Finite Group Databasebeta

← #28512393

Subgroups — #28512393

Order 15104.

2366 conjugacy classes of subgroups.

The subgroup lattice has 714 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837297C212yesmaximal, complemented
2C2×#16837275C211yesmaximal, characteristic
3C2×#16837275C211yesmaximal, characteristic
4C2×#16837275C211yesmaximal, characteristic
5C2×C4×C22⋊Dic59C211yesmaximal, characteristic
6#21422359C212yesmaximal, complemented
7#21422346C212yesmaximal, complemented
8#21422328C212yesmaximal, complemented
9#21422319C211yesmaximal, characteristic
10#21422319C211yesmaximal, characteristic
11C23×C4⋊C4×C59C211yesmaximal, characteristic
12C22×Dic59⋊C4C2211yescharacteristic
13C22×Dic59⋊C4C2212yes—
14C22×Dic59⋊C4C2212yes—
15C22×Dic59⋊C4C2211yescharacteristic
16C22×C22⋊Dic59C2211yescharacteristic
17C22×C22⋊Dic59C2211yescharacteristic
18C22×C22⋊Dic59C2211yescharacteristic
19C22×C22⋊Dic59C2211yescharacteristic
20C22×C4×Dic59C2212yes—
21#16837297—28no—
22#16837275—24no—
23#16837275—24no—
24#16837275C418yescomplemented
25C4×C22⋊Dic59—24no—
26C2×C59⋊#95C2211yescharacteristic
27C2×C59⋊#95C2212yes—
28C2×C59⋊#95C2212yes—
29C2×C59⋊#95C2212yes—
30C2×C59⋊#95C2212yes—
31C2×C59⋊#95C2212yes—
32C2×C59⋊#95C2211yescharacteristic
33C2×C59⋊#95C2212yes—
34C2×C59⋊#95C2212yes—
35C24×C4×C59C2211yescharacteristic
36C24×C4×C59C2211yescharacteristic
37C24×C4×C59C2211yescharacteristic
38C22×C4⋊C4×C59—24no—
39C22×C4⋊C4×C59—28no—
40C22×C4⋊C4×C59C2212yes—
41C22×C4⋊C4×C59C2212yes—
42C23×Dic59C2311yescharacteristic
43C23×Dic59C2311yescharacteristic
44C23×Dic59C2311yescharacteristic
45C23×Dic59C2311yescharacteristic
46C23×Dic59C2312yes—
47C23×Dic59C2312yes—
48C2×Dic59⋊C4—24no—
49C2×Dic59⋊C4—24no—
50C2×Dic59⋊C4—22no—
51C2×Dic59⋊C4—22no—
52C2×Dic59⋊C4—24no—
53C2×Dic59⋊C4—24no—
54C2×Dic59⋊C4—24no—
55C2×Dic59⋊C4—42no—
56C2×Dic59⋊C4—42no—
57C2×Dic59⋊C4C2×C418yescomplemented
58C2×C22⋊Dic59—22no—
59C2×C22⋊Dic59—22no—
60C2×C22⋊Dic59—22no—
61C2×C22⋊Dic59—22no—
62C2×C22⋊Dic59—22no—
63C2×C22⋊Dic59—22no—
64C2×C22⋊Dic59—22no—
65C2×C22⋊Dic59C2×C414yes—
66C2×C22⋊Dic59C2×C414yes—
67C2×C22⋊Dic59D414yes—
68C2×C22⋊Dic59Q814yes—
69C2×C22⋊Dic59Q814yes—
70C2×C4×Dic59—24no—
71C2×C4×Dic59—24no—
72C2×C4×Dic59—42no—
73C59⋊#95—22no—
74C59⋊#95—22no—
75C59⋊#95—24no—
76C59⋊#95—24no—
77C59⋊#95—24no—
78C59⋊#95—24no—
79C59⋊#95—24no—
80C59⋊#95—42no—
81C59⋊#95C2×C418yescomplemented
82C25×C59C2311yescharacteristic
83C23×C4×C59—22no—
84C23×C4×C59—22no—
85C23×C4×C59—24no—
86C23×C4×C59—24no—
87C23×C4×C59—22no—
88C23×C4×C59—22no—
89C23×C4×C59—22no—
90C23×C4×C59—24no—
91C23×C4×C59—24no—
92C23×C4×C59—22no—
93C23×C4×C59—22no—
94C23×C4×C59—42no—
95C23×C4×C59—42no—
