Finite Group Databasebeta

← C59×#24101 #28436210

Subgroups — C59×#24101 #28436210

Order 15104.

1152 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C59×#553C211yesmaximal, characteristic
2C2×C59×#481C211yesmaximal, characteristic, complemented
3C2×C59×#428C211yesmaximal, characteristic, complemented
4C59×#2486C211yesmaximal, characteristic, complemented
5C59×#2059C212yesmaximal, complemented
6C59×#2033C212yesmaximal, complemented
7C59×#1895C211yesmaximal, characteristic, complemented
8C59×#1870C211yesmaximal, characteristic, complemented
9C59×#1864C212yesmaximal, complemented
10C59×#1853C212yesmaximal, complemented
11C59×#1825C211yesmaximal, characteristic, complemented
12C22×M16×C59C2211yescharacteristic
13C59×#553—24no—
14C59×#553—24no—
15C2×#126×C59—21no—
16C2×#125×C59C2211yescharacteristic
17C2×#123×C59—21no—
18C2×#123×C59—21no—
19C2×#121×C59—21no—
20C2×#121×C59C2211yescharacteristic
21C2×#121×C59C2211yescharacteristic
22C2×C4×D4×C59—21no—
23C2×C4×D4×C59C2211yescharacteristic
24C2×C4×D4×C59C2211yescharacteristic
25C2×#117×C59C2211yescharacteristic
26C22×C4⋊C4×C59C2211yescharacteristic
27C22×C4⋊C4×C59C2211yescharacteristic
28C59×#481—24no—
29C59×#428—24no—
30C2×#107×C59C2212yes—
31C2×#106×C59C2212yes—
32C2×#106×C59C2212yes—
33C2×#102×C59C2212yes—
34C2×#102×C59C2212yes—
35C2×C22⋊C8×C59C2212yes—
36C2×C22⋊C8×C59C2211yescharacteristic
37C59×#398—21no—
38C59×#397—21no—
39C59×#389C2212yes—
40C59×#381—21no—
41C59×#380C2212yes—
42C59×#380C2211yescharacteristic
43C59×#340C2212yes—
44C59×#340C2212yes—
45C59×#340C2212yes—
46C59×#336C2212yes—
47C22×D4×C59—21no—
48C22×D4×C59—21no—
49C22×D4×C59D411yescharacteristic
50C22×D4×C59C2311yescharacteristic
51C23×C4×C59—21no—
52C23×C4×C59—21no—
53C23×C4×C59—21no—
54C23×C4×C59C2311yescharacteristic
55C23×C4×C59C2311yescharacteristic
56C2×M16×C59—22no—
57C2×M16×C59—24no—
58C22×C8×C59C2312yes—
59C22×C8×C59C2312yes—
60#126×C59—28no—
61#125×C59—22no—
62#125×C59—22no—
63#123×C59—28no—
64#123×C59—44no—
65#121×C59—28no—
66#121×C59—22no—
67#121×C59—22no—
68#121×C59—22no—
69#121×C59D414yes—
70C4×D4×C59—28no—
71C4×D4×C59—22no—
72C4×D4×C59—22no—
73C4×D4×C59—22no—
74C4×D4×C59—22no—
75#117×C59—22no—
76#117×C59D414yes—
77C2×C4⋊C4×C59—21no—
78C2×C4⋊C4×C59—21no—
79C2×C4⋊C4×C59—21no—
80C2×C4⋊C4×C59—22no—
81C2×C4⋊C4×C59—22no—
82C2×C4⋊C4×C59—22no—
83C2×C4⋊C4×C59—22no—
84C2×C4⋊C4×C59—22no—
85C2×C4⋊C4×C59—21no—
86C2×C4⋊C4×C59D411yescharacteristic
87C2×C4⋊C4×C59C2312yes—
88C2×C4⋊C4×C59C2312yes—
89C2×C4⋊C4×C59C2311yescharacteristic
90C2×C4⋊C4×C59C2311yescharacteristic
91C2×C4⋊C4×C59C2311yescharacteristic
92C2×C22⋊C4×C59—21no—
93C2×C22⋊C4×C59—21no—
94C2×C22⋊C4×C59—21no—
95C2×C22⋊C4×C59—21no—
