Finite Group Databasebeta

← C59×#16363 #28428472

Subgroups — C59×#16363 #28428472

Order 15104.

2394 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#121×C59C211yesmaximal, characteristic
2C2×C59×#399C212yesmaximal, complemented
3C2×C59×#394C214yesmaximal, complemented
4C2×C59×#380C211yesmaximal, characteristic, complemented
5C59×#1444C212yesmaximal, complemented
6C59×#1439C212yesmaximal, complemented
7C59×#1438C212yesmaximal, complemented
8C59×C22⋊#95C211yesmaximal, characteristic, complemented
9C23×D4×C59C2212yes—
10C23×D4×C59C2211yescharacteristic
11C24×C4×C59C2211yescharacteristic
12C2×#121×C59—24no—
13C2×#121×C59—28no—
14C22×C4⋊C4×C59C2211yescharacteristic
15C22×C4⋊C4×C59C2211yescharacteristic
16C22×C4⋊C4×C59C2214yes—
17C22×C4⋊C4×C59C2211yescharacteristic
18C22×C22⋊C4×C59C2212yes—
19C22×C22⋊C4×C59C2214yes—
20C22×C22⋊C4×C59C2212yes—
21C22×C22⋊C4×C59C2214yes—
22C22×C22⋊C4×C59C2212yes—
23C59×#399—28no—
24C59×#394—216no—
25C59×#380—24no—
26C2×#95×C59C2212yes—
27C2×#95×C59C2214yes—
28C2×#95×C59C2212yes—
29C2×#95×C59C2212yes—
30C25×C59C2312yes—
31C25×C59C2311yescharacteristic
32C22×D4×C59—24no—
33C22×D4×C59—24no—
34C22×D4×C59—24no—
35C22×D4×C59—28no—
36C22×D4×C59—24no—
37C22×D4×C59—22no—
38C22×D4×C59—24no—
39C22×D4×C59—42no—
40C22×D4×C59—44no—
41C23×C4×C59—24no—
42C23×C4×C59—24no—
43C23×C4×C59—42no—
44C23×C4×C59D414yes—
45C23×C4×C59C2312yes—
46C23×C4×C59C2312yes—
47C23×C4×C59C2314yes—
48C23×C4×C59C2312yes—
49C23×C4×C59C2311yescharacteristic
50C23×C4×C59C2311yescharacteristic
51#121×C59—232no—
52C2×C4⋊C4×C59—24no—
53C2×C4⋊C4×C59—22no—
54C2×C4⋊C4×C59—22no—
55C2×C4⋊C4×C59—22no—
56C2×C4⋊C4×C59—28no—
57C2×C4⋊C4×C59—28no—
58C2×C4⋊C4×C59—24no—
59C2×C4⋊C4×C59—44no—
60C2×C4⋊C4×C59—42no—
61C2×C22⋊C4×C59—24no—
62C2×C22⋊C4×C59—24no—
63C2×C22⋊C4×C59—24no—
64C2×C22⋊C4×C59—28no—
65C2×C22⋊C4×C59—28no—
66C2×C22⋊C4×C59—28no—
67C2×C22⋊C4×C59—28no—
68C2×C22⋊C4×C59—42no—
69C2×C22⋊C4×C59—42no—
70C2×C22⋊C4×C59—44no—
71C2×C22⋊C4×C59—44no—
72C2×C22⋊C4×C59—44no—
73C2×C22⋊C4×C59D418yes—
74C2×C22⋊C4×C59D418yescomplemented
75#95×C59—24no—
76#95×C59—28no—
77#95×C59—24no—
78#95×C59—24no—
79C24×C59—22no—
80C24×C59—22no—
81C24×C59—21no—
82C24×C59—22no—
83C24×C59—22no—
84C24×C59—22no—
85C24×C59—21no—
86C24×C59—24no—
87C24×C59—22no—
88C24×C59—22no—
89C24×C59—24no—
90C24×C59—22no—
91C24×C59—24no—
92C24×C59—24no—
93C24×C59—22no—
94C24×C59—22no—
95C24×C59—22no—
96C24×C59C2×D414yes—
97C24×C59C2×D414yes—
98C24×C59C2×D412yes—
99C24×C59C2411yescharacteristic
100C2×D4×C59—28no—
101C2×D4×C59—216no—
102C2×D4×C59—416no—
103C2×D4×C59—416no—
