Finite Group Databasebeta

← C4×#16810816 #27390264

Subgroups — C4×#16810816 #27390264

Order 13568.

1272 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
1C2×#16810816C211yesmaximal, characteristic
2C2×C4×#11719922C211yesmaximal, characteristic, complemented
3C4×#13133213C211yesmaximal, characteristic, complemented
4C4×D4×Dic53C211yesmaximal, characteristic, complemented
5#20275640C211yesmaximal, characteristic, complemented
6#20275470C211yesmaximal, characteristic, complemented
7#20275338C211yesmaximal, characteristic, complemented
8#20275334C211yesmaximal, characteristic, complemented
9#20275065C211yesmaximal, characteristic, complemented
10#20275061C211yesmaximal, characteristic, complemented
11#20274713C211yesmaximal, characteristic, complemented
12C4×#13133146C211yesmaximal, characteristic, complemented
13C4×#13133139C211yesmaximal, characteristic, complemented
14C4×#13133138C211yesmaximal, characteristic, complemented
15C2×C4×D8×C53C211yesmaximal, characteristic, complemented
16C22×#11719922C2211yescharacteristic
17C2×#13133213C2211yescharacteristic
18C2×C4×D212C2211yescharacteristic
19C2×D4×Dic53C2211yescharacteristic
20C2×D4×Dic53C2211yescharacteristic
21C2×C4×C22⋊D53—21no—
22C2×C4×C22⋊D53—21no—
23C22×C4×Dic53—21no—
24#16810816C418yesdirect product factor
25C4×#11719922—24no—
26C2×#13133150C2211yescharacteristic
27C2×#13133146C2211yescharacteristic
28C2×#13133146C2211yescharacteristic
29C2×#13133139C2211yescharacteristic
30C2×#13133139C2211yescharacteristic
31C2×#13133138C2211yescharacteristic
32C2×#13133138C2211yescharacteristic
33C2×#13133138C2211yescharacteristic
34C2×#13133137C2211yescharacteristic
35C2×C4×#88322C2211yescharacteristic
36#16810526C2211yescharacteristic
37#16810524C2211yescharacteristic
38#16810523—21no—
39#16810523—21no—
40#16810492C2211yescharacteristic
41C4⋊C4×Dic53C2211yescharacteristic
42C4⋊C4×Dic53C2211yescharacteristic
43C4×C4⋊Dic53C2211yescharacteristic
44C22⋊C4×Dic53—21no—
45C22⋊C4×Dic53—21no—
46C4×C22⋊Dic53—21no—
47C42×Dic53C2211yescharacteristic
48#16810386C2211yescharacteristic
49#16810386C2211yescharacteristic
50#16810385C2211yescharacteristic
51#16810385C2211yescharacteristic
52#16810377C2211yescharacteristic
53#16810377C2211yescharacteristic
54C22×D8×C53C2211yescharacteristic
55C2×C4×D4×C53C2211yescharacteristic
56C2×C4×D4×C53C2211yescharacteristic
57C4×D8×C53—24no—
58C2×#107×C53C2211yescharacteristic
59C2×#102×C53C2211yescharacteristic
60C2×#102×C53C2211yescharacteristic
61C2×C4×C8×C53C2211yescharacteristic
62C22×D212C2311yescharacteristic
63C22×C22⋊D53—21no—
64C22×C22⋊D53—21no—
65C23×Dic53—21no—
