Finite Group Databasebeta

← C2×#20284249 #28251012

Subgroups — C2×#20284249 #28251012

Order 13568.

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×#13133241C211yesmaximal, characteristic, complemented
2C22×#13133236C211yesmaximal, characteristic, complemented
3C2×#16811186C211yesmaximal, characteristic, complemented
4C2×#16811102C211yesmaximal, characteristic, complemented
5#20284249C2116yesmaximal, direct product factor
6C2×#16810846C211yesmaximal, characteristic, complemented
7C2×#16810844C211yesmaximal, characteristic, complemented
8C2×#16810822C211yesmaximal, characteristic, complemented
9C2×#16810820C211yesmaximal, characteristic, complemented
10C2×#16810838C211yesmaximal, characteristic, complemented
11C2×#16810836C211yesmaximal, characteristic, complemented
12C2×#16810816C211yesmaximal, characteristic, complemented
13C2×#16810648C211yesmaximal, characteristic, complemented
14C2×#16810621C211yesmaximal, characteristic, complemented
15C2×#102×D53C211yesmaximal, characteristic, complemented
16C2×C53×#459C211yesmaximal, characteristic, complemented
17C22×#11719947C2211yescharacteristic
18C22×#11719947C2211yescharacteristic
19C22×D4×D53C2211yescharacteristic
20C2×#13133241—28no—
21C2×#13133241C2218yescomplemented
22C2×#13133236—28no—
23C2×#13133236C2218yescomplemented
24C22×Dic212C2211yescharacteristic, complemented
25C22×#11719913C2211yescharacteristic
26C22×#11719923C2211yescharacteristic
27C22×#11719923C2211yescharacteristic, complemented
28C22×#11719923C2211yescharacteristic, complemented
29C22×#11719922C2211yescharacteristic
30C22×#11719912C2211yescharacteristic
31C22×C8×D53C2211yescharacteristic
32#16811186—24no—
33#16811186C2218yescomplemented
34C2×#13133213C2211yescharacteristic
35C2×#13133205C2211yescharacteristic
36C2×#13133204C2211yescharacteristic
37C2×#13133189—21no—
38C2×#13133189—21no—
39C2×#13133185—21no—
40C2×#13133185—21no—
41#16811102—24no—
42#16811102C2218yescomplemented
43C2×C4×Dic106C2211yescharacteristic, complemented
44C2×#13133182C2211yescharacteristic, complemented
45C2×D4×Dic53C2211yescharacteristic, complemented
46C2×C4×C22⋊D53—21no—
47C2×#13133177—21no—
48C2×#13133174C2211yescharacteristic
49C2×#13133173—21no—
50C22×#11719919—21no—
51C2×C4⋊C4×D53C2211yescharacteristic
52#16810846C2218yescomplemented
53#16810844C2218yescomplemented
54#16810838C2218yescomplemented
55#16810836C2218yescomplemented
56#16810822C2218yescomplemented
57#16810820C2218yescomplemented
58#16810816C2218yescomplemented
59#16810648C2218yescomplemented
60C2×C4⋊#88322C2211yescharacteristic, complemented
61C2×#13133146C2211yescharacteristic, complemented
62C2×#13133146C2211yescharacteristic, complemented
63#16810621C2218yescomplemented
64C2×#13133142C2211yescharacteristic, complemented
