Finite Group Databasebeta

← #28637418

Subgroups — #28637418

Order 15104.

968 conjugacy classes of subgroups.

The subgroup lattice has 726 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837718C211yesmaximal, characteristic, complemented
2C2×D4×C59⋊C8C211yesmaximal, characteristic, complemented
3#21428413C211yesmaximal, characteristic, complemented
4#21425597C211yesmaximal, characteristic, complemented
5#21425532C211yesmaximal, characteristic, complemented
6#21425470C211yesmaximal, characteristic, complemented
7#21425282C211yesmaximal, characteristic, complemented
8#21424821C211yesmaximal, characteristic, complemented
9#21424782C211yesmaximal, characteristic, complemented
10#21424525C211yesmaximal, characteristic, complemented
11#21424525C211yesmaximal, characteristic, complemented
12#21424289C211yesmaximal, characteristic, complemented
13#21424119C211yesmaximal, characteristic, complemented
14C2×#16837164C211yesmaximal, characteristic, complemented
15C59×#2416C211yesmaximal, characteristic
16C23×C59⋊C8C2211yescharacteristic
17C23×C59⋊C8C2211yescharacteristic
18C22×C4⋊Dic59C2211yescharacteristic
19#16837718—24no—
20D4×C59⋊C8—24no—
21C2×#14273658C2211yescharacteristic
22C2×#14273658C2211yescharacteristic
23C2×#14273658C2211yescharacteristic
24C2×#14273658C2211yescharacteristic
25C2×C4⋊(C59⋊C8)C2211yescharacteristic
26C2×#14273648C2211yescharacteristic
27C2×#14273648C2211yescharacteristic
28C2×#14273648C2211yescharacteristic
29C2×#14273648C2211yescharacteristic
30C2×C22⋊(C59⋊C8)C2211yescharacteristic
31C2×C22⋊(C59⋊C8)C2211yescharacteristic
32C2×C4×C59⋊C8C2211yescharacteristic
33#16837341—21no—
34#16837338—21no—
35#16837300C2211yescharacteristic
36#16837300C2211yescharacteristic
37#16837282—21no—
38#16837274—21no—
39#16837262C2211yescharacteristic
40#16837262C2211yescharacteristic
41#16837262C2211yescharacteristic
42#16837164C2211yescharacteristic
43#16837164C2211yescharacteristic
44#16837164C2211yescharacteristic
45#16837164C2211yescharacteristic
46#16837164C2211yescharacteristic
47#16837164C2211yescharacteristic
48#16837164C2211yescharacteristic
49#16837164C2211yescharacteristic
50C2×#121×C59—21no—
51C2×#121×C59C2211yescharacteristic
52C2×#121×C59C2211yescharacteristic
53C2×C4×D4×C59C2211yescharacteristic
54C22×C4⋊C4×C59C2211yescharacteristic
55C59×#396—21no—
56C59×#394—21no—
57C59×#390C2211yescharacteristic
58C59×#389C2211yescharacteristic
59C59×#386—21no—
60C59×#380C2211yescharacteristic
61C23×Dic59—21no—
62C22×C59⋊C8—22no—
63C22×C59⋊C8—22no—
64C22×C59⋊C8—22no—
65C22×C59⋊C8—22no—
66C22×C59⋊C8—41no—
67C22×C59⋊C8—41no—
68C22×C59⋊C8C2311yescharacteristic
69C22×C59⋊C8C2311yescharacteristic
70C22×C59⋊C8C2311yescharacteristic
71C22×C59⋊C8C2311yescharacteristic
72C2×C4⋊Dic59—22no—
