Finite Group Databasebeta

← #27384837

Subgroups — #27384837

Order 13568.

1630 conjugacy classes of subgroups.

The subgroup lattice has 818 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#117×D53C211yesmaximal, characteristic
2C2×#16810664C211yesmaximal, characteristic, complemented
3C2×#16810662C211yesmaximal, characteristic, complemented
4C2×#16810585C211yesmaximal, characteristic
5#380×D53C211yesmaximal, characteristic
6#20274916C211yesmaximal, characteristic, complemented
7#20274914C211yesmaximal, characteristic, complemented
8#20274912C211yesmaximal, characteristic, complemented
9#20274909C211yesmaximal, characteristic, complemented
10#20274906C211yesmaximal, characteristic, complemented
11#20274904C211yesmaximal, characteristic, complemented
12#20274901C211yesmaximal, characteristic, complemented
13#20274433C211yesmaximal, characteristic, complemented
14#20274433C211yesmaximal, characteristic, complemented
15C53×#1854C211yesmaximal, characteristic, complemented
16C23×C4×D53C2211yescharacteristic
17C22×#11719912C2211yescharacteristic
18C22×#11719912C2211yescharacteristic
19C2×#13133176C2211yescharacteristic
20C2×#13133175C2211yescharacteristic
21C2×#13133175C2211yescharacteristic
22C2×#13133174—21no—
23C2×#13133173—21no—
24#117×D53—24no—
25#117×D53—24no—
26C2×C4⋊C4×D53C2211yescharacteristic
27C2×C4⋊C4×D53C2211yescharacteristic
28C2×C4⋊C4×D53C2211yescharacteristic
29C2×C4⋊C4×D53C2211yescharacteristic
30C2×C22⋊C4×D53—21no—
31C2×C22⋊C4×D53—21no—
32C2×C42×D53—21no—
33#16810664—24no—
34#16810662—24no—
35C2×#13133151C2211yescharacteristic, complemented
36C2×#13133150C2211yescharacteristic, complemented
37C2×#13133150C2211yescharacteristic, complemented
38C2×#13133149C2211yescharacteristic, complemented
39C2×#13133148C2211yescharacteristic, complemented
40C2×#13133148C2211yescharacteristic, complemented
41#16810585C418yescomplemented
42C2×C22⋊#88322C2211yescharacteristic
43C2×#13133129C2211yescharacteristic
44C2×#13133129C2211yescharacteristic
45#16810483C2211yescharacteristic
46#16810482—21no—
47#16810481—21no—
48#16810480C2211yescharacteristic
49#16810480C2211yescharacteristic
50#95×D53—21no—
51#16810386C2211yescharacteristic, complemented
52#16810386C2211yescharacteristic, complemented
53#16810385C2211yescharacteristic, complemented
54#16810385C2211yescharacteristic, complemented
55#16810385C2211yescharacteristic, complemented
56#16810385C2211yescharacteristic, complemented
57C2×#117×C53C2211yescharacteristic
58C2×#107×C53C2211yescharacteristic, complemented
59C2×#106×C53C2211yescharacteristic, complemented
60C2×C22⋊C8×C53C2211yescharacteristic
61C53×#380C2211yescharacteristic
62C53×#340C2211yescharacteristic, complemented
63C53×#340C2211yescharacteristic, complemented
64C24×D53D411yescharacteristic
65C23×Dic53D411yescharacteristic
