Finite Group Databasebeta

← #28560651

Subgroups — #28560651

Order 15104.

572 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21434700C211yesmaximal, characteristic
2#21433259C211yesmaximal, characteristic
3#21433194C211yesmaximal, characteristic, complemented
4#21422985C211yesmaximal, characteristic, complemented
5#21422971C211yesmaximal, characteristic, complemented
6#21422964C211yesmaximal, characteristic, complemented
7#21422944C211yesmaximal, characteristic, complemented
8#21422930C211yesmaximal, characteristic, complemented
9#21422910C211yesmaximal, characteristic, complemented
10Q16×C59⋊C8C211yesmaximal, characteristic, complemented
11#21422845C211yesmaximal, characteristic, complemented
12#21422503C211yesmaximal, characteristic
13#21422497C211yesmaximal, characteristic, complemented
14#21422394C211yesmaximal, characteristic, complemented
15C59×#1593C211yesmaximal, characteristic, complemented
16#16837956C2211yescharacteristic
17#16837939C2211yescharacteristic
18#16837810C411yescharacteristic
19#16837795C411yescharacteristic
20#16837769C411yescharacteristic
21#16837763C411yescharacteristic
22#16837659C411yescharacteristic
23#16837657C411yescharacteristic
24#16837651C411yescharacteristic
25#16837649C411yescharacteristic
26#16837530—21no—
27#16837529C2211yescharacteristic
28Q8×C59⋊C8C2211yescharacteristic
29Q8×C59⋊C8C2211yescharacteristic
30C8×Dic118C2211yescharacteristic
31#16837526—21no—
32C4×#11745672C2211yescharacteristic
33C4×#11745660C2211yescharacteristic
34C4×#11745671C2211yescharacteristic
35#16837479C2211yescharacteristic
36#16837475—21no—
37C8×D236C2211yescharacteristic
38#16837467—21no—
39#16837464—21no—
40#16837464—21no—
41#16837462—21no—
42#16837454C2211yescharacteristic
43#16837453C2211yescharacteristic
44#16837453C2211yescharacteristic
45#16837427—21no—
46C4⋊C8×D59C2211yescharacteristic
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#16837123C2211yescharacteristic
58#16837123C2211yescharacteristic
59C8×C59⋊C8C2211yescharacteristic
60C59×#446C2211yescharacteristic
61C59×#446C2211yescharacteristic
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×#11745659C2×C411yescharacteristic
72C2×#11745659C2×C411yescharacteristic
73C2×C8×D59—21no—
74C2×C8×D59—21no—
75#14273726C2×C411yescharacteristic
76#14273725C2×C411yescharacteristic
77#14273722—21no—
78#14273718C2×C411yescharacteristic
79#14273717—21no—
80#14273716C2×C411yescharacteristic
81#14273712—21no—
82#14273707C2×C411yescharacteristic
83#14273705—21no—
84#14273703C2×C411yescharacteristic
85#14273703C2×C411yescharacteristic
86#14273702C2×C411yescharacteristic
87C4×Dic118—21no—
88C4×Dic118C2311yescharacteristic
89C4×D236—21no—
90C4×D236C2311yescharacteristic
91#14273684—21no—
92#14273684—21no—
93C42×D59C2311yescharacteristic
94#14273660C2×C411yescharacteristic
95#14273659C2×C411yescharacteristic
