Finite Group Databasebeta

← C2×#20286424 #28259322

Subgroups — C2×#20286424 #28259322

Order 13568.

2934 conjugacy classes of subgroups.

The subgroup lattice has 916 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13133238C211yesmaximal, characteristic, complemented
2C22×SD16×D53C211yesmaximal, characteristic, complemented
3C2×#16811285C211yesmaximal, characteristic, complemented
4C2×#16811268C211yesmaximal, characteristic, complemented
5#20286424C2116yesmaximal, direct product factor
6C2×#16811007C211yesmaximal, characteristic, complemented
7C2×#16810853C211yesmaximal, characteristic, complemented
8C2×#16810853C211yesmaximal, characteristic, complemented
9C2×#16810845C211yesmaximal, characteristic, complemented
10C2×#16810838C211yesmaximal, characteristic, complemented
11C2×#16810786C211yesmaximal, characteristic, complemented
12C2×#16810771C211yesmaximal, characteristic, complemented
13C2×#16810780C211yesmaximal, characteristic, complemented
14C2×#16810758C211yesmaximal, characteristic, complemented
15C2×C8×D212C211yesmaximal, characteristic, complemented
16C2×C4×SD16×C53C211yesmaximal, characteristic, complemented
17C22×#11719949C2211yescharacteristic, complemented
18C22×#11719947C2211yescharacteristic
19C22×Q8×D53C2211yescharacteristic
20C22×D4×D53C2211yescharacteristic
21C2×#13133238—28no—
22C2×#13133238C2218yescomplemented
23C22×Dic212C2211yescharacteristic, complemented
24C22×#11719925C2211yescharacteristic, complemented
25C22×#11719913C2211yescharacteristic
26C22×#11719913C2211yescharacteristic, complemented
27C22×#11719923C2211yescharacteristic
28C22×#11719924C2211yescharacteristic
29C2×SD16×D53—28no—
30C2×SD16×D53C2218yescomplemented
31C22×D424C2211yescharacteristic
32C22×#11719922C2211yescharacteristic
33C22×C8×D53C2211yescharacteristic
34C22×C8×D53C2211yescharacteristic, complemented
35#16811285—24no—
36#16811285C2218yescomplemented
37#16811268—24no—
38#16811268C2218yescomplemented
39C2×#13133205—21no—
40C2×#13133205C2211yescharacteristic
41C2×#13133205C2211yescharacteristic, complemented
42C2×#13133201—21no—
43C2×#13133197—21no—
44C2×#13133197C2211yescharacteristic
45C2×#13133197C2211yescharacteristic, complemented
46C2×#13133192—21no—
47C2×#13133192C2211yescharacteristic
48C2×#13133192C2211yescharacteristic
49C2×#13133191—21no—
50C2×#13133187—21no—
51C2×C4×D212—21no—
52C2×C4×D212C2211yescharacteristic
53C22×#11719921—21no—
54#16811007C2218yescomplemented
55#16810853C2218yescomplemented
56#16810853C2218yescomplemented
57#16810845C2218yescomplemented
58#16810838C2218yescomplemented
59#16810786C2218yescomplemented
60#16810780C2218yescomplemented
61#16810771C2218yescomplemented
62#16810758C2218yescomplemented
63C8×D212C2218yescomplemented
64C2×C4⋊#88322C2211yescharacteristic, complemented
65C2×#13133140C2211yescharacteristic, complemented
66C2×#13133140C2211yescharacteristic, complemented