65C2×#13133140C2211yescharacteristic, complemented
66C2×#13133139C2211yescharacteristic
67C2×#13133138C2211yescharacteristic
68C2×#13133138C2211yescharacteristic, complemented
69C2×#13133137C2211yescharacteristic
70#102×D53C2218yescomplemented
71C22×D8×C53C2211yescharacteristic
72C22×D8×C53C2211yescharacteristic, complemented
73C2×#127×C53C2211yescharacteristic
74C2×C4×D4×C53C2211yescharacteristic, complemented
75C53×#459C2218yescomplemented
76C2×C4⋊C8×C53C2211yescharacteristic, complemented
77C2×#102×C53C2211yescharacteristic
78C2×#102×C53C2211yescharacteristic, complemented
79C24×D53—21no—
80C2×#11719947—22no—
81C2×#11719947—24no—
82C2×#11719947—22no—
83C2×#11719947—24no—
84C2×#11719947—24no—
85C2×#11719947D418yescomplemented
86C2×#11719947C2314yes—
87C2×#11719947C2314yes—
88C22×Dic106C2311yescharacteristic
89C22×Dic106C2311yescharacteristic
90C22×D212C2311yescharacteristic
91C22×C22⋊D53—21no—
92C22×C22⋊D53—21no—
93C22×C22⋊D53—21no—
94C22×C22⋊D53—21no—
95C22×C22⋊D53—21no—
96C2×D4×D53—24no—
97C2×D4×D53—22no—
98C2×D4×D53—24no—
99C2×D4×D53C2314yes—
100C23×Dic53—21no—
101C23×Dic53—21no—
102C23×Dic53—21no—
103C22×C4×D53—21no—
104C22×C4×D53C2311yescharacteristic
105#13133241—232no—
106#13133236—232no—
107C2×Dic212—24no—
108C2×Dic212C2314yescomplemented
109C2×#11719913—24no—
110C2×#11719913C2314yes—
111C2×#11719923—24no—
112C2×#11719923—24no—
113C2×#11719923—24no—
114C2×#11719923C2314yes—
115C2×#11719923C2314yescomplemented
116C2×#11719923C2314yescomplemented
117C2×#11719922—24no—
118C2×#11719922C2314yes—
119C2×#11719912—24no—
120C2×#11719912C2314yes—
121C22×#88322C2311yescharacteristic
122C22×#88322C2311yescharacteristic
123C2×C8×D53—24no—
124C2×C8×D53C2314yes—
125#13133213—22no—
126#13133213C2314yes—
127#13133205—22no—
128#13133205C2314yes—
129#13133204—22no—
130#13133204C2314yes—
131#13133189—28no—
132#13133189—28no—
133#13133185—28no—
134#13133185—28no—
135C4×Dic106—22no—
136C4×Dic106C2314yescomplemented
137#13133182—22no—
138#13133182C2314yescomplemented
139D4×Dic53—22no—
140D4×Dic53C2314yescomplemented
141C4×C22⋊D53—28no—
142#13133177—28no—
143#13133174D414yes—
144#13133174C2314yes—
145#13133173—28no—
146C2×C4⋊Dic53C2311yescharacteristic
147C2×#11719919—28no—
148C2×#11719919—21no—
149C2×#11719919—21no—
150C2×#11719919—21no—
151C2×#11719919D411yescharacteristic
152C2×#11719919D411yescharacteristic
153C4⋊C4×D53—22no—
154C4⋊C4×D53C2314yes—
155C2×C22⋊Dic53—21no—
156C2×C22⋊Dic53—21no—
157C2×C22⋊Dic53—21no—
158C2×#11719921—21no—
159C2×#11719921—21no—
160C2×#11719921D411yescharacteristic
161C2×#11719921D411yescharacteristic
162C2×C4×Dic53—21no—
163C2×C4×Dic53—21no—
164C2×C4×Dic53C2311yescharacteristic
165C4⋊#88322C2314yescomplemented
166#13133146C2314yescomplemented
167#13133146C2314yescomplemented
168#13133142C2314yescomplemented
