Finite Group Databasebeta

← C2×#20285533 #28254696

Subgroups — C2×#20285533 #28254696

Order 13568.

2686 conjugacy classes of subgroups.

The subgroup lattice has 908 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811135C211yesmaximal, characteristic, complemented
2C2×#121×D53C211yesmaximal, characteristic, complemented
3#20285533C2116yesmaximal, direct product factor
4C2×#16810947C211yesmaximal, characteristic, complemented
5C2×#16810955C211yesmaximal, characteristic, complemented
6C2×#16810938C211yesmaximal, characteristic, complemented
7C2×#16810877C211yesmaximal, characteristic, complemented
8C2×#16810875C211yesmaximal, characteristic, complemented
9C2×#16810870C211yesmaximal, characteristic, complemented
10C2×#16810868C211yesmaximal, characteristic, complemented
11C2×#16810770C211yesmaximal, characteristic, complemented
12C2×#16810766C211yesmaximal, characteristic, complemented
13C2×#16810775C211yesmaximal, characteristic, complemented
14C2×#16810758C211yesmaximal, characteristic, complemented
15C2×#16810585C211yesmaximal, characteristic, complemented
16C2×C53×#482C211yesmaximal, characteristic, complemented
17C22×#11719945C2211yescharacteristic, complemented
18C22×D4×D53—21no—
19C22×D4×D53C2211yescharacteristic
20C23×C4×D53C2211yescharacteristic
21C22×#11719913C2211yescharacteristic, complemented
22C22×#11719923C2211yescharacteristic, complemented
23C22×D424C2211yescharacteristic, complemented
24C22×#11719922C2211yescharacteristic, complemented
25C22×#11719912C2211yescharacteristic, complemented
26C22×#11719912C2211yescharacteristic, complemented
27#16811135—24no—
28#16811135C2218yescomplemented
29C2×#13133201—21no—
30C2×#13133197C2211yescharacteristic
31C2×#13133197C2211yescharacteristic, complemented
32C2×#13133192C2211yescharacteristic
33C2×#13133192C2211yescharacteristic
34C2×#13133192C2211yescharacteristic, complemented
35C2×#13133191C2211yescharacteristic
36C2×#13133190—21no—
37C2×#13133189—21no—
38C2×#13133188C2211yescharacteristic
39#121×D53—24no—
40#121×D53C2218yescomplemented
41C2×#13133187—21no—
42C2×C4×D212—21no—
43C2×C4×D212—21no—
44C2×C4⋊C4×D53C2211yescharacteristic
45C2×C22⋊C4×D53—21no—
46#16810955C2218yescomplemented
47#16810947C2218yescomplemented
48#16810938C2218yescomplemented
49#16810877C2218yescomplemented
50#16810875C2218yescomplemented
51#16810870C2218yescomplemented
52#16810868C2218yescomplemented
53#16810775C2218yescomplemented
54#16810770C2218yescomplemented
55#16810766C2218yescomplemented
56#16810758C2218yescomplemented
57C2×#13133150C2211yescharacteristic, complemented
58C2×#13133148C2211yescharacteristic, complemented
59C2×#13133142C2211yescharacteristic, complemented
60C2×#13133140C2211yescharacteristic, complemented
61C2×#13133139C2211yescharacteristic, complemented
62C2×#13133137C2211yescharacteristic, complemented
63C2×#13133137C2211yescharacteristic, complemented