66C22×C4×D53—22no—
67C22×C4×D53—22no—
68C22×C4×D53—22no—
69C22×C4×D53—22no—
70C22×C4×D53—21no—
71C22×C4×D53—21no—
72C22×C4×D53—21no—
73C22×C4×D53—21no—
74C22×C4×D53C2×C414yes—
75C22×C4×D53D411yescharacteristic
76C22×C4×D53D411yescharacteristic
77C22×C4×D53Q814yes—
78C22×C4×D53C2311yescharacteristic
79C22×C4×D53C2311yescharacteristic
80C2×#11719912—22no—
81C2×#11719912—22no—
82C2×#11719912—22no—
83C2×#11719912—22no—
84C2×#11719912C2×C414yescomplemented
85C2×#11719912C2×C414yescomplemented
86C22×#88322C2311yescharacteristic
87C22×#88322C2311yescharacteristic
88#13133176—22no—
89#13133176—22no—
90#13133175—22no—
91#13133175—22no—
92#13133175D414yes—
93#13133175D414yes—
94#13133174—28no—
95#13133173—28no—
96C2×C4⋊Dic53C2311yescharacteristic
97C2×C4⋊Dic53C2311yescharacteristic
98C2×C4⋊Dic53C2311yescharacteristic
99C2×C4⋊Dic53C2311yescharacteristic
100C2×#11719919—21no—
101C2×#11719919—21no—
102C2×#11719919—21no—
103C2×#11719919—21no—
104C4⋊C4×D53—22no—
105C4⋊C4×D53—22no—
106C4⋊C4×D53—22no—
107C4⋊C4×D53—22no—
108C4⋊C4×D53—22no—
109C4⋊C4×D53—22no—
110C4⋊C4×D53—22no—
111C4⋊C4×D53—22no—
112C2×C22⋊Dic53—21no—
113C2×C22⋊Dic53—21no—
114C2×#11719921—21no—
115C2×#11719921—21no—
116C2×#11719921—21no—
117C2×#11719921—21no—
118C22⋊C4×D53—28no—
119C22⋊C4×D53—44no—
120C2×C4×Dic53—21no—
121C2×C4×Dic53—21no—
122C2×C4×Dic53—21no—
123C42×D53—28no—
124#13133151—22no—
125#13133150—22no—
126#13133150—22no—
127#13133149—22no—
128#13133148—22no—
129#13133148—22no—
130C22⋊#88322C2×C414yescomplemented
131#13133129C2×C414yescomplemented
132#13133129C2×C414yescomplemented
133#13133124—21no—
134#13133124—21no—
135#13133124—21no—
136C23×C4×C53C2311yescharacteristic
137C22×C8×C53C2311yescharacteristic
138C22×C8×C53C2311yescharacteristic
139#117×C53—22no—
140#117×C53—22no—
141C2×C4⋊C4×C53C2311yescharacteristic
142C2×C4⋊C4×C53C2311yescharacteristic
143C2×C4⋊C4×C53C2311yescharacteristic
144C2×C4⋊C4×C53C2311yescharacteristic
145C2×C22⋊C4×C53—21no—
146C2×C22⋊C4×C53—21no—
147C2×C42×C53—21no—
148#107×C53—22no—
149#106×C53—22no—
150C22⋊C8×C53C2×C414yescomplemented
151#95×C53—21no—
152C24×C53C2×D411yescharacteristic
153C23×D53—22no—
154C23×D53—22no—
155C23×D53—22no—
156C23×D53—22no—
157C23×D53—41no—
158C23×D53—41no—
159C23×D53C4⋊C414yes—
160C23×D53C2×D411yescharacteristic
161C23×D53C2×D411yescharacteristic
162C22×C4×C53—21no—
163C22×C4×C53—21no—
164C22×C4×C53—21no—
165C22×C4×C53—21no—
166C22×C4×C53—21no—
167C22×C4×C53—21no—
168C22×C4×C53—21no—
169C22×C4×C53—21no—
170C22×C4×C53C22×C412yes—
171C22×C4×C53C2×D411yescharacteristic
172C22×C4×C53C2×Q812yes—
173C22×C4×C53C2411yescharacteristic
174C22×Dic53—22no—
175C22×Dic53—22no—
176C22×Dic53—21no—
177C22×Dic53—21no—
178C22×Dic53—21no—
179C22×Dic53—21no—
180C22×Dic53C4⋊C414yes—
181C22×Dic53C2×D411yescharacteristic
