Finite Group Databasebeta

← C2×#21433632 #29455611

Subgroups — C2×#21433632 #29455611

Order 15104.

2934 conjugacy classes of subgroups.

The subgroup lattice has 896 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14273754C211yesmaximal, characteristic, complemented
2C22×#14273748C211yesmaximal, characteristic, complemented
3C2×#16837965C211yesmaximal, characteristic, complemented
4C2×#16837884C211yesmaximal, characteristic, complemented
5#21433632C2116yesmaximal, direct product factor
6C2×#16837624C211yesmaximal, characteristic, complemented
7C2×#16837622C211yesmaximal, characteristic, complemented
8C2×#16837600C211yesmaximal, characteristic, complemented
9C2×#16837618C211yesmaximal, characteristic, complemented
10C2×#16837616C211yesmaximal, characteristic, complemented
11C2×#16837596C211yesmaximal, characteristic, complemented
12C2×#16837594C211yesmaximal, characteristic, complemented
13C2×#16837427C211yesmaximal, characteristic, complemented
14C2×#16837400C211yesmaximal, characteristic, complemented
15C2×#102×D59C211yesmaximal, characteristic, complemented
16C2×C59×#460C211yesmaximal, characteristic, complemented
17C22×#11745689C2211yescharacteristic
18C22×#11745687C2211yescharacteristic
19C22×D4×D59C2211yescharacteristic
20C2×#14273754—28no—
21C2×#14273754C2218yescomplemented
22C2×#14273748—28no—
23C2×#14273748C2218yescomplemented
24C22×#11745672C2211yescharacteristic, complemented
25C22×#11745660C2211yescharacteristic, complemented
26C22×#11745671C2211yescharacteristic
27C22×D472C2211yescharacteristic
28C22×#11745669C2211yescharacteristic
29C22×#11745669C2211yescharacteristic, complemented
30C22×#11745659C2211yescharacteristic
31C22×C8×D59C2211yescharacteristic
32#16837965—24no—
33#16837965C2218yescomplemented
34C2×#14273723C2211yescharacteristic
35C2×#14273715C2211yescharacteristic
36C2×#14273714C2211yescharacteristic
37C2×#14273699—21no—
38C2×#14273699—21no—
39C2×#14273695—21no—
40C2×#14273695—21no—
41#16837884—24no—
42#16837884C2218yescomplemented
43C2×Q8×Dic59C2211yescharacteristic, complemented
44C2×C4×D236—21no—
45C2×C4×D236C2211yescharacteristic, complemented
46C2×#14273689—21no—
47C2×#14273689C2211yescharacteristic, complemented
48C2×#14273684—21no—
49C2×#14273684C2211yescharacteristic
50C2×C4⋊C4×D59—21no—
51C2×C4⋊C4×D59C2211yescharacteristic
52#16837624C2218yescomplemented
53#16837622C2218yescomplemented
54#16837618C2218yescomplemented
55#16837616C2218yescomplemented
56#16837600C2218yescomplemented
57#16837596C2218yescomplemented
58#16837594C2218yescomplemented
59#16837427C2218yescomplemented
60C2×C4⋊(C59⋊C8)C2211yescharacteristic, complemented
61C2×Dic59⋊C8C2211yescharacteristic, complemented
62C2×Dic59⋊C8C2211yescharacteristic, complemented
63#16837400C2218yescomplemented
64C2×#14273652C2211yescharacteristic, complemented