169#13133140C2314yescomplemented
170#13133139C2314yes—
171#13133138C2314yes—
172#13133138C2314yescomplemented
173#13133137C2314yes—
174C22×D4×C53—21no—
175C22×D4×C53—21no—
176C22×D4×C53C2311yescharacteristic
177C22×D4×C53C2311yescharacteristic
178C22×D4×C53C2311yescharacteristic
179C23×C4×C53—21no—
180C2×D8×C53—24no—
181C2×D8×C53—24no—
182C2×D8×C53C2314yes—
183C2×D8×C53C2314yescomplemented
184C22×C8×C53C2311yescharacteristic
185C22×C8×C53C2311yescharacteristic
186#127×C53—22no—
187#127×C53C2314yes—
188C4×D4×C53—22no—
189C4×D4×C53C2314yescomplemented
190C2×C4⋊C4×C53C2311yescharacteristic
191C2×C22⋊C4×C53—21no—
192C2×C42×C53C2311yescharacteristic
193C4⋊C8×C53C2314yescomplemented
194#102×C53C2314yes—
195#102×C53C2314yescomplemented
196C24×C53—21no—
197C24×C53—21no—
198C24×C53—21no—
199C23×D53—21no—
200C23×D53—24no—
201C23×D53—44no—
202C23×D53—82no—
203C23×D53—82no—
204C23×D53C2×D411yescharacteristic
205C2×D4×C53—21no—
206C2×D4×C53—22no—
207C2×D4×C53—22no—
208C2×D4×C53—21no—
209C2×D4×C53—21no—
210C2×D4×C53—24no—
211C2×D4×C53—24no—
212C2×D4×C53—22no—
213C2×D4×C53—22no—
214C2×D4×C53—22no—
215C2×D4×C53—82no—
216C2×D4×C53—82no—
217C2×D4×C53C2×D414yes—
218C2×D4×C53C2412yes—
219C2×D4×C53C2412yes—
220C2×D4×C53C2412yes—
221C22×C4×C53—21no—
222C22×C4×C53—24no—
223C22×C4×C53—82no—
224C22×C4×C53C2×D411yescharacteristic
225C22×C4×C53C2×D411yescharacteristic
226C22×C4×C53C2411yescharacteristic
227C2×C22⋊D53—28no—
228C2×C22⋊D53—24no—
229C2×C22⋊D53—24no—
230C2×C22⋊D53—24no—
231C2×C22⋊D53—24no—
232C2×C22⋊D53—24no—
233C2×C22⋊D53—44no—
234C2×C22⋊D53—44no—
235C2×C22⋊D53—82no—
236C2×C22⋊D53—82no—
237C22×Dic53—21no—
238C22×Dic53—28no—
239C22×Dic53—24no—
240C22×Dic53—21no—
241C22×Dic53—21no—
242C22×Dic53—24no—
243C22×Dic53—24no—
244C22×Dic53—44no—
245C22×Dic53—82no—
246C22×Dic53C2×D411yescharacteristic
247C22×Dic53C2×D411yescharacteristic
248C22×Dic53C2×D411yescharacteristic
249#11719947—216no—
250#11719947—28no—
251#11719947—28no—
252#11719947—28no—
253#11719947—48no—
254#11719947C2×D4116yescomplemented
255D4×D53—28no—
256D4×D53—28no—
257D4×D53—48no—
258C2×D212—22no—
259C2×D212—22no—
260C2×D212—21no—
261C2×D212C2412yes—
262C2×C4×D53—24no—
263C2×C4×D53—82no—
264C2×C4×D53C2×D412yes—
265C2×C4×D53C2×D414yes—
266C2×C4×D53#4114yes—
267C2×C4×D53C2412yes—
268C2×Dic106—21no—
269C2×Dic106—22no—
270C2×Dic106—22no—
271C2×Dic106—22no—
272C2×Dic106—21no—
273C2×Dic106C2×D414yes—
274C2×Dic106C2412yes—
275C2×Dic106C2412yes—
276D8×C53—28no—
277D8×C53—28no—
278C2×C8×C53—22no—
279C2×C8×C53—22no—
280C2×C8×C53C2412yes—
281C2×C8×C53C2412yes—
282C4⋊C4×C53—21no—
283C4⋊C4×C53C2412yes—
284C22⋊C4×C53—24no—
285C42×C53C2×D412yes—
286C42×C53C2412yes—
287C22⋊Dic53—24no—
288C22⋊Dic53—24no—
289C22⋊Dic53—24no—
290#11719923—28no—
291#11719923—28no—
292#11719923—28no—
293#11719922—28no—
