Finite Group Databasebeta

← #28560553

Subgroups — #28560553

Order 15104.

588 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21434700C211yesmaximal, characteristic
2#21433099C211yesmaximal, characteristic
3#21433044C211yesmaximal, characteristic, complemented
4#21422996C211yesmaximal, characteristic, complemented
5#21422990C211yesmaximal, characteristic, complemented
6#21422976C211yesmaximal, characteristic, complemented
7#21422947C211yesmaximal, characteristic, complemented
8#21422931C211yesmaximal, characteristic, complemented
9#21422913C211yesmaximal, characteristic, complemented
10#21422893C211yesmaximal, characteristic, complemented
11#21422845C211yesmaximal, characteristic, complemented
12#21422515C211yesmaximal, characteristic, complemented
13#21422508C211yesmaximal, characteristic
14#21422400C211yesmaximal, characteristic, complemented
15C59×#1587C211yesmaximal, characteristic, complemented
16#16837956C2211yescharacteristic
17#16837939C2211yescharacteristic
18#16837810C411yescharacteristic
19#16837795C411yescharacteristic
20#16837769C411yescharacteristic
21#16837763C411yescharacteristic
22#16837659C411yescharacteristic
23#16837657C411yescharacteristic
24#16837651C411yescharacteristic
25#16837649C411yescharacteristic
26#16837533C2211yescharacteristic
27#16837530—21no—
28#16837529—21no—
29#16837529C2211yescharacteristic
30Q8×C59⋊C8C2211yescharacteristic
31C8×Dic118C2211yescharacteristic
32C4×#11745672C2211yescharacteristic
33C4×#11745660C2211yescharacteristic
34C4×#11745671C2211yescharacteristic
35#16837481—21no—
36#16837481C2211yescharacteristic
37#16837472—21no—
38#16837467C2211yescharacteristic
39#16837462—21no—
40#16837454C2211yescharacteristic
41#16837427—21no—
42C4⋊C8×D59C2211yescharacteristic
43#16837359—21no—
44#16837356—21no—
45C4×#11745659C2211yescharacteristic
46C4×#11745659C2211yescharacteristic
47C4×#11745659C2211yescharacteristic
48#16837155C2211yescharacteristic
49#16837154C2211yescharacteristic
50#16837152C2211yescharacteristic
51#16837134C2211yescharacteristic
52Q8⋊(C59⋊C8)C2211yescharacteristic
53Q8⋊(C59⋊C8)C2211yescharacteristic
54#16837132C2211yescharacteristic
55#16837131C2211yescharacteristic
56#16837129C2211yescharacteristic
57#16837124C2211yescharacteristic
58#16837124C2211yescharacteristic
59C8×C59⋊C8C2211yescharacteristic
60C59×#446C2211yescharacteristic
61C8×Q8×C59C2211yescharacteristic
62C4×Q16×C59C2211yescharacteristic
63C59×#334C2211yescharacteristic
64C59×Q8⋊C8C2211yescharacteristic
65C59×Q8⋊C8C2211yescharacteristic
66C59×#322C2211yescharacteristic
67C2×#11745672C2×C411yescharacteristic
68C2×#11745660C2×C411yescharacteristic
69C2×#11745671C2×C411yescharacteristic
70C2×#11745659—21no—
71C2×#11745659—21no—
72C2×#11745659C2×C411yescharacteristic
73C2×#11745659C2×C411yescharacteristic
74C2×#11745659D411yescharacteristic