65C2×#14273650C2211yescharacteristic, complemented
66C2×#14273649C2211yescharacteristic
67C2×#14273648C2211yescharacteristic
68C2×#14273648C2211yescharacteristic, complemented
69C2×#14273647C2211yescharacteristic
70#102×D59C2218yescomplemented
71C22×SD16×C59C2211yescharacteristic
72C22×SD16×C59C2211yescharacteristic, complemented
73C2×#127×C59C2211yescharacteristic
74C2×C4×Q8×C59C2211yescharacteristic, complemented
75C59×#460C2218yescomplemented
76C2×C4⋊C8×C59C2211yescharacteristic, complemented
77C2×#102×C59C2211yescharacteristic
78C2×#102×C59C2211yescharacteristic, complemented
79C24×D59—21no—
80C2×#11745689—22no—
81C2×#11745689—24no—
82C2×#11745689D418yescomplemented
83C2×#11745689C2314yes—
84C2×#11745687—24no—
85C2×#11745687—22no—
86C2×#11745687—24no—
87C2×#11745687C2314yes—
88C22×Dic118C2311yescharacteristic
89C22×D236—21no—
90C22×D236C2311yescharacteristic
91C22×D236C2311yescharacteristic
92C22×C22⋊D59—21no—
93C22×C22⋊D59—21no—
94C22×C22⋊D59—21no—
95C22×C22⋊D59—21no—
96C2×D4×D59—24no—
97C2×D4×D59—22no—
98C2×D4×D59—24no—
99C2×D4×D59C2314yes—
100C23×Dic59—21no—
101C22×C4×D59—21no—
102C22×C4×D59—21no—
103C22×C4×D59—21no—
104C22×C4×D59—21no—
105C22×C4×D59C2311yescharacteristic
106#14273754—232no—
107#14273748—232no—
108C2×#11745672—24no—
109C2×#11745672C2314yescomplemented
110C2×#11745660—24no—
111C2×#11745660C2314yescomplemented
112C2×#11745671—24no—
113C2×#11745671C2314yes—
114C2×D472—24no—
115C2×D472C2314yes—
116C2×#11745669—24no—
117C2×#11745669—24no—
118C2×#11745669C2314yes—
119C2×#11745669C2314yescomplemented
120C2×#11745659—24no—
121C2×#11745659C2314yes—
122C22×C59⋊C8C2311yescharacteristic
123C22×C59⋊C8C2311yescharacteristic
124C2×C8×D59—24no—
125C2×C8×D59C2314yes—
126#14273723—22no—
127#14273723C2314yes—
128#14273715—22no—
129#14273715C2314yes—
130#14273714—22no—
131#14273714C2314yes—
132#14273699—28no—
133#14273699—28no—
134#14273695—28no—
135#14273695—28no—
136Q8×Dic59—22no—
137Q8×Dic59C2314yescomplemented
138C4×D236—22no—
139C4×D236—28no—
140C4×D236C2314yescomplemented
141#14273689—28no—
142#14273689—22no—
143#14273689C2314yescomplemented
144#14273684—28no—
145#14273684D414yes—
146#14273684C2314yes—
147C2×C4⋊Dic59—21no—
148C2×C4⋊Dic59C2311yescharacteristic
149C2×Dic59⋊C4—21no—
150C2×Dic59⋊C4D411yescharacteristic
151C2×Dic59⋊C4D411yescharacteristic
152C4⋊C4×D59—22no—
153C4⋊C4×D59—28no—
154C4⋊C4×D59C2314yes—
155C2×C22⋊Dic59—21no—
156C2×C22⋊Dic59—21no—
157C2×(C2×D59)⋊C4—21no—
158C2×(C2×D59)⋊C4—21no—
159C2×(C2×D59)⋊C4—21no—
160C2×(C2×D59)⋊C4—21no—
161C2×(C2×D59)⋊C4D411yescharacteristic
162C2×(C2×D59)⋊C4D411yescharacteristic
163C2×C4×Dic59—21no—
164C2×C4×Dic59C2311yescharacteristic
165C4⋊(C59⋊C8)C2314yescomplemented
166Dic59⋊C8C2314yescomplemented
167Dic59⋊C8C2314yescomplemented
168#14273652C2314yescomplemented
