Finite Group Databasebeta

← C2×#20285812 #28255450

Subgroups — C2×#20285812 #28255450

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×#16811247C211yesmaximal, characteristic, complemented
2C2×#16811186C211yesmaximal, characteristic, complemented
3#20285812C2116yesmaximal, direct product factor
4C2×#16811010C211yesmaximal, characteristic, complemented
5C2×#16811007C211yesmaximal, characteristic, complemented
6C2×#16810985C211yesmaximal, characteristic, complemented
7C2×#16810844C211yesmaximal, characteristic, complemented
8C2×#16810822C211yesmaximal, characteristic, complemented
9C2×#16810837C211yesmaximal, characteristic, complemented
10C2×#16810817C211yesmaximal, characteristic, complemented
11C2×#16810786C211yesmaximal, characteristic, complemented
12C2×#16810769C211yesmaximal, characteristic, complemented
13C2×#16810775C211yesmaximal, characteristic, complemented
14C2×#16810758C211yesmaximal, characteristic, complemented
15C2×#16810682C211yesmaximal, characteristic, complemented
16C2×C53×#486C211yesmaximal, characteristic, complemented
17C22×#11719947C2211yescharacteristic
18C22×D4×D53C2211yescharacteristic
19C22×Dic212C2211yescharacteristic, complemented
20C22×#11719913C2211yescharacteristic
21C22×#11719913C2211yescharacteristic, complemented
22C22×#11719923C2211yescharacteristic
23C22×#11719923C2211yescharacteristic, complemented
24C22×D424C2211yescharacteristic
25C22×#11719922C2211yescharacteristic
26C22×#11719922C2211yescharacteristic, complemented
27#16811247—24no—
28#16811247C2218yescomplemented
29#16811186—24no—
30#16811186C2218yescomplemented
31C2×#13133213C2211yescharacteristic
32C2×#13133212—21no—
33C2×#13133206—21no—
34C2×#13133205C2211yescharacteristic
35C2×#13133205C2211yescharacteristic, complemented
36C2×#13133204C2211yescharacteristic
37C2×#13133202—21no—
38C2×#13133197C2211yescharacteristic
39C2×#13133193—21no—
40C2×#13133192C2211yescharacteristic
41C2×#13133189—21no—
42C2×#13133189—21no—
43C2×#13133185—21no—
44C2×#13133185—21no—
45C2×#13133182C2211yescharacteristic, complemented
46C2×#13133179C2211yescharacteristic, complemented
47C2×#13133174C2211yescharacteristic
48#16811010C2218yescomplemented
49#16811007C2218yescomplemented
50#16810985C2218yescomplemented
51#16810844C2218yescomplemented
52#16810837C2218yescomplemented
53#16810822C2218yescomplemented
54#16810817C2218yescomplemented
55#16810786C2218yescomplemented
56#16810775C2218yescomplemented
57#16810769C2218yescomplemented
58#16810758C2218yescomplemented
59#16810682C2218yescomplemented
60C2×#13133146C2211yescharacteristic, complemented
61C2×#13133146C2211yescharacteristic, complemented
62C2×#13133140C2211yescharacteristic, complemented
63C2×#13133140C2211yescharacteristic, complemented
64C2×#13133137C2211yescharacteristic
65C2×#13133137C2211yescharacteristic
66C2×#13133129C2211yescharacteristic
67C2×#13133129C2211yescharacteristic