104C2×D4×C59—44no—
105C2×D4×C59—416no—
106C2×D4×C59—48no—
107C2×D4×C59—48no—
108C2×D4×C59—44no—
109C22×C4×C59—22no—
110C22×C4×C59—22no—
111C22×C4×C59—22no—
112C22×C4×C59—22no—
113C22×C4×C59—24no—
114C22×C4×C59—24no—
115C22×C4×C59—22no—
116C22×C4×C59—22no—
117C22×C4×C59—24no—
118C22×C4×C59—24no—
119C22×C4×C59—24no—
120C22×C4×C59—24no—
121C22×C4×C59—24no—
122C22×C4×C59—24no—
123C22×C4×C59—28no—
124C22×C4×C59—28no—
125C22×C4×C59—24no—
126C22×C4×C59—22no—
127C22×C4×C59—22no—
128C22×C4×C59—24no—
129C22×C4×C59—24no—
130C22×C4×C59—22no—
131C22×C4×C59—22no—
132C22×C4×C59—24no—
133C22×C4×C59—22no—
134C22×C4×C59—22no—
135C22×C4×C59—44no—
136C22×C4×C59—416no—
137C22×C4×C59C2×D418yes—
138C22×C4×C59C2×D414yes—
139C22×C4×C59C2×D414yes—
140C22×C4×C59C2×D412yes—
141C22×C4×C59C2×D412yes—
142C22×C4×C59#4114yes—
143C4⋊C4×C59—28no—
144C4⋊C4×C59—416no—
145C4⋊C4×C59—44no—
146C4⋊C4×C59—44no—
147C22⋊C4×C59—216no—
148C22⋊C4×C59—48no—
149C22⋊C4×C59—416no—
150C22⋊C4×C59—416no—
151C22⋊C4×C59—48no—
152C23×C59—22no—
153C23×C59—22no—
154C23×C59—24no—
155C23×C59—22no—
156C23×C59—22no—
157C23×C59—22no—
158C23×C59—22no—
159C23×C59—24no—
160C23×C59—28no—
161C23×C59—28no—
162C23×C59—24no—
163C23×C59—24no—
164C23×C59—24no—
165C23×C59—28no—
166C23×C59—28no—
167C23×C59—42no—
168C23×C59—42no—
169C23×C59—42no—
170C23×C59—42no—
171C23×C59—44no—
172C23×C59—44no—
173C23×C59—42no—
174C23×C59—42no—
175C23×C59—44no—
176C23×C59—42no—
177C23×C59—42no—
178C23×C59—42no—
179C23×C59—42no—
180C23×C59—42no—
181C23×C59—42no—
182C23×C59—44no—
183C23×C59—44no—
184C23×C59—44no—
185C23×C59—44no—
186C23×C59—44no—
187C23×C59—44no—
188C23×C59—44no—
189C23×C59—44no—
190C23×C59—44no—
191C23×C59#12714yes—
192C23×C59C22×D411yescharacteristic
193C23×C59C22×D412yes—
194C23×C59C22×D412yes—
195C23×C59C2×#4112yes—
196C23×C59H(5,𝔽2)11yescharacteristic
197C23×C59H(5,𝔽2)12yes—
198C23×C59H(5,𝔽2)12yes—
199C23×C592−1+411yescharacteristic
200C23×C592−1+412yes—
201D4×C59—416no—
202D4×C59—432no—
203C2×C4×C59—22no—
204C2×C4×C59—22no—
205C2×C4×C59—22no—
206C2×C4×C59—22no—
207C2×C4×C59—28no—
208C2×C4×C59—28no—
209C2×C4×C59—24no—
210C2×C4×C59—28no—
211C2×C4×C59—28no—
212C2×C4×C59—28no—
213C2×C4×C59—28no—
214C2×C4×C59—416no—
215C2×C4×C59—42no—
216C2×C4×C59—42no—
217C2×C4×C59—44no—
218C2×C4×C59—44no—
219C2×C4×C59—44no—
220C2×C4×C59—44no—
221C2×C4×C59—44no—
222C2×C4×C59—42no—
223C2×C4×C59—42no—
224C2×C4×C59—42no—
225C2×C4×C59—44no—
226C2×C4×C59—42no—
227C2×C4×C59—42no—
228C2×C4×C59—42no—
229C2×C4×C59—44no—
230C2×C4×C59—44no—
231C2×C4×C59—44no—
232C2×C4×C59#12014yes—
233C2×C4×C59#12314yes—