66C23×Dic53—21no—
67C22×C4×D53—21no—
68C2×#11719922—22no—
69C2×#11719922—22no—
70C2×#11719922C2×C414yescomplemented
71C22×#88322C2311yescharacteristic
72C22×#88322C2311yescharacteristic
73#13133213—22no—
74#13133213C2×C414yescomplemented
75C4×D212—22no—
76C4×D212—22no—
77D4×Dic53—22no—
78D4×Dic53—22no—
79D4×Dic53—22no—
80D4×Dic53C2×C414yescomplemented
81C4×C22⋊D53—44no—
82C4×C22⋊D53—44no—
83C2×C4⋊Dic53C2311yescharacteristic
84C2×C4⋊Dic53C2311yescharacteristic
85C2×C4⋊Dic53C2311yescharacteristic
86C2×#11719919—21no—
87C2×#11719919—21no—
88C2×C22⋊Dic53—21no—
89C2×C22⋊Dic53—21no—
90C2×C22⋊Dic53—21no—
91C2×C22⋊Dic53—21no—
92C2×#11719921—21no—
93C2×#11719921—21no—
94C2×#11719921—21no—
95C2×C4×Dic53—21no—
96C2×C4×Dic53—21no—
97C2×C4×Dic53—21no—
98C2×C4×Dic53—44no—
99C2×C4×Dic53D411yescharacteristic
100C2×C4×Dic53D411yescharacteristic
101C2×C4×Dic53D411yescharacteristic
102C2×C4×Dic53D411yescharacteristic
103C2×C4×Dic53C2311yescharacteristic
104C2×C4×Dic53C2311yescharacteristic
105#13133150—22no—
106#13133146—22no—
107#13133146C2×C414yescomplemented
108#13133139—22no—
109#13133139C2×C414yescomplemented
110#13133138—22no—
111#13133138—22no—
112#13133138C2×C414yescomplemented
113#13133137—22no—
114C4×#88322—22no—
115#13133124—21no—
116#13133124—21no—
117#13133124—21no—
118C22×D4×C53C2311yescharacteristic
119C22×D4×C53C2311yescharacteristic
120C23×C4×C53—21no—
121C23×C4×C53—21no—
122C2×D8×C53—22no—
123C2×D8×C53—22no—
124C2×D8×C53C2×C414yescomplemented
125C22×C8×C53C2311yescharacteristic
126C22×C8×C53C2311yescharacteristic
127C4×D4×C53—22no—
128C4×D4×C53—22no—
129C4×D4×C53—22no—
130C4×D4×C53D414yescomplemented
131C2×C4⋊C4×C53C2311yescharacteristic
132C2×C4⋊C4×C53C2311yescharacteristic
133C2×C22⋊C4×C53—21no—
134C2×C22⋊C4×C53—21no—
135C2×C42×C53C2311yescharacteristic
136#107×C53—22no—
137#102×C53—22no—
138#102×C53—22no—
139C4×C8×C53—22no—
140C24×C53—21no—
141C24×C53—21no—
142C23×D53—21no—
143C2×D4×C53—21no—
144C2×D4×C53—21no—
145C2×D4×C53—21no—
146C2×D4×C53—21no—
147C2×D4×C53—21no—
148C2×D4×C53—21no—
149C2×D4×C53—21no—
150C2×D4×C53—21no—
151C2×D4×C53C22×C412yes—
152C2×D4×C53C22×C412yes—
153C2×D4×C53C2×D412yes—
154C2×D4×C53#4112yes—
155C22×C4×C53—21no—
156C22×C4×C53—24no—
157C22×C4×C53—21no—
158C22×C4×C53—42no—
159C22×C4×C53—42no—
160C22×C4×C53—42no—
161C22×C4×C53—42no—
162C22×C4×C53—42no—
163C22×C4×C53C2×D411yescharacteristic
164C22×C4×C53C2×D411yescharacteristic
165C22×C4×C53C2411yescharacteristic
166C2×C22⋊D53—24no—
167C2×C22⋊D53—24no—
168C2×C22⋊D53—42no—
169C2×C22⋊D53—42no—
170C2×C22⋊D53—42no—
171C2×C22⋊D53—42no—
172C22×Dic53—24no—
173C22×Dic53—21no—
174C22×Dic53—21no—
