Finite Group Databasebeta

← C2×#21427441 #28757002

Subgroups — C2×#21427441 #28757002

Order 15104.

5998 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#11745685C211yesmaximal, characteristic, complemented
2C22×#14273706C211yesmaximal, characteristic, complemented
3C22×#14273701C211yesmaximal, characteristic, complemented
4#21427441C2116yesmaximal, direct product factor
5C2×#16837317C212yesmaximal, complemented
6C2×#16837310C212yesmaximal, complemented
7C2×#16837308C211yesmaximal, characteristic, complemented
8C2×#16837304C211yesmaximal, characteristic, complemented
9C2×#16837278C212yesmaximal, complemented
10C2×#16837273C212yesmaximal, complemented
11C2×#16837262C211yesmaximal, characteristic, complemented
12C22×C4×D4×C59C211yesmaximal, characteristic, complemented
13C22×#11745685—28no—
14C22×#11745685—28no—
15C22×#11745685—28no—
16C22×#11745685C2218yescomplemented
17C23×Dic118C2211yescharacteristic
18C23×D236C2211yescharacteristic
19C23×C22⋊D59C2212yes—
20C23×C22⋊D59C2212yes—
21C23×C4×D59C2212yes—
22C2×#14273706—28no—
23C2×#14273706C2218yescomplemented
24C2×#14273701—28no—
25C2×#14273701C2218yescomplemented
26C22×C4⋊Dic59C2211yescharacteristic
27C22×C4⋊Dic59C2211yescharacteristic
28C22×Dic59⋊C4C2212yes—
29C22×C22⋊Dic59C2212yes—
30C22×C22⋊Dic59C2212yes—
31C22×(C2×D59)⋊C4C2212yes—
32C22×(C2×D59)⋊C4C2212yes—
33C22×(C2×D59)⋊C4C2212yes—
34#16837317C22116yescomplemented
35#16837310C22116yescomplemented
36#16837308C2218yescomplemented
37#16837304C2218yescomplemented
38#16837278C22116yescomplemented
39#16837273C22116yescomplemented
40#16837262C2218yescomplemented
41C2×C59⋊#95C2212yes—
42C2×C59⋊#95C2212yes—
43C2×C59⋊#95C2212yes—
44C23×D4×C59C2211yescharacteristic
45C24×C4×C59C2211yescharacteristic
46C24×C4×C59C2211yescharacteristic
47C2×C4×D4×C59—28no—
48C2×C4×D4×C59C2218yescomplemented
49C22×C4⋊C4×C59C2211yescharacteristic
50C22×C22⋊C4×C59C2211yescharacteristic
51C22×C22⋊C4×C59C2211yescharacteristic
52C22×C42×C59C2211yescharacteristic
53C24×D59C2312yes—
54C2×#11745685—2128no—
55C2×#11745685—232no—
56C2×#11745685—232no—
57C2×#11745685—232no—
58C22×Dic118—24no—
59C22×Dic118—24no—
60C22×Dic118D418yescomplemented
61C22×Dic118C2314yes—
62C22×D236—24no—
63C22×D236—24no—
64C22×D236D418yescomplemented
65C22×D236C2314yes—
66C22×C22⋊D59—28no—
67C22×C22⋊D59—28no—
68C22×C22⋊D59—28no—
69C22×C22⋊D59—28no—
70C22×C22⋊D59—28no—
71C22×C22⋊D59—44no—
72C22×C22⋊D59C2318yes—
73C22×C22⋊D59C2318yes—
74C23×Dic59C2312yes—
75C23×Dic59C2312yes—
76C23×Dic59C2312yes—
77C22×C4×D59—28no—
78C22×C4×D59—28no—
79C22×C4×D59—28no—