64C2×#13133137C2211yescharacteristic, complemented
65#16810585C2218yescomplemented
66C2×C22⋊#88322C2211yescharacteristic, complemented
67C2×#13133129C2211yescharacteristic
68C2×#13133129C2211yescharacteristic
69C2×#121×C53C2211yescharacteristic
70C2×#117×C53C2211yescharacteristic, complemented
71C53×#482C2218yescomplemented
72C2×#107×C53C2211yescharacteristic, complemented
73C2×#106×C53C2211yescharacteristic, complemented
74C2×#102×C53C2211yescharacteristic, complemented
75C2×#102×C53C2211yescharacteristic, complemented
76C2×C22⋊C8×C53C2211yescharacteristic, complemented
77C24×D53—21no—
78C24×D53D411yescharacteristic
79C2×#11719945—22no—
80C2×#11719945—42no—
81C2×#11719945—42no—
82C2×#11719945C2314yescomplemented
83C22×Dic106C2311yescharacteristic
84C22×D212—21no—
85C22×D212—21no—
86C22×D212—21no—
87C22×D212C2311yescharacteristic
88C22×D212C2311yescharacteristic
89C22×C22⋊D53—21no—
90C22×C22⋊D53—21no—
91C22×C22⋊D53—21no—
92C22×C22⋊D53—21no—
93C2×D4×D53—28no—
94C2×D4×D53—22no—
95C2×D4×D53—42no—
96C2×D4×D53—42no—
97C2×D4×D53—48no—
98C2×D4×D53C2314yes—
99C23×Dic53D411yescharacteristic
100C22×C4×D53—21no—
101C22×C4×D53—21no—
102C22×C4×D53—42no—
103C22×C4×D53—42no—
104C22×C4×D53D411yescharacteristic
105C22×C4×D53D411yescharacteristic
106C22×C4×D53D414yes—
107C22×C4×D53C2311yescharacteristic
108C22×C4×D53C2311yescharacteristic
109C22×C4×D53C2314yes—
110C2×#11719913—42no—
111C2×#11719913C2314yescomplemented
112C2×#11719923—42no—
113C2×#11719923C2314yescomplemented
114C2×D424—42no—
115C2×D424C2314yescomplemented
116C2×#11719922—42no—
117C2×#11719922C2314yescomplemented
118C2×#11719912—42no—
119C2×#11719912—42no—
120C2×#11719912C2314yescomplemented
121C2×#11719912C2314yescomplemented
122C22×#88322C2311yescharacteristic
123C22×#88322C2311yescharacteristic
124#13133201—28no—
125#13133197—22no—
126#13133197—22no—
127#13133197C2314yes—
128#13133197C2314yescomplemented
129#13133192—22no—
130#13133192—22no—
131#13133192—22no—
132#13133192C2314yes—
133#13133192C2314yes—
134#13133192C2314yescomplemented
135#13133191—22no—
136#13133191C2314yes—
137#13133190—28no—
138#13133189—28no—
139#13133188—22no—
140#13133188C2314yes—
141#13133187—28no—
142C4×D212—28no—
143C4×D212—28no—
144C2×C4⋊Dic53—21no—
145C2×C4⋊Dic53—21no—
146C2×C4⋊Dic53C2311yescharacteristic
147C2×#11719919—21no—
148C4⋊C4×D53—22no—
149C4⋊C4×D53C2314yes—
150C2×C22⋊Dic53—21no—
151C2×#11719921—21no—
152C2×#11719921—21no—
153C2×#11719921—21no—
154C2×#11719921—21no—
155C2×#11719921—21no—
156C2×#11719921—21no—
157C22⋊C4×D53—28no—
158#13133150C2314yescomplemented
159#13133148C2314yescomplemented
160#13133142C2314yescomplemented
161#13133140C2314yescomplemented
162#13133139C2314yescomplemented
163#13133137C2314yescomplemented
164#13133137C2314yescomplemented
165#13133137C2314yescomplemented
166C22⋊#88322C2314yescomplemented
167#13133129C2314yes—
168#13133129C2314yes—
169C22×D4×C53—21no—