75C2×#11745659D411yescharacteristic
76C2×C8×D59—21no—
77C2×C8×D59—21no—
78#14273726C2×C411yescharacteristic
79#14273725C2×C411yescharacteristic
80#14273722—21no—
81#14273718C2×C411yescharacteristic
82#14273717—21no—
83#14273716C2×C411yescharacteristic
84#14273712—21no—
85#14273707C2×C411yescharacteristic
86#14273705—21no—
87#14273703C2×C411yescharacteristic
88#14273703C2×C411yescharacteristic
89#14273702C2×C411yescharacteristic
90C4×Dic118—21no—
91C4×Dic118C2311yescharacteristic
92C4×D236—21no—
93C4×D236C2311yescharacteristic
94#14273684—21no—
95#14273684—21no—
96C42×D59C2311yescharacteristic
97#14273660C2×C411yescharacteristic
98#14273659C2×C411yescharacteristic
99#14273658C2×C411yescharacteristic
100C4⋊(C59⋊C8)—21no—
101C4⋊(C59⋊C8)—21no—
102C4⋊(C59⋊C8)C2311yescharacteristic
103C4⋊(C59⋊C8)C2311yescharacteristic
104Dic59⋊C8—21no—
105Dic59⋊C8—21no—
106Dic59⋊C8—21no—
107#14273652C2×C411yescharacteristic
108#14273651C2×C411yescharacteristic
109#14273651C2×C411yescharacteristic
110#14273650C2×C411yescharacteristic
111#14273649C2×C411yescharacteristic
112#14273647C2×C411yescharacteristic
113(C2×D59)⋊C8—21no—
114(C2×D59)⋊C8—21no—
115(C2×D59)⋊C8—21no—
116#14273638—21no—
117#14273637—21no—
118#14273637—21no—
119#14273637C2×C411yescharacteristic
120#14273637C2×C411yescharacteristic
121#14273637D411yescharacteristic
122#14273637D411yescharacteristic
123C4×C59⋊C8—21no—
124C4×C59⋊C8C2311yescharacteristic
125C4×C59⋊C8C2311yescharacteristic
126C4×C59⋊C8C2311yescharacteristic
127C8×Dic59—21no—
128C8×Dic59—21no—
129C2×Q16×C59C2×C411yescharacteristic
130C4×Q8×C59C2311yescharacteristic
131C4×Q8×C59C2311yescharacteristic
132#107×C59C2×C411yescharacteristic
133C4⋊C8×C59—21no—
134C4⋊C8×C59—21no—
135C4⋊C8×C59C2311yescharacteristic
136C4⋊C8×C59C2311yescharacteristic
137#103×C59C2×C411yescharacteristic
138#103×C59C2×C411yescharacteristic
139#97×C59—21no—
140C4×C8×C59—21no—
141C4×C8×C59C2311yescharacteristic
142C4×C8×C59C2311yescharacteristic
143C4×C8×C59C2311yescharacteristic
144C2×Q8×C59C22×C411yescharacteristic
145C2×Q8×C59C22×C411yescharacteristic
146C2×D236—21no—
147C2×D236C22×C411yescharacteristic
148C2×C4×D59—21no—
149C2×C4×D59C22×C411yescharacteristic
150C2×C4×D59C2×D411yescharacteristic
151C2×C4×D59#4111yescharacteristic
152C2×Dic118—21no—
153C2×Dic118C22×C411yescharacteristic
154Q16×C59—41no—
155C2×C8×C59—21no—
156C2×C8×C59—21no—
157C2×C8×C59—21no—
158C2×C8×C59C22×C411yescharacteristic
159C2×C8×C59C22×C411yescharacteristic
160C2×C8×C59C2×D411yescharacteristic
161C2×C8×C59C2×D411yescharacteristic
162C4⋊C4×C59—21no—
163C4⋊C4×C59—21no—
164C4⋊C4×C59C22×C411yescharacteristic
165C4⋊C4×C59C22×C411yescharacteristic
166C42×C59—21no—
167C42×C59—21no—
168C42×C59C2411yescharacteristic
169#11745672—22no—
170#11745671—22no—
171(C2×D59)⋊C4—21no—
172(C2×D59)⋊C4—21no—
173(C2×D59)⋊C4—21no—
174(C2×D59)⋊C4—21no—
