Finite Group Databasebeta

← #27399617

Subgroups — #27399617

Order 13568.

1530 conjugacy classes of subgroups.

The subgroup lattice has 882 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16810695C211yesmaximal, characteristic, complemented
2C2×#16810624C211yesmaximal, characteristic, complemented
3C2×#16810619C211yesmaximal, 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#20274730C211yesmaximal, characteristic, complemented
12#20274655C211yesmaximal, characteristic, complemented
13#20274655C211yesmaximal, characteristic, complemented
14#20274545C211yesmaximal, characteristic, complemented
15C2×C53×#550C211yesmaximal, characteristic
16C22×#11719917C2211yescharacteristic
17C23×#88322C2211yescharacteristic
18C2×#13133176C2211yescharacteristic
19C22×C4⋊Dic53C2211yescharacteristic
20#16810695—24no—
21C2×C4⋊#88322C2211yescharacteristic
22#16810624—24no—
23#16810619—24no—
24C2×#13133141C2211yescharacteristic
25C2×#13133141C2211yescharacteristic
26C2×#13133141C2211yescharacteristic
27C2×#13133141C2211yescharacteristic
28C2×#13133138C2211yescharacteristic
29C2×#13133138C2211yescharacteristic
30C2×#13133138C2211yescharacteristic
31C2×#13133138C2211yescharacteristic
32C2×#13133138C2211yescharacteristic
33C2×#13133138C2211yescharacteristic
34C2×#13133138C2211yescharacteristic
35C2×#13133138C2211yescharacteristic
36C2×C22⋊#88322C2211yescharacteristic
37C2×C22⋊#88322C2211yescharacteristic
38C2×#13133128C2211yescharacteristic
39#16810516—21no—
40#16810509—21no—
41#16810503—21no—
42#16810489C2211yescharacteristic
43#16810483C2211yescharacteristic
44#16810483C2211yescharacteristic
45C4×C4⋊Dic53C2211yescharacteristic
46C22⋊C4×Dic53—21no—
47#16810385C2211yescharacteristic
48#16810385C2211yescharacteristic
49#16810385C2211yescharacteristic
50#16810385C2211yescharacteristic
51C22×#41×C53C2211yescharacteristic
52C22×#41×C53C2211yescharacteristic
53C53×#550—24no—
54C53×#550C418yescomplemented
55C2×#127×C53—21no—
56C2×#127×C53C2211yescharacteristic
57C2×#121×C53—21no—
58C2×#121×C53—21no—
59C2×#121×C53C2211yescharacteristic
60C2×#121×C53C2211yescharacteristic
61C2×C4×Q8×C53C2211yescharacteristic
62C2×C4×D4×C53—21no—
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#13133141—22no—
91#13133141—22no—
92#13133141—22no—
93#13133141D414yescomplemented
94#13133138—22no—
95#13133138—22no—
96#13133138—22no—
97#13133138—22no—
98#13133138—41no—
99#13133138—41no—
100#13133138—41no—
101#13133138—41no—
102C22⋊#88322—22no—
103C22⋊#88322—22no—
104#13133128—22no—
105#13133124—21no—
106#13133124—21no—
107#13133124—21no—
108#13133124—21no—
109#13133124—21no—
110C2×#41×C53—22no—
111C2×#41×C53—22no—
112C2×#41×C53—22no—
113C2×#41×C53—22no—
114C2×#41×C53—22no—