80C22×C4×D59C2318yes—
81#14273706—232no—
82#14273701—232no—
83C2×C4⋊Dic59—24no—
84C2×C4⋊Dic59—24no—
85C2×C4⋊Dic59C2314yes—
86C2×C4⋊Dic59C2314yes—
87C2×Dic59⋊C4—28no—
88C2×Dic59⋊C4C2318yes—
89C2×C22⋊Dic59—28no—
90C2×C22⋊Dic59—44no—
91C2×C22⋊Dic59C2318yes—
92C2×C22⋊Dic59C2318yes—
93C2×(C2×D59)⋊C4—28no—
94C2×(C2×D59)⋊C4—28no—
95C2×(C2×D59)⋊C4—44no—
96C2×(C2×D59)⋊C4C2318yes—
97C2×(C2×D59)⋊C4C2318yes—
98C2×(C2×D59)⋊C4C2318yes—
99C59⋊#95C2318yes—
100C59⋊#95C2318yes—
101C59⋊#95C2318yes—
102C25×C59C2311yescharacteristic
103C25×C59C2311yescharacteristic
104C22×D4×C59—24no—
105C22×D4×C59—24no—
106C22×D4×C59—24no—
107C22×D4×C59C2314yes—
108C23×C4×C59—24no—
109C23×C4×C59—24no—
110C23×C4×C59—24no—
111C23×C4×C59—24no—
112C23×C4×C59—24no—
113C23×C4×C59D418yescomplemented
114C23×C4×C59C2314yes—
115C23×C4×C59C2311yescharacteristic
116C23×C4×C59C2311yescharacteristic
117C23×C4×C59C2311yescharacteristic
118C23×C4×C59C2314yes—
119C23×C4×C59C2311yescharacteristic
120C23×C4×C59C2311yescharacteristic
121C4×D4×C59—232no—
122C2×C4⋊C4×C59—24no—
123C2×C4⋊C4×C59C2314yes—
124C2×C22⋊C4×C59—24no—
125C2×C22⋊C4×C59—24no—
126C2×C22⋊C4×C59C2314yes—
127C2×C22⋊C4×C59C2314yes—
128C2×C42×C59—24no—
129C2×C42×C59C2314yes—
130C24×C59—22no—
131C24×C59—22no—
132C24×C59—22no—
133C24×C59—22no—
134C24×C59—22no—
135C24×C59—22no—
136C24×C59—22no—
137C24×C59—22no—
138C24×C59—22no—
139C24×C59—22no—
140C24×C59—22no—
141C24×C59—22no—
142C24×C59C2×D414yes—
143C24×C59#4114yescomplemented
144C24×C59C2412yes—
145C24×C59C2412yes—
146C24×C59C2411yescharacteristic
147C23×D59—24no—
148C23×D59—24no—
149C23×D59—24no—
150C23×D59—24no—
151C23×D59—24no—
152C23×D59—24no—
153C23×D59C2×D418yes—
154C23×D59C2414yes—
155C2×D4×C59—232no—
156C2×D4×C59—28no—
157C2×D4×C59—28no—
158C2×D4×C59—28no—
159C22×C4×C59—22no—
160C22×C4×C59—22no—
161C22×C4×C59—22no—
162C22×C4×C59—22no—
163C22×C4×C59—232no—
164C22×C4×C59—28no—
165C22×C4×C59—28no—
166C22×C4×C59—22no—
167C22×C4×C59—22no—
168C22×C4×C59—22no—
169C22×C4×C59—22no—
170C22×C4×C59—22no—
171C22×C4×C59—22no—
172C22×C4×C59—28no—
173C22×C4×C59—28no—
174C22×C4×C59—28no—
175C22×C4×C59—416no—
176C22×C4×C59C2×D414yes—
177C22×C4×C59C2×D414yes—
178C22×C4×C59C2×D414yes—
179C22×C4×C59C2×D414yes—
180C22×C4×C59C2×D4116yescomplemented
181C22×C4×C59#4114yescomplemented
182C22×C4×C59C2412yes—
183C22×C4×C59C2412yes—
184C22×C4×C59C2412yes—
185C22×C4×C59C2412yes—
186C22×C4×C59C2412yes—
187C2×C22⋊D59—264no—
188C2×C22⋊D59—216no—
189C2×C22⋊D59—216no—
190C2×C22⋊D59—216no—
191C2×C22⋊D59—216no—
192C2×C22⋊D59—216no—
193C2×C22⋊D59—48no—
194C2×C22⋊D59—432no—
