Finite Group Databasebeta

← #28560711

Subgroups — #28560711

Order 15104.

604 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21434652C211yesmaximal, characteristic
2#21433194C211yesmaximal, characteristic, complemented
3#21433161C211yesmaximal, characteristic
4#21422997C211yesmaximal, characteristic, complemented
5#21422937C211yesmaximal, characteristic, complemented
6#21422936C211yesmaximal, characteristic, complemented
7#21422930C211yesmaximal, characteristic, complemented
8#21422929C211yesmaximal, characteristic, complemented
9#21422910C211yesmaximal, characteristic, complemented
10SD16⋊(C59⋊C8)C211yesmaximal, characteristic, complemented
11#21422843C211yesmaximal, characteristic, complemented
12#21422515C211yesmaximal, characteristic, complemented
13#21422511C211yesmaximal, characteristic
14#21422382C211yesmaximal, characteristic, complemented
15C59×#1592C211yesmaximal, characteristic, complemented
16#16837956C2211yescharacteristic
17#16837949C2211yescharacteristic
18#16837799C411yescharacteristic
19#16837773C411yescharacteristic
20#16837751C411yescharacteristic
21#16837747C411yescharacteristic
22#16837634C411yescharacteristic
23#16837632C411yescharacteristic
24#16837630C411yescharacteristic
25#16837628C411yescharacteristic
26#16837530—21no—
27#16837529C2211yescharacteristic
28Q8×C59⋊C8C2211yescharacteristic
29C8×Dic118C2211yescharacteristic
30#16837526—21no—
31C4×#11745660C2211yescharacteristic
32C4×#11745671C2211yescharacteristic
33C4×#11745670C2211yescharacteristic
34#16837479C2211yescharacteristic
35#16837478—21no—
36C8×D236C2211yescharacteristic
37D4×C59⋊C8C2211yescharacteristic
38(C22⋊D59)⋊C8—21no—
39#16837464—21no—
40#16837462—21no—
41#16837454C2211yescharacteristic
42#16837454C2211yescharacteristic
43#16837453C2211yescharacteristic
44#16837370—21no—
45#16837367—21no—
46C4×#11745659C2211yescharacteristic
47C4×C8×D59C2211yescharacteristic
48#16837155C2211yescharacteristic
49#16837152C2211yescharacteristic
50#16837152C2211yescharacteristic
51#16837134C2211yescharacteristic
52Q8⋊(C59⋊C8)C2211yescharacteristic
53#16837132C2211yescharacteristic
54#16837131C2211yescharacteristic
55D4⋊(C59⋊C8)C2211yescharacteristic
56#16837129C2211yescharacteristic
57#16837124C2211yescharacteristic
58#16837123C2211yescharacteristic
59#16837123C2211yescharacteristic
60C59×#446C2211yescharacteristic
61C4×SD16×C59C2211yescharacteristic
62C59×#436C2211yescharacteristic
63C59×#335C2211yescharacteristic
64C59×Q8⋊C8C2211yescharacteristic
65C59×D4⋊C8C2211yescharacteristic
66C59×#322C2211yescharacteristic
67C2×#11745685—21no—
68C2×#11745660C2×C411yescharacteristic
69C2×#11745670C2×C411yescharacteristic
70C2×#11745671C2×C411yescharacteristic
71C2×#11745659—21no—
72C2×#11745659—21no—
73C22×C59⋊C8—21no—
74C2×C8×D59—21no—
75C2×C8×D59C2×C411yescharacteristic
76C2×C8×D59C2×C411yescharacteristic
77#14273726C2×C411yescharacteristic
78#14273726C2×C411yescharacteristic