115C2×#41×C53—22no—
116C2×#41×C53—41no—
117C2×#41×C53—41no—
118C2×#41×C53—41no—
119C2×#41×C53—41no—
120C2×#41×C53C2×C414yes—
121C2×#41×C53C2×C414yescomplemented
122C22×Q8×C53C2311yescharacteristic
123C22×D4×C53—21no—
124C22×D4×C53—21no—
125C22×D4×C53—21no—
126C22×D4×C53—21no—
127C22×D4×C53—21no—
128C22×D4×C53—21no—
129C22×D4×C53D411yescharacteristic
130C22×D4×C53C2311yescharacteristic
131C22×D4×C53C2311yescharacteristic
132C23×C4×C53—21no—
133C23×C4×C53—21no—
134C23×C4×C53C2311yescharacteristic
135C23×C4×C53C2311yescharacteristic
136#127×C53—22no—
137#127×C53—28no—
138#127×C53C2×C414yescomplemented
139#121×C53—28no—
140#121×C53—28no—
141#121×C53—22no—
142#121×C53—22no—
143#121×C53C2×C414yes—
144#121×C53C2×C414yescomplemented
145C4×Q8×C53—22no—
146C4×Q8×C53C2×C414yescomplemented
147C4×D4×C53—28no—
148C4×D4×C53C2×C414yes—
149C4×D4×C53D414yes—
150C2×C4⋊C4×C53—21no—
151C2×C4⋊C4×C53D411yescharacteristic
152C2×C4⋊C4×C53C2311yescharacteristic
153C2×C22⋊C4×C53—21no—
154C2×C22⋊C4×C53—21no—
155C2×C22⋊C4×C53D411yescharacteristic
156C2×C22⋊C4×C53D411yescharacteristic
157C2×C42×C53—21no—
158C2×C42×C53C2311yescharacteristic
159C24×C53—21no—
160C24×C53—21no—
161C24×C53C2×D411yescharacteristic
162C24×C53C2×D411yescharacteristic
163#41×C53—28no—
164#41×C53—28no—
165#41×C53—44no—
166#41×C53—44no—
167#41×C53—44no—
168#41×C53—44no—
169#41×C53—44no—
170#41×C53—44no—
171C2×Q8×C53—21no—
172C2×Q8×C53—21no—
173C2×Q8×C53—21no—
174C2×Q8×C53C22×C412yes—
175C2×Q8×C53C2×D412yes—
176C2×Q8×C53#4112yes—
177C2×D4×C53—24no—
178C2×D4×C53—24no—
179C2×D4×C53—24no—
180C2×D4×C53—24no—
181C2×D4×C53—24no—
182C2×D4×C53—24no—
183C2×D4×C53—21no—
184C2×D4×C53—21no—
185C2×D4×C53—21no—
186C2×D4×C53—21no—
187C2×D4×C53—21no—
188C2×D4×C53—21no—
189C2×D4×C53—21no—
190C2×D4×C53—21no—
191C2×D4×C53—21no—
192C2×D4×C53—21no—
193C2×D4×C53—41no—
194C2×D4×C53—41no—
195C2×D4×C53—42no—
196C2×D4×C53—42no—
197C2×D4×C53—42no—
198C2×D4×C53—42no—
199C2×D4×C53—42no—
200C2×D4×C53—42no—
201C2×D4×C53—81no—
202C2×D4×C53—81no—
203C2×D4×C53—81no—
204C2×D4×C53—81no—
205C2×D4×C53—81no—
206C2×D4×C53—81no—
207C2×D4×C53C22⋊C414yes—
208C2×D4×C53C22×C412yes—
209C2×D4×C53C22×C412yes—
210C22×C4×C53—21no—
211C22×C4×C53—21no—
212C22×C4×C53—21no—
213C22×C4×C53—21no—
214C22×C4×C53—21no—
215C22×C4×C53—21no—
216C22×C4×C53—21no—
217C22×C4×C53—21no—
218C22×C4×C53—21no—
219C22×C4×C53—21no—
220C22×C4×C53—24no—
221C22×C4×C53—24no—
222C22×C4×C53—42no—
223C22×C4×C53—42no—
224C22×C4×C53—42no—
225C22×C4×C53—42no—
226C22×C4×C53C22×C412yes—
227C22×C4×C53C22×C412yes—
228C22×C4×C53C2×D411yescharacteristic
229C22×C4×C53C2×D411yescharacteristic
230C22×C4×C53C2×D411yescharacteristic
231C22×C4×C53C2×D411yescharacteristic
232C22×C4×C53C2×D412yes—