175C22×Dic53—24no—
176C22×Dic53—21no—
177C22×Dic53—42no—
178C22×Dic53—42no—
179C22×Dic53—42no—
180C22×Dic53—42no—
181C22×Dic53C2×D411yescharacteristic
182C22×Dic53C2×D411yescharacteristic
183C22×Dic53C2×D411yescharacteristic
184C22×Dic53C2×D411yescharacteristic
185C2×D212—21no—
186C2×D212—21no—
187C2×D212—21no—
188C2×D212—21no—
189C2×D212—21no—
190C2×D212C22×C412yes—
191C2×C4×D53—42no—
192C2×C4×D53—42no—
193C2×C4×D53—42no—
194D8×C53—28no—
195C2×C8×C53—21no—
196C2×C8×C53—21no—
197C2×C8×C53—21no—
198C2×C8×C53—21no—
199C2×C8×C53—21no—
200C2×C8×C53C22×C412yes—
201C4⋊C4×C53—21no—
202C4⋊C4×C53—21no—
203C4⋊C4×C53—21no—
204C4⋊C4×C53C2×D412yes—
205C22⋊C4×C53—24no—
206C22⋊C4×C53—42no—
207C42×C53C2×D412yes—
208C42×C53#4112yes—
209C22⋊Dic53—24no—
210C22⋊Dic53—24no—
211C22⋊Dic53—42no—
212C22⋊Dic53—42no—
213#11719922—28no—
214#11719921—42no—
215#11719921—42no—
216#11719921—42no—
217C4⋊Dic53—21no—
218C4⋊Dic53—21no—
219C4⋊Dic53—21no—
220C4⋊Dic53—21no—
221C4⋊Dic53C22×C412yes—
222C4⋊Dic53#4112yes—
223#11719919—42no—
224#11719919—42no—
225C4×Dic53—22no—
226C4×Dic53—21no—
227C4×Dic53—21no—
228C4×Dic53—22no—
229C4×Dic53—41no—
230C4×Dic53—42no—
231C4×Dic53—42no—
232C4×Dic53—42no—
233C4×Dic53D814yescomplemented
234C4×Dic53C22×C412yes—
235C4×Dic53#4112yes—
236C2×#88322—21no—
237C2×#88322—21no—
238C2×#88322—21no—
239C2×#88322—21no—
240C2×#88322—21no—
241C2×#88322C22×C412yes—
242C23×C53—22no—
243C23×C53—22no—
244C23×C53—22no—
245C23×C53—22no—
246C23×C53—41no—
247C23×C53—41no—
248C23×C53—41no—
249C23×C53—41no—
250C23×C53—41no—
251C23×C53—41no—
252C23×C53—41no—
253C23×C53—41no—
254C23×C53—41no—
255C23×C53—41no—
256C23×C53C22×D411yescharacteristic
257C22×D53—22no—
258C22×D53—41no—
259C22×D53—41no—
260C22×D53—41no—
261C22×D53—41no—
262C22×D53—41no—
263C22×D53—41no—
264D4×C53—22no—
265D4×C53—22no—
266D4×C53—22no—
267D4×C53—22no—
268D4×C53—22no—
269D4×C53—41no—
270D4×C53—41no—
271D4×C53C4×D414yescomplemented
272C2×C4×C53—21no—
273C2×C4×C53—21no—
274C2×C4×C53—22no—
275C2×C4×C53—41no—
276C2×C4×C53—41no—
277C2×C4×C53—48no—
278C2×C4×C53—41no—
279C2×C4×C53—41no—
280C2×C4×C53—41no—
281C2×C4×C53—84no—
282C2×C4×C53#12112yes—
283C2×C4×C53#12112yes—
284C2×C4×C53C2×D812yes—
285C2×C4×C53AGL(1,ℤ/8)12yes—
286C2×C4×C53C23×C411yescharacteristic
287C2×C4×C53C22×D411yescharacteristic
288C2×C4×C53C2×#4111yescharacteristic
289C2×C4×C53C2×#4111yescharacteristic
290C2×C4×C53C2×#4111yescharacteristic
291C2×C4×C53C2×#4111yescharacteristic
292C22⋊D53—48no—
293C22⋊D53—48no—
294C2×Dic53—21no—
295C2×Dic53—21no—
296C2×Dic53—21no—
297C2×Dic53—21no—
298C2×Dic53—22no—
299C2×Dic53—22no—
300C2×Dic53—21no—
