Finite Group Databasebeta

← #28598980

Subgroups — #28598980

Order 15104.

1162 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
1C2×#16837364C211yesmaximal, characteristic
2#21426475C211yesmaximal, characteristic
3#380×D59C211yesmaximal, characteristic
4#21424297C211yesmaximal, characteristic, complemented
5#21424295C211yesmaximal, characteristic, complemented
6#21424293C211yesmaximal, characteristic, complemented
7#21424290C211yesmaximal, characteristic, complemented
8#21424287C211yesmaximal, characteristic, complemented
9#21424285C211yesmaximal, characteristic, complemented
10#21424282C211yesmaximal, characteristic, complemented
11#21424130C211yesmaximal, characteristic, complemented
12#21424128C211yesmaximal, characteristic, complemented
13#21424128C211yesmaximal, characteristic, complemented
14#21424126C211yesmaximal, characteristic, complemented
15C59×#1854C211yesmaximal, characteristic, complemented
16C23×C4×D59C2211yescharacteristic
17C22×#11745659C2211yescharacteristic
18C22×#11745659C2211yescharacteristic
19C2×#14273686C2211yescharacteristic
20C2×C4⋊C4×D59C2211yescharacteristic
21C2×C4⋊C4×D59C2211yescharacteristic
22C2×C22⋊C4×D59—21no—
23C2×#14273661C2211yescharacteristic, complemented
24C2×#14273660C2211yescharacteristic, complemented
25C2×#14273660C2211yescharacteristic, complemented
26C2×#14273659C2211yescharacteristic, complemented
27C2×#14273658C2211yescharacteristic, complemented
28C2×#14273658C2211yescharacteristic, complemented
29#16837364C418yescomplemented
30C2×C22⋊(C59⋊C8)C2211yescharacteristic
31C2×(C2×D59)⋊C8C2211yescharacteristic
32C2×(C2×D59)⋊C8C2211yescharacteristic
33#16837263—21no—
34#16837262C2211yescharacteristic
35#16837261—21no—
36#16837260—21no—
37#16837259C2211yescharacteristic
38#16837259C2211yescharacteristic
39#16837259C2211yescharacteristic
40#16837259C2211yescharacteristic
41#16837259C2211yescharacteristic
42#16837259C2211yescharacteristic
43#16837257—21no—
44C4×(C2×D59)⋊C4—21no—
45C4×(C2×D59)⋊C4—21no—
46#95×D59—21no—
47#16837165C2211yescharacteristic, complemented
48#16837165C2211yescharacteristic, complemented
49#16837164C2211yescharacteristic, complemented
50#16837164C2211yescharacteristic, complemented
51#16837164C2211yescharacteristic, complemented
52#16837164C2211yescharacteristic, complemented
53C2×#117×C59C2211yescharacteristic
54C2×#107×C59C2211yescharacteristic, complemented
55C2×#106×C59C2211yescharacteristic, complemented
56C2×C22⋊C8×C59C2211yescharacteristic
57C59×#380C2211yescharacteristic
58C59×#340C2211yescharacteristic, complemented