233C22×C4×C53C2×D412yes—
234C22×C4×C53C2411yescharacteristic
235C22×Dic53—21no—
236C22×Dic53—21no—
237C22×Dic53—21no—
238C22×Dic53—21no—
239C22×Dic53—42no—
240C22×Dic53—42no—
241C22×Dic53—81no—
242C4⋊C4×C53—24no—
243C4⋊C4×C53—21no—
244C4⋊C4×C53C22⋊C414yes—
245C4⋊C4×C53C22×C412yes—
246C22⋊C4×C53—24no—
247C22⋊C4×C53—24no—
248C22⋊C4×C53C22⋊C414yes—
249C22⋊C4×C53C22⋊C414yes—
250C42×C53—24no—
251C42×C53C22×C412yes—
252C42×C53C2×D412yes—
253C22⋊Dic53—42no—
254C22⋊Dic53—42no—
255C22⋊Dic53—81no—
256C4⋊Dic53—21no—
257C4⋊Dic53—21no—
258C4⋊Dic53—21no—
259C4⋊Dic53—21no—
260C4⋊Dic53—21no—
261C4⋊Dic53—21no—
262C4⋊Dic53—21no—
263C4⋊Dic53—42no—
264C4⋊Dic53C2×D412yes—
265C4×Dic53—42no—
266C4×Dic53—81no—
267#11719917—44no—
268C2×#88322—21no—
269C2×#88322—21no—
270C2×#88322—21no—
271C2×#88322—21no—
272C2×#88322—21no—
273C2×#88322—21no—
274C2×#88322—21no—
275C2×#88322—21no—
276C2×#88322—21no—
277C2×#88322—21no—
278C2×#88322—21no—
279C2×#88322—44no—
280C2×#88322C2×D412yes—
281C23×C53—21no—
282C23×C53—21no—
283C23×C53—21no—
284C23×C53—21no—
285C23×C53—21no—
286C23×C53—21no—
287C23×C53—21no—
288C23×C53—21no—
289C23×C53—21no—
290C23×C53—21no—
291C23×C53—21no—
292C23×C53—21no—
293C23×C53—22no—
294C23×C53—22no—
295C23×C53—41no—
296C23×C53—41no—
297C23×C53—41no—
298C23×C53—41no—
299C23×C53—41no—
300C23×C53—41no—
301C23×C53—41no—
302C23×C53—41no—
303C23×C53—41no—
304C23×C53—41no—
305C23×C53—41no—
306C23×C53—41no—
307C23×C53C2×C22⋊C412yes—
308C23×C53C2×C22⋊C412yes—
309C23×C53C22×D411yescharacteristic
310Q8×C53—22no—
311Q8×C53—22no—
312Q8×C53—22no—
313Q8×C53C4×D414yes—
314D4×C53—22no—
315D4×C53—22no—
316D4×C53—22no—
317D4×C53—22no—
318D4×C53—44no—
319D4×C53—48no—
320D4×C53—48no—
321D4×C53—48no—
322D4×C53—41no—
323D4×C53—41no—
324D4×C53—41no—
325D4×C53—41no—
326D4×C53—84no—
327D4×C53—84no—
328D4×C53—84no—
329C2×C4×C53—22no—
330C2×C4×C53—21no—
331C2×C4×C53—21no—
332C2×C4×C53—22no—
333C2×C4×C53—21no—
334C2×C4×C53—21no—
335C2×C4×C53—22no—
336C2×C4×C53—21no—
337C2×C4×C53—21no—
338C2×C4×C53—21no—
339C2×C4×C53—21no—
340C2×C4×C53—22no—
341C2×C4×C53—22no—
342C2×C4×C53—22no—
343C2×C4×C53—22no—
344C2×C4×C53—22no—
345C2×C4×C53—22no—
346C2×C4×C53—22no—
347C2×C4×C53—22no—
348C2×C4×C53—22no—
349C2×C4×C53—48no—
350C2×C4×C53—48no—
351C2×C4×C53—41no—
352C2×C4×C53—41no—
353C2×C4×C53C2×C22⋊C412yes—
354C2×C4×C53C2×C22⋊C412yes—
355C2×C4×C53C2×C22⋊C412yes—
356C2×C4×C53C2×C22⋊C412yes—
357C2×C4×C53C23×C411yescharacteristic
358C2×C4×C53C22×D411yescharacteristic
359C2×C4×C53C22×D411yescharacteristic
360C2×C4×C53C2×#4111yescharacteristic
361C2×C4×C53H(5,𝔽2)11yescharacteristic
362C2×C4×C53H(5,𝔽2)11yescharacteristic
363C2×Dic53—22no—
364C2×Dic53—41no—
365C2×Dic53—41no—
366C2×Dic53—41no—