170C22×D4×C53C2311yescharacteristic
171C23×C4×C53C2311yescharacteristic
172C22×C8×C53C2311yescharacteristic
173C22×C8×C53C2311yescharacteristic
174#121×C53—22no—
175#121×C53C2314yes—
176#117×C53—22no—
177#117×C53C2314yescomplemented
178C2×C4⋊C4×C53C2311yescharacteristic
179C2×C4⋊C4×C53C2311yescharacteristic
180C2×C4⋊C4×C53C2311yescharacteristic
181C2×C22⋊C4×C53—21no—
182C2×C22⋊C4×C53—21no—
183C2×C42×C53—21no—
184#107×C53C2314yescomplemented
185#106×C53C2314yescomplemented
186#102×C53C2314yescomplemented
187#102×C53C2314yescomplemented
188C22⋊C8×C53C2314yescomplemented
189C24×C53—21no—
190C24×C53C2×D411yescharacteristic
191C23×D53—24no—
192C23×D53—21no—
193C23×D53—21no—
194C23×D53—24no—
195C23×D53—42no—
196C23×D53—42no—
197C23×D53—44no—
198C23×D53—44no—
199C23×D53—44no—
200C23×D53C2×D411yescharacteristic
201C23×D53C2×D411yescharacteristic
202C23×D53C2×D414yes—
203C2×D4×C53—24no—
204C2×D4×C53—21no—
205C2×D4×C53—22no—
206C2×D4×C53—22no—
207C2×D4×C53—44no—
208C2×D4×C53C2412yes—
209C22×C4×C53—22no—
210C22×C4×C53—22no—
211C22×C4×C53—21no—
212C22×C4×C53—21no—
213C22×C4×C53—21no—
214C22×C4×C53C2×D411yescharacteristic
215C22×C4×C53C2×D412yes—
216C22×C4×C53C2412yes—
217C22×C4×C53C2411yescharacteristic
218C2×C22⋊D53—24no—
219C2×C22⋊D53—24no—
220C2×C22⋊D53—24no—
221C2×C22⋊D53—24no—
222C2×C22⋊D53—44no—
223C2×C22⋊D53—44no—
224C2×C22⋊D53—44no—
225C2×C22⋊D53—44no—
226C22×Dic53—21no—
227C22×Dic53—21no—
228C22×Dic53—42no—
229C22×Dic53C2×D411yescharacteristic
230C22×Dic53C2×D411yescharacteristic
231C22×Dic53C2×D414yes—
232D4×D53—44no—
233D4×D53—44no—
234D4×D53—48no—
235D4×D53—432no—
236#11719945—44no—
237#11719945—44no—
238#11719945—48no—
239C2×D212—22no—
240C2×D212—22no—
241C2×D212—22no—
242C2×D212—22no—
243C2×D212—24no—
244C2×D212—24no—
245C2×D212—24no—
246C2×D212—21no—
247C2×D212—21no—
248C2×D212—44no—
249C2×D212—44no—
250C2×D212—44no—
251C2×D212C2412yes—
252C2×D212C2412yes—
253C2×C4×D53—22no—
254C2×C4×D53—22no—
255C2×C4×D53—22no—
256C2×C4×D53—22no—
257C2×C4×D53—24no—
258C2×C4×D53—24no—
259C2×C4×D53—48no—
260C2×C4×D53—44no—
261C2×C4×D53—44no—
262C2×C4×D53—42no—
263C2×C4×D53—42no—
264C2×C4×D53—44no—
265C2×C4×D53—44no—
266C2×C4×D53C2×D412yes—
267C2×C4×D53C2×D412yes—
268C2×C4×D53C2×D414yes—
269C2×C4×D53C2×D414yes—
270C2×C4×D53C2412yes—
271C2×C4×D53C2412yes—
272C2×Dic106—22no—
273C2×Dic106—22no—
274C2×Dic106—21no—
275C2×Dic106C2412yes—
276C2×C8×C53—22no—
277C2×C8×C53—22no—
278C2×C8×C53C2412yes—
279C2×C8×C53C2412yes—
280C4⋊C4×C53—21no—
281C4⋊C4×C53—21no—
282C4⋊C4×C53—21no—
283C4⋊C4×C53C2412yes—
284C4⋊C4×C53C2412yes—
285C4⋊C4×C53C2412yes—
286C22⋊C4×C53—24no—
287C22⋊C4×C53—24no—
288C42×C53—24no—
289C22⋊Dic53—24no—
290#11719923—44no—
291#11719922—44no—
292#11719921—24no—
293#11719921—24no—
294#11719921—24no—
295#11719921—24no—
296#11719921—24no—
297#11719921—24no—
298C4⋊Dic53—21no—
299C4⋊Dic53—24no—
300C4⋊Dic53—24no—
301C4⋊Dic53C2412yes—
302#11719919—24no—
