Finite Group Databasebeta

← #28515862

Subgroups — #28515862

Order 15104.

2142 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4⋊C4×D59C211yesmaximal, characteristic
2C2×#16837264C212yesmaximal
3C2×#16837261C211yesmaximal, characteristic
4C2×#16837259C211yesmaximal, characteristic
5#21422350C211yesmaximal, characteristic, complemented
6#21422349C211yesmaximal, characteristic, complemented
7#21422348C212yesmaximal, complemented
8#21422347C212yesmaximal, complemented
9#21422346C211yesmaximal, characteristic, complemented
10(C2×D59)⋊#95C212yesmaximal
11C59×#1441C211yesmaximal, characteristic, complemented
12C23×C4×D59C2211yescharacteristic
13C23×C4×D59C2211yescharacteristic
14C23×C4×D59C2211yescharacteristic
15C22×C4⋊Dic59C2211yescharacteristic
16C22×C4⋊Dic59C2211yescharacteristic
17C22×Dic59⋊C4C2211yescharacteristic
18C22×Dic59⋊C4C2211yescharacteristic
19C22×Dic59⋊C4C2212yes—
20C2×C4⋊C4×D59—24no—
21C2×C4⋊C4×D59—24no—
22C2×C4⋊C4×D59C418yescomplemented
23C22×(C2×D59)⋊C4C2212yes—
24C22×(C2×D59)⋊C4C2212yes—
25#16837264—28no—
26#16837261—24no—
27#16837259—24no—
28C2×C59⋊#95C2212yes—
29C2×C59⋊#95C2211yescharacteristic
30C2×C59⋊#95C2212yes—
31C2×C59⋊#95C2212yes—
32C2×C59⋊#95C2212yes—
33C2×C59⋊#95C2212yes—
34C2×C59⋊#95C2212yes—
35C2×C59⋊#95C2212yes—
36C22×C4⋊C4×C59C2211yescharacteristic
37C22×C4⋊C4×C59C2211yescharacteristic
38C2×#95×C59C2212yes—
39C2×#95×C59C2211yescharacteristic
40C2×#95×C59C2212yes—
41C24×D59C2311yescharacteristic
42C23×Dic59C2312yes—
43C23×Dic59C2312yes—
44C23×Dic59C2311yescharacteristic
45C23×Dic59C2311yescharacteristic
46C23×Dic59C2311yescharacteristic
47C22×C4×D59—22no—
48C22×C4×D59—22no—
49C22×C4×D59—22no—
50C22×C4×D59—22no—
51C22×C4×D59—22no—
52C22×C4×D59—22no—
53C22×C4×D59—42no—
54C22×C4×D59—42no—
55C22×C4×D59—42no—
56C22×C4×D59—42no—
57C22×C4×D59C2×C414yes—
58C22×C4×D59C2×C414yes—
59C22×C4×D59C2×C414yes—
60C22×C4×D59D414yes—
61C22×C4×D59D414yes—
62C22×C4×D59D414yes—
63C22×C4×D59Q814yes—
64C2×C4⋊Dic59—22no—
65C2×C4⋊Dic59—22no—
66C2×C4⋊Dic59—22no—
67C2×C4⋊Dic59—42no—
68C2×C4⋊Dic59C2×C414yes—
69C2×Dic59⋊C4—22no—
70C2×Dic59⋊C4—22no—
71C2×Dic59⋊C4—22no—
72C2×Dic59⋊C4—22no—
73C2×Dic59⋊C4—24no—
74C2×Dic59⋊C4—42no—
75C2×Dic59⋊C4—42no—
76C2×Dic59⋊C4C2×C414yes—
77C2×Dic59⋊C4C2×C414yes—
78C4⋊C4×D59—232no—
79C2×(C2×D59)⋊C4—24no—
80C2×(C2×D59)⋊C4—24no—
81C2×(C2×D59)⋊C4—24no—
82C2×(C2×D59)⋊C4—24no—
83C2×(C2×D59)⋊C4—24no—
84C2×(C2×D59)⋊C4—24no—
85C59⋊#95—22no—
86C59⋊#95—24no—
87C59⋊#95—24no—
88C59⋊#95—24no—
89C59⋊#95—24no—
90C59⋊#95—42no—
91C59⋊#95—42no—
92C59⋊#95—42no—
93C23×C4×C59C2312yes—
94C23×C4×C59C2312yes—
95C23×C4×C59C2311yescharacteristic