367C2×Dic53—41no—
368C2×Dic53—41no—
369C2×Dic53—41no—
370C2×Dic53—41no—
371C2×Dic53—41no—
372C2×Dic53—41no—
373C2×Dic53—41no—
374C2×Dic53—41no—
375C2×Dic53—84no—
376#88322—22no—
377#88322—41no—
378#88322—41no—
379#88322—41no—
380#22422—531nomaximal, Sylow
381C22×C53—22no—
382C22×C53—22no—
383C22×C53—22no—
384C22×C53—22no—
385C22×C53—22no—
386C22×C53—22no—
387C22×C53—41no—
388C22×C53—41no—
389C22×C53—41no—
390C22×C53—41no—
391C22×C53—41no—
392C22×C53—41no—
393C22×C53—41no—
394C22×C53—41no—
395C22×C53—42no—
396C22×C53—42no—
397C22×C53—42no—
398C22×C53—42no—
399C22×C53—42no—
400C22×C53—42no—
401C22×C53—81no—
402C22×C53—81no—
403C22×C53—81no—
404C22×C53—81no—
405C22×C53—81no—
406C22×C53—81no—
407C22×C53—81no—
408C22×C53—81no—
409C22×C53C22×C22⋊C411yescharacteristic
410C22×C53D4211yescharacteristic
411C22×C53#54611yescharacteristic
412C22×C53#57511yescharacteristic
413C22×C53#57511yescharacteristic
414C22×C53#57611yescharacteristic
415C22×C53#57711yescharacteristic
416C4×C53—22no—
417C4×C53—22no—
418C4×C53—24no—
419C4×C53—22no—
420C4×C53—22no—
421C4×C53—42no—
422C4×C53C2×C4×D411yescharacteristic
423C4×C53#51811yescharacteristic
424C4×C53D4211yescharacteristic
425C4×C53#54611yescharacteristic
426Dic53—42no—
427Dic53—81no—
428Dic53—81no—
429Dic53—81no—
430C2×#550D5311yescharacteristic
431C2×#435—531no—
432C2×#417—531no—
433C2×#416—531no—
434#2352—531no—
435#1982—531no—
436#1961—531no—
437#1895—531no—
438#1893—531no—
439#1875—531no—
440#1874—531no—
441#1805—531no—
442#1788—531no—
443#1788—531no—
444#1763—531no—
445C2×C53—42no—
446C2×C53—42no—
447C2×C53—82no—
448C2×C53—82no—
449C2×C53D4×C22⋊C411yescharacteristic
450C2×C53#289611yescharacteristic
451C2×C53#289711yescharacteristic
452C2×C53#326811yescharacteristic
453C2×C53#327111yescharacteristic
454C2×C53#330911yescharacteristic
455C2×C53#331711yescharacteristic
456C22×#41C2×D5311yescharacteristic
457C22×#41C2×D5311yescharacteristic
458C22×M16—531no—
459C23×C8—531no—
460#550—24no—
461#550Dic5318yescomplemented
462C2×#127—21no—
463C2×#127C2×D5311yescharacteristic
464C2×#121—21no—
465C2×#121—21no—
466C2×#121C2×D5311yescharacteristic
467C2×#121C2×D5311yescharacteristic
468C2×C4×Q8C2×D5311yescharacteristic
469C2×C4×D4—21no—
470C2×C4×D4C2×D5311yescharacteristic
471C2×#117—531no—
472C22×C4⋊C4—531no—
473#435—1064no—
474C2×C4⋊C8—531no—
475#417—1064no—
476#416—1064no—
477C2×#103—531no—
478C2×#103—531no—
479C2×#103—531no—
480C2×#103—531no—
481C2×#102—531no—
482C2×#102—531no—
483C2×#102—531no—
484C2×#102—531no—
485C2×#102—531no—
486C2×#102—531no—
487C2×#102—531no—
488C2×#102—531no—
489C2×C22⋊C8—531no—
490C2×C22⋊C8—531no—
491C2×#97—531no—
492#388—1061no—
493#387—1061no—
494#386—1061no—
495#382—531no—