68C2×#13133128C2211yescharacteristic, complemented
69C2×C4⋊Q8×C53C2211yescharacteristic, complemented
70C2×#127×C53C2211yescharacteristic
71C53×#486C2218yescomplemented
72C2×#102×C53C2211yescharacteristic
73C2×#102×C53C2211yescharacteristic
74C2×#102×C53C2211yescharacteristic, complemented
75C2×#102×C53C2211yescharacteristic, complemented
76C2×C4×C8×C53C2211yescharacteristic, complemented
77C24×D53—21no—
78C2×#11719947—22no—
79C2×#11719947—42no—
80C2×#11719947—42no—
81C2×#11719947C2314yes—
82C22×Dic106C2311yescharacteristic
83C22×Dic106C2311yescharacteristic
84C22×D212—21no—
85C22×D212C2311yescharacteristic
86C22×D212C2311yescharacteristic
87C22×C22⋊D53—21no—
88C22×C22⋊D53—21no—
89C22×C22⋊D53—21no—
90C22×C22⋊D53—21no—
91C2×D4×D53—22no—
92C2×D4×D53—42no—
93C2×D4×D53—42no—
94C2×D4×D53C2314yes—
95C23×Dic53—21no—
96C22×C4×D53—21no—
97C22×C4×D53C2311yescharacteristic
98C2×Dic212—42no—
99C2×Dic212C2314yescomplemented
100C2×#11719913—42no—
101C2×#11719913—42no—
102C2×#11719913C2314yes—
103C2×#11719913C2314yescomplemented
104C2×#11719923—42no—
105C2×#11719923—42no—
106C2×#11719923C2314yes—
107C2×#11719923C2314yescomplemented
108C2×D424—42no—
109C2×D424C2314yes—
110C2×#11719922—42no—
111C2×#11719922—42no—
112C2×#11719922C2314yes—
113C2×#11719922C2314yescomplemented
114C22×#88322C2311yescharacteristic
115C22×#88322C2311yescharacteristic
116#13133213—22no—
117#13133213C2314yes—
118#13133212—28no—
119#13133206—28no—
120#13133205—22no—
121#13133205—22no—
122#13133205C2314yes—
123#13133205C2314yescomplemented
124#13133204—22no—
125#13133204C2314yes—
126#13133202—28no—
127#13133197—22no—
128#13133197C2314yes—
129#13133193—28no—
130#13133192—22no—
131#13133192C2314yes—
132#13133189—28no—
133#13133189—28no—
134#13133185—28no—
135#13133185—28no—
136#13133182—22no—
137#13133182C2314yescomplemented
138#13133179—22no—
139#13133179C2314yescomplemented
140#13133174D414yes—
141#13133174C2314yes—
142C2×C4⋊Dic53—21no—
143C2×#11719919—21no—
144C2×#11719919D411yescharacteristic
145C2×#11719919D411yescharacteristic
146C2×C22⋊Dic53—21no—
147C2×C22⋊Dic53—21no—
148C2×#11719921—21no—
149C2×#11719921—21no—
150C2×#11719921—21no—
151C2×#11719921—21no—
152C2×#11719921—21no—
153C2×#11719921—21no—
154C2×#11719921—21no—
155C2×#11719921D411yescharacteristic
156C2×#11719921D411yescharacteristic
157C2×C4×Dic53—21no—
158C2×C4×Dic53C2311yescharacteristic
159#13133146C2314yescomplemented
160#13133146C2314yescomplemented
161#13133140C2314yescomplemented
162#13133140C2314yescomplemented
163#13133137C2314yes—
164#13133137C2314yes—
165#13133129C2314yes—
166#13133129C2314yes—
167#13133128C2314yescomplemented
168C22×Q8×C53—21no—
169C22×D4×C53—21no—
170C22×D4×C53—21no—
171C22×D4×C53C2311yescharacteristic
172C22×D4×C53C2311yescharacteristic
173C22×C8×C53C2311yescharacteristic
174C22×C8×C53C2311yescharacteristic
175C4⋊Q8×C53—22no—
176C4⋊Q8×C53C2314yescomplemented