96C23×C4×C59C2311yescharacteristic
97C23×C4×C59C2311yescharacteristic
98C2×C4⋊C4×C59—22no—
99C2×C4⋊C4×C59—22no—
100C2×C4⋊C4×C59—22no—
101C2×C4⋊C4×C59—42no—
102C2×C4⋊C4×C59C2×C414yes—
103#95×C59—22no—
104#95×C59—24no—
105#95×C59—42no—
106C24×C59C2411yescharacteristic
107C23×D59—22no—
108C23×D59—22no—
109C23×D59—22no—
110C23×D59—22no—
111C23×D59C22×C412yes—
112C23×D59C2×D412yes—
113C23×D59C2×D412yes—
114C23×D59C2×D412yes—
115C23×D59C2×Q812yes—
116C23×D59#4112yes—
117C23×D59#4112yes—
118C22×C4×C59—21no—
119C22×C4×C59—21no—
120C22×C4×C59—21no—
121C22×C4×C59—21no—
122C22×C4×C59—22no—
123C22×C4×C59—22no—
124C22×C4×C59—21no—
125C22×C4×C59—21no—
126C22×C4×C59—22no—
127C22×C4×C59—22no—
128C22×C4×C59—22no—
129C22×C4×C59—22no—
130C22×C4×C59—22no—
131C22×C4×C59—22no—
132C22×C4×C59—22no—
133C22×C4×C59—22no—
134C22×C4×C59—22no—
135C22×C4×C59—22no—
136C22×C4×C59—22no—
137C22×C4×C59—22no—
138C22×C4×C59—22no—
139C22×C4×C59—22no—
140C22×C4×C59—22no—
141C22×C4×C59—22no—
142C22×C4×C59C22×C412yes—
143C22×C4×C59C22×C412yes—
144C22×C4×C59C22×C412yes—
145C22×C4×C59C2×D412yes—
146C22×C4×C59C2×D412yes—
147C22×C4×C59C2×D412yes—
148C22×C4×C59C2×Q812yes—
149C22×Dic59—21no—
150C22×Dic59—21no—
151C22×Dic59—21no—
152C22×Dic59—21no—
153C22×Dic59—22no—
154C22×Dic59—22no—
155C22×Dic59—21no—
156C22×Dic59—21no—
157C22×Dic59—22no—
158C22×Dic59—22no—
159C22×Dic59—22no—
160C22×Dic59—22no—
161C22×Dic59—22no—
162C22×Dic59—22no—
163C22×Dic59—22no—
164C22×Dic59—22no—
165C22×Dic59—22no—
166C22×Dic59—22no—
167C22×Dic59—22no—
168C22×Dic59—22no—
169C22×Dic59—22no—
170C22×Dic59—22no—
171C22×Dic59—22no—
172C22×Dic59—22no—
173C22×Dic59C22×C412yes—
174C22×Dic59C22×C412yes—
175C22×Dic59C22×C412yes—
176C22×Dic59C2×D412yes—
177C22×Dic59C2×D412yes—
178C22×Dic59C2×D412yes—
179C22×Dic59C2×Q812yes—
180C2×C4×D59—28no—
181C2×C4×D59—28no—
182C2×C4×D59—28no—
183C2×C4×D59—28no—
184C2×C4×D59—28no—
185C2×C4×D59—28no—
186C2×C4×D59—28no—
187C2×C4×D59—48no—
188C2×C4×D59—48no—
189C2×C4×D59—48no—
190C2×C4×D59—44no—
191C2×C4×D59—44no—
192C2×C4×D59—48no—
193C2×C4×D59—44no—
194C2×C4×D59—44no—
195C2×C4×D59C22⋊C4116yes—
196C2×C4×D59C4⋊C4116yescomplemented
197C4⋊C4×C59—28no—
198C4⋊C4×C59—44no—
199(C2×D59)⋊C4—48no—
200(C2×D59)⋊C4—48no—
201C4⋊Dic59—28no—
202C4⋊Dic59—44no—
203Dic59⋊C4—28no—
204Dic59⋊C4—28no—
205Dic59⋊C4—48no—
206C23×C59C23×C411yescharacteristic
207C23×C59C22×D411yescharacteristic
208C23×C59C22×D411yescharacteristic
209C23×C59C22×D411yescharacteristic
210C23×C59C22×Q811yescharacteristic
211C23×C59C2×#4111yescharacteristic
212C23×C59C2×#4111yescharacteristic
213C23×C59H(5,𝔽2)12yes—
214C23×C59H(5,𝔽2)12yes—
