Finite Group Databasebeta

← #27399632

Subgroups — #27399632

Order 13568.

1930 conjugacy classes of subgroups.

The subgroup lattice has 960 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16810695C211yesmaximal, characteristic, complemented
2C2×#16810628C211yesmaximal, characteristic, complemented
3C22×#13133138C211yesmaximal, characteristic, complemented
4#20277644C211yesmaximal, characteristic, complemented
5#20275643C211yesmaximal, characteristic, complemented
6#20275540C211yesmaximal, characteristic, complemented
7#20275154C211yesmaximal, characteristic, complemented
8#20275144C211yesmaximal, characteristic, complemented
9#20275038C211yesmaximal, characteristic, complemented
10#20275033C211yesmaximal, characteristic, complemented
11#20274725C211yesmaximal, characteristic, complemented
12#20274646C211yesmaximal, characteristic, complemented
13#20274646C211yesmaximal, characteristic, complemented
14#20274540C211yesmaximal, characteristic, complemented
15C2×D42×C53C211yesmaximal, characteristic
16C22×#11719917C2211yescharacteristic, complemented
17C23×#88322C2211yescharacteristic, complemented
18C2×#13133176C2211yescharacteristic, complemented
19C22×C4⋊Dic53C2211yescharacteristic, complemented
20#16810695—24no—
21C2×C4⋊#88322C2211yescharacteristic, complemented
22#16810628—24no—
23C2×#13133138—24no—
24C2×#13133138C2211yescharacteristic
25C2×#13133138C2211yescharacteristic
26C2×#13133138C2211yescharacteristic
27C2×#13133138C2211yescharacteristic
28C2×#13133138C2211yescharacteristic, complemented
29C2×#13133138C2211yescharacteristic, complemented
30C2×#13133138C2211yescharacteristic, complemented
31C2×#13133138C2211yescharacteristic, complemented
32C2×#13133138C2211yescharacteristic, complemented
33C2×#13133138C2211yescharacteristic, complemented
34C2×#13133138C2211yescharacteristic, complemented
35C2×#13133138C2211yescharacteristic, complemented
36C2×C22⋊#88322C2211yescharacteristic, complemented
37C2×C22⋊#88322C2211yescharacteristic, complemented
38C2×#13133128C2211yescharacteristic, complemented
39#16810516—21no—
40#16810509—21no—
41#16810503—21no—
42#16810489C2211yescharacteristic, complemented
43#16810483C2211yescharacteristic, complemented
44#16810483C2211yescharacteristic, complemented
45C4×C4⋊Dic53C2211yescharacteristic, complemented
46C22⋊C4×Dic53—21no—
47#16810385C2211yescharacteristic, complemented
48#16810385C2211yescharacteristic, complemented
49#16810385C2211yescharacteristic, complemented
50#16810385C2211yescharacteristic, complemented
51C23×D4×C53—21no—
52C23×D4×C53C2211yescharacteristic
53C23×D4×C53C2211yescharacteristic
54D42×C53—24no—
55D42×C53C418yescomplemented
56C2×#127×C53C2211yescharacteristic
57C2×#121×C53—21no—
58C2×#121×C53C2211yescharacteristic
59C2×#121×C53C2211yescharacteristic
60C2×#120×C53—21no—
61C2×#120×C53—21no—