177#127×C53—22no—
178#127×C53C2314yes—
179C2×C4⋊C4×C53—21no—
180C2×C4⋊C4×C53C2311yescharacteristic
181C2×C4⋊C4×C53C2311yescharacteristic
182C2×C42×C53C2311yescharacteristic
183#102×C53C2314yes—
184#102×C53C2314yes—
185#102×C53C2314yescomplemented
186#102×C53C2314yescomplemented
187C4×C8×C53C2314yescomplemented
188C24×C53—21no—
189C24×C53—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—24no—
198C2×Q8×C53—82no—
199C2×D4×C53—21no—
200C2×D4×C53—21no—
201C2×D4×C53—24no—
202C2×D4×C53—24no—
203C2×D4×C53—22no—
204C2×D4×C53—22no—
205C2×D4×C53—22no—
206C2×D4×C53—22no—
207C2×D4×C53—82no—
208C2×D4×C53—82no—
209C2×D4×C53C2412yes—
210C2×D4×C53C2412yes—
211C22×C4×C53—21no—
212C22×C4×C53—21no—
213C22×C4×C53C2×D411yescharacteristic
214C22×C4×C53C2×D411yescharacteristic
215C22×C4×C53C2411yescharacteristic
216C2×C22⋊D53—24no—
217C2×C22⋊D53—24no—
218C2×C22⋊D53—24no—
219C2×C22⋊D53—24no—
220C2×C22⋊D53—44no—
221C2×C22⋊D53—44no—
222C2×C22⋊D53—82no—
223C2×C22⋊D53—82no—
224C22×Dic53—21no—
225C22×Dic53—21no—
226C22×Dic53—24no—
227C22×Dic53—44no—
228C22×Dic53C2×D411yescharacteristic
229C22×Dic53C2×D411yescharacteristic
230C22×Dic53C2×D411yescharacteristic
231#11719947—44no—
232#11719947—44no—
233#11719947—48no—
234D4×D53—44no—
235D4×D53—44no—
236D4×D53—48no—
237C2×D212—22no—
238C2×D212—22no—
239C2×D212—22no—
240C2×D212—22no—
241C2×D212—21no—
242C2×D212—21no—
243C2×D212—24no—
244C2×D212—82no—
245C2×D212C2412yes—
246C2×D212C2412yes—
247C2×C4×D53—22no—
248C2×C4×D53—22no—
249C2×C4×D53—24no—
250C2×C4×D53—82no—
251C2×C4×D53C2×D412yes—
252C2×C4×D53C2412yes—
253C2×Dic106—22no—
254C2×Dic106—22no—
255C2×Dic106—22no—
256C2×Dic106—22no—
257C2×Dic106—21no—
258C2×Dic106—21no—
259C2×Dic106C2412yes—
260C2×Dic106C2412yes—
261C2×C8×C53—22no—
262C2×C8×C53—22no—
263C2×C8×C53C2412yes—
264C2×C8×C53C2412yes—
265C4⋊C4×C53—24no—
266C4⋊C4×C53—21no—
267C4⋊C4×C53—21no—
268C4⋊C4×C53C2412yes—
269C4⋊C4×C53C2412yes—
270C42×C53C2×D412yes—
271C42×C53C2412yes—
272C22⋊Dic53—24no—
273C22⋊Dic53—24no—
274#11719923—44no—
275#11719923—44no—
276#11719922—44no—
277#11719922—44no—
278#11719921—24no—
279#11719921—24no—
280#11719921—24no—
281#11719921—24no—
282#11719921—24no—
283#11719921—24no—
284#11719921—24no—
285#11719921C2×D414yes—
286#11719921C2×D414yes—
287C4⋊Dic53—24no—
288#11719919—24no—
289#11719919C2×D414yes—
290#11719919C2×D414yes—
291C4×Dic53—24no—
292C4×Dic53C2×D412yes—
293C4×Dic53C2412yes—
294C2×#88322—22no—
295C2×#88322—22no—
296C2×#88322C2412yes—
297C2×#88322C2412yes—
298Dic212—44no—
299D424—44no—
300#11719913—44no—
301#11719913—44no—
302C23×C53—22no—
303C23×C53—22no—
304C23×C53—42no—
305C23×C53—42no—
306C23×C53—42no—
307C23×C53—42no—
308C23×C53—42no—
309C23×C53—42no—
310C23×C53C22×D411yescharacteristic
311C22×D53—22no—
312C22×D53—22no—
313C22×D53—22no—
314C22×D53—22no—
315C22×D53—22no—
316C22×D53—48no—
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—84no—