301C2×Dic53—21no—
302C2×Dic53—21no—
303C2×Dic53—48no—
304C2×Dic53—41no—
305C2×Dic53—41no—
306C2×Dic53—41no—
307C2×Dic53—41no—
308C2×Dic53—48no—
309C2×Dic53—41no—
310C2×Dic53—41no—
311C2×Dic53—41no—
312C2×Dic53C4×D412yes—
313C2×Dic53C4×D412yes—
314C2×Dic53C2×D812yes—
315C2×Dic53C2×D812yes—
316C2×Dic53#13512yes—
317D212—22no—
318D212—22no—
319D212—41no—
320D212—41no—
321C4×D53—84no—
322C8×C53—22no—
323C8×C53—41no—
324#88322—22no—
325#88322—41no—
326C4×#459—531nomaximal, Sylow
327C22×C53—24no—
328C22×C53—42no—
329C22×C53—42no—
330C22×C53—42no—
331C22×C53—42no—
332C22×C53—42no—
333C22×C53—42no—
334C22×C53—42no—
335C22×C53—42no—
336C22×C53—42no—
337C22×C53—81no—
338C22×C53—81no—
339C22×C53—81no—
340C22×C53—81no—
341C22×C53C2×C4×D411yescharacteristic
342C22×C53C2×#12111yescharacteristic
343C22×C53#52511yescharacteristic
344C22×C53C22×D811yescharacteristic
345C22×C53C2×#13511yescharacteristic
346C22×C53C2×AGL(1,ℤ/8)11yescharacteristic
347C22×C53#57511yescharacteristic
348C2×D53—42no—
349C2×D53—42no—
350C2×D53—42no—
351C2×D53—81no—
352C2×D53—81no—
353C2×D53—81no—
354C2×D53—81no—
355C4×C53—22no—
356C4×C53—42no—
357C4×C53—81no—
358C4×C53#45914yescomplemented
359C4×C53C2×C4×D411yescharacteristic
360C4×C53C4×#4111yescharacteristic
361C4×C53#52911yescharacteristic
362C4×C53#53211yescharacteristic
363Dic53—22no—
364Dic53—22no—
365Dic53—42no—
366Dic53—41no—
367Dic53—42no—
368Dic53—81no—
369Dic53C4×D814yescomplemented
370C2×#459—531no—
371C2×C4×D8—531no—
372C2×C4×D8D5311yescharacteristic, complemented
373C4×#127—531no—
374C42×D4—531no—
375#1982—531no—
376#1947—531no—
377#1925—531no—
378#1925—531no—
379#1879—531no—
380#1879—531no—
381#1802—531no—
382C4×C4⋊C8—531no—
383C4×#102—531no—
384C4×#102—531no—
385C2×C53—44no—
386C2×C53—82no—
387C2×C53C4×#12111yescharacteristic
388C2×C53C2×C4×D811yescharacteristic
389C2×C53C4×AGL(1,ℤ/8)11yescharacteristic
390C2×C53C2×#45911yescharacteristic
391C2×C53#303511yescharacteristic
392C2×C53#310011yescharacteristic
393C2×C53#310611yescharacteristic
394D53—82no—
395C22×D8—531no—
396C22×D8C2×D5311yescharacteristic
397C2×#127—531no—
398C2×C4×D4—531no—
399C2×C4×D4—531no—
400C2×C4×D4—531no—
401C2×C4×D4—1061no—
402C2×C4×D4—1061no—
403C2×C4×D4C2×D5311yescharacteristic
404C2×C4×D4C2×D5311yescharacteristic
405C22×C42—1061no—
406#459—538no—
407C4×D8—24no—
408C4×D8—1064no—
409C2×#107—531no—
410C2×#107C2×D5311yescharacteristic
411C2×C4⋊C8—531no—
412C2×C4⋊C8—531no—
413C2×#102—531no—
414C2×#102—531no—
415C2×#102—531no—
416C2×#102—531no—
417C2×#102—531no—
418C2×#102—531no—
419C2×#102C2×D5311yescharacteristic
420C2×#102C2×D5311yescharacteristic
421C2×C4×C8—531no—