303C2×#88322—22no—
304C2×#88322—22no—
305C2×#88322C2412yes—
306C2×#88322C2412yes—
307D424—44no—
308#11719913—44no—
309#11719912—44no—
310#11719912—44no—
311C23×C53—22no—
312C23×C53—22no—
313C23×C53—22no—
314C23×C53—22no—
315C23×C53—42no—
316C23×C53—42no—
317C23×C53—42no—
318C23×C53C22×D412yes—
319C23×C53C22×D411yescharacteristic
320C22×D53—22no—
321C22×D53—22no—
322C22×D53—22no—
323C22×D53—22no—
324C22×D53—22no—
325C22×D53—28no—
326C22×D53—22no—
327C22×D53—22no—
328C22×D53—44no—
329C22×D53—44no—
330C22×D53—416no—
331C22×D53—48no—
332C22×D53—48no—
333C22×D53—42no—
334C22×D53—42no—
335C22×D53—42no—
336C22×D53—42no—
337C22×D53—42no—
338C22×D53—42no—
339C22×D53—48no—
340C22×D53—816no—
341C22×D53AGL(1,ℤ/8)14yes—
342C22×D53C22×D412yes—
343C22×D53C22×D412yes—
344D4×C53—22no—
345D4×C53—22no—
346D4×C53—48no—
347D4×C53—42no—
348C2×C4×C53—22no—
349C2×C4×C53—24no—
350C2×C4×C53—22no—
351C2×C4×C53—22no—
352C2×C4×C53—22no—
353C2×C4×C53—22no—
354C2×C4×C53—22no—
355C2×C4×C53—42no—
356C2×C4×C53—42no—
357C2×C4×C53—42no—
358C2×C4×C53C22×D412yes—
359C2×C4×C53C22×D411yescharacteristic
360C2×C4×C53H(5,𝔽2)12yes—
361C2×C4×C53H(5,𝔽2)12yes—
362C2×C4×C53C2511yescharacteristic
363C22⋊D53—48no—
364C22⋊D53—48no—
365C22⋊D53—48no—
366C22⋊D53—48no—
367C2×Dic53—22no—
368C2×Dic53—22no—
369C2×Dic53—22no—
370C2×Dic53—22no—
371C2×Dic53—44no—
372C2×Dic53—42no—
373C2×Dic53—42no—
374C2×Dic53C22×D412yes—
375C2×Dic53C22×D412yes—
376D212—22no—
377D212—22no—
378D212—22no—
379D212—22no—
380D212—48no—
381D212—48no—
382D212—48no—
383D212—42no—
384D212—42no—
385C4×D53—24no—
386C4×D53—24no—
387C4×D53—22no—
388C4×D53—22no—
389C4×D53—22no—
390C4×D53—22no—
391C4×D53—44no—
392C4×D53—44no—
393C4×D53—48no—
394C4×D53—48no—
395Dic106—22no—
396Dic106—22no—
397Dic106—42no—
398C8×C53—22no—
399C8×C53—22no—
400#88322—22no—
401#88322—22no—
402C2×#3194—531nomaximal, Sylow
403C22×C53—22no—
404C22×C53—22no—
405C22×C53—22no—
406C22×C53—44no—
407C22×C53—42no—
408C22×C53—42no—
409C22×C53—42no—
410C22×C53—84no—
411C22×C53#53412yes—
412C22×C53C2×AGL(1,ℤ/8)12yes—
413C22×C53#57512yes—
414C22×C53C23×D411yescharacteristic
415C2×D53—22no—
416C2×D53—28no—
417C2×D53—22no—
418C2×D53—22no—
419C2×D53—22no—
420C2×D53—22no—
421C2×D53—416no—
422C2×D53—44no—
423C2×D53—42no—
424C2×D53—42no—
425C2×D53—42no—
426C2×D53—42no—
427C2×D53—42no—
428C2×D53—42no—
429C2×D53—816no—
430C2×D53—84no—
431C2×D53—84no—
432C2×D53C2×AGL(1,ℤ/8)14yes—
433C4×C53—22no—
434C4×C53—42no—
435C4×C53—42no—
436C4×C53—42no—
437C4×C53#53412yes—
438C4×C53C2×H(5,𝔽2)11yescharacteristic
439C4×C53C2×H(5,𝔽2)11yescharacteristic
440Dic53—22no—
441Dic53—22no—
442Dic53—42no—
443Dic53—42no—
444C2×#525—531no—
445C22×#121—531no—
446#3194—5316no—
447C2×#482—531no—
448C2×#482D5311yescharacteristic, complemented
449C2×#483—531no—
450C2×#480—531no—
451C2×#469—531no—
452C2×#469—531no—
453C2×#468—531no—
454C2×#468—531no—
455C2×#449—531no—
456C2×#449—531no—
