Finite Group Databasebeta

← #28560552

Subgroups — #28560552

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#21434696C211yesmaximal, characteristic
2#21433094C211yesmaximal, characteristic
3#21433045C211yesmaximal, characteristic, complemented
4#21423001C211yesmaximal, characteristic, complemented
5#21422990C211yesmaximal, characteristic, complemented
6#21422971C211yesmaximal, characteristic, complemented
7#21422970C211yesmaximal, characteristic, complemented
8#21422943C211yesmaximal, characteristic, complemented
9#21422935C211yesmaximal, characteristic, complemented
10#21422912C211yesmaximal, characteristic, complemented
11#21422893C211yesmaximal, characteristic, complemented
12#21422849C211yesmaximal, characteristic, complemented
13#21422510C211yesmaximal, characteristic
14#21422399C211yesmaximal, characteristic, complemented
15C59×#1485C211yesmaximal, characteristic, complemented
16#16837936C2211yescharacteristic
17#16837808C411yescharacteristic
18#16837794C411yescharacteristic
19#16837770C411yescharacteristic
20#16837764C411yescharacteristic
21#16837658C411yescharacteristic
22#16837658C411yescharacteristic
23#16837650C411yescharacteristic
24#16837650C411yescharacteristic
25#16837533—21no—
26#16837533—21no—
27#16837533C2211yescharacteristic
28#16837533C2211yescharacteristic
29#16837529C2211yescharacteristic
30Q8×C59⋊C8C2211yescharacteristic
31Q8×C59⋊C8C2211yescharacteristic
32#16837526C2211yescharacteristic
33C4×#11745672C2211yescharacteristic
34C4×#11745672C2211yescharacteristic
35C4×#11745671C2211yescharacteristic
36C4×#11745671C2211yescharacteristic
37#16837479C2211yescharacteristic
38#16837477—21no—
39#16837476—21no—
40#16837467C2211yescharacteristic
41#16837461—21no—
42#16837429—21no—
43C2×C4⋊(C59⋊C8)C2211yescharacteristic
44#16837358—21no—
45#16837356—21no—
46C4×#11745664C2211yescharacteristic
47C4×#11745664C2211yescharacteristic
48#16837154C2211yescharacteristic
49#16837154C2211yescharacteristic
50#16837152C2211yescharacteristic
51#16837152C2211yescharacteristic
52#16837134C2211yescharacteristic
53#16837134C2211yescharacteristic
54#16837131C2211yescharacteristic
55#16837131C2211yescharacteristic
56#16837124C2211yescharacteristic
57#16837124C2211yescharacteristic
58#16837123C2211yescharacteristic
59C8×C59⋊C8C2211yescharacteristic
60C59×#533C2211yescharacteristic
61C59×#431C2211yescharacteristic
62C4×M16×C59C2211yescharacteristic
63C59×Q8⋊C8C2211yescharacteristic
64C59×Q8⋊C8C2211yescharacteristic
65C59×Q8⋊C8C2211yescharacteristic
66C59×Q8⋊C8C2211yescharacteristic
67C2×#11745672C2×C411yescharacteristic
68C2×#11745672C2×C411yescharacteristic
69C2×#11745671C2×C411yescharacteristic
70C2×#11745671C2×C411yescharacteristic
71C2×#11745664C2×C411yescharacteristic