195C22×Dic59—24no—
196C22×Dic59—24no—
197C22×Dic59—24no—
198C22×Dic59—24no—
199C22×Dic59—24no—
200C22×Dic59—24no—
201C22×Dic59—24no—
202C22×Dic59—24no—
203C22×Dic59C2×D418yes—
204C22×Dic59C2414yes—
205C22×Dic59C2414yes—
206C22×Dic59C2414yes—
207#11745685—2256no—
208C2×D236—232no—
209C2×D236—28no—
210C2×D236—28no—
211C2×D236C2×D4116yescomplemented
212C2×C4×D59—264no—
213C2×C4×D59—216no—
214C2×C4×D59—216no—
215C2×C4×D59—216no—
216C2×Dic118—232no—
217C2×Dic118—28no—
218C2×Dic118—28no—
219C2×Dic118C2×D4116yescomplemented
220C4⋊C4×C59—28no—
221C22⋊C4×C59—28no—
222C22⋊C4×C59—28no—
223C42×C59—28no—
224C22⋊Dic59—216no—
225C22⋊Dic59—48no—
226(C2×D59)⋊C4—216no—
227(C2×D59)⋊C4—216no—
228(C2×D59)⋊C4—48no—
229C4⋊Dic59—28no—
230C4⋊Dic59—28no—
231Dic59⋊C4—216no—
232C23×C59—28no—
233C23×C59—28no—
234C23×C59—28no—
235C23×C59—28no—
236C23×C59—28no—
237C23×C59—28no—
238C23×C59—22no—
239C23×C59—22no—
240C23×C59—22no—
241C23×C59—22no—
242C23×C59—22no—
243C23×C59—22no—
244C23×C59—22no—
245C23×C59—22no—
246C23×C59—22no—
247C23×C59—22no—
248C23×C59—22no—
249C23×C59—22no—
250C23×C59—44no—
251C23×C59—44no—
252C23×C59—44no—
253C23×C59—44no—
254C23×C59—44no—
255C23×C59—44no—
256C23×C59—44no—
257C23×C59—44no—
258C23×C59C22×D412yes—
259C23×C59C22×D412yes—
260C23×C59C22×D414yes—
261C23×C59C22×D412yes—
262C23×C59C2×#4112yes—
263C23×C59C2×#4112yes—
264C23×C59C2×#4114yescomplemented
265C23×C59H(5,𝔽2)12yes—
266C23×C592−1+412yes—
267C23×C59C2511yescharacteristic
268C22×D59—216no—
269C22×D59—216no—
270C22×D59—216no—
271C22×D59—24no—
272C22×D59—24no—
273C22×D59—24no—
274C22×D59—24no—
275C22×D59—24no—
276C22×D59—24no—
277C22×D59—48no—
278C22×D59—48no—
279C22×D59—48no—
280C22×D59—48no—
281C22×D59C22×D418yes—
282D4×C59—232no—
283C2×C4×C59—28no—
284C2×C4×C59—28no—
285C2×C4×C59—22no—
286C2×C4×C59—22no—
287C2×C4×C59—22no—
288C2×C4×C59—22no—
289C2×C4×C59—232no—
290C2×C4×C59—22no—
291C2×C4×C59—22no—
292C2×C4×C59—22no—
293C2×C4×C59—22no—
294C2×C4×C59—22no—
295C2×C4×C59—22no—
296C2×C4×C59—44no—
297C2×C4×C59—44no—
298C2×C4×C59—416no—
299C2×C4×C59#120116yes—
300C2×C4×C59C22×D414yes—
301C2×C4×C59C22×D414yes—
302C2×C4×C59C22×D414yes—
303C2×C4×C59C22×D414yes—
304C2×C4×C59C2×#4114yescomplemented
305C22⋊D59—264no—
306C22⋊D59—432no—
307C2×Dic59—216no—
308C2×Dic59—24no—
309C2×Dic59—24no—
310C2×Dic59—24no—
311C2×Dic59—24no—
312C2×Dic59—24no—
313C2×Dic59—24no—
314C2×Dic59—24no—
315C2×Dic59—24no—
316C2×Dic59—48no—
317C2×Dic59—48no—
318C2×Dic59C22×D418yes—
319D236—232no—
320C4×D59—264no—
321Dic118—232no—
322C2×#2407—591nomaximal, Sylow
323C22×C59—24no—