422C2×C4×C8C2×D5311yescharacteristic
423#390—531no—
424#390—531no—
425#390—1061no—
426#390—1061no—
427#384—531no—
428C4×C4⋊C4—531no—
429C4×C4⋊C4—531no—
430C4×C4⋊C4—531no—
431C4×C22⋊C4—1061no—
432C4×C22⋊C4—1061no—
433C4×C22⋊C4—1061no—
434C43—531no—
435#340—531no—
436#340—531no—
437#340—531no—
438#340—531no—
439#336—531no—
440#336—531no—
441C53C4×#45911yescharacteristic, complemented, Sylow
442C22×D4—531no—
443C22×D4—1061no—
444C22×D4—1061no—
445C22×D4C22×D5311yescharacteristic
446C22×D4C22×D5311yescharacteristic
447C23×C4—21no—
448C23×C4—21no—
449C23×C4—1061no—
450C23×C4—1061no—
451C23×C4—1061no—
452C2×D8—22no—
453C2×D8—22no—
454C2×D8—534no—
455C2×D8—1062no—
456C2×D8—1062no—
457C2×D8C4×D5314yescomplemented
458C22×C8—531no—
459C22×C8—531no—
460C22×C8C22×D5311yescharacteristic
461C22×C8C22×D5311yescharacteristic
462#127—534no—
463#127—1062no—
464C4×D4—22no—
465C4×D4—22no—
466C4×D4—22no—
467C4×D4—534no—
468C4×D4—1062no—
469C4×D4—1062no—
470C4×D4—1062no—
471C4×D4—1062no—
472C4×D4—1062no—
473C4×D4—2124no—
474C4×D4—2124no—
475C4×D4C22⋊D5314yescomplemented
476C2×C4⋊C4—531no—
477C2×C4⋊C4—531no—
478C2×C4⋊C4—531no—
479C2×C4⋊C4—1061no—
480C2×C4⋊C4—1061no—
481C2×C4⋊C4C22×D5311yescharacteristic
482C2×C4⋊C4C22×D5311yescharacteristic
483C2×C22⋊C4—21no—
484C2×C22⋊C4—21no—
485C2×C22⋊C4—1061no—
486C2×C22⋊C4—1061no—
487C2×C22⋊C4—1061no—
488C2×C22⋊C4—1061no—
489C2×C22⋊C4—1061no—
490C2×C22⋊C4—1061no—
491C2×C22⋊C4—1061no—
492C2×C42—531no—
493C2×C42—531no—
494C2×C42—531no—
495C2×C42—531no—
496C2×C42—531no—
497C2×C42—531no—
498C2×C42—1061no—
499C2×C42—1061no—
500C2×C42—1061no—
501C2×C42—2124no—
502C2×C42C22×D5311yescharacteristic
503#107—22no—
504#107—1062no—
505C4⋊C8—534no—
506C4⋊C8—1062no—
507#102—22no—
508#102—22no—
509#102—534no—
510#102—534no—
511#102—1062no—
512#102—1062no—
513#102—1062no—
514#102—1062no—
515C4×C8—22no—
516C4×C8—1062no—
517#95—1061no—
518#95—1061no—
519#95—1061no—
520C24—21no—
521C24—21no—
522C24—1061no—
523C2×D4—21no—
524C2×D4—21no—
525C2×D4—21no—
526C2×D4—21no—
527C2×D4—21no—
528C2×D4—21no—
529C2×D4—21no—
530C2×D4—21no—
531C2×D4—532no—
532C2×D4—1064no—
533C2×D4—1064no—
534C2×D4—1061no—
535C2×D4—1061no—
536C2×D4—1061no—
537C2×D4—1061no—
538C2×D4—1061no—
539C2×D4—2122no—
540C2×D4—2122no—
541C2×D4—2122no—
542C2×D4—2122no—
543C2×D4C2×C4×D5312yes—
544C2×D4C2×C4×D5312yes—
545C2×D4#1171994512yes—
546C2×D4C2×C22⋊D5312yes—
547C22×C4—21no—
548C22×C4—24no—
549C22×C4—21no—
550C22×C4—42no—
551C22×C4—42no—
552C22×C4—42no—
553C22×C4—42no—
554C22×C4—42no—
555C22×C4—531no—
556C22×C4—531no—
557C22×C4—531no—
558C22×C4—531no—
559C22×C4—1064no—
560C22×C4—1064no—
