Finite Group Databasebeta

← #27389901

Subgroups — #27389901

Order 13568.

1476 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16810768C211yesmaximal, characteristic
2C2×#16810733C211yesmaximal, characteristic, complemented
3C2×C4×#11719924C211yesmaximal, characteristic, complemented
4#20277408C211yesmaximal, characteristic, complemented
5#20275070C211yesmaximal, characteristic, complemented
6#20275063C211yesmaximal, characteristic, complemented
7#20275032C211yesmaximal, characteristic, complemented
8#20274983C211yesmaximal, characteristic, complemented
9#20274976C211yesmaximal, characteristic, complemented
10#20274908C211yesmaximal, characteristic, complemented
11#20274655C211yesmaximal, characteristic, complemented
12#20274545C211yesmaximal, characteristic, complemented
13C4×#13133138C211yesmaximal, characteristic, complemented
14#20274481C211yesmaximal, characteristic, complemented
15C2×C53×#520C211yesmaximal, characteristic, complemented
16C22×#11719924C2211yescharacteristic
17C22×#11719922C2211yescharacteristic
18C2×#13133191C2211yescharacteristic
19C2×C4×D212C2211yescharacteristic
20#16810768C418yescomplemented
21#16810733—24no—
22C4×#11719924—24no—
23C2×#13133148C2211yescharacteristic
24C2×#13133148C2211yescharacteristic
25C2×#13133141C2211yescharacteristic