215C23×C592−1+412yes—
216C23×C592−1+412yes—
217C22×D59—24no—
218C22×D59—24no—
219C22×D59—24no—
220C22×D59—22no—
221C22×D59—22no—
222C22×D59—22no—
223C22×D59—24no—
224C22×D59—22no—
225C22×D59—24no—
226C22×D59—24no—
227C22×D59—24no—
228C22×D59—24no—
229C22×D59—24no—
230C22×D59—24no—
231C22×D59—24no—
232C22×D59—24no—
233C22×D59C2×C22⋊C414yes—
234C22×D59C2×C4⋊C414yes—
235C22×D59#11714yes—
236C22×D59#12114yes—
237C22×D59#12114yes—
238C22×D59C22⋊Q814yes—
239C22×D59C22⋊Q814yes—
240C2×C4×C59—22no—
241C2×C4×C59—22no—
242C2×C4×C59—24no—
243C2×C4×C59—22no—
244C2×C4×C59—22no—
245C2×C4×C59—22no—
246C2×C4×C59—22no—
247C2×C4×C59—22no—
248C2×C4×C59—22no—
249C2×C4×C59—24no—
250C2×C4×C59—22no—
251C2×C4×C59—24no—
252C2×C4×C59—42no—
253C2×C4×C59—41no—
254C2×C4×C59—41no—
255C2×C4×C59—42no—
256C2×C4×C59—42no—
257C2×C4×C59—42no—
258C2×C4×C59—42no—
259C2×C4×C59—42no—
260C2×C4×C59—42no—
261C2×C4×C59—42no—
262C2×C4×C59—42no—
263C2×C4×C59—42no—
264C2×C4×C59—42no—
265C2×C4×C59—42no—
266C2×C4×C59—42no—
267C2×C4×C59—42no—
268C2×C4×C59—42no—
269C2×C4×C59C2×C22⋊C414yes—
270C2×C4×C59C2×C4⋊C414yes—
271C2×Dic59—22no—
272C2×Dic59—22no—
273C2×Dic59—24no—
274C2×Dic59—22no—
275C2×Dic59—22no—
276C2×Dic59—22no—
277C2×Dic59—22no—
278C2×Dic59—24no—
279C2×Dic59—22no—
280C2×Dic59—22no—
281C2×Dic59—22no—
282C2×Dic59—24no—
283C2×Dic59—42no—
284C2×Dic59—41no—
285C2×Dic59—41no—
286C2×Dic59—42no—
287C2×Dic59—42no—
288C2×Dic59—42no—
289C2×Dic59—42no—
290C2×Dic59—42no—
291C2×Dic59—42no—
292C2×Dic59—42no—
293C2×Dic59—42no—
294C2×Dic59—42no—
295C2×Dic59—42no—
296C2×Dic59—42no—
297C2×Dic59—42no—
298C2×Dic59—42no—
299C2×Dic59—42no—
300C2×Dic59C2×C22⋊C414yes—
301C2×Dic59C2×C4⋊C414yes—
302C4×D59—232no—
303C4×D59—416no—
304C4×D59—416no—
305#14339—591nomaximal, Sylow
306C22×C59C22×C22⋊C411yescharacteristic
307C22×C59C22×C4⋊C411yescharacteristic
308C22×C59C2×#11711yescharacteristic
309C22×C59#51812yes—
310C22×C59#51912yes—
311C22×C59C2×#12111yescharacteristic
312C22×C59C2×#12111yescharacteristic
313C22×C59C2×C22⋊Q811yescharacteristic
314C22×C59C2×C22⋊Q811yescharacteristic
315C22×C59#53412yes—
316C22×C59#53411yescharacteristic
317C22×C59#53411yescharacteristic
318C22×C59#53611yescharacteristic
319C22×C59#53612yes—
320C22×C59#53611yescharacteristic
321C22×C59#53712yes—
322C22×C59#53712yes—
323C22×C59#53912yes—
324C22×C59#53912yes—
325C22×C59#53912yes—
326C22×C59#53912yes—
327C22×C59#54412yes—
328C22×C59#54412yes—
329C2×D59—24no—
330C2×D59—24no—
331C2×D59—28no—
332C2×D59—28no—
333C2×D59—24no—
334C2×D59—24no—
335C2×D59—28no—
336C2×D59—24no—
337C2×D59—24no—
338C2×D59—28no—
339C2×D59#38018yes—
340C4×C59—24no—
341C4×C59—24no—
