Finite Group Databasebeta

← #28649262

Subgroups — #28649262

Order 15104.

944 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
1D4×C4⋊Dic59C211yesmaximal, characteristic, complemented
2#21425654C211yesmaximal, characteristic, complemented
3#21425522C211yesmaximal, characteristic, complemented
4#21425499C211yesmaximal, characteristic, complemented
5#21425275C211yesmaximal, characteristic, complemented
6#21424713C211yesmaximal, characteristic, complemented
7#21424664C211yesmaximal, characteristic, complemented
8#21424525C211yesmaximal, characteristic, complemented
9#21424414C211yesmaximal, characteristic, complemented
10#21424414C211yesmaximal, characteristic, complemented
11#21424389C211yesmaximal, characteristic, complemented
12#21424284C211yesmaximal, characteristic, complemented
13#21424180C211yesmaximal, characteristic, complemented
14C2×#16837164C211yesmaximal, characteristic, complemented
15C59×#2416C211yesmaximal, characteristic
16C23×C59⋊C8C2211yescharacteristic
17C2×D4×Dic59—21no—
18C22×C4⋊Dic59C2211yescharacteristic
19C22×C4⋊Dic59C2211yescharacteristic
20C2×#14273660C2211yescharacteristic
21C2×#14273660C2211yescharacteristic
22C2×#14273648C2211yescharacteristic
23C2×#14273648C2211yescharacteristic
24C2×#14273648C2211yescharacteristic
25C2×#14273648C2211yescharacteristic
26C2×C22⋊(C59⋊C8)C2211yescharacteristic
27C2×C22⋊(C59⋊C8)C2211yescharacteristic
28C2×C22⋊(C59⋊C8)C2211yescharacteristic
29#16837301—21no—
30#16837277—21no—
31#16837277—21no—
32#16837272C2211yescharacteristic
33#16837262C2211yescharacteristic
34#16837262C2211yescharacteristic
35C4×C4⋊Dic59C2211yescharacteristic
36#16837164C2211yescharacteristic
37#16837164C2211yescharacteristic
38#16837164C2211yescharacteristic
39#16837164C2211yescharacteristic
40#16837164C2211yescharacteristic
41#16837164C2211yescharacteristic
42#16837164C2211yescharacteristic
43#16837164C2211yescharacteristic
44#16837164C2211yescharacteristic
45#16837164C2211yescharacteristic
46#16837157C2211yescharacteristic
47#16837157C2211yescharacteristic
48C2×#121×C59—21no—
49C2×#121×C59C2211yescharacteristic
50C2×#121×C59C2211yescharacteristic
51C2×C4×D4×C59C2211yescharacteristic
52C22×C4⋊C4×C59C2211yescharacteristic
53C59×#396—21no—
54C59×#394—21no—
55C59×#390C2211yescharacteristic
56C59×#389C2211yescharacteristic
57C59×#386—21no—
58C59×#380C2211yescharacteristic
59C23×Dic59—21no—
60C23×Dic59—21no—
61C22×C59⋊C8—22no—
62C22×C59⋊C8—41no—
63C22×C59⋊C8—41no—
64C22×C59⋊C8C2311yescharacteristic
65C22×C59⋊C8C2311yescharacteristic
66C22×C59⋊C8C2311yescharacteristic