182C22×Dic53C2×D411yescharacteristic
183C2×C4×D53—22no—
184C2×C4×D53—22no—
185C2×C4×D53—21no—
186C2×C4×D53—21no—
187C2×C4×D53—21no—
188C2×C4×D53—21no—
189C2×C4×D53—22no—
190C2×C4×D53—22no—
191C2×C4×D53—28no—
192C2×C4×D53—28no—
193C2×C4×D53—28no—
194C2×C4×D53—28no—
195C2×C4×D53—24no—
196C2×C4×D53—24no—
197C2×C4×D53—42no—
198C2×C4×D53—42no—
199C2×C4×D53—42no—
200C2×C4×D53—42no—
201C2×C4×D53—42no—
202C2×C4×D53—42no—
203C2×C4×D53—42no—
204C2×C4×D53—42no—
205C2×C4×D53—42no—
206C2×C4×D53—42no—
207C2×C4×D53C4⋊C414yes—
208C2×C4×D53C4⋊C414yes—
209C2×C4×D53C22×C412yes—
210C2×C4×D53C22×C412yes—
211C2×C4×D53C2×D412yes—
212C2×C4×D53C2×D412yes—
213C2×C4×D53C2×Q812yes—
214C2×C4×D53C2×Q812yes—
215C2×C4×D53#4112yes—
216C2×C4×D53#4112yes—
217C2×C8×C53—21no—
218C2×C8×C53—21no—
219C2×C8×C53—21no—
220C2×C8×C53—21no—
221C2×C8×C53C22×C412yes—
222C2×C8×C53C22×C412yes—
223C4⋊C4×C53—21no—
224C4⋊C4×C53—21no—
225C4⋊C4×C53—21no—
226C4⋊C4×C53—21no—
227C4⋊C4×C53—21no—
228C4⋊C4×C53—21no—
229C4⋊C4×C53C2×D412yes—
230C4⋊C4×C53C2×D412yes—
231C22⋊C4×C53—24no—
232C22⋊C4×C53—42no—
233C42×C53—24no—
234C22⋊Dic53—24no—
235C22⋊Dic53—42no—
236#11719921—24no—
237#11719921—24no—
238#11719921—42no—
239#11719921—42no—
240C4⋊Dic53—21no—
241C4⋊Dic53—21no—
242C4⋊Dic53—21no—
243C4⋊Dic53—21no—
244C4⋊Dic53—21no—
245C4⋊Dic53—21no—
246C4⋊Dic53C2×D412yes—
247C4⋊Dic53C2×D412yes—
248#11719919—24no—
249#11719919—24no—
250#11719919—42no—
251#11719919—42no—
252C4×Dic53—24no—
253C4×Dic53—24no—
254C4×Dic53—24no—
255C2×#88322—21no—
256C2×#88322—21no—
257C2×#88322—21no—
258C2×#88322—21no—
259C2×#88322C22×C412yes—
260C2×#88322C22×C412yes—
261#11719912—28no—
262#11719912—28no—
263C23×C53—21no—
264C23×C53—21no—
265C23×C53—21no—
266C23×C53—21no—
267C23×C53—21no—
268C23×C53—21no—
269C23×C53C2×C4⋊C412yes—
270C23×C53C22×D411yescharacteristic
271C22×D53—21no—
272C22×D53—21no—
273C22×D53—21no—
274C22×D53—21no—
275C22×D53—21no—
276C22×D53—21no—
277C22×D53—21no—
278C22×D53—21no—
279C22×D53—28no—
280C22×D53—28no—
281C22×D53—44no—
282C22×D53—44no—
283C22×D53—44no—
284C22×D53—44no—
285C22×D53—44no—
286C22×D53C2×C4⋊C412yes—
287C22×D53C2×C4⋊C412yes—
288C22×D53#12012yes—
289C22×D53#12312yes—
290C22×D53AGL(1,ℤ/8)12yes—
291C22×D53#13712yes—
292C2×C4×C53—21no—
293C2×C4×C53—21no—
294C2×C4×C53—22no—
295C2×C4×C53—22no—
296C2×C4×C53—22no—
297C2×C4×C53—22no—
298C2×C4×C53—22no—
299C2×C4×C53—22no—
300C2×C4×C53—41no—
301C2×C4×C53—41no—
302C2×C4×C53—41no—
303C2×C4×C53—41no—
304C2×C4×C53—41no—
305C2×C4×C53—41no—
306C2×C4×C53—41no—
307C2×C4×C53—41no—
308C2×C4×C53—41no—
309C2×C4×C53—41no—
310C2×C4×C53C2×C4⋊C412yes—
311C2×C4×C53C23×C411yescharacteristic
312C2×C4×C53C22×D411yescharacteristic
313C2×C4×C53C22×D411yescharacteristic
314C2×C4×C53C22×Q811yescharacteristic
315C2×C4×C53C2×#4111yescharacteristic
316C2×C4×C53C2×#4111yescharacteristic