67C2×#13133137C2211yescharacteristic
68C2×#13133137C2211yescharacteristic, complemented
69C2×#13133129C2211yescharacteristic
70C2×#13133129C2211yescharacteristic, complemented
71C22×SD16×C53C2211yescharacteristic
72C2×C4×Q8×C53C2211yescharacteristic, complemented
73C2×C4×D4×C53C2211yescharacteristic
74C4×SD16×C53C2218yescomplemented
75C2×#106×C53C2211yescharacteristic, complemented
76C2×#103×C53C2211yescharacteristic, complemented
77C2×#102×C53C2211yescharacteristic
78C2×C4×C8×C53C2211yescharacteristic, complemented
79C24×D53—21no—
80C2×#11719949—22no—
81C2×#11719949—24no—
82C2×#11719949—42no—
83C2×#11719949C2314yescomplemented
84C2×#11719947—24no—
85C2×#11719947—22no—
86C2×#11719947—42no—
87C2×#11719947C2314yes—
88C22×Dic106—21no—
89C22×Dic106C2311yescharacteristic
90C22×Dic106C2311yescharacteristic
91C2×Q8×D53—22no—
92C2×Q8×D53—24no—
93C2×Q8×D53—42no—
94C2×Q8×D53C2314yes—
95C22×D212—21no—
96C22×D212—21no—
97C22×D212—21no—
98C22×D212D411yescharacteristic
99C22×D212C2311yescharacteristic
100C22×D212C2311yescharacteristic
101C22×C22⋊D53—21no—
102C22×C22⋊D53—21no—
103C2×D4×D53—24no—
104C2×D4×D53—22no—
105C2×D4×D53—42no—
106C2×D4×D53C2314yes—
107C23×Dic53—21no—
108C22×C4×D53—21no—
109C22×C4×D53—21no—
110C22×C4×D53C2311yescharacteristic
111C22×C4×D53C2311yescharacteristic
112#13133238—232no—
113C2×Dic212—42no—
114C2×Dic212C2314yescomplemented
115C2×#11719925—24no—
116C2×#11719925C2314yescomplemented
117C2×#11719913—24no—
118C2×#11719913—24no—
119C2×#11719913C2314yes—
120C2×#11719913C2314yescomplemented
121C2×#11719923—24no—
122C2×#11719923C2314yes—
123C2×#11719924—24no—
124C2×#11719924C2314yes—
125SD16×D53—232no—
126C2×D424—42no—
127C2×D424C2314yes—
128C2×#11719922—24no—
129C2×#11719922C2314yes—
130C22×#88322C2311yescharacteristic
131C22×#88322C2311yescharacteristic
132C2×C8×D53—24no—
133C2×C8×D53—24no—
134C2×C8×D53C2314yes—
135C2×C8×D53C2314yescomplemented
136#13133205—22no—
137#13133205—22no—
138#13133205—28no—
139#13133205C2314yes—
140#13133205C2314yescomplemented
141#13133201—28no—
142#13133197—28no—
143#13133197—22no—
144#13133197—22no—
145#13133197C2314yes—
146#13133197C2314yescomplemented
147#13133192—28no—
148#13133192—22no—
149#13133192—22no—
150#13133192C2314yes—
151#13133192C2314yes—
152#13133191—28no—
153#13133187—28no—
154C4×D212—28no—
155C4×D212D414yes—
156C4×D212C2314yes—
157C2×C4⋊Dic53—21no—
158C2×C4⋊Dic53—21no—
159C2×C4⋊Dic53D411yescharacteristic
160C2×#11719921—28no—
161C2×#11719921—21no—
162C2×#11719921—21no—
163C2×#11719921—21no—
164C2×#11719921—21no—
165C2×#11719921—21no—
166C2×#11719921—21no—
167C2×#11719921—21no—
168C2×#11719921—21no—
169C2×#11719921D411yescharacteristic
170C2×#11719921D411yescharacteristic
171C4⋊#88322C2314yescomplemented
172#13133140C2314yescomplemented
173#13133140C2314yescomplemented
174#13133137C2314yes—
175#13133137C2314yescomplemented
