Finite Group Databasebeta

← C2×#20285816 #28255454

Subgroups — C2×#20285816 #28255454

Order 13568.

2278 conjugacy classes of subgroups.

The subgroup lattice has 862 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811245C211yesmaximal, characteristic, complemented
2C2×#16811191C211yesmaximal, characteristic, complemented
3#20285816C2116yesmaximal, direct product factor
4C2×#16811009C211yesmaximal, characteristic, complemented
5C2×#16811008C211yesmaximal, characteristic, complemented
6C2×#16810984C211yesmaximal, characteristic, complemented
7C2×#16810968C211yesmaximal, characteristic, complemented
8C2×#16810823C211yesmaximal, characteristic, complemented
9C2×#16810835C211yesmaximal, characteristic, complemented
10C2×#16810819C211yesmaximal, characteristic, complemented
11C2×#16810784C211yesmaximal, characteristic, complemented
12C2×#16810771C211yesmaximal, characteristic, complemented
13C2×#16810772C211yesmaximal, characteristic, complemented
14C2×#16810758C211yesmaximal, characteristic, complemented
15C2×#16810683C211yesmaximal, characteristic, complemented
16C2×C53×#464C211yesmaximal, characteristic, complemented
17C22×#11719949C2211yescharacteristic
18C22×D4×D53C2211yescharacteristic
19C22×#11719924C2211yescharacteristic
20C22×#11719924C2211yescharacteristic, complemented
21C22×#11719924C2211yescharacteristic, complemented
22C22×D424C2211yescharacteristic
23C22×D424C2211yescharacteristic, complemented
24C22×#11719922C2211yescharacteristic
25#16811245—24no—
26#16811245C2218yescomplemented
27#16811191—24no—
28#16811191C2218yescomplemented
29C2×#13133216C2211yescharacteristic, complemented
30C2×#13133214C2211yescharacteristic
31C2×#13133213C2211yescharacteristic
32C2×#13133211—21no—
33C2×#13133206C2211yescharacteristic
34C2×#13133206C2211yescharacteristic, complemented
35C2×#13133205—21no—
36C2×#13133202—21no—
37C2×#13133195—21no—
38C2×#13133193C2211yescharacteristic
39C2×#13133192C2211yescharacteristic
40C2×#13133190—21no—
41C2×#13133190—21no—
42C2×#13133187—21no—
43C2×#13133187—21no—
44C2×C4×D212C2211yescharacteristic, complemented
45C2×#13133174C2211yescharacteristic
46#16811009C2218yescomplemented
47#16811008C2218yescomplemented
48#16810984C2218yescomplemented
49#16810968C2218yescomplemented
50#16810835C2218yescomplemented
51#16810823C2218yescomplemented
52#16810819C2218yescomplemented
53#16810784C2218yescomplemented
54#16810772C2218yescomplemented
55#16810771C2218yescomplemented
56#16810758C2218yescomplemented
57#16810683C2218yescomplemented
58C2×C4⋊#88322C2211yescharacteristic, complemented
59C2×#13133141C2211yescharacteristic, complemented
60C2×#13133139C2211yescharacteristic