79#14273725C2×C411yescharacteristic
80#14273723C2×C411yescharacteristic
81#14273717—21no—
82#14273713—21no—
83#14273707C2×C411yescharacteristic
84#14273705—21no—
85#14273703C2×C411yescharacteristic
86#14273702C2×C411yescharacteristic
87#14273700—21no—
88#14273698C2×C411yescharacteristic
89C4×Dic118—21no—
90C4×Dic118C2311yescharacteristic
91C4×D236C2311yescharacteristic
92C4×C22⋊D59—21no—
93#14273684—21no—
94C42×D59C2311yescharacteristic
95#14273659C2×C411yescharacteristic
96#14273658C2×C411yescharacteristic
97#14273658C2×C411yescharacteristic
98C4⋊(C59⋊C8)—21no—
99C4⋊(C59⋊C8)C2311yescharacteristic
100C4⋊(C59⋊C8)C2311yescharacteristic
101Dic59⋊C8—21no—
102Dic59⋊C8—21no—
103Dic59⋊C8D411yescharacteristic
104Dic59⋊C8D411yescharacteristic
105#14273652C2×C411yescharacteristic
106#14273651C2×C411yescharacteristic
107#14273650C2×C411yescharacteristic
108#14273649C2×C411yescharacteristic
109#14273648C2×C411yescharacteristic
110#14273647C2×C411yescharacteristic
111C22⋊(C59⋊C8)—21no—
112(C2×D59)⋊C8—21no—
113(C2×D59)⋊C8—21no—
114(C2×D59)⋊C8—21no—
115(C2×D59)⋊C8—21no—
116(C2×D59)⋊C8D411yescharacteristic
117(C2×D59)⋊C8D411yescharacteristic
118#14273637—21no—
119#14273637—21no—
120C4×C59⋊C8—21no—
121C4×C59⋊C8C2311yescharacteristic
122C4×C59⋊C8C2311yescharacteristic
123C4×C59⋊C8C2311yescharacteristic
124C8×Dic59—21no—
125C8×Dic59—21no—
126C8×Dic59—21no—
127C8×Dic59C2×C411yescharacteristic
128C8×Dic59C2×C411yescharacteristic
129C2×SD16×C59C2×C411yescharacteristic
130C2×M16×C59—21no—
131C4×Q8×C59C2311yescharacteristic
132C4×D4×C59C2311yescharacteristic
133#106×C59C2×C411yescharacteristic
134C4⋊C8×C59—21no—
135C4⋊C8×C59C2311yescharacteristic
136C4⋊C8×C59C2311yescharacteristic
137#103×C59C2×C411yescharacteristic
138#102×C59C2×C411yescharacteristic
139C22⋊C8×C59—21no—
140#97×C59—21no—
141C4×C8×C59C2311yescharacteristic
142C4×C8×C59C2311yescharacteristic
143C4×C8×C59C2311yescharacteristic
144C2×Q8×C59C22×C411yescharacteristic
145C2×D4×C59C22×C411yescharacteristic
146C22×C4×C59—21no—
147C2×C22⋊D59—21no—
148C2×C22⋊D59—21no—
149C2×C22⋊D59—21no—
150#11745685—81no—
151#11745685—81no—
152C2×D236—21no—
153C2×D236C22×C411yescharacteristic
154C2×C4×D59—21no—
155C2×C4×D59C22×C411yescharacteristic
156C2×C4×D59C2×D411yescharacteristic
157C2×C4×D59#4111yescharacteristic
158C2×Dic118—21no—
159C2×Dic118—21no—
160C2×Dic118C22×C411yescharacteristic
161SD16×C59—22no—
162M16×C59—81no—
163C2×C8×C59—21no—
164C2×C8×C59—21no—
165C2×C8×C59—21no—
166C2×C8×C59C22×C411yescharacteristic
167C2×C8×C59C22×C411yescharacteristic
168C2×C8×C59C2×D411yescharacteristic
169C2×C8×C59C2×D411yescharacteristic
170C4⋊C4×C59—21no—
171C4⋊C4×C59C22×C411yescharacteristic
172C4⋊C4×C59C22×C411yescharacteristic
173C22⋊C4×C59—21no—
174C42×C59—21no—
175C42×C59C2411yescharacteristic
176C22⋊Dic59—21no—
177#11745671—41no—
178#11745670—41no—
179(C2×D59)⋊C4—21no—
180(C2×D59)⋊C4—21no—
181(C2×D59)⋊C4—21no—