328D4×C53—22no—
329D4×C53—22no—
330D4×C53—22no—
331D4×C53—22no—
332D4×C53—42no—
333D4×C53—42no—
334D4×C53—84no—
335D4×C53—84no—
336C2×C4×C53—22no—
337C2×C4×C53—22no—
338C2×C4×C53—22no—
339C2×C4×C53—22no—
340C2×C4×C53—42no—
341C2×C4×C53—42no—
342C2×C4×C53C22×D412yes—
343C2×C4×C53C22×D412yes—
344C2×C4×C53C22×D411yescharacteristic
345C2×C4×C53H(5,𝔽2)12yes—
346C2×C4×C53H(5,𝔽2)12yes—
347C2×C4×C53C2511yescharacteristic
348C22⋊D53—48no—
349C22⋊D53—48no—
350C22⋊D53—84no—
351C22⋊D53—84no—
352C2×Dic53—22no—
353C2×Dic53—22no—
354C2×Dic53—22no—
355C2×Dic53—22no—
356C2×Dic53—22no—
357C2×Dic53—48no—
358C2×Dic53—42no—
359C2×Dic53—42no—
360C2×Dic53C22×D412yes—
361C2×Dic53C22×D412yes—
362C2×Dic53C22×D412yes—
363D212—22no—
364D212—22no—
365D212—22no—
366D212—22no—
367D212—42no—
368D212—42no—
369D212—84no—
370C4×D53—24no—
371C4×D53—22no—
372C4×D53—22no—
373C4×D53—84no—
374Dic106—22no—
375Dic106—22no—
376Dic106—22no—
377Dic106—22no—
378Dic106—42no—
379Dic106—42no—
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—42no—
389C22×C53—42no—
390C22×C53—42no—
391C22×C53—84no—
392C22×C53—84no—
393C22×C53#53512yes—
394C22×C53#57612yes—
395C22×C53#57712yes—
396C22×C53C23×D411yescharacteristic
397C2×D53—22no—
398C2×D53—22no—
399C2×D53—22no—
400C2×D53—44no—
401C2×D53—42no—
402C2×D53—42no—
403C2×D53—42no—
404C2×D53—42no—
405C2×D53—42no—
406C2×D53—42no—
407C2×D53—816no—
408C2×D53—84no—
409C2×D53—84no—
410C4×C53—22no—
411C4×C53—22no—
412C4×C53—42no—
413C4×C53—42no—
414C4×C53#53512yes—
415C4×C53C2×H(5,𝔽2)11yescharacteristic
416C4×C53C2×H(5,𝔽2)11yescharacteristic
417Dic53—22no—
418Dic53—22no—
419Dic53—22no—
420Dic53—42no—
421Dic53—42no—
422C2×#542—531no—
423C2×#535—531no—
424#3224—5316no—
425C2×#496—531no—
426C2×#495—531no—
427C2×#489—531no—
428C2×#486D5311yescharacteristic, complemented
429C2×#464—531no—
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—82no—
440C2×C53#322414yescomplemented
441C2×C53C2×#53511yescharacteristic
442C2×C53C2×#57611yescharacteristic
443C2×C53C2×#57711yescharacteristic
444D53—42no—
445D53—82no—
446D53—82no—
447C22×#41—531no—
448C23×D4—531no—
449C22×Q16—531no—
450C22×SD16—531no—
451C22×SD16—531no—
452C22×SD16—531no—
453C22×SD16—531no—
454C22×D8—531no—
455C22×D8—531no—
456C22×D8—531no—
457#542—538no—
458#542—1064no—
459#535—538no—
460#535—1064no—
461C2×C4⋊Q8C2×D5311yescharacteristic, complemented
462C2×#127—531no—
463C2×#127C2×D5311yescharacteristic
464C2×#126—1061no—
465C2×#124—531no—
466C2×#124—531no—
467C2×#124—531no—
468C2×#124—1061no—
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×Q8—531no—
478C2×C4×D4—531no—
479C2×#117—531no—
480#496—538no—
481#495—538no—
482#489—538no—
483#486C2×D5318yescomplemented
484#464—538no—
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⋊C8—531no—
495C2×#103—531no—
496C2×#103—531no—
497C2×#102—531no—
498C2×#102—531no—
499C2×#102C2×D5311yescharacteristic