175(C2×D59)⋊C4—21no—
176(C2×D59)⋊C4—21no—
177(C2×D59)⋊C4—21no—
178C4⋊Dic59—21no—
179C4⋊Dic59—21no—
180C4⋊Dic59C22×C411yescharacteristic
181C4⋊Dic59C22×C411yescharacteristic
182Dic59⋊C4—21no—
183Dic59⋊C4—21no—
184Dic59⋊C4—21no—
185Dic59⋊C4—21no—
186Dic59⋊C4—21no—
187Dic59⋊C4—21no—
188Dic59⋊C4—21no—
189C4×Dic59—21no—
190C4×Dic59C22×C411yescharacteristic
191C4×Dic59C2×D411yescharacteristic
192C4×Dic59#4111yescharacteristic
193C2×C59⋊C8—21no—
194C2×C59⋊C8—21no—
195C2×C59⋊C8—21no—
196C2×C59⋊C8C22×C411yescharacteristic
197C2×C59⋊C8C22×C411yescharacteristic
198C2×C59⋊C8C2×D411yescharacteristic
199C2×C59⋊C8C2×D411yescharacteristic
200#11745660—41no—
201#11745659—22no—
202#11745659—22no—
203#11745659—41no—
204#11745659—41no—
205#11745659—42no—
206#11745659—42no—
207C8×D59—42no—
208C8×D59—42no—
209C22×D59—21no—
210C22×D59C4×D411yescharacteristic
211Q8×C59—21no—
212Q8×C59—21no—
213Q8×C59—21no—
214Q8×C59—21no—
215C2×C4×C59—21no—
216C2×C4×C59—21no—
217C2×C4×C59—21no—
218C2×C4×C59—21no—
219C2×C4×C59C23×C411yescharacteristic
220C2×C4×C59C22×D411yescharacteristic
221C2×C4×C59C2×#4111yescharacteristic
222C2×Dic59—21no—
223C2×Dic59—21no—
224C2×Dic59—21no—
225C2×Dic59C4×D411yescharacteristic
226C2×Dic59C4×D411yescharacteristic
227C2×Dic59C4×D411yescharacteristic
228D236—21no—
229D236—21no—
230D236—81no—
231C4×D59—21no—
232C4×D59—21no—
233C4×D59—21no—
234C4×D59—21no—
235C4×D59—41no—
236C4×D59—41no—
237C4×D59—41no—
238Dic118—21no—
239Dic118—21no—
240Dic118—81no—
241C8×C59—22no—
242C8×C59—21no—
243C8×C59—21no—
244C8×C59—21no—
245C8×C59—21no—
246C8×C59—41no—
247C8×C59—41no—
248C59⋊C8—21no—
249C59⋊C8—21no—
250C59⋊C8—41no—
251C59⋊C8—41no—
252C59⋊C8—41no—
253C59⋊C8#13112yes—
254C59⋊C8#13712yes—
255#18077—591nomaximal, Sylow
256C22×C59C2×C4×D411yescharacteristic
257C2×D59—21no—
258C2×D59—21no—
259C2×D59—21no—
260C2×D59—41no—
261C2×D59—41no—
262C2×D59—41no—
263C4×C59—21no—
264C4×C59—41no—
265C4×C59—41no—
266C4×C59—41no—
267C4×C59—41no—
268C4×C59C2×#13111yescharacteristic
269C4×C59#56811yescharacteristic
270C4×C59C2×#13711yescharacteristic
271C4×C59#57511yescharacteristic
272Dic59—21no—
273Dic59—21no—
274Dic59—21no—
275Dic59—41no—
276Dic59—41no—
277Dic59—41no—
278#3172—591no—
279#2969—591no—
280#2962—591no—
281#1592—591no—
282#1591—591no—
283#1588—591no—
284#1587D5911yescharacteristic, complemented
285#1584—591no—
286#1582—591no—
287#1579—591no—
288C8×SD16—591no—
289#1565—591no—
290#1485—591no—
291#1483—591no—
292#1455—591no—
293C2×C59#293511yescharacteristic
294C2×C59C4×#13711yescharacteristic
295C2×C59#295611yescharacteristic
296D59—41no—
297D59—81no—
298#533—591no—
299#529—591no—
300#501—591no—
301#497—591no—
302#491—591no—
303#489—591no—
304#470—591no—
305#470—591no—
306#468—591no—
307#468—591no—
308#446—591no—
309#446—591no—
310#446—1181no—
311#446—1181no—
312#446C2×D5911yescharacteristic
