Finite Group Databasebeta

← C2×#20284185 #28250929

Subgroups — C2×#20284185 #28250929

Order 13568.

2810 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13133249C211yesmaximal, characteristic, complemented
2C22×#13133246C211yesmaximal, characteristic, complemented
3C2×#16811172C211yesmaximal, characteristic
4C2×C4×Q8×D53C211yesmaximal, characteristic, complemented
5#20284185C2116yesmaximal, direct product factor
6C2×#16810846C211yesmaximal, characteristic, complemented
7C2×#16810845C211yesmaximal, characteristic, complemented
8C2×#16810842C211yesmaximal, characteristic, complemented
9C2×#16810832C211yesmaximal, characteristic, complemented
10C2×#16810831C211yesmaximal, characteristic, complemented
11C2×#16810822C211yesmaximal, characteristic, complemented
12C2×#16810821C211yesmaximal, characteristic, complemented
13C2×#16810645C211yesmaximal, characteristic, complemented
14C2×#16810623C211yesmaximal, characteristic, complemented
15C2×#16810621C211yesmaximal, characteristic, complemented
16C2×C53×#464C211yesmaximal, characteristic, complemented
17C22×#11719949C2211yescharacteristic
18C22×#11719947C2211yescharacteristic
19C22×Q8×D53C2211yescharacteristic
20C2×#13133249—28no—
21C2×#13133249C2218yescomplemented
22C2×#13133246—28no—
23C2×#13133246C2218yescomplemented
24C22×Dic212C2211yescharacteristic
25C22×#11719925C2211yescharacteristic
26C22×#11719925C2211yescharacteristic
27C22×#11719913C2211yescharacteristic
28C22×#11719923C2211yescharacteristic
29C22×#11719924C2211yescharacteristic
30C22×#11719912C2211yescharacteristic
31C22×#11719912C2211yescharacteristic
32#16811172—24no—
33#16811172C2218yes—
34C2×#13133215C2211yescharacteristic
35C2×#13133213C2211yescharacteristic
36C2×#13133205C2211yescharacteristic
37C2×#13133190—21no—
38C2×#13133190—21no—
39C2×Q8×Dic53C2211yescharacteristic
40C2×C4×Dic106—21no—
41C2×C4×Dic106C2211yescharacteristic
42C2×#13133182—21no—
43C2×#13133182C2211yescharacteristic
44C4×Q8×D53—24no—
45C4×Q8×D53C2218yescomplemented
46C2×#13133177—21no—
47C2×#13133177—21no—
48C2×C4⋊C4×D53—21no—
49C2×C4⋊C4×D53C2211yescharacteristic
50C2×C42×D53—21no—
51C2×C42×D53C2211yescharacteristic
52#16810846C2218yescomplemented
53#16810845C2218yescomplemented
54#16810842C2218yescomplemented
55#16810832C2218yescomplemented
56#16810831C2218yescomplemented
57#16810822C2218yescomplemented
58#16810821C2218yescomplemented
59#16810645C2218yescomplemented
60C2×C4⋊#88322C2211yescharacteristic
61C2×#13133146C2211yescharacteristic
62C2×#13133146C2211yescharacteristic
63#16810623C2218yescomplemented
64#16810621C2218yescomplemented
65C2×#13133142C2211yescharacteristic
66C2×#13133141C2211yescharacteristic
67C2×#13133140C2211yescharacteristic
68C2×#13133139C2211yescharacteristic
69C2×#13133138C2211yescharacteristic
70C2×#13133137C2211yescharacteristic
71C22×Q16×C53C2211yescharacteristic