96C23×C4×C59C2×C414yes—
97C23×C4×C59D414yes—
98C23×C4×C59C2311yescharacteristic
99C23×C4×C59C2312yes—
100C23×C4×C59C2312yes—
101C23×C4×C59C2311yescharacteristic
102C2×C4⋊C4×C59—232no—
103C2×C4⋊C4×C59—24no—
104C2×C4⋊C4×C59—24no—
105C2×C4⋊C4×C59—24no—
106C2×C4⋊C4×C59—24no—
107C2×C4⋊C4×C59—24no—
108C2×C4⋊C4×C59D418yes—
109C24×C59—22no—
110C24×C59—22no—
111C24×C59—22no—
112C24×C59—22no—
113C24×C59C22×C412yes—
114C24×C59C2×D412yes—
115C24×C59C2×D412yes—
116C24×C59C2×Q812yes—
117C24×C59C2×Q812yes—
118C24×C59#4112yes—
119C24×C59#4112yes—
120C24×C59C2411yescharacteristic
121C22×C4×C59—28no—
122C22×C4×C59—216no—
123C22×C4×C59—28no—
124C22×C4×C59—28no—
125C22×C4×C59—22no—
126C22×C4×C59—22no—
127C22×C4×C59—21no—
128C22×C4×C59—22no—
129C22×C4×C59—22no—
130C22×C4×C59—21no—
131C22×C4×C59—22no—
132C22×C4×C59—216no—
133C22×C4×C59—28no—
134C22×C4×C59—28no—
135C22×C4×C59—22no—
136C22×C4×C59—22no—
137C22×C4×C59—22no—
138C22×C4×C59—21no—
139C22×C4×C59—22no—
140C22×C4×C59—21no—
141C22×C4×C59—22no—
142C22×C4×C59—22no—
143C22×C4×C59—22no—
144C22×C4×C59—22no—
145C22×C4×C59—28no—
146C22×C4×C59—44no—
147C22×C4×C59—48no—
148C22×C4×C59—48no—
149C22×C4×C59—48no—
150C22×C4×C59—48no—
151C22×C4×C59—44no—
152C22×C4×C59—44no—
153C22×C4×C59C22×C414yes—
154C22×C4×C59C2×D412yes—
155C22×C4×C59C2×D414yes—
156C22×C4×C59C2×D414yes—
157C22×C4×C59C2×D412yes—
158C22×C4×C59C2×D414yes—
159C22×C4×C59#4114yes—
160C22×Dic59—22no—
161C22×Dic59—22no—
162C22×Dic59—22no—
163C22×Dic59—22no—
164C22×Dic59—22no—
165C22×Dic59—22no—
166C22×Dic59—21no—
167C22×Dic59—21no—
168C22×Dic59—22no—
169C22×Dic59—22no—
170C22×Dic59—21no—
171C22×Dic59—21no—
172C22×Dic59—22no—
173C22×Dic59—22no—
174C22×Dic59—22no—
175C22×Dic59—22no—
176C22×Dic59—22no—
177C22×Dic59—22no—
178C22×Dic59—21no—
179C22×Dic59—21no—
180C22×Dic59—22no—
181C22×Dic59—21no—
182C22×Dic59—21no—
183C22×Dic59—22no—
184C22×Dic59—21no—
185C22×Dic59—21no—
186C22×Dic59—22no—
187C22×Dic59—22no—
188C22×Dic59C22×C412yes—
189C22×Dic59C22×C412yes—
190C22×Dic59C22×C414yes—
191C22×Dic59C2×D414yes—
192C22×Dic59C2×Q814yes—
193C22×Dic59C2×Q814yes—
194C4⋊C4×C59—216no—
195C4⋊C4×C59—216no—
196C22⋊Dic59—28no—
197C22⋊Dic59—28no—
198C22⋊Dic59—44no—
199C22⋊Dic59C4⋊C4116yescomplemented
200Dic59⋊C4—216no—
201Dic59⋊C4—48no—
202Dic59⋊C4—44no—
203Dic59⋊C4—44no—
204C4×Dic59—48no—
205C23×C59—24no—
206C23×C59—24no—
207C23×C59—22no—
208C23×C59—22no—
209C23×C59—24no—
210C23×C59—22no—
211C23×C59—22no—
212C23×C59—24no—
213C23×C59—24no—
214C23×C59—24no—
215C23×C59—24no—
216C23×C59—24no—
217C23×C59—24no—
218C23×C59—24no—
219C23×C59—24no—
220C23×C59—24no—
221C23×C59C2×C4⋊C414yes—
222C23×C59C4×D414yes—
223C23×C59C4×Q814yes—
224C23×C59#12114yes—