61C2×#13133139C2211yescharacteristic, complemented
62C2×#13133138C2211yescharacteristic
63C2×#13133137C2211yescharacteristic
64C2×#13133137C2211yescharacteristic, complemented
65C2×#13133129C2211yescharacteristic
66C2×#13133129C2211yescharacteristic
67C2×#13133127C2211yescharacteristic, complemented
68C2×C8×Dic53C2211yescharacteristic, complemented
69C22×Q16×C53C2211yescharacteristic, complemented
70C22×SD16×C53C2211yescharacteristic
71C2×#124×C53C2211yescharacteristic
72C2×C4×Q8×C53C2211yescharacteristic, complemented
73C53×#464C2218yescomplemented
74C2×C4⋊C8×C53C2211yescharacteristic, complemented
75C2×#103×C53C2211yescharacteristic, complemented
76C2×#102×C53C2211yescharacteristic
77C24×D53—21no—
78C2×#11719949—22no—
79C2×#11719949—42no—
80C2×#11719949—42no—
81C2×#11719949C2314yes—
82C22×Dic106—21no—
83C22×D212—21no—
84C22×D212—21no—
85C22×D212—21no—
86C22×D212—21no—
87C22×D212C2311yescharacteristic
88C22×D212C2311yescharacteristic
89C22×D212C2311yescharacteristic
90C22×C22⋊D53—21no—
91C22×C22⋊D53—21no—
92C22×C22⋊D53—21no—
93C2×D4×D53—22no—
94C2×D4×D53—42no—
95C2×D4×D53—42no—
96C2×D4×D53C2314yes—
97C22×C4×D53—21no—
98C22×C4×D53—21no—
99C22×C4×D53C2311yescharacteristic
100C2×#11719924—42no—
101C2×#11719924—42no—
102C2×#11719924—42no—
103C2×#11719924C2314yes—
104C2×#11719924C2314yescomplemented
105C2×#11719924C2314yescomplemented
106C2×D424—42no—
107C2×D424—42no—
108C2×D424C2314yes—
109C2×D424C2314yescomplemented
110C2×#11719922—42no—
111C2×#11719922C2314yes—
112C22×#88322C2311yescharacteristic
113C22×#88322C2311yescharacteristic
114#13133216—22no—
115#13133216C2314yescomplemented
116#13133214—22no—
117#13133214C2314yes—
118#13133213—22no—
119#13133213C2314yes—
120#13133211—28no—
121#13133206—22no—
122#13133206—22no—
123#13133206C2314yes—
124#13133206C2314yescomplemented
125#13133205—28no—
126#13133202—28no—
127#13133195—28no—
128#13133193—22no—
129#13133193C2314yes—
130#13133192—22no—
131#13133192C2314yes—
132#13133190—28no—
133#13133190—28no—
134#13133187—28no—
135#13133187—28no—
136C4×D212—22no—
137C4×D212C2314yescomplemented
138#13133174D414yes—
139#13133174C2314yes—
140C2×C4⋊Dic53C2311yescharacteristic
141C2×#11719919—21no—
142C2×#11719919—21no—
143C2×#11719919D411yescharacteristic
144C2×#11719919D411yescharacteristic
145C2×#11719921—21no—
146C2×#11719921—21no—
147C2×#11719921—21no—
148C2×#11719921—21no—
149C2×#11719921—21no—
150C2×#11719921—21no—
151C2×#11719921—21no—
152C2×#11719921D411yescharacteristic
153C2×#11719921D411yescharacteristic
154C2×C4×Dic53C2311yescharacteristic
155C4⋊#88322C2314yescomplemented
156#13133141C2314yescomplemented
157#13133139C2314yes—