294#11719921—24no—
295#11719921—24no—
296#11719921C2×D414yes—
297#11719921C2×D414yes—
298C4⋊Dic53—21no—
299C4⋊Dic53C2412yes—
300#11719919—24no—
301#11719919—24no—
302#11719919—24no—
303#11719919C2×D414yes—
304#11719919C2×D414yes—
305C4×Dic53—24no—
306C4×Dic53—24no—
307C4×Dic53C2×D412yes—
308C4×Dic53C2412yes—
309C2×#88322—22no—
310C2×#88322—22no—
311C2×#88322C2412yes—
312C2×#88322C2412yes—
313Dic212—28no—
314#11719913—28no—
315#11719912—28no—
316C8×D53—28no—
317C23×C53—24no—
318C23×C53—22no—
319C23×C53—22no—
320C23×C53—22no—
321C23×C53—42no—
322C23×C53—42no—
323C23×C53—42no—
324C23×C53—42no—
325C23×C53—42no—
326C23×C53—42no—
327C23×C53—42no—
328C23×C53—42no—
329C23×C53C22×D411yescharacteristic
330C22×D53—22no—
331C22×D53—22no—
332C22×D53—22no—
333C22×D53—42no—
334C22×D53—42no—
335C22×D53—42no—
336C22×D53—48no—
337C22×D53—84no—
338C22×D53—84no—
339C22×D53—816no—
340C22×D53#12114yes—
341C22×D53C22×D412yes—
342D4×C53—24no—
343D4×C53—22no—
344D4×C53—22no—
345D4×C53—22no—
346D4×C53—22no—
347D4×C53—22no—
348D4×C53—42no—
349D4×C53—42no—
350D4×C53—84no—
351D4×C53—84no—
352D4×C53C22×D414yes—
353C2×C4×C53—22no—
354C2×C4×C53—22no—
355C2×C4×C53—22no—
356C2×C4×C53—42no—
357C2×C4×C53—84no—
358C2×C4×C53C22×D412yes—
359C2×C4×C53C22×D412yes—
360C2×C4×C53C22×D411yescharacteristic
361C2×C4×C53C22×D412yes—
362C2×C4×C53C2×#4112yes—
363C2×C4×C53C2511yescharacteristic
364C22⋊D53—216no—
365C22⋊D53—48no—
366C22⋊D53—48no—
367C22⋊D53—84no—
368C22⋊D53—84no—
369C2×Dic53—24no—
370C2×Dic53—22no—
371C2×Dic53—22no—
372C2×Dic53—22no—
373C2×Dic53—216no—
374C2×Dic53—22no—
375C2×Dic53—22no—
376C2×Dic53—42no—
377C2×Dic53—42no—
378C2×Dic53—48no—
379C2×Dic53—84no—
380C2×Dic53#12114yes—
381C2×Dic53C22×D412yes—
382C2×Dic53C22×D412yes—
383C2×Dic53C22×D412yes—
384D212—22no—
385D212—22no—
386D212—42no—
387C4×D53—84no—
388C4×D53#12118yes—
389C4×D53C22×D414yes—
390C4×D53C2×#4114yes—
391Dic106—24no—
392Dic106—22no—
393Dic106—22no—
394Dic106—22no—
395Dic106—42no—
396Dic106C22×D414yes—
397C8×C53—22no—
398C8×C53—22no—
399#88322—22no—
400#88322—22no—
401C2×#3045—531nomaximal, Sylow
402C22×C53—24no—
403C22×C53—48no—
404C22×C53—42no—
405C22×C53—42no—
406C22×C53—42no—
407C22×C53—42no—
408C22×C53—42no—
409C22×C53—42no—
410C22×C53—42no—
411C22×C53—42no—
412C22×C53—84no—
413C22×C53—84no—
414C22×C53C2×#12112yes—
415C22×C53#57612yes—
416C22×C53#57712yes—
417C22×C53C23×D411yescharacteristic
418C2×D53—28no—
419C2×D53—22no—
420C2×D53—22no—
421C2×D53—42no—
422C2×D53—42no—
423C2×D53—42no—
424C2×D53—816no—
425C2×D53—84no—
426C2×D53C2×#12114yes—
427C4×C53—22no—
428C4×C53—22no—
429C4×C53—42no—
430C4×C53C2×#12112yes—
431C4×C53C23×D411yescharacteristic
432C4×C53C22×#4111yescharacteristic
433Dic53—24no—
434Dic53—22no—
435Dic53—22no—
436Dic53—42no—
437Dic53—42no—
438Dic53C2×#12114yes—