96C2×C22⋊C4×C59—21no—
97C2×C22⋊C4×C59—22no—
98C2×C22⋊C4×C59D411yescharacteristic
99C2×C22⋊C4×C59D411yescharacteristic
100C2×C42×C59—21no—
101C2×C42×C59C2311yescharacteristic
102#107×C59—24no—
103#106×C59—24no—
104#106×C59—24no—
105#102×C59—24no—
106#102×C59—24no—
107C22⋊C8×C59—22no—
108C22⋊C8×C59—24no—
109#95×C59—22no—
110#95×C59—21no—
111#95×C59—22no—
112C24×C59—21no—
113C24×C59C2×D411yescharacteristic
114C24×C59C2×D411yescharacteristic
115C2×D4×C59—24no—
116C2×D4×C59—22no—
117C2×D4×C59—22no—
118C2×D4×C59—24no—
119C2×D4×C59—21no—
120C2×D4×C59—22no—
121C2×D4×C59—22no—
122C2×D4×C59—41no—
123C2×D4×C59—42no—
124C2×D4×C59—42no—
125C2×D4×C59—82no—
126C2×D4×C59C2×D412yes—
127C22×C4×C59—22no—
128C22×C4×C59—22no—
129C22×C4×C59—21no—
130C22×C4×C59—21no—
131C22×C4×C59—21no—
132C22×C4×C59—24no—
133C22×C4×C59—24no—
134C22×C4×C59—21no—
135C22×C4×C59—21no—
136C22×C4×C59—22no—
137C22×C4×C59—22no—
138C22×C4×C59—22no—
139C22×C4×C59—22no—
140C22×C4×C59—42no—
141C22×C4×C59—42no—
142C22×C4×C59—42no—
143C22×C4×C59—82no—
144C22×C4×C59—82no—
145C22×C4×C59C2×D411yescharacteristic
146C22×C4×C59C2×D411yescharacteristic
147C22×C4×C59C2×D411yescharacteristic
148C22×C4×C59C2×D411yescharacteristic
149C22×C4×C59C2×D412yes—
150C22×C4×C59C2×D412yes—
151C22×C4×C59C2411yescharacteristic
152M16×C59—28no—
153C2×C8×C59—22no—
154C2×C8×C59—22no—
155C2×C8×C59—22no—
156C2×C8×C59—22no—
157C2×C8×C59—22no—
158C2×C8×C59#4114yes—
159C4⋊C4×C59—24no—
160C4⋊C4×C59—24no—
161C4⋊C4×C59—24no—
162C4⋊C4×C59—22no—
163C4⋊C4×C59—21no—
164C4⋊C4×C59—21no—
165C4⋊C4×C59—21no—
166C4⋊C4×C59—22no—
167C4⋊C4×C59—22no—
168C4⋊C4×C59—22no—
169C4⋊C4×C59—22no—
170C4⋊C4×C59—44no—
171C4⋊C4×C59—42no—
172C4⋊C4×C59C2×D412yes—
173C4⋊C4×C59C2×D412yes—
174C4⋊C4×C59C2×D412yes—
175C22⋊C4×C59—24no—
176C22⋊C4×C59—24no—
177C22⋊C4×C59—24no—
178C22⋊C4×C59—22no—
179C22⋊C4×C59—24no—
180C22⋊C4×C59—22no—
181C22⋊C4×C59—42no—
182C22⋊C4×C59—44no—
183C42×C59—24no—
184C42×C59—21no—
185C42×C59—21no—
186C23×C59—21no—
187C23×C59—22no—
188C23×C59—22no—
189C23×C59—21no—
190C23×C59—21no—
191C23×C59—21no—
192C23×C59—22no—
193C23×C59—22no—
194C23×C59—22no—
195C23×C59—42no—
196C23×C59—41no—
197C23×C59—41no—
198C23×C59—42no—
199C23×C59#12012yes—
200C23×C59AGL(1,ℤ/8)12yes—
201C23×C59C22×D411yescharacteristic
202D4×C59—24no—
203D4×C59—44no—
204D4×C59—48no—
205D4×C59—41no—
206D4×C59—41no—
207D4×C59—84no—
208C2×C4×C59—22no—
209C2×C4×C59—22no—
210C2×C4×C59—22no—
211C2×C4×C59—24no—
212C2×C4×C59—21no—
213C2×C4×C59—22no—
214C2×C4×C59—21no—
215C2×C4×C59—22no—
216C2×C4×C59—21no—
217C2×C4×C59—22no—
218C2×C4×C59—22no—
219C2×C4×C59—21no—
220C2×C4×C59—21no—
221C2×C4×C59—22no—
222C2×C4×C59—41no—
223C2×C4×C59—41no—
224C2×C4×C59—42no—
225C2×C4×C59—42no—