59C59×#340C2211yescharacteristic, complemented
60C24×D59D411yescharacteristic
61C23×Dic59D411yescharacteristic
62C22×C4×D59—21no—
63C22×C4×D59—21no—
64C22×C4×D59—41no—
65C22×C4×D59—41no—
66C22×C4×D59—41no—
67C22×C4×D59—41no—
68C22×C4×D59C2×C414yes—
69C22×C4×D59D411yescharacteristic
70C22×C4×D59D411yescharacteristic
71C22×C4×D59Q814yes—
72C22×C4×D59C2311yescharacteristic
73C22×C4×D59C2311yescharacteristic
74C2×#11745659—41no—
75C2×#11745659—41no—
76C2×#11745659—41no—
77C2×#11745659—41no—
78C2×#11745659C2×C414yescomplemented
79C2×#11745659C2×C414yescomplemented
80C22×C59⋊C8C2311yescharacteristic
81C22×C59⋊C8C2311yescharacteristic
82#14273686—41no—
83#14273686—41no—
84C2×C4⋊Dic59C2311yescharacteristic
85C2×C4⋊Dic59C2311yescharacteristic
86C2×C4⋊Dic59C2311yescharacteristic
87C2×C4⋊Dic59C2311yescharacteristic
88C2×Dic59⋊C4—21no—
89C2×Dic59⋊C4—21no—
90C4⋊C4×D59—41no—
91C4⋊C4×D59—41no—
92C4⋊C4×D59—41no—
93C4⋊C4×D59—41no—
94C2×C22⋊Dic59—21no—
95C2×C22⋊Dic59—21no—
96C2×(C2×D59)⋊C4—21no—
97C2×(C2×D59)⋊C4—21no—
98C2×(C2×D59)⋊C4—21no—
99C2×(C2×D59)⋊C4—21no—
100C2×(C2×D59)⋊C4—21no—
101C2×(C2×D59)⋊C4—21no—
102C22⋊C4×D59—44no—
103C2×C4×Dic59—21no—
104#14273661—41no—
105#14273660—41no—
106#14273660—41no—
107#14273659—41no—
108#14273658—41no—
109#14273658—41no—
110C22⋊(C59⋊C8)C2×C414yescomplemented
111(C2×D59)⋊C8C2×C414yes—
112(C2×D59)⋊C8C2×C414yes—
113C59⋊#95—21no—
114C59⋊#95—21no—
115C59⋊#95—21no—
116C59⋊#95—21no—
117C59⋊#95—21no—
118C59⋊#95—21no—
119C59⋊#95—21no—
120C23×C4×C59C2311yescharacteristic
121C22×C8×C59C2311yescharacteristic
122C22×C8×C59C2311yescharacteristic
123#117×C59—41no—
124#117×C59—41no—
125C2×C4⋊C4×C59C2311yescharacteristic
126C2×C4⋊C4×C59C2311yescharacteristic
127C2×C4⋊C4×C59C2311yescharacteristic
128C2×C4⋊C4×C59C2311yescharacteristic
129C2×C22⋊C4×C59—21no—
130C2×C22⋊C4×C59—21no—
131C2×C42×C59—21no—
132#107×C59—41no—
133#106×C59—41no—
134C22⋊C8×C59C2×C414yescomplemented
135#95×C59—21no—
136C24×C59C2×D411yescharacteristic
137C23×D59—22no—
138C23×D59—22no—
139C23×D59—41no—
140C23×D59—41no—
141C23×D59—41no—
142C23×D59—41no—
143C23×D59C4⋊C414yes—
144C23×D59C2×D411yescharacteristic
145C23×D59C2×D411yescharacteristic
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×C59C22×C412yes—
155C22×C4×C59C2×D411yescharacteristic
156C22×C4×C59C2×Q812yes—
157C22×C4×C59C2411yescharacteristic
158C22×Dic59—21no—
159C22×Dic59—21no—
160C22×Dic59—21no—
161C22×Dic59—21no—
162C22×Dic59—41no—
163C22×Dic59—41no—
164C22×Dic59C4⋊C414yes—
165C22×Dic59C2×D411yescharacteristic
166C22×Dic59C2×D411yescharacteristic
167C2×C4×D59—21no—