342C4×C59—42no—
343C4×C59—82no—
344C4×C59—82no—
345Dic59—24no—
346Dic59—24no—
347Dic59—42no—
348Dic59—82no—
349Dic59—82no—
350C23×C4⋊C4—591no—
351C2×#381—592no—
352C2×#380—591no—
353C2×#380—591no—
354#1441—592no—
355#1441—592no—
356#1441—591no—
357#1441—591no—
358#1441—591no—
359#1441D5911yescharacteristic, complemented
360C22⋊#95—592no—
361C2×C59C2×#38011yescharacteristic
362C2×C59#230811yescharacteristic
363C2×C59#231011yescharacteristic
364C2×C59#231312yes—
365C2×C59#231612yes—
366C2×C59#261811yescharacteristic
367C2×C59#261811yescharacteristic
368C2×C59#261812yes—
369C2×C59#262711yescharacteristic
370C2×C59#262711yescharacteristic
371C2×C59#262712yes—
372D59—28no—
373C24×C4—591no—
374C24×C4—591no—
375C24×C4—591no—
376C22×C4⋊C4—591no—
377C22×C4⋊C4—591no—
378C22×C4⋊C4—591no—
379C22×C4⋊C4—598no—
380C22×C4⋊C4—592no—
381C22×C4⋊C4—591no—
382C22×C4⋊C4—1184no—
383C22×C4⋊C4—1184no—
384C22×C4⋊C4C2×D5911yescharacteristic
385C22×C4⋊C4C2×D5911yescharacteristic
386C22×C22⋊C4—592no—
387C22×C22⋊C4—592no—
388#381—1188no—
389#380—1184no—
390#380—1184no—
391C2×#95—592no—
392C2×#95—591no—
393C2×#95—592no—
394C2×#95—592no—
395C2×#95—592no—
396C2×#95—592no—
397C2×#95—592no—
398C2×#95—592no—
399C2×#95C2×D5911yescharacteristic
400C2×#95C2×D5912yes—
401C2×#95C2×D5912yes—
402C59#1433911yescharacteristic, complemented, Sylow
403C25—591no—
404C23×C4—591no—
405C23×C4—591no—
406C23×C4—594no—
407C23×C4—594no—
408C23×C4—594no—
409C23×C4—594no—
410C23×C4—594no—
411C23×C4—594no—
412C23×C4—591no—
413C23×C4—594no—
414C23×C4—592no—
415C23×C4—592no—
416C23×C4—1182no—
417C23×C4—1182no—
418C23×C4—1182no—
419C23×C4—1182no—
420C23×C4—1182no—
421C23×C4—1182no—
422C23×C4—2362no—
423C23×C4—2362no—
424C23×C4—2362no—
425C23×C4—2362no—
426C23×C4C22×D5912yes—
427C23×C4C22×D5912yes—
428C23×C4C22×D5911yescharacteristic
429C23×C4C22×D5911yescharacteristic
430C23×C4C22×D5911yescharacteristic
431C2×C4⋊C4—22no—
432C2×C4⋊C4—22no—
433C2×C4⋊C4—22no—
434C2×C4⋊C4—42no—
435C2×C4⋊C4—594no—
436C2×C4⋊C4—594no—
437C2×C4⋊C4—594no—
438C2×C4⋊C4—11832no—
439C2×C4⋊C4—1182no—
440C2×C4⋊C4—1182no—
441C2×C4⋊C4—1182no—
442C2×C4⋊C4—1182no—
443C2×C4⋊C4—1182no—
444C2×C4⋊C4—1182no—
445C2×C4⋊C4—1184no—
446C2×C4⋊C4—1182no—
447C2×C4⋊C4—2362no—
448C2×C4⋊C4—2362no—
449C2×C4⋊C4—2362no—
450C2×C4⋊C4C4×D5914yes—
451C2×C22⋊C4—1184no—
452C2×C22⋊C4—1184no—
453C2×C22⋊C4—1184no—
454C2×C22⋊C4—1184no—
455C2×C22⋊C4—1184no—
456C2×C22⋊C4—1184no—
457#95—22no—
458#95—24no—
459#95—42no—
460#95—1184no—
461#95—1184no—
462#95—1184no—
463#95—1182no—
464#95—1184no—
465#95—2362no—
466#95—2362no—
467#95—2362no—
468C24—592no—
469C24—592no—
470C24—592no—
