Finite Group Databasebeta

← #28599885

Subgroups — #28599885

Order 15104.

1096 conjugacy classes of subgroups.

The subgroup lattice has 766 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#121×Dic59C211yesmaximal, characteristic, complemented
2#21426587C211yesmaximal, characteristic, complemented
3#21424963C211yesmaximal, characteristic, complemented
4#21424952C211yesmaximal, characteristic, complemented
5#21424781C211yesmaximal, characteristic, complemented
6#21424774C211yesmaximal, characteristic, complemented
7#21424739C211yesmaximal, characteristic, complemented
8#21424725C211yesmaximal, characteristic, complemented
9#21424446C211yesmaximal, characteristic, complemented
10#21424432C211yesmaximal, characteristic, complemented
11#21424419C211yesmaximal, characteristic, complemented
12#21424297C211yesmaximal, characteristic, complemented
13#21424036C211yesmaximal, characteristic, complemented
14C22⋊C8×Dic59C211yesmaximal, characteristic, complemented
15C2×C59×#449C211yesmaximal, characteristic
16C2×D4×Dic59—21no—
17C2×D4×Dic59C2211yescharacteristic
18C2×#14273686C2211yescharacteristic
19C22×C4×Dic59C2211yescharacteristic
20C2×#14273661C2211yescharacteristic
21C2×#14273659C2211yescharacteristic
22C2×#14273651C2211yescharacteristic
23C2×#14273651C2211yescharacteristic
24C2×#14273648C2211yescharacteristic
25C2×#14273648C2211yescharacteristic
26C2×#14273648C2211yescharacteristic
27C2×#14273648C2211yescharacteristic
28C2×C22⋊(C59⋊C8)C2211yescharacteristic
29C2×C8×Dic59C2211yescharacteristic
30C2×C8×Dic59C2211yescharacteristic
31#16837309C2211yescharacteristic
32#16837309C2211yescharacteristic
33#16837305C2211yescharacteristic
34#16837305C2211yescharacteristic
35#16837305C2211yescharacteristic
36#16837301C2211yescharacteristic
37#16837295—21no—
38#16837282—21no—
39#16837282—21no—
40#16837282—21no—
41#16837262C2211yescharacteristic
42C4⋊C4×Dic59C2211yescharacteristic
43C22⋊C4×Dic59—21no—
44C4×C22⋊Dic59—21no—
45C4×C22⋊Dic59—21no—
46#16837165C2211yescharacteristic
47#16837165C2211yescharacteristic
48#16837164C2211yescharacteristic
49#16837164C2211yescharacteristic
50#16837156C2211yescharacteristic
51#16837156C2211yescharacteristic
52C22×#41×C59C2211yescharacteristic
53C22×SD16×C59C2211yescharacteristic
54C22×D8×C59C2211yescharacteristic
55C2×#121×C59C2211yescharacteristic
56C59×#449C418yescomplemented
57C2×#103×C59C2211yescharacteristic
58C2×#102×C59C2211yescharacteristic
59C2×C22⋊C8×C59C2211yescharacteristic
60C23×Dic59—21no—
61C23×Dic59D411yescharacteristic
62C23×Dic59D411yescharacteristic