169#14273650C2314yescomplemented
170#14273649C2314yes—
171#14273648C2314yes—
172#14273648C2314yescomplemented
173#14273647C2314yes—
174C22×Q8×C59C2311yescharacteristic
175C22×D4×C59—21no—
176C22×D4×C59—21no—
177C22×D4×C59C2311yescharacteristic
178C22×D4×C59C2311yescharacteristic
179C2×SD16×C59—24no—
180C2×SD16×C59—24no—
181C2×SD16×C59C2314yes—
182C2×SD16×C59C2314yescomplemented
183C22×C8×C59C2311yescharacteristic
184C22×C8×C59C2311yescharacteristic
185#127×C59—22no—
186#127×C59C2314yes—
187C4×Q8×C59—22no—
188C4×Q8×C59C2314yescomplemented
189C2×C4⋊C4×C59—21no—
190C2×C4⋊C4×C59C2311yescharacteristic
191C2×C42×C59—21no—
192C2×C42×C59C2311yescharacteristic
193C4⋊C8×C59C2314yescomplemented
194#102×C59C2314yes—
195#102×C59C2314yescomplemented
196C24×C59—21no—
197C24×C59—21no—
198C23×D59—21no—
199C23×D59—21no—
200C23×D59—24no—
201C23×D59—44no—
202C23×D59—82no—
203C23×D59—82no—
204C23×D59C2×D411yescharacteristic
205C2×Q8×C59—21no—
206C2×Q8×C59—22no—
207C2×Q8×C59C2×D414yes—
208C2×Q8×C59C2412yes—
209C2×D4×C59—22no—
210C2×D4×C59—22no—
211C2×D4×C59—21no—
212C2×D4×C59—21no—
213C2×D4×C59—24no—
214C2×D4×C59—24no—
215C2×D4×C59—22no—
216C2×D4×C59—22no—
217C2×D4×C59—82no—
218C2×D4×C59—82no—
219C2×D4×C59C2412yes—
220C2×D4×C59C2412yes—
221C22×C4×C59—21no—
222C22×C4×C59—21no—
223C22×C4×C59C2×D411yescharacteristic
224C22×C4×C59C2×D411yescharacteristic
225C22×C4×C59C2411yescharacteristic
226C2×C22⋊D59—24no—
227C2×C22⋊D59—24no—
228C2×C22⋊D59—24no—
229C2×C22⋊D59—24no—
230C2×C22⋊D59—44no—
231C2×C22⋊D59—44no—
232C2×C22⋊D59—82no—
233C2×C22⋊D59—82no—
234C22×Dic59—21no—
235C22×Dic59—21no—
236C22×Dic59—24no—
237C22×Dic59—44no—
238C22×Dic59C2×D411yescharacteristic
239C22×Dic59C2×D411yescharacteristic
240C22×Dic59C2×D411yescharacteristic
241#11745689—216no—
242#11745689—28no—
243#11745689C2×D4116yescomplemented
244#11745687—28no—
245#11745687—28no—
246#11745687—48no—
247D4×D59—28no—
248D4×D59—28no—
249D4×D59—48no—
250C2×D236—28no—
251C2×D236—24no—
252C2×D236—21no—
253C2×D236—22no—
254C2×D236—22no—
255C2×D236—22no—
256C2×D236—21no—
257C2×D236C2×D414yes—
258C2×D236C2412yes—
259C2×D236C2412yes—
260C2×C4×D59—28no—
261C2×C4×D59—24no—
262C2×C4×D59—24no—
263C2×C4×D59—24no—
264C2×C4×D59—24no—
265C2×C4×D59—82no—
266C2×C4×D59—82no—
267C2×C4×D59—82no—
268C2×C4×D59C2×D412yes—
269C2×C4×D59C2×D414yes—
270C2×C4×D59#4114yes—
271C2×C4×D59C2412yes—
272C2×Dic118—22no—
273C2×Dic118—22no—
274C2×Dic118—21no—
275C2×Dic118C2412yes—
276SD16×C59—28no—
277SD16×C59—28no—
278C2×C8×C59—22no—
279C2×C8×C59—22no—
280C2×C8×C59C2412yes—
281C2×C8×C59C2412yes—
282C4⋊C4×C59—24no—
283C4⋊C4×C59—21no—
284C4⋊C4×C59C2412yes—
285C42×C59—24no—
286C42×C59C2×D412yes—
287C42×C59C2412yes—
288C22⋊Dic59—24no—
289C22⋊Dic59—24no—
290#11745672—28no—
291#11745671—28no—
292#11745669—28no—
293#11745669—28no—