72C22×SD16×C53C2211yescharacteristic
73C2×#124×C53C2211yescharacteristic
74C2×C4×Q8×C53C2211yescharacteristic
75C53×#464C2218yescomplemented
76C2×C4⋊C8×C53C2211yescharacteristic
77C2×#103×C53C2211yescharacteristic
78C2×#102×C53C2211yescharacteristic
79C2×#11719949—22no—
80C2×#11719949—24no—
81C2×#11719949—24no—
82C2×#11719949C2314yes—
83C2×#11719947—24no—
84C2×#11719947—22no—
85C2×#11719947—24no—
86C2×#11719947C2314yes—
87C22×Dic106—21no—
88C22×Dic106C2311yescharacteristic
89C22×Dic106C2311yescharacteristic
90C2×Q8×D53—22no—
91C2×Q8×D53—24no—
92C2×Q8×D53D418yescomplemented
93C2×Q8×D53C2314yes—
94C22×D212—21no—
95C22×D212C2311yescharacteristic
96C22×C22⋊D53—21no—
97C22×C22⋊D53—21no—
98C22×C22⋊D53—21no—
99C23×Dic53—21no—
100C22×C4×D53—21no—
101C22×C4×D53—21no—
102C22×C4×D53—21no—
103C22×C4×D53D411yescharacteristic
104C22×C4×D53D411yescharacteristic
105C22×C4×D53C2311yescharacteristic
106#13133249—232no—
107#13133246—232no—
108C2×Dic212—24no—
109C2×Dic212C2314yes—
110C2×#11719925—24no—
111C2×#11719925—24no—
112C2×#11719925C2314yes—
113C2×#11719925C2314yes—
114C2×#11719913—24no—
115C2×#11719913C2314yes—
116C2×#11719923—24no—
117C2×#11719923C2314yes—
118C2×#11719924—24no—
119C2×#11719924C2314yes—
120C2×#11719912—24no—
121C2×#11719912—24no—
122C2×#11719912C2314yes—
123C2×#11719912C2314yes—
124C22×#88322C2311yescharacteristic
125C22×#88322C2311yescharacteristic
126#13133215—22no—
127#13133215C2314yes—
128#13133213—22no—
129#13133213C2314yes—
130#13133205—22no—
131#13133205C2314yes—
132#13133190—28no—
133#13133190—28no—
134Q8×Dic53—22no—
135Q8×Dic53C2314yes—
136C4×Dic106—22no—
137C4×Dic106—28no—
138C4×Dic106C2314yes—
139#13133182—22no—
140#13133182—28no—
141#13133182C2314yes—
142#13133177—28no—
143#13133177—28no—
144C2×C4⋊Dic53—21no—
145C2×C4⋊Dic53C2311yescharacteristic
146C2×#11719919—21no—
147C2×#11719919—21no—
148C2×#11719919—21no—
149C2×#11719919—21no—
150C2×#11719919—21no—
151C4⋊C4×D53—28no—
152C4⋊C4×D53—22no—
153C4⋊C4×D53C2314yes—
154C2×#11719921—21no—
155C2×#11719921—21no—
156C2×C4×Dic53—21no—
157C2×C4×Dic53—21no—
158C2×C4×Dic53—21no—
159C2×C4×Dic53D411yescharacteristic
160C2×C4×Dic53D411yescharacteristic
161C2×C4×Dic53C2311yescharacteristic
162C42×D53—28no—
163C42×D53D414yes—
164C42×D53C2314yes—
165C4⋊#88322C2314yes—
166#13133146C2314yes—
167#13133146C2314yes—
168#13133142C2314yes—
169#13133141C2314yes—
170#13133140C2314yes—
171#13133139C2314yes—
172#13133138C2314yes—
173#13133137C2314yes—
174C22×Q8×C53C2311yescharacteristic
175C22×Q8×C53C2311yescharacteristic
176C22×D4×C53C2311yescharacteristic
177C2×Q16×C53—24no—
178C2×Q16×C53C2314yes—
179C2×SD16×C53—24no—
180C2×SD16×C53C2314yes—
181C22×C8×C53C2311yescharacteristic
182C22×C8×C53C2311yescharacteristic
183#124×C53—22no—
184#124×C53C2314yes—
185C4×Q8×C53—22no—
186C4×Q8×C53C2314yes—
187C2×C4⋊C4×C53—21no—