225C23×C59C22⋊Q814yes—
226C23×C59#12514yes—
227C23×C59C4⋊Q814yes—
228C23×C59C23×C411yescharacteristic
229C23×C59C22×D411yescharacteristic
230C23×C59C22×D411yescharacteristic
231C23×C59C22×D412yes—
232C23×C59C22×Q811yescharacteristic
233C23×C59C22×Q811yescharacteristic
234C23×C59C2×#4111yescharacteristic
235C23×C59C2×#4111yescharacteristic
236C23×C59C2×#4112yes—
237C23×C59H(5,𝔽2)12yes—
238C23×C592−1+412yes—
239C2×C4×C59—232no—
240C2×C4×C59—24no—
241C2×C4×C59—24no—
242C2×C4×C59—24no—
243C2×C4×C59—22no—
244C2×C4×C59—24no—
245C2×C4×C59—24no—
246C2×C4×C59—24no—
247C2×C4×C59—22no—
248C2×C4×C59—24no—
249C2×C4×C59—24no—
250C2×C4×C59—22no—
251C2×C4×C59—24no—
252C2×C4×C59—22no—
253C2×C4×C59—22no—
254C2×C4×C59—24no—
255C2×C4×C59—24no—
256C2×C4×C59—416no—
257C2×C4×C59—416no—
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×C59C4×D418yes—
265C2×C4×C59#12014yes—
266C2×Dic59—24no—
267C2×Dic59—24no—
268C2×Dic59—24no—
269C2×Dic59—24no—
270C2×Dic59—24no—
271C2×Dic59—24no—
272C2×Dic59—24no—
273C2×Dic59—22no—
274C2×Dic59—22no—
275C2×Dic59—24no—
276C2×Dic59—24no—
277C2×Dic59—24no—
278C2×Dic59—24no—
279C2×Dic59—41no—
280C2×Dic59—42no—
281C2×Dic59—41no—
282C2×Dic59—42no—
283C2×Dic59—41no—
284C2×Dic59—41no—
285C2×Dic59—42no—
286C2×Dic59—42no—
287C2×Dic59—42no—
288C2×Dic59—42no—
289C2×Dic59—41no—
290C2×Dic59—41no—
291C2×Dic59—41no—
292C2×Dic59—41no—
293C2×Dic59—41no—
294C2×Dic59—41no—
295C2×Dic59—42no—
296C2×Dic59—42no—
297C2×Dic59—42no—
298C2×Dic59—42no—
299C2×Dic59C2×C4⋊C418yescomplemented
300#14043—591nomaximal, Sylow
301C22×C59—24no—
302C22×C59—24no—
303C22×C59—28no—
304C22×C59—28no—
305C22×C59—24no—
306C22×C59—24no—
307C22×C59—24no—
308C22×C59—28no—
309C22×C59—28no—
310C22×C59—24no—
311C22×C59#38918yescomplemented
312C22×C59C22×C4⋊C411yescharacteristic
313C22×C59C2×C4×D411yescharacteristic
314C22×C59C2×C4×D412yes—
315C22×C59C2×C4×Q811yescharacteristic
316C22×C59#52012yes—
317C22×C59C2×#12011yescharacteristic
318C22×C59C2×#12111yescharacteristic
319C22×C59C2×C22⋊Q811yescharacteristic
320C22×C59#52511yescharacteristic
321C22×C59#52512yes—
322C22×C59C2×#12511yescharacteristic
323C22×C59C2×C4⋊Q811yescharacteristic
324C22×C59#53411yescharacteristic
325C22×C59#53611yescharacteristic
326C22×C59#53912yes—
327C22×C59D4212yes—
328C22×C59#54612yes—
329C22×C59#54712yes—
330C22×C59D4×Q812yes—
331C22×C59D4×Q812yes—
332C22×C59#55212yes—
333C22×C59#55412yes—
334C22×C59#55412yes—
335C4×C59—24no—
336C4×C59—28no—
337C4×C59—42no—
338C4×C59—44no—
339Dic59—28no—
340Dic59—42no—
341Dic59—44no—
342Dic59—42no—
343Dic59—81no—
344Dic59—81no—
345C23×C4⋊C4D5911yescharacteristic
346C2×#389—592no—
347C2×#385—591no—
348C2×#385—591no—