226C2×C4×C59—41no—
227C2×C4×C59—41no—
228C2×C4×C59—42no—
229C2×C4×C59—42no—
230C2×C4×C59—42no—
231C2×C4×C59—42no—
232C2×C4×C59—42no—
233C2×C4×C59—42no—
234C2×C4×C59—42no—
235C2×C4×C59—84no—
236C2×C4×C59—84no—
237C2×C4×C59—84no—
238C2×C4×C59#12012yes—
239C2×C4×C59C22×D411yescharacteristic
240C2×C4×C59C22×D411yescharacteristic
241C2×C4×C59C2×#4112yes—
242C2×C4×C592−1+412yes—
243C8×C59—24no—
244C8×C59—42no—
245#24101C5911yesmaximal, characteristic, direct product factor, Sylow
246C22×C59—24no—
247C22×C59—22no—
248C22×C59—22no—
249C22×C59—22no—
250C22×C59—22no—
251C22×C59—42no—
252C22×C59—42no—
253C22×C59—42no—
254C22×C59—41no—
255C22×C59—41no—
256C22×C59—42no—
257C22×C59—42no—
258C22×C59—42no—
259C22×C59—82no—
260C22×C59—82no—
261C22×C59C2×#12011yescharacteristic
262C22×C59#54712yes—
263C22×C59C2×AGL(1,ℤ/8)11yescharacteristic
264C22×C59#57511yescharacteristic
265C22×C59#57712yes—
266C4×C59—22no—
267C4×C59—41no—
268C4×C59—41no—
269C4×C59—42no—
270C4×C59—41no—
271C4×C59—42no—
272C4×C59—42no—
273C4×C59—82no—
274C4×C59—82no—
275C4×C59#52511yescharacteristic
276C4×C59#53611yescharacteristic
277C4×C59#54712yes—
278C2×#553C2×C5911yescharacteristic
279C2×#481C2×C5911yescharacteristic, complemented
280C2×#428C2×C5911yescharacteristic, complemented
281#2486C2×C5911yescharacteristic, complemented
282#2059C2×C5912yescomplemented
283#2033C2×C5912yescomplemented
284#1895C2×C5911yescharacteristic, complemented
285#1870C2×C5911yescharacteristic, complemented
286#1864C2×C5912yescomplemented
287#1853C2×C5912yescomplemented
288#1825C2×C5911yescharacteristic, complemented
289C2×C59—42no—
290C2×C59—42no—
291C2×C59—82no—
292C2×C59#240611yescharacteristic
293C2×C59#300611yescharacteristic
294C2×C59#300911yescharacteristic
295C2×C59#334512yes—
296C2×C59#335112yes—
297C22×M16C22×C5911yescharacteristic
298#553—24no—
299#553—24no—
300C2×#126—21no—
301C2×#125C22×C5911yescharacteristic
302C2×#123—21no—
303C2×#123—21no—
304C2×#121—21no—
305C2×#121C22×C5911yescharacteristic
306C2×#121C22×C5911yescharacteristic
307C2×C4×D4—21no—
308C2×C4×D4C22×C5911yescharacteristic
309C2×C4×D4C22×C5911yescharacteristic
310C2×#117C22×C5911yescharacteristic
311C22×C4⋊C4C22×C5911yescharacteristic
312C22×C4⋊C4C22×C5911yescharacteristic
313#481—24no—
314#428—24no—
315C2×#107C22×C5912yes—
316C2×#106C22×C5912yes—
317C2×#106C22×C5912yes—
318C2×#102C22×C5912yes—
319C2×#102C22×C5912yes—
320C2×C22⋊C8C22×C5911yescharacteristic
321C2×C22⋊C8C22×C5912yes—
322#398—21no—
323#397—21no—
324#389C22×C5912yes—
325#381—21no—
326#380C22×C5911yescharacteristic
327#380C22×C5912yes—
328#340C22×C5912yes—
329#340C22×C5912yes—
330#340C22×C5912yes—
331#336C22×C5912yes—