96#14273658C2×C411yescharacteristic
97C4⋊(C59⋊C8)—21no—
98C4⋊(C59⋊C8)—21no—
99C4⋊(C59⋊C8)C2311yescharacteristic
100C4⋊(C59⋊C8)C2311yescharacteristic
101Dic59⋊C8—21no—
102Dic59⋊C8—21no—
103Dic59⋊C8—21no—
104Dic59⋊C8—21no—
105Dic59⋊C8D411yescharacteristic
106Dic59⋊C8D411yescharacteristic
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(C2×D59)⋊C8—21no—
117(C2×D59)⋊C8D411yescharacteristic
118(C2×D59)⋊C8D411yescharacteristic
119#14273637—21no—
120#14273637C2×C411yescharacteristic
121#14273637C2×C411yescharacteristic
122C4×C59⋊C8—21no—
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—
140#97×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—22no—
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—41no—
170#11745671—41no—
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—22no—
201#11745659—22no—
202#11745659—41no—
203#11745659—81no—
204C8×D59—81no—
205C8×D59—81no—
206C22×D59—21no—
207C22×D59C4×D411yescharacteristic
208Q8×C59—21no—
209Q8×C59—21no—
210Q8×C59—21no—
211Q8×C59—21no—
212C2×C4×C59—21no—
213C2×C4×C59—21no—
214C2×C4×C59—21no—
215C2×C4×C59—21no—
216C2×C4×C59C23×C411yescharacteristic
217C2×C4×C59C22×D411yescharacteristic
218C2×C4×C59C2×#4111yescharacteristic
219C2×Dic59—21no—
220C2×Dic59—21no—
221C2×Dic59—21no—
222C2×Dic59C4×D411yescharacteristic
223C2×Dic59C4×D411yescharacteristic
224C2×Dic59C4×D411yescharacteristic
225D236—21no—
226D236—21no—
227D236—42no—
228C4×D59—21no—
229C4×D59—21no—
230C4×D59—21no—
231C4×D59—21no—
232C4×D59—41no—
233C4×D59—41no—
234C4×D59—41no—
235Dic118—21no—
236Dic118—21no—
237Dic118—42no—
238C8×C59—21no—
239C8×C59—21no—
240C8×C59—21no—
241C8×C59—41no—
242C8×C59—41no—
243C8×C59—41no—
244C8×C59#13112yes—
245C59⋊C8—21no—
246C59⋊C8—21no—
247C59⋊C8—21no—
248C59⋊C8—21no—
249C59⋊C8—41no—
250C59⋊C8—41no—
251C59⋊C8—41no—
252#18083—591nomaximal, Sylow
253C22×C59C2×C4×D411yescharacteristic
254C2×D59—21no—
255C2×D59—21no—
256C2×D59—21no—
257C2×D59—41no—
258C2×D59—41no—
259C2×D59—41no—
260C4×C59—21no—
261C4×C59—41no—
262C4×C59—41no—
263C4×C59—41no—
264C4×C59—41no—
265C4×C59C2×#13111yescharacteristic
266C4×C59#56811yescharacteristic
267C4×C59#57711yescharacteristic
268C4×C59#57811yescharacteristic
269Dic59—21no—
270Dic59—21no—
271Dic59—21no—
272Dic59—41no—
273Dic59—41no—
274Dic59—41no—
275#3172—591no—
276#2994—591no—
277#2986—591no—
278#1593D5911yescharacteristic, complemented
279#1590—591no—
280#1588—591no—
281#1587—591no—
282#1584—591no—
283#1582—591no—
284SD16⋊C8—591no—
285C8×Q16—591no—
286#1565—591no—
287#1482—591no—
288#1481—591no—
289#1453—591no—
290C2×C59#293511yescharacteristic
291C2×C59#294711yescharacteristic
292C2×C59#295511yescharacteristic
293D59—41no—
294D59—81no—
295#533—591no—
296#529—591no—
297#501—591no—
298#497—591no—
299#491—591no—
300#489—591no—
301#470—591no—
302#470—591no—
303#468—591no—
304#468—591no—
305#446—591no—
306#446—1181no—