62C2×C4×D4×C53C2211yescharacteristic
63C2×C4×D4×C53C2211yescharacteristic
64C23×Dic53—21no—
65C2×#11719917—22no—
66C2×#11719917—22no—
67C2×#11719917—41no—
68C22×#88322—22no—
69C22×#88322—22no—
70C22×#88322—41no—
71C22×#88322C2311yescharacteristic
72C22×#88322C2311yescharacteristic
73C22×#88322C2311yescharacteristic
74C22×#88322C2311yescharacteristic
75#13133176—22no—
76#13133176—41no—
77C2×C4⋊Dic53—21no—
78C2×C4⋊Dic53—22no—
79C2×C4⋊Dic53—41no—
80C2×C4⋊Dic53C2311yescharacteristic
81C2×C4⋊Dic53C2311yescharacteristic
82C2×C4⋊Dic53C2311yescharacteristic
83C2×C4⋊Dic53C2311yescharacteristic
84C2×C22⋊Dic53—21no—
85C2×C22⋊Dic53—21no—
86C2×C22⋊Dic53—21no—
87C2×C4×Dic53—21no—
88C2×C4×Dic53—21no—
89C4⋊#88322—22no—
90#13133138—22no—
91#13133138—22no—
92#13133138—22no—
93#13133138—22no—
94#13133138—22no—
95#13133138—22no—
96#13133138—22no—
97#13133138—41no—
98#13133138—41no—
99#13133138—41no—
100#13133138—41no—
101#13133138D414yescomplemented
102C22⋊#88322—22no—
103C22⋊#88322—22no—
104#13133128—22no—
105#13133124—21no—
106#13133124—21no—
107#13133124—21no—
108#13133124—21no—
109#13133124—21no—
110C25×C53—21no—
111C25×C53—21no—
112C22×D4×C53—22no—
113C22×D4×C53—22no—
114C22×D4×C53—22no—
115C22×D4×C53—22no—
116C22×D4×C53—21no—
117C22×D4×C53—21no—
118C22×D4×C53—28no—
119C22×D4×C53—21no—
120C22×D4×C53—21no—
121C22×D4×C53—21no—
122C22×D4×C53—22no—
123C22×D4×C53—22no—
124C22×D4×C53—21no—
125C22×D4×C53—41no—
126C22×D4×C53—41no—
127C22×D4×C53—41no—
128C22×D4×C53—41no—
129C22×D4×C53—44no—
130C22×D4×C53—44no—
131C22×D4×C53C2×C414yes—
132C22×D4×C53C2×C414yescomplemented
133C22×D4×C53D411yescharacteristic
134C22×D4×C53C2311yescharacteristic
135C22×D4×C53C2311yescharacteristic
136C22×D4×C53C2311yescharacteristic
137C23×C4×C53—21no—
138C23×C4×C53C2311yescharacteristic
139C23×C4×C53C2311yescharacteristic
140#127×C53—22no—
141#127×C53C2×C414yescomplemented
142#121×C53—28no—
143#121×C53—22no—
144#121×C53—22no—
145#121×C53C2×C414yes—
146#121×C53C2×C414yescomplemented
147#120×C53—28no—
148#120×C53—28no—
149C4×D4×C53—22no—
150C4×D4×C53C2×C414yes—
151C4×D4×C53C2×C414yescomplemented
152C4×D4×C53D414yes—
153C2×C4⋊C4×C53D411yescharacteristic
154C2×C4⋊C4×C53C2311yescharacteristic
155C2×C22⋊C4×C53—21no—
156C2×C22⋊C4×C53—21no—
157C2×C22⋊C4×C53—21no—
158C2×C22⋊C4×C53D411yescharacteristic
159C2×C22⋊C4×C53D411yescharacteristic
160C2×C42×C53C2311yescharacteristic
161C24×C53—21no—
162C24×C53—21no—
163C24×C53—21no—
164C24×C53—24no—
165C24×C53—24no—
166C24×C53—42no—
167C24×C53—42no—
168C24×C53—42no—
169C24×C53—42no—
170C24×C53—42no—
171C24×C53—42no—
172C24×C53—42no—
173C24×C53—42no—
174C24×C53—81no—
175C24×C53—81no—
176C24×C53—81no—
177C24×C53—81no—
178C24×C53C2×D411yescharacteristic
179C24×C53C2×D411yescharacteristic
180C2×D4×C53—22no—
181C2×D4×C53—22no—
182C2×D4×C53—28no—