73C2×C4⋊Dic59—22no—
74C2×C4⋊Dic59—21no—
75C2×C4⋊Dic59C2311yescharacteristic
76C2×C4⋊Dic59C2311yescharacteristic
77C2×C4⋊Dic59C2311yescharacteristic
78C2×C4⋊Dic59C2311yescharacteristic
79C2×Dic59⋊C4—21no—
80C2×Dic59⋊C4—21no—
81C2×C22⋊Dic59—21no—
82C2×C22⋊Dic59—21no—
83C2×C22⋊Dic59—21no—
84#14273658—22no—
85#14273658—22no—
86#14273658—22no—
87#14273658—41no—
88C4⋊(C59⋊C8)—22no—
89#14273648—22no—
90#14273648—22no—
91#14273648—22no—
92#14273648—41no—
93C22⋊(C59⋊C8)—22no—
94C22⋊(C59⋊C8)D414yescomplemented
95C4×C59⋊C8—22no—
96C59⋊#95—21no—
97C59⋊#95—21no—
98C59⋊#95—21no—
99C59⋊#95—21no—
100C59⋊#95—21no—
101C22×D4×C59—21no—
102C22×D4×C59—21no—
103C22×D4×C59D411yescharacteristic
104C22×D4×C59C2311yescharacteristic
105C23×C4×C59—21no—
106C23×C4×C59C2311yescharacteristic
107C23×C4×C59C2311yescharacteristic
108#121×C59—22no—
109#121×C59—22no—
110#121×C59—22no—
111#121×C59—41no—
112#121×C59—44no—
113C4×D4×C59—22no—
114C4×D4×C59—22no—
115C2×C4⋊C4×C59—22no—
116C2×C4⋊C4×C59—21no—
117C2×C4⋊C4×C59—21no—
118C2×C4⋊C4×C59—41no—
119C2×C4⋊C4×C59D411yescharacteristic
120C2×C4⋊C4×C59C2311yescharacteristic
121C2×C4⋊C4×C59C2311yescharacteristic
122C2×C4⋊C4×C59C2311yescharacteristic
123C2×C22⋊C4×C59—21no—
124C2×C22⋊C4×C59—21no—
125C2×C22⋊C4×C59—21no—
126C2×C22⋊C4×C59—21no—
127C2×C22⋊C4×C59—21no—
128C2×C22⋊C4×C59D411yescharacteristic
129C2×C22⋊C4×C59D411yescharacteristic
130C2×C42×C59C2311yescharacteristic
131#95×C59—21no—
132#95×C59—21no—
133C24×C59—21no—
134C24×C59C2×D411yescharacteristic
135C24×C59C2×D411yescharacteristic
136C2×D4×C59—22no—
137C2×D4×C59—22no—
138C2×D4×C59—21no—
139C2×D4×C59—21no—
140C2×D4×C59—21no—
141C2×D4×C59—21no—
142C2×D4×C59—21no—
143C2×D4×C59—21no—
144C2×D4×C59—42no—
145C2×D4×C59—42no—
146C2×D4×C59—42no—
147C2×D4×C59—42no—
148C2×D4×C59—42no—
149C2×D4×C59—81no—
150C2×D4×C59SD1614yes—
151C22×C4×C59—21no—
152C22×C4×C59—21no—
153C22×C4×C59—21no—
154C22×C4×C59—21no—
155C22×C4×C59—21no—
156C22×C4×C59—21no—
157C22×C4×C59—21no—
158C22×C4×C59—21no—
159C22×C4×C59—21no—
160C22×C4×C59—21no—
161C22×C4×C59—21no—
162C22×C4×C59—21no—
163C22×C4×C59—21no—
164C22×C4×C59—42no—
165C22×C4×C59—42no—
166C22×C4×C59—81no—
167C22×C4×C59C2×D411yescharacteristic
168C22×C4×C59C2×D411yescharacteristic
169C22×C4×C59C2×D411yescharacteristic
170C22×C4×C59C2×D412yes—
171C22×C4×C59C2×D411yescharacteristic
172C22×C4×C59#4112yes—
173C22×C4×C59C2411yescharacteristic
174C22×Dic59—21no—
175C22×Dic59—21no—
176C22×Dic59—21no—
177C22×Dic59—21no—
178C22×Dic59—42no—
179C22×Dic59—81no—
180C22×Dic59—81no—
181C4⋊C4×C59—22no—
182C4⋊C4×C59—21no—
183C4⋊C4×C59—21no—
184C4⋊C4×C59—21no—
185C4⋊C4×C59—21no—
186C4⋊C4×C59—21no—
187C4⋊C4×C59—42no—
188C4⋊C4×C59—42no—
189C4⋊C4×C59#4112yes—
190C22⋊C4×C59—22no—
191C22⋊C4×C59—22no—
192C22⋊C4×C59—42no—
193C22⋊C4×C59—42no—