349C2×#385—591no—
350C2×C4×C22⋊C4—591no—
351#1444—592no—
352#1441—592no—
353#1436—592no—
354C22⋊#95—591no—
355C22⋊#95—591no—
356C2×C59—28no—
357C2×C59C2×#38911yescharacteristic
358C2×C59C4×#12011yescharacteristic
359C2×C59#232211yescharacteristic
360C2×C59D4×C4⋊C412yes—
361C2×C59#236012yes—
362C2×C59#241011yescharacteristic
363C2×C59#241311yescharacteristic
364C2×C59#243411yescharacteristic
365C2×C59#244912yes—
366C2×C59#247312yes—
367C2×C59#258311yescharacteristic
368C24×C4C2×D5911yescharacteristic
369C24×C4C2×D5911yescharacteristic
370C24×C4C2×D5911yescharacteristic
371C22×C4⋊C4—24no—
372C22×C4⋊C4—28no—
373C22×C4⋊C4—592no—
374C22×C4⋊C4—591no—
375C22×C4⋊C4—592no—
376C22×C4⋊C4—591no—
377C22×C4⋊C4C2×D5912yes—
378C22×C4⋊C4C2×D5912yes—
379C22×C22⋊C4—591no—
380C22×C22⋊C4—591no—
381C22×C22⋊C4—591no—
382C22×C22⋊C4—591no—
383C22×C42—592no—
384#389—1188no—
385#385—598no—
386#385—1184no—
387#385—1184no—
388C4×C22⋊C4—1184no—
389C2×#95—592no—
390C2×#95—592no—
391C2×#95—592no—
392C2×#95—592no—
393C2×#95—591no—
394C2×#95—592no—
395C2×#95—591no—
396C2×#95—592no—
397C2×#95—592no—
398C59#1404311yescharacteristic, complemented, Sylow
399C25C22×D5911yescharacteristic
400C23×C4—22no—
401C23×C4—22no—
402C23×C4—24no—
403C23×C4—24no—
404C23×C4—22no—
405C23×C4—22no—
406C23×C4—22no—
407C23×C4—24no—
408C23×C4—24no—
409C23×C4—22no—
410C23×C4—22no—
411C23×C4—42no—
412C23×C4—42no—
413C23×C4—592no—
414C23×C4—591no—
415C23×C4—591no—
416C23×C4—592no—
417C23×C4—591no—
418C23×C4—591no—
419C23×C4C4×D5914yes—
420C23×C4C22⋊D5914yes—
421C23×C4C22×D5911yescharacteristic
422C23×C4C22×D5912yes—
423C23×C4C22×D5912yes—
424C23×C4C22×D5911yescharacteristic
425C2×C4⋊C4—232no—
426C2×C4⋊C4—24no—
427C2×C4⋊C4—24no—
428C2×C4⋊C4—24no—
429C2×C4⋊C4—24no—
430C2×C4⋊C4—24no—
431C2×C4⋊C4—598no—
432C2×C4⋊C4—1184no—
433C2×C4⋊C4—1184no—
434C2×C4⋊C4—1184no—
435C2×C4⋊C4—1182no—
436C2×C4⋊C4—1182no—
437C2×C4⋊C4—1184no—
438C2×C4⋊C4—1184no—
439C2×C4⋊C4—2362no—
440C2×C4⋊C4—2362no—
441C2×C4⋊C4C22⋊D5918yes—
442C2×C22⋊C4—594no—
443C2×C22⋊C4—594no—
444C2×C22⋊C4—594no—
445C2×C22⋊C4—594no—
446C2×C22⋊C4—594no—
447C2×C22⋊C4—1182no—
448C2×C22⋊C4—1182no—
449C2×C22⋊C4—1182no—
450C2×C22⋊C4—1182no—
451C2×C22⋊C4—1182no—
452C2×C22⋊C4—1182no—
453C2×C22⋊C4—1182no—
454C2×C42—1184no—
455C2×C42—1184no—
456C2×C42—2362no—
457#95—598no—
458#95—1184no—
459#95—1184no—
460#95—1184no—
461#95—1182no—
462#95—1182no—
463#95—1184no—
464#95—1184no—
465#95—2362no—
466C24—22no—
467C24—22no—
468C24—22no—
469C24—22no—
470C24C2×C4×D5912yes—
471C24#1174568512yes—
472C24D4×D5912yes—
473C24#1174568712yes—
474C24Q8×D5912yes—
475C24Q8×D5912yes—
476C24C2×C22⋊D5912yes—
477C24C23×D5911yescharacteristic
478C22×C4—28no—