188C2×C4⋊C4×C53C2311yescharacteristic
189C2×C22⋊C4×C53—21no—
190C2×C22⋊C4×C53—21no—
191C2×C42×C53—21no—
192C2×C42×C53C2311yescharacteristic
193C4⋊C8×C53C2314yes—
194#103×C53C2314yes—
195#102×C53C2314yes—
196C24×C53—21no—
197C23×D53—21no—
198C23×D53C2×D411yescharacteristic
199C2×Q8×C53—21no—
200C2×Q8×C53—21no—
201C2×Q8×C53—22no—
202C2×Q8×C53—22no—
203C2×Q8×C53—22no—
204C2×Q8×C53C2×D414yes—
205C2×Q8×C53C2412yes—
206C2×Q8×C53C2412yes—
207C2×D4×C53—22no—
208C2×D4×C53—21no—
209C2×D4×C53—22no—
210C2×D4×C53C2412yes—
211C22×C4×C53—21no—
212C22×C4×C53—21no—
213C22×C4×C53—21no—
214C22×C4×C53C2×D411yescharacteristic
215C22×C4×C53C2×D411yescharacteristic
216C22×C4×C53C2411yescharacteristic
217C2×C22⋊D53—24no—
218C2×C22⋊D53—24no—
219C2×C22⋊D53—24no—
220C2×C22⋊D53—44no—
221C2×C22⋊D53—44no—
222C2×C22⋊D53—44no—
223C22×Dic53—21no—
224C22×Dic53—21no—
225C22×Dic53—21no—
226C22×Dic53—24no—
227C22×Dic53—44no—
228C22×Dic53C2×D411yescharacteristic
229C22×Dic53C2×D411yescharacteristic
230C22×Dic53C2×D411yescharacteristic
231#11719949—28no—
232#11719949—28no—
233#11719949—48no—
234Q8×D53—216no—
235Q8×D53—28no—
236Q8×D53C2×D4116yescomplemented
237#11719947—28no—
238#11719947—28no—
239#11719947—48no—
240C2×D212—22no—
241C2×D212—22no—
242C2×D212—24no—
243C2×D212—21no—
244C2×D212—44no—
245C2×D212C2412yes—
246C2×C4×D53—28no—
247C2×C4×D53—24no—
248C2×C4×D53—24no—
249C2×C4×D53—24no—
250C2×C4×D53—24no—
251C2×C4×D53—42no—
252C2×C4×D53—44no—
253C2×C4×D53—44no—
254C2×C4×D53C2×D414yes—
255C2×C4×D53C2×D414yes—
256C2×C4×D53C2×D412yes—
257C2×C4×D53C2×D414yes—
258C2×C4×D53#4114yes—
259C2×C4×D53C2412yes—
260C2×Dic106—21no—
261C2×Dic106—22no—
262C2×Dic106—28no—
263C2×Dic106—24no—
264C2×Dic106—22no—
265C2×Dic106—22no—
266C2×Dic106—21no—
267C2×Dic106C2×D414yes—
268C2×Dic106C2412yes—
269C2×Dic106C2412yes—
270Q16×C53—28no—
271SD16×C53—28no—
272C2×C8×C53—22no—
273C2×C8×C53—22no—
274C2×C8×C53C2412yes—
275C2×C8×C53C2412yes—
276C4⋊C4×C53—24no—
277C4⋊C4×C53—21no—
278C4⋊C4×C53C2412yes—
279C22⋊C4×C53—24no—
280C22⋊C4×C53—24no—
281C42×C53—24no—
282C42×C53C2×D412yes—
283C42×C53C2412yes—
284#11719925—28no—
285#11719925—28no—
286#11719924—28no—
287#11719923—28no—
288#11719921—24no—
289#11719921—24no—
290C4⋊Dic53—21no—
291C4⋊Dic53—24no—
292C4⋊Dic53C2412yes—
293#11719919—24no—
294#11719919—24no—
295#11719919—24no—
296#11719919—24no—
297#11719919—24no—
298C4×Dic53—24no—
299C4×Dic53—24no—
300C4×Dic53—24no—
301C4×Dic53C2×D412yes—
302C4×Dic53C2×D414yes—
303C4×Dic53C2×D414yes—
304C4×Dic53C2412yes—
305C2×#88322—22no—
306C2×#88322—22no—
307C2×#88322C2412yes—
308C2×#88322C2412yes—
309Dic212—28no—
310#11719913—28no—
311#11719912—28no—
312#11719912—28no—
313C23×C53—22no—
314C23×C53—42no—
315C23×C53—42no—
316C23×C53—42no—
317C23×C53C22×D411yescharacteristic
318C22×D53—22no—
319C22×D53—22no—
320C22×D53—22no—
321C22×D53—42no—
322C22×D53—42no—
323C22×D53—42no—