194C22⋊C4×C59—42no—
195C22⋊C4×C59—42no—
196C22⋊C4×C59—81no—
197C42×C59—21no—
198C42×C59—21no—
199C22⋊Dic59—42no—
200C22⋊Dic59—81no—
201C22⋊Dic59—81no—
202C4⋊Dic59—21no—
203C4⋊Dic59—21no—
204C4⋊Dic59—21no—
205C4⋊Dic59—21no—
206C4⋊Dic59—21no—
207C4⋊Dic59—21no—
208C4⋊Dic59—21no—
209C4⋊Dic59—21no—
210C4⋊Dic59—42no—
211Dic59⋊C4—81no—
212Dic59⋊C4—81no—
213C2×C59⋊C8—21no—
214C2×C59⋊C8—21no—
215C2×C59⋊C8—21no—
216C2×C59⋊C8—21no—
217C2×C59⋊C8—21no—
218C2×C59⋊C8—21no—
219C2×C59⋊C8—21no—
220C2×C59⋊C8—21no—
221C2×C59⋊C8—21no—
222C2×C59⋊C8—44no—
223C2×C59⋊C8—44no—
224C2×C59⋊C8C2×D412yes—
225C2×C59⋊C8C2×D412yes—
226C2×C59⋊C8#4112yes—
227C23×C59—21no—
228C23×C59—21no—
229C23×C59—21no—
230C23×C59—21no—
231C23×C59—21no—
232C23×C59—21no—
233C23×C59—21no—
234C23×C59—21no—
235C23×C59—21no—
236C23×C59—21no—
237C23×C59—41no—
238C23×C59—41no—
239C23×C59—41no—
240C23×C59—41no—
241C23×C59—41no—
242C23×C59—41no—
243C23×C59—41no—
244C23×C59#12112yes—
245C23×C59C2×SD1612yes—
246C23×C59C2×SD1612yes—
247C23×C59#13512yes—
248C23×C59C22×D411yescharacteristic
249D4×C59—28no—
250D4×C59—41no—
251D4×C59—41no—
252D4×C59—41no—
253D4×C59—41no—
254D4×C59—84no—
255D4×C59—84no—
256C2×C4×C59—21no—
257C2×C4×C59—21no—
258C2×C4×C59—21no—
259C2×C4×C59—21no—
260C2×C4×C59—22no—
261C2×C4×C59—22no—
262C2×C4×C59—22no—
263C2×C4×C59—22no—
264C2×C4×C59—21no—
265C2×C4×C59—21no—
266C2×C4×C59—21no—
267C2×C4×C59—22no—
268C2×C4×C59—21no—
269C2×C4×C59—21no—
270C2×C4×C59—21no—
271C2×C4×C59—41no—
272C2×C4×C59—41no—
273C2×C4×C59—41no—
274C2×C4×C59—41no—
275C2×C4×C59—41no—
276C2×C4×C59—41no—
277C2×C4×C59—41no—
278C2×C4×C59—41no—
279C2×C4×C59—41no—
280C2×C4×C59—41no—
281C2×C4×C59—41no—
282C2×C4×C59—41no—
283C2×C4×C59—84no—
284C2×C4×C59#12112yes—
285C2×C4×C59C2×SD1612yes—
286C2×C4×C59C22×D411yescharacteristic
287C2×C4×C59C2×#4111yescharacteristic
288C2×C4×C59C2×#4111yescharacteristic
289C2×C4×C59C2×#4111yescharacteristic
290C2×C4×C59H(5,𝔽2)11yescharacteristic
291C2×C4×C592−1+411yescharacteristic
292C2×Dic59—41no—
293C2×Dic59—41no—
294C2×Dic59—41no—
295C2×Dic59—41no—
296C2×Dic59—41no—
297C2×Dic59—41no—
298C2×Dic59—41no—
299C2×Dic59—41no—
300C2×Dic59—41no—
301C2×Dic59—41no—
302C2×Dic59—41no—
303C2×Dic59—41no—
304C2×Dic59—84no—
305C59⋊C8—22no—
306C59⋊C8—22no—
307C59⋊C8—22no—
308C59⋊C8—41no—
309#25238—591nomaximal, Sylow
310C22×C59—22no—
311C22×C59—22no—
312C22×C59—22no—
313C22×C59—22no—
314C22×C59—22no—
315C22×C59—22no—
316C22×C59—22no—
317C22×C59—22no—
318C22×C59—22no—
319C22×C59—41no—
320C22×C59—41no—
321C22×C59—41no—
322C22×C59—41no—
323C22×C59—81no—
324C22×C59—81no—
325C22×C59—81no—
326C22×C59—81no—
327C22×C59—81no—
328C22×C59—81no—
329C22×C59—81no—
330C22×C59#46514yes—
331C22×C59C2×#12111yescharacteristic
332C22×C59#54611yescharacteristic