500C2×#102C2×D5311yescharacteristic
501C2×#102C2×D5311yescharacteristic, complemented
502C2×#102C2×D5311yescharacteristic, complemented
503C2×C22⋊C8—531no—
504C2×C22⋊C8—531no—
505C2×#97—531no—
506C2×C4×C8C2×D5311yescharacteristic, complemented
507C53C2×#322411yescharacteristic, complemented, Sylow
508C25—1061no—
509C2×#41—534no—
510C2×#41—1062no—
511C2×#41—2122no—
512C2×#41—2122no—
513C22×Q8—21no—
514C22×Q8—531no—
515C22×Q8—531no—
516C22×D4—21no—
517C22×D4—21no—
518C22×D4—534no—
519C22×D4—531no—
520C22×D4—531no—
521C22×D4—1061no—
522C22×D4—1062no—
523C22×D4—1061no—
524C22×D4—1061no—
525C22×D4—1061no—
526C22×D4—1061no—
527C22×D4—2122no—
528C22×D4—2122no—
529C22×D4C22×D5311yescharacteristic
530C22×D4C22×D5311yescharacteristic
531C23×C4—531no—
532C23×C4—1061no—
533C23×C4—1061no—
534C2×Q16—534no—
535C2×Q16—2122no—
536C2×SD16—534no—
537C2×SD16—534no—
538C2×SD16—534no—
539C2×SD16—534no—
540C2×SD16—2122no—
541C2×SD16—2122no—
542C2×SD16—2122no—
543C2×SD16—2122no—
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—22no—
555C4⋊Q8C22×D5314yescomplemented
556#127—22no—
557#127—534no—
558#127—1062no—
559#127C22×D5314yes—
560#126—1068no—
561#124—534no—
562#124—534no—
563#124—534no—
564#124—1062no—
565#124—1068no—
566#124—1062no—
567#124—1062no—
568#123—1068no—
569C22⋊Q8—534no—
570C22⋊Q8—1062no—
571C22⋊Q8—1068no—
572#121—534no—
573#121—1062no—
574#121—1068no—
575#121—1068no—
576#120—1068no—
577#120—1068no—
578C4×Q8—534no—
579C4×Q8—1062no—
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—1061no—
588C2×C4⋊C4—1061no—
589C2×C4⋊C4C22×D5311yescharacteristic
590C2×C4⋊C4C22×D5311yescharacteristic
591C2×C22⋊C4—531no—
592C2×C22⋊C4—531no—
593C2×C22⋊C4—1061no—
594C2×C22⋊C4—1061no—
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—531no—
603C2×C42—1061no—
604C2×C42C22×D5311yescharacteristic
605C4⋊C8—534no—
606C4⋊C8—534no—
607#103—534no—
608#103—534no—
609#102—534no—
610#102—534no—
611#102C22×D5314yes—
612#102C22×D5314yes—
613#102C22×D5314yescomplemented
614#102C22×D5314yescomplemented
615C22⋊C8—534no—
616C22⋊C8—534no—
617#97—534no—
618C4×C8C22×D5314yescomplemented
619C24—21no—
620C24—21no—
621C24—531no—
622C24—1064no—
623C24—1061no—
624C24—1061no—
625C24—4242no—
626C24—4242no—
627C24—2124no—
628#41—2124no—
629#41—2124no—
630#41—2128no—
631C2×Q8—24no—
632C2×Q8—82no—
633C2×Q8—532no—
634C2×Q8—532no—
635C2×Q8—1061no—
636C2×Q8—1061no—
637C2×Q8—1062no—
638C2×Q8—1062no—
639C2×Q8—1062no—
640C2×Q8—1062no—
641C2×D4—21no—
642C2×D4—21no—
643C2×D4—24no—
644C2×D4—24no—
645C2×D4—22no—
646C2×D4—22no—
647C2×D4—22no—
648C2×D4—22no—
649C2×D4—82no—
650C2×D4—82no—
651C2×D4—532no—
652C2×D4—532no—
653C2×D4—1064no—
654C2×D4—1064no—
655C2×D4—1064no—
656C2×D4—1064no—
657C2×D4—1064no—
658C2×D4—1061no—
659C2×D4—1061no—
660C2×D4—1062no—
661C2×D4—1062no—
662C2×D4—1062no—
663C2×D4—1062no—
664C2×D4—4242no—
665C2×D4—4242no—
666C2×D4—4242no—
667C2×D4—2124no—
668C2×D4—2124no—