176#13133129C2314yes—
177#13133129C2314yescomplemented
178C22×Q8×C53C2311yescharacteristic
179C22×D4×C53C2311yescharacteristic
180C23×C4×C53—21no—
181C2×SD16×C53D418yescomplemented
182C2×SD16×C53C2314yes—
183C22×C8×C53C2311yescharacteristic
184C22×C8×C53C2311yescharacteristic
185C4×Q8×C53—22no—
186C4×Q8×C53C2314yescomplemented
187C4×D4×C53—22no—
188C4×D4×C53C2314yes—
189C2×C4⋊C4×C53—21no—
190C2×C4⋊C4×C53C2311yescharacteristic
191C2×C4⋊C4×C53C2311yescharacteristic
192C2×C22⋊C4×C53—21no—
193C2×C42×C53—21no—
194C2×C42×C53C2311yescharacteristic
195#106×C53C2314yescomplemented
196#103×C53C2314yescomplemented
197#102×C53C2314yes—
198C4×C8×C53C2314yescomplemented
199C24×C53—21no—
200C23×D53—21no—
201C23×D53—21no—
202C23×D53—24no—
203C23×D53—44no—
204C23×D53—44no—
205C23×D53—82no—
206C23×D53C2×D411yescharacteristic
207C23×D53C2×D411yescharacteristic
208C2×Q8×C53—21no—
209C2×Q8×C53—22no—
210C2×Q8×C53C2×D414yes—
211C2×Q8×C53C2412yes—
212C2×D4×C53—21no—
213C2×D4×C53—22no—
214C2×D4×C53C2×D414yes—
215C2×D4×C53C2412yes—
216C22×C4×C53—21no—
217C22×C4×C53—21no—
218C22×C4×C53—21no—
219C22×C4×C53—24no—
220C22×C4×C53—82no—
221C22×C4×C53C2×D411yescharacteristic
222C22×C4×C53C2×D411yescharacteristic
223C22×C4×C53C2411yescharacteristic
224C2×C22⋊D53—24no—
225C2×C22⋊D53—24no—
226C2×C22⋊D53—44no—
227C2×C22⋊D53—44no—
228C22×Dic53—21no—
229C22×Dic53—21no—
230C22×Dic53—24no—
231C22×Dic53—44no—
232C22×Dic53C2×D411yescharacteristic
233C22×Dic53C2×D411yescharacteristic
234#11719949—28no—
235#11719949—44no—
236#11719949—48no—
237Q8×D53—28no—
238Q8×D53—44no—
239Q8×D53—48no—
240#11719947—28no—
241#11719947—44no—
242#11719947—48no—
243D4×D53—28no—
244D4×D53—44no—
245D4×D53—48no—
246C2×D212—24no—
247C2×D212—22no—
248C2×D212—22no—
249C2×D212—22no—
250C2×D212—22no—
251C2×D212—24no—
252C2×D212—24no—
253C2×D212—21no—
254C2×D212—21no—
255C2×D212—24no—
256C2×D212—44no—
257C2×D212—44no—
258C2×D212—82no—
259C2×D212C2×D414yes—
260C2×D212C2412yes—
261C2×D212C2412yes—
262C2×C4×D53—22no—
263C2×C4×D53—22no—
264C2×C4×D53—22no—
265C2×C4×D53—22no—
266C2×C4×D53—24no—
267C2×C4×D53—24no—
268C2×C4×D53—44no—
269C2×C4×D53—44no—
270C2×C4×D53C2×D412yes—
271C2×C4×D53C2×D412yes—
272C2×C4×D53C2412yes—
273C2×C4×D53C2412yes—
274C2×Dic106—22no—
275C2×Dic106—22no—
276C2×Dic106—22no—
277C2×Dic106—22no—
278C2×Dic106—21no—
279C2×Dic106—21no—
280C2×Dic106—24no—
281C2×Dic106—44no—
282C2×Dic106C2412yes—
283C2×Dic106C2412yes—
284SD16×C53C2×D4116yescomplemented
285C2×C8×C53—22no—
286C2×C8×C53C2×D414yes—
287C2×C8×C53C2412yes—
288C2×C8×C53C2412yes—
289C4⋊C4×C53—24no—
290C4⋊C4×C53—21no—
291C4⋊C4×C53—21no—
292C4⋊C4×C53C2412yes—
293C4⋊C4×C53C2412yes—
294C22⋊C4×C53—24no—
295C42×C53—24no—
296C42×C53C2×D412yes—
297C42×C53C2412yes—
298#11719925—28no—
299#11719924—28no—
300#11719923—28no—
301#11719922—28no—
302#11719921—24no—
303#11719921—24no—
304#11719921—24no—