333C22×C59#54711yescharacteristic
334C22×C59C22×SD1611yescharacteristic
335C22×C59C2×#13511yescharacteristic
336C22×C59#57611yescharacteristic
337C22×C59#57711yescharacteristic
338C4×C59—22no—
339C4×C59—22no—
340C4×C59—41no—
341C4×C59—42no—
342C4×C59—41no—
343C4×C59—81no—
344C4×C59—81no—
345C4×C59#52911yescharacteristic
346C4×C59#53911yescharacteristic
347C4×C59#54611yescharacteristic
348C4×C59#54711yescharacteristic
349Dic59—81no—
350Dic59—81no—
351Dic59—81no—
352Dic59—81no—
353C2×#481—591no—
354C2×C8×D4—591no—
355#2487—591no—
356#2416D5911yescharacteristic
357#2088—591no—
358#2077—591no—
359#2065—591no—
360#2034—591no—
361#1941—591no—
362#1934—591no—
363#1893—591no—
364#1893—591no—
365#1853—591no—
366#1807—591no—
367C2×#340—591no—
368C2×C59—24no—
369C2×C59—42no—
370C2×C59—161no—
371C2×C59#242511yescharacteristic
372C2×C59C2×#46511yescharacteristic
373C2×C59#306211yescharacteristic
374C2×C59#329511yescharacteristic
375C2×C59#330111yescharacteristic
376C2×C59#333511yescharacteristic
377C2×C59#333911yescharacteristic
378C23×C8—591no—
379C23×C8—591no—
380C2×#121—21no—
381C2×#121C2×D5911yescharacteristic
382C2×#121C2×D5911yescharacteristic
383C2×C4×D4C2×D5911yescharacteristic
384C22×C4⋊C4—591no—
385C22×C4⋊C4C2×D5911yescharacteristic
386#481—1184no—
387C8×D4—1184no—
388C2×#106—591no—
389C2×#106—591no—
390C2×#106—591no—
391C2×#106—591no—
392C2×C4⋊C8—591no—
393C2×#102—591no—
394C2×#102—591no—
395C2×#102—591no—
396C2×#102—591no—
397C2×C22⋊C8—591no—
398C2×C22⋊C8—591no—
399C2×C4×C8—591no—
400#400—1181no—
401#399—1181no—
402#396—21no—
403#394—21no—
404#390C2×D5911yescharacteristic
405#389—591no—
406#389—591no—
407#389C2×D5911yescharacteristic
408#386—21no—
409#386—1181no—
410#385—1181no—
411#380—591no—
412#380—591no—
413#380—591no—
414#380C2×D5911yescharacteristic
415#340—591no—
416#340—591no—
417#340—591no—
418#340—591no—
419#340—591no—
420#340—591no—
421#340—591no—
422#340—591no—
423C59#2523811yescharacteristic, complemented, Sylow
424C22×D4—21no—
425C22×D4—21no—
426C22×D4C22⋊D5911yescharacteristic
427C22×D4C22×D5911yescharacteristic
428C23×C4—21no—
429C23×C4—1181no—
430C23×C4C22×D5911yescharacteristic
431C23×C4C22×D5911yescharacteristic
432C22×C8—591no—
433C22×C8—591no—
434C22×C8—591no—
435C22×C8—591no—
436C22×C8—1182no—
437C22×C8—1182no—
438C22×C8—1182no—
439C22×C8—1182no—
440C22×C8—2361no—
441C22×C8—2361no—
442#121—22no—
443#121—22no—
444#121—22no—
445#121—41no—
446#121—44no—
447C4×D4—22no—
448C4×D4—22no—
449C2×C4⋊C4—22no—
450C2×C4⋊C4—21no—
451C2×C4⋊C4—21no—
452C2×C4⋊C4—41no—
453C2×C4⋊C4—591no—
454C2×C4⋊C4—591no—
455C2×C4⋊C4—591no—
456C2×C4⋊C4—591no—
457C2×C4⋊C4—1182no—
458C2×C4⋊C4—1182no—
459C2×C4⋊C4—1181no—
460C2×C4⋊C4—1181no—
461C2×C4⋊C4—1181no—
462C2×C4⋊C4C22⋊D5911yescharacteristic
463C2×C4⋊C4C22×D5911yescharacteristic