158#13133139C2314yescomplemented
159#13133138C2314yes—
160#13133137C2314yes—
161#13133137C2314yescomplemented
162#13133129C2314yes—
163#13133129C2314yes—
164#13133127C2314yescomplemented
165C8×Dic53C2314yescomplemented
166C22×Q8×C53C2311yescharacteristic
167C22×Q8×C53C2311yescharacteristic
168C22×D4×C53C2311yescharacteristic
169C2×Q16×C53—42no—
170C2×Q16×C53C2314yescomplemented
171C2×SD16×C53—42no—
172C2×SD16×C53C2314yes—
173C22×C8×C53C2311yescharacteristic
174C22×C8×C53C2311yescharacteristic
175#124×C53—22no—
176#124×C53C2314yes—
177C4×Q8×C53—22no—
178C4×Q8×C53C2314yescomplemented
179C2×C4⋊C4×C53—21no—
180C2×C4⋊C4×C53C2311yescharacteristic
181C2×C22⋊C4×C53—21no—
182C2×C22⋊C4×C53—21no—
183C2×C42×C53—21no—
184C2×C42×C53C2311yescharacteristic
185C4⋊C8×C53C2314yescomplemented
186#103×C53C2314yescomplemented
187#102×C53C2314yes—
188C24×C53—21no—
189C23×D53—21no—
190C23×D53—21no—
191C23×D53—21no—
192C23×D53—24no—
193C23×D53—44no—
194C23×D53—82no—
195C23×D53—82no—
196C23×D53C2×D411yescharacteristic
197C2×Q8×C53—21no—
198C2×Q8×C53—21no—
199C2×Q8×C53—22no—
200C2×Q8×C53—22no—
201C2×Q8×C53—22no—
202C2×Q8×C53—22no—
203C2×Q8×C53C2412yes—
204C2×Q8×C53C2412yes—
205C2×D4×C53—21no—
206C2×D4×C53—22no—
207C2×D4×C53—22no—
208C2×D4×C53C2412yes—
209C22×C4×C53—21no—
210C22×C4×C53—21no—
211C22×C4×C53—21no—
212C22×C4×C53C2×D411yescharacteristic
213C22×C4×C53C2×D411yescharacteristic
214C22×C4×C53C2411yescharacteristic
215C2×C22⋊D53—24no—
216C2×C22⋊D53—24no—
217C2×C22⋊D53—24no—
218C2×C22⋊D53—44no—
219C2×C22⋊D53—82no—
220C2×C22⋊D53—82no—
221C22×Dic53—21no—
222C22×Dic53C2×D411yescharacteristic
223C22×Dic53C2×D411yescharacteristic
224C22×Dic53C2×D411yescharacteristic
225#11719949—44no—
226#11719949—44no—
227#11719949—48no—
228D4×D53—44no—
229D4×D53—44no—
230D4×D53—48no—
231C2×D212—22no—
232C2×D212—22no—
233C2×D212—22no—
234C2×D212—22no—
235C2×D212—22no—
236C2×D212—22no—
237C2×D212—24no—
238C2×D212—21no—
239C2×D212—21no—
240C2×D212—21no—
241C2×D212—24no—
242C2×D212—24no—
243C2×D212—24no—
244C2×D212—44no—
245C2×D212—82no—
246C2×D212—82no—
247C2×D212—82no—
248C2×D212C2412yes—
249C2×D212C2412yes—
250C2×D212C2412yes—
251C2×C4×D53—22no—
252C2×C4×D53—22no—
253C2×C4×D53—24no—
254C2×C4×D53—24no—
255C2×C4×D53—44no—
256C2×C4×D53—82no—
257C2×C4×D53C2×D412yes—
258C2×C4×D53C2412yes—
259C2×Dic106—24no—
260C2×Dic106—82no—
261Q16×C53—44no—
262SD16×C53—44no—
263C2×C8×C53—22no—
264C2×C8×C53—22no—
265C2×C8×C53C2412yes—
266C2×C8×C53C2412yes—
267C4⋊C4×C53—24no—
268C4⋊C4×C53—21no—
269C4⋊C4×C53C2412yes—
270C22⋊C4×C53—24no—
271C22⋊C4×C53—24no—
272C42×C53—24no—
273C42×C53C2×D412yes—
274C42×C53C2412yes—
275#11719924—44no—
276#11719924—44no—
277#11719924—44no—