294(C2×D59)⋊C4—24no—
295(C2×D59)⋊C4—24no—
296(C2×D59)⋊C4—24no—
297(C2×D59)⋊C4—24no—
298(C2×D59)⋊C4C2×D414yes—
299(C2×D59)⋊C4C2×D414yes—
300C4⋊Dic59—21no—
301C4⋊Dic59—24no—
302C4⋊Dic59C2412yes—
303Dic59⋊C4—24no—
304Dic59⋊C4C2×D414yes—
305Dic59⋊C4C2×D414yes—
306C4×Dic59—24no—
307C4×Dic59C2×D412yes—
308C4×Dic59C2412yes—
309C2×C59⋊C8—22no—
310C2×C59⋊C8—22no—
311C2×C59⋊C8C2412yes—
312C2×C59⋊C8C2412yes—
313D472—28no—
314#11745660—28no—
315#11745659—28no—
316C8×D59—28no—
317C23×C59—22no—
318C23×C59—22no—
319C23×C59—42no—
320C23×C59—42no—
321C23×C59—42no—
322C23×C59—42no—
323C23×C59—42no—
324C23×C59—42no—
325C23×C59C22×D411yescharacteristic
326C22×D59—22no—
327C22×D59—22no—
328C22×D59—24no—
329C22×D59—22no—
330C22×D59—22no—
331C22×D59—42no—
332C22×D59—42no—
333C22×D59—42no—
334C22×D59—42no—
335C22×D59—42no—
336C22×D59—48no—
337C22×D59—84no—
338C22×D59—84no—
339C22×D59—816no—
340C22×D59#12114yes—
341C22×D59C22×D412yes—
342Q8×C59—24no—
343Q8×C59—22no—
344Q8×C59C22×D414yes—
345D4×C59—22no—
346D4×C59—22no—
347D4×C59—22no—
348D4×C59—22no—
349D4×C59—42no—
350D4×C59—42no—
351D4×C59—84no—
352D4×C59—84no—
353C2×C4×C59—24no—
354C2×C4×C59—22no—
355C2×C4×C59—22no—
356C2×C4×C59—22no—
357C2×C4×C59—22no—
358C2×C4×C59—42no—
359C2×C4×C59C22×D412yes—
360C2×C4×C59C22×D412yes—
361C2×C4×C59C22×D411yescharacteristic
362C2×C4×C59C22×D412yes—
363C2×C4×C59C2×#4112yes—
364C2×C4×C59C2511yescharacteristic
365C22⋊D59—48no—
366C22⋊D59—48no—
367C22⋊D59—84no—
368C22⋊D59—84no—
369C2×Dic59—22no—
370C2×Dic59—22no—
371C2×Dic59—22no—
372C2×Dic59—22no—
373C2×Dic59—42no—
374C2×Dic59—42no—
375C2×Dic59—48no—
376C2×Dic59#12114yes—
377C2×Dic59C22×D412yes—
378C2×Dic59C22×D412yes—
379C2×Dic59C22×D412yes—
380D236—216no—
381D236—24no—
382D236—22no—
383D236—22no—
384D236—22no—
385D236—42no—
386D236C22×D414yes—
387C4×D59—216no—
388C4×D59—84no—
389C4×D59—84no—
390C4×D59—84no—
391C4×D59#12118yes—
392C4×D59C22×D414yes—
393C4×D59C2×#4114yes—
394Dic118—22no—
395Dic118—22no—
396Dic118—42no—
397C8×C59—22no—
398C8×C59—22no—
399C59⋊C8—22no—
400C59⋊C8—22no—
401C2×#3045—591nomaximal, Sylow
402C22×C59—42no—
403C22×C59—42no—
404C22×C59—42no—
405C22×C59—42no—
406C22×C59—42no—
407C22×C59—42no—
408C22×C59—84no—
409C22×C59—84no—
410C22×C59C2×#12112yes—
411C22×C59#57612yes—
412C22×C59#57712yes—
413C22×C59C23×D411yescharacteristic
414C2×D59—28no—
415C2×D59—22no—
416C2×D59—22no—
417C2×D59—24no—
418C2×D59—48no—
419C2×D59—42no—
420C2×D59—42no—
421C2×D59—42no—
422C2×D59—42no—
423C2×D59—42no—
424C2×D59—816no—
425C2×D59—84no—
426C2×D59C2×#12114yes—
427C4×C59—24no—
428C4×C59—22no—
429C4×C59—22no—
430C4×C59—42no—
431C4×C59C2×#12112yes—
432C4×C59C23×D411yescharacteristic
433C4×C59C22×#4111yescharacteristic
434Dic59—22no—
435Dic59—22no—
436Dic59—42no—
437Dic59—42no—
438Dic59C2×#12114yes—
439C22×AGL(1,ℤ/8)—591no—