183C2×D4×C53—28no—
184C2×D4×C53—24no—
185C2×D4×C53—24no—
186C2×D4×C53—24no—
187C2×D4×C53—24no—
188C2×D4×C53—24no—
189C2×D4×C53—24no—
190C2×D4×C53—21no—
191C2×D4×C53—21no—
192C2×D4×C53—21no—
193C2×D4×C53—21no—
194C2×D4×C53—21no—
195C2×D4×C53—21no—
196C2×D4×C53—21no—
197C2×D4×C53—21no—
198C2×D4×C53—21no—
199C2×D4×C53—21no—
200C2×D4×C53—21no—
201C2×D4×C53—21no—
202C2×D4×C53—21no—
203C2×D4×C53—44no—
204C2×D4×C53—44no—
205C2×D4×C53—44no—
206C2×D4×C53—44no—
207C2×D4×C53—44no—
208C2×D4×C53—44no—
209C2×D4×C53—42no—
210C2×D4×C53—42no—
211C2×D4×C53—42no—
212C2×D4×C53—42no—
213C2×D4×C53—42no—
214C2×D4×C53—42no—
215C2×D4×C53—432no—
216C2×D4×C53—42no—
217C2×D4×C53—42no—
218C2×D4×C53—42no—
219C2×D4×C53—42no—
220C2×D4×C53—81no—
221C2×D4×C53—81no—
222C2×D4×C53C22⋊C414yes—
223C2×D4×C53C22×C412yes—
224C2×D4×C53C22×C412yes—
225C2×D4×C53C22×C412yes—
226C2×D4×C53C2×D412yes—
227C2×D4×C53#4112yes—
228C22×C4×C53—21no—
229C22×C4×C53—21no—
230C22×C4×C53—21no—
231C22×C4×C53—21no—
232C22×C4×C53—21no—
233C22×C4×C53—21no—
234C22×C4×C53—21no—
235C22×C4×C53—21no—
236C22×C4×C53—21no—
237C22×C4×C53—24no—
238C22×C4×C53—42no—
239C22×C4×C53—42no—
240C22×C4×C53C22×C412yes—
241C22×C4×C53C22×C412yes—
242C22×C4×C53C2×D411yescharacteristic
243C22×C4×C53C2×D411yescharacteristic
244C22×C4×C53C2×D411yescharacteristic
245C22×C4×C53C2×D411yescharacteristic
246C22×C4×C53C2×D412yes—
247C22×C4×C53C2×D412yes—
248C22×C4×C53C2411yescharacteristic
249C22×Dic53—21no—
250C22×Dic53—21no—
251C22×Dic53—21no—
252C22×Dic53—21no—
253C22×Dic53—42no—
254C22×Dic53—42no—
255C22×Dic53—81no—
256C4⋊C4×C53—21no—
257C4⋊C4×C53C22⋊C414yes—
258C4⋊C4×C53C22×C412yes—
259C22⋊C4×C53—24no—
260C22⋊C4×C53—24no—
261C22⋊C4×C53—24no—
262C22⋊C4×C53C22⋊C414yes—
263C22⋊C4×C53C22⋊C414yes—
264C42×C53C22×C412yes—
265C42×C53C2×D412yes—
266C22⋊Dic53—42no—
267C22⋊Dic53—42no—
268C22⋊Dic53—81no—
269C4⋊Dic53—21no—
270C4⋊Dic53—21no—
271C4⋊Dic53—21no—
272C4⋊Dic53—21no—
273C4⋊Dic53—21no—
274C4⋊Dic53—21no—
275C4⋊Dic53—21no—
276C4⋊Dic53—42no—
277C4⋊Dic53C2×D412yescomplemented
278C4×Dic53—42no—
279C4×Dic53—81no—
280#11719917—44no—
281C2×#88322—21no—
282C2×#88322—21no—
283C2×#88322—21no—
284C2×#88322—21no—
285C2×#88322—21no—
286C2×#88322—21no—
287C2×#88322—21no—
288C2×#88322—21no—
289C2×#88322—21no—
290C2×#88322—21no—
291C2×#88322—21no—
292C2×#88322—44no—
293C2×#88322C2×D412yescomplemented
294C23×C53—21no—
295C23×C53—21no—
296C23×C53—21no—
297C23×C53—21no—
298C23×C53—22no—
299C23×C53—21no—
300C23×C53—22no—
301C23×C53—21no—
302C23×C53—22no—
303C23×C53—21no—
304C23×C53—21no—
305C23×C53—21no—
306C23×C53—21no—
307C23×C53—22no—
308C23×C53—22no—
309C23×C53—48no—
310C23×C53—48no—
311C23×C53—48no—
312C23×C53—41no—
313C23×C53—41no—
314C23×C53—41no—
315C23×C53—41no—
316C23×C53—41no—
317C23×C53—41no—
318C23×C53—41no—
319C23×C53—41no—
320C23×C53—41no—
321C23×C53—41no—