278#11719922—44no—
279#11719921—24no—
280#11719921—24no—
281#11719921—24no—
282#11719921—24no—
283#11719921—24no—
284#11719921—24no—
285#11719921—24no—
286#11719921C2×D414yes—
287#11719921C2×D414yes—
288C4⋊Dic53—21no—
289C4⋊Dic53C2412yes—
290#11719919—24no—
291#11719919—24no—
292#11719919C2×D414yes—
293#11719919C2×D414yes—
294C4×Dic53C2×D412yes—
295C4×Dic53C2412yes—
296C2×#88322—22no—
297C2×#88322—22no—
298C2×#88322C2412yes—
299C2×#88322C2412yes—
300D424—44no—
301D424—44no—
302C23×C53—22no—
303C23×C53—42no—
304C23×C53—42no—
305C23×C53—42no—
306C23×C53C22×D411yescharacteristic
307C22×D53—22no—
308C22×D53—22no—
309C22×D53—22no—
310C22×D53—22no—
311C22×D53—22no—
312C22×D53—22no—
313C22×D53—48no—
314C22×D53—42no—
315C22×D53—42no—
316C22×D53—42no—
317C22×D53—42no—
318C22×D53—42no—
319C22×D53—42no—
320C22×D53—42no—
321C22×D53—42no—
322C22×D53—42no—
323C22×D53—84no—
324C22×D53—84no—
325C22×D53—816no—
326C22×D53C22×D412yes—
327Q8×C53—22no—
328Q8×C53—22no—
329Q8×C53—22no—
330Q8×C53—22no—
331Q8×C53—42no—
332Q8×C53—42no—
333D4×C53—22no—
334D4×C53—22no—
335D4×C53—42no—
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×C53—42no—
344C2×C4×C53C22×D412yes—
345C2×C4×C53C22×D412yes—
346C2×C4×C53C22×D411yescharacteristic
347C2×C4×C53H(5,𝔽2)12yes—
348C2×C4×C53H(5,𝔽2)12yes—
349C2×C4×C53C2511yescharacteristic
350C22⋊D53—48no—
351C22⋊D53—84no—
352C22⋊D53—84no—
353C2×Dic53—22no—
354C2×Dic53—22no—
355C2×Dic53—22no—
356C2×Dic53—22no—
357C2×Dic53—42no—
358C2×Dic53C22×D412yes—
359C2×Dic53C22×D412yes—
360C2×Dic53C22×D412yes—
361D212—22no—
362D212—22no—
363D212—22no—
364D212—22no—
365D212—22no—
366D212—22no—
367D212—48no—
368D212—42no—
369D212—42no—
370D212—42no—
371D212—84no—
372D212—84no—
373D212—84no—
374C4×D53—24no—
375C4×D53—22no—
376C4×D53—22no—
377C4×D53—48no—
378C4×D53—84no—
379Dic106—84no—
380C8×C53—22no—
381C8×C53—22no—
382#88322—22no—
383#88322—22no—
384C2×#3224—531nomaximal, Sylow
385C22×C53—42no—
386C22×C53—42no—
387C22×C53—42no—
388C22×C53—84no—
389C22×C53#53512yes—
390C22×C53#57612yes—
391C22×C53#57712yes—
392C22×C53C23×D411yescharacteristic
393C2×D53—22no—
394C2×D53—22no—
395C2×D53—22no—
396C2×D53—44no—
397C2×D53—42no—
398C2×D53—42no—
399C2×D53—42no—
400C2×D53—42no—
401C2×D53—42no—
402C2×D53—42no—
403C2×D53—42no—
404C2×D53—42no—
405C2×D53—42no—
406C2×D53—816no—
407C2×D53—84no—
408C2×D53—84no—
409C2×D53—84no—
410C4×C53—22no—
411C4×C53—22no—
412C4×C53—42no—
413C4×C53—42no—
414C4×C53—42no—
415C4×C53#53512yes—
416C4×C53C2×H(5,𝔽2)11yescharacteristic
417C4×C53C2×H(5,𝔽2)11yescharacteristic
418Dic53—22no—
419Dic53—22no—
420Dic53—22no—
421Dic53—42no—
422C2×#542—531no—
423C2×#535—531no—
424#3224—5316no—