457C2×#450—531no—
458C2×#447—531no—
459C2×#407—531no—
460C2×C53—42no—
461C2×C53—82no—
462C2×C53#319414yescomplemented
463C2×C53C2×#53411yescharacteristic
464C2×C53C22×AGL(1,ℤ/8)11yescharacteristic
465C2×C53C2×#57511yescharacteristic
466D53—24no—
467D53—42no—
468D53—82no—
469D53—82no—
470C22×#41—531no—
471C23×D4—531no—
472C23×D4—1061no—
473C24×C4—531no—
474C22×SD16—531no—
475C22×SD16—531no—
476C22×D8—531no—
477C22×D8—531no—
478C22×M16—531no—
479C22×M16—531no—
480#525—538no—
481#525—1064no—
482C2×#123—1061no—
483C2×C22⋊Q8—531no—
484C2×C22⋊Q8—531no—
485C2×#121—531no—
486C2×#121—531no—
487C2×#121—538no—
488C2×#121—531no—
489C2×#121—531no—
490C2×#121—531no—
491C2×#121—1061no—
492C2×#121—1064no—
493C2×#121—1061no—
494C2×#121C2×D5311yescharacteristic
495C2×#120—1061no—
496C2×C4×D4—1061no—
497C2×C4×D4—1061no—
498C2×#117C2×D5311yescharacteristic, complemented
499C22×C4⋊C4—531no—
500C22×C22⋊C4—1061no—
501#483—538no—
502#482—538no—
503#482C2×D5318yescomplemented
504#480—538no—
505#469—538no—
506#469—538no—
507#468—538no—
508#468—538no—
509#450—538no—
510#449—538no—
511#449—538no—
512#447—538no—
513C2×#107—531no—
514C2×#107C2×D5311yescharacteristic, complemented
515C2×#106—531no—
516C2×#106C2×D5311yescharacteristic, complemented
517C2×#103—531no—
518C2×#103—531no—
519C2×#102—531no—
520C2×#102—531no—
521C2×#102—531no—
522C2×#102—531no—
523C2×#102C2×D5311yescharacteristic, complemented
524C2×#102C2×D5311yescharacteristic, complemented
525#407—538no—
526C2×C22⋊C8—531no—
527C2×C22⋊C8—531no—
528C2×C22⋊C8—531no—
529C2×C22⋊C8C2×D5311yescharacteristic, complemented
530C53C2×#319411yescharacteristic, complemented, Sylow
531C25—531no—
532C25—1061no—
533C2×#41—534no—
534C2×#41—1062no—
535C2×#41—2122no—
536C2×#41—2122no—
537C22×Q8—531no—
538C22×D4—21no—
539C22×D4—534no—
540C22×D4—531no—
541C22×D4—531no—
542C22×D4—1061no—
543C22×D4—1061no—
544C22×D4—1061no—
545C22×D4—1062no—
546C22×D4—1061no—
547C22×D4—1068no—
548C22×D4—1061no—
549C22×D4—1061no—
550C22×D4—1061no—
551C22×D4—2122no—
552C22×D4—2122no—
553C22×D4—2128no—
554C22×D4C22×D5311yescharacteristic
555C23×C4—531no—
556C23×C4—531no—
557C23×C4—531no—
558C23×C4—531no—
559C23×C4—531no—
560C23×C4—534no—
561C23×C4—534no—
562C23×C4—1061no—
563C23×C4—1061no—
564C23×C4—2122no—
565C23×C4—2122no—
566C23×C4C22×D5311yescharacteristic
567C2×SD16—534no—
568C2×SD16—534no—
569C2×SD16—2122no—
570C2×SD16—2122no—
571C2×D8—534no—
572C2×D8—534no—
573C2×D8—2122no—
574C2×D8—2122no—
575C2×M16—534no—
576C2×M16—534no—
577C2×M16—2122no—
578C2×M16—2122no—
579C22×C8—531no—
580C22×C8—531no—
581C22×C8C22×D5311yescharacteristic
582C22×C8C22×D5311yescharacteristic
583#123—1068no—
584C22⋊Q8—534no—
585C22⋊Q8—534no—
586C22⋊Q8—1062no—
587C22⋊Q8—1062no—
588#121—22no—
589#121—534no—
590#121—534no—
591#121—534no—
592#121—534no—
593#121—534no—
594#121—1068no—
595#121—1062no—
596#121—1062no—
597#121—1062no—
598#121—1062no—