67C22×C59⋊C8C2311yescharacteristic
68D4×Dic59—44no—
69C2×C4⋊Dic59—22no—
70C2×C4⋊Dic59—22no—
71C2×C4⋊Dic59—21no—
72C2×C4⋊Dic59—21no—
73C2×C4⋊Dic59—21no—
74C2×C4⋊Dic59—21no—
75C2×C4⋊Dic59—41no—
76C2×C4⋊Dic59—41no—
77C2×C4⋊Dic59C2311yescharacteristic
78C2×C4⋊Dic59C2311yescharacteristic
79C2×C4⋊Dic59C2311yescharacteristic
80C2×C4⋊Dic59C2311yescharacteristic
81C2×C22⋊Dic59—21no—
82C2×C22⋊Dic59—21no—
83C2×C4×Dic59—21no—
84#14273660—22no—
85#14273660—41no—
86#14273648—22no—
87#14273648—41no—
88#14273648—41no—
89#14273648—41no—
90C22⋊(C59⋊C8)—22no—
91C22⋊(C59⋊C8)—41no—
92C22⋊(C59⋊C8)—41no—
93C59⋊#95—21no—
94C59⋊#95—21no—
95C59⋊#95—21no—
96C22×D4×C59—21no—
97C22×D4×C59—21no—
98C22×D4×C59D411yescharacteristic
99C22×D4×C59C2311yescharacteristic
100C23×C4×C59—21no—
101C23×C4×C59C2311yescharacteristic
102C23×C4×C59C2311yescharacteristic
103#121×C59—22no—
104#121×C59—22no—
105#121×C59—22no—
106#121×C59—41no—
107#121×C59—44no—
108C4×D4×C59—22no—
109C4×D4×C59—22no—
110C2×C4⋊C4×C59—22no—
111C2×C4⋊C4×C59—21no—
112C2×C4⋊C4×C59—21no—
113C2×C4⋊C4×C59—41no—
114C2×C4⋊C4×C59D411yescharacteristic
115C2×C4⋊C4×C59C2311yescharacteristic
116C2×C4⋊C4×C59C2311yescharacteristic
117C2×C4⋊C4×C59C2311yescharacteristic
118C2×C22⋊C4×C59—21no—
119C2×C22⋊C4×C59—21no—
120C2×C22⋊C4×C59—21no—
121C2×C22⋊C4×C59—21no—
122C2×C22⋊C4×C59—21no—
123C2×C22⋊C4×C59D411yescharacteristic
124C2×C22⋊C4×C59D411yescharacteristic
125C2×C42×C59C2311yescharacteristic
126#95×C59—21no—
127#95×C59—21no—
128C24×C59—21no—
129C24×C59C2×D411yescharacteristic
130C24×C59C2×D411yescharacteristic
131C2×D4×C59—22no—
132C2×D4×C59—22no—
133C2×D4×C59—21no—
134C2×D4×C59—21no—
135C2×D4×C59—21no—
136C2×D4×C59—21no—
137C2×D4×C59—21no—
138C2×D4×C59—21no—
139C2×D4×C59—42no—
140C2×D4×C59—42no—
141C2×D4×C59—42no—
142C2×D4×C59—42no—
143C2×D4×C59—42no—
144C2×D4×C59—81no—
145C2×D4×C59D814yes—
146C22×C4×C59—21no—
147C22×C4×C59—21no—
148C22×C4×C59—21no—
149C22×C4×C59—21no—
150C22×C4×C59—21no—
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—42no—
160C22×C4×C59—42no—
161C22×C4×C59—81no—
162C22×C4×C59C2×D411yescharacteristic
163C22×C4×C59C2×D411yescharacteristic
164C22×C4×C59C2×D411yescharacteristic
165C22×C4×C59C2×D411yescharacteristic
166C22×C4×C59#4112yes—
167C22×C4×C59#4112yes—
168C22×C4×C59C2411yescharacteristic
169C22×Dic59—21no—
170C22×Dic59—21no—
171C22×Dic59—21no—
172C22×Dic59—21no—
173C22×Dic59—42no—
174C22×Dic59—42no—
175C22×Dic59—42no—
176C22×Dic59—42no—
177C22×Dic59—81no—
178C22×Dic59—81no—
179C4⋊C4×C59—22no—
180C4⋊C4×C59—21no—
181C4⋊C4×C59—21no—
182C4⋊C4×C59—21no—
183C4⋊C4×C59—21no—
184C4⋊C4×C59—21no—