63C22×C59⋊C8C2311yescharacteristic
64C22×C59⋊C8C2311yescharacteristic
65D4×Dic59—41no—
66D4×Dic59—41no—
67D4×Dic59—44no—
68#14273686—41no—
69#14273686—41no—
70C2×C4⋊Dic59—21no—
71C2×C4⋊Dic59C2311yescharacteristic
72C2×C4⋊Dic59C2311yescharacteristic
73C2×C4⋊Dic59C2311yescharacteristic
74C2×C4⋊Dic59C2311yescharacteristic
75C2×C22⋊Dic59—21no—
76C2×C22⋊Dic59—21no—
77C2×C22⋊Dic59—21no—
78C2×C22⋊Dic59—21no—
79C2×C22⋊Dic59—21no—
80C2×C22⋊Dic59—21no—
81C2×C22⋊Dic59—21no—
82C2×C22⋊Dic59—21no—
83C2×C22⋊Dic59—21no—
84C2×C4×Dic59—21no—
85C2×C4×Dic59—21no—
86C2×C4×Dic59—41no—
87C2×C4×Dic59—41no—
88C2×C4×Dic59D411yescharacteristic
89C2×C4×Dic59D411yescharacteristic
90C2×C4×Dic59C2311yescharacteristic
91C2×C4×Dic59C2311yescharacteristic
92#14273661—41no—
93#14273659—41no—
94#14273651—41no—
95#14273651—41no—
96#14273648—41no—
97#14273648—41no—
98#14273648—41no—
99#14273648—41no—
100C22⋊(C59⋊C8)—22no—
101C8×Dic59—41no—
102C8×Dic59—41no—
103C59⋊#95—21no—
104C59⋊#95—21no—
105C59⋊#95—21no—
106C59⋊#95—21no—
107C59⋊#95—21no—
108C59⋊#95—21no—
109C59⋊#95—21no—
110C2×#41×C59—22no—
111C2×#41×C59—41no—
112C2×#41×C59—41no—
113C2×#41×C59—41no—
114C2×#41×C59—41no—
115C2×#41×C59C2×C414yescomplemented
116C22×Q8×C59C2311yescharacteristic
117C22×D4×C59—21no—
118C22×D4×C59—21no—
119C22×D4×C59C2311yescharacteristic
120C22×D4×C59C2311yescharacteristic
121C23×C4×C59—21no—
122C23×C4×C59C2311yescharacteristic
123C2×SD16×C59—41no—
124C2×SD16×C59—41no—
125C2×SD16×C59C2×C414yescomplemented
126C2×D8×C59—41no—
127C2×D8×C59—41no—
128C2×D8×C59C2×C414yescomplemented
129C22×C8×C59C2311yescharacteristic
130C22×C8×C59C2311yescharacteristic
131#121×C59—22no—
132#121×C59C2×C414yes—
133C2×C4⋊C4×C59C2311yescharacteristic
134C2×C22⋊C4×C59—21no—
135#103×C59C2×C414yescomplemented
136#102×C59C2×C414yescomplemented
137C22⋊C8×C59C2×C414yescomplemented
138C24×C59—21no—
139C24×C59—21no—
140C24×C59C2×D411yescharacteristic
141#41×C59—44no—
142#41×C59—44no—
143#41×C59—44no—
144#41×C59—44no—
145C2×Q8×C59—21no—
146C2×Q8×C59—21no—
147C2×Q8×C59—21no—
148C2×Q8×C59—21no—
149C2×Q8×C59—21no—
150C2×Q8×C59C22×C412yes—
151C2×D4×C59—24no—
152C2×D4×C59—24no—
153C2×D4×C59—21no—
154C2×D4×C59—21no—
155C2×D4×C59—21no—
156C2×D4×C59—21no—
157C2×D4×C59—21no—
158C2×D4×C59—21no—
159C2×D4×C59—21no—
160C2×D4×C59—21no—
161C2×D4×C59—21no—
162C2×D4×C59—21no—
163C2×D4×C59—42no—
164C2×D4×C59—42no—
165C2×D4×C59—42no—
166C2×D4×C59—42no—
167C2×D4×C59C22×C412yes—
168C2×D4×C59C22×C412yes—
169C22×C4×C59—21no—
170C22×C4×C59—21no—
171C22×C4×C59—21no—
172C22×C4×C59—21no—
173C22×C4×C59—21no—