168C2×C4×D59—21no—
169C2×C4×D59—21no—
170C2×C4×D59—21no—
171C2×C4×D59—21no—
172C2×C4×D59—21no—
173C2×C4×D59—21no—
174C2×C4×D59—21no—
175C2×C4×D59—44no—
176C2×C4×D59—44no—
177C2×C4×D59—44no—
178C2×C4×D59—44no—
179C2×C4×D59—41no—
180C2×C4×D59—41no—
181C2×C4×D59—41no—
182C2×C4×D59—41no—
183C2×C4×D59—42no—
184C2×C4×D59—42no—
185C2×C4×D59—42no—
186C2×C4×D59—42no—
187C2×C4×D59—42no—
188C2×C4×D59—42no—
189C2×C4×D59C4⋊C414yes—
190C2×C4×D59C4⋊C414yes—
191C2×C4×D59C22×C412yes—
192C2×C4×D59C22×C412yes—
193C2×C4×D59C2×Q812yes—
194C2×C4×D59C2×Q812yes—
195C2×C8×C59—21no—
196C2×C8×C59—21no—
197C2×C8×C59—21no—
198C2×C8×C59—21no—
199C2×C8×C59C22×C412yes—
200C2×C8×C59C22×C412yes—
201C4⋊C4×C59—21no—
202C4⋊C4×C59—21no—
203C4⋊C4×C59—21no—
204C4⋊C4×C59—21no—
205C4⋊C4×C59—21no—
206C4⋊C4×C59—21no—
207C4⋊C4×C59—21no—
208C4⋊C4×C59—21no—
209C22⋊C4×C59—42no—
210C22⋊C4×C59—42no—
211C42×C59—42no—
212C22⋊Dic59—42no—
213C22⋊Dic59—42no—
214(C2×D59)⋊C4—42no—
215(C2×D59)⋊C4—42no—
216(C2×D59)⋊C4—42no—
217(C2×D59)⋊C4—42no—
218(C2×D59)⋊C4—42no—
219(C2×D59)⋊C4—42no—
220C4⋊Dic59—21no—
221C4⋊Dic59—21no—
222C4⋊Dic59—21no—
223C4⋊Dic59—21no—
224C4⋊Dic59—21no—
225C4⋊Dic59—21no—
226C4⋊Dic59—21no—
227C4⋊Dic59—21no—
228Dic59⋊C4—42no—
229Dic59⋊C4—42no—
230C4×Dic59—42no—
231C2×C59⋊C8—21no—
232C2×C59⋊C8—21no—
233C2×C59⋊C8—21no—
234C2×C59⋊C8—21no—
235C2×C59⋊C8C22×C412yes—
236C2×C59⋊C8C22×C412yes—
237#11745659—44no—
238#11745659—44no—
239C23×C59—21no—
240C23×C59—21no—
241C23×C59—21no—
242C23×C59—21no—
243C23×C59—21no—
244C23×C59—21no—
245C23×C59C2×C4⋊C412yes—
246C23×C59C22×D411yescharacteristic
247C22×D59—21no—
248C22×D59—21no—
249C22×D59—21no—
250C22×D59—21no—
251C22×D59—21no—
252C22×D59—21no—
253C22×D59—21no—
254C22×D59—21no—
255C22×D59—21no—
256C22×D59—21no—
257C22×D59—28no—
258C22×D59—44no—
259C22×D59—44no—
260C22×D59—44no—
261C22×D59—44no—
262C22×D59—44no—
263C22×D59—44no—
264C22×D59C2×C4⋊C412yes—
265C22×D59C2×C4⋊C412yes—
266C22×D59AGL(1,ℤ/8)12yes—
267C22×D59#13712yes—
268C2×C4×C59—21no—
269C2×C4×C59—21no—
270C2×C4×C59—22no—
271C2×C4×C59—22no—
272C2×C4×C59—22no—
273C2×C4×C59—22no—
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—41no—
284C2×C4×C59—41no—
285C2×C4×C59—41no—
286C2×C4×C59C2×C4⋊C412yes—
287C2×C4×C59C23×C411yescharacteristic
288C2×C4×C59C22×Q811yescharacteristic
289C2×C4×C59H(5,𝔽2)11yescharacteristic
290C2×C4×C59H(5,𝔽2)11yescharacteristic
291C2×C4×C59H(5,𝔽2)11yescharacteristic
292C2×C4×C59H(5,𝔽2)11yescharacteristic
293C2×Dic59—21no—
294C2×Dic59—21no—
295C2×Dic59—21no—
296C2×Dic59—21no—
297C2×Dic59—44no—
298C2×Dic59—41no—
299C2×Dic59—41no—