185C4⋊C4×C59—42no—
186C4⋊C4×C59—42no—
187C4⋊C4×C59#4112yes—
188C22⋊C4×C59—22no—
189C22⋊C4×C59—22no—
190C22⋊C4×C59—42no—
191C22⋊C4×C59—42no—
192C22⋊C4×C59—42no—
193C22⋊C4×C59—42no—
194C22⋊C4×C59—81no—
195C42×C59—21no—
196C42×C59—21no—
197C22⋊Dic59—42no—
198C22⋊Dic59—42no—
199C4⋊Dic59—21no—
200C4⋊Dic59—21no—
201C4⋊Dic59—21no—
202C4⋊Dic59—21no—
203C4⋊Dic59—21no—
204C4⋊Dic59—21no—
205C4⋊Dic59—21no—
206C4⋊Dic59—42no—
207C4⋊Dic59—42no—
208C4⋊Dic59—42no—
209C4⋊Dic59—81no—
210C4⋊Dic59#4112yes—
211C4×Dic59—42no—
212C2×C59⋊C8—21no—
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—21no—
223C2×C59⋊C8—21no—
224C2×C59⋊C8—44no—
225C23×C59—21no—
226C23×C59—21no—
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—41no—
236C23×C59—41no—
237C23×C59—41no—
238C23×C59—41no—
239C23×C59—41no—
240C23×C59—41no—
241C23×C59—41no—
242C23×C59#12312yes—
243C23×C59C2×D812yes—
244C23×C59C2×D812yes—
245C23×C59#13712yes—
246C23×C59C22×D411yescharacteristic
247D4×C59—28no—
248D4×C59—41no—
249D4×C59—41no—
250D4×C59—41no—
251D4×C59—41no—
252D4×C59—84no—
253D4×C59—84no—
254C2×C4×C59—21no—
255C2×C4×C59—21no—
256C2×C4×C59—21no—
257C2×C4×C59—21no—
258C2×C4×C59—22no—
259C2×C4×C59—22no—
260C2×C4×C59—22no—
261C2×C4×C59—22no—
262C2×C4×C59—21no—
263C2×C4×C59—21no—
264C2×C4×C59—21no—
265C2×C4×C59—21no—
266C2×C4×C59—22no—
267C2×C4×C59—21no—
268C2×C4×C59—21no—
269C2×C4×C59—41no—
270C2×C4×C59—41no—
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—84no—
282C2×C4×C59#12312yes—
283C2×C4×C59C2×D812yes—
284C2×C4×C59C2×#4111yescharacteristic
285C2×C4×C59C2×#4111yescharacteristic
286C2×C4×C59C2×#4111yescharacteristic
287C2×C4×C59C2×#4111yescharacteristic
288C2×C4×C59H(5,𝔽2)11yescharacteristic
289C2×C4×C59H(5,𝔽2)11yescharacteristic
290C2×Dic59—22no—
291C2×Dic59—41no—
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—84no—
303C2×Dic59—84no—
304C59⋊C8—41no—
305C59⋊C8—41no—
306C59⋊C8—41no—
307C59⋊C8—41no—
308#26198—591nomaximal, Sylow
309C22×C59—22no—
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—41no—
319C22×C59—41no—
320C22×C59—41no—
321C22×C59—41no—
322C22×C59—81no—
323C22×C59—81no—
324C22×C59—81no—
325C22×C59—81no—
326C22×C59—81no—
327C22×C59—81no—
328C22×C59—81no—
329C22×C59#48014yes—
330C22×C59C2×#12311yescharacteristic
331C22×C59#54611yescharacteristic
332C22×C59#54611yescharacteristic
333C22×C59C22×D811yescharacteristic
334C22×C59C2×#13711yescharacteristic
335C22×C59#57711yescharacteristic
336C22×C59#57711yescharacteristic
337C4×C59—22no—
338C4×C59—22no—
339C4×C59—41no—
340C4×C59—41no—
341C4×C59—42no—
342C4×C59—81no—
343C4×C59—81no—