496#380—531no—
497#380—531no—
498C4×C4⋊C4—531no—
499C4×C22⋊C4—1061no—
500#340—531no—
501#340—531no—
502#340—531no—
503#340—531no—
504C53#2242211yescharacteristic, complemented, Sylow
505C2×#41—22no—
506C2×#41—22no—
507C2×#41—22no—
508C2×#41—22no—
509C2×#41—22no—
510C2×#41—22no—
511C2×#41—41no—
512C2×#41—41no—
513C2×#41—41no—
514C2×#41—41no—
515C2×#41C2×Dic5314yes—
516C2×#41C2×Dic5314yescomplemented
517C22×Q8C22×D5311yescharacteristic
518C22×D4—21no—
519C22×D4—21no—
520C22×D4—21no—
521C22×D4—21no—
522C22×D4—21no—
523C22×D4—21no—
524C22×D4C22⋊D5311yescharacteristic
525C22×D4C22×D5311yescharacteristic
526C22×D4C22×D5311yescharacteristic
527C23×C4—21no—
528C23×C4—21no—
529C23×C4—1061no—
530C23×C4C22×D5311yescharacteristic
531C23×C4C22×D5311yescharacteristic
532C2×M16—1062no—
533C2×M16—1062no—
534C2×M16—2121no—
535C22×C8—531no—
536C22×C8—531no—
537C22×C8—531no—
538C22×C8—531no—
539C22×C8—1062no—
540C22×C8—1062no—
541C22×C8—2121no—
542#127—28no—
543#127—22no—
544#127C2×Dic5314yescomplemented
545#121—22no—
546#121—22no—
547#121—28no—
548#121—28no—
549#121C2×Dic5314yes—
550#121C2×Dic5314yescomplemented
551C4×Q8—22no—
552C4×Q8C2×Dic5314yescomplemented
553C4×D4—28no—
554C4×D4C2×Dic5314yes—
555C4×D4C22⋊D5314yes—
556#117—1062no—
557#117—2121no—
558C2×C4⋊C4—21no—
559C2×C4⋊C4—531no—
560C2×C4⋊C4—531no—
561C2×C4⋊C4—531no—
562C2×C4⋊C4—531no—
563C2×C4⋊C4—1062no—
564C2×C4⋊C4—1061no—
565C2×C4⋊C4—2121no—
566C2×C4⋊C4C22⋊D5311yescharacteristic
567C2×C4⋊C4C22×D5311yescharacteristic
568C2×C22⋊C4—21no—
569C2×C22⋊C4—21no—
570C2×C22⋊C4—1061no—
571C2×C22⋊C4—1061no—
572C2×C22⋊C4—1061no—
573C2×C22⋊C4C22⋊D5311yescharacteristic
574C2×C22⋊C4C22⋊D5311yescharacteristic
575C2×C42—21no—
576C2×C42—1061no—
577C2×C42—1061no—
578C2×C42C22×D5311yescharacteristic
579C4⋊C8—1062no—
580#103—534no—
581#103—1062no—
582#103—1062no—
583#103—1062no—
584#102—1062no—
585#102—1062no—
586#102—1062no—
587#102—1062no—
588#102—2121no—
589#102—2121no—
590#102—2121no—
591#102—2121no—
592C22⋊C8—1062no—
593C22⋊C8—1062no—
594#97—1062no—
595#95—1061no—
596#95—1061no—
597#95—1061no—
598#95—1061no—
599#95—1061no—
600C24—21no—
601C24—21no—
602C24C2×C22⋊D5311yescharacteristic
603C24C2×C22⋊D5311yescharacteristic
604#41—28no—
605#41—28no—
606#41—44no—
607#41—44no—
608#41—44no—
609#41—44no—
610#41—44no—
611#41—44no—
612C2×Q8—21no—
613C2×Q8—21no—
614C2×Q8—21no—
615C2×Q8D4×D5312yes—
616C2×Q8#1171994712yes—
617C2×Q8C22×Dic5312yes—
618C2×D4—24no—
619C2×D4—24no—
620C2×D4—24no—
621C2×D4—24no—
622C2×D4—24no—
623C2×D4—24no—
624C2×D4—21no—
625C2×D4—21no—
626C2×D4—21no—
627C2×D4—21no—
628C2×D4—21no—
629C2×D4—21no—
630C2×D4—21no—
631C2×D4—21no—
632C2×D4—21no—
633C2×D4—21no—
634C2×D4—41no—
635C2×D4—41no—