439C22×AGL(1,ℤ/8)—531no—
440C22×#135—531no—
441C2×#535—531no—
442C2×#520—531no—
443#3045—5316no—
444C2×#464—531no—
445C2×#464—531no—
446C2×#460—531no—
447C2×#460—531no—
448C2×#463—531no—
449C2×#463—531no—
450C2×#459—531no—
451C2×#459D5311yescharacteristic, complemented
452C2×#424—531no—
453C2×#417—531no—
454C22×#102—531no—
455C2×C53—44no—
456C2×C53—82no—
457C2×C53—82no—
458C2×C53#304514yescomplemented
459C2×C53C22×#12111yescharacteristic
460C2×C53C2×#57611yescharacteristic
461C2×C53C2×#57711yescharacteristic
462D53—24no—
463D53—82no—
464C22×#41—531no—
465C22×#41—531no—
466C23×D4—531no—
467C2×AGL(1,ℤ/8)—538no—
468C2×AGL(1,ℤ/8)—1068no—
469C2×#135—538no—
470C2×#135—1068no—
471C22×Q16—531no—
472C22×SD16—531no—
473C22×SD16—531no—
474C22×SD16—531no—
475C22×SD16—531no—
476C22×D8—531no—
477C22×D8C2×D5311yescharacteristic
478C22×D8C2×D5311yescharacteristic, complemented
479C22×M16—531no—
480C23×C8—531no—
481#535—538no—
482#535—1064no—
483C2×#127—531no—
484C2×#127C2×D5311yescharacteristic
485C2×#124—531no—
486C2×#124—531no—
487C2×#121—1061no—
488C2×#121—1061no—
489C2×#120—1061no—
490C2×#120—1061no—
491#520—538no—
492#520—1064no—
493C2×C4×Q8—531no—
494C2×C4×Q8—531no—
495C2×C4×D4—531no—
496C2×C4×D4—1061no—
497C2×C4×D4—1061no—
498C2×C4×D4C2×D5311yescharacteristic, complemented
499C2×#117—531no—
500C2×#117—1061no—
501C22×C4⋊C4—531no—
502C22×C4⋊C4—1061no—
503#464—538no—
504#464—538no—
505#463—538no—
506#463—538no—
507#460—538no—
508#460—538no—
509#459—538no—
510#459C2×D5318yescomplemented
511#424—538no—
512C2×C4⋊C8—531no—
513C2×C4⋊C8—531no—
514C2×C4⋊C8—531no—
515C2×C4⋊C8C2×D5311yescharacteristic, complemented
516#417—538no—
517C2×#103—531no—
518C2×#103—531no—
519C2×#102—531no—
520C2×#102—531no—
521C2×#102—531no—
522C2×#102—531no—
523C2×#102—538no—
524C2×#102C2×D5311yescharacteristic
525C2×#102C2×D5311yescharacteristic, complemented
526C53C2×#304511yescharacteristic, complemented, Sylow
527C25—1061no—
528C2×#41—538no—
529C2×#41—534no—
530C2×#41—534no—
531C2×#41—1062no—
532C2×#41—1064no—
533C2×#41—1062no—
534C2×#41—1064no—
535C2×#41—1064no—
536C22×Q8—531no—
537C22×Q8—531no—
538C22×D4—21no—
539C22×D4—21no—
540C22×D4—534no—
541C22×D4—531no—
542C22×D4—1064no—
543C22×D4—1064no—
544C22×D4—1062no—
545C22×D4—1061no—
546C22×D4—1061no—
547C22×D4—1061no—
548C22×D4—1061no—
549C22×D4—1061no—
550C22×D4C22×D5311yescharacteristic
551C22×D4C22×D5311yescharacteristic
552C22×D4C22×D5311yescharacteristic
553C23×C4—21no—
554C23×C4—531no—
555C23×C4—1061no—
556C23×C4—1061no—
557C23×C4—1061no—
558C23×C4—1061no—
559AGL(1,ℤ/8)—10632no—
560#135—10632no—
561C2×Q16—534no—
562C2×Q16—1064no—
563C2×SD16—534no—
564C2×SD16—534no—
565C2×SD16—534no—
566C2×SD16—534no—
567C2×SD16—1064no—
568C2×SD16—1064no—
569C2×SD16—1064no—
570C2×SD16—1064no—
571C2×D8—24no—
572C2×D8—24no—