599#121—1068no—
600#121—1062no—
601#121C22×D5314yes—
602#120—1068no—
603C4×D4—1068no—
604C4×D4—1068no—
605#117—22no—
606#117C22×D5314yescomplemented
607C2×C4⋊C4—531no—
608C2×C4⋊C4—534no—
609C2×C4⋊C4—1062no—
610C2×C4⋊C4—1061no—
611C2×C4⋊C4—1061no—
612C2×C4⋊C4—1061no—
613C2×C4⋊C4C22×D5311yescharacteristic
614C2×C4⋊C4C22×D5311yescharacteristic
615C2×C4⋊C4C22×D5311yescharacteristic
616C2×C22⋊C4—21no—
617C2×C22⋊C4—21no—
618C2×C22⋊C4—1068no—
619C2×C22⋊C4—1061no—
620C2×C22⋊C4—1061no—
621C2×C22⋊C4—1061no—
622C2×C22⋊C4—1061no—
623C2×C22⋊C4—1061no—
624C2×C22⋊C4—1061no—
625C2×C22⋊C4—1061no—
626C2×C42—21no—
627#107—534no—
628#107C22×D5314yescomplemented
629#106—534no—
630#106C22×D5314yescomplemented
631#103—534no—
632#103—534no—
633#102—534no—
634#102—534no—
635#102—534no—
636#102—534no—
637#102C22×D5314yescomplemented
638#102C22×D5314yescomplemented
639C22⋊C8—534no—
640C22⋊C8—534no—
641C22⋊C8—534no—
642C22⋊C8C22×D5314yescomplemented
643C24—21no—
644C24—531no—
645C24—531no—
646C24—534no—
647C24—1064no—
648C24—1064no—
649C24—1061no—
650C24—1061no—
651C24—2122no—
652C24—2122no—
653C24—2124no—
654C24—2124no—
655C24—2124no—
656C24D4×D5311yescharacteristic
657#41—2124no—
658#41—2124no—
659#41—2128no—
660C2×Q8—532no—
661C2×Q8—1061no—
662C2×Q8—1062no—
663C2×Q8—1062no—
664C2×D4—24no—
665C2×D4—21no—
666C2×D4—22no—
667C2×D4—22no—
668C2×D4—44no—
669C2×D4—532no—
670C2×D4—532no—
671C2×D4—1064no—
672C2×D4—1064no—
673C2×D4—1064no—
674C2×D4—1064no—
675C2×D4—1064no—
676C2×D4—1064no—
677C2×D4—1064no—
678C2×D4—1061no—
679C2×D4—1061no—
680C2×D4—1062no—
681C2×D4—1062no—
682C2×D4—1062no—
683C2×D4—1062no—
684C2×D4—2124no—
685C2×D4—2124no—
686C2×D4—2124no—
687C2×D4—2124no—
688C2×D4—2124no—
689C2×D4—2128no—
690C2×D4—2124no—
691C2×D4—21232no—
692C2×D4—2124no—
693C2×D4—2124no—
694C2×D4—2124no—
695C2×D4C23×D5312yes—
696C22×C4—22no—
697C22×C4—22no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—531no—
702C22×C4—531no—
703C22×C4—534no—
704C22×C4—532no—
705C22×C4—532no—
706C22×C4—532no—
707C22×C4—532no—
708C22×C4—534no—
709C22×C4—534no—
710C22×C4—1064no—
711C22×C4—1062no—
712C22×C4—1062no—
713C22×C4—1062no—
714C22×C4—1062no—
715C22×C4—1061no—
716C22×C4—1061no—
717C22×C4—1064no—
718C22×C4—2128no—
719C22×C4—2124no—
720C22×C4—2124no—
721C22×C4—2122no—
722C22×C4—2122no—
723C22×C4—2124no—
724C22×C4—2124no—
725C22×C4—2122no—
726C22×C4D4×D5312yes—
727C22×C4D4×D5311yescharacteristic
728C22×C4C23×D5312yes—
729C22×C4C23×D5311yescharacteristic
730SD16—2124no—
731SD16—2124no—
732D8—2124no—
733D8—2124no—
734M16—2124no—
735M16—2124no—
736C2×C8—22no—
737C2×C8—22no—
738C2×C8—532no—
739C2×C8—532no—
740C2×C8—1062no—
741C2×C8—1062no—
742C2×C8C23×D5312yes—
743C2×C8C23×D5312yes—
744C4⋊C4—21no—
745C4⋊C4—21no—
746C4⋊C4—21no—
747C4⋊C4—532no—
748C4⋊C4—1064no—
749C4⋊C4—1064no—
750C4⋊C4—1064no—
751C4⋊C4—1061no—
752C4⋊C4C23×D5312yes—
753C4⋊C4C23×D5312yes—
754C4⋊C4C23×D5312yes—
755C22⋊C4—24no—