471C24—592no—
472C24—592no—
473C24—592no—
474C24—592no—
475C24—1182no—
476C24—1182no—
477C24—1182no—
478C24—1182no—
479C24C23×D5911yescharacteristic
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—592no—
505C22×C4—592no—
506C22×C4—592no—
507C22×C4—592no—
508C22×C4—592no—
509C22×C4—592no—
510C22×C4—5916no—
511C22×C4—5916no—
512C22×C4—592no—
513C22×C4—1188no—
514C22×C4—1188no—
515C22×C4—1188no—
516C22×C4—1188no—
517C22×C4—1188no—
518C22×C4—1188no—
519C22×C4—1188no—
520C22×C4—1181no—
521C22×C4—1181no—
522C22×C4—1181no—
523C22×C4—1181no—
524C22×C4—1182no—
525C22×C4—1182no—
526C22×C4—1181no—
527C22×C4—1181no—
528C22×C4—1182no—
529C22×C4—1182no—
530C22×C4—1182no—
531C22×C4—1182no—
532C22×C4—1182no—
533C22×C4—1182no—
534C22×C4—1182no—
535C22×C4—1182no—
536C22×C4—1182no—
537C22×C4—1182no—
538C22×C4—1182no—
539C22×C4—1182no—
540C22×C4—1182no—
541C22×C4—1182no—
542C22×C4—1182no—
543C22×C4—1182no—
544C22×C4—2368no—
545C22×C4—2364no—
546C22×C4—2364no—
547C22×C4—2368no—
548C22×C4—2368no—
549C22×C4—2368no—
550C22×C4—2364no—
551C22×C4—2364no—
552C22×C4C2×C4×D5912yes—
553C22×C4C2×C4×D5912yes—
554C22×C4C2×C4×D5912yes—
555C22×C4D4×D5912yes—
556C22×C4D4×D5912yes—
557C22×C4D4×D5912yes—
558C22×C4Q8×D5912yes—
559C4⋊C4—28no—
560C4⋊C4—44no—
561C4⋊C4—1188no—
562C4⋊C4—1188no—
563C4⋊C4—1188no—
564C4⋊C4—2364no—
565C4⋊C4—2368no—
566C22⋊C4—2368no—
567C22⋊C4—2368no—
568C23—594no—
569C23—594no—
570C23—594no—
571C23—594no—
572C23—594no—
573C23—594no—
574C23—594no—
575C23—1184no—
576C23—1182no—
577C23—1182no—
578C23—1182no—
579C23—1184no—
580C23—1182no—
581C23—1184no—
582C23—1184no—
583C23—1184no—
584C23—1184no—
585C23—1184no—
586C23—1184no—
587C23—1184no—
588C23—1184no—
589C23—1184no—
590C23—1184no—
591C23C22×C4×D5911yescharacteristic
592C23C2×D4×D5911yescharacteristic
593C23C2×D4×D5911yescharacteristic
594C23C2×D4×D5911yescharacteristic
595C23C2×Q8×D5911yescharacteristic
596C23#41×D5911yescharacteristic
597C23#41×D5911yescharacteristic
598C23#1427377212yes—
599C23#1427377312yes—
600C23#1427377412yes—
601C23#1427377512yes—
602C2×C4—22no—
603C2×C4—22no—
604C2×C4—22no—
605C2×C4—22no—
606C2×C4—24no—
607C2×C4—22no—
608C2×C4—22no—
609C2×C4—22no—
610C2×C4—22no—
611C2×C4—24no—
612C2×C4—22no—
613C2×C4—24no—
614C2×C4—42no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—42no—
618C2×C4—42no—
619C2×C4—42no—
620C2×C4—42no—
621C2×C4—42no—
622C2×C4—42no—
623C2×C4—42no—
624C2×C4—42no—
625C2×C4—42no—
626C2×C4—42no—
627C2×C4—42no—
628C2×C4—42no—
629C2×C4—42no—
630C2×C4—42no—
631C2×C4—594no—
632C2×C4—594no—
633C2×C4—11832no—
634C2×C4—1182no—
635C2×C4—1182no—
636C2×C4—1182no—
637C2×C4—1182no—