573C2×D8—534no—
574C2×D8—1064no—
575C2×D8C22×D5314yes—
576C2×D8C22×D5314yescomplemented
577C2×M16—534no—
578C2×M16—1064no—
579C22×C8—531no—
580C22×C8—531no—
581C22×C8—534no—
582C22×C8—1064no—
583C22×C8C22×D5311yescharacteristic
584C22×C8C22×D5311yescharacteristic
585#127—22no—
586#127—534no—
587#127—1062no—
588#127C22×D5314yes—
589#124—534no—
590#124—534no—
591#124—1062no—
592#124—1062no—
593#121—1068no—
594#121—1068no—
595#120—1068no—
596#120—1068no—
597C4×Q8—534no—
598C4×Q8—534no—
599C4×Q8—1062no—
600C4×Q8—1062no—
601C4×D4—22no—
602C4×D4—534no—
603C4×D4—1062no—
604C4×D4—1068no—
605C4×D4—1068no—
606C4×D4C22×D5314yescomplemented
607#117—534no—
608#117—534no—
609#117—1068no—
610C2×C4⋊C4—531no—
611C2×C4⋊C4—531no—
612C2×C4⋊C4—531no—
613C2×C4⋊C4—534no—
614C2×C4⋊C4—1062no—
615C2×C4⋊C4—1068no—
616C2×C4⋊C4—1061no—
617C2×C4⋊C4—1061no—
618C2×C4⋊C4—1061no—
619C2×C4⋊C4C22×D5311yescharacteristic
620C2×C22⋊C4—21no—
621C2×C22⋊C4—531no—
622C2×C22⋊C4—531no—
623C2×C22⋊C4—1061no—
624C2×C22⋊C4—1061no—
625C2×C22⋊C4—1061no—
626C2×C22⋊C4—1061no—
627C2×C22⋊C4—1061no—
628C2×C42—531no—
629C2×C42—1061no—
630C2×C42—1061no—
631C2×C42C22×D5311yescharacteristic
632C4⋊C8—534no—
633C4⋊C8—534no—
634C4⋊C8—534no—
635C4⋊C8C22×D5314yescomplemented
636#103—534no—
637#103—534no—
638#102—534no—
639#102—534no—
640#102—534no—
641#102—534no—
642#102C22×D5314yes—
643#102C22×D5314yescomplemented
644C24—21no—
645C24—21no—
646C24—21no—
647C24—531no—
648C24—1064no—
649C24—1061no—
650C24—4242no—
651C24—4242no—
652C24—2124no—
653#41—5316no—
654#41—10616no—
655#41—1068no—
656#41—1068no—
657#41—1068no—
658#41—2128no—
659C2×Q8—534no—
660C2×Q8—532no—
661C2×Q8—532no—
662C2×Q8—1061no—
663C2×Q8—1061no—
664C2×Q8—1062no—
665C2×Q8—1062no—
666C2×Q8—1062no—
667C2×D4—21no—
668C2×D4—22no—
669C2×D4—22no—
670C2×D4—21no—
671C2×D4—21no—
672C2×D4—24no—
673C2×D4—24no—
674C2×D4—22no—
675C2×D4—22no—
676C2×D4—22no—
677C2×D4—82no—
678C2×D4—82no—
679C2×D4—532no—
680C2×D4—1068no—
681C2×D4—1068no—
682C2×D4—1064no—
683C2×D4—1064no—
684C2×D4—1064no—
685C2×D4—1064no—
686C2×D4—1068no—
687C2×D4—1064no—
688C2×D4—1062no—
689C2×D4—1061no—
690C2×D4—1062no—
691C2×D4—4242no—
692C2×D4—4242no—
693C2×D4—2128no—
694C2×D4—2124no—
695C2×D4—2124no—
696C2×D4D4×D5314yes—
697C2×D4C23×D5312yes—
698C2×D4C23×D5312yes—
699C2×D4C23×D5312yes—
700C22×C4—21no—
701C22×C4—24no—
702C22×C4—82no—
703C22×C4—531no—
704C22×C4—532no—
705C22×C4—534no—
706C22×C4—534no—
707C22×C4—532no—
708C22×C4—531no—
709C22×C4—531no—
710C22×C4—1064no—
711C22×C4—1064no—
712C22×C4—1068no—
713C22×C4—1064no—
714C22×C4—1064no—
715C22×C4—1061no—
716C22×C4—1061no—
717C22×C4—1061no—
718C22×C4—4242no—
719C22×C4—4242no—
720C22×C4—2124no—
721C22×C4D4×D5311yescharacteristic
722C22×C4D4×D5311yescharacteristic
723C22×C4C23×D5311yescharacteristic
724Q16—1068no—