182(C2×D59)⋊C4—21no—
183C4⋊Dic59—21no—
184C4⋊Dic59C22×C411yescharacteristic
185C4⋊Dic59C22×C411yescharacteristic
186Dic59⋊C4—21no—
187Dic59⋊C4—21no—
188Dic59⋊C4—21no—
189Dic59⋊C4—21no—
190Dic59⋊C4—21no—
191Dic59⋊C4—21no—
192C4×Dic59—21no—
193C4×Dic59C22×C411yescharacteristic
194C4×Dic59C2×D411yescharacteristic
195C4×Dic59#4111yescharacteristic
196C2×C59⋊C8—21no—
197C2×C59⋊C8—21no—
198C2×C59⋊C8—21no—
199C2×C59⋊C8—81no—
200C2×C59⋊C8C22×C411yescharacteristic
201C2×C59⋊C8C22×C411yescharacteristic
202C2×C59⋊C8C2×D411yescharacteristic
203C2×C59⋊C8C2×D411yescharacteristic
204#11745660—22no—
205#11745659—42no—
206#11745659—81no—
207C8×D59—22no—
208C8×D59—41no—
209C8×D59—81no—
210C23×C59—21no—
211C22×D59—21no—
212C22×D59C4×D411yescharacteristic
213Q8×C59—21no—
214Q8×C59—21no—
215D4×C59—21no—
216D4×C59—21no—
217C2×C4×C59—21no—
218C2×C4×C59—21no—
219C2×C4×C59—21no—
220C2×C4×C59—41no—
221C2×C4×C59—41no—
222C2×C4×C59C23×C411yescharacteristic
223C2×C4×C59C22×D411yescharacteristic
224C2×C4×C59C2×#4111yescharacteristic
225C22⋊D59—42no—
226C22⋊D59—81no—
227C22⋊D59—81no—
228C2×Dic59—21no—
229C2×Dic59—21no—
230C2×Dic59—21no—
231C2×Dic59C4×D411yescharacteristic
232C2×Dic59C4×D411yescharacteristic
233C2×Dic59C4×D411yescharacteristic
234D236—21no—
235D236—21no—
236D236—81no—
237C4×D59—21no—
238C4×D59—21no—
239C4×D59—21no—
240C4×D59—21no—
241C4×D59—22no—
242C4×D59—41no—
243C4×D59—41no—
244Dic118—21no—
245Dic118—21no—
246Dic118—42no—
247Dic118—81no—
248C8×C59—21no—
249C8×C59—21no—
250C8×C59—21no—
251C8×C59—41no—
252C8×C59—41no—
253C8×C59—41no—
254C8×C59#13112yes—
255C59⋊C8—21no—
256C59⋊C8—21no—
257C59⋊C8—21no—
258C59⋊C8—21no—
259C59⋊C8—41no—
260C59⋊C8—41no—
261C59⋊C8—41no—
262#18089—591nomaximal, Sylow
263C22×C59—41no—
264C22×C59—41no—
265C22×C59—41no—
266C22×C59C2×C4×D411yescharacteristic
267C2×D59—21no—
268C2×D59—21no—
269C2×D59—21no—
270C2×D59—41no—
271C2×D59—41no—
272C2×D59—41no—
273C4×C59—21no—
274C4×C59—41no—
275C4×C59—41no—
276C4×C59—41no—
277C4×C59C2×#13111yescharacteristic
278C4×C59#56811yescharacteristic
279C4×C59#57711yescharacteristic
280C4×C59#57711yescharacteristic
281Dic59—21no—
282Dic59—21no—
283Dic59—41no—
284Dic59—41no—
285Dic59—41no—
286Dic59#44412yes—
287#3167—591no—
288#2986—591no—
289#2979—591no—
290#1592—591no—
291#1592D5911yescharacteristic, complemented
292#1583—591no—
293#1583—591no—
294#1582—591no—
295#1582—591no—
296SD16⋊C8—591no—
297SD16⋊C8—591no—
298#1564—591no—
299#1485—591no—
300#1484—591no—
301#1451—591no—
302C2×C59—81no—
303C2×C59#293511yescharacteristic
304C2×C59#294911yescharacteristic
305C2×C59C2×#44411yescharacteristic
306D59—41no—
307D59—81no—
308#533—591no—
309#532—591no—
310#498—591no—
311#492—591no—
312#487—591no—
313#486—591no—
314#465—591no—
315#465—591no—
316#465—591no—
317#465—591no—
318#446—591no—
319#446—1181no—
320#446C2×D5911yescharacteristic
321C8×Q8—591no—
322C8×Q8—591no—
323C8×Q8—1181no—
324C4×SD16—591no—