322C23×C53—41no—
323C23×C53—41no—
324C23×C53—41no—
325C23×C53—41no—
326C23×C53—41no—
327C23×C53—41no—
328C23×C53—48no—
329C23×C53—84no—
330C23×C53—84no—
331C23×C53—84no—
332C23×C53—84no—
333C23×C53—84no—
334C23×C53—84no—
335C23×C53—84no—
336C23×C53—84no—
337C23×C53—84no—
338C23×C53—84no—
339C23×C53C2×C22⋊C412yes—
340C23×C53C2×C22⋊C412yes—
341C23×C53AGL(1,ℤ/8)12yes—
342C23×C53AGL(1,ℤ/8)12yes—
343C23×C53C22×D411yescharacteristic
344D4×C53—28no—
345D4×C53—22no—
346D4×C53—22no—
347D4×C53—22no—
348D4×C53—22no—
349D4×C53—22no—
350D4×C53—22no—
351D4×C53—22no—
352D4×C53—48no—
353D4×C53—48no—
354D4×C53—48no—
355D4×C53—48no—
356D4×C53—48no—
357D4×C53—41no—
358D4×C53—41no—
359D4×C53—41no—
360D4×C53—41no—
361D4×C53—84no—
362D4×C53C4×D414yes—
363C2×C4×C53—21no—
364C2×C4×C53—21no—
365C2×C4×C53—21no—
366C2×C4×C53—21no—
367C2×C4×C53—21no—
368C2×C4×C53—21no—
369C2×C4×C53—21no—
370C2×C4×C53—21no—
371C2×C4×C53—22no—
372C2×C4×C53—22no—
373C2×C4×C53—22no—
374C2×C4×C53—22no—
375C2×C4×C53—22no—
376C2×C4×C53—22no—
377C2×C4×C53—22no—
378C2×C4×C53—22no—
379C2×C4×C53—22no—
380C2×C4×C53—48no—
381C2×C4×C53—41no—
382C2×C4×C53—41no—
383C2×C4×C53C2×C22⋊C412yes—
384C2×C4×C53C2×C22⋊C412yes—
385C2×C4×C53C2×C22⋊C412yes—
386C2×C4×C53C2×C22⋊C412yes—
387C2×C4×C53C23×C411yescharacteristic
388C2×C4×C53C22×D411yescharacteristic
389C2×C4×C53C22×D411yescharacteristic
390C2×C4×C53C2×#4111yescharacteristic
391C2×C4×C53H(5,𝔽2)11yescharacteristic
392C2×C4×C53H(5,𝔽2)11yescharacteristic
393C2×Dic53—22no—
394C2×Dic53—41no—
395C2×Dic53—41no—
396C2×Dic53—41no—
397C2×Dic53—41no—
398C2×Dic53—41no—
399C2×Dic53—41no—
400C2×Dic53—41no—
401C2×Dic53—41no—
402C2×Dic53—41no—
403C2×Dic53—41no—
404C2×Dic53—41no—
405C2×Dic53—84no—
406#88322—22no—
407#88322—41no—
408#88322—41no—
409#88322—41no—
410#22423—531nomaximal, Sylow
411C22×C53—22no—
412C22×C53—22no—
413C22×C53—22no—
414C22×C53—22no—
415C22×C53—22no—
416C22×C53—22no—
417C22×C53—22no—
418C22×C53—24no—
419C22×C53—22no—
420C22×C53—22no—
421C22×C53—42no—
422C22×C53—42no—
423C22×C53—41no—
424C22×C53—42no—
425C22×C53—41no—
426C22×C53—42no—
427C22×C53—41no—
428C22×C53—42no—
429C22×C53—41no—
430C22×C53—42no—
431C22×C53—42no—
432C22×C53—42no—
433C22×C53—42no—
434C22×C53—42no—
435C22×C53—42no—
436C22×C53—42no—
437C22×C53—816no—
438C22×C53—816no—
439C22×C53—81no—
440C22×C53—81no—
441C22×C53—81no—
442C22×C53—81no—
443C22×C53—81no—
444C22×C53—81no—
445C22×C53—81no—
446C22×C53—81no—
447C22×C53#41814yescomplemented
448C22×C53C22×C22⋊C411yescharacteristic
449C22×C53D4211yescharacteristic
450C22×C53#54611yescharacteristic
451C22×C53C2×AGL(1,ℤ/8)11yescharacteristic
452C22×C53C2×AGL(1,ℤ/8)11yescharacteristic
453C22×C53#57611yescharacteristic
454C22×C53#57711yescharacteristic
455C4×C53—22no—
456C4×C53—22no—
457C4×C53—22no—
458C4×C53—22no—
459C4×C53—42no—