305#11719921—24no—
306#11719921—24no—
307#11719921—24no—
308#11719921—24no—
309#11719921—24no—
310#11719921C2×D414yes—
311#11719921C2×D414yes—
312C4⋊Dic53—24no—
313C4⋊Dic53—24no—
314C4⋊Dic53C2×D414yes—
315C2×#88322—22no—
316C2×#88322—22no—
317C2×#88322C2412yes—
318C2×#88322C2412yes—
319Dic212—44no—
320D424—44no—
321#11719913—28no—
322#11719913—28no—
323C8×D53—28no—
324C8×D53—28no—
325C23×C53—24no—
326C23×C53—22no—
327C23×C53—42no—
328C23×C53—42no—
329C23×C53C22×D411yescharacteristic
330C22×D53—22no—
331C22×D53—22no—
332C22×D53—22no—
333C22×D53—22no—
334C22×D53—22no—
335C22×D53—22no—
336C22×D53—22no—
337C22×D53—48no—
338C22×D53—42no—
339C22×D53—42no—
340C22×D53—42no—
341C22×D53—42no—
342C22×D53—42no—
343C22×D53—42no—
344C22×D53—48no—
345C22×D53—84no—
346C22×D53—816no—
347C22×D53#13514yescomplemented
348C22×D53C22×D412yes—
349C22×D53C22×D412yes—
350Q8×C53—24no—
351Q8×C53—22no—
352Q8×C53C22×D414yes—
353D4×C53—24no—
354D4×C53—22no—
355D4×C53C22×D414yes—
356C2×C4×C53—24no—
357C2×C4×C53—22no—
358C2×C4×C53—22no—
359C2×C4×C53—22no—
360C2×C4×C53—22no—
361C2×C4×C53—22no—
362C2×C4×C53—42no—
363C2×C4×C53—42no—
364C2×C4×C53—84no—
365C2×C4×C53C22×D412yes—
366C2×C4×C53C22×D412yes—
367C2×C4×C53C22×D411yescharacteristic
368C2×C4×C53C22×D412yes—
369C2×C4×C53H(5,𝔽2)12yes—
370C2×C4×C53C2511yescharacteristic
371C22⋊D53—48no—
372C22⋊D53—48no—
373C2×Dic53—22no—
374C2×Dic53—22no—
375C2×Dic53—22no—
376C2×Dic53—22no—
377C2×Dic53—48no—
378C2×Dic53—42no—
379C2×Dic53—42no—
380C2×Dic53C22×D412yes—
381C2×Dic53C22×D412yes—
382D212—28no—
383D212—22no—
384D212—22no—
385D212—22no—
386D212—22no—
387D212—48no—
388D212—48no—
389D212—42no—
390D212—42no—
391D212—84no—
392C4×D53—24no—
393C4×D53—24no—
394C4×D53—22no—
395C4×D53—22no—
396C4×D53—22no—
397C4×D53—22no—
398C4×D53—48no—
399C4×D53—48no—
400Dic106—22no—
401Dic106—22no—
402Dic106—22no—
403Dic106—22no—
404Dic106—48no—
405Dic106—42no—
406Dic106—42no—
407C8×C53—22no—
408C8×C53C22×D414yes—
409#88322—22no—
410#88322—22no—
411C2×#3282—531nomaximal, Sylow
412C22×C53—24no—
413C22×C53—48no—
414C22×C53—42no—
415C22×C53—42no—
416C22×C53D4212yes—
417C22×C53C2×#13512yes—
418C22×C53#57712yes—
419C22×C53C23×D411yescharacteristic
420C2×D53—22no—
421C2×D53—28no—
422C2×D53—22no—
423C2×D53—22no—
424C2×D53—22no—
425C2×D53—22no—
426C2×D53—44no—
427C2×D53—42no—
428C2×D53—42no—
429C2×D53—42no—
430C2×D53—42no—
431C2×D53—42no—
432C2×D53—42no—
433C2×D53—816no—
434C2×D53—84no—
435C2×D53—84no—
436C2×D53C2×#13514yescomplemented
437C4×C53—24no—
438C4×C53—22no—
439C4×C53—22no—
440C4×C53—42no—
441C4×C53—42no—
442C4×C53D4212yes—
443C4×C53C23×D411yescharacteristic
444C4×C53C2×H(5,𝔽2)11yescharacteristic
445Dic53—22no—
446Dic53—22no—
447Dic53—42no—
448Dic53—42no—
449C22×#135—531no—
450C23×SD16—531no—
451C2×#548—531no—
452C2×#546—531no—
453#3282—5316no—
454C2×#495—531no—
455C2×#465—531no—
456C2×#465—531no—