300C2×Dic59—41no—
301C2×Dic59—41no—
302C2×Dic59—41no—
303C2×Dic59—41no—
304C2×Dic59—41no—
305C2×Dic59—41no—
306C2×Dic59—41no—
307C2×Dic59—41no—
308C2×Dic59—41no—
309C2×Dic59—41no—
310C2×Dic59C2×C4⋊C412yes—
311C2×Dic59C2×C4⋊C412yes—
312C4×D59—22no—
313C4×D59—22no—
314C4×D59—22no—
315C4×D59—22no—
316C4×D59—22no—
317C4×D59—22no—
318C4×D59—22no—
319C4×D59—22no—
320C4×D59—44no—
321C4×D59—44no—
322C4×D59—84no—
323C4×D59—84no—
324C8×C59—22no—
325C8×C59—22no—
326C59⋊C8—22no—
327C59⋊C8—22no—
328#21944—591nomaximal, Sylow
329C22×C59—22no—
330C22×C59—22no—
331C22×C59—22no—
332C22×C59—41no—
333C22×C59—41no—
334C22×C59—41no—
335C22×C59—41no—
336C22×C59C22×C4⋊C411yescharacteristic
337C22×C59#53411yescharacteristic
338C22×C59#53411yescharacteristic
339C22×C59C2×AGL(1,ℤ/8)11yescharacteristic
340C22×C59C2×#13711yescharacteristic
341C22×C59#57511yescharacteristic
342C22×C59#57511yescharacteristic
343C2×D59—22no—
344C2×D59—22no—
345C2×D59—22no—
346C2×D59—22no—
347C2×D59—22no—
348C2×D59—22no—
349C2×D59—22no—
350C2×D59—22no—
351C2×D59—22no—
352C2×D59—416no—
353C2×D59—41no—
354C2×D59—41no—
355C2×D59—41no—
356C2×D59—41no—
357C2×D59#42814yes—
358C4×C59—22no—
359C4×C59—81no—
360C4×C59—81no—
361C4×C59—81no—
362C4×C59—81no—
363C4×C59#51811yescharacteristic
364C4×C59#51811yescharacteristic
365C4×C59#54311yescharacteristic
366C4×C59#54311yescharacteristic
367Dic59—22no—
368Dic59—22no—
369Dic59—81no—
370Dic59—81no—
371Dic59—81no—
372Dic59—81no—
373C2×#407—591no—
374#2280—591no—
375C2×#380—591no—
376#1854—591no—
377#1854—591no—
378#1854—591no—
379#1854D5911yescharacteristic, complemented
380#1853—591no—
381#1853—591no—
382#1852—591no—
383#1852—591no—
384#1809—591no—
385#1809—591no—
386#1809—591no—
387#1809—591no—
388C2×C59—42no—
389C2×C59#231511yescharacteristic
390C2×C59C2×#42811yescharacteristic
391C2×C59#291111yescharacteristic
392C2×C59#319411yescharacteristic
393C2×C59#319411yescharacteristic
394C2×C59#319611yescharacteristic
395C2×C59#319611yescharacteristic
396D59—24no—
397D59—42no—
398C24×C4—591no—
399C22×M16—591no—
400C22×M16—591no—
401C2×#117—591no—
402C2×#117C2×D5911yescharacteristic
403C22×C4⋊C4—591no—
404C22×C4⋊C4—591no—
405C22×C22⋊C4—1181no—
406C2×#107—591no—
407C2×#107—591no—
408C2×#107—591no—
409C2×#107C2×D5911yescharacteristic, complemented
410C2×#106—591no—
411C2×#106—591no—
412C2×#106—591no—
413C2×#106C2×D5911yescharacteristic, complemented
414#407—598no—
415C2×C22⋊C8—591no—
416C2×C22⋊C8—591no—
417C2×C22⋊C8—591no—
418C2×C22⋊C8C2×D5911yescharacteristic
419#381—1181no—
420#380—591no—
421#380—591no—
422#380—591no—