174C22×C4×C59—21no—
175C22×C4×C59—24no—
176C22×C4×C59—42no—
177C22×C4×C59—42no—
178C22×C4×C59C22×C412yes—
179C22×C4×C59C2×D411yescharacteristic
180C22×C4×C59#4112yes—
181C22×C4×C59C2411yescharacteristic
182C22×Dic59—22no—
183C22×Dic59—22no—
184C22×Dic59—22no—
185C22×Dic59—21no—
186C22×Dic59—21no—
187C22×Dic59—21no—
188C22×Dic59—21no—
189C22×Dic59—41no—
190C22×Dic59—41no—
191C22×Dic59—41no—
192C22×Dic59—42no—
193C22×Dic59—42no—
194C22×Dic59—42no—
195C22×Dic59C2×D411yescharacteristic
196C22×Dic59C2×D411yescharacteristic
197C22×Dic59C2×D411yescharacteristic
198C22×Dic59C2×D411yescharacteristic
199SD16×C59—44no—
200D8×C59—44no—
201C2×C8×C59—21no—
202C2×C8×C59—21no—
203C2×C8×C59—21no—
204C2×C8×C59—21no—
205C2×C8×C59C22×C412yes—
206C2×C8×C59C22×C412yes—
207C4⋊C4×C59—21no—
208C4⋊C4×C59C22×C412yes—
209C22⋊C4×C59—24no—
210C22⋊Dic59—42no—
211C22⋊Dic59—42no—
212C22⋊Dic59—42no—
213C22⋊Dic59—42no—
214C22⋊Dic59—42no—
215C22⋊Dic59—42no—
216C22⋊Dic59—42no—
217C22⋊Dic59—42no—
218C22⋊Dic59—42no—
219C4⋊Dic59—21no—
220C4⋊Dic59—21no—
221C4⋊Dic59—21no—
222C4⋊Dic59—21no—
223C4⋊Dic59—21no—
224C4⋊Dic59—21no—
225C4⋊Dic59—21no—
226C4⋊Dic59—21no—
227C4⋊Dic59—42no—
228C4×Dic59—21no—
229C4×Dic59—21no—
230C4×Dic59—21no—
231C4×Dic59—21no—
232C4×Dic59—41no—
233C4×Dic59—41no—
234C4×Dic59—42no—
235C4×Dic59—42no—
236C2×C59⋊C8—21no—
237C2×C59⋊C8—21no—
238C2×C59⋊C8—21no—
239C2×C59⋊C8—21no—
240C2×C59⋊C8—21no—
241C2×C59⋊C8—21no—
242C23×C59—21no—
243C23×C59—21no—
244C23×C59—21no—
245C23×C59—21no—
246C23×C59—21no—
247C23×C59—21no—
248C23×C59—22no—
249C23×C59—22no—
250C23×C59—41no—
251C23×C59—41no—
252C23×C59—41no—
253C23×C59—41no—
254C23×C59—41no—
255C23×C59—41no—
256C23×C59—41no—
257C23×C59—41no—
258C23×C59—41no—
259C23×C59—41no—
260C23×C59—41no—
261C23×C59—41no—
262C23×C59C4×D412yes—
263C23×C59C22×D411yescharacteristic
264Q8×C59—22no—
265Q8×C59—22no—
266Q8×C59—41no—
267Q8×C59—41no—
268D4×C59—22no—
269D4×C59—22no—
270D4×C59—22no—
271D4×C59—22no—
272D4×C59—48no—
273D4×C59—48no—
274D4×C59—41no—
275D4×C59—41no—
276D4×C59—41no—
277D4×C59—41no—
278C2×C4×C59—21no—
279C2×C4×C59—21no—
280C2×C4×C59—22no—
281C2×C4×C59—22no—
282C2×C4×C59—22no—
283C2×C4×C59—22no—
284C2×C4×C59—22no—
285C2×C4×C59—22no—
286C2×C4×C59—48no—
287C2×C4×C59—41no—
288C2×C4×C59—41no—
289C2×C4×C59—41no—
290C2×C4×C59—41no—
291C2×C4×C59C4×D412yes—
292C2×C4×C59C23×C411yescharacteristic
293C2×C4×C59C2×#4111yescharacteristic
294C2×C4×C59H(5,𝔽2)11yescharacteristic
295C2×C4×C59H(5,𝔽2)11yescharacteristic
296C2×C4×C59H(5,𝔽2)11yescharacteristic
297C2×C4×C59H(5,𝔽2)11yescharacteristic