72C2×#11745664C2×C411yescharacteristic
73C2×#11745664D411yescharacteristic
74C2×#11745664D411yescharacteristic
75C2×#11745659—21no—
76C22×C59⋊C8—21no—
77C2×C8×D59—21no—
78#14273721—21no—
79#14273719C2×C411yescharacteristic
80#14273715C2×C411yescharacteristic
81#14273710—21no—
82#14273706C2×C411yescharacteristic
83#14273701C2×C411yescharacteristic
84C4×Dic118C2311yescharacteristic
85C4×D236C2311yescharacteristic
86C4×C22⋊D59—21no—
87#14273684—21no—
88#14273660C2×C411yescharacteristic
89#14273660C2×C411yescharacteristic
90#14273658C2×C411yescharacteristic
91#14273658C2×C411yescharacteristic
92C4⋊(C59⋊C8)—21no—
93C4⋊(C59⋊C8)—21no—
94C4⋊(C59⋊C8)—21no—
95C4⋊(C59⋊C8)—21no—
96C4⋊(C59⋊C8)—21no—
97C4⋊(C59⋊C8)C2311yescharacteristic
98C4⋊(C59⋊C8)C2311yescharacteristic
99Dic59⋊C8—21no—
100Dic59⋊C8—21no—
101#14273651C2×C411yescharacteristic
102#14273651C2×C411yescharacteristic
103#14273651C2×C411yescharacteristic
104#14273651C2×C411yescharacteristic
105#14273650C2×C411yescharacteristic
106#14273650C2×C411yescharacteristic
107#14273647C2×C411yescharacteristic
108#14273647C2×C411yescharacteristic
109(C2×D59)⋊C8—21no—
110(C2×D59)⋊C8—21no—
111#14273638—21no—
112#14273638—21no—
113#14273638C2×C411yescharacteristic
114#14273638C2×C411yescharacteristic
115#14273638D411yescharacteristic
116#14273638D411yescharacteristic
117#14273637—21no—
118C4×C59⋊C8—21no—
119C4×C59⋊C8—21no—
120C4×C59⋊C8C2311yescharacteristic
121C4×C59⋊C8C2311yescharacteristic
122C4×C59⋊C8C2311yescharacteristic
123C4×C59⋊C8C2311yescharacteristic
124C8×Dic59—21no—
125C2×M16×C59—21no—
126C4⋊Q8×C59C2×C411yescharacteristic
127C4⋊Q8×C59C2×C411yescharacteristic
128#125×C59—21no—
129C22⋊Q8×C59—21no—
130C22⋊Q8×C59C2×C411yescharacteristic
131C22⋊Q8×C59C2×C411yescharacteristic
132C4×Q8×C59—21no—
133C4×Q8×C59C2311yescharacteristic
134C4×Q8×C59C2311yescharacteristic
135#117×C59—21no—
136C2×C42×C59C2311yescharacteristic
137C4⋊C8×C59C2311yescharacteristic
138C4⋊C8×C59C2311yescharacteristic
139C22⋊C8×C59—21no—
140#97×C59—21no—
141C4×C8×C59—21no—
142C4×C8×C59C2311yescharacteristic
143C4×C8×C59C2311yescharacteristic
144C2×Q8×C59—21no—
145C2×Q8×C59C22×C411yescharacteristic
146C2×Q8×C59C22×C411yescharacteristic
147C22×C4×C59C22×C411yescharacteristic
148C22×C4×C59C2×D411yescharacteristic
149C22×C4×C59#4111yescharacteristic
150C2×C22⋊D59—21no—
151C2×D236C22×C411yescharacteristic
152C2×C4×D59—21no—
153C2×Dic118C22×C411yescharacteristic
154M16×C59—42no—
155C2×C8×C59—21no—
156C2×C8×C59—21no—
157C2×C8×C59—21no—
158C2×C8×C59—21no—
159C4⋊C4×C59—21no—
160C4⋊C4×C59—21no—
161C4⋊C4×C59—21no—
162C4⋊C4×C59—21no—
163C4⋊C4×C59—21no—
164C4⋊C4×C59—21no—
165C4⋊C4×C59—21no—
166C4⋊C4×C59C22×C411yescharacteristic
167C4⋊C4×C59C22×C411yescharacteristic
168C22⋊C4×C59—21no—