423#380—591no—
424#380—591no—
425#380—591no—
426#380—591no—
427#380—1181no—
428#380—1181no—
429#380C2×D5911yescharacteristic
430#379—1181no—
431C4×C22⋊C4—1181no—
432C4×C22⋊C4—1181no—
433C2×#95—1181no—
434#340—591no—
435#340—591no—
436#340—591no—
437#340—591no—
438#340—591no—
439#340—591no—
440#340C2×D5911yescharacteristic, complemented
441#340C2×D5911yescharacteristic, complemented
442C59#2194411yescharacteristic, complemented, Sylow
443C25—591no—
444C23×C4—591no—
445C23×C4—591no—
446C23×C4—591no—
447C23×C4—594no—
448C23×C4—591no—
449C23×C4—591no—
450C23×C4—594no—
451C23×C4—1181no—
452C23×C4—1181no—
453C23×C4—2361no—
454C23×C4—2361no—
455C23×C4—2361no—
456C23×C4—2361no—
457C23×C4C22×D5911yescharacteristic
458C2×M16—594no—
459C2×M16—594no—
460C2×M16—2361no—
461C2×M16—2361no—
462C2×M16—2361no—
463C2×M16—2361no—
464C22×C8—591no—
465C22×C8—591no—
466C22×C8C22×D5911yescharacteristic
467C22×C8C22×D5911yescharacteristic
468#117—41no—
469#117—41no—
470#117—2361no—
471#117—2361no—
472C2×C4⋊C4—591no—
473C2×C4⋊C4—591no—
474C2×C4⋊C4—591no—
475C2×C4⋊C4—591no—
476C2×C4⋊C4—1181no—
477C2×C4⋊C4—1181no—
478C2×C4⋊C4—2361no—
479C2×C4⋊C4—2361no—
480C2×C4⋊C4—2361no—
481C2×C4⋊C4—2361no—
482C2×C4⋊C4C22×D5911yescharacteristic
483C2×C4⋊C4C22×D5911yescharacteristic
484C2×C4⋊C4C22×D5911yescharacteristic
485C2×C4⋊C4C22×D5911yescharacteristic
486C2×C22⋊C4—21no—
487C2×C22⋊C4—21no—
488C2×C22⋊C4—1181no—
489C2×C22⋊C4—1181no—
490C2×C22⋊C4—1181no—
491C2×C22⋊C4—1181no—
492C2×C22⋊C4—1181no—
493C2×C22⋊C4—1181no—
494C2×C22⋊C4—1181no—
495C2×C22⋊C4—1181no—
496C2×C22⋊C4—2364no—
497C2×C42—21no—
498C2×C42—1181no—
499#107—41no—
500#107—2361no—
501#107—2361no—
502#107—2361no—
503#106—41no—
504#106—2361no—
505#106—2361no—
506#106—2361no—
507C22⋊C8—594no—
508C22⋊C8—594no—
509C22⋊C8—594no—
510C22⋊C8C4×D5914yescomplemented
511#95—21no—
512#95—1181no—
513#95—1181no—
514#95—1181no—
515#95—1181no—
516#95—1181no—
517#95—1181no—
518#95—1181no—
519C24—591no—
520C24—591no—
521C24—594no—
522C24—1182no—
523C24—1182no—
524C24—2361no—
525C24—2361no—
526C24—2361no—
527C24—2361no—
528C24D4×D5911yescharacteristic
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—591no—
538C22×C4—591no—
539C22×C4—594no—
540C22×C4—592no—
541C22×C4—592no—
542C22×C4—592no—
543C22×C4—592no—
544C22×C4—594no—
545C22×C4—594no—
546C22×C4—1181no—
547C22×C4—1181no—
548C22×C4—1181no—
549C22×C4—1181no—
550C22×C4—1181no—
551C22×C4—1181no—
552C22×C4—1181no—
553C22×C4—1181no—
554C22×C4—1181no—
555C22×C4—1181no—
556C22×C4—1181no—
557C22×C4—1181no—
558C22×C4—2364no—
559C22×C4—2364no—
560C22×C4—2364no—