298C2×Dic59—21no—
299C2×Dic59—21no—
300C2×Dic59—21no—
301C2×Dic59—21no—
302C2×Dic59—21no—
303C2×Dic59—21no—
304C2×Dic59—21no—
305C2×Dic59—21no—
306C2×Dic59—21no—
307C2×Dic59—44no—
308C2×Dic59—44no—
309C2×Dic59—41no—
310C2×Dic59—41no—
311C2×Dic59—41no—
312C2×Dic59—41no—
313C2×Dic59—41no—
314C2×Dic59—41no—
315C2×Dic59—41no—
316C2×Dic59—41no—
317C2×Dic59—41no—
318C2×Dic59—41no—
319C2×Dic59—41no—
320C2×Dic59—41no—
321C2×Dic59—84no—
322C2×Dic59#13512yes—
323C2×Dic59#13512yes—
324C2×Dic59AGL(1,ℤ/8)12yes—
325C8×C59—22no—
326C8×C59—22no—
327C59⋊C8—41no—
328C59⋊C8—41no—
329#22045—591nomaximal, Sylow
330C22×C59—22no—
331C22×C59—22no—
332C22×C59—22no—
333C22×C59—41no—
334C22×C59—41no—
335C22×C59—41no—
336C22×C59—41no—
337C22×C59—42no—
338C22×C59—42no—
339C22×C59—42no—
340C22×C59—42no—
341C22×C59—42no—
342C22×C59—42no—
343C22×C59—81no—
344C22×C59—81no—
345C22×C59—81no—
346C22×C59—81no—
347C22×C59—81no—
348C22×C59—81no—
349C22×C59—81no—
350C22×C59—81no—
351C22×C59C2×C4×D411yescharacteristic
352C22×C59#53411yescharacteristic
353C22×C59#53511yescharacteristic
354C22×C59C2×#13511yescharacteristic
355C22×C59C2×#13511yescharacteristic
356C22×C59C2×AGL(1,ℤ/8)11yescharacteristic
357C22×C59#57511yescharacteristic
358C4×C59—22no—
359C4×C59—42no—
360C4×C59—42no—
361C4×C59#51811yescharacteristic
362C4×C59#51811yescharacteristic
363C4×C59#53811yescharacteristic
364C4×C59#53811yescharacteristic
365Dic59—22no—
366Dic59—22no—
367Dic59—22no—
368Dic59—41no—
369Dic59—81no—
370Dic59—81no—
371Dic59—81no—
372Dic59—81no—
373C2×#449D5911yescharacteristic
374C4×#121—591no—
375#2297—591no—
376#1970—591no—
377#1968—591no—
378#1934—591no—
379#1933—591no—
380#1928—591no—
381#1926—591no—
382#1879—591no—
383#1877—591no—
384#1875—591no—
385#1854—591no—
386#1788—591no—
387C4×C22⋊C8—591no—
388C2×C59—42no—
389C2×C59—82no—
390C2×C59—82no—
391C2×C59#232111yescharacteristic
392C2×C59C4×#13511yescharacteristic
393C2×C59C4×AGL(1,ℤ/8)11yescharacteristic
394C2×C59#318811yescharacteristic
395C2×C59#319111yescharacteristic
396C2×C59#320711yescharacteristic
397C2×C59#321211yescharacteristic
398C22×#41C2×D5911yescharacteristic
399C22×SD16C2×D5911yescharacteristic
400C22×D8C2×D5911yescharacteristic
401C2×#121C2×D5911yescharacteristic
402C2×C4×D4—591no—
403C2×C4×D4—1181no—
404C2×#117—591no—
405C22×C42—591no—
406#449Dic5918yescomplemented
407C2×#107—591no—
408C2×#106—591no—
409C2×#103—591no—
410C2×#103—591no—
411C2×#103C2×D5911yescharacteristic
412C2×#102—591no—
413C2×#102—591no—
414C2×#102—591no—
415C2×#102—591no—
416C2×#102C2×D5911yescharacteristic