169C22⋊C4×C59—21no—
170C42×C59—21no—
171C42×C59—21no—
172C42×C59C22×C411yescharacteristic
173C42×C59C2×D411yescharacteristic
174C42×C59#4111yescharacteristic
175C42×C59C2411yescharacteristic
176C22⋊Dic59—21no—
177#11745672—22no—
178#11745672—41no—
179#11745671—22no—
180#11745671—41no—
181(C2×D59)⋊C4—21no—
182(C2×D59)⋊C4—21no—
183(C2×D59)⋊C4—21no—
184(C2×D59)⋊C4—21no—
185C4⋊Dic59C22×C411yescharacteristic
186C4⋊Dic59C22×C411yescharacteristic
187Dic59⋊C4—21no—
188Dic59⋊C4—21no—
189Dic59⋊C4—21no—
190Dic59⋊C4—21no—
191C4×Dic59—21no—
192#11745664—22no—
193#11745664—22no—
194#11745664—41no—
195#11745664—41no—
196C2×C59⋊C8—21no—
197C2×C59⋊C8—21no—
198C2×C59⋊C8—42no—
199C2×C59⋊C8C22×C411yescharacteristic
200C2×C59⋊C8C22×C411yescharacteristic
201C2×C59⋊C8C22×C411yescharacteristic
202C2×C59⋊C8C22×C411yescharacteristic
203C2×C59⋊C8C2×D411yescharacteristic
204C2×C59⋊C8C2×D411yescharacteristic
205C2×C59⋊C8C2×D411yescharacteristic
206C2×C59⋊C8C2×D411yescharacteristic
207#11745659—42no—
208C8×D59—42no—
209C23×C59C4×D411yescharacteristic
210C22×D59—21no—
211Q8×C59—21no—
212Q8×C59—21no—
213Q8×C59—21no—
214Q8×C59—21no—
215Q8×C59—81no—
216C2×C4×C59—21no—
217C2×C4×C59—21no—
218C2×C4×C59—21no—
219C2×C4×C59—21no—
220C2×C4×C59—21no—
221C2×C4×C59—21no—
222C2×C4×C59—21no—
223C2×C4×C59—21no—
224C2×C4×C59—41no—
225C2×C4×C59C4×D411yescharacteristic
226C2×C4×C59C4×D411yescharacteristic
227C2×C4×C59C4×D411yescharacteristic
228C2×C4×C59C23×C411yescharacteristic
229C2×C4×C59C22×D411yescharacteristic
230C2×C4×C59C2×#4111yescharacteristic
231C22⋊D59—81no—
232C2×Dic59—21no—
233C2×Dic59—21no—
234C2×Dic59—21no—
235D236—21no—
236D236—21no—
237C4×D59—41no—
238C4×D59—41no—
239Dic118—21no—
240Dic118—21no—
241C8×C59—22no—
242C8×C59—41no—
243C8×C59—41no—
244C8×C59—41no—
245C59⋊C8—21no—
246C59⋊C8—21no—
247C59⋊C8—21no—
248C59⋊C8—21no—
249C59⋊C8—21no—
250C59⋊C8—21no—
251C59⋊C8—41no—
252C59⋊C8—41no—
253C59⋊C8#13112yes—
254C59⋊C8#13712yes—
255#18077—591nomaximal, Sylow
256C22×C59—21no—
257C22×C59—21no—
258C22×C59—21no—
259C22×C59C2×C4×D411yescharacteristic
260C2×D59—41no—
261C2×D59—41no—
262C2×D59—41no—
263C4×C59—21no—
264C4×C59—21no—
265C4×C59—21no—
266C4×C59—21no—
267C4×C59—41no—
268C4×C59—41no—
269C4×C59—41no—
270C4×C59—41no—
271C4×C59C2×#13111yescharacteristic
272C4×C59#56811yescharacteristic
273C4×C59C2×#13711yescharacteristic
274C4×C59#57511yescharacteristic
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#1587—591no—
285#1584—591no—
286#1582—591no—
287#1579—591no—
288C8×SD16—591no—
289#1565—591no—
290#1485D5911yescharacteristic, complemented
291#1483—591no—
292#1455—591no—
293C2×C59—41no—
294C2×C59#293511yescharacteristic
295C2×C59C4×#13711yescharacteristic
296C2×C59#295611yescharacteristic
297D59—81no—