561C22×C4—2364no—
562C22×C4—2361no—
563C22×C4—2361no—
564C22×C4—2361no—
565C22×C4—2361no—
566C22×C4—2362no—
567C22×C4—2362no—
568C22×C4—2362no—
569C22×C4—2362no—
570C22×C4—2362no—
571C22×C4—2362no—
572C22×C4—2361no—
573C22×C4—2361no—
574C22×C4C2×C4×D5912yes—
575C22×C4D4×D5911yescharacteristic
576C22×C4Q8×D5912yes—
577C22×C4C23×D5911yescharacteristic
578M16—2364no—
579M16—2364no—
580C2×C8—21no—
581C2×C8—21no—
582C2×C8—21no—
583C2×C8—21no—
584C2×C8—592no—
585C2×C8—592no—
586C2×C8—1181no—
587C2×C8—1181no—
588C2×C8—1181no—
589C2×C8—1181no—
590C2×C8C2×C4×D5912yes—
591C2×C8C2×C4×D5912yes—
592C4⋊C4—21no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—21no—
596C4⋊C4—21no—
597C4⋊C4—21no—
598C4⋊C4—21no—
599C4⋊C4—21no—
600C4⋊C4—1181no—
601C4⋊C4—1181no—
602C4⋊C4—1181no—
603C4⋊C4—1181no—
604C4⋊C4—1181no—
605C4⋊C4—1181no—
606C4⋊C4—1181no—
607C4⋊C4—1181no—
608C4⋊C4—2362no—
609C4⋊C4—2362no—
610C22⋊C4—42no—
611C22⋊C4—42no—
612C22⋊C4—2362no—
613C22⋊C4—2362no—
614C22⋊C4—2362no—
615C22⋊C4—2362no—
616C22⋊C4—2362no—
617C22⋊C4—2362no—
618C22⋊C4—2362no—
619C22⋊C4—2362no—
620C42—42no—
621C42—2362no—
622C23—21no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—21no—
627C23—21no—
628C23—592no—
629C23—592no—
630C23—592no—
631C23—592no—
632C23—1188no—
633C23—1181no—
634C23—1181no—
635C23—1181no—
636C23—1181no—
637C23—1181no—
638C23—1181no—
639C23—1181no—
640C23—1181no—
641C23—1181no—
642C23—1181no—
643C23—2364no—
644C23—2364no—
645C23—2364no—
646C23—2364no—
647C23—2364no—
648C23—2364no—
649C23C4⋊C4×D5912yes—
650C23C2×D4×D5911yescharacteristic
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—592no—
670C2×C4—592no—
671C2×C4—1181no—
672C2×C4—1181no—
673C2×C4—1181no—
674C2×C4—1181no—
675C2×C4—1182no—
676C2×C4—1182no—
677C2×C4—1182no—
678C2×C4—1182no—
679C2×C4—1182no—
680C2×C4—1182no—
681C2×C4—1182no—
682C2×C4—1182no—
683C2×C4—4724no—
684C2×C4—4724no—
685C2×C4—2364no—
686C2×C4—2364no—
687C2×C4—2364no—
688C2×C4—2361no—
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×C4C4⋊C4×D5912yes—
701C2×C4C22×C4×D5911yescharacteristic
702C2×C4C2×Q8×D5911yescharacteristic
703C2×C4#1427377211yescharacteristic
704C2×C4#1427377211yescharacteristic
705C2×C4#1427377311yescharacteristic
706C2×C4#1427377311yescharacteristic
707C8—22no—
708C8—22no—
709C8—1182no—
710C8—1182no—
711C22—22no—
712C22—22no—
713C22—22no—
714C22—41no—
715C22—41no—
716C22—41no—
717C22—41no—
718C22—594no—
719C22—1182no—
720C22—1182no—
721C22—1182no—
722C22—1182no—
723C22—1182no—
724C22—1182no—
725C22—1182no—
726C22—1182no—
727C22—1182no—
728C22—23616no—
729C22—2361no—