417C2×C22⋊C8—591no—
418C2×C22⋊C8C2×D5911yescharacteristic
419C2×C4×C8—591no—
420C2×C4×C8—591no—
421#391—591no—
422#391—591no—
423#390—591no—
424#390—591no—
425#390—591no—
426#389—591no—
427#388—1181no—
428#386—1181no—
429#386—1181no—
430#386—1181no—
431#380—591no—
432C4×C4⋊C4—591no—
433C4×C22⋊C4—1181no—
434C4×C22⋊C4—1181no—
435C4×C22⋊C4—1181no—
436#340—591no—
437#340—591no—
438#340—591no—
439#340—591no—
440#336—591no—
441#336—591no—
442C59#2204511yescharacteristic, complemented, Sylow
443C2×#41—22no—
444C2×#41—41no—
445C2×#41—41no—
446C2×#41—41no—
447C2×#41—41no—
448C2×#41C2×Dic5914yescomplemented
449C22×Q8C22×D5911yescharacteristic
450C22×D4—21no—
451C22×D4—21no—
452C22×D4C22×D5911yescharacteristic
453C22×D4C22×D5911yescharacteristic
454C23×C4—21no—
455C23×C4—591no—
456C23×C4—591no—
457C23×C4—1181no—
458C23×C4C22×D5911yescharacteristic
459C2×SD16—41no—
460C2×SD16—41no—
461C2×SD16C2×Dic5914yescomplemented
462C2×D8—41no—
463C2×D8—41no—
464C2×D8C2×Dic5914yescomplemented
465C22×C8—591no—
466C22×C8—591no—
467C22×C8C22×D5911yescharacteristic
468C22×C8C22×D5911yescharacteristic
469#121—22no—
470#121C2×Dic5914yes—
471C4×D4—2361no—
472C4×D4—2361no—
473C4×D4—2364no—
474#117—2361no—
475#117—2361no—
476C2×C4⋊C4—591no—
477C2×C4⋊C4—591no—
478C2×C4⋊C4—591no—
479C2×C4⋊C4—591no—
480C2×C4⋊C4—1181no—
481C2×C4⋊C4C22×D5911yescharacteristic
482C2×C22⋊C4—21no—
483C2×C22⋊C4—1181no—
484C2×C22⋊C4—1181no—
485C2×C22⋊C4—1181no—
486C2×C22⋊C4—1181no—
487C2×C22⋊C4—1181no—
488C2×C22⋊C4—1181no—
489C2×C22⋊C4—1181no—
490C2×C22⋊C4—1181no—
491C2×C22⋊C4—1181no—
492C2×C42—591no—
493C2×C42—591no—
494C2×C42—591no—
495C2×C42—591no—
496C2×C42—1181no—
497C2×C42—1181no—
498C2×C42—2361no—
499C2×C42—2361no—
500#107—2361no—
501#106—2361no—
502#103—2361no—
503#103—2361no—
504#103C2×Dic5914yescomplemented
505#102—2361no—
506#102—2361no—
507#102—2361no—
508#102—2361no—
509#102C2×Dic5914yescomplemented
510C22⋊C8—1182no—
511C22⋊C8C2×Dic5914yescomplemented
512C4×C8—2361no—
513C4×C8—2361no—
514#95—1181no—
515#95—1181no—
516#95—1181no—
517#95—1181no—
518#95—1181no—
519#95—1181no—
520#95—1181no—
521C24—21no—
522C24—21no—
523C24D4×D5911yescharacteristic
524#41—44no—
525#41—44no—
526#41—44no—
527#41—44no—
528C2×Q8—21no—
529C2×Q8—21no—
530C2×Q8—21no—
531C2×Q8—21no—
532C2×Q8—21no—
533C2×Q8C22×Dic5912yes—
534C2×D4—24no—
535C2×D4—24no—
536C2×D4—21no—
537C2×D4—21no—
538C2×D4—21no—
539C2×D4—21no—
540C2×D4—21no—
541C2×D4—21no—
542C2×D4—21no—
543C2×D4—21no—
544C2×D4—21no—
545C2×D4—21no—
546C2×D4—42no—
547C2×D4—42no—
548C2×D4—42no—
549C2×D4—42no—
550C2×D4C22×Dic5912yes—