561C22×C4—1061no—
562C22×C4—1061no—
563C22×C4—1061no—
564C22×C4—2122no—
565C22×C4—2122no—
566C22×C4—2122no—
567C22×C4—2122no—
568C22×C4—2122no—
569C22×C4—2122no—
570C22×C4—2122no—
571C22×C4D4×D5311yescharacteristic
572C22×C4D4×D5311yescharacteristic
573C22×C4C23×D5311yescharacteristic
574D8—28no—
575D8—1068no—
576C2×C8—21no—
577C2×C8—21no—
578C2×C8—21no—
579C2×C8—21no—
580C2×C8—21no—
581C2×C8—532no—
582C2×C8—1061no—
583C2×C8—1061no—
584C2×C8—1061no—
585C2×C8—1061no—
586C2×C8—1061no—
587C2×C8C2×C4×D5312yes—
588C4⋊C4—21no—
589C4⋊C4—21no—
590C4⋊C4—21no—
591C4⋊C4—532no—
592C4⋊C4—532no—
593C4⋊C4—1061no—
594C4⋊C4—1061no—
595C4⋊C4—1061no—
596C4⋊C4—1061no—
597C4⋊C4—2122no—
598C4⋊C4—2122no—
599C4⋊C4C2×C22⋊D5312yes—
600C22⋊C4—24no—
601C22⋊C4—42no—
602C22⋊C4—1064no—
603C22⋊C4—1064no—
604C22⋊C4—2122no—
605C22⋊C4—2122no—
606C22⋊C4—2122no—
607C22⋊C4—2122no—
608C22⋊C4—2122no—
609C42—534no—
610C42—532no—
611C42—532no—
612C42—1062no—
613C42—1062no—
614C42—1061no—
615C42—1061no—
616C42—2121no—
617C42—2122no—
618C42—2122no—
619C42—2122no—
620C42#1171994712yes—
621C42C2×C22⋊D5312yes—
622C23—22no—
623C23—22no—
624C23—22no—
625C23—22no—
626C23—41no—
627C23—41no—
628C23—41no—
629C23—41no—
630C23—41no—
631C23—41no—
632C23—41no—
633C23—41no—
634C23—41no—
635C23—41no—
636C23—1062no—
637C23—2121no—
638C23—2121no—
639C23—2121no—
640C23—2121no—
641C23—2121no—
642C23—2121no—
643C23C2×D4×D5311yescharacteristic
644D4—22no—
645D4—22no—
646D4—22no—
647D4—22no—
648D4—22no—
649D4—41no—
650D4—41no—
651D4—1062no—
652D4—1062no—
653D4—2128no—
654D4—2128no—
655D4—2121no—
656D4—2121no—
657D4C4×C22⋊D5314yescomplemented
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—22no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—48no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—84no—
668C2×C4—532no—
669C2×C4—532no—
670C2×C4—532no—
671C2×C4—532no—
672C2×C4—532no—
673C2×C4—1061no—
674C2×C4—1061no—
675C2×C4—1061no—
676C2×C4—1061no—
677C2×C4—1062no—
678C2×C4—1061no—
679C2×C4—1062no—
680C2×C4—1061no—
681C2×C4—1061no—
682C2×C4—4244no—
683C2×C4—2128no—
684C2×C4—2128no—
685C2×C4—2121no—
686C2×C4—2121no—
687C2×C4—2121no—
688C2×C4—2121no—
689C2×C4—2121no—
690C2×C4—2121no—
691C2×C4—2121no—
692C2×C4#1313318912yes—
693C2×C4#1313318912yes—
694C2×C4D8×D5312yes—
695C2×C4#1313324112yes—
696C2×C4C22×C4×D5311yescharacteristic
697C2×C4C22×C22⋊D5311yescharacteristic
698C2×C4#41×D5311yescharacteristic
699C2×C4#41×D5311yescharacteristic
700C2×C4C2×#1171994711yescharacteristic
701C2×C4C2×#1171994511yescharacteristic
702C8—22no—
703C8—41no—
704C8—1062no—
705C8—2121no—
706C22—24no—
707C22—42no—
708C22—42no—
709C22—42no—