234#16363C5911yesmaximal, characteristic, direct product factor, Sylow
235C22×C59—24no—
236C22×C59—24no—
237C22×C59—24no—
238C22×C59—42no—
239C22×C59—42no—
240C22×C59—42no—
241C22×C59—42no—
242C22×C59—48no—
243C22×C59—48no—
244C22×C59—44no—
245C22×C59—44no—
246C22×C59—48no—
247C22×C59—48no—
248C22×C59—44no—
249C22×C59—82no—
250C22×C59—82no—
251C22×C59—82no—
252C22×C59—84no—
253C22×C59—84no—
254C22×C59—82no—
255C22×C59C2×#12011yescharacteristic
256C22×C59C2×#12311yescharacteristic
257C22×C59C2×#12711yescharacteristic
258C22×C59#53411yescharacteristic
259C22×C59#53412yes—
260C22×C59#53511yescharacteristic
261C22×C59#53611yescharacteristic
262C22×C59#53612yes—
263C22×C59#53711yescharacteristic
264C22×C59#53712yes—
265C22×C59#53712yes—
266C22×C59#54012yes—
267C22×C59#54212yes—
268C22×C59D4214yes—
269C22×C59#54614yes—
270C22×C59#54714yes—
271C22×C59#56214yes—
272C4×C59—24no—
273C4×C59—24no—
274C4×C59—48no—
275C4×C59—44no—
276C4×C59—82no—
277C4×C59—82no—
278C22×#121C2×C5911yescharacteristic
279C2×#399C2×C5912yescomplemented
280C2×#394C2×C5914yescomplemented
281C2×#380C2×C5911yescharacteristic, complemented
282#1444C2×C5912yescomplemented
283#1439C2×C5912yescomplemented
284#1438C2×C5912yescomplemented
285C22⋊#95C2×C5911yescharacteristic, complemented
286C2×C59—44no—
287C2×C59—84no—
288C2×C59#240511yescharacteristic
289C2×C59#243311yescharacteristic
290C2×C59#250111yescharacteristic
291C2×C59#261611yescharacteristic
292C2×C59#262411yescharacteristic
293C2×C59#265611yescharacteristic
294C2×C59#267114yes—
295C2×C59#267214yes—
296C2×C59#281611yescharacteristic
297C23×D4C22×C5912yes—
298C23×D4C22×C5911yescharacteristic
299C24×C4C22×C5911yescharacteristic
300C2×#121—24no—
301C2×#121—28no—
302C22×C4⋊C4C22×C5911yescharacteristic
303C22×C4⋊C4C22×C5911yescharacteristic
304C22×C4⋊C4C22×C5914yes—
305C22×C4⋊C4C22×C5911yescharacteristic
306C22×C22⋊C4C22×C5912yes—
307C22×C22⋊C4C22×C5914yes—
308C22×C22⋊C4C22×C5912yes—
309C22×C22⋊C4C22×C5914yes—
310C22×C22⋊C4C22×C5912yes—
311#399—28no—
312#394—216no—
313#380—24no—
314C2×#95C22×C5914yes—
315C2×#95C22×C5912yes—
316C2×#95C22×C5912yes—
317C2×#95C22×C5912yes—
318C59#1636311yescharacteristic, direct product factor, Sylow
319C25C23×C5912yes—
320C25C23×C5911yescharacteristic
321C22×D4—24no—
322C22×D4—24no—
323C22×D4—24no—
324C22×D4—28no—
325C22×D4—24no—
326C22×D4—22no—
327C22×D4—24no—
328C22×D4—42no—
329C22×D4—44no—
330C23×C4—24no—
331C23×C4—24no—
332C23×C4—42no—
333C23×C4D4×C5914yes—
334C23×C4C23×C5912yes—
335C23×C4C23×C5912yes—
336C23×C4C23×C5914yes—
337C23×C4C23×C5912yes—