317C2×Dic53—21no—
318C2×Dic53—21no—
319C2×Dic53—28no—
320C2×Dic53—22no—
321C2×Dic53—22no—
322C2×Dic53—41no—
323C2×Dic53—41no—
324C2×Dic53—41no—
325C2×Dic53—41no—
326C2×Dic53—41no—
327C2×Dic53—41no—
328C2×Dic53—41no—
329C2×Dic53—41no—
330C2×Dic53—41no—
331C2×Dic53—41no—
332C2×Dic53C2×C4⋊C412yes—
333C2×Dic53C2×C4⋊C412yes—
334C2×Dic53#12012yes—
335C2×Dic53#12312yes—
336C4×D53—28no—
337C4×D53—22no—
338C4×D53—22no—
339C4×D53—22no—
340C4×D53—22no—
341C4×D53—28no—
342C4×D53—48no—
343C4×D53—48no—
344C4×D53—84no—
345C4×D53—84no—
346C4×D53C4×D414yes—
347C4×D53C4×D414yes—
348C4×D53C22⋊Q814yes—
349C4×D53C22⋊Q814yes—
350C8×C53—22no—
351C8×C53—22no—
352#88322—22no—
353#88322—22no—
354#20846—531nomaximal, Sylow
355C22×C53—22no—
356C22×C53—22no—
357C22×C53—22no—
358C22×C53—41no—
359C22×C53—41no—
360C22×C53—41no—
361C22×C53—41no—
362C22×C53C22×C4⋊C411yescharacteristic
363C22×C53C2×#12011yescharacteristic
364C22×C53C2×#12311yescharacteristic
365C22×C53C2×AGL(1,ℤ/8)11yescharacteristic
366C22×C53C2×#13711yescharacteristic
367C22×C53#57511yescharacteristic
368C22×C53#57511yescharacteristic
369C2×D53—22no—
370C2×D53—22no—
371C2×D53—22no—
372C2×D53—22no—
373C2×D53—22no—
374C2×D53—22no—
375C2×D53—22no—
376C2×D53—22no—
377C2×D53—22no—
378C2×D53—22no—
379C2×D53—22no—
380C2×D53—22no—
381C2×D53—416no—
382C2×D53#38514yes—
383C2×D53#42814yescomplemented
384C4×C53—22no—
385C4×C53—42no—
386C4×C53—42no—
387C4×C53—81no—
388C4×C53—81no—
389C4×C53C2×C4×D411yescharacteristic
390C4×C53C2×C4×D411yescharacteristic
391C4×C53C2×C22⋊Q811yescharacteristic
392C4×C53C2×C22⋊Q811yescharacteristic
393Dic53—22no—
394Dic53—42no—
395Dic53—42no—
396Dic53—81no—
397Dic53—81no—
398Dic53#38514yes—
399C22×#117—531no—
400C2×#428—531no—
401C2×#428—531no—
402C2×#407—531no—
403C2×#380—531no—
404#1854—531no—
405#1854—531no—
406#1854—531no—
407#1854D5311yescharacteristic, complemented
408#1853—531no—
409#1853—531no—
410#1852—531no—
411#1852—531no—
412#1736—531no—
413#1736—531no—
414C2×C53—42no—
415C2×C53C2×#38511yescharacteristic
416C2×C53C2×#42811yescharacteristic
417C2×C53#291111yescharacteristic
418C2×C53#300611yescharacteristic
419C2×C53#300711yescharacteristic
420C2×C53#309411yescharacteristic
421C2×C53#309511yescharacteristic
422D53—24no—
423D53—24no—
424C24×C4—531no—
425C22×M16—531no—
426C22×M16—531no—
427C2×#117—531no—
428C2×#117—531no—
429C2×#117—531no—
430C2×#117—1061no—
431C2×#117—1061no—
432C2×#117—1064no—
433C2×#117—1064no—
434C2×#117C2×D5311yescharacteristic
435C22×C4⋊C4—531no—
436C22×C4⋊C4—531no—
437C22×C4⋊C4—531no—
438C22×C4⋊C4—531no—
439C22×C22⋊C4—1061no—
440C22×C22⋊C4—1061no—
441C22×C42—1061no—
442#428—1064no—
443#428—1064no—
444C2×#107—531no—
445C2×#107—531no—
446C2×#107—531no—
447C2×#107C2×D5311yescharacteristic, complemented
448C2×#106—531no—
449C2×#106—531no—
450C2×#106—531no—