669C2×D4—2128no—
670C2×D4—2124no—
671C2×D4—2124no—
672C2×D4C23×D5312yes—
673C2×D4C23×D5312yes—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—531no—
677C22×C4—531no—
678C22×C4—531no—
679C22×C4—532no—
680C22×C4—532no—
681C22×C4—1064no—
682C22×C4—1064no—
683C22×C4—1062no—
684C22×C4—1062no—
685C22×C4—1061no—
686C22×C4—1061no—
687C22×C4—4242no—
688C22×C4—2124no—
689C22×C4D4×D5311yescharacteristic
690C22×C4D4×D5311yescharacteristic
691C22×C4C23×D5311yescharacteristic
692Q16—2124no—
693SD16—2124no—
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—21no—
711C4⋊C4—534no—
712C4⋊C4—534no—
713C4⋊C4—1064no—
714C4⋊C4—1064no—
715C4⋊C4C23×D5312yes—
716C4⋊C4C23×D5312yes—
717C22⋊C4—534no—
718C22⋊C4—534no—
719C22⋊C4—1064no—
720C22⋊C4—1064no—
721C22⋊C4—1064no—
722C22⋊C4—1064no—
723C22⋊C4—1064no—
724C22⋊C4—1064no—
725C22⋊C4—1064no—
726C22⋊C4—1064no—
727C22⋊C4—1064no—
728C42—532no—
729C42—532no—
730C42—1064no—
731C42D4×D5312yes—
732C42C23×D5312yes—
733C23—22no—
734C23—22no—
735C23—42no—
736C23—42no—
737C23—42no—
738C23—42no—
739C23—42no—
740C23—42no—
741C23—532no—
742C23—1062no—
743C23—1062no—
744C23—1062no—
745C23—1062no—
746C23—1062no—
747C23—4244no—
748C23—4244no—
749C23—42416no—
750C23—2128no—
751C23—2122no—
752C23—2122no—
753C23—2122no—
754C23—2122no—
755C23—2122no—
756C23—2122no—
757C23C2×D4×D5311yescharacteristic
758Q8—84no—
759Q8—1062no—
760Q8—1062no—
761Q8—1062no—
762Q8—1062no—
763Q8—2122no—
764Q8—2122no—
765D4—22no—
766D4—22no—
767D4—22no—
768D4—22no—
769D4—42no—
770D4—42no—
771D4—84no—
772D4—84no—
773D4—1062no—
774D4—1062no—
775D4—1062no—
776D4—1062no—
777D4—4244no—
778D4—4244no—
779D4—4244no—
780D4—2128no—
781D4—2128no—
782D4—2122no—
783D4—2122no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—42no—
789C2×C4—42no—
790C2×C4—532no—
791C2×C4—532no—
792C2×C4—532no—
793C2×C4—1062no—
794C2×C4—1062no—
795C2×C4—1062no—
796C2×C4—1064no—
797C2×C4—1062no—
798C2×C4—1062no—
799C2×C4—1062no—
800C2×C4—1062no—
801C2×C4—4244no—
802C2×C4—2128no—
803C2×C4—2122no—
804C2×C4—2122no—
805C2×C4C2×D4×D5312yes—
806C2×C4C2×D4×D5312yes—
807C2×C4C2×D4×D5311yescharacteristic
808C2×C4#1313326312yes—
809C2×C4#1313326312yes—
810C2×C4C24×D5311yescharacteristic
811C8—22no—
812C8—22no—
813C8—1062no—
814C8—1062no—
815C22—42no—
816C22—42no—
817C22—42no—
818C22—42no—
819C22—42no—
820C22—42no—
821C22—84no—
822C22—84no—
823C22—1062no—
824C22—1062no—
825C22—1062no—
826C22—42416no—
827C22—4244no—
828C22—4244no—
829C22—2122no—
830C22—2122no—
831C22—2122no—
832C22—2122no—
833C22—2122no—
834C22—2122no—
835C22—2124no—
836C22#1681119112yes—
837C22#1681142412yes—
838C22#1681142912yes—
839C22C22×D4×D5311yescharacteristic
840C4—22no—
841C4—22no—
842C4—42no—
843C4—42no—
844C4—1062no—
845C4—1062no—
846C4—1062no—
847C4—2122no—
848C4—2122no—
849C4#1681119112yes—
850C4C2×#1313326311yescharacteristic
851C4C2×#1313326311yescharacteristic
852C2—82no—
853C2—82no—