332C59#2410111yescharacteristic, direct product factor, Sylow
333C22×D4—21no—
334C22×D4—21no—
335C22×D4D4×C5911yescharacteristic
336C22×D4C23×C5911yescharacteristic
337C23×C4—21no—
338C23×C4—21no—
339C23×C4—21no—
340C23×C4C23×C5911yescharacteristic
341C23×C4C23×C5911yescharacteristic
342C2×M16—22no—
343C2×M16—24no—
344C22×C8C23×C5912yes—
345C22×C8C23×C5912yes—
346#126—28no—
347#125—22no—
348#125—22no—
349#123—28no—
350#123—44no—
351#121—28no—
352#121—22no—
353#121—22no—
354#121—22no—
355#121D4×C5914yes—
356C4×D4—28no—
357C4×D4—22no—
358C4×D4—22no—
359C4×D4—22no—
360C4×D4—22no—
361#117—22no—
362#117D4×C5914yes—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—22no—
367C2×C4⋊C4—22no—
368C2×C4⋊C4—22no—
369C2×C4⋊C4—22no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—22no—
372C2×C4⋊C4D4×C5911yescharacteristic
373C2×C4⋊C4C23×C5912yes—
374C2×C4⋊C4C23×C5912yes—
375C2×C4⋊C4C23×C5911yescharacteristic
376C2×C4⋊C4C23×C5911yescharacteristic
377C2×C4⋊C4C23×C5911yescharacteristic
378C2×C22⋊C4—21no—
379C2×C22⋊C4—21no—
380C2×C22⋊C4—21no—
381C2×C22⋊C4—21no—
382C2×C22⋊C4—21no—
383C2×C22⋊C4—22no—
384C2×C22⋊C4D4×C5911yescharacteristic
385C2×C22⋊C4D4×C5911yescharacteristic
386C2×C42—21no—
387C2×C42C23×C5911yescharacteristic
388#107—24no—
389#106—24no—
390#106—24no—
391#102—24no—
392#102—24no—
393C22⋊C8—22no—
394C22⋊C8—24no—
395#95—22no—
396#95—21no—
397#95—22no—
398C24—21no—
399C24C2×D4×C5911yescharacteristic
400C24C2×D4×C5911yescharacteristic
401C2×D4—24no—
402C2×D4—22no—
403C2×D4—22no—
404C2×D4—24no—
405C2×D4—21no—
406C2×D4—22no—
407C2×D4—22no—
408C2×D4—41no—
409C2×D4—42no—
410C2×D4—42no—
411C2×D4—82no—
412C2×D4C2×D4×C5912yes—
413C22×C4—22no—
414C22×C4—22no—
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—24no—
419C22×C4—24no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—42no—
427C22×C4—42no—
428C22×C4—42no—
429C22×C4—82no—
430C22×C4—82no—
431C22×C4C2×D4×C5911yescharacteristic
432C22×C4C2×D4×C5911yescharacteristic
433C22×C4C2×D4×C5911yescharacteristic
434C22×C4C2×D4×C5911yescharacteristic
435C22×C4C2×D4×C5912yes—
436C22×C4C2×D4×C5912yes—
437C22×C4C24×C5911yescharacteristic
438M16—28no—
439C2×C8—22no—
440C2×C8—22no—
441C2×C8—22no—
442C2×C8—22no—
443C2×C8—22no—
444C2×C8#41×C5914yes—
445C4⋊C4—24no—
446C4⋊C4—24no—
447C4⋊C4—24no—
448C4⋊C4—22no—
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—22no—
453C4⋊C4—22no—
454C4⋊C4—22no—
455C4⋊C4—22no—
456C4⋊C4—44no—
457C4⋊C4—42no—
458C4⋊C4C2×D4×C5912yes—
459C4⋊C4C2×D4×C5912yes—
460C4⋊C4C2×D4×C5912yes—
461C22⋊C4—24no—
462C22⋊C4—24no—
463C22⋊C4—24no—
464C22⋊C4—22no—
465C22⋊C4—24no—
466C22⋊C4—22no—
467C22⋊C4—42no—
468C22⋊C4—44no—
469C42—24no—
470C42—21no—
471C42—21no—
472C23—21no—
473C23—22no—
474C23—22no—