344C4×C59#52911yescharacteristic
345C4×C59#53811yescharacteristic
346C4×C59#55311yescharacteristic
347C4×C59#55311yescharacteristic
348Dic59—42no—
349Dic59—81no—
350Dic59—81no—
351Dic59—81no—
352#2416D5911yescharacteristic
353D4×C4⋊C4—591no—
354#2099—591no—
355#2075—591no—
356#2071—591no—
357#2033—591no—
358#1925—591no—
359#1918—591no—
360#1893—591no—
361#1874—591no—
362#1874—591no—
363#1869—591no—
364#1852—591no—
365#1823—591no—
366C2×#340—591no—
367C2×C59—24no—
368C2×C59—42no—
369C2×C59—161no—
370C2×C59#244411yescharacteristic
371C2×C59C2×#48011yescharacteristic
372C2×C59#309911yescharacteristic
373C2×C59#329411yescharacteristic
374C2×C59#329411yescharacteristic
375C2×C59#331611yescharacteristic
376C2×C59#332011yescharacteristic
377C23×C8—591no—
378C2×#121—21no—
379C2×#121C2×D5911yescharacteristic
380C2×#121C2×D5911yescharacteristic
381C2×C4×D4—1181no—
382C2×C4×D4C2×D5911yescharacteristic
383C22×C4⋊C4—591no—
384C22×C4⋊C4—591no—
385C22×C4⋊C4C2×D5911yescharacteristic
386C2×#107—591no—
387C2×#107—591no—
388C2×#102—591no—
389C2×#102—591no—
390C2×#102—591no—
391C2×#102—591no—
392C2×C22⋊C8—591no—
393C2×C22⋊C8—591no—
394C2×C22⋊C8—591no—
395#396—21no—
396#394—21no—
397#390C2×D5911yescharacteristic
398#389—1181no—
399#389C2×D5911yescharacteristic
400#386—21no—
401#385—1181no—
402#385—1181no—
403#384—591no—
404#380—591no—
405#380—591no—
406#380C2×D5911yescharacteristic
407C4×C4⋊C4—591no—
408#340—591no—
409#340—591no—
410#340—591no—
411#340—591no—
412#340—591no—
413#340—591no—
414#340—591no—
415#340—591no—
416#340—591no—
417#340—591no—
418#336—591no—
419#336—591no—
420C59#2619811yescharacteristic, complemented, Sylow
421C22×D4—21no—
422C22×D4—21no—
423C22×D4C22⋊D5911yescharacteristic
424C22×D4C22×D5911yescharacteristic
425C23×C4—21no—
426C23×C4—1181no—
427C23×C4—1181no—
428C23×C4C22×D5911yescharacteristic
429C23×C4C22×D5911yescharacteristic
430C22×C8—591no—
431C22×C8—591no—
432C22×C8—591no—
433C22×C8—591no—
434C22×C8—1182no—
435C22×C8—2361no—
436C22×C8—2361no—
437#121—22no—
438#121—22no—
439#121—22no—
440#121—41no—
441#121—44no—
442C4×D4—22no—
443C4×D4—22no—
444C4×D4—2364no—
445C2×C4⋊C4—22no—
446C2×C4⋊C4—21no—
447C2×C4⋊C4—21no—
448C2×C4⋊C4—41no—
449C2×C4⋊C4—591no—
450C2×C4⋊C4—591no—
451C2×C4⋊C4—591no—
452C2×C4⋊C4—591no—
453C2×C4⋊C4—1182no—
454C2×C4⋊C4—1182no—
455C2×C4⋊C4—1181no—
456C2×C4⋊C4—1181no—
457C2×C4⋊C4—1181no—
458C2×C4⋊C4—1181no—
459C2×C4⋊C4—2361no—
460C2×C4⋊C4—2361no—
461C2×C4⋊C4C22⋊D5911yescharacteristic
462C2×C4⋊C4C22×D5911yescharacteristic
463C2×C4⋊C4C22×D5911yescharacteristic
464C2×C4⋊C4C22×D5911yescharacteristic