325C4×SD16—591no—
326C4×SD16—591no—
327C4×SD16C2×D5911yescharacteristic
328#436—591no—
329#436—1181no—
330#436C2×D5911yescharacteristic
331C8×D4—591no—
332C8×D4—591no—
333C8×D4—1181no—
334#433—1181no—
335#433—1181no—
336#431—591no—
337#431—591no—
338#431—591no—
339#408—1181no—
340#408—1181no—
341C4×M16—591no—
342C2×C4×C8—591no—
343#335—591no—
344#335C2×D5911yescharacteristic
345#334—591no—
346#334—591no—
347Q8⋊C8—591no—
348Q8⋊C8—591no—
349Q8⋊C8—591no—
350Q8⋊C8C2×D5911yescharacteristic
351D4⋊C8—591no—
352D4⋊C8—591no—
353D4⋊C8—591no—
354D4⋊C8C2×D5911yescharacteristic
355#322—591no—
356#322—591no—
357#322—591no—
358#322C2×D5911yescharacteristic
359C59#1808911yescharacteristic, complemented, Sylow
360C2×#41—1181no—
361C2×SD16—591no—
362C2×SD16—591no—
363C2×SD16—591no—
364C2×SD16C4×D5911yescharacteristic
365C2×M16—21no—
366C2×M16—1181no—
367C2×M16—1181no—
368C22×C8—591no—
369C22×C8—591no—
370C22×C8—1181no—
371C22×C8—1181no—
372C4⋊Q8—591no—
373C4⋊Q8—591no—
374C4⋊Q8—591no—
375#127—591no—
376#125—1181no—
377#124—1181no—
378C22⋊Q8—591no—
379C22⋊Q8—591no—
380C22⋊Q8—1181no—
381#121—591no—
382#121—591no—
383#121—1181no—
384C4×Q8—591no—
385C4×Q8—1181no—
386C4×Q8C22×D5911yescharacteristic
387C4×D4—591no—
388C4×D4—1181no—
389C4×D4C22×D5911yescharacteristic
390#117—1181no—
391C2×C42—591no—
392#106—591no—
393#106—591no—
394#106—591no—
395#106C4×D5911yescharacteristic
396C4⋊C8—21no—
397C4⋊C8—591no—
398C4⋊C8—591no—
399C4⋊C8—591no—
400C4⋊C8—591no—
401C4⋊C8—1181no—
402C4⋊C8—1181no—
403C4⋊C8—1181no—
404C4⋊C8C22×D5911yescharacteristic
405C4⋊C8C22×D5911yescharacteristic
406#103—591no—
407#103—591no—
408#103—591no—
409#103C4×D5911yescharacteristic
410#102—591no—
411#102—591no—
412#102—591no—
413#102C4×D5911yescharacteristic
414C22⋊C8—21no—
415C22⋊C8—591no—
416C22⋊C8—591no—
417C22⋊C8—1181no—
418C22⋊C8—1181no—
419C22⋊C8—1181no—
420C22⋊C8—1181no—
421C22⋊C8—1181no—
422#97—21no—
423#97—1181no—
424#97—1181no—
425C4×C8—591no—
426C4×C8—591no—
427C4×C8—591no—
428C4×C8—591no—
429C4×C8—591no—
430C4×C8—1181no—
431C4×C8—1181no—
432C4×C8—1181no—
433C4×C8—1181no—
434C4×C8C22×D5911yescharacteristic
435C4×C8C22×D5911yescharacteristic
436C4×C8C22×D5911yescharacteristic
437#41—4721no—
438#41—4721no—
439C2×Q8—591no—
440C2×Q8—1181no—
441C2×Q8—1181no—
442C2×Q8C2×C4×D5911yescharacteristic
443C2×D4—591no—
444C2×D4—1181no—
445C2×D4—1181no—
446C2×D4—1181no—
447C2×D4—1181no—
448C2×D4C2×C4×D5911yescharacteristic
449C22×C4—21no—
450C22×C4—591no—
451C22×C4—591no—
452C22×C4—591no—
453C22×C4—1181no—
454SD16—22no—
455SD16—1182no—
456SD16—2361no—
457SD16—2361no—
458M16—81no—
459M16—4721no—
460M16—2362no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—21no—
464C2×C8—591no—
465C2×C8—591no—
466C2×C8—591no—
467C2×C8—591no—
468C2×C8—1182no—
469C2×C8—1181no—
470C2×C8—1181no—
471C2×C8—1181no—
472C2×C8—4721no—
473C2×C8—4721no—
474C2×C8—2361no—
475C2×C8C2×C4×D5911yescharacteristic