479C22×C4—28no—
480C22×C4—216no—
481C22×C4—28no—
482C22×C4—21no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—21no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—216no—
490C22×C4—28no—
491C22×C4—28no—
492C22×C4—21no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—21no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—28no—
503C22×C4—44no—
504C22×C4—48no—
505C22×C4—48no—
506C22×C4—48no—
507C22×C4—48no—
508C22×C4—44no—
509C22×C4—44no—
510C22×C4—594no—
511C22×C4—594no—
512C22×C4—594no—
513C22×C4—592no—
514C22×C4—592no—
515C22×C4—594no—
516C22×C4—1182no—
517C22×C4—1182no—
518C22×C4—1182no—
519C22×C4—1182no—
520C22×C4—1182no—
521C22×C4—1182no—
522C22×C4—1181no—
523C22×C4—1181no—
524C22×C4—1182no—
525C22×C4—1182no—
526C22×C4—1182no—
527C22×C4—1181no—
528C22×C4—1181no—
529C22×C4—1182no—
530C22×C4—1182no—
531C22×C4—1182no—
532C22×C4—1182no—
533C22×C4—1182no—
534C22×C4—1181no—
535C22×C4—1181no—
536C22×C4—1181no—
537C22×C4—1182no—
538C22×C4—1181no—
539C22×C4—1181no—
540C22×C4—1181no—
541C22×C4—1182no—
542C22×C4—1182no—
543C22×C4—1182no—
544C22×C4C2×C4×D5914yes—
545C22×C4#1174568514yes—
546C22×C4C2×C22⋊D5912yes—
547C22×C4C2×C22⋊D5914yes—
548C22×C4C2×C22⋊D5914yes—
549C22×C4C2×C22⋊D5912yes—
550C22×C4C2×C22⋊D5914yes—
551C4⋊C4—216no—
552C4⋊C4—216no—
553C4⋊C4—11816no—
554C4⋊C4—2368no—
555C4⋊C4—2364no—
556C4⋊C4—2364no—
557C22⋊C4—5916no—
558C22⋊C4—1188no—
559C22⋊C4—1188no—
560C22⋊C4—2364no—
561C42—2368no—
562C23—22no—
563C23—24no—
564C23—22no—
565C23—22no—
566C23—22no—
567C23—24no—
568C23—24no—
569C23—24no—
570C23—24no—
571C23—24no—
572C23—24no—
573C23—24no—
574C23—24no—
575C23—24no—
576C23—24no—
577C23—24no—
578C23C4⋊C4×D5914yes—
579C23C4×C22⋊D5914yes—
580C23#1427369214yes—
581C23#1427369914yes—
582C23#1427370514yes—
583C23#1427371714yes—
584C23#1427372514yes—
585C23C22×C4×D5911yescharacteristic
586C23C2×D4×D5911yescharacteristic
587C23C22×C22⋊D5911yescharacteristic
588C23C22×C22⋊D5912yes—
589C23C2×Q8×D5911yescharacteristic
590C23C2×Q8×D5911yescharacteristic
591C23C2×#1174568711yescharacteristic
592C23C2×#1174568511yescharacteristic
593C23C2×#1174568512yes—
594C23#1427377212yes—
595C23#1427377512yes—
596C2×C4—232no—
597C2×C4—24no—
598C2×C4—22no—
599C2×C4—24no—
600C2×C4—24no—
601C2×C4—24no—
602C2×C4—22no—
603C2×C4—24no—
604C2×C4—24no—
605C2×C4—24no—
606C2×C4—24no—
607C2×C4—22no—
608C2×C4—24no—
609C2×C4—22no—
610C2×C4—22no—
611C2×C4—24no—
612C2×C4—24no—
613C2×C4—416no—
614C2×C4—416no—
615C2×C4—42no—
616C2×C4—42no—
617C2×C4—42no—
618C2×C4—42no—
619C2×C4—42no—
620C2×C4—42no—
621C2×C4—598no—
622C2×C4—1184no—
623C2×C4—1184no—
624C2×C4—1184no—
625C2×C4—1184no—
626C2×C4—1184no—
627C2×C4—1184no—