313C8×Q8—591no—
314C8×Q8—591no—
315C8×Q8C2×D5911yescharacteristic
316C4×Q16—591no—
317C4×Q16C2×D5911yescharacteristic
318C4×SD16—591no—
319C4×SD16—591no—
320#436—591no—
321#436—1181no—
322#435—1181no—
323C8×D4—591no—
324#433—1181no—
325#431—591no—
326#424—1181no—
327C2×C4⋊C8—591no—
328#405—1181no—
329#405—1181no—
330C4×M16—591no—
331C4×M16—591no—
332C4×M16—591no—
333#335—591no—
334#335—591no—
335#334—591no—
336#334C2×D5911yescharacteristic
337Q8⋊C8—591no—
338Q8⋊C8—591no—
339Q8⋊C8—591no—
340Q8⋊C8—591no—
341Q8⋊C8C2×D5911yescharacteristic
342Q8⋊C8C2×D5911yescharacteristic
343D4⋊C8—591no—
344D4⋊C8—591no—
345#322—591no—
346#322—591no—
347#322C2×D5911yescharacteristic
348C82—591no—
349C59#1807711yescharacteristic, complemented, Sylow
350C2×Q16—591no—
351C2×Q16C4×D5911yescharacteristic
352C2×SD16—591no—
353C2×SD16—591no—
354C2×M16—591no—
355C2×M16—591no—
356C2×M16—591no—
357C2×M16—591no—
358C2×M16—1181no—
359C2×M16—1181no—
360C22×C8—1181no—
361C22×C8—1181no—
362C4⋊Q8—591no—
363C4⋊Q8—591no—
364#126—1181no—
365#125—591no—
366#125—1181no—
367#124—591no—
368#123—1181no—
369C22⋊Q8—591no—
370C22⋊Q8—591no—
371C22⋊Q8—591no—
372C22⋊Q8—1181no—
373#121—591no—
374C4×Q8—591no—
375C4×Q8—1181no—
376C4×Q8C22×D5911yescharacteristic
377C4×Q8C22×D5911yescharacteristic
378C4×D4—591no—
379C4×D4—1181no—
380#117—1181no—
381#117—1181no—
382C2×C42—591no—
383#107—591no—
384#107C4×D5911yescharacteristic
385#106—591no—
386#106—591no—
387C4⋊C8—21no—
388C4⋊C8—21no—
389C4⋊C8—591no—
390C4⋊C8—591no—
391C4⋊C8—1181no—
392C4⋊C8—1181no—
393C4⋊C8—1181no—
394C4⋊C8—1181no—
395C4⋊C8—1181no—
396C4⋊C8C22×D5911yescharacteristic
397C4⋊C8C22×D5911yescharacteristic
398#103—591no—
399#103—591no—
400#103—591no—
401#103—591no—
402#103C4×D5911yescharacteristic
403#103C4×D5911yescharacteristic
404#102—591no—
405#102—591no—
406C22⋊C8—1181no—
407C22⋊C8—1181no—
408C22⋊C8—1181no—
409#97—21no—
410#97—591no—
411#97—591no—
412#97—591no—
413#97—591no—
414#97—1181no—
415#97—1181no—
416#97—1181no—
417C4×C8—21no—
418C4×C8—591no—
419C4×C8—591no—
420C4×C8—591no—
421C4×C8—1181no—
422C4×C8—1181no—
423C4×C8—1181no—
424C4×C8C22×D5911yescharacteristic
425C4×C8C22×D5911yescharacteristic
426C4×C8C22×D5911yescharacteristic
427C2×Q8—591no—
428C2×Q8—1181no—
429C2×Q8C2×C4×D5911yescharacteristic
430C2×Q8C2×C4×D5911yescharacteristic
431C2×D4—591no—
432C2×D4—1181no—
433C22×C4—591no—
434C22×C4—591no—
435C22×C4—591no—
436C22×C4—1181no—
437Q16—41no—
438Q16—1182no—
439SD16—1182no—
440SD16—2361no—
441M16—1182no—
442M16—1182no—
443M16—2361no—
444M16—2361no—
445M16—2362no—
446M16—2362no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—591no—
451C2×C8—591no—
452C2×C8—591no—
453C2×C8—591no—
454C2×C8—1181no—
455C2×C8—1181no—
456C2×C8—1181no—
457C2×C8—2362no—
458C2×C8—2362no—
459C2×C8C2×C4×D5911yescharacteristic
460C2×C8C2×C4×D5911yescharacteristic