465C2×C22⋊C4—21no—
466C2×C22⋊C4—21no—
467C2×C22⋊C4—21no—
468C2×C22⋊C4—21no—
469C2×C22⋊C4—21no—
470C2×C22⋊C4—1181no—
471C2×C22⋊C4—1181no—
472C2×C22⋊C4C22⋊D5911yescharacteristic
473C2×C22⋊C4C22⋊D5911yescharacteristic
474C2×C42—1181no—
475C2×C42C22×D5911yescharacteristic
476#107—1182no—
477#107—2361no—
478#102—1182no—
479#102—2361no—
480#102—2361no—
481#102—2361no—
482C22⋊C8—1182no—
483C22⋊C8—2361no—
484C22⋊C8—2361no—
485#95—21no—
486#95—21no—
487#95—1181no—
488#95—1181no—
489#95—1181no—
490C24—21no—
491C24C2×C22⋊D5911yescharacteristic
492C24C2×C22⋊D5911yescharacteristic
493C2×D4—22no—
494C2×D4—22no—
495C2×D4—21no—
496C2×D4—21no—
497C2×D4—21no—
498C2×D4—21no—
499C2×D4—21no—
500C2×D4—21no—
501C2×D4—42no—
502C2×D4—42no—
503C2×D4—42no—
504C2×D4—42no—
505C2×D4—42no—
506C2×D4—81no—
507C2×D4#1174566914yes—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—42no—
522C22×C4—42no—
523C22×C4—81no—
524C22×C4—1181no—
525C22×C4—1181no—
526C22×C4—1181no—
527C22×C4—1181no—
528C22×C4—4721no—
529C22×C4—4721no—
530C22×C4—2362no—
531C22×C4—2362no—
532C22×C4—2362no—
533C22×C4—2362no—
534C22×C4#1174568712yes—
535C22×C4#1174568712yes—
536C22×C4C2×C22⋊D5911yescharacteristic
537C22×C4C2×C22⋊D5911yescharacteristic
538C22×C4C2×C22⋊D5911yescharacteristic
539C22×C4C2×C22⋊D5911yescharacteristic
540C22×C4C23×D5911yescharacteristic
541C2×C8—1181no—
542C2×C8—1181no—
543C2×C8—1181no—
544C2×C8—1181no—
545C2×C8—1181no—
546C2×C8—1181no—
547C2×C8—1181no—
548C2×C8—1181no—
549C2×C8—1181no—
550C2×C8—1181no—
551C2×C8—1181no—
552C2×C8—1181no—
553C2×C8—2364no—
554C4⋊C4—22no—
555C4⋊C4—21no—
556C4⋊C4—21no—
557C4⋊C4—21no—
558C4⋊C4—21no—
559C4⋊C4—21no—
560C4⋊C4—42no—
561C4⋊C4—42no—
562C4⋊C4—592no—
563C4⋊C4—1181no—
564C4⋊C4—1181no—
565C4⋊C4—1181no—
566C4⋊C4—1181no—
567C4⋊C4—1181no—
568C4⋊C4—1181no—
569C4⋊C4—1181no—
570C4⋊C4—4721no—
571C4⋊C4—2362no—
572C4⋊C4—2362no—
573C4⋊C4—2362no—
574C4⋊C4#1174568712yes—
575C22⋊C4—22no—
576C22⋊C4—22no—
577C22⋊C4—42no—
578C22⋊C4—42no—
579C22⋊C4—42no—
580C22⋊C4—42no—
581C22⋊C4—81no—
582C22⋊C4—2362no—
583C22⋊C4—2362no—
584C42—21no—
585C42—21no—
586C42—2362no—
587C23—21no—
588C23—21no—
589C23—21no—
590C23—21no—
591C23—21no—
592C23—21no—
593C23—21no—
594C23—21no—
595C23—21no—
596C23—21no—
597C23—41no—
598C23—41no—
599C23—41no—
600C23—41no—
601C23—41no—
602C23—41no—
603C23—41no—
604C23#1427370812yes—
605C23C2×#1174566912yes—
606C23C2×#1174566912yes—
607C23#1427375712yes—
608C23C22×C22⋊D5911yescharacteristic
609D4—28no—
610D4—41no—
611D4—41no—
612D4—41no—
613D4—41no—
614D4—84no—