307#446C2×D5911yescharacteristic
308#446C2×D5911yescharacteristic
309C8×Q8—591no—
310C8×Q8—591no—
311C8×Q8—591no—
312C8×Q8—1181no—
313C4×Q16—591no—
314C4×Q16C2×D5911yescharacteristic
315C4×SD16—591no—
316C4×SD16—591no—
317#436—591no—
318#435—1181no—
319C8×D4—591no—
320C8×D4—1181no—
321#433—1181no—
322#433—1181no—
323#433—1181no—
324#431—591no—
325#431—591no—
326#431—591no—
327#424—1181no—
328C2×C4⋊C8—591no—
329C4×M16—591no—
330#335—591no—
331#335—591no—
332#334—591no—
333#334C2×D5911yescharacteristic
334Q8⋊C8—591no—
335Q8⋊C8—591no—
336Q8⋊C8—591no—
337Q8⋊C8—591no—
338Q8⋊C8C2×D5911yescharacteristic
339Q8⋊C8C2×D5911yescharacteristic
340D4⋊C8—591no—
341D4⋊C8—591no—
342#322—591no—
343#322—591no—
344#322C2×D5911yescharacteristic
345C82—591no—
346C59#1808311yescharacteristic, complemented, Sylow
347C2×Q16—591no—
348C2×Q16C4×D5911yescharacteristic
349C2×SD16—591no—
350C2×SD16—591no—
351C2×M16—591no—
352C2×M16—591no—
353C2×M16—1181no—
354C22×C8—1181no—
355C22×C8—1181no—
356C4⋊Q8—591no—
357C4⋊Q8—591no—
358#126—1181no—
359#125—591no—
360#125—1181no—
361#124—591no—
362#123—1181no—
363C22⋊Q8—591no—
364C22⋊Q8—591no—
365C22⋊Q8—591no—
366C22⋊Q8—1181no—
367#121—591no—
368C4×Q8—591no—
369C4×Q8—1181no—
370C4×Q8C22×D5911yescharacteristic
371C4×Q8C22×D5911yescharacteristic
372C4×D4—591no—
373C4×D4—1181no—
374#117—1181no—
375#117—1181no—
376C2×C42—591no—
377#107—591no—
378#107C4×D5911yescharacteristic
379#106—591no—
380#106—591no—
381C4⋊C8—21no—
382C4⋊C8—21no—
383C4⋊C8—591no—
384C4⋊C8—591no—
385C4⋊C8—591no—
386C4⋊C8—591no—
387C4⋊C8—1181no—
388C4⋊C8—1181no—
389C4⋊C8—1181no—
390C4⋊C8—1181no—
391C4⋊C8—1181no—
392C4⋊C8—1181no—
393C4⋊C8C22×D5911yescharacteristic
394C4⋊C8C22×D5911yescharacteristic
395#103—591no—
396#103—591no—
397#103—591no—
398#103—591no—
399#103C4×D5911yescharacteristic
400#103C4×D5911yescharacteristic
401#102—591no—
402#102—591no—
403C22⋊C8—591no—
404C22⋊C8—591no—
405C22⋊C8—1181no—
406C22⋊C8—1181no—
407C22⋊C8—1181no—
408C22⋊C8—1181no—
409#97—21no—
410#97—21no—
411#97—591no—
412#97—591no—
413#97—1181no—
414C4×C8—591no—
415C4×C8—591no—
416C4×C8—591no—
417C4×C8—1181no—
418C4×C8—1181no—
419C4×C8—1181no—
420C4×C8—1181no—
421C4×C8C22×D5911yescharacteristic
422C4×C8C22×D5911yescharacteristic
423C4×C8C22×D5911yescharacteristic
424C2×Q8—591no—
425C2×Q8—1181no—
426C2×Q8C2×C4×D5911yescharacteristic
427C2×Q8C2×C4×D5911yescharacteristic
428C2×D4—591no—
429C2×D4—1181no—
430C22×C4—591no—
431C22×C4—591no—
432C22×C4—591no—
433C22×C4—1181no—
434Q16—22no—
435Q16—2361no—
436SD16—1182no—
437SD16—2361no—
438M16—1182no—
439M16—4721no—
440M16—2361no—
441C2×C8—21no—
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—591no—
445C2×C8—591no—
446C2×C8—591no—
447C2×C8—591no—
448C2×C8—1181no—
449C2×C8—1181no—
450C2×C8—1181no—
451C2×C8—4721no—
452C2×C8—4721no—
453C2×C8C2×C4×D5911yescharacteristic
454C2×C8C2×C4×D5911yescharacteristic