710C22—42no—
711C22—42no—
712C22—42no—
713C22—42no—
714C22—42no—
715C22—42no—
716C22—81no—
717C22—81no—
718C22—81no—
719C22—81no—
720C22—4241no—
721C22—4241no—
722C22—4241no—
723C22—4241no—
724C22—2122no—
725C22—2122no—
726C22—2122no—
727C22C4×D4×D5311yescharacteristic
728C22C2×#1313318911yescharacteristic
729C22#1681113211yescharacteristic
730C22C2×D8×D5311yescharacteristic
731C22#135×D5311yescharacteristic
732C22C2×#1313324111yescharacteristic
733C22#1681142011yescharacteristic
734C4—22no—
735C4—42no—
736C4—81no—
737C4—534no—
738C4—1062no—
739C4—1062no—
740C4—4241no—
741C4—2122no—
742C4—2122no—
743C4—2121no—
744C4#1681081614yesdirect product factor
745C4C2×C4×C22⋊D5311yescharacteristic
746C4C4×#1171994711yescharacteristic
747C4#1681115311yescharacteristic
748C4#1681116911yescharacteristic
749C2—44no—
750C2—82no—
751C2—4242no—
752C2C4×#1313318911yescharacteristic
753C2C4×D8×D5311yescharacteristic
754C2C4×#1313324111yescharacteristic
755C2C2×#1681081611yescharacteristic
756C2#2028416611yescharacteristic
757C2#2028471311yescharacteristic
758C2#2028477111yescharacteristic
subgroupG/H
centerC22×C4D4×D53
commutatorC2×C4×C53C23×C4
FrattiniC22×C4C23×D53
FittingC2×C4×D8×C53C2
socleC23×C53C22×D4
prime radicalC2×#16810816C2
cosocleC22×C4×C53C24
hypercenterC2×C4×D8D53
hypocenterC53C4×#459
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4×D8

Complements

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

NH ≅ G/Ntype
2. C2×C4×#11719922C2semidirect
3. C4×#13133213C2semidirect
4. C4×D4×Dic53C2semidirect
5. #20275640C2semidirect
6. #20275470C2semidirect
7. #20275338C2semidirect
8. #20275334C2semidirect
9. #20275065C2semidirect
10. #20275061C2semidirect
11. #20274713C2semidirect
12. C4×#13133146C2semidirect
13. C4×#13133139C2semidirect
14. C4×#13133138C2semidirect
15. C2×C4×D8×C53C2semidirect
24. #16810816C4direct (N × H)
70. C2×#11719922C2×C4semidirect
74. #13133213C2×C4semidirect
80. D4×Dic53C2×C4semidirect
107. #13133146C2×C4semidirect
109. #13133139C2×C4semidirect
112. #13133138C2×C4semidirect
124. C2×D8×C53C2×C4semidirect
130. C4×D4×C53D4semidirect
233. C4×Dic53D8semidirect
271. D4×C53C4×D4semidirect
358. C4×C53#459semidirect
369. Dic53C4×D8semidirect
372. C2×C4×D8D53semidirect
441. C53C4×#459semidirect
457. C2×D8C4×D53semidirect
475. C4×D4C22⋊D53semidirect
657. D4C4×C22⋊D53semidirect
744. C4#16810816direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168108162
C2×C4×#117199222
C4×#131332132
C4×D4×Dic532
#202756402
#202754702
#202753382
#202753342
#202750652
#202750612
#202747132
C4×#131331462
C4×#131331392
C4×#131331382
C2×C4×D8×C532
C4×#45953