425C2×#496—531no—
426C2×#495—531no—
427C2×#489—531no—
428C2×#486—531no—
429C2×#464D5311yescharacteristic, complemented
430C2×#460—531no—
431C2×#463—531no—
432C2×#459—531no—
433C2×#452—531no—
434C2×#449—531no—
435C2×#450—531no—
436C2×#447—531no—
437C2×#433—531no—
438C2×C53—82no—
439C2×C53#322414yescomplemented
440C2×C53C2×#53511yescharacteristic
441C2×C53C2×#57611yescharacteristic
442C2×C53C2×#57711yescharacteristic
443D53—42no—
444D53—82no—
445D53—82no—
446D53—82no—
447C22×#41—531no—
448C23×D4—531no—
449C22×Q16C2×D5311yescharacteristic, complemented
450C22×SD16—531no—
451C22×SD16—531no—
452C22×SD16—531no—
453C22×SD16C2×D5311yescharacteristic
454C22×D8—531no—
455C22×D8—531no—
456C22×D8—531no—
457#542—538no—
458#542—1064no—
459#535—538no—
460#535—1064no—
461C2×C4⋊Q8—531no—
462C2×#127—531no—
463C2×#127—531no—
464C2×#126—1061no—
465C2×#124—531no—
466C2×#124—531no—
467C2×#124—1061no—
468C2×#124C2×D5311yescharacteristic
469C2×#123—1061no—
470C2×C22⋊Q8—531no—
471C2×C22⋊Q8—1061no—
472C2×#121—531no—
473C2×#121—1061no—
474C2×#121—1061no—
475C2×#120—1061no—
476C2×#120—1061no—
477C2×C4×Q8C2×D5311yescharacteristic, complemented
478C2×C4×D4—531no—
479C2×#117—531no—
480#496—538no—
481#495—538no—
482#489—538no—
483#486—538no—
484#464C2×D5318yescomplemented
485#463—538no—
486#460—538no—
487#459—538no—
488#452—538no—
489#450—538no—
490#449—538no—
491#447—538no—
492#433—538no—
493C2×C4⋊C8—531no—
494C2×C4⋊C8C2×D5311yescharacteristic, complemented
495C2×#103—531no—
496C2×#103C2×D5311yescharacteristic, complemented
497C2×#102—531no—
498C2×#102—531no—
499C2×#102—531no—
500C2×#102—531no—
501C2×#102—531no—
502C2×#102C2×D5311yescharacteristic
503C2×C22⋊C8—531no—
504C2×C22⋊C8—531no—
505C2×#97—531no—
506C2×C4×C8—531no—
507C53C2×#322411yescharacteristic, complemented, Sylow
508C25—1061no—
509C2×#41—534no—
510C2×#41—1062no—
511C2×#41—2122no—
512C2×#41—2122no—
513C22×Q8—1061no—
514C22×Q8C22×D5311yescharacteristic
515C22×Q8C22×D5311yescharacteristic
516C22×D4—534no—
517C22×D4—531no—
518C22×D4—531no—
519C22×D4—531no—
520C22×D4—1061no—
521C22×D4—1061no—
522C22×D4—1062no—
523C22×D4—1061no—
524C22×D4—1061no—
525C22×D4—1061no—
526C22×D4—1061no—
527C22×D4—1061no—
528C22×D4—2122no—
529C22×D4—2122no—
530C22×D4C22×D5311yescharacteristic
531C23×C4—531no—
532C23×C4—1061no—
533C23×C4—1061no—
534C2×Q16—42no—
535C2×Q16C22×D5314yescomplemented
536C2×SD16—42no—
537C2×SD16—534no—
538C2×SD16—534no—
539C2×SD16—534no—
540C2×SD16—2122no—
541C2×SD16—2122no—
542C2×SD16—2122no—
543C2×SD16C22×D5314yes—
544C2×D8—534no—
545C2×D8—534no—
546C2×D8—534no—
547C2×D8—2122no—
548C2×D8—2122no—
549C2×D8—2122no—
550C22×C8—531no—
551C22×C8—531no—