440C22×#135—591no—
441C2×#535—591no—
442C2×#520—591no—
443#3045—5916no—
444C2×#464—591no—
445C2×#464—591no—
446C2×#460—591no—
447C2×#460D5911yescharacteristic, complemented
448C2×#463—591no—
449C2×#463—591no—
450C2×#459—591no—
451C2×#459—591no—
452C2×#424—591no—
453C2×#417—591no—
454C22×#102—591no—
455C2×C59—82no—
456C2×C59—82no—
457C2×C59#304514yescomplemented
458C2×C59C22×#12111yescharacteristic
459C2×C59C2×#57611yescharacteristic
460C2×C59C2×#57711yescharacteristic
461D59—24no—
462D59—44no—
463D59—82no—
464C22×#41—591no—
465C22×#41—591no—
466C23×D4—591no—
467C2×AGL(1,ℤ/8)—598no—
468C2×AGL(1,ℤ/8)—1188no—
469C2×#135—598no—
470C2×#135—1188no—
471C22×Q16—591no—
472C22×SD16—591no—
473C22×SD16—591no—
474C22×SD16C2×D5911yescharacteristic
475C22×SD16C2×D5911yescharacteristic, complemented
476C22×D8—591no—
477C22×D8—591no—
478C22×D8—591no—
479C22×M16—591no—
480C23×C8—591no—
481#535—598no—
482#535—1184no—
483C2×#127—591no—
484C2×#127C2×D5911yescharacteristic
485C2×#124—591no—
486C2×#124—591no—
487C2×#121—1181no—
488C2×#121—1181no—
489C2×#120—1181no—
490C2×#120—1181no—
491#520—598no—
492#520—1184no—
493C2×C4×Q8—591no—
494C2×C4×Q8C2×D5911yescharacteristic, complemented
495C2×C4×D4—591no—
496C2×C4×D4—591no—
497C2×C4×D4—1181no—
498C2×C4×D4—1181no—
499C2×#117—591no—
500C2×#117—1181no—
501C22×C4⋊C4—591no—
502C22×C4⋊C4—1181no—
503#464—598no—
504#464—598no—
505#463—598no—
506#463—598no—
507#460—598no—
508#460C2×D5918yescomplemented
509#459—598no—
510#459—598no—
511#424—598no—
512C2×C4⋊C8—591no—
513C2×C4⋊C8—591no—
514C2×C4⋊C8—591no—
515C2×C4⋊C8C2×D5911yescharacteristic, complemented
516#417—598no—
517C2×#103—591no—
518C2×#103—591no—
519C2×#102—591no—
520C2×#102—591no—
521C2×#102—591no—
522C2×#102—591no—
523C2×#102—598no—
524C2×#102C2×D5911yescharacteristic
525C2×#102C2×D5911yescharacteristic, complemented
526C59C2×#304511yescharacteristic, complemented, Sylow
527C25—1181no—
528C2×#41—598no—
529C2×#41—594no—
530C2×#41—594no—
531C2×#41—1182no—
532C2×#41—1182no—
533C2×#41—1184no—
534C2×#41—1184no—
535C2×#41—1184no—
536C22×Q8—591no—
537C22×Q8C22×D5911yescharacteristic
538C22×D4—21no—
539C22×D4—21no—
540C22×D4—594no—
541C22×D4—591no—
542C22×D4—591no—
543C22×D4—1181no—
544C22×D4—1184no—
545C22×D4—1184no—
546C22×D4—1182no—
547C22×D4—1181no—
548C22×D4—1181no—
549C22×D4—1181no—
550C22×D4—1181no—
551C22×D4C22×D5911yescharacteristic
552C22×D4C22×D5911yescharacteristic
553C23×C4—591no—
554C23×C4—1181no—
555C23×C4—1181no—
556C23×C4—1181no—
557C23×C4—1181no—
558C23×C4—1181no—
559AGL(1,ℤ/8)—11832no—
560#135—11832no—
561C2×Q16—594no—
562C2×Q16—1184no—
563C2×SD16—24no—
564C2×SD16—24no—
565C2×SD16—594no—
566C2×SD16—594no—
567C2×SD16—1184no—
568C2×SD16—1184no—
569C2×SD16C22×D5914yes—
570C2×SD16C22×D5914yescomplemented
571C2×D8—594no—
572C2×D8—594no—
573C2×D8—594no—