725SD16—1068no—
726SD16—1068no—
727SD16—1068no—
728SD16—1068no—
729D8—28no—
730D8—28no—
731D8—1068no—
732M16—1068no—
733C2×C8—22no—
734C2×C8—22no—
735C2×C8—532no—
736C2×C8—532no—
737C2×C8—1068no—
738C2×C8—1062no—
739C2×C8—1062no—
740C2×C8C23×D5312yes—
741C2×C8C23×D5312yes—
742C4⋊C4—21no—
743C4⋊C4—534no—
744C4⋊C4—534no—
745C4⋊C4—532no—
746C4⋊C4—1064no—
747C4⋊C4—1064no—
748C4⋊C4—1061no—
749C4⋊C4—1064no—
750C4⋊C4C23×D5312yes—
751C22⋊C4—24no—
752C22⋊C4—534no—
753C22⋊C4—534no—
754C22⋊C4—1064no—
755C22⋊C4—1064no—
756C22⋊C4—1064no—
757C22⋊C4—1064no—
758C22⋊C4—1064no—
759C42—532no—
760C42—532no—
761C42—1064no—
762C42—1064no—
763C42D4×D5312yes—
764C42C23×D5312yes—
765C23—24no—
766C23—22no—
767C23—22no—
768C23—22no—
769C23—42no—
770C23—42no—
771C23—42no—
772C23—42no—
773C23—42no—
774C23—42no—
775C23—42no—
776C23—42no—
777C23—534no—
778C23—532no—
779C23—1062no—
780C23—1062no—
781C23—1062no—
782C23—4244no—
783C23—4244no—
784C23—42416no—
785C23—2128no—
786C23—2122no—
787C23—2122no—
788C23—2122no—
789C23C2×D4×D5311yescharacteristic
790Q8—534no—
791Q8—1064no—
792Q8—1062no—
793Q8—1062no—
794Q8—1062no—
795Q8—2122no—
796D4—24no—
797D4—22no—
798D4—22no—
799D4—22no—
800D4—22no—
801D4—22no—
802D4—42no—
803D4—42no—
804D4—84no—
805D4—84no—
806D4—10616no—
807D4—1062no—
808D4—1062no—
809D4—4244no—
810D4—4244no—
811D4—2128no—
812D4—2128no—
813D4—2122no—
814D4C2×D4×D5314yes—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—42no—
819C2×C4—84no—
820C2×C4—534no—
821C2×C4—532no—
822C2×C4—538no—
823C2×C4—534no—
824C2×C4—534no—
825C2×C4—532no—
826C2×C4—532no—
827C2×C4—10616no—
828C2×C4—1064no—
829C2×C4—1062no—
830C2×C4—1062no—
831C2×C4—1062no—
832C2×C4—1062no—
833C2×C4—1062no—
834C2×C4—4244no—
835C2×C4—4244no—
836C2×C4—2128no—
837C2×C4—2122no—
838C2×C4—2122no—
839C2×C4C2×D4×D5312yes—
840C2×C4C2×D4×D5312yes—
841C2×C4C2×D4×D5311yescharacteristic
842C2×C4C2×D4×D5312yes—
843C2×C4#41×D5312yes—
844C2×C4C24×D5311yescharacteristic
845C8—22no—
846C8—22no—
847C8—1062no—
848C8—1062no—
849C22—24no—
850C22—48no—
851C22—42no—
852C22—42no—
853C22—42no—
854C22—42no—
855C22—42no—
856C22—42no—
857C22—42no—
858C22—42no—
859C22—84no—
860C22—84no—
861C22—534no—
862C22—1068no—
863C22—1062no—
864C22—1062no—
865C22—42416no—
866C22—4244no—
867C22—2122no—
868C22—2122no—
869C22—2122no—
870C22#121×D5312yes—
871C22#1681142412yes—
872C22#1681143312yes—
873C22C22×D4×D5311yescharacteristic
874C4—22no—
875C4—22no—
876C4—42no—
877C4—534no—
878C4—1062no—
879C4—1064no—
880C4—1062no—
881C4—2122no—
882C4—2122no—
883C4#121×D5312yes—
884C4C22×D4×D5311yescharacteristic
885C4C2×#41×D5311yescharacteristic
886C2—44no—
887C2—82no—
888C2—82no—
889C2—1064no—
890C2—4242no—
891C2#2028424914yesdirect product factor
892C2C2×#121×D5311yescharacteristic
893C2C2×#1681142411yescharacteristic