451C2×#106C2×D5311yescharacteristic, complemented
452#407—538no—
453C2×C22⋊C8—531no—
454C2×C22⋊C8—531no—
455C2×C22⋊C8—531no—
456C2×C22⋊C8C2×D5311yescharacteristic
457#380—531no—
458#380—531no—
459#380—531no—
460#380—1061no—
461#380—1061no—
462#380C2×D5311yescharacteristic
463C2×#95—1061no—
464#340—531no—
465#340—531no—
466#340—531no—
467#340—531no—
468#340—531no—
469#340—531no—
470#340C2×D5311yescharacteristic, complemented
471#340C2×D5311yescharacteristic, complemented
472C53#2084611yescharacteristic, complemented, Sylow
473C25—531no—
474C23×C4—531no—
475C23×C4—531no—
476C23×C4—534no—
477C23×C4—531no—
478C23×C4—531no—
479C23×C4—534no—
480C23×C4—531no—
481C23×C4—1062no—
482C23×C4—1062no—
483C23×C4—1062no—
484C23×C4—1062no—
485C23×C4—1061no—
486C23×C4—1061no—
487C23×C4—1061no—
488C23×C4—1061no—
489C23×C4C22×D5311yescharacteristic
490C2×M16—534no—
491C2×M16—534no—
492C2×M16—1062no—
493C2×M16—1062no—
494C2×M16—1062no—
495C2×M16—1062no—
496C22×C8—531no—
497C22×C8—531no—
498C22×C8C22×D5311yescharacteristic
499C22×C8C22×D5311yescharacteristic
500#117—22no—
501#117—22no—
502#117—534no—
503#117—534no—
504#117—1068no—
505#117—1068no—
506#117—1062no—
507#117—1062no—
508#117—1062no—
509#117—1062no—
510C2×C4⋊C4—531no—
511C2×C4⋊C4—531no—
512C2×C4⋊C4—531no—
513C2×C4⋊C4—531no—
514C2×C4⋊C4—1062no—
515C2×C4⋊C4—1062no—
516C2×C4⋊C4—1062no—
517C2×C4⋊C4—1062no—
518C2×C4⋊C4—1062no—
519C2×C4⋊C4—1062no—
520C2×C4⋊C4—1061no—
521C2×C4⋊C4—1061no—
522C2×C4⋊C4—1062no—
523C2×C4⋊C4—1062no—
524C2×C4⋊C4—1061no—
525C2×C4⋊C4—1061no—
526C2×C4⋊C4C22×D5311yescharacteristic
527C2×C4⋊C4C22×D5311yescharacteristic
528C2×C4⋊C4C22×D5311yescharacteristic
529C2×C4⋊C4C22×D5311yescharacteristic
530C2×C22⋊C4—21no—
531C2×C22⋊C4—21no—
532C2×C22⋊C4—1068no—
533C2×C22⋊C4—1061no—
534C2×C22⋊C4—1061no—
535C2×C22⋊C4—1061no—
536C2×C22⋊C4—1061no—
537C2×C22⋊C4—1061no—
538C2×C22⋊C4—1061no—
539C2×C22⋊C4—2124no—
540C2×C42—21no—
541C2×C42—1068no—
542C2×C42—1061no—
543C2×C42—1061no—
544C2×C42—1061no—
545#107—22no—
546#107—1062no—
547#107—1062no—
548#107—1062no—
549#106—22no—
550#106—1062no—
551#106—1062no—
552#106—1062no—
553C22⋊C8—534no—
554C22⋊C8—534no—
555C22⋊C8—534no—
556C22⋊C8C4×D5314yescomplemented
557#95—21no—
558#95—1061no—
559#95—1061no—
560#95—1061no—
561C24—531no—
562C24—531no—
563C24—534no—
564C24—1062no—
565C24—1062no—
566C24—1062no—
567C24—1062no—
568C24—2121no—
569C24—2121no—
570C24D4×D5311yescharacteristic
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—531no—
580C22×C4—532no—
581C22×C4—532no—
582C22×C4—532no—
583C22×C4—532no—
584C22×C4—532no—
585C22×C4—532no—
586C22×C4—534no—
587C22×C4—531no—
588C22×C4—534no—
589C22×C4—534no—
590C22×C4—532no—
591C22×C4—532no—
592C22×C4—1062no—
593C22×C4—1062no—
594C22×C4—1068no—
595C22×C4—1068no—
596C22×C4—1068no—
597C22×C4—1068no—
598C22×C4—1062no—