457C2×#464—531no—
458C2×#463—531no—
459C2×#452—531no—
460C2×#449—531no—
461C2×#451—531no—
462C2×#447—531no—
463C2×C4×SD16D5311yescharacteristic, complemented
464C2×C8×D4—531no—
465C2×C53—44no—
466C2×C53#328214yescomplemented
467C2×C53C2×D4211yescharacteristic
468C2×C53C22×#13511yescharacteristic
469C2×C53C2×#57711yescharacteristic
470D53—24no—
471D53—42no—
472D53—82no—
473D53—82no—
474C22×#41—531no—
475C22×#41—531no—
476C23×Q8—531no—
477C23×D4—531no—
478C2×#135—538no—
479C2×#135—1068no—
480C22×Q16—531no—
481C22×Q16—531no—
482C22×SD16—531no—
483C22×SD16—531no—
484C22×SD16—538no—
485C22×SD16—531no—
486C22×SD16—531no—
487C22×SD16—1068no—
488C22×SD16C2×D5311yescharacteristic
489C22×D8—531no—
490C22×D8—531no—
491C23×C8—531no—
492C23×C8—531no—
493#548—538no—
494#548—1064no—
495#546—538no—
496#546—1064no—
497C2×#124—531no—
498C2×#124—531no—
499C2×#124—1061no—
500C2×#123—1061no—
501C2×C22⋊Q8—531no—
502C2×C22⋊Q8—531no—
503C2×C22⋊Q8—1061no—
504C2×#121—531no—
505C2×#121—531no—
506C2×#121—1061no—
507C2×#121—1061no—
508C2×#120—1061no—
509C2×C4×Q8C2×D5311yescharacteristic, complemented
510C2×C4×D4—531no—
511C2×C4×D4—1061no—
512C2×C4×D4C2×D5311yescharacteristic
513C22×C22⋊C4—1061no—
514#495—538no—
515#465—538no—
516#465—538no—
517#464—538no—
518#463—538no—
519#452—538no—
520#451—538no—
521#449—538no—
522#447—538no—
523C4×SD16C2×D5318yescomplemented
524C8×D4—538no—
525C2×#106C2×D5311yescharacteristic, complemented
526C2×C4⋊C8—531no—
527C2×#103—531no—
528C2×#103—531no—
529C2×#103C2×D5311yescharacteristic, complemented
530C2×#102—531no—
531C2×#102—531no—
532C2×#102C2×D5311yescharacteristic
533C2×C22⋊C8—531no—
534C2×C22⋊C8—531no—
535C2×C4×C8C2×D5311yescharacteristic, complemented
536C53C2×#328211yescharacteristic, complemented, Sylow
537C25—1061no—
538C2×#41—534no—
539C2×#41—534no—
540C2×#41—1062no—
541C2×#41—1062no—
542C2×#41—1064no—
543C2×#41—1064no—
544C2×#41—2122no—
545C2×#41—2122no—
546C22×Q8—534no—
547C22×Q8—531no—
548C22×Q8—531no—
549C22×Q8—1061no—
550C22×Q8—1062no—
551C22×Q8—1064no—
552C22×Q8—2122no—
553C22×Q8C22×D5311yescharacteristic
554C22×D4—534no—
555C22×D4—531no—
556C22×D4—531no—
557C22×D4—531no—
558C22×D4—1061no—
559C22×D4—1061no—
560C22×D4—1061no—
561C22×D4—1062no—
562C22×D4—1061no—
563C22×D4—1064no—
564C22×D4—1061no—
565C22×D4—2122no—
566C22×D4C22×D5311yescharacteristic
567C23×C4—21no—
568C23×C4—531no—
569C23×C4—531no—
570C23×C4—1061no—
571C23×C4—1061no—
572C23×C4—1061no—
573#135—10632no—
574C2×Q16—534no—
575C2×Q16—534no—
576C2×Q16—1064no—
577C2×Q16—2122no—
578C2×SD16—534no—
579C2×SD16—534no—
580C2×SD16—534no—
581C2×SD16—534no—
582C2×SD16—1064no—
583C2×SD16—1064no—
584C2×SD16—10632no—
585C2×SD16—1064no—
586C2×SD16—1064no—
587C2×SD16D21218yescomplemented
588C2×SD16C22×D5314yes—
589C2×D8—534no—
590C2×D8—534no—
591C2×D8—1064no—
592C2×D8—2122no—
593C22×C8—531no—
594C22×C8—531no—
595C22×C8—534no—