638C2×C4—1184no—
639C2×C4—1182no—
640C2×C4—1182no—
641C2×C4—1182no—
642C2×C4—1182no—
643C2×C4—1184no—
644C2×C4—1182no—
645C2×C4—1184no—
646C2×C4—23616no—
647C2×C4—23616no—
648C2×C4—2362no—
649C2×C4—2362no—
650C2×C4—2362no—
651C2×C4—2362no—
652C2×C4—2362no—
653C2×C4—2362no—
654C2×C4—2362no—
655C2×C4—2362no—
656C2×C4—2362no—
657C2×C4—2362no—
658C2×C4—2362no—
659C2×C4—2362no—
660C2×C4—2362no—
661C2×C4—2362no—
662C2×C4—2362no—
663C2×C4—2361no—
664C2×C4—2361no—
665C2×C4C22⋊C4×D5914yes—
666C2×C4C4⋊C4×D5914yes—
667C22—598no—
668C22—1188no—
669C22—1188no—
670C22—1184no—
671C22—1184no—
672C22—1188no—
673C22—1184no—
674C22—1184no—
675C22—1188no—
676C22—1184no—
677C22—1184no—
678C22C2×C22⋊C4×D5911yescharacteristic
679C22C2×C4⋊C4×D5911yescharacteristic
680C22#117×D5911yescharacteristic
681C22#1683787412yes—
682C22#1683787812yes—
683C22#121×D5911yescharacteristic
684C22#121×D5911yescharacteristic
685C22C22⋊Q8×D5911yescharacteristic
686C22C22⋊Q8×D5911yescharacteristic
687C22#1683796012yes—
688C22#1683796211yescharacteristic
689C22#1683796311yescharacteristic
690C22#1683797211yescharacteristic
691C22#1683797512yes—
692C22#1683797711yescharacteristic
693C22#1683798112yes—
694C22#1683798212yes—
695C22#1683799312yes—
696C22#1683799512yes—
697C22#1683799812yes—
698C22#1683800012yes—
699C22#1683802912yes—
700C22#1683803212yes—
701C4—24no—
702C4—24no—
703C4—42no—
704C4—82no—
705C4—82no—
706C4—1184no—
707C4—1184no—
708C4—4722no—
709C4—4722no—
710C4—2362no—
711C2—1188no—
712C2#380×D5911yescharacteristic
713C2#2142667011yescharacteristic
714C2#2142667911yescharacteristic
715C2#2142669512yes—
716C2#2142671112yes—
717C2#2142983711yescharacteristic
718C2#2142983911yescharacteristic
719C2#2142984312yes—
720C2#2142990811yescharacteristic
721C2#2142991011yescharacteristic
722C2#2142991412yes—
subgroupG/H
center, FrattiniC24C23×D59
commutatorC23×C59C23×C4
FittingC59×#1441C2
socle, cosocleC24×C59C24
prime radicalC24×D59C23
hypercenter#1441D59
hypocenterC59#14339
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C24 ◁ #1441

Complements

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

NH ≅ G/Ntype
5. #21422350C2semidirect
6. #21422349C2semidirect
7. #21422348C2semidirect
8. #21422347C2semidirect
9. #21422346C2semidirect
11. C59×#1441C2semidirect
22. C2×C4⋊C4×D59C4semidirect
196. C2×C4×D59C4⋊C4semidirect
359. #1441D59semidirect
402. C59#14339semidirect

Maximal subgroups

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

subgroupindex
C22×C4⋊C4×D592
C2×#168372642
C2×#168372612
C2×#168372592
#214223502
#214223492
#214223482
#214223472
#214223462
(C2×D59)⋊#952
C59×#14412
#1433959