615D4—84no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—22no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
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—84no—
644C2×C4—1182no—
645C2×C4—4724no—
646C2×C4—4724no—
647C2×C4—2361no—
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#1427370812yes—
659C2×C4C2×#1174566912yes—
660C2×C4#41×D5911yescharacteristic
661C2×C4C2×#1174568711yescharacteristic
662C2×C4C2×#1174568711yescharacteristic
663C2×C4C2×#1174568711yescharacteristic
664C2×C4#1427377211yescharacteristic
665C2×C4#1427377311yescharacteristic
666C8—2361no—
667C8—2361no—
668C8—2361no—
669C8—2361no—
670C22—22no—
671C22—22no—
672C22—22no—
673C22—22no—
674C22—22no—
675C22—22no—
676C22—22no—
677C22—22no—
678C22—22no—
679C22—41no—
680C22—41no—
681C22—41no—
682C22—41no—
683C22—81no—
684C22—81no—
685C22—81no—
686C22—81no—
687C22—81no—
688C22—81no—
689C22—81no—
690C22#1683771314yes—
691C22C2×#1427370811yescharacteristic
692C22#1683804011yescharacteristic
693C22#1683804611yescharacteristic
694C22C22×#1174566911yescharacteristic
695C22C2×#1427375711yescharacteristic
696C22#1683821011yescharacteristic
697C22#1683821311yescharacteristic
698C4—22no—
699C4—22no—
700C4—42no—
701C4—41no—
702C4—41no—
703C4—81no—
704C4—81no—
705C4—4721no—
706C4—4721no—
707C4—4721no—
708C4—2362no—
709C4#1683793311yescharacteristic
710C4#1683798911yescharacteristic
711C4#1683809511yescharacteristic
712C4#1683810411yescharacteristic
713C2—24no—
714C2—42no—
715C2—161no—
716C2#2142784211yescharacteristic
717C2C2×#1683771311yescharacteristic
718C2#2143408111yescharacteristic
719C2#2143590311yescharacteristic
720C2#2143590911yescharacteristic
721C2#2143620711yescharacteristic
722C2#2143626111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D59
commutator, cosocleC22×C4×C59C24
FrattiniC22×C4C23×D59
Fitting, prime radicalC59×#2416C2
socleC23×C59C22×D4
hypercenter#2416D59
hypocenterC59#26198
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. D4×C4⋊Dic59C2semidirect
2. #21425654C2semidirect
3. #21425522C2semidirect
4. #21425499C2semidirect
5. #21425275C2semidirect
6. #21424713C2semidirect
7. #21424664C2semidirect
8. #21424525C2semidirect
9. #21424414C2semidirect
10. #21424414C2semidirect
11. #21424389C2semidirect
12. #21424284C2semidirect
13. #21424180C2semidirect
14. C2×#16837164C2semidirect
420. C59#26198semidirect

Maximal subgroups

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

subgroupindex
D4×C4⋊Dic592
#214256542
#214255222
#214254992
#214252752
#214247132
#214246642
#214245252
#214244142
#214243892
#214242842
#214241802
C2×#168371642
C59×#24162
#2619859