552C22×C8C22×D5311yescharacteristic
553C22×C8C22×D5311yescharacteristic
554C4⋊Q8—534no—
555C4⋊Q8—1062no—
556#127—534no—
557#127—534no—
558#127—1062no—
559#127—1062no—
560#126—1068no—
561#124—22no—
562#124—534no—
563#124—534no—
564#124—1068no—
565#124—1062no—
566#124—1062no—
567#124C22×D5314yes—
568#123—1068no—
569C22⋊Q8—534no—
570C22⋊Q8—1068no—
571C22⋊Q8—1062no—
572#121—534no—
573#121—1068no—
574#121—1068no—
575#121—1062no—
576#120—1068no—
577#120—1068no—
578C4×Q8—22no—
579C4×Q8C22×D5314yescomplemented
580C4×D4—534no—
581C4×D4—1062no—
582#117—534no—
583#117—534no—
584C2×C4⋊C4—21no—
585C2×C4⋊C4—531no—
586C2×C4⋊C4—531no—
587C2×C4⋊C4—531no—
588C2×C4⋊C4—1061no—
589C2×C4⋊C4—1061no—
590C2×C4⋊C4C22×D5311yescharacteristic
591C2×C22⋊C4—21no—
592C2×C22⋊C4—21no—
593C2×C22⋊C4—531no—
594C2×C22⋊C4—531no—
595C2×C22⋊C4—1061no—
596C2×C22⋊C4—1061no—
597C2×C22⋊C4—1061no—
598C2×C22⋊C4—1061no—
599C2×C22⋊C4—1061no—
600C2×C22⋊C4—1061no—
601C2×C22⋊C4—1061no—
602C2×C42—21no—
603C2×C42—531no—
604C2×C42C22×D5311yescharacteristic
605C4⋊C8—534no—
606C4⋊C8C22×D5314yescomplemented
607#103—534no—
608#103C22×D5314yescomplemented
609#102—534no—
610#102—534no—
611#102—534no—
612#102—534no—
613#102—534no—
614#102C22×D5314yes—
615C22⋊C8—534no—
616C22⋊C8—534no—
617#97—534no—
618C4×C8—534no—
619C24—21no—
620C24—531no—
621C24—1064no—
622C24—1061no—
623C24—1061no—
624C24—1061no—
625C24—4242no—
626C24—4242no—
627C24—2124no—
628#41—2124no—
629#41—2124no—
630#41—2128no—
631C2×Q8—21no—
632C2×Q8—21no—
633C2×Q8—22no—
634C2×Q8—22no—
635C2×Q8—22no—
636C2×Q8—22no—
637C2×Q8—1064no—
638C2×Q8—4242no—
639C2×Q8C23×D5312yes—
640C2×Q8C23×D5312yes—
641C2×D4—21no—
642C2×D4—22no—
643C2×D4—22no—
644C2×D4—532no—
645C2×D4—532no—
646C2×D4—532no—
647C2×D4—1064no—
648C2×D4—1064no—
649C2×D4—1064no—
650C2×D4—1064no—
651C2×D4—1064no—
652C2×D4—1064no—
653C2×D4—1064no—
654C2×D4—1061no—
655C2×D4—1061no—
656C2×D4—1061no—
657C2×D4—1062no—
658C2×D4—1062no—
659C2×D4—1062no—
660C2×D4—1062no—
661C2×D4—1062no—
662C2×D4—1062no—
663C2×D4—4242no—
664C2×D4—4242no—
665C2×D4—4242no—
666C2×D4—4242no—
667C2×D4—4242no—
668C2×D4—2124no—
669C2×D4—2124no—
670C2×D4—2124no—
671C2×D4—2128no—
672C2×D4—2124no—
673C2×D4C23×D5312yes—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—531no—
678C22×C4—531no—
679C22×C4—531no—
680C22×C4—532no—
681C22×C4—532no—
682C22×C4—1064no—
683C22×C4—1062no—
684C22×C4—1062no—
685C22×C4—1061no—
686C22×C4—1064no—
687C22×C4—4242no—
688C22×C4—2124no—
689C22×C4D4×D5311yescharacteristic
690C22×C4D4×D5311yescharacteristic
691C22×C4C23×D5311yescharacteristic
692Q16—44no—
693SD16—44no—
694SD16—2124no—
695SD16—2124no—
696SD16—2124no—
697D8—2124no—
698D8—2124no—