596C22×C8—534no—
597C22×C8—1064no—
598C22×C8—1064no—
599C22×C8C22×D5311yescharacteristic
600C22×C8C22×D5311yescharacteristic
601#124—534no—
602#124—534no—
603#124—1068no—
604#124—1062no—
605#124—1062no—
606#123—1068no—
607C22⋊Q8—534no—
608C22⋊Q8—534no—
609C22⋊Q8—1068no—
610C22⋊Q8—1062no—
611C22⋊Q8—1062no—
612#121—534no—
613#121—534no—
614#121—1068no—
615#121—1062no—
616#121—1062no—
617#121—1068no—
618#120—1068no—
619C4×Q8—22no—
620C4×Q8C22×D5314yescomplemented
621C4×D4—22no—
622C4×D4—534no—
623C4×D4—534no—
624C4×D4—1068no—
625C4×D4C22×D5314yes—
626C2×C4⋊C4—21no—
627C2×C4⋊C4—531no—
628C2×C4⋊C4—1061no—
629C2×C4⋊C4—1061no—
630C2×C4⋊C4C22×D5311yescharacteristic
631C2×C4⋊C4C22×D5311yescharacteristic
632C2×C22⋊C4—21no—
633C2×C22⋊C4—531no—
634C2×C22⋊C4—531no—
635C2×C22⋊C4—1068no—
636C2×C22⋊C4—1061no—
637C2×C22⋊C4—1061no—
638C2×C22⋊C4—1061no—
639C2×C22⋊C4—1061no—
640C2×C22⋊C4—1061no—
641C2×C22⋊C4—1061no—
642C2×C22⋊C4—1061no—
643C2×C22⋊C4—1061no—
644C2×C42—21no—
645C2×C42C22×D5311yescharacteristic
646#106C22×D5314yescomplemented
647C4⋊C8—534no—
648#103—534no—
649#103—534no—
650#103C22×D5314yescomplemented
651#102—534no—
652#102—534no—
653#102C22×D5314yes—
654C22⋊C8—534no—
655C22⋊C8—534no—
656C4×C8C22×D5314yescomplemented
657C24—21no—
658C24—531no—
659C24—531no—
660C24—1064no—
661C24—1061no—
662C24—1061no—
663C24—4242no—
664C24—2124no—
665C24—2124no—
666#41—1068no—
667#41—1068no—
668#41—2124no—
669#41—2128no—
670#41—2124no—
671#41—2128no—
672C2×Q8—21no—
673C2×Q8—22no—
674C2×Q8—532no—
675C2×Q8—532no—
676C2×Q8—1064no—
677C2×Q8—1061no—
678C2×Q8—1061no—
679C2×Q8—1068no—
680C2×Q8—1062no—
681C2×Q8—1062no—
682C2×Q8—1062no—
683C2×Q8—1062no—
684C2×Q8—2124no—
685C2×Q8—2124no—
686C2×Q8—2128no—
687C2×Q8C2×D21214yes—
688C2×Q8C23×D5312yes—
689C2×D4—21no—
690C2×D4—22no—
691C2×D4—534no—
692C2×D4—532no—
693C2×D4—532no—
694C2×D4—1064no—
695C2×D4—1064no—
696C2×D4—1064no—
697C2×D4—1064no—
698C2×D4—1064no—
699C2×D4—1068no—
700C2×D4—1064no—
701C2×D4—1061no—
702C2×D4—1061no—
703C2×D4—1062no—
704C2×D4—1062no—
705C2×D4—1062no—
706C2×D4—1062no—
707C2×D4—4242no—
708C2×D4—2124no—
709C2×D4—2124no—
710C2×D4—2124no—
711C2×D4—2128no—
712C2×D4—2124no—
713C2×D4—2124no—
714C2×D4C2×D21214yes—
715C2×D4C23×D5312yes—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—24no—
720C22×C4—82no—
721C22×C4—531no—
722C22×C4—531no—
723C22×C4—532no—
724C22×C4—532no—
725C22×C4—532no—
726C22×C4—532no—
727C22×C4—1064no—
728C22×C4—1064no—
729C22×C4—1064no—
730C22×C4—1062no—
731C22×C4—1062no—
732C22×C4—1062no—
733C22×C4—1062no—
734C22×C4—1061no—
735C22×C4—1061no—
736C22×C4—2124no—
737C22×C4—2124no—
738C22×C4—2124no—
739C22×C4D4×D5311yescharacteristic
740C22×C4D4×D5311yescharacteristic
741C22×C4C23×D5311yescharacteristic
742Q16—1068no—
743Q16—2124no—
744SD16—1068no—
745SD16—1068no—
746SD16—1068no—
747SD16—1068no—
748SD16C2×D212116yescomplemented