894C2C2×#1681143311yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#459C2
socleC23×C53C22×D4
hypercenterC2×#459D53
hypocenterC53C2×#3045
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#459

Complements

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

NH ≅ G/Ntype
1. C22×#13133241C2semidirect
2. C22×#13133236C2semidirect
3. C2×#16811186C2semidirect
4. C2×#16811102C2semidirect
5. #20284249C2direct (N × H)
6. C2×#16810846C2semidirect
7. C2×#16810844C2semidirect
8. C2×#16810822C2semidirect
9. C2×#16810820C2semidirect
10. C2×#16810838C2semidirect
11. C2×#16810836C2semidirect
12. C2×#16810816C2semidirect
13. C2×#16810648C2semidirect
14. C2×#16810621C2semidirect
15. C2×#102×D53C2semidirect
16. C2×C53×#459C2semidirect
21. C2×#13133241C22semidirect
23. C2×#13133236C22semidirect
24. C22×Dic212C22semidirect
27. C22×#11719923C22semidirect
28. C22×#11719923C22semidirect
33. #16811186C22semidirect
42. #16811102C22semidirect
43. C2×C4×Dic106C22semidirect
44. C2×#13133182C22semidirect
45. C2×D4×Dic53C22semidirect
52. #16810846C22semidirect
53. #16810844C22semidirect
54. #16810838C22semidirect
55. #16810836C22semidirect
56. #16810822C22semidirect
57. #16810820C22semidirect
58. #16810816C22semidirect
59. #16810648C22semidirect
60. C2×C4⋊#88322C22semidirect
61. C2×#13133146C22semidirect
62. C2×#13133146C22semidirect
63. #16810621C22semidirect
64. C2×#13133142C22semidirect
65. C2×#13133140C22semidirect
68. C2×#13133138C22semidirect
70. #102×D53C22semidirect
72. C22×D8×C53C22semidirect
74. C2×C4×D4×C53C22semidirect
75. C53×#459C22semidirect
76. C2×C4⋊C8×C53C22semidirect
78. C2×#102×C53C22semidirect
85. C2×#11719947D4semidirect
108. C2×Dic212C23semidirect
115. C2×#11719923C23semidirect
116. C2×#11719923C23semidirect
136. C4×Dic106C23semidirect
138. #13133182C23semidirect
140. D4×Dic53C23semidirect
165. C4⋊#88322C23semidirect
166. #13133146C23semidirect
167. #13133146C23semidirect
168. #13133142C23semidirect
169. #13133140C23semidirect
172. #13133138C23semidirect
183. C2×D8×C53C23semidirect
189. C4×D4×C53C23semidirect
193. C4⋊C8×C53C23semidirect
195. #102×C53C23semidirect
254. #11719947C2×D4semidirect
451. C2×#459D53semidirect
458. C2×C53#3045semidirect
478. C22×D8C2×D53semidirect
498. C2×C4×D4C2×D53semidirect
510. #459C2×D53semidirect
515. C2×C4⋊C8C2×D53semidirect
525. C2×#102C2×D53semidirect
526. C53C2×#3045semidirect
576. C2×D8C22×D53semidirect
606. C4×D4C22×D53semidirect
635. C4⋊C8C22×D53semidirect
643. #102C22×D53semidirect
891. C2#20284249direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#131332412
C22×#131332362
C2×#168111862
C2×#168111022
#202842492
C2×#168108462
C2×#168108442
C2×#168108222
C2×#168108202
C2×#168108382
C2×#168108362
C2×#168108162
C2×#168106482
C2×#168106212
C2×#102×D532
C2×C53×#4592
C2×#304553