699D8—2124no—
700C2×C8—22no—
701C2×C8—22no—
702C2×C8—532no—
703C2×C8—532no—
704C2×C8—1062no—
705C2×C8—1062no—
706C2×C8C23×D5312yes—
707C2×C8C23×D5312yes—
708C4⋊C4—24no—
709C4⋊C4—21no—
710C4⋊C4—534no—
711C4⋊C4—534no—
712C4⋊C4—532no—
713C4⋊C4—1064no—
714C4⋊C4—1064no—
715C4⋊C4—1061no—
716C4⋊C4C23×D5312yes—
717C22⋊C4—24no—
718C22⋊C4—24no—
719C22⋊C4—534no—
720C22⋊C4—534no—
721C22⋊C4—1064no—
722C22⋊C4—1064no—
723C22⋊C4—1064no—
724C22⋊C4—1064no—
725C22⋊C4—1064no—
726C22⋊C4—1064no—
727C22⋊C4—1064no—
728C42—24no—
729C42—532no—
730C42—532no—
731C42D4×D5312yes—
732C42C23×D5312yes—
733C23—22no—
734C23—42no—
735C23—42no—
736C23—42no—
737C23—532no—
738C23—1062no—
739C23—1062no—
740C23—1062no—
741C23—1062no—
742C23—1062no—
743C23—1062no—
744C23—4244no—
745C23—4244no—
746C23—42416no—
747C23—2128no—
748C23—2122no—
749C23—2122no—
750C23—2122no—
751C23—2122no—
752C23—2122no—
753C23—2122no—
754C23—2122no—
755C23—2122no—
756C23—2122no—
757C23C2×D4×D5311yescharacteristic
758Q8—22no—
759Q8—22no—
760Q8—22no—
761Q8—22no—
762Q8—42no—
763Q8—42no—
764Q8—4244no—
765D4—22no—
766D4—22no—
767D4—42no—
768D4—1062no—
769D4—1062no—
770D4—1062no—
771D4—1062no—
772D4—1062no—
773D4—1062no—
774D4—4244no—
775D4—4244no—
776D4—4244no—
777D4—4244no—
778D4—4244no—
779D4—2128no—
780D4—2128no—
781D4—2122no—
782D4—2122no—
783D4—2122no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—42no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—532no—
793C2×C4—532no—
794C2×C4—532no—
795C2×C4—1062no—
796C2×C4—1062no—
797C2×C4—1062no—
798C2×C4—1064no—
799C2×C4—1062no—
800C2×C4—1062no—
801C2×C4—1062no—
802C2×C4—4244no—
803C2×C4—2128no—
804C2×C4—2122no—
805C2×C4C2×D4×D5312yes—
806C2×C4C2×D4×D5312yes—
807C2×C4C2×D4×D5311yescharacteristic
808C2×C4#1313326212yes—
809C2×C4#1313326312yes—
810C2×C4C24×D5311yescharacteristic
811C8—22no—
812C8—22no—
813C8—1062no—
814C8—1062no—
815C22—42no—
816C22—42no—
817C22—42no—
818C22—84no—
819C22—1062no—
820C22—1062no—
821C22—1062no—
822C22—42416no—
823C22—4244no—
824C22—4244no—
825C22—4244no—
826C22—2122no—
827C22—2122no—
828C22—2122no—
829C22—2122no—
830C22—2122no—
831C22—2122no—
832C22—2122no—
833C22—2122no—
834C22—2122no—
835C22—2124no—
836C22#1681118912yes—
837C22#1681142512yes—
838C22#1681143212yes—
839C22C22×D4×D5311yescharacteristic
840C4—22no—
841C4—22no—
842C4—42no—
843C4—42no—
844C4—42no—
845C4—1062no—
846C4—1062no—
847C4—1062no—
848C4—2122no—
849C4#1681118912yes—
850C4C2×#1313326211yescharacteristic
851C4C2×#1313326311yescharacteristic
852C2—82no—
853C2—4242no—
854C2—4242no—
855C2—4242no—
856C2—2122no—
857C2#2028581614yesdirect product factor
858C2C2×#1681118911yescharacteristic