749D8—1068no—
750D8—2124no—
751C2×C8—22no—
752C2×C8—532no—
753C2×C8—532no—
754C2×C8—1062no—
755C2×C8—1062no—
756C2×C8—1068no—
757C2×C8—1068no—
758C2×C8C2×D21214yes—
759C2×C8C23×D5312yes—
760C2×C8C23×D5312yes—
761C4⋊C4—24no—
762C4⋊C4—21no—
763C4⋊C4—21no—
764C4⋊C4—534no—
765C4⋊C4—1064no—
766C4⋊C4—1064no—
767C4⋊C4C23×D5312yes—
768C4⋊C4C23×D5312yes—
769C22⋊C4—24no—
770C22⋊C4—534no—
771C22⋊C4—534no—
772C22⋊C4—1064no—
773C22⋊C4—1064no—
774C22⋊C4—1064no—
775C22⋊C4—1064no—
776C22⋊C4—1064no—
777C22⋊C4—1064no—
778C22⋊C4—1064no—
779C22⋊C4—1064no—
780C42—24no—
781C42D4×D5312yes—
782C42C23×D5312yes—
783C23—22no—
784C23—24no—
785C23—42no—
786C23—42no—
787C23—534no—
788C23—532no—
789C23—532no—
790C23—1062no—
791C23—1062no—
792C23—1062no—
793C23—1062no—
794C23—1062no—
795C23—1062no—
796C23—1062no—
797C23—42416no—
798C23—4244no—
799C23—2128no—
800C23—2128no—
801C23—2122no—
802C23—2122no—
803C23—2122no—
804C23—2122no—
805C23—2122no—
806C23—2122no—
807C23C2×D4×D5311yescharacteristic
808Q8—22no—
809Q8—24no—
810Q8—1062no—
811Q8—1062no—
812Q8—1062no—
813Q8—1062no—
814Q8—2128no—
815Q8—2122no—
816Q8—2122no—
817Q8C22×D21214yes—
818D4—22no—
819D4—24no—
820D4—1068no—
821D4—1062no—
822D4—1062no—
823D4—1062no—
824D4—1062no—
825D4—4244no—
826D4—2128no—
827D4—2128no—
828D4—2128no—
829D4—2128no—
830D4—2122no—
831D4—2122no—
832D4C22×D21214yes—
833C2×C4—22no—
834C2×C4—22no—
835C2×C4—22no—
836C2×C4—24no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—42no—
840C2×C4—42no—
841C2×C4—84no—
842C2×C4—532no—
843C2×C4—532no—
844C2×C4—1062no—
845C2×C4—1062no—
846C2×C4—1062no—
847C2×C4—1062no—
848C2×C4—1062no—
849C2×C4—1062no—
850C2×C4—1064no—
851C2×C4—1064no—
852C2×C4—1062no—
853C2×C4—1062no—
854C2×C4—2128no—
855C2×C4—2128no—
856C2×C4—2128no—
857C2×C4—2122no—
858C2×C4—2122no—
859C2×C4C2×D4×D5312yes—
860C2×C4C2×D4×D5312yes—
861C2×C4C2×D4×D5311yescharacteristic
862C2×C4C22×D21212yes—
863C2×C4#1313326312yes—
864C2×C4C24×D5311yescharacteristic
865C8—22no—
866C8—1062no—
867C8—1062no—
868C8C22×D21214yes—
869C22—24no—
870C22—42no—
871C22—42no—
872C22—48no—
873C22—534no—
874C22—1062no—
875C22—1062no—
876C22—1068no—
877C22—1062no—
878C22—1062no—
879C22—1062no—
880C22—42416no—
881C22—4244no—
882C22—4244no—
883C22—2122no—
884C22—2122no—
885C22—2122no—
886C22—2122no—
887C22—2122no—
888C22—2122no—
889C22—2124no—
890C22D4×D21212yes—
891C22#135×D5312yes—
892C22#1681142912yes—
893C22C22×D4×D5311yescharacteristic
894C4—24no—
895C4—22no—
896C4—22no—
897C4—42no—
898C4—42no—
899C4—1062no—
900C4—1062no—
901C4—2122no—
902C4—2122no—
903C4D4×D21212yes—
904C4C23×D21211yescharacteristic
905C4C2×#1313326311yescharacteristic
906C2—44no—
907C2—1064no—
908C2—4242no—
909C2—4242no—
910C2—2122no—
911C2#2028642414yesdirect product factor
912C2C2×D4×D21211yescharacteristic
913C2C2×#135×D5311yescharacteristic
914C2C2×#1681142911yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C4×SD16×C53C2