599C22×C4—1062no—
600C22×C4—1064no—
601C22×C4—1064no—
602C22×C4—1062no—
603C22×C4—1062no—
604C22×C4—1061no—
605C22×C4—1061no—
606C22×C4—1061no—
607C22×C4—1061no—
608C22×C4—1061no—
609C22×C4—1061no—
610C22×C4—1061no—
611C22×C4—1061no—
612C22×C4—2122no—
613C22×C4—2122no—
614C22×C4—2122no—
615C22×C4—2122no—
616C22×C4—2122no—
617C22×C4—2122no—
618C22×C4—2122no—
619C22×C4—2122no—
620C22×C4—2122no—
621C22×C4—2122no—
622C22×C4C2×C4×D5312yes—
623C22×C4D4×D5311yescharacteristic
624C22×C4Q8×D5312yes—
625C22×C4C23×D5311yescharacteristic
626M16—1068no—
627M16—1068no—
628C2×C8—21no—
629C2×C8—21no—
630C2×C8—21no—
631C2×C8—21no—
632C2×C8—532no—
633C2×C8—532no—
634C2×C8—1061no—
635C2×C8—1061no—
636C2×C8—1061no—
637C2×C8—1061no—
638C2×C8C2×C4×D5312yes—
639C2×C8C2×C4×D5312yes—
640C4⋊C4—21no—
641C4⋊C4—21no—
642C4⋊C4—21no—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—21no—
646C4⋊C4—532no—
647C4⋊C4—532no—
648C4⋊C4—1064no—
649C4⋊C4—1064no—
650C4⋊C4—1061no—
651C4⋊C4—1061no—
652C4⋊C4—1061no—
653C4⋊C4—1061no—
654C4⋊C4—1061no—
655C4⋊C4—1061no—
656C4⋊C4—2122no—
657C4⋊C4—2122no—
658C4⋊C4D4×D5312yes—
659C4⋊C4D4×D5312yes—
660C22⋊C4—24no—
661C22⋊C4—42no—
662C22⋊C4—1064no—
663C22⋊C4—1064no—
664C22⋊C4—1064no—
665C22⋊C4—2122no—
666C22⋊C4—2122no—
667C22⋊C4—2122no—
668C42—24no—
669C42—1064no—
670C42—1064no—
671C42—1064no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—21no—
677C23—21no—
678C23—532no—
679C23—532no—
680C23—532no—
681C23—532no—
682C23—532no—
683C23—532no—
684C23—1068no—
685C23—1068no—
686C23—1061no—
687C23—1061no—
688C23—1061no—
689C23—1061no—
690C23—1061no—
691C23—1061no—
692C23—1061no—
693C23—1061no—
694C23—2124no—
695C23—2124no—
696C23—2124no—
697C23—2124no—
698C23—2124no—
699C23C4⋊C4×D5312yes—
700C23C2×D4×D5311yescharacteristic
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—532no—
720C2×C4—532no—
721C2×C4—532no—
722C2×C4—534no—
723C2×C4—534no—
724C2×C4—534no—
725C2×C4—534no—
726C2×C4—532no—
727C2×C4—1068no—
728C2×C4—1068no—
729C2×C4—1068no—
730C2×C4—1061no—
731C2×C4—1061no—
732C2×C4—1062no—
733C2×C4—1062no—
734C2×C4—1062no—
735C2×C4—1062no—
736C2×C4—1062no—
737C2×C4—1062no—
738C2×C4—4244no—
739C2×C4—4244no—
740C2×C4—2128no—
741C2×C4—2128no—
742C2×C4—2121no—
743C2×C4—2121no—
744C2×C4—2121no—
745C2×C4—2121no—
746C2×C4—2121no—
747C2×C4—2121no—
748C2×C4—2121no—
749C2×C4—2121no—
750C2×C4—2121no—
751C2×C4—2121no—
752C2×C4C4⋊C4×D5312yes—
753C2×C4C22×C4×D5311yescharacteristic
754C2×C4C2×D4×D5311yescharacteristic
755C2×C4C2×D4×D5311yescharacteristic
756C2×C4C2×Q8×D5311yescharacteristic
757C2×C4#41×D5311yescharacteristic
758C2×C4#41×D5311yescharacteristic
759C8—22no—
760C8—22no—
761C8—1062no—
762C8—1062no—
763C22—22no—
764C22—22no—
765C22—22no—
766C22—41no—
767C22—41no—
768C22—41no—
769C22—41no—
770C22—534no—
771C22—534no—
772C22—1062no—