636C2×D4—42no—
637C2×D4—42no—
638C2×D4—42no—
639C2×D4—42no—
640C2×D4—42no—
641C2×D4—42no—
642C2×D4—81no—
643C2×D4—81no—
644C2×D4—81no—
645C2×D4—81no—
646C2×D4—81no—
647C2×D4—81no—
648C2×D4C22⋊Dic5314yes—
649C2×D4C22×Dic5312yes—
650C2×D4C22×Dic5312yes—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—24no—
662C22×C4—24no—
663C22×C4—42no—
664C22×C4—42no—
665C22×C4—42no—
666C22×C4—42no—
667C22×C4—1061no—
668C22×C4—1061no—
669C22×C4—1061no—
670C22×C4—1061no—
671C22×C4—4241no—
672C22×C4—2122no—
673C22×C4—2122no—
674C22×C4C22×Dic5312yes—
675C22×C4C22×Dic5312yes—
676C22×C4C2×C22⋊D5311yescharacteristic
677C22×C4C2×C22⋊D5311yescharacteristic
678C22×C4C2×C22⋊D5311yescharacteristic
679C22×C4C2×C22⋊D5311yescharacteristic
680C22×C4C2×C22⋊D5312yes—
681C22×C4C2×C22⋊D5312yes—
682C22×C4C23×D5311yescharacteristic
683M16—2124no—
684C2×C8—532no—
685C2×C8—1061no—
686C2×C8—1061no—
687C2×C8—1061no—
688C2×C8—1061no—
689C2×C8—1061no—
690C2×C8—1061no—
691C2×C8—1061no—
692C2×C8—1061no—
693C2×C8—1061no—
694C2×C8—1061no—
695C2×C8—1061no—
696C2×C8—2124no—
697C4⋊C4—24no—
698C4⋊C4—21no—
699C4⋊C4—532no—
700C4⋊C4—1061no—
701C4⋊C4—1061no—
702C4⋊C4—1061no—
703C4⋊C4—1061no—
704C4⋊C4—1061no—
705C4⋊C4—1061no—
706C4⋊C4—1061no—
707C4⋊C4—2122no—
708C4⋊C4C22⋊Dic5314yes—
709C4⋊C4C22×Dic5312yes—
710C22⋊C4—24no—
711C22⋊C4—24no—
712C22⋊C4—4241no—
713C22⋊C4—2122no—
714C22⋊C4—2122no—
715C22⋊C4C22⋊Dic5314yes—
716C22⋊C4C22⋊Dic5314yes—
717C42—24no—
718C42—4241no—
719C42—2122no—
720C42C22×Dic5312yes—
721C42C2×C22⋊D5312yes—
722C23—21no—
723C23—21no—
724C23—21no—
725C23—21no—
726C23—21no—
727C23—21no—
728C23—21no—
729C23—21no—
730C23—21no—
731C23—21no—
732C23—21no—
733C23—21no—
734C23—22no—
735C23—22no—
736C23—41no—
737C23—41no—
738C23—41no—
739C23—41no—
740C23—41no—
741C23—41no—
742C23—41no—
743C23—41no—
744C23—41no—
745C23—41no—
746C23—41no—
747C23—41no—
748C23C2×C22⋊Dic5312yes—
749C23C2×C22⋊Dic5312yes—
750C23C22×C22⋊D5311yescharacteristic
751Q8—22no—
752Q8—22no—
753Q8—22no—
754Q8D4×Dic5314yes—
755D4—22no—
756D4—22no—
757D4—22no—
758D4—22no—
759D4—44no—
760D4—48no—
761D4—48no—
762D4—48no—
763D4—41no—
764D4—41no—
765D4—41no—
766D4—41no—
767D4—84no—
768D4—84no—
769D4—84no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—48no—
791C2×C4—48no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—1062no—
795C2×C4—4244no—
796C2×C4—2121no—
797C2×C4—2121no—
798C2×C4—2121no—
799C2×C4—2121no—
800C2×C4—2121no—
801C2×C4—2121no—
802C2×C4—2121no—
803C2×C4—2121no—
804C2×C4—2121no—
805C2×C4—2121no—
806C2×C4—2121no—
807C2×C4C2×C22⋊Dic5312yes—
808C2×C4C2×C22⋊Dic5312yes—
809C2×C4C2×C22⋊Dic5312yes—
810C2×C4C2×C22⋊Dic5312yes—
811C2×C4C23×Dic5311yescharacteristic
812C2×C4C2×D4×D5311yescharacteristic