455C2×C8D4×D5911yescharacteristic
456C2×C8D4×D5911yescharacteristic
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—591no—
460C4⋊C4—591no—
461C4⋊C4—1181no—
462C4⋊C4—1181no—
463C4⋊C4—1181no—
464C4⋊C4—1181no—
465C4⋊C4—1181no—
466C4⋊C4—1181no—
467C4⋊C4—1181no—
468C4⋊C4—1181no—
469C4⋊C4—1181no—
470C4⋊C4C2×C4×D5911yescharacteristic
471C4⋊C4C2×C4×D5911yescharacteristic
472C22⋊C4—1181no—
473C22⋊C4—1181no—
474C22⋊C4—1181no—
475C22⋊C4—1181no—
476C22⋊C4—1181no—
477C22⋊C4—1181no—
478C22⋊C4—1181no—
479C42—21no—
480C42—21no—
481C42—591no—
482C42—591no—
483C42—591no—
484C42—1181no—
485C42C23×D5911yescharacteristic
486C23—591no—
487C23—1181no—
488Q8—21no—
489Q8—21no—
490Q8—21no—
491Q8—21no—
492Q8—1181no—
493Q8—1181no—
494Q8—2362no—
495D4—1181no—
496D4—1181no—
497D4—2362no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—591no—
503C2×C4—591no—
504C2×C4—591no—
505C2×C4—1181no—
506C2×C4—1181no—
507C2×C4—1181no—
508C2×C4—1181no—
509C2×C4—1181no—
510C2×C4—1181no—
511C2×C4—1181no—
512C2×C4—2361no—
513C2×C4—2361no—
514C2×C4—2361no—
515C2×C4C22×C4×D5911yescharacteristic
516C2×C4C2×D4×D5911yescharacteristic
517C2×C4#41×D5911yescharacteristic
518C8—21no—
519C8—21no—
520C8—21no—
521C8—41no—
522C8—41no—
523C8—41no—
524C8—1181no—
525C8—1181no—
526C8—1181no—
527C8—1181no—
528C8—2361no—
529C8—2361no—
530C8—2361no—
531C8#1427373512yes—
532C22—1181no—
533C22—1181no—
534C22—1181no—
535C22—2361no—
536C22—2361no—
537C22—2361no—
538C22C4×D4×D5911yescharacteristic
539C4—21no—
540C4—41no—
541C4—41no—
542C4—41no—
543C4—41no—
544C4—1181no—
545C4—1181no—
546C4—1181no—
547C4—2361no—
548C4—2361no—
549C4—2361no—
550C4C2×#1427373511yescharacteristic
551C4#1683816711yescharacteristic
552C4#1683821111yescharacteristic
553C4#1683821811yescharacteristic
554C2—4721no—
555C2—2361no—
556C2#2143284111yescharacteristic
557C2#2143293811yescharacteristic
558C2#2143299611yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D59
commutatorC2×C4×C59C23×C4
FrattiniC42C23×D59
FittingC59×#1593C2
socleC22×C59C2×C4×D4
prime radical#14273702C2×C4
cosocleC42×C59C24
hypercenter#1593D59
hypocenterC59#18083
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1593

Complements

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

NH ≅ G/Ntype
3. #21433194C2semidirect
4. #21422985C2semidirect
5. #21422971C2semidirect
6. #21422964C2semidirect
7. #21422944C2semidirect
8. #21422930C2semidirect
9. #21422910C2semidirect
10. Q16×C59⋊C8C2semidirect
11. #21422845C2semidirect
13. #21422497C2semidirect
14. #21422394C2semidirect
15. C59×#1593C2semidirect
278. #1593D59semidirect
346. C59#18083semidirect

Maximal subgroups

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

subgroupindex
#214347002
#214332592
#214331942
#214229852
#214229712
#214229642
#214229442
#214229302
#214229102
Q16×C59⋊C82
#214228452
#214225032
#214224972
#214223942
C59×#15932
#1808359