460C4×C53C2×C4×D411yescharacteristic
461C4×C53#51811yescharacteristic
462C4×C53D4211yescharacteristic
463C4×C53#54611yescharacteristic
464Dic53—42no—
465Dic53—81no—
466Dic53—81no—
467Dic53—81no—
468C2×D42D5311yescharacteristic
469C2×#435—531no—
470C2×#418—531no—
471C22×#102—531no—
472#2352—531no—
473#1982—531no—
474#1961—531no—
475#1895—531no—
476#1893—531no—
477#1875—531no—
478#1874—531no—
479#1804—531no—
480#1786—531no—
481#1786—531no—
482#1762—531no—
483C2×C53—24no—
484C2×C53—42no—
485C2×C53—44no—
486C2×C53—82no—
487C2×C53—82no—
488C2×C53D4×C22⋊C411yescharacteristic
489C2×C53C2×#41811yescharacteristic
490C2×C53#289711yescharacteristic
491C2×C53#326411yescharacteristic
492C2×C53#326511yescharacteristic
493C2×C53#331011yescharacteristic
494C2×C53#331811yescharacteristic
495C23×D4—21no—
496C23×D4C2×D5311yescharacteristic
497C23×D4C2×D5311yescharacteristic
498C22×M16—531no—
499C23×C8—531no—
500D42—24no—
501D42Dic5318yescomplemented
502C2×#127C2×D5311yescharacteristic
503C2×#121—21no—
504C2×#121C2×D5311yescharacteristic
505C2×#121C2×D5311yescharacteristic
506C2×#120—21no—
507C2×#120—21no—
508C2×C4×D4C2×D5311yescharacteristic
509C2×C4×D4C2×D5311yescharacteristic
510C2×#117—531no—
511C22×C4⋊C4—531no—
512#435—1064no—
513C2×C4⋊C8—531no—
514#418—1064no—
515C2×#102—531no—
516C2×#102—531no—
517C2×#102—531no—
518C2×#102—531no—
519C2×#102—531no—
520C2×#102—531no—
521C2×#102—531no—
522C2×#102—531no—
523C2×#102—531no—
524C2×#102—531no—
525C2×#102—531no—
526C2×#102—531no—
527C2×#102—1064no—
528C2×C22⋊C8—531no—
529C2×C22⋊C8—531no—
530C2×#97—531no—
531#388—1061no—
532#387—1061no—
533#386—1061no—
534#382—531no—
535#380—531no—
536#380—531no—
537C4×C4⋊C4—531no—
538C4×C22⋊C4—1061no—
539#340—531no—
540#340—531no—
541#340—531no—
542#340—531no—
543C53#2242311yescharacteristic, complemented, Sylow
544C25—21no—
545C25—21no—
546C22×D4—22no—
547C22×D4—22no—
548C22×D4—22no—
549C22×D4—22no—
550C22×D4—21no—
551C22×D4—21no—
552C22×D4—28no—
553C22×D4—21no—
554C22×D4—21no—
555C22×D4—21no—
556C22×D4—22no—
557C22×D4—22no—
558C22×D4—21no—
559C22×D4—41no—
560C22×D4—41no—
561C22×D4—41no—
562C22×D4—41no—
563C22×D4—44no—
564C22×D4—44no—
565C22×D4C2×Dic5314yes—
566C22×D4C2×Dic5314yescomplemented
567C22×D4C22⋊D5311yescharacteristic
568C22×D4C22×D5311yescharacteristic
569C22×D4C22×D5311yescharacteristic
570C22×D4C22×D5311yescharacteristic
571C23×C4—21no—
572C23×C4—1061no—
573C23×C4C22×D5311yescharacteristic
574C23×C4C22×D5311yescharacteristic
575C2×M16—1062no—
576C2×M16—1062no—
577C2×M16—2121no—
578C22×C8—531no—
579C22×C8—531no—
580C22×C8—531no—
581C22×C8—531no—
582C22×C8—1062no—
583C22×C8—1062no—
584C22×C8—2121no—
585#127—22no—
586#127C2×Dic5314yescomplemented
587#121—22no—
588#121—22no—
589#121—28no—
590#121C2×Dic5314yes—
591#121C2×Dic5314yescomplemented
592#120—28no—
593#120—28no—
594C4×D4—22no—