574C2×D8—1184no—
575C2×D8—1184no—
576C2×D8—1184no—
577C2×M16—594no—
578C2×M16—1184no—
579C22×C8—591no—
580C22×C8—591no—
581C22×C8—594no—
582C22×C8—1184no—
583C22×C8C22×D5911yescharacteristic
584C22×C8C22×D5911yescharacteristic
585#127—22no—
586#127—594no—
587#127—1182no—
588#127C22×D5914yes—
589#124—594no—
590#124—594no—
591#124—1182no—
592#124—1182no—
593#121—1188no—
594#121—1188no—
595#120—1188no—
596#120—1188no—
597C4×Q8—22no—
598C4×Q8—594no—
599C4×Q8—1182no—
600C4×Q8C22×D5914yescomplemented
601C4×D4—594no—
602C4×D4—594no—
603C4×D4—1188no—
604C4×D4—1182no—
605C4×D4—1188no—
606C4×D4—1182no—
607#117—594no—
608#117—594no—
609#117—1188no—
610C2×C4⋊C4—21no—
611C2×C4⋊C4—591no—
612C2×C4⋊C4—591no—
613C2×C4⋊C4—591no—
614C2×C4⋊C4—594no—
615C2×C4⋊C4—1188no—
616C2×C4⋊C4—1182no—
617C2×C4⋊C4—1181no—
618C2×C4⋊C4—1181no—
619C2×C4⋊C4C22×D5911yescharacteristic
620C2×C22⋊C4—591no—
621C2×C22⋊C4—591no—
622C2×C22⋊C4—1181no—
623C2×C22⋊C4—1181no—
624C2×C22⋊C4—1181no—
625C2×C22⋊C4—1181no—
626C2×C22⋊C4—1181no—
627C2×C22⋊C4—1181no—
628C2×C42—21no—
629C2×C42—591no—
630C2×C42—1181no—
631C2×C42C22×D5911yescharacteristic
632C4⋊C8—594no—
633C4⋊C8—594no—
634C4⋊C8—594no—
635C4⋊C8C22×D5914yescomplemented
636#103—594no—
637#103—594no—
638#102—594no—
639#102—594no—
640#102—594no—
641#102—594no—
642#102C22×D5914yes—
643#102C22×D5914yescomplemented
644C24—21no—
645C24—21no—
646C24—591no—
647C24—1184no—
648C24—1181no—
649C24—1181no—
650C24—4722no—
651C24—4722no—
652C24—2364no—
653#41—5916no—
654#41—11816no—
655#41—1188no—
656#41—1188no—
657#41—1188no—
658#41—2368no—
659C2×Q8—21no—
660C2×Q8—22no—
661C2×Q8—592no—
662C2×Q8—1181no—
663C2×Q8—1182no—
664C2×Q8—1182no—
665C2×Q8D4×D5914yes—
666C2×Q8C23×D5912yes—
667C2×D4—22no—
668C2×D4—22no—
669C2×D4—21no—
670C2×D4—21no—
671C2×D4—24no—
672C2×D4—24no—
673C2×D4—22no—
674C2×D4—22no—
675C2×D4—82no—
676C2×D4—82no—
677C2×D4—594no—
678C2×D4—592no—
679C2×D4—592no—
680C2×D4—1184no—
681C2×D4—1188no—
682C2×D4—1188no—
683C2×D4—1188no—
684C2×D4—1184no—
685C2×D4—1184no—
686C2×D4—1184no—
687C2×D4—1184no—
688C2×D4—1181no—
689C2×D4—1182no—
690C2×D4—1181no—
691C2×D4—1182no—
692C2×D4—1182no—
693C2×D4—4722no—
694C2×D4—4722no—
695C2×D4—2368no—
696C2×D4—2364no—
697C2×D4—2364no—
698C2×D4C23×D5912yes—
699C2×D4C23×D5912yes—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—591no—
703C22×C4—592no—
704C22×C4—594no—
705C22×C4—594no—
706C22×C4—592no—
707C22×C4—591no—
708C22×C4—591no—
709C22×C4—1184no—
710C22×C4—1188no—
711C22×C4—1184no—
712C22×C4—1184no—
713C22×C4—1184no—
714C22×C4—1181no—
715C22×C4—1181no—
716C22×C4—1184no—
717C22×C4—4722no—
718C22×C4—4722no—
719C22×C4—4722no—
720C22×C4—2364no—
721C22×C4D4×D5911yescharacteristic
722C22×C4D4×D5911yescharacteristic
723C22×C4C23×D5911yescharacteristic
724Q16—1188no—
725SD16—28no—
726SD16—28no—