551C2×D4C22×Dic5912yes—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—24no—
559C22×C4—42no—
560C22×C4—42no—
561C22×C4—591no—
562C22×C4—591no—
563C22×C4—591no—
564C22×C4—591no—
565C22×C4—1182no—
566C22×C4—1182no—
567C22×C4—1182no—
568C22×C4—1181no—
569C22×C4—1181no—
570C22×C4—1181no—
571C22×C4—1181no—
572C22×C4—2362no—
573C22×C4—2361no—
574C22×C4—2361no—
575C22×C4—2361no—
576C22×C4—2362no—
577C22×C4—2362no—
578C22×C4D4×D5911yescharacteristic
579C22×C4#1174568712yes—
580C22×C4C22×Dic5912yes—
581C22×C4C23×D5911yescharacteristic
582SD16—44no—
583D8—44no—
584C2×C8—21no—
585C2×C8—21no—
586C2×C8—21no—
587C2×C8—21no—
588C2×C8—1181no—
589C2×C8—1181no—
590C2×C8—1181no—
591C2×C8—1181no—
592C2×C8—1181no—
593C2×C8—1181no—
594C2×C8C22×Dic5912yes—
595C2×C8C22×Dic5912yes—
596C4⋊C4—21no—
597C4⋊C4—1181no—
598C4⋊C4—1181no—
599C4⋊C4—1181no—
600C4⋊C4—1181no—
601C4⋊C4—1181no—
602C4⋊C4—1181no—
603C4⋊C4—1181no—
604C4⋊C4—1181no—
605C4⋊C4—2362no—
606C4⋊C4C22×Dic5912yes—
607C22⋊C4—24no—
608C22⋊C4—2362no—
609C22⋊C4—2362no—
610C22⋊C4—2362no—
611C22⋊C4—2362no—
612C22⋊C4—2362no—
613C22⋊C4—2362no—
614C22⋊C4—2362no—
615C22⋊C4—2362no—
616C22⋊C4—2362no—
617C42—1181no—
618C42—1181no—
619C42—1181no—
620C42—1181no—
621C42—2361no—
622C42—2361no—
623C42—2362no—
624C42—2362no—
625C23—21no—
626C23—21no—
627C23—21no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—22no—
632C23—22no—
633C23—41no—
634C23—41no—
635C23—41no—
636C23—41no—
637C23—41no—
638C23—41no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23D4×Dic5912yes—
646C23C2×D4×D5911yescharacteristic
647Q8—22no—
648Q8—22no—
649Q8—41no—
650Q8—41no—
651D4—22no—
652D4—22no—
653D4—22no—
654D4—22no—
655D4—48no—
656D4—48no—
657D4—41no—
658D4—41no—
659D4—41no—
660D4—41no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—48no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—592no—
675C2×C4—592no—
676C2×C4—592no—
677C2×C4—1181no—
678C2×C4—1181no—
679C2×C4—1181no—
680C2×C4—1181no—
681C2×C4—1181no—
682C2×C4—1181no—
683C2×C4—1181no—
684C2×C4—1181no—
685C2×C4—1181no—
686C2×C4—4724no—
687C2×C4—2364no—
688C2×C4—2364no—
689C2×C4—2361no—
690C2×C4—2361no—
691C2×C4—2361no—
692C2×C4—2361no—
693C2×C4—2361no—
694C2×C4—2361no—
695C2×C4—2361no—
696C2×C4—2361no—
697C2×C4—2361no—
698C2×C4—2361no—
699C2×C4—2361no—
700C2×C4—2361no—
701C2×C4D4×Dic5912yes—
702C2×C4C23×Dic5911yescharacteristic
703C2×C4C2×#1174568711yescharacteristic
704C2×C4#1427377211yescharacteristic
705C2×C4#1427377211yescharacteristic
706C2×C4#1427377211yescharacteristic
707C2×C4#1427377211yescharacteristic