595C4×D4C2×Dic5314yes—
596C4×D4C2×Dic5314yescomplemented
597C4×D4C22⋊D5314yes—
598#117—1062no—
599#117—2121no—
600C2×C4⋊C4—531no—
601C2×C4⋊C4—531no—
602C2×C4⋊C4—531no—
603C2×C4⋊C4—531no—
604C2×C4⋊C4—1062no—
605C2×C4⋊C4—1061no—
606C2×C4⋊C4—2121no—
607C2×C4⋊C4C22⋊D5311yescharacteristic
608C2×C4⋊C4C22×D5311yescharacteristic
609C2×C22⋊C4—21no—
610C2×C22⋊C4—21no—
611C2×C22⋊C4—21no—
612C2×C22⋊C4—1061no—
613C2×C22⋊C4—1061no—
614C2×C22⋊C4—1061no—
615C2×C22⋊C4C22⋊D5311yescharacteristic
616C2×C22⋊C4C22⋊D5311yescharacteristic
617C2×C42—1061no—
618C2×C42—1061no—
619C2×C42C22×D5311yescharacteristic
620C4⋊C8—1062no—
621#102—534no—
622#102—1062no—
623#102—1062no—
624#102—1062no—
625#102—1062no—
626#102—1062no—
627#102—1062no—
628#102—1062no—
629#102—2121no—
630#102—2121no—
631#102—2121no—
632#102—2121no—
633C22⋊C8—1062no—
634C22⋊C8—1062no—
635#97—1062no—
636#95—1061no—
637#95—1061no—
638#95—1061no—
639#95—1061no—
640#95—1061no—
641C24—21no—
642C24—21no—
643C24—21no—
644C24—24no—
645C24—24no—
646C24—42no—
647C24—42no—
648C24—42no—
649C24—42no—
650C24—42no—
651C24—42no—
652C24—42no—
653C24—42no—
654C24—81no—
655C24—81no—
656C24—81no—
657C24—81no—
658C24C2×C22⋊D5311yescharacteristic
659C24C2×C22⋊D5311yescharacteristic
660C2×D4—22no—
661C2×D4—22no—
662C2×D4—28no—
663C2×D4—28no—
664C2×D4—24no—
665C2×D4—24no—
666C2×D4—24no—
667C2×D4—24no—
668C2×D4—24no—
669C2×D4—24no—
670C2×D4—21no—
671C2×D4—21no—
672C2×D4—21no—
673C2×D4—21no—
674C2×D4—21no—
675C2×D4—21no—
676C2×D4—21no—
677C2×D4—21no—
678C2×D4—21no—
679C2×D4—21no—
680C2×D4—21no—
681C2×D4—21no—
682C2×D4—21no—
683C2×D4—44no—
684C2×D4—44no—
685C2×D4—44no—
686C2×D4—44no—
687C2×D4—44no—
688C2×D4—44no—
689C2×D4—42no—
690C2×D4—42no—
691C2×D4—42no—
692C2×D4—42no—
693C2×D4—42no—
694C2×D4—42no—
695C2×D4—432no—
696C2×D4—42no—
697C2×D4—42no—
698C2×D4—42no—
699C2×D4—42no—
700C2×D4—81no—
701C2×D4—81no—
702C2×D4C22⋊Dic5314yes—
703C2×D4D4×D5312yes—
704C2×D4#1171994712yes—
705C2×D4C22×Dic5312yes—
706C2×D4C22×Dic5312yes—
707C2×D4C22×Dic5312yes—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—24no—
718C22×C4—42no—
719C22×C4—42no—
720C22×C4—1061no—
721C22×C4—1061no—
722C22×C4—1061no—
723C22×C4—1061no—
724C22×C4—4241no—
725C22×C4—2122no—
726C22×C4—2122no—
727C22×C4C22×Dic5312yes—
728C22×C4C22×Dic5312yes—
729C22×C4C2×C22⋊D5311yescharacteristic
730C22×C4C2×C22⋊D5311yescharacteristic
731C22×C4C2×C22⋊D5311yescharacteristic
732C22×C4C2×C22⋊D5311yescharacteristic
733C22×C4C2×C22⋊D5312yes—
734C22×C4C2×C22⋊D5312yes—
735C22×C4C23×D5311yescharacteristic
736M16—2124no—
737C2×C8—532no—
738C2×C8—1061no—
739C2×C8—1061no—
740C2×C8—1061no—
741C2×C8—1061no—
742C2×C8—1061no—
743C2×C8—1061no—
744C2×C8—1061no—
745C2×C8—1061no—
746C2×C8—1061no—
747C2×C8—1061no—
748C2×C8—1061no—
749C2×C8—2124no—
750C4⋊C4—21no—
751C4⋊C4—532no—
752C4⋊C4—1061no—
753C4⋊C4—1061no—