727SD16—1188no—
728SD16—1188no—
729D8—1188no—
730D8—1188no—
731D8—1188no—
732M16—1188no—
733C2×C8—22no—
734C2×C8—22no—
735C2×C8—592no—
736C2×C8—592no—
737C2×C8—1188no—
738C2×C8—1182no—
739C2×C8—1182no—
740C2×C8C23×D5912yes—
741C2×C8C23×D5912yes—
742C4⋊C4—24no—
743C4⋊C4—21no—
744C4⋊C4—594no—
745C4⋊C4—594no—
746C4⋊C4—592no—
747C4⋊C4—1184no—
748C4⋊C4—1184no—
749C4⋊C4—1181no—
750C4⋊C4C23×D5912yes—
751C22⋊C4—594no—
752C22⋊C4—594no—
753C22⋊C4—1184no—
754C22⋊C4—1184no—
755C22⋊C4—1184no—
756C22⋊C4—1184no—
757C22⋊C4—1184no—
758C22⋊C4—1184no—
759C42—24no—
760C42—592no—
761C42—592no—
762C42—1184no—
763C42D4×D5912yes—
764C42C23×D5912yes—
765C23—22no—
766C23—22no—
767C23—42no—
768C23—42no—
769C23—42no—
770C23—42no—
771C23—42no—
772C23—42no—
773C23—594no—
774C23—592no—
775C23—1182no—
776C23—1182no—
777C23—1184no—
778C23—1182no—
779C23—1182no—
780C23—4724no—
781C23—4724no—
782C23—47216no—
783C23—2368no—
784C23—2362no—
785C23—2362no—
786C23—2362no—
787C23—2362no—
788C23—2362no—
789C23C2×D4×D5911yescharacteristic
790Q8—24no—
791Q8—22no—
792Q8—1182no—
793Q8—1182no—
794Q8—2362no—
795Q8C2×D4×D5914yes—
796D4—22no—
797D4—22no—
798D4—22no—
799D4—22no—
800D4—42no—
801D4—42no—
802D4—84no—
803D4—84no—
804D4—594no—
805D4—11816no—
806D4—1184no—
807D4—1182no—
808D4—1182no—
809D4—1182no—
810D4—4724no—
811D4—4724no—
812D4—2368no—
813D4—2368no—
814D4—2362no—
815C2×C4—24no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—42no—
821C2×C4—594no—
822C2×C4—592no—
823C2×C4—598no—
824C2×C4—594no—
825C2×C4—594no—
826C2×C4—592no—
827C2×C4—592no—
828C2×C4—11816no—
829C2×C4—1182no—
830C2×C4—1182no—
831C2×C4—1182no—
832C2×C4—1182no—
833C2×C4—4724no—
834C2×C4—4724no—
835C2×C4—4724no—
836C2×C4—2368no—
837C2×C4—2362no—
838C2×C4—2362no—
839C2×C4C2×D4×D5912yes—
840C2×C4C2×D4×D5912yes—
841C2×C4C2×D4×D5911yescharacteristic
842C2×C4C2×D4×D5912yes—
843C2×C4#41×D5912yes—
844C2×C4C24×D5911yescharacteristic
845C8—22no—
846C8—22no—
847C8—1182no—
848C8—1182no—
849C22—42no—
850C22—42no—
851C22—42no—
852C22—42no—
853C22—42no—
854C22—42no—
855C22—84no—
856C22—84no—
857C22—594no—
858C22—1188no—
859C22—1182no—
860C22—1182no—
861C22—1184no—
862C22—47216no—
863C22—4724no—
864C22—2362no—
865C22—2362no—
866C22—2362no—
867C22—2368no—
868C22—2362no—
869C22—2362no—
870C22#121×D5912yes—
871C22#1683820612yes—
872C22#1683820812yes—
873C22C22×D4×D5911yescharacteristic
874C4—22no—
875C4—24no—
876C4—22no—
877C4—42no—
878C4—594no—
879C4—1182no—
880C4—1182no—
881C4—2362no—
882C4—2362no—
883C4#121×D5912yes—
884C4C22×D4×D5911yescharacteristic
885C4C2×#41×D5911yescharacteristic
886C2—82no—
887C2—82no—
888C2—1184no—
889C2—4722no—
890C2—2364no—
891C2#2143363214yesdirect product factor
892C2C2×#121×D5911yescharacteristic
893C2C2×#1683820611yescharacteristic
894C2C2×#1683820811yescharacteristic
subgroupG/H