324C22×D53#12114yes—
325C22×D53C22×D412yes—
326Q8×C53—24no—
327Q8×C53—22no—
328Q8×C53—22no—
329Q8×C53—22no—
330Q8×C53—42no—
331Q8×C53C22×D414yes—
332D4×C53—22no—
333D4×C53—22no—
334D4×C53—42no—
335C2×C4×C53—24no—
336C2×C4×C53—22no—
337C2×C4×C53—22no—
338C2×C4×C53—22no—
339C2×C4×C53—22no—
340C2×C4×C53—22no—
341C2×C4×C53—42no—
342C2×C4×C53—42no—
343C2×C4×C53C22×D412yes—
344C2×C4×C53C22×D412yes—
345C2×C4×C53C22×D411yescharacteristic
346C2×C4×C53C22×D412yes—
347C2×C4×C53C2×#4112yes—
348C2×C4×C53C2511yescharacteristic
349C22⋊D53—48no—
350C22⋊D53—48no—
351C22⋊D53—48no—
352C2×Dic53—24no—
353C2×Dic53—22no—
354C2×Dic53—22no—
355C2×Dic53—22no—
356C2×Dic53—22no—
357C2×Dic53—42no—
358C2×Dic53—42no—
359C2×Dic53—48no—
360C2×Dic53#12114yes—
361C2×Dic53#13714yescomplemented
362C2×Dic53C22×D412yes—
363C2×Dic53C22×D412yes—
364C2×Dic53C22×D412yes—
365D212—22no—
366D212—22no—
367D212—48no—
368D212—42no—
369C4×D53—216no—
370C4×D53—28no—
371C4×D53—44no—
372C4×D53—48no—
373C4×D53—48no—
374C4×D53#12118yes—
375C4×D53C22×D414yes—
376C4×D53C2×#4114yes—
377Dic106—24no—
378Dic106—22no—
379Dic106—216no—
380Dic106—22no—
381Dic106—22no—
382Dic106—42no—
383Dic106C22×D414yes—
384C8×C53—22no—
385C8×C53—22no—
386#88322—22no—
387#88322—22no—
388C2×#3037—531nomaximal, Sylow
389C22×C53—42no—
390C22×C53—42no—
391C22×C53—42no—
392C22×C53—84no—
393C22×C53C2×#12112yes—
394C22×C53C2×#13712yes—
395C22×C53#57512yes—
396C22×C53C23×D411yescharacteristic
397C2×D53—28no—
398C2×D53—22no—
399C2×D53—22no—
400C2×D53—42no—
401C2×D53—42no—
402C2×D53—42no—
403C2×D53—84no—
404C2×D53C2×#12114yes—
405C4×C53—24no—
406C4×C53—22no—
407C4×C53—22no—
408C4×C53—42no—
409C4×C53—42no—
410C4×C53C2×#12112yes—
411C4×C53C23×D411yescharacteristic
412C4×C53C22×#4111yescharacteristic
413Dic53—24no—
414Dic53—22no—
415Dic53—42no—
416Dic53—42no—
417Dic53C2×#12114yes—
418Dic53C2×#13714yescomplemented
419C22×#137—531no—
420C22×#137—531no—
421C2×#532—531no—
422C22×C4×Q8—531no—
423#3037—5316no—
424C2×#464—531no—
425C2×#464—531no—
426C2×#464—531no—
427C2×#464D5311yescharacteristic, complemented
428C2×#462—531no—
429C2×#462—531no—
430C2×#460—531no—
431C2×#460—531no—
432C2×#423—531no—
433C2×#417—531no—
434C2×#417—531no—
435C2×C53—82no—
436C2×C53#303714yescomplemented
437C2×C53C22×#12111yescharacteristic
438C2×C53C22×#13711yescharacteristic
439C2×C53C2×#57511yescharacteristic
440D53—24no—
441D53—82no—
442C22×#41—531no—
443C22×#41—531no—
444C23×Q8—531no—
445C2×#137—538no—
446C2×#137—538no—
447C2×#137—1068no—
448C2×#137—1068no—
449C22×Q16—531no—
450C22×Q16—531no—
451C22×Q16—531no—
452C22×Q16C2×D5311yescharacteristic
453C22×SD16—531no—
454C22×SD16—531no—
455C22×SD16—531no—
456C22×SD16C2×D5311yescharacteristic
457C22×M16—531no—
458C22×M16—531no—
459#532—538no—
460#532—1064no—
461C2×C4⋊Q8—531no—
462C2×#127—531no—
463C2×#124—531no—
464C2×#124C2×D5311yescharacteristic