464C2×C4⋊C4C22×D5911yescharacteristic
465C2×C4⋊C4C22×D5911yescharacteristic
466C2×C22⋊C4—21no—
467C2×C22⋊C4—21no—
468C2×C22⋊C4—21no—
469C2×C22⋊C4—21no—
470C2×C22⋊C4—21no—
471C2×C22⋊C4—1181no—
472C2×C22⋊C4—1181no—
473C2×C22⋊C4—1181no—
474C2×C22⋊C4C22⋊D5911yescharacteristic
475C2×C22⋊C4C22⋊D5911yescharacteristic
476C2×C42C22×D5911yescharacteristic
477#106—1182no—
478#106—1182no—
479#106—1182no—
480#106—2361no—
481C4⋊C8—1182no—
482#102—1182no—
483#102—1182no—
484#102—1182no—
485#102—2361no—
486C22⋊C8—594no—
487C22⋊C8—1182no—
488C4×C8—1182no—
489#95—21no—
490#95—21no—
491#95—1181no—
492#95—1181no—
493#95—1181no—
494#95—1181no—
495#95—1181no—
496C24—21no—
497C24C2×C22⋊D5911yescharacteristic
498C24C2×C22⋊D5911yescharacteristic
499C2×D4—22no—
500C2×D4—22no—
501C2×D4—21no—
502C2×D4—21no—
503C2×D4—21no—
504C2×D4—21no—
505C2×D4—21no—
506C2×D4—21no—
507C2×D4—42no—
508C2×D4—42no—
509C2×D4—42no—
510C2×D4—42no—
511C2×D4—42no—
512C2×D4—81no—
513C2×D4#1174567014yes—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—42no—
528C22×C4—42no—
529C22×C4—81no—
530C22×C4—1181no—
531C22×C4—1181no—
532C22×C4—1181no—
533C22×C4—1181no—
534C22×C4—4721no—
535C22×C4—4721no—
536C22×C4—2362no—
537C22×C4D4×D5912yes—
538C22×C4#1174568712yes—
539C22×C4C2×C22⋊D5911yescharacteristic
540C22×C4C2×C22⋊D5911yescharacteristic
541C22×C4C2×C22⋊D5911yescharacteristic
542C22×C4C2×C22⋊D5911yescharacteristic
543C22×C4C23×D5911yescharacteristic
544C2×C8—592no—
545C2×C8—592no—
546C2×C8—592no—
547C2×C8—1181no—
548C2×C8—1181no—
549C2×C8—1181no—
550C2×C8—1181no—
551C2×C8—1181no—
552C2×C8—1181no—
553C2×C8—1181no—
554C2×C8—1181no—
555C2×C8—1181no—
556C2×C8—2364no—
557C2×C8—2364no—
558C4⋊C4—22no—
559C4⋊C4—21no—
560C4⋊C4—21no—
561C4⋊C4—21no—
562C4⋊C4—21no—
563C4⋊C4—21no—
564C4⋊C4—42no—
565C4⋊C4—42no—
566C4⋊C4—1181no—
567C4⋊C4—1181no—
568C4⋊C4—1181no—
569C4⋊C4—1181no—
570C4⋊C4—1181no—
571C4⋊C4—1181no—
572C4⋊C4—1181no—
573C4⋊C4—1181no—
574C4⋊C4—4721no—
575C4⋊C4—4721no—
576C4⋊C4—2362no—
577C4⋊C4#1174568712yes—
578C22⋊C4—22no—
579C22⋊C4—22no—
580C22⋊C4—42no—
581C22⋊C4—42no—
582C22⋊C4—42no—
583C22⋊C4—42no—
584C22⋊C4—81no—
585C22⋊C4—4721no—
586C22⋊C4—4721no—
587C22⋊C4—2362no—
588C42—21no—
589C42—21no—
590C23—21no—
591C23—21no—
592C23—21no—
593C23—21no—
594C23—21no—
595C23—21no—
596C23—21no—
597C23—21no—
598C23—21no—
599C23—21no—
600C23—41no—
601C23—41no—
602C23—41no—
603C23—41no—
604C23—41no—
605C23—41no—
606C23—41no—
607C23#1427369912yes—
608C23C2×#1174567012yes—
609C23C2×#1174567012yes—
610C23#1427374712yes—
611C23C22×C22⋊D5911yescharacteristic
612D4—28no—
613D4—41no—
614D4—41no—
615D4—41no—
616D4—41no—
617D4—84no—
618D4—84no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—22no—