338C23×C4C23×C5911yescharacteristic
339C23×C4C23×C5911yescharacteristic
340#121—232no—
341C2×C4⋊C4—24no—
342C2×C4⋊C4—22no—
343C2×C4⋊C4—22no—
344C2×C4⋊C4—22no—
345C2×C4⋊C4—28no—
346C2×C4⋊C4—28no—
347C2×C4⋊C4—24no—
348C2×C4⋊C4—44no—
349C2×C4⋊C4—42no—
350C2×C22⋊C4—24no—
351C2×C22⋊C4—24no—
352C2×C22⋊C4—24no—
353C2×C22⋊C4—28no—
354C2×C22⋊C4—28no—
355C2×C22⋊C4—28no—
356C2×C22⋊C4—28no—
357C2×C22⋊C4—42no—
358C2×C22⋊C4—42no—
359C2×C22⋊C4—44no—
360C2×C22⋊C4—44no—
361C2×C22⋊C4—44no—
362C2×C22⋊C4D4×C5918yes—
363C2×C22⋊C4D4×C5918yescomplemented
364#95—24no—
365#95—28no—
366#95—24no—
367#95—24no—
368C24—22no—
369C24—22no—
370C24—21no—
371C24—22no—
372C24—22no—
373C24—22no—
374C24—21no—
375C24—24no—
376C24—22no—
377C24—22no—
378C24—24no—
379C24—22no—
380C24—24no—
381C24—24no—
382C24—22no—
383C24—22no—
384C24—22no—
385C24C2×D4×C5914yes—
386C24C2×D4×C5914yes—
387C24C2×D4×C5912yes—
388C24C24×C5911yescharacteristic
389C2×D4—28no—
390C2×D4—216no—
391C2×D4—416no—
392C2×D4—416no—
393C2×D4—44no—
394C2×D4—416no—
395C2×D4—48no—
396C2×D4—48no—
397C2×D4—44no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—24no—
403C22×C4—24no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—24no—
407C22×C4—24no—
408C22×C4—24no—
409C22×C4—24no—
410C22×C4—24no—
411C22×C4—24no—
412C22×C4—28no—
413C22×C4—28no—
414C22×C4—24no—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—24no—
418C22×C4—24no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—24no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—44no—
425C22×C4—416no—
426C22×C4C2×D4×C5918yes—
427C22×C4C2×D4×C5914yes—
428C22×C4C2×D4×C5914yes—
429C22×C4C2×D4×C5912yes—
430C22×C4C2×D4×C5912yes—
431C22×C4#41×C5914yes—
432C4⋊C4—28no—
433C4⋊C4—416no—
434C4⋊C4—44no—
435C4⋊C4—44no—
436C22⋊C4—216no—
437C22⋊C4—48no—
438C22⋊C4—416no—
439C22⋊C4—416no—
440C22⋊C4—48no—
441C23—22no—
442C23—22no—
443C23—24no—
444C23—22no—
445C23—22no—
446C23—22no—
447C23—22no—
448C23—24no—
449C23—28no—
450C23—28no—
451C23—24no—
452C23—24no—
453C23—24no—
454C23—28no—
455C23—28no—
456C23—42no—
457C23—42no—
458C23—42no—
459C23—42no—
460C23—44no—
461C23—44no—
462C23—42no—
463C23—42no—
464C23—44no—
465C23—42no—
466C23—42no—
467C23—42no—
468C23—42no—
469C23—42no—
470C23—42no—
471C23—44no—
472C23—44no—
473C23—44no—
474C23—44no—
475C23—44no—
476C23—44no—
477C23—44no—
478C23—44no—
479C23—44no—
480C23#127×C5914yes—
481C23C22×D4×C5911yescharacteristic
482C23C22×D4×C5912yes—
483C23C22×D4×C5912yes—
484C23C2×#41×C5912yes—
485C23H(5,𝔽2)×C5911yescharacteristic
486C23H(5,𝔽2)×C5912yes—
487C23H(5,𝔽2)×C5912yes—