475C23—21no—
476C23—21no—
477C23—21no—
478C23—22no—
479C23—22no—
480C23—22no—
481C23—42no—
482C23—41no—
483C23—41no—
484C23—42no—
485C23#120×C5912yes—
486C23AGL(1,ℤ/8)×C5912yes—
487C23C22×D4×C5911yescharacteristic
488D4—24no—
489D4—44no—
490D4—48no—
491D4—41no—
492D4—41no—
493D4—84no—
494C2×C4—22no—
495C2×C4—22no—
496C2×C4—22no—
497C2×C4—24no—
498C2×C4—21no—
499C2×C4—22no—
500C2×C4—21no—
501C2×C4—22no—
502C2×C4—21no—
503C2×C4—22no—
504C2×C4—22no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—22no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—42no—
511C2×C4—42no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—42no—
515C2×C4—42no—
516C2×C4—42no—
517C2×C4—42no—
518C2×C4—42no—
519C2×C4—42no—
520C2×C4—42no—
521C2×C4—84no—
522C2×C4—84no—
523C2×C4—84no—
524C2×C4#120×C5912yes—
525C2×C4C22×D4×C5911yescharacteristic
526C2×C4C22×D4×C5911yescharacteristic
527C2×C4C2×#41×C5912yes—
528C2×C42−1+4×C5912yes—
529C8—24no—
530C8—42no—
531C22—22no—
532C22—22no—
533C22—22no—
534C22—24no—
535C22—22no—
536C22—41no—
537C22—42no—
538C22—42no—
539C22—42no—
540C22—41no—
541C22—42no—
542C22—42no—
543C22—42no—
544C22—82no—
545C22—82no—
546C22C2×#120×C5911yescharacteristic
547C22C59×#54712yes—
548C22C2×AGL(1,ℤ/8)×C5911yescharacteristic
549C22C59×#57511yescharacteristic
550C22C59×#57712yes—
551C4—22no—
552C4—41no—
553C4—42no—
554C4—41no—
555C4—42no—
556C4—42no—
557C4—41no—
558C4—82no—
559C4—82no—
560C4C59×#52511yescharacteristic
561C4C59×#53611yescharacteristic
562C4C59×#54712yes—
563C2—42no—
564C2—42no—
565C2—82no—
566C2C59×#240611yescharacteristic
567C2C59×#300611yescharacteristic
568C2C59×#300911yescharacteristic
569C2C59×#334512yes—
570C2C59×#335112yes—
subgroupG/H
center, socleC23×C59C22×D4
commutator, Frattini, cosocleC22×C4C24×C59
prime radicalC2×C59×#553C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C59 ◁ C2×C4×D4×C59 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C59×#481C2semidirect
3. C2×C59×#428C2semidirect
4. C59×#2486C2semidirect
5. C59×#2059C2semidirect
6. C59×#2033C2semidirect
7. C59×#1895C2semidirect
8. C59×#1870C2semidirect
9. C59×#1864C2semidirect
10. C59×#1853C2semidirect
11. C59×#1825C2semidirect
245. #24101C59direct (N × H)
279. C2×#481C2×C59semidirect
280. C2×#428C2×C59semidirect
281. #2486C2×C59semidirect
282. #2059C2×C59semidirect
283. #2033C2×C59semidirect
284. #1895C2×C59semidirect
285. #1870C2×C59semidirect
286. #1864C2×C59semidirect
287. #1853C2×C59semidirect
288. #1825C2×C59semidirect
332. C59#24101direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C59×#5532
C2×C59×#4812
C2×C59×#4282
C59×#24862
C59×#20592
C59×#20332
C59×#18952
C59×#18702
C59×#18642
C59×#18532
C59×#18252
#2410159