633C2×C4—21no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—41no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—84no—
647C2×C4—4724no—
648C2×C4—2361no—
649C2×C4—2361no—
650C2×C4—2361no—
651C2×C4—2361no—
652C2×C4—2361no—
653C2×C4—2361no—
654C2×C4—2361no—
655C2×C4—2361no—
656C2×C4—2361no—
657C2×C4—2361no—
658C2×C4—2361no—
659C2×C4—2361no—
660C2×C4#1427369912yes—
661C2×C4C2×#1174567012yes—
662C2×C4C2×D4×D5911yescharacteristic
663C2×C4#41×D5911yescharacteristic
664C2×C4C2×#1174568711yescharacteristic
665C2×C4C2×#1174568711yescharacteristic
666C2×C4#1427377211yescharacteristic
667C2×C4#1427377411yescharacteristic
668C8—1182no—
669C8—1182no—
670C8—1182no—
671C8—2361no—
672C22—22no—
673C22—22no—
674C22—22no—
675C22—22no—
676C22—22no—
677C22—22no—
678C22—22no—
679C22—22no—
680C22—22no—
681C22—41no—
682C22—41no—
683C22—41no—
684C22—41no—
685C22—81no—
686C22—81no—
687C22—81no—
688C22—81no—
689C22—81no—
690C22—81no—
691C22—81no—
692C22#1683762914yes—
693C22C2×#1427369911yescharacteristic
694C22#1683804611yescharacteristic
695C22#1683805111yescharacteristic
696C22C22×#1174567011yescharacteristic
697C22C2×#1427374711yescharacteristic
698C22#1683820511yescharacteristic
699C22#1683821011yescharacteristic
700C4—22no—
701C4—22no—
702C4—42no—
703C4—41no—
704C4—41no—
705C4—81no—
706C4—81no—
707C4—4721no—
708C4—4721no—
709C4—4721no—
710C4—4721no—
711C4#1683793311yescharacteristic
712C4#1683799711yescharacteristic
713C4#1683804111yescharacteristic
714C4#1683805211yescharacteristic
715C2—24no—
716C2—42no—
717C2—161no—
718C2#2142765311yescharacteristic
719C2C2×#1683762911yescharacteristic
720C2#2143377811yescharacteristic
721C2#2143592011yescharacteristic
722C2#2143599811yescharacteristic
723C2#2143645311yescharacteristic
724C2#2143649211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D59
commutator, cosocleC22×C4×C59C24
FrattiniC22×C4C23×D59
Fitting, prime radicalC59×#2416C2
socleC23×C59C22×D4
hypercenter#2416D59
hypocenterC59#25238
LCSG ▷ C22×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2416

Complements

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

NH ≅ G/Ntype
1. C2×#16837718C2semidirect
2. C2×D4×C59⋊C8C2semidirect
3. #21428413C2semidirect
4. #21425597C2semidirect
5. #21425532C2semidirect
6. #21425470C2semidirect
7. #21425282C2semidirect
8. #21424821C2semidirect
9. #21424782C2semidirect
10. #21424525C2semidirect
11. #21424525C2semidirect
12. #21424289C2semidirect
13. #21424119C2semidirect
14. C2×#16837164C2semidirect
94. C22⋊(C59⋊C8)D4semidirect
423. C59#25238semidirect

Maximal subgroups

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

subgroupindex
C2×#168377182
C2×D4×C59⋊C82
#214284132
#214255972
#214255322
#214254702
#214252822
#214248212
#214247822
#214245252
#214242892
#214241192
C2×#168371642
C59×#24162
#2523859