854C2—4242no—
855C2—4242no—
856C2—2122no—
857C2#2028581214yesdirect product factor
858C2C2×#1681119111yescharacteristic
859C2C2×#1681142411yescharacteristic
860C2C2×#1681142911yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#486C2
socleC23×C53C22×D4
hypercenterC2×#486D53
hypocenterC53C2×#3224
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#486

Complements

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

NH ≅ G/Ntype
1. C2×#16811247C2semidirect
2. C2×#16811186C2semidirect
3. #20285812C2direct (N × H)
4. C2×#16811010C2semidirect
5. C2×#16811007C2semidirect
6. C2×#16810985C2semidirect
7. C2×#16810844C2semidirect
8. C2×#16810822C2semidirect
9. C2×#16810837C2semidirect
10. C2×#16810817C2semidirect
11. C2×#16810786C2semidirect
12. C2×#16810769C2semidirect
13. C2×#16810775C2semidirect
14. C2×#16810758C2semidirect
15. C2×#16810682C2semidirect
16. C2×C53×#486C2semidirect
19. C22×Dic212C22semidirect
21. C22×#11719913C22semidirect
23. C22×#11719923C22semidirect
26. C22×#11719922C22semidirect
28. #16811247C22semidirect
30. #16811186C22semidirect
35. C2×#13133205C22semidirect
45. C2×#13133182C22semidirect
46. C2×#13133179C22semidirect
48. #16811010C22semidirect
49. #16811007C22semidirect
50. #16810985C22semidirect
51. #16810844C22semidirect
52. #16810837C22semidirect
53. #16810822C22semidirect
54. #16810817C22semidirect
55. #16810786C22semidirect
56. #16810775C22semidirect
57. #16810769C22semidirect
58. #16810758C22semidirect
59. #16810682C22semidirect
60. C2×#13133146C22semidirect
61. C2×#13133146C22semidirect
62. C2×#13133140C22semidirect
63. C2×#13133140C22semidirect
68. C2×#13133128C22semidirect
69. C2×C4⋊Q8×C53C22semidirect
71. C53×#486C22semidirect
74. C2×#102×C53C22semidirect
75. C2×#102×C53C22semidirect
76. C2×C4×C8×C53C22semidirect
99. C2×Dic212C23semidirect
103. C2×#11719913C23semidirect
107. C2×#11719923C23semidirect
113. C2×#11719922C23semidirect
123. #13133205C23semidirect
137. #13133182C23semidirect
139. #13133179C23semidirect
159. #13133146C23semidirect
160. #13133146C23semidirect
161. #13133140C23semidirect
162. #13133140C23semidirect
167. #13133128C23semidirect
176. C4⋊Q8×C53C23semidirect
185. #102×C53C23semidirect
186. #102×C53C23semidirect
187. C4×C8×C53C23semidirect
428. C2×#486D53semidirect
440. C2×C53#3224semidirect
461. C2×C4⋊Q8C2×D53semidirect
483. #486C2×D53semidirect
501. C2×#102C2×D53semidirect
502. C2×#102C2×D53semidirect
506. C2×C4×C8C2×D53semidirect
507. C53C2×#3224semidirect
555. C4⋊Q8C22×D53semidirect
613. #102C22×D53semidirect
614. #102C22×D53semidirect
618. C4×C8C22×D53semidirect
857. C2#20285812direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168112472
C2×#168111862
#202858122
C2×#168110102
C2×#168110072
C2×#168109852
C2×#168108442
C2×#168108222
C2×#168108372
C2×#168108172
C2×#168107862
C2×#168107692
C2×#168107752
C2×#168107582
C2×#168106822
C2×C53×#4862
C2×#322453