324C22×C59—24no—
325C22×C59—24no—
326C22×C59—24no—
327C22×C59—24no—
328C22×C59—24no—
329C22×C59—416no—
330C22×C59—416no—
331C22×C59—42no—
332C22×C59—42no—
333C22×C59—42no—
334C22×C59—42no—
335C22×C59—42no—
336C22×C59—42no—
337C22×C59—42no—
338C22×C59—42no—
339C22×C59C2×#12014yes—
340C22×C59#52514yes—
341C22×C59#53714yes—
342C22×C59#54614yes—
343C22×C59#54714yes—
344C22×C59#54814yes—
345C22×C59#55014yes—
346C22×C59C23×D411yescharacteristic
347C22×C59C23×D411yescharacteristic
348C22×C59C23×D411yescharacteristic
349C22×C59C22×#4111yescharacteristic
350C22×C59C22×#4111yescharacteristic
351C22×C59C2×H(5,𝔽2)11yescharacteristic
352C22×C59C2×2−1+411yescharacteristic
353C2×D59—28no—
354C2×D59—28no—
355C2×D59—28no—
356C2×D59—432no—
357C2×D59—44no—
358C2×D59—44no—
359C2×D59—44no—
360C2×D59—44no—
361C4×C59—24no—
362C4×C59—24no—
363C4×C59—42no—
364C4×C59—42no—
365C4×C59C2×#12018yes—
366Dic59—28no—
367Dic59—44no—
368Dic59—44no—
369C23×#41—591no—
370C22×C22⋊Q8—591no—
371C22×#121—591no—
372C22×C4×D4D5911yescharacteristic, complemented
373#2407—5916no—
374C2×#394—592no—
375C2×#392—592no—
376C2×#391—591no—
377C2×#390—591no—
378C2×#386—592no—
379C2×#385—592no—
380C2×#380—591no—
381C2×C59—44no—
382C2×C59—44no—
383C2×C59#240718yescomplemented
384C2×C59C22×#12011yescharacteristic
385C2×C59C2×#52511yescharacteristic
386C2×C59C2×#53711yescharacteristic
387C2×C59C2×#54611yescharacteristic
388C2×C59C2×#54711yescharacteristic
389C2×C59C2×#54811yescharacteristic
390C2×C59C2×#55011yescharacteristic
391D59—48no—
392C22×#41—598no—
393C22×#41—1188no—
394C22×#41—1188no—
395C22×#41—1188no—
396C23×Q8—591no—
397C23×D4—592no—
398C23×D4—592no—
399C23×D4—591no—
400C23×D4C2×D5911yescharacteristic
401C24×C4—592no—
402C24×C4C2×D5911yescharacteristic
403C24×C4C2×D5911yescharacteristic
404C2×C22⋊Q8—598no—
405C2×C22⋊Q8—1188no—
406C2×#121—598no—
407C2×#121—1188no—
408C2×C4×D4—28no—
409C2×C4×D4C2×D5918yescomplemented
410C22×C4⋊C4—592no—
411C22×C4⋊C4—591no—
412C22×C4⋊C4—591no—
413C22×C4⋊C4C2×D5911yescharacteristic
414C22×C22⋊C4—592no—
415C22×C22⋊C4—592no—
416C22×C22⋊C4—592no—
417C22×C22⋊C4—592no—
418C22×C22⋊C4—592no—
419C22×C22⋊C4C2×D5911yescharacteristic
420C22×C22⋊C4C2×D5911yescharacteristic
421C22×C42C2×D5911yescharacteristic
422#394—5916no—
423#392—5916no—
424#391—598no—
425#390—598no—
426#386—5916no—
427#385—5916no—
428#380—598no—
429C2×#95—592no—
430C2×#95—592no—
431C2×#95—592no—
432C59C2×#240711yescharacteristic, complemented, Sylow
433C25—592no—
434C25C22×D5911yescharacteristic
435C25C22×D5911yescharacteristic
436C2×#41—11832no—
437C2×#41—11832no—