859C2C2×#1681142511yescharacteristic
860C2C2×#1681143211yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#464C2
socleC23×C53C22×D4
hypercenterC2×#464D53
hypocenterC53C2×#3224
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. C2×#16811245C2semidirect
2. C2×#16811191C2semidirect
3. #20285816C2direct (N × H)
4. C2×#16811009C2semidirect
5. C2×#16811008C2semidirect
6. C2×#16810984C2semidirect
7. C2×#16810968C2semidirect
8. C2×#16810823C2semidirect
9. C2×#16810835C2semidirect
10. C2×#16810819C2semidirect
11. C2×#16810784C2semidirect
12. C2×#16810771C2semidirect
13. C2×#16810772C2semidirect
14. C2×#16810758C2semidirect
15. C2×#16810683C2semidirect
16. C2×C53×#464C2semidirect
20. C22×#11719924C22semidirect
21. C22×#11719924C22semidirect
23. C22×D424C22semidirect
26. #16811245C22semidirect
28. #16811191C22semidirect
29. C2×#13133216C22semidirect
34. C2×#13133206C22semidirect
44. C2×C4×D212C22semidirect
46. #16811009C22semidirect
47. #16811008C22semidirect
48. #16810984C22semidirect
49. #16810968C22semidirect
50. #16810835C22semidirect
51. #16810823C22semidirect
52. #16810819C22semidirect
53. #16810784C22semidirect
54. #16810772C22semidirect
55. #16810771C22semidirect
56. #16810758C22semidirect
57. #16810683C22semidirect
58. C2×C4⋊#88322C22semidirect
59. C2×#13133141C22semidirect
61. C2×#13133139C22semidirect
64. C2×#13133137C22semidirect
67. C2×#13133127C22semidirect
68. C2×C8×Dic53C22semidirect
69. C22×Q16×C53C22semidirect
72. C2×C4×Q8×C53C22semidirect
73. C53×#464C22semidirect
74. C2×C4⋊C8×C53C22semidirect
75. C2×#103×C53C22semidirect
104. C2×#11719924C23semidirect
105. C2×#11719924C23semidirect
109. C2×D424C23semidirect
115. #13133216C23semidirect
124. #13133206C23semidirect
137. C4×D212C23semidirect
155. C4⋊#88322C23semidirect
156. #13133141C23semidirect
158. #13133139C23semidirect
161. #13133137C23semidirect
164. #13133127C23semidirect
165. C8×Dic53C23semidirect
170. C2×Q16×C53C23semidirect
178. C4×Q8×C53C23semidirect
185. C4⋊C8×C53C23semidirect
186. #103×C53C23semidirect
429. C2×#464D53semidirect
439. C2×C53#3224semidirect
449. C22×Q16C2×D53semidirect
477. C2×C4×Q8C2×D53semidirect
484. #464C2×D53semidirect
494. C2×C4⋊C8C2×D53semidirect
496. C2×#103C2×D53semidirect
507. C53C2×#3224semidirect
535. C2×Q16C22×D53semidirect
579. C4×Q8C22×D53semidirect
606. C4⋊C8C22×D53semidirect
608. #103C22×D53semidirect
857. C2#20285816direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168112452
C2×#168111912
#202858162
C2×#168110092
C2×#168110082
C2×#168109842
C2×#168109682
C2×#168108232
C2×#168108352
C2×#168108192
C2×#168107842
C2×#168107712
C2×#168107722
C2×#168107582
C2×#168106832
C2×C53×#4642
C2×#322453