628C2×C4—1184no—
629C2×C4—1184no—
630C2×C4—1184no—
631C2×C4—1182no—
632C2×C4—1182no—
633C2×C4—1184no—
634C2×C4—1184no—
635C2×C4—2361no—
636C2×C4—2361no—
637C2×C4—2361no—
638C2×C4—2361no—
639C2×C4—2361no—
640C2×C4—2361no—
641C2×C4—2362no—
642C2×C4—2362no—
643C2×C4—2362no—
644C2×C4—2362no—
645C2×C4—2361no—
646C2×C4—2362no—
647C2×C4—2361no—
648C2×C4—2362no—
649C2×C4—2361no—
650C2×C4—2361no—
651C2×C4—2362no—
652C2×C4—2362no—
653C2×C4—2362no—
654C2×C4—2362no—
655C2×C4C4×C22⋊D5918yes—
656C2×C4#1427369614yes—
657C22—28no—
658C22—24no—
659C22—24no—
660C22—24no—
661C22—28no—
662C22—24no—
663C22—28no—
664C22—24no—
665C22—28no—
666C22—24no—
667C22#1683729718yescomplemented
668C22C2×C4⋊C4×D5911yescharacteristic
669C22C2×C4×C22⋊D5912yes—
670C22C2×C4×C22⋊D5911yescharacteristic
671C22C2×#1427369211yescharacteristic
672C22#1683788312yes—
673C22C2×#1427369611yescharacteristic
674C22C2×#1427369911yescharacteristic
675C22C2×#1427370511yescharacteristic
676C22#1683791312yes—
677C22#1683791311yescharacteristic
678C22C2×#1427371711yescharacteristic
679C22C2×#1427372511yescharacteristic
680C22#1683796111yescharacteristic
681C22#1683797611yescharacteristic
682C22#1683799912yes—
683C22D4×C22⋊D5912yes—
684C22#1683804612yes—
685C22#1683805312yes—
686C22Q8×C22⋊D5912yes—
687C22Q8×C22⋊D5912yes—
688C22#1683808712yes—
689C22#1683810712yes—
690C22#1683810712yes—
691C4—24no—
692C4—28no—
693C4—42no—
694C4—44no—
695C4—1188no—
696C4—4721no—
697C4—4721no—
698C4—2362no—
699C4—2362no—
700C4—2364no—
701C2—28no—
702C2C2×#1683729711yescharacteristic
703C2C4×#1427369611yescharacteristic
704C2#2142676511yescharacteristic
705C2C4⋊C4×C22⋊D5912yes—
706C2#2142710112yes—
707C2#2142747011yescharacteristic
708C2#2142750311yescharacteristic
709C2#2142773611yescharacteristic
710C2#2142790512yes—
711C2#2142823112yes—
712C2#2142947611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D59
commutatorC23×C59C23×C4
FittingC23×C4⋊C4×C59C2
socle, cosocleC24×C59C24
prime radicalC25×C59C23
hypercenterC23×C4⋊C4D59
hypocenterC59#14043
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C24 ◁ C23×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#16837297C2semidirect
6. #21422359C2semidirect
7. #21422346C2semidirect
8. #21422328C2semidirect
24. #16837275C4semidirect
57. C2×Dic59⋊C4C2×C4semidirect
81. C59⋊#95C2×C4semidirect
199. C22⋊Dic59C4⋊C4semidirect
299. C2×Dic59C2×C4⋊C4semidirect
311. C22×C59#389semidirect
398. C59#14043semidirect
667. C22#16837297semidirect

Maximal subgroups

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

subgroupindex
C2×#168372972
C2×#168372752
C2×C4×C22⋊Dic592
#214223592
#214223462
#214223282
#214223192
C23×C4⋊C4×C592
#1404359