438C2×#41—118128no—
439C2×#41—11832no—
440C22×Q8—598no—
441C22×Q8—594no—
442C22×Q8—1184no—
443C22×Q8—1184no—
444C22×D4—24no—
445C22×D4—24no—
446C22×D4—24no—
447C22×D4—598no—
448C22×D4—598no—
449C22×D4—598no—
450C22×D4—594no—
451C22×D4—1188no—
452C22×D4—1188no—
453C22×D4—1188no—
454C22×D4—1188no—
455C22×D4—1188no—
456C22×D4—1184no—
457C22×D4—1184no—
458C22×D4—2364no—
459C22×D4C22×D5914yes—
460C23×C4—24no—
461C23×C4—24no—
462C23×C4—24no—
463C23×C4—24no—
464C23×C4—24no—
465C23×C4—592no—
466C23×C4—592no—
467C23×C4—592no—
468C23×C4—598no—
469C23×C4—1188no—
470C23×C4—1188no—
471C23×C4—1188no—
472C23×C4C22⋊D5918yescomplemented
473C23×C4C22×D5914yes—
474C23×C4C22×D5911yescharacteristic
475C23×C4C22×D5911yescharacteristic
476C23×C4C22×D5911yescharacteristic
477C23×C4C22×D5911yescharacteristic
478C23×C4C22×D5914yes—
479C23×C4C22×D5911yescharacteristic
480C22⋊Q8—11832no—
481#121—11832no—
482C4×D4—232no—
483C2×C4⋊C4—24no—
484C2×C4⋊C4—594no—
485C2×C4⋊C4—594no—
486C2×C4⋊C4—598no—
487C2×C4⋊C4—1188no—
488C2×C4⋊C4—1184no—
489C2×C4⋊C4—1184no—
490C2×C4⋊C4C22×D5914yes—
491C2×C22⋊C4—24no—
492C2×C22⋊C4—24no—
493C2×C22⋊C4—598no—
494C2×C22⋊C4—598no—
495C2×C22⋊C4—598no—
496C2×C22⋊C4—598no—
497C2×C22⋊C4—598no—
498C2×C22⋊C4—1188no—
499C2×C22⋊C4—1188no—
500C2×C22⋊C4—1188no—
501C2×C22⋊C4—2364no—
502C2×C22⋊C4—2364no—
503C2×C22⋊C4C22×D5914yes—
504C2×C22⋊C4C22×D5914yes—
505C2×C42—24no—
506C2×C42C22×D5914yes—
507#95—598no—
508#95—598no—
509#95—598no—
510C24—22no—
511C24—22no—
512C24—22no—
513C24—22no—
514C24—22no—
515C24—22no—
516C24—22no—
517C24—22no—
518C24—22no—
519C24—22no—
520C24—22no—
521C24—22no—
522C24—598no—
523C24—594no—
524C24—1184no—
525C24—1184no—
526C24—1184no—
527C24—1184no—
528C24—1184no—
529C24—1184no—
530C24#1174568514yescomplemented
531C24C2×C22⋊D5914yes—
532C24C23×D5912yes—
533C24C23×D5912yes—
534C24C23×D5911yescharacteristic
535#41—118256no—
536C2×Q8—5916no—
537C2×Q8—11832no—
538C2×Q8—1188no—
539C2×Q8—1188no—
540C2×D4—232no—
541C2×D4—28no—
542C2×D4—28no—
543C2×D4—28no—
544C2×D4—5916no—
545C2×D4—11816no—
546C2×D4—11816no—
547C2×D4—11864no—
548C2×D4—11816no—
549C2×D4—11816no—
550C2×D4—11816no—
551C2×D4—11832no—
552C2×D4—1188no—
553C2×D4—1188no—
554C2×D4—2368no—
555C2×D4—23632no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—232no—
561C22×C4—28no—
562C22×C4—28no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—28no—
570C22×C4—28no—
571C22×C4—28no—
572C22×C4—416no—
573C22×C4—598no—
574C22×C4—594no—
575C22×C4—594no—
576C22×C4—594no—
577C22×C4—11816no—
578C22×C4—11816no—
579C22×C4—11864no—