465C2×#121—1061no—
466C2×#121—1061no—
467C2×C4×Q8—531no—
468C2×C4×Q8—538no—
469C2×C4×Q8—531no—
470C2×C4×Q8—531no—
471C2×C4×Q8—1061no—
472C2×C4×Q8—1061no—
473C2×C4×Q8—1064no—
474C2×C4×Q8C2×D5311yescharacteristic
475C2×C4×D4—1061no—
476C2×C4×D4—1061no—
477C22×C4⋊C4—531no—
478C22×C4⋊C4—1061no—
479C22×C42—531no—
480C22×C42—1061no—
481#464—538no—
482#464—538no—
483#464—538no—
484#464C2×D5318yescomplemented
485#462—538no—
486#462—538no—
487#460—538no—
488#460—538no—
489#423—538no—
490C2×C4⋊C8—531no—
491C2×C4⋊C8—531no—
492C2×C4⋊C8—531no—
493C2×C4⋊C8C2×D5311yescharacteristic
494#417—538no—
495#417—538no—
496C2×#103—531no—
497C2×#103—531no—
498C2×#103—531no—
499C2×#103C2×D5311yescharacteristic
500C2×#102—531no—
501C2×#102—531no—
502C2×#102—531no—
503C2×#102C2×D5311yescharacteristic
504C53C2×#303711yescharacteristic, complemented, Sylow
505C2×#41—534no—
506C2×#41—534no—
507C2×#41—1062no—
508C2×#41—1062no—
509C2×#41—1064no—
510C2×#41—1064no—
511C2×#41—1064no—
512C2×#41—1064no—
513C22×Q8—538no—
514C22×Q8—534no—
515C22×Q8—531no—
516C22×Q8—531no—
517C22×Q8—1061no—
518C22×Q8—1062no—
519C22×Q8—1064no—
520C22×Q8C22×D5311yescharacteristic
521C22×Q8C22×D5311yescharacteristic
522C22×D4—531no—
523C22×D4—1061no—
524C22×D4—1061no—
525C22×D4—1061no—
526C22×D4—1061no—
527C22×D4C22×D5311yescharacteristic
528C23×C4—531no—
529C23×C4—531no—
530C23×C4—531no—
531C23×C4—1061no—
532C23×C4—1061no—
533C23×C4—1061no—
534C23×C4—1061no—
535#137—10632no—
536#137—10632no—
537C2×Q16—24no—
538C2×Q16—534no—
539C2×Q16—534no—
540C2×Q16—534no—
541C2×Q16—1064no—
542C2×Q16—1064no—
543C2×Q16—1064no—
544C2×Q16C22×D5314yes—
545C2×SD16—24no—
546C2×SD16—534no—
547C2×SD16—534no—
548C2×SD16—534no—
549C2×SD16—1064no—
550C2×SD16—1064no—
551C2×SD16—1064no—
552C2×SD16C22×D5314yes—
553C2×M16—534no—
554C2×M16—534no—
555C2×M16—1064no—
556C2×M16—1064no—
557C22×C8—531no—
558C22×C8—531no—
559C22×C8C22×D5311yescharacteristic
560C22×C8C22×D5311yescharacteristic
561C4⋊Q8—534no—
562C4⋊Q8—1062no—
563#127—534no—
564#127—1062no—
565#124—22no—
566#124—534no—
567#124—1062no—
568#124C22×D5314yes—
569#121—1068no—
570#121—1068no—
571C4×Q8—22no—
572C4×Q8—534no—
573C4×Q8—534no—
574C4×Q8—534no—
575C4×Q8—1068no—
576C4×Q8—1068no—
577C4×Q8—1062no—
578C4×Q8—1062no—
579C4×Q8—1062no—
580C4×Q8C22×D5314yes—
581C4×D4—1068no—
582C4×D4—1068no—
583C2×C4⋊C4—21no—
584C2×C4⋊C4—531no—
585C2×C4⋊C4—534no—
586C2×C4⋊C4—1062no—
587C2×C4⋊C4—1068no—
588C2×C4⋊C4—1061no—
589C2×C4⋊C4—1061no—
590C2×C4⋊C4—1061no—
591C2×C4⋊C4—1061no—
592C2×C4⋊C4—1061no—
593C2×C4⋊C4—1061no—
594C2×C4⋊C4C22×D5311yescharacteristic
595C2×C22⋊C4—21no—
596C2×C22⋊C4—21no—
597C2×C22⋊C4—1061no—
598C2×C22⋊C4—1061no—
599C2×C42—21no—
600C2×C42—531no—
601C2×C42—531no—
602C2×C42—531no—
603C2×C42—534no—
604C2×C42—534no—
605C2×C42—1068no—
606C2×C42—1061no—
607C2×C42—1061no—
608C2×C42—1061no—
609C2×C42C22×D5311yescharacteristic