756C22⋊C4—24no—
757C22⋊C4—1064no—
758C22⋊C4—1064no—
759C22⋊C4—1064no—
760C22⋊C4—1064no—
761C22⋊C4—1064no—
762C22⋊C4—1064no—
763C22⋊C4—1064no—
764C42—24no—
765C23—22no—
766C23—22no—
767C23—22no—
768C23—22no—
769C23—42no—
770C23—42no—
771C23—42no—
772C23—534no—
773C23—532no—
774C23—532no—
775C23—1068no—
776C23—1062no—
777C23—1062no—
778C23—1062no—
779C23—1062no—
780C23—1062no—
781C23—1062no—
782C23—1062no—
783C23—42416no—
784C23—2124no—
785C23—2124no—
786C23—2128no—
787C23—2128no—
788C23—2128no—
789C23—21216no—
790C23—2122no—
791C23—2122no—
792C23—2122no—
793C23—2122no—
794C23—2122no—
795C23—2122no—
796C23C2×D4×D5312yes—
797C23C2×D4×D5311yescharacteristic
798Q8—1062no—
799Q8—1062no—
800Q8—2122no—
801D4—22no—
802D4—22no—
803D4—48no—
804D4—42no—
805D4—1062no—
806D4—1062no—
807D4—1062no—
808D4—1062no—
809D4—2128no—
810D4—2128no—
811D4—2128no—
812D4—2128no—
813D4—2128no—
814D4—2128no—
815D4—2128no—
816D4—2122no—
817D4—2122no—
818C2×C4—22no—
819C2×C4—24no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—42no—
826C2×C4—42no—
827C2×C4—42no—
828C2×C4—532no—
829C2×C4—532no—
830C2×C4—1062no—
831C2×C4—1062no—
832C2×C4—1064no—
833C2×C4—1064no—
834C2×C4—1062no—
835C2×C4—1062no—
836C2×C4—1062no—
837C2×C4—1062no—
838C2×C4—1062no—
839C2×C4—1062no—
840C2×C4—2124no—
841C2×C4—2124no—
842C2×C4—2128no—
843C2×C4—2128no—
844C2×C4—2124no—
845C2×C4—2122no—
846C2×C4—2122no—
847C2×C4C2×D4×D5312yes—
848C2×C4C2×D4×D5311yescharacteristic
849C2×C4#1313326312yes—
850C2×C4#1313326312yes—
851C2×C4C24×D5311yescharacteristic
852C8—22no—
853C8—22no—
854C8—1062no—
855C8—1062no—
856C22—22no—
857C22—22no—
858C22—22no—
859C22—44no—
860C22—42no—
861C22—42no—
862C22—42no—
863C22—84no—
864C22—534no—
865C22—1062no—
866C22—1068no—
867C22—1062no—
868C22—1062no—
869C22—1062no—
870C22—1062no—
871C22—42416no—
872C22—4244no—
873C22—4244no—
874C22—21216no—
875C22—2122no—
876C22—2122no—
877C22—2122no—
878C22—2122no—
879C22—2122no—
880C22—2122no—
881C22—2124no—
882C22#1681118412yes—
883C22AGL(1,ℤ/8)×D5312yes—
884C22#1681142012yes—
885C22C22×D4×D5311yescharacteristic
886C4—22no—
887C4—42no—
888C4—42no—
889C4—42no—
890C4—1062no—
891C4—1062no—
892C4—2122no—
893C4—2122no—
894C4#1681118412yes—
895C4C2×#1313326311yescharacteristic
896C4C2×#1313326311yescharacteristic
897C2—42no—
898C2—82no—
899C2—1064no—
900C2—4242no—
901C2—4242no—
902C2—2122no—
903C2#2028553314yesdirect product factor
904C2C2×#1681118411yescharacteristic
905C2C2×AGL(1,ℤ/8)×D5311yescharacteristic
906C2C2×#1681142011yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#482C2
socleC23×C53C22×D4
hypercenterC2×#482D53
hypocenterC53C2×#3194
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#482

Complements

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

NH ≅ G/Ntype
1. C2×#16811135C2semidirect
2. C2×#121×D53C2semidirect
3. #20285533C2direct (N × H)
4. C2×#16810947C2semidirect
5. C2×#16810955C2semidirect