580C22×C4—1184no—
581C22×C4—1184no—
582C22×C4—11816no—
583C22×C4—1184no—
584C22×C4—1184no—
585C22×C4—1184no—
586C22×C4—1184no—
587C22×C4—1184no—
588C22×C4—1184no—
589C22×C4#1174568514yescomplemented
590C22×C4D4×D5914yes—
591C22×C4D4×D5914yes—
592C22×C4C2×C22⋊D5914yes—
593C22×C4C2×C22⋊D5914yes—
594C22×C4C2×C22⋊D59116yescomplemented
595C22×C4C23×D5912yes—
596C22×C4C23×D5912yes—
597C22×C4C23×D5912yes—
598C22×C4C23×D5912yes—
599C22×C4C23×D5912yes—
600C4⋊C4—28no—
601C4⋊C4—11816no—
602C4⋊C4—1188no—
603C4⋊C4—1188no—
604C22⋊C4—28no—
605C22⋊C4—28no—
606C22⋊C4—11816no—
607C22⋊C4—11816no—
608C22⋊C4—11816no—
609C22⋊C4—2368no—
610C22⋊C4—2368no—
611C42—28no—
612C23—28no—
613C23—28no—
614C23—22no—
615C23—22no—
616C23—22no—
617C23—22no—
618C23—22no—
619C23—22no—
620C23—22no—
621C23—22no—
622C23—22no—
623C23—22no—
624C23—22no—
625C23—22no—
626C23—28no—
627C23—28no—
628C23—28no—
629C23—28no—
630C23—44no—
631C23—44no—
632C23—44no—
633C23—44no—
634C23—44no—
635C23—44no—
636C23—44no—
637C23—44no—
638C23—598no—
639C23—1184no—
640C23—1184no—
641C23—1184no—
642C23—1184no—
643C23—1184no—
644C23—1184no—
645C23—11816no—
646C23—11816no—
647C23—11816no—
648C23—2368no—
649C23—2368no—
650C23—2368no—
651C23—2368no—
652C23C2×D4×D5912yes—
653C23C2×D4×D5912yes—
654C23C22×C22⋊D5914yes—
655C23C22×C22⋊D5912yes—
656C23C2×#1174568512yes—
657C23C2×#1174568512yes—
658C23C2×#1174568514yescomplemented
659C23#1427377312yes—
660C23#1427377412yes—
661C23C24×D5911yescharacteristic
662Q8—11832no—
663D4—232no—
664D4—11864no—
665D4—11832no—
666D4—23632no—
667C2×C4—28no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—28no—
673C2×C4—232no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—44no—
681C2×C4—44no—
682C2×C4—416no—
683C2×C4—598no—
684C2×C4—11864no—
685C2×C4—1184no—
686C2×C4—1184no—
687C2×C4—11816no—
688C2×C4—1184no—
689C2×C4—1184no—
690C2×C4—1184no—
691C2×C4—1184no—
692C2×C4—1184no—
693C2×C4—1184no—
694C2×C4—2368no—
695C2×C4—2368no—
696C2×C4#14273695116yes—
697C2×C4C2×D4×D5914yes—
698C2×C4C2×D4×D5914yes—
699C2×C4C22×C22⋊D5914yes—
700C2×C4C22×C22⋊D5914yes—
701C2×C4C2×#1174568514yescomplemented
702C22—24no—
703C22—24no—
704C22—24no—
705C22—24no—
706C22—24no—
707C22—24no—
708C22—42no—
709C22—42no—
710C22—42no—
711C22—42no—
712C22—42no—
713C22—42no—
714C22—42no—
715C22—42no—
716C22—416no—
717C22—416no—
718C22—1188no—
719C22—1188no—
720C22—1188no—
721C22—2364no—
722C22—2364no—
723C22—2364no—
724C22—2364no—
725C22—23632no—
726C22C2×#1427369514yes—
727C22#1683791314yes—
728C22#1683798014yes—
729C22#1683804814yes—
730C22#1683805714yes—
731C22#1683806114yes—