610C4⋊C8—534no—
611C4⋊C8—534no—
612C4⋊C8—534no—
613C4⋊C8C22×D5314yes—
614#103—534no—
615#103—534no—
616#103—534no—
617#103C22×D5314yes—
618#102—534no—
619#102—534no—
620#102—534no—
621#102C22×D5314yes—
622C24—21no—
623C24—531no—
624C24—1061no—
625#41—1068no—
626#41—1068no—
627#41—1068no—
628#41—1068no—
629#41—2128no—
630#41—2128no—
631C2×Q8—21no—
632C2×Q8—21no—
633C2×Q8—22no—
634C2×Q8—22no—
635C2×Q8—22no—
636C2×Q8—5316no—
637C2×Q8—534no—
638C2×Q8—532no—
639C2×Q8—532no—
640C2×Q8—1064no—
641C2×Q8—1068no—
642C2×Q8—10616no—
643C2×Q8—1068no—
644C2×Q8—1061no—
645C2×Q8—1061no—
646C2×Q8—1062no—
647C2×Q8—1062no—
648C2×Q8—1062no—
649C2×Q8D4×D5314yes—
650C2×Q8C23×D5312yes—
651C2×Q8C23×D5312yes—
652C2×D4—22no—
653C2×D4—21no—
654C2×D4—22no—
655C2×D4—532no—
656C2×D4—1064no—
657C2×D4—1064no—
658C2×D4—1064no—
659C2×D4—1064no—
660C2×D4—1062no—
661C2×D4—1061no—
662C2×D4—1062no—
663C2×D4—2124no—
664C2×D4—2124no—
665C2×D4—2124no—
666C2×D4—2124no—
667C2×D4C23×D5312yes—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—531no—
672C22×C4—531no—
673C22×C4—532no—
674C22×C4—534no—
675C22×C4—534no—
676C22×C4—532no—
677C22×C4—531no—
678C22×C4—534no—
679C22×C4—534no—
680C22×C4—1064no—
681C22×C4—1064no—
682C22×C4—1064no—
683C22×C4—1068no—
684C22×C4—1064no—
685C22×C4—1064no—
686C22×C4—1061no—
687C22×C4—1061no—
688C22×C4—1061no—
689C22×C4—2122no—
690C22×C4—2124no—
691C22×C4—2124no—
692C22×C4—2124no—
693C22×C4D4×D5311yescharacteristic
694C22×C4D4×D5311yescharacteristic
695C22×C4C23×D5311yescharacteristic
696Q16—28no—
697Q16—1068no—
698Q16—1068no—
699Q16—1068no—
700SD16—28no—
701SD16—1068no—
702SD16—1068no—
703SD16—1068no—
704M16—1068no—
705M16—1068no—
706C2×C8—22no—
707C2×C8—22no—
708C2×C8—532no—
709C2×C8—532no—
710C2×C8—1062no—
711C2×C8—1062no—
712C2×C8C23×D5312yes—
713C2×C8C23×D5312yes—
714C4⋊C4—24no—
715C4⋊C4—21no—
716C4⋊C4—532no—
717C4⋊C4—1064no—
718C4⋊C4—1064no—
719C4⋊C4—1064no—
720C4⋊C4—1064no—
721C4⋊C4—1064no—
722C4⋊C4—1061no—
723C4⋊C4—1064no—
724C4⋊C4C23×D5312yes—
725C22⋊C4—24no—
726C22⋊C4—24no—
727C22⋊C4—1064no—
728C22⋊C4—1064no—
729C42—24no—
730C42—534no—
731C42—534no—
732C42—532no—
733C42—532no—
734C42—1064no—
735C42—1064no—
736C42—1064no—
737C42D4×D5312yes—
738C42C23×D5312yes—
739C23—22no—
740C23—42no—
741C23—42no—
742C23—42no—
743C23—534no—
744C23—532no—
745C23—1062no—
746C23—1062no—
747C23—1062no—
748C23—2122no—
749C23—2122no—
750C23—2122no—
751C23C2×D4×D5311yescharacteristic
752Q8—24no—
753Q8—22no—
754Q8—22no—
755Q8—22no—
756Q8—42no—
757Q8—534no—
758Q8—10616no—
759Q8—1064no—
760Q8—1062no—
761Q8—1062no—
762Q8—1062no—
763Q8—2122no—
764Q8C2×D4×D5314yes—
765D4—22no—
766D4—22no—
767D4—42no—
768D4—1062no—
769D4—1062no—
770D4—2128no—
771D4—2128no—
772D4—2128no—
773D4—2128no—
774D4—2122no—
775C2×C4—24no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—534no—
784C2×C4—534no—