476C2×C8C2×C4×D5911yescharacteristic
477C2×C8D4×D5911yescharacteristic
478C2×C8D4×D5911yescharacteristic
479C4⋊C4—21no—
480C4⋊C4—591no—
481C4⋊C4—591no—
482C4⋊C4—1181no—
483C4⋊C4—1181no—
484C4⋊C4—1181no—
485C4⋊C4—1181no—
486C4⋊C4—1181no—
487C4⋊C4—1181no—
488C4⋊C4—1181no—
489C4⋊C4C2×C4×D5911yescharacteristic
490C4⋊C4C2×C4×D5911yescharacteristic
491C22⋊C4—21no—
492C22⋊C4—1181no—
493C22⋊C4—1181no—
494C22⋊C4—1181no—
495C22⋊C4—1181no—
496C22⋊C4—1181no—
497C42—21no—
498C42—591no—
499C42—591no—
500C42—591no—
501C42—1181no—
502C42C23×D5911yescharacteristic
503C23—21no—
504C23—591no—
505C23—1181no—
506Q8—21no—
507Q8—21no—
508Q8—1181no—
509Q8—1181no—
510Q8—4721no—
511Q8—2362no—
512D4—21no—
513D4—21no—
514D4—1181no—
515D4—1181no—
516D4—4721no—
517D4—4721no—
518D4—4721no—
519D4—2362no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—591no—
526C2×C4—591no—
527C2×C4—591no—
528C2×C4—1182no—
529C2×C4—1181no—
530C2×C4—1181no—
531C2×C4—1181no—
532C2×C4—1181no—
533C2×C4—1181no—
534C2×C4—1181no—
535C2×C4—1181no—
536C2×C4—2361no—
537C2×C4—2361no—
538C2×C4C22×C4×D5911yescharacteristic
539C2×C4C2×D4×D5911yescharacteristic
540C2×C4#41×D5911yescharacteristic
541C8—21no—
542C8—21no—
543C8—21no—
544C8—41no—
545C8—41no—
546C8—41no—
547C8—1181no—
548C8—1181no—
549C8—1181no—
550C8—1181no—
551C8—2361no—
552C8—2361no—
553C8—2361no—
554C8#1427373512yes—
555C22—41no—
556C22—41no—
557C22—41no—
558C22—1181no—
559C22—1181no—
560C22—1181no—
561C22—2361no—
562C22—2361no—
563C22—2361no—
564C22C4×D4×D5911yescharacteristic
565C4—21no—
566C4—41no—
567C4—41no—
568C4—41no—
569C4—592no—
570C4—1181no—
571C4—1181no—
572C4—2361no—
573C4—2361no—
574C4—2361no—
575C4C2×#1427373511yescharacteristic
576C4#1683816711yescharacteristic
577C4#1683821111yescharacteristic
578C4#1683821211yescharacteristic
579C2—81no—
580C2—4721no—
581C2—2361no—
582C2#2143284111yescharacteristic
583C2#2143295211yescharacteristic
584C2#444×D5911yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D59
commutatorC2×C4×C59C23×C4
FrattiniC42C23×D59
FittingC59×#1592C2
socleC22×C59C2×C4×D4
prime radical#16837949C22
cosocleC42×C59C24
hypercenter#1592D59
hypocenterC59#18089
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1592

Complements

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

NH ≅ G/Ntype
2. #21433194C2semidirect
4. #21422997C2semidirect
5. #21422937C2semidirect
6. #21422936C2semidirect
7. #21422930C2semidirect
8. #21422929C2semidirect
9. #21422910C2semidirect
10. SD16⋊(C59⋊C8)C2semidirect
11. #21422843C2semidirect
12. #21422515C2semidirect
14. #21422382C2semidirect
15. C59×#1592C2semidirect
291. #1592D59semidirect
359. C59#18089semidirect

Maximal subgroups

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

subgroupindex
#214346522
#214331942
#214331612
#214229972
#214229372
#214229362
#214229302
#214229292
#214229102
SD16⋊(C59⋊C8)2
#214228432
#214225152
#214225112
#214223822
C59×#15922
#1808959