298#533C2×D5911yescharacteristic
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—591no—
311#446—1181no—
312#446—1181no—
313C8×Q8—591no—
314C8×Q8—591no—
315C8×Q8—591no—
316C4×Q16—591no—
317C4×Q16—591no—
318C4×SD16—591no—
319C4×SD16—591no—
320#436—591no—
321#436—1181no—
322#435—1181no—
323C8×D4—591no—
324#433—1181no—
325#431C2×D5911yescharacteristic
326#424—1181no—
327C2×C4⋊C8—591no—
328#405—1181no—
329#405—1181no—
330C4×M16—591no—
331C4×M16—591no—
332C4×M16C2×D5911yescharacteristic
333#335—591no—
334#335—591no—
335#334—591no—
336#334—591no—
337Q8⋊C8—591no—
338Q8⋊C8—591no—
339Q8⋊C8C2×D5911yescharacteristic
340Q8⋊C8C2×D5911yescharacteristic
341Q8⋊C8C2×D5911yescharacteristic
342Q8⋊C8C2×D5911yescharacteristic
343D4⋊C8—591no—
344D4⋊C8—591no—
345#322—591no—
346#322—591no—
347#322—591no—
348C82—591no—
349C59#1807711yescharacteristic, complemented, Sylow
350C2×Q16—591no—
351C2×Q16—591no—
352C2×SD16—591no—
353C2×SD16—591no—
354C2×M16—21no—
355C2×M16—591no—
356C2×M16—591no—
357C2×M16—591no—
358C2×M16—591no—
359C2×M16—1181no—
360C22×C8—1181no—
361C22×C8—1181no—
362C4⋊Q8C4×D5911yescharacteristic
363C4⋊Q8C4×D5911yescharacteristic
364#126—1181no—
365#125—21no—
366#125—591no—
367#124—591no—
368#123—1181no—
369C22⋊Q8—21no—
370C22⋊Q8—591no—
371C22⋊Q8C4×D5911yescharacteristic
372C22⋊Q8C4×D5911yescharacteristic
373#121—591no—
374C4×Q8—21no—
375C4×Q8—591no—
376C4×Q8C22×D5911yescharacteristic
377C4×Q8C22×D5911yescharacteristic
378C4×D4—591no—
379C4×D4—1181no—
380#117—21no—
381#117—1181no—
382C2×C42C22×D5911yescharacteristic
383#107—591no—
384#107—591no—
385#106—591no—
386#106—591no—
387C4⋊C8—591no—
388C4⋊C8—591no—
389C4⋊C8—1181no—
390C4⋊C8—1181no—
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#103—591no—
403#103—591no—
404#102—591no—
405#102—591no—
406C22⋊C8—21no—
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—591no—
422C4×C8—1181no—
423C4×C8—1181no—
424C4×C8—1181no—
425C4×C8C22×D5911yescharacteristic
426C4×C8C22×D5911yescharacteristic
427C2×Q8—21no—
428C2×Q8—591no—
429C2×Q8C2×C4×D5911yescharacteristic
430C2×Q8C2×C4×D5911yescharacteristic
431C2×D4—591no—
432C2×D4—1181no—
433C22×C4—1181no—
434C22×C4C2×C4×D5911yescharacteristic
435C22×C4D4×D5911yescharacteristic
436C22×C4#1174568711yescharacteristic
437Q16—1182no—
438Q16—2361no—
439SD16—1182no—
440SD16—2361no—
441M16—42no—
442M16—1182no—
443M16—1182no—
444M16—2362no—
445M16—2361no—
446M16—2361no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—591no—
452C2×C8—591no—
453C2×C8—591no—
454C2×C8—591no—
455C2×C8—591no—
456C2×C8—591no—
457C2×C8—591no—
458C2×C8—591no—
459C2×C8—1181no—
460C2×C8—1181no—
461C2×C8—2362no—
462C2×C8—2362no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—591no—
471C4⋊C4—591no—
472C4⋊C4—1181no—
473C4⋊C4—1181no—