813C2×C4C22×C22⋊D5311yescharacteristic
814C2×C4C2×#1171994711yescharacteristic
815C2×C4#1313326211yescharacteristic
816C2×C4#1313326211yescharacteristic
817C8—1062no—
818C8—2121no—
819C8—2121no—
820C8—2121no—
821C22—22no—
822C22—22no—
823C22—22no—
824C22—22no—
825C22—22no—
826C22—22no—
827C22—41no—
828C22—41no—
829C22—41no—
830C22—41no—
831C22—41no—
832C22—41no—
833C22—41no—
834C22—41no—
835C22—42no—
836C22—42no—
837C22—42no—
838C22—42no—
839C22—42no—
840C22—42no—
841C22—81no—
842C22—81no—
843C22—81no—
844C22—81no—
845C22—81no—
846C22—81no—
847C22—81no—
848C22—81no—
849C22C22×C22⋊Dic5311yescharacteristic
850C22D4×C22⋊D5311yescharacteristic
851C22#1681126711yescharacteristic
852C22#1681142111yescharacteristic
853C22#1681142111yescharacteristic
854C22#1681142611yescharacteristic
855C22#1681143411yescharacteristic
856C4—22no—
857C4—22no—
858C4—24no—
859C4—22no—
860C4—22no—
861C4—42no—
862C4—4241no—
863C4—4241no—
864C4—4241no—
865C4—2122no—
866C4C2×D4×Dic5311yescharacteristic
867C4#1681109811yescharacteristic
868C4D4×C22⋊D5311yescharacteristic
869C4#1681126711yescharacteristic
870C2—42no—
871C2—42no—
872C2—82no—
873C2—82no—
874C2D4×C22⋊Dic5311yescharacteristic
875C2#2028323411yescharacteristic
876C2#2028324111yescharacteristic
877C2#2028625611yescharacteristic
878C2#2028629611yescharacteristic
879C2#2028672111yescharacteristic
880C2#2028684111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D53
commutatorC2×C4×C53C23×C4
FrattiniC22×C4C23×D53
Fitting, prime radicalC2×C53×#550C2
socleC23×C53C22×D4
cosocleC22×C4×C53C24
hypercenterC2×#550D53
hypocenterC53#22422
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#550

Complements

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

NH ≅ G/Ntype
1. C2×#16810695C2semidirect
2. C2×#16810624C2semidirect
3. C2×#16810619C2semidirect
4. #20277644C2semidirect
5. #20275643C2semidirect
6. #20275540C2semidirect
7. #20275154C2semidirect
8. #20275144C2semidirect
9. #20275038C2semidirect
10. #20275033C2semidirect
11. #20274730C2semidirect
12. #20274655C2semidirect
13. #20274655C2semidirect
14. #20274545C2semidirect
54. C53×#550C4semidirect
93. #13133141D4semidirect
121. C2×#41×C53C2×C4semidirect
138. #127×C53C2×C4semidirect
144. #121×C53C2×C4semidirect
146. C4×Q8×C53C2×C4semidirect
461. #550Dic53semidirect
504. C53#22422semidirect
516. C2×#41C2×Dic53semidirect
544. #127C2×Dic53semidirect
550. #121C2×Dic53semidirect
552. C4×Q8C2×Dic53semidirect

Maximal subgroups

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

subgroupindex
C2×#168106952
C2×#168106242
C2×#168106192
#202776442
#202756432
#202755402
#202751542
#202751442
#202750382
#202750332
#202747302
#202746552
#202745452
C2×C53×#5502
#2242253