754C4⋊C4—1061no—
755C4⋊C4—1061no—
756C4⋊C4—1061no—
757C4⋊C4—1061no—
758C4⋊C4—1061no—
759C4⋊C4—2122no—
760C4⋊C4C22⋊Dic5314yes—
761C4⋊C4C22×Dic5312yes—
762C22⋊C4—24no—
763C22⋊C4—24no—
764C22⋊C4—24no—
765C22⋊C4—4241no—
766C22⋊C4—2122no—
767C22⋊C4—2122no—
768C22⋊C4C22⋊Dic5314yes—
769C22⋊C4C22⋊Dic5314yes—
770C42—4241no—
771C42—2122no—
772C42C22×Dic5312yes—
773C42C2×C22⋊D5312yes—
774C23—21no—
775C23—21no—
776C23—21no—
777C23—21no—
778C23—21no—
779C23—22no—
780C23—22no—
781C23—21no—
782C23—21no—
783C23—21no—
784C23—21no—
785C23—21no—
786C23—22no—
787C23—22no—
788C23—22no—
789C23—48no—
790C23—48no—
791C23—48no—
792C23—41no—
793C23—41no—
794C23—41no—
795C23—41no—
796C23—41no—
797C23—41no—
798C23—48no—
799C23—41no—
800C23—41no—
801C23—41no—
802C23—41no—
803C23—41no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23—41no—
809C23—84no—
810C23—84no—
811C23—84no—
812C23—84no—
813C23—84no—
814C23—84no—
815C23—84no—
816C23—84no—
817C23—84no—
818C23—84no—
819C23C2×C22⋊Dic5312yes—
820C23C2×C22⋊Dic5312yes—
821C23#1313324312yes—
822C23#1313324312yes—
823C23C22×C22⋊D5311yescharacteristic
824D4—28no—
825D4—22no—
826D4—22no—
827D4—22no—
828D4—22no—
829D4—22no—
830D4—22no—
831D4—22no—
832D4—48no—
833D4—48no—
834D4—48no—
835D4—48no—
836D4—48no—
837D4—41no—
838D4—41no—
839D4—41no—
840D4—41no—
841D4—84no—
842D4D4×Dic5314yes—
843C2×C4—21no—
844C2×C4—21no—
845C2×C4—21no—
846C2×C4—21no—
847C2×C4—21no—
848C2×C4—21no—
849C2×C4—21no—
850C2×C4—21no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—48no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—1062no—
864C2×C4—4244no—
865C2×C4—2121no—
866C2×C4—2121no—
867C2×C4—2121no—
868C2×C4—2121no—
869C2×C4—2121no—
870C2×C4—2121no—
871C2×C4—2121no—
872C2×C4—2121no—
873C2×C4—2121no—
874C2×C4—2121no—
875C2×C4—2121no—
876C2×C4C2×C22⋊Dic5312yes—
877C2×C4C2×C22⋊Dic5312yes—
878C2×C4C2×C22⋊Dic5312yes—
879C2×C4C2×C22⋊Dic5312yes—
880C2×C4C23×Dic5311yescharacteristic
881C2×C4C2×D4×D5311yescharacteristic
882C2×C4C22×C22⋊D5311yescharacteristic
883C2×C4C2×#1171994711yescharacteristic
884C2×C4#1313326211yescharacteristic
885C2×C4#1313326211yescharacteristic
886C8—1062no—
887C8—2121no—
888C8—2121no—
889C8—2121no—
890C22—22no—
891C22—22no—
892C22—22no—
893C22—22no—
894C22—22no—
895C22—22no—
896C22—22no—
897C22—24no—
898C22—22no—
899C22—22no—
900C22—41no—
901C22—42no—
902C22—42no—
903C22—42no—
904C22—41no—
905C22—42no—
906C22—41no—
907C22—42no—
908C22—41no—
909C22—42no—
910C22—42no—
911C22—42no—
912C22—42no—
913C22—42no—
914C22—42no—
915C22—42no—
916C22—816no—
917C22—816no—
918C22—81no—
919C22—81no—
920C22—81no—
921C22—81no—
922C22—81no—
923C22—81no—
924C22—81no—
925C22—81no—
926C22#1681062814yescomplemented
927C22C22×C22⋊Dic5311yescharacteristic
928C22D4×C22⋊D5311yescharacteristic
929C22#1681126711yescharacteristic
930C22C2×#1313324311yescharacteristic