461C2×C8D4×D5911yescharacteristic
462C2×C8D4×D5911yescharacteristic
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—591no—
466C4⋊C4—591no—
467C4⋊C4—1181no—
468C4⋊C4—1181no—
469C4⋊C4—1181no—
470C4⋊C4—1181no—
471C4⋊C4—1181no—
472C4⋊C4—1181no—
473C4⋊C4—1181no—
474C4⋊C4—1181no—
475C4⋊C4—1181no—
476C4⋊C4C2×C4×D5911yescharacteristic
477C4⋊C4C2×C4×D5911yescharacteristic
478C22⋊C4—1181no—
479C22⋊C4—1181no—
480C22⋊C4—1181no—
481C22⋊C4—1181no—
482C22⋊C4—1181no—
483C22⋊C4—1181no—
484C22⋊C4—1181no—
485C42—21no—
486C42—21no—
487C42—591no—
488C42—591no—
489C42—591no—
490C42—1181no—
491C42C23×D5911yescharacteristic
492C23—591no—
493C23—1181no—
494Q8—21no—
495Q8—21no—
496Q8—21no—
497Q8—21no—
498Q8—1181no—
499Q8—1181no—
500Q8—4721no—
501D4—1181no—
502D4—1181no—
503D4—4721no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—591no—
509C2×C4—591no—
510C2×C4—591no—
511C2×C4—1181no—
512C2×C4—1181no—
513C2×C4—1181no—
514C2×C4—1181no—
515C2×C4—1181no—
516C2×C4—1181no—
517C2×C4—1181no—
518C2×C4—2361no—
519C2×C4—2361no—
520C2×C4—2361no—
521C2×C4C22×C4×D5911yescharacteristic
522C2×C4C2×D4×D5911yescharacteristic
523C2×C4#41×D5911yescharacteristic
524C8—22no—
525C8—21no—
526C8—21no—
527C8—21no—
528C8—21no—
529C8—41no—
530C8—41no—
531C8—592no—
532C8—592no—
533C8—1181no—
534C8—1181no—
535C8—2361no—
536C8—2361no—
537C8—2361no—
538C22—1181no—
539C22—1181no—
540C22—1181no—
541C22—2361no—
542C22—2361no—
543C22—2361no—
544C22C4×D4×D5911yescharacteristic
545C4—21no—
546C4—41no—
547C4—41no—
548C4—41no—
549C4—41no—
550C4—1181no—
551C4—1181no—
552C4—1181no—
553C4—2361no—
554C4—2361no—
555C4—2361no—
556C4#131×D5911yescharacteristic
557C4#1683816811yescharacteristic
558C4#137×D5911yescharacteristic
559C4#1683820111yescharacteristic
560C2—4721no—
561C2—2361no—
562C2#2143283711yescharacteristic
563C2#2143291211yescharacteristic
564C2#2143300111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D59
commutatorC2×C4×C59C23×C4
FrattiniC42C23×D59
FittingC59×#1587C2
socleC22×C59C2×C4×D4
prime radical#14273702C2×C4
cosocleC42×C59C24
hypercenter#1587D59
hypocenterC59#18077
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1587

Complements

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

NH ≅ G/Ntype
3. #21433044C2semidirect
4. #21422996C2semidirect
5. #21422990C2semidirect
6. #21422976C2semidirect
7. #21422947C2semidirect
8. #21422931C2semidirect
9. #21422913C2semidirect
10. #21422893C2semidirect
11. #21422845C2semidirect
12. #21422515C2semidirect
14. #21422400C2semidirect
15. C59×#1587C2semidirect
284. #1587D59semidirect
349. C59#18077semidirect

Maximal subgroups

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

subgroupindex
#214347002
#214330992
#214330442
#214229962
#214229902
#214229762
#214229472
#214229312
#214229132
#214228932
#214228452
#214225152
#214225082
#214224002
C59×#15872
#1807759