socleC23×C53C22×D4
hypercenterC2×C4×SD16D53
hypocenterC53C2×#3282
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×SD16

Complements

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

NH ≅ G/Ntype
1. C22×#13133238C2semidirect
2. C22×SD16×D53C2semidirect
3. C2×#16811285C2semidirect
4. C2×#16811268C2semidirect
5. #20286424C2direct (N × H)
6. C2×#16811007C2semidirect
7. C2×#16810853C2semidirect
8. C2×#16810853C2semidirect
9. C2×#16810845C2semidirect
10. C2×#16810838C2semidirect
11. C2×#16810786C2semidirect
12. C2×#16810771C2semidirect
13. C2×#16810780C2semidirect
14. C2×#16810758C2semidirect
15. C2×C8×D212C2semidirect
16. C2×C4×SD16×C53C2semidirect
17. C22×#11719949C22semidirect
22. C2×#13133238C22semidirect
23. C22×Dic212C22semidirect
24. C22×#11719925C22semidirect
26. C22×#11719913C22semidirect
30. C2×SD16×D53C22semidirect
34. C22×C8×D53C22semidirect
36. #16811285C22semidirect
38. #16811268C22semidirect
41. C2×#13133205C22semidirect
45. C2×#13133197C22semidirect
54. #16811007C22semidirect
55. #16810853C22semidirect
56. #16810853C22semidirect
57. #16810845C22semidirect
58. #16810838C22semidirect
59. #16810786C22semidirect
60. #16810780C22semidirect
61. #16810771C22semidirect
62. #16810758C22semidirect
63. C8×D212C22semidirect
64. C2×C4⋊#88322C22semidirect
65. C2×#13133140C22semidirect
66. C2×#13133140C22semidirect
68. C2×#13133137C22semidirect
70. C2×#13133129C22semidirect
72. C2×C4×Q8×C53C22semidirect
74. C4×SD16×C53C22semidirect
75. C2×#106×C53C22semidirect
76. C2×#103×C53C22semidirect
78. C2×C4×C8×C53C22semidirect
83. C2×#11719949C23semidirect
114. C2×Dic212C23semidirect
116. C2×#11719925C23semidirect
120. C2×#11719913C23semidirect
135. C2×C8×D53C23semidirect
140. #13133205C23semidirect
146. #13133197C23semidirect
171. C4⋊#88322C23semidirect
172. #13133140C23semidirect
173. #13133140C23semidirect
175. #13133137C23semidirect
177. #13133129C23semidirect
181. C2×SD16×C53D4semidirect
186. C4×Q8×C53C23semidirect
195. #106×C53C23semidirect
196. #103×C53C23semidirect
198. C4×C8×C53C23semidirect
284. SD16×C53C2×D4semidirect
347. C22×D53#135semidirect
436. C2×D53C2×#135semidirect
463. C2×C4×SD16D53semidirect
466. C2×C53#3282semidirect
509. C2×C4×Q8C2×D53semidirect
523. C4×SD16C2×D53semidirect
525. C2×#106C2×D53semidirect
529. C2×#103C2×D53semidirect
535. C2×C4×C8C2×D53semidirect
536. C53C2×#3282semidirect
587. C2×SD16D212semidirect
620. C4×Q8C22×D53semidirect
646. #106C22×D53semidirect
650. #103C22×D53semidirect
656. C4×C8C22×D53semidirect
748. SD16C2×D212semidirect
911. C2#20286424direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#131332382
C22×SD16×D532
C2×#168112852
C2×#168112682
#202864242
C2×#168110072
C2×#168108532
C2×#168108452
C2×#168108382
C2×#168107862
C2×#168107712
C2×#168107802
C2×#168107582
C2×C8×D2122
C2×C4×SD16×C532
C2×#328253