931C22C2×#1313324311yescharacteristic
932C22#1681142611yescharacteristic
933C22#1681143411yescharacteristic
934C4—22no—
935C4—22no—
936C4—22no—
937C4—22no—
938C4—42no—
939C4—4241no—
940C4—4241no—
941C4—4241no—
942C4—2122no—
943C4C2×D4×Dic5311yescharacteristic
944C4#1681109811yescharacteristic
945C4D4×C22⋊D5311yescharacteristic
946C4#1681126711yescharacteristic
947C2—24no—
948C2—42no—
949C2—44no—
950C2—82no—
951C2—82no—
952C2D4×C22⋊Dic5311yescharacteristic
953C2C2×#1681062811yescharacteristic
954C2#2028324111yescharacteristic
955C2#2028619111yescharacteristic
956C2#2028620611yescharacteristic
957C2#2028673611yescharacteristic
958C2#2028685611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D53
commutatorC2×C4×C53C23×C4
FrattiniC22×C4C23×D53
Fitting, prime radicalC2×D42×C53C2
socleC23×C53C22×D4
cosocleC22×C4×C53C24
hypercenterC2×D42D53
hypocenterC53#22423
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×D42

Complements

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

NH ≅ G/Ntype
1. C2×#16810695C2semidirect
2. C2×#16810628C2semidirect
3. C22×#13133138C2semidirect
4. #20277644C2semidirect
5. #20275643C2semidirect
6. #20275540C2semidirect
7. #20275154C2semidirect
8. #20275144C2semidirect
9. #20275038C2semidirect
10. #20275033C2semidirect
11. #20274725C2semidirect
12. #20274646C2semidirect
13. #20274646C2semidirect
14. #20274540C2semidirect
16. C22×#11719917C22semidirect
17. C23×#88322C22semidirect
18. C2×#13133176C22semidirect
19. C22×C4⋊Dic53C22semidirect
21. C2×C4⋊#88322C22semidirect
28. C2×#13133138C22semidirect
29. C2×#13133138C22semidirect
30. C2×#13133138C22semidirect
31. C2×#13133138C22semidirect
32. C2×#13133138C22semidirect
33. C2×#13133138C22semidirect
34. C2×#13133138C22semidirect
35. C2×#13133138C22semidirect
36. C2×C22⋊#88322C22semidirect
37. C2×C22⋊#88322C22semidirect
38. C2×#13133128C22semidirect
42. #16810489C22semidirect
43. #16810483C22semidirect
44. #16810483C22semidirect
45. C4×C4⋊Dic53C22semidirect
47. #16810385C22semidirect
48. #16810385C22semidirect
49. #16810385C22semidirect
50. #16810385C22semidirect
55. D42×C53C4semidirect
101. #13133138D4semidirect
132. C22×D4×C53C2×C4semidirect
141. #127×C53C2×C4semidirect
146. #121×C53C2×C4semidirect
151. C4×D4×C53C2×C4semidirect
277. C4⋊Dic53C2×D4semidirect
293. C2×#88322C2×D4semidirect
447. C22×C53#418semidirect
501. D42Dic53semidirect
543. C53#22423semidirect
566. C22×D4C2×Dic53semidirect
586. #127C2×Dic53semidirect
591. #121C2×Dic53semidirect
596. C4×D4C2×Dic53semidirect
926. C22#16810628semidirect

Maximal subgroups

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

subgroupindex
C2×#168106952
C2×#168106282
C22×#131331382
#202776442
#202756432
#202755402
#202751542
#202751442
#202750382
#202750332
#202747252
#202746462
#202745402
C2×D42×C532
#2242353