474C4⋊C4—1181no—
475C4⋊C4—1181no—
476C4⋊C4C2×C4×D5911yescharacteristic
477C4⋊C4C2×C4×D5911yescharacteristic
478C22⋊C4—21no—
479C22⋊C4—21no—
480C22⋊C4—1181no—
481C22⋊C4—1181no—
482C22⋊C4—1181no—
483C22⋊C4—1181no—
484C22⋊C4—1181no—
485C42—21no—
486C42—21no—
487C42—1181no—
488C42C2×C4×D5911yescharacteristic
489C42D4×D5911yescharacteristic
490C42#1174568711yescharacteristic
491C42C23×D5911yescharacteristic
492C23—1181no—
493C23(C22⋊D59)⋊C411yescharacteristic
494Q8—21no—
495Q8—21no—
496Q8—21no—
497Q8—21no—
498Q8—81no—
499Q8—1181no—
500Q8—1181no—
501D4—1181no—
502D4—1181no—
503D4—4721no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—41no—
513C2×C4—1181no—
514C2×C4—1181no—
515C2×C4—1181no—
516C2×C4—2361no—
517C2×C4—2361no—
518C2×C4(C22⋊D59)⋊C411yescharacteristic
519C2×C4(C22⋊D59)⋊C411yescharacteristic
520C2×C4(C22⋊D59)⋊C411yescharacteristic
521C2×C4C22×C4×D5911yescharacteristic
522C2×C4C2×D4×D5911yescharacteristic
523C2×C4C2×#1174568711yescharacteristic
524C8—22no—
525C8—41no—
526C8—41no—
527C8—41no—
528C8—592no—
529C8—592no—
530C8—1181no—
531C8—1181no—
532C8—1181no—
533C8—1181no—
534C8—1181no—
535C8—1181no—
536C8—2361no—
537C8—2361no—
538C22—21no—
539C22—21no—
540C22—21no—
541C22—2361no—
542C22—2361no—
543C22—2361no—
544C22C2×(C22⋊D59)⋊C411yescharacteristic
545C4—21no—
546C4—21no—
547C4—21no—
548C4—21no—
549C4—41no—
550C4—41no—
551C4—41no—
552C4—41no—
553C4—2361no—
554C4—2361no—
555C4—2361no—
556C4#131×D5911yescharacteristic
557C4#1683816711yescharacteristic
558C4#137×D5911yescharacteristic
559C4#1683820111yescharacteristic
560C2—41no—
561C2—4721no—
562C2#2143283611yescharacteristic
563C2#2143291111yescharacteristic
564C2#2143300211yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D59
commutatorC2×C4×C59C23×C4
FrattiniC42C23×D59
FittingC59×#1485C2
socleC22×C59C2×C4×D4
prime radical#14273701C2×C4
cosocleC42×C59C24
hypercenter#1485D59
hypocenterC59#18077
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1485

Complements

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

NH ≅ G/Ntype
3. #21433045C2semidirect
4. #21423001C2semidirect
5. #21422990C2semidirect
6. #21422971C2semidirect
7. #21422970C2semidirect
8. #21422943C2semidirect
9. #21422935C2semidirect
10. #21422912C2semidirect
11. #21422893C2semidirect
12. #21422849C2semidirect
14. #21422399C2semidirect
15. C59×#1485C2semidirect
290. #1485D59semidirect
349. C59#18077semidirect

Maximal subgroups

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

subgroupindex
#214346962
#214330942
#214330452
#214230012
#214229902
#214229712
#214229702
#214229432
#214229352
#214229122
#214228932
#214228492
#214225102
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C59×#14852
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