6. C2×#16810938C2semidirect
7. C2×#16810877C2semidirect
8. C2×#16810875C2semidirect
9. C2×#16810870C2semidirect
10. C2×#16810868C2semidirect
11. C2×#16810770C2semidirect
12. C2×#16810766C2semidirect
13. C2×#16810775C2semidirect
14. C2×#16810758C2semidirect
15. C2×#16810585C2semidirect
16. C2×C53×#482C2semidirect
17. C22×#11719945C22semidirect
21. C22×#11719913C22semidirect
22. C22×#11719923C22semidirect
23. C22×D424C22semidirect
24. C22×#11719922C22semidirect
25. C22×#11719912C22semidirect
26. C22×#11719912C22semidirect
28. #16811135C22semidirect
31. C2×#13133197C22semidirect
34. C2×#13133192C22semidirect
40. #121×D53C22semidirect
46. #16810955C22semidirect
47. #16810947C22semidirect
48. #16810938C22semidirect
49. #16810877C22semidirect
50. #16810875C22semidirect
51. #16810870C22semidirect
52. #16810868C22semidirect
53. #16810775C22semidirect
54. #16810770C22semidirect
55. #16810766C22semidirect
56. #16810758C22semidirect
57. C2×#13133150C22semidirect
58. C2×#13133148C22semidirect
59. C2×#13133142C22semidirect
60. C2×#13133140C22semidirect
61. C2×#13133139C22semidirect
62. C2×#13133137C22semidirect
63. C2×#13133137C22semidirect
64. C2×#13133137C22semidirect
65. #16810585C22semidirect
66. C2×C22⋊#88322C22semidirect
70. C2×#117×C53C22semidirect
71. C53×#482C22semidirect
72. C2×#107×C53C22semidirect
73. C2×#106×C53C22semidirect
74. C2×#102×C53C22semidirect
75. C2×#102×C53C22semidirect
76. C2×C22⋊C8×C53C22semidirect
82. C2×#11719945C23semidirect
111. C2×#11719913C23semidirect
113. C2×#11719923C23semidirect
115. C2×D424C23semidirect
117. C2×#11719922C23semidirect
120. C2×#11719912C23semidirect
121. C2×#11719912C23semidirect
128. #13133197C23semidirect
134. #13133192C23semidirect
158. #13133150C23semidirect
159. #13133148C23semidirect
160. #13133142C23semidirect
161. #13133140C23semidirect
162. #13133139C23semidirect
163. #13133137C23semidirect
164. #13133137C23semidirect
165. #13133137C23semidirect
166. C22⋊#88322C23semidirect
177. #117×C53C23semidirect
184. #107×C53C23semidirect
185. #106×C53C23semidirect
186. #102×C53C23semidirect
187. #102×C53C23semidirect
188. C22⋊C8×C53C23semidirect
448. C2×#482D53semidirect
462. C2×C53#3194semidirect
498. C2×#117C2×D53semidirect
503. #482C2×D53semidirect
514. C2×#107C2×D53semidirect
516. C2×#106C2×D53semidirect
523. C2×#102C2×D53semidirect
524. C2×#102C2×D53semidirect
529. C2×C22⋊C8C2×D53semidirect
530. C53C2×#3194semidirect
606. #117C22×D53semidirect
628. #107C22×D53semidirect
630. #106C22×D53semidirect
637. #102C22×D53semidirect
638. #102C22×D53semidirect
642. C22⋊C8C22×D53semidirect
903. C2#20285533direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168111352
C2×#121×D532
#202855332
C2×#168109472
C2×#168109552
C2×#168109382
C2×#168108772
C2×#168108752
C2×#168108702
C2×#168108682
C2×#168107702
C2×#168107662
C2×#168107752
C2×#168107582
C2×#168105852
C2×C53×#4822
C2×#319453