785C2×C4—532no—
786C2×C4—532no—
787C2×C4—538no—
788C2×C4—534no—
789C2×C4—534no—
790C2×C4—532no—
791C2×C4—1068no—
792C2×C4—10616no—
793C2×C4—1064no—
794C2×C4—1062no—
795C2×C4—1062no—
796C2×C4—1062no—
797C2×C4—1062no—
798C2×C4—2124no—
799C2×C4—2128no—
800C2×C4—2128no—
801C2×C4—2128no—
802C2×C4—2122no—
803C2×C4—2122no—
804C2×C4C2×D4×D5312yes—
805C2×C4C2×D4×D5312yes—
806C2×C4C2×D4×D5311yescharacteristic
807C2×C4C2×D4×D5312yes—
808C2×C4#41×D5312yes—
809C2×C4C24×D5311yescharacteristic
810C8—22no—
811C8—22no—
812C8—1062no—
813C8—1062no—
814C22—42no—
815C22—42no—
816C22—42no—
817C22—84no—
818C22—534no—
819C22—1068no—
820C22—1062no—
821C22—1062no—
822C22—4244no—
823C22—2122no—
824C22—2122no—
825C22—2122no—
826C22#121×D5312yes—
827C22#137×D5312yes—
828C22#1681142012yes—
829C22C22×D4×D5311yescharacteristic
830C4—22no—
831C4—22no—
832C4—24no—
833C4—42no—
834C4—42no—
835C4—534no—
836C4—534no—
837C4—1062no—
838C4—1064no—
839C4—2122no—
840C4—2122no—
841C4#121×D5312yes—
842C4C22×D4×D5311yescharacteristic
843C4C2×#41×D5311yescharacteristic
844C2—82no—
845C2—1064no—
846C2—4242no—
847C2#2028418514yesdirect product factor
848C2C2×#121×D5311yescharacteristic
849C2C2×#137×D5311yescharacteristic
850C2C2×#1681142011yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#464C2
socleC23×C53C22×D4
prime radicalC2×#16811172C2
hypercenterC2×#464D53
hypocenterC53C2×#3037
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#464

Complements

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

NH ≅ G/Ntype
1. C22×#13133249C2semidirect
2. C22×#13133246C2semidirect
4. C2×C4×Q8×D53C2semidirect
5. #20284185C2direct (N × H)
6. C2×#16810846C2semidirect
7. C2×#16810845C2semidirect
8. C2×#16810842C2semidirect
9. C2×#16810832C2semidirect
10. C2×#16810831C2semidirect
11. C2×#16810822C2semidirect
12. C2×#16810821C2semidirect
13. C2×#16810645C2semidirect
14. C2×#16810623C2semidirect
15. C2×#16810621C2semidirect
16. C2×C53×#464C2semidirect
21. C2×#13133249C22semidirect
23. C2×#13133246C22semidirect
45. C4×Q8×D53C22semidirect
52. #16810846C22semidirect
53. #16810845C22semidirect
54. #16810842C22semidirect
55. #16810832C22semidirect
56. #16810831C22semidirect
57. #16810822C22semidirect
58. #16810821C22semidirect
59. #16810645C22semidirect
63. #16810623C22semidirect
64. #16810621C22semidirect
75. C53×#464C22semidirect
92. C2×Q8×D53D4semidirect
236. Q8×D53C2×D4semidirect
361. C2×Dic53#137semidirect
418. Dic53C2×#137semidirect
427. C2×#464D53semidirect
436. C2×C53#3037semidirect
484. #464C2×D53semidirect
504. C53C2×#3037semidirect
847. C2#20284185direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#131332492
C22×#131332462
C2×#168111722
C2×C4×Q8×D532
#202841852
C2×#168108462
C2×#168108452
C2×#168108422
C2×#168108322
C2×#168108312
C2×#168108222
C2×#168108212
C2×#168106452
C2×#168106232
C2×#168106212
C2×C53×#4642
C2×#303753