773C22—1062no—
774C22—1062no—
775C22—1062no—
776C22—1062no—
777C22—1062no—
778C22—1062no—
779C22—1062no—
780C22—1062no—
781C22—1062no—
782C22—1062no—
783C22—1062no—
784C22—21216no—
785C22C2×C4⋊C4×D5311yescharacteristic
786C22#120×D5311yescharacteristic
787C22#123×D5311yescharacteristic
788C22AGL(1,ℤ/8)×D5311yescharacteristic
789C22#137×D5311yescharacteristic
790C22#1681142011yescharacteristic
791C22#1681142011yescharacteristic
792C4—22no—
793C4—42no—
794C4—42no—
795C4—81no—
796C4—81no—
797C4—534no—
798C4—1062no—
799C4—4241no—
800C4—4241no—
801C4—2122no—
802C4—2122no—
803C4C4×D4×D5311yescharacteristic
804C4C4×D4×D5311yescharacteristic
805C4C22⋊Q8×D5311yescharacteristic
806C4C22⋊Q8×D5311yescharacteristic
807C2—42no—
808C2—1064no—
809C2—1064no—
810C2#385×D5311yescharacteristic
811C2#428×D5311yescharacteristic
812C2#2028330311yescharacteristic
813C2#2028396411yescharacteristic
814C2#2028397211yescharacteristic
815C2#2028465411yescharacteristic
816C2#2028466211yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutatorC2×C4×C53C23×C4
FrattiniC22×C4C23×D53
FittingC53×#1854C2
socleC23×C53C22×D4
prime radicalC24×D53D4
cosocleC22×C4×C53C24
hypercenter#1854D53
hypocenterC53#20846
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1854

Complements

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

NH ≅ G/Ntype
2. C2×#16810664C2semidirect
3. C2×#16810662C2semidirect
6. #20274916C2semidirect
7. #20274914C2semidirect
8. #20274912C2semidirect
9. #20274909C2semidirect
10. #20274906C2semidirect
11. #20274904C2semidirect
12. #20274901C2semidirect
13. #20274433C2semidirect
14. #20274433C2semidirect
15. C53×#1854C2semidirect
35. C2×#13133151C22semidirect
36. C2×#13133150C22semidirect
37. C2×#13133150C22semidirect
38. C2×#13133149C22semidirect
39. C2×#13133148C22semidirect
40. C2×#13133148C22semidirect
41. #16810585C4semidirect
51. #16810386C22semidirect
52. #16810386C22semidirect
53. #16810385C22semidirect
54. #16810385C22semidirect
55. #16810385C22semidirect
56. #16810385C22semidirect
58. C2×#107×C53C22semidirect
59. C2×#106×C53C22semidirect
62. C53×#340C22semidirect
63. C53×#340C22semidirect
84. C2×#11719912C2×C4semidirect
85. C2×#11719912C2×C4semidirect
130. C22⋊#88322C2×C4semidirect
131. #13133129C2×C4semidirect
132. #13133129C2×C4semidirect
150. C22⋊C8×C53C2×C4semidirect
383. C2×D53#428semidirect
407. #1854D53semidirect
447. C2×#107C2×D53semidirect
451. C2×#106C2×D53semidirect
470. #340C2×D53semidirect
471. #340C2×D53semidirect
472. C53#20846semidirect
556. C22⋊C8C4×D53semidirect

Maximal subgroups

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

subgroupindex
C2×#117×D532
C2×#168106642
C2×#168106622
C2×#168105852
#380×D532
#202749162
#202749142
#202749122
#202749092
#202749062
#202749042
#202749012
#202744332
C53×#18542
#2084653