centerC23C2×D4×D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C59×#460C2
socleC23×C59C22×D4
hypercenterC2×#460D59
hypocenterC59C2×#3045
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#460

Complements

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

NH ≅ G/Ntype
1. C22×#14273754C2semidirect
2. C22×#14273748C2semidirect
3. C2×#16837965C2semidirect
4. C2×#16837884C2semidirect
5. #21433632C2direct (N × H)
6. C2×#16837624C2semidirect
7. C2×#16837622C2semidirect
8. C2×#16837600C2semidirect
9. C2×#16837618C2semidirect
10. C2×#16837616C2semidirect
11. C2×#16837596C2semidirect
12. C2×#16837594C2semidirect
13. C2×#16837427C2semidirect
14. C2×#16837400C2semidirect
15. C2×#102×D59C2semidirect
16. C2×C59×#460C2semidirect
21. C2×#14273754C22semidirect
23. C2×#14273748C22semidirect
24. C22×#11745672C22semidirect
25. C22×#11745660C22semidirect
29. C22×#11745669C22semidirect
33. #16837965C22semidirect
42. #16837884C22semidirect
43. C2×Q8×Dic59C22semidirect
45. C2×C4×D236C22semidirect
47. C2×#14273689C22semidirect
52. #16837624C22semidirect
53. #16837622C22semidirect
54. #16837618C22semidirect
55. #16837616C22semidirect
56. #16837600C22semidirect
57. #16837596C22semidirect
58. #16837594C22semidirect
59. #16837427C22semidirect
60. C2×C4⋊(C59⋊C8)C22semidirect
61. C2×Dic59⋊C8C22semidirect
62. C2×Dic59⋊C8C22semidirect
63. #16837400C22semidirect
64. C2×#14273652C22semidirect
65. C2×#14273650C22semidirect
68. C2×#14273648C22semidirect
70. #102×D59C22semidirect
72. C22×SD16×C59C22semidirect
74. C2×C4×Q8×C59C22semidirect
75. C59×#460C22semidirect
76. C2×C4⋊C8×C59C22semidirect
78. C2×#102×C59C22semidirect
82. C2×#11745689D4semidirect
109. C2×#11745672C23semidirect
111. C2×#11745660C23semidirect
119. C2×#11745669C23semidirect
137. Q8×Dic59C23semidirect
140. C4×D236C23semidirect
143. #14273689C23semidirect
165. C4⋊(C59⋊C8)C23semidirect
166. Dic59⋊C8C23semidirect
167. Dic59⋊C8C23semidirect
168. #14273652C23semidirect
169. #14273650C23semidirect
172. #14273648C23semidirect
182. C2×SD16×C59C23semidirect
188. C4×Q8×C59C23semidirect
193. C4⋊C8×C59C23semidirect
195. #102×C59C23semidirect
243. #11745689C2×D4semidirect
447. C2×#460D59semidirect
457. C2×C59#3045semidirect
475. C22×SD16C2×D59semidirect
494. C2×C4×Q8C2×D59semidirect
508. #460C2×D59semidirect
515. C2×C4⋊C8C2×D59semidirect
525. C2×#102C2×D59semidirect
526. C59C2×#3045semidirect
570. C2×SD16C22×D59semidirect
600. C4×Q8C22×D59semidirect
635. C4⋊C8C22×D59semidirect
643. #102C22×D59semidirect
891. C2#21433632direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#142737542
C22×#142737482
C2×#168379652
C2×#168378842
#214336322
C2×#168376242
C2×#168376222
C2×#168376002
C2×#168376182
C2×#168376162
C2×#168375962
C2×#168375942
C2×#168374272
C2×#168374002
C2×#102×D592
C2×C59×#4602
C2×#304559