488C232−1+4×C5911yescharacteristic
489C232−1+4×C5912yes—
490D4—416no—
491D4—432no—
492C2×C4—22no—
493C2×C4—22no—
494C2×C4—22no—
495C2×C4—22no—
496C2×C4—28no—
497C2×C4—28no—
498C2×C4—24no—
499C2×C4—28no—
500C2×C4—28no—
501C2×C4—28no—
502C2×C4—28no—
503C2×C4—416no—
504C2×C4—42no—
505C2×C4—42no—
506C2×C4—44no—
507C2×C4—44no—
508C2×C4—44no—
509C2×C4—44no—
510C2×C4—44no—
511C2×C4—42no—
512C2×C4—42no—
513C2×C4—42no—
514C2×C4—44no—
515C2×C4—42no—
516C2×C4—42no—
517C2×C4—42no—
518C2×C4—44no—
519C2×C4—44no—
520C2×C4—44no—
521C2×C4#120×C5914yes—
522C2×C4#123×C5914yes—
523C22—24no—
524C22—24no—
525C22—24no—
526C22—42no—
527C22—42no—
528C22—42no—
529C22—42no—
530C22—48no—
531C22—48no—
532C22—44no—
533C22—44no—
534C22—48no—
535C22—48no—
536C22—44no—
537C22—82no—
538C22—82no—
539C22—82no—
540C22—82no—
541C22—84no—
542C22—84no—
543C22C2×#120×C5911yescharacteristic
544C22C2×#123×C5911yescharacteristic
545C22C2×#127×C5911yescharacteristic
546C22C59×#53411yescharacteristic
547C22C59×#53412yes—
548C22C59×#53511yescharacteristic
549C22C59×#53611yescharacteristic
550C22C59×#53612yes—
551C22C59×#53711yescharacteristic
552C22C59×#53712yes—
553C22C59×#53712yes—
554C22C59×#54012yes—
555C22C59×#54212yes—
556C22D42×C5914yes—
557C22C59×#54614yes—
558C22C59×#54714yes—
559C22C59×#56214yes—
560C4—24no—
561C4—24no—
562C4—48no—
563C4—44no—
564C4—82no—
565C4—82no—
566C2—44no—
567C2—84no—
568C2C59×#240511yescharacteristic
569C2C59×#243311yescharacteristic
570C2C59×#250111yescharacteristic
571C2C59×#261611yescharacteristic
572C2C59×#262411yescharacteristic
573C2C59×#265611yescharacteristic
574C2C59×#267114yes—
575C2C59×#267214yes—
576C2C59×#281611yescharacteristic
subgroupG/H
center, socleC24×C59C24
commutator, Frattini, cosocleC24C24×C59
prime radicalC22×#121×C59C2
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C59 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C59×#399C2semidirect
3. C2×C59×#394C2semidirect
4. C2×C59×#380C2semidirect
5. C59×#1444C2semidirect
6. C59×#1439C2semidirect
7. C59×#1438C2semidirect
8. C59×C22⋊#95C2semidirect
74. C2×C22⋊C4×C59D4semidirect
234. #16363C59direct (N × H)
279. C2×#399C2×C59semidirect
280. C2×#394C2×C59semidirect
281. C2×#380C2×C59semidirect
282. #1444C2×C59semidirect
283. #1439C2×C59semidirect
284. #1438C2×C59semidirect
285. C22⋊#95C2×C59semidirect
318. C59#16363direct (N × H)
363. C2×C22⋊C4D4×C59semidirect

Maximal subgroups

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

subgroupindex
C22×#121×C592
C2×C59×#3992
C2×C59×#3942
C2×C59×#3802
C59×#14442
C59×#14392
C59×#14382
C59×C22⋊#952
#1636359