×C4—594no—
353C22×C4—594no—
354C22×C4—592no—
355C22×C4—591no—
356C22×C4—591no—
357C22×C4—594no—
358C22×C4—594no—
359C22×C4—1182no—
360C22×C4—1182no—
361C22×C4—1182no—
362C22×C4—1182no—
363C22×C4—1184no—
364C22×C4—1181no—
365C22×C4—1181no—
366C22×C4—1182no—
367C22×C4—2364no—
368C22×C4—2362no—
369C22×C4—2364no—
370C22×C4—2362no—
371C22×C4—2364no—
372C22×C4—2362no—
373C22×C4—2362no—
374C22×C4—2362no—
375C22×C4D4×D5911yescharacteristic
376C22×C4D4×D5911yescharacteristic
377C22×C4C23×D5911yescharacteristic
378C2×C8—22no—
379C2×C8—22no—
380C2×C8—594no—
381C2×C8—11816no—
382C2×C8—1182no—
383C2×C8—1182no—
384C2×C8Q8×D5914yes—
385C4⋊C4—21no—
386C4⋊C4—22no—
387C4⋊C4—22no—
388C4⋊C4—22no—
389C4⋊C4—42no—
390C4⋊C4—42no—
391C4⋊C4—42no—
392C4⋊C4—592no—
393C4⋊C4—1184no—
394C4⋊C4—1181no—
395C4⋊C4—1182no—
396C4⋊C4—1182no—
397C4⋊C4—1182no—
398C4⋊C4—2362no—
399C4⋊C4—2364no—
400C4⋊C4—2362no—
401C4⋊C4—2364no—
402C4⋊C4—2362no—
403C4⋊C4—2362no—
404C4⋊C4—2364no—
405C4⋊C4—2362no—
406C4⋊C4—2362no—
407C4⋊C4D4×D5912yes—
408C42—22no—
409C42—1182no—
410C42—1182no—
411C42—1182no—
412C23—592no—
413C23—592no—
414C23—592no—
415C23—592no—
416C23—592no—
417C23—592no—
418C23—592no—
419C23C2×D4×D5911yescharacteristic
420C2×C4—21no—
421C2×C4—21no—
422C2×C4—21no—
423C2×C4—21no—
424C2×C4—22no—
425C2×C4—41no—
426C2×C4—41no—
427C2×C4—42no—
428C2×C4—41no—
429C2×C4—41no—
430C2×C4—42no—
431C2×C4—42no—
432C2×C4—41no—
433C2×C4—592no—
434C2×C4—592no—
435C2×C4—592no—
436C2×C4—598no—
437C2×C4—598no—
438C2×C4—592no—
439C2×C4—592no—
440C2×C4—1188no—
441C2×C4—1188no—
442C2×C4—1181no—
443C2×C4—1181no—
444C2×C4—1181no—
445C2×C4—1181no—
446C2×C4—1182no—
447C2×C4—4724no—
448C2×C4—4728no—
449C2×C4—2368no—
450C2×C4—2362no—
451C2×C4—2361no—
452C2×C4—2361no—
453C2×C4—2362no—
454C2×C4—2362no—
455C2×C4—2361no—
456C2×C4—2361no—
457C2×C4—2361no—
458C2×C4SD16×D5912yes—
459C2×C4SD16×D5912yes—
460C2×C4C2×D4×D5911yescharacteristic
461C2×C4C2×Q8×D5912yes—
462C2×C4#41×D5912yes—
463C2×C4#41×D5911yescharacteristic
464C8—24no—
465C8—1184no—
466C22—594no—
467C22—594no—
468C22—594no—
469C22—594no—
470C22—594no—
471C22—594no—
472C22—594no—
473C22#121×D5911yescharacteristic
474C22#123×D5911yescharacteristic
475C22C4⋊Q8×D5911yescharacteristic
476C22C2×SD16×D5911yescharacteristic
477C22C2×SD16×D5911yescharacteristic
478C22AGL(1,ℤ/8)×D5911yescharacteristic
479C22#137×D5911yescharacteristic
480C4—22no—
481C4—22no—
482C4—42no—
483C4—81no—
484C4—82no—
485C4—594no—
486C4—1182no—
487C4—1182no—
488C4—4721no—
489C4—4722no—
490C4—2362no—
491C4C22⋊Q8×D5912yes—
492C4#125×D5912yes—
493C2—598no—
494C2#398×D5911yescharacteristic
495C2#461×D5911yescharacteristic
496C2#460×D5911yescharacteristic
497C2#483×D5911yescharacteristic
498C2#481×D5911yescharacteristic
499C2#498×D5911yescharacteristic
500C2#501×D5911yescharacteristic
subgroupG/H
centerC23C2×D4×D59
commutator, cosocleC22×C4×C59C24
FrattiniC22×C4C23×D59
FittingC59×#2084C2
socleC23×C59C22×D4
prime radicalC23×D59C2×D4
hypercenter#2084D59
hypocenterC59C2×#2084
LCSG ▷ C22×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2084

Complements

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

NH ≅ G/Ntype
4. #21425576C2semidirect
5. #21425575C2semidirect
6. #21425574C2semidirect
7. #21425573C2semidirect
8. #21425572C2semidirect
11. C59×#2084C2semidirect
251. #2084D59direct (N × H)
261. D59#2084direct (N × H)
294. C59C2×#2084semidirect

Maximal subgroups

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

subgroupindex
C2×#106×D592
#389×D592
#384×D592
#214255762
#214255752
#214255742
#214255732
#214255722
#340×D592
#336×D592
C59×#20842
C2×#208459