708C8—22no—
709C8—22no—
710C8—2361no—
711C8—2361no—
712C22—22no—
713C22—22no—
714C22—22no—
715C22—41no—
716C22—41no—
717C22—41no—
718C22—41no—
719C22—42no—
720C22—42no—
721C22—42no—
722C22—42no—
723C22—42no—
724C22—42no—
725C22—81no—
726C22—81no—
727C22—81no—
728C22—81no—
729C22—81no—
730C22—81no—
731C22—81no—
732C22—81no—
733C22C2×D4×Dic5911yescharacteristic
734C22#1683796211yescharacteristic
735C22#1683796711yescharacteristic
736C22#135×D5911yescharacteristic
737C22#135×D5911yescharacteristic
738C22AGL(1,ℤ/8)×D5911yescharacteristic
739C22#1683819811yescharacteristic
740C4—22no—
741C4—42no—
742C4—42no—
743C4—1182no—
744C4—1182no—
745C4—1182no—
746C4—4721no—
747C4—4721no—
748C4—4721no—
749C4—4721no—
750C4—2361no—
751C4#1683787711yescharacteristic
752C4#1683787711yescharacteristic
753C4#1683798711yescharacteristic
754C4#1683798711yescharacteristic
755C2—42no—
756C2—82no—
757C2—82no—
758C2#2142675711yescharacteristic
759C2#135×Dic5911yescharacteristic
760C2AGL(1,ℤ/8)×Dic5911yescharacteristic
761C2#2143485911yescharacteristic
762C2#2143488611yescharacteristic
763C2#2143502711yescharacteristic
764C2#2143506911yescharacteristic
subgroupG/H
centerC23C2×D4×D59
commutatorC2×C4×C59C23×C4
FrattiniC22×C4C23×D59
Fitting, prime radicalC2×C59×#449C2
socleC23×C59C22×D4
cosocleC22×C4×C59C24
hypercenterC2×#449D59
hypocenterC59#22045
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#449

Complements

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

NH ≅ G/Ntype
1. #121×Dic59C2semidirect
2. #21426587C2semidirect
3. #21424963C2semidirect
4. #21424952C2semidirect
5. #21424781C2semidirect
6. #21424774C2semidirect
7. #21424739C2semidirect
8. #21424725C2semidirect
9. #21424446C2semidirect
10. #21424432C2semidirect
11. #21424419C2semidirect
12. #21424297C2semidirect
13. #21424036C2semidirect
14. C22⋊C8×Dic59C2semidirect
56. C59×#449C4semidirect
115. C2×#41×C59C2×C4semidirect
125. C2×SD16×C59C2×C4semidirect
128. C2×D8×C59C2×C4semidirect
135. #103×C59C2×C4semidirect
136. #102×C59C2×C4semidirect
137. C22⋊C8×C59C2×C4semidirect
406. #449Dic59semidirect
442. C59#22045semidirect
448. C2×#41C2×Dic59semidirect
461. C2×SD16C2×Dic59semidirect
464. C2×D8C2×Dic59semidirect
504. #103C2×Dic59semidirect
509. #102C2×Dic59semidirect
511. C22⋊C8C2×Dic59semidirect

Maximal subgroups

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

subgroupindex
#121×Dic592
#214265872
#214249632
#214249522
#214247812
#214247742
#214247392
#214247252
#214244462
#214244322
#214244192
#214242972
#214240362
C22⋊C8×Dic592
C2×C59×#4492
#2204559