732C22#1683807314yes—
733C22C22×D4×D5911yescharacteristic
734C22C22×D4×D5911yescharacteristic
735C22C23×C22⋊D5911yescharacteristic
736C22C22×#1174568511yescharacteristic
737C22C22×#1174568511yescharacteristic
738C22C2×#1427377311yescharacteristic
739C22C2×#1427377411yescharacteristic
740C4—24no—
741C4—24no—
742C4—42no—
743C4—42no—
744C4—1188no—
745C4—2364no—
746C4—2364no—
747C4C2×#1427369518yes—
748C2—44no—
749C2—44no—
750C2—2368no—
751C2#2142744118yesdirect product factor
752C2C22×#1427369511yescharacteristic
753C2C2×#1683791311yescharacteristic
754C2C2×#1683798011yescharacteristic
755C2C2×#1683804811yescharacteristic
756C2C2×#1683805711yescharacteristic
757C2C2×#1683806111yescharacteristic
758C2C2×#1683807311yescharacteristic
subgroupG/H
centerC24C23×D59
commutator, cosocleC23×C59C25
FrattiniC23C24×D59
FittingC22×C4×D4×C59C2
socleC24×C59C24
hypercenterC22×C4×D4D59
hypocenterC59C2×#2407
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C24 ◁ C22×C4×D4

Complements

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

NH ≅ G/Ntype
1. C23×#11745685C2semidirect
2. C22×#14273706C2semidirect
3. C22×#14273701C2semidirect
4. #21427441C2direct (N × H)
5. C2×#16837317C2semidirect
6. C2×#16837310C2semidirect
7. C2×#16837308C2semidirect
8. C2×#16837304C2semidirect
9. C2×#16837278C2semidirect
10. C2×#16837273C2semidirect
11. C2×#16837262C2semidirect
12. C22×C4×D4×C59C2semidirect
16. C22×#11745685C22semidirect
23. C2×#14273706C22semidirect
25. C2×#14273701C22semidirect
34. #16837317C22semidirect
35. #16837310C22semidirect
36. #16837308C22semidirect
37. #16837304C22semidirect
38. #16837278C22semidirect
39. #16837273C22semidirect
40. #16837262C22semidirect
48. C2×C4×D4×C59C22semidirect
60. C22×Dic118D4semidirect
64. C22×D236D4semidirect
113. C23×C4×C59D4semidirect
143. C24×C59#41semidirect
180. C22×C4×C59C2×D4semidirect
181. C22×C4×C59#41semidirect
211. C2×D236C2×D4semidirect
219. C2×Dic118C2×D4semidirect
264. C23×C59C2×#41semidirect
304. C2×C4×C59C2×#41semidirect
372. C22×C4×D4D59semidirect
383. C2×C59#2407semidirect
409. C2×C4×D4C2×D59semidirect
432. C59C2×#2407semidirect
472. C23×C4C22⋊D59semidirect
530. C24#11745685semidirect
589. C22×C4#11745685semidirect
594. C22×C4C2×C22⋊D59semidirect
658. C23C2×#11745685semidirect
701. C2×C4C2×#11745685semidirect
751. C2#21427441direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#117456852
C22×#142737062
C22×#142737012
#214274412
C2×#168373172
C2×#168373102
C2×#168373082
C2×#168373042
C2×#168372782
C2×#168372732
C2×#168372622
C22×C4×D4×C592
C2×#240759