730C22—2361no—
731C22—2361no—
732C22—2361no—
733C22C2×C4⋊C4×D5911yescharacteristic
734C22#1683796211yescharacteristic
735C22#1683796311yescharacteristic
736C22AGL(1,ℤ/8)×D5911yescharacteristic
737C22#137×D5911yescharacteristic
738C22#1683819911yescharacteristic
739C22#1683819911yescharacteristic
740C4—22no—
741C4—81no—
742C4—81no—
743C4—81no—
744C4—81no—
745C4—1182no—
746C4—1182no—
747C4—4721no—
748C4—4721no—
749C4—4721no—
750C4—4721no—
751C4#1683787411yescharacteristic
752C4#1683787411yescharacteristic
753C4#1683802711yescharacteristic
754C4#1683802711yescharacteristic
755C2—42no—
756C2—1184no—
757C2—2362no—
758C2#2142670711yescharacteristic
759C2#428×D5911yescharacteristic
760C2#2143268411yescharacteristic
761C2#2143490811yescharacteristic
762C2#2143491411yescharacteristic
763C2#2143492411yescharacteristic
764C2#2143493011yescharacteristic
subgroupG/H
centerC23C2×D4×D59
commutatorC2×C4×C59C23×C4
FrattiniC22×C4C23×D59
FittingC59×#1854C2
socleC23×C59C22×D4
prime radicalC24×D59D4
cosocleC22×C4×C59C24
hypercenter#1854D59
hypocenterC59#21944
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1854

Complements

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

NH ≅ G/Ntype
4. #21424297C2semidirect
5. #21424295C2semidirect
6. #21424293C2semidirect
7. #21424290C2semidirect
8. #21424287C2semidirect
9. #21424285C2semidirect
10. #21424282C2semidirect
11. #21424130C2semidirect
12. #21424128C2semidirect
13. #21424128C2semidirect
14. #21424126C2semidirect
15. C59×#1854C2semidirect
23. C2×#14273661C22semidirect
24. C2×#14273660C22semidirect
25. C2×#14273660C22semidirect
26. C2×#14273659C22semidirect
27. C2×#14273658C22semidirect
28. C2×#14273658C22semidirect
29. #16837364C4semidirect
47. #16837165C22semidirect
48. #16837165C22semidirect
49. #16837164C22semidirect
50. #16837164C22semidirect
51. #16837164C22semidirect
52. #16837164C22semidirect
54. C2×#107×C59C22semidirect
55. C2×#106×C59C22semidirect
58. C59×#340C22semidirect
59. C59×#340C22semidirect
78. C2×#11745659C2×C4semidirect
79. C2×#11745659C2×C4semidirect
110. C22⋊(C59⋊C8)C2×C4semidirect
134. C22⋊C8×C59C2×C4semidirect
379. #1854D59semidirect
409. C2×#107C2×D59semidirect
413. C2×#106C2×D59semidirect
440. #340C2×D59semidirect
441. #340C2×D59semidirect
442. C59#21944semidirect
510. C22⋊C8C4×D59semidirect

Maximal subgroups

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

subgroupindex
C2×#168373642
#214264752
#380×D592
#214242972
#214242952
#214242932
#214242902
#214242872
#214242852
#214242822
#214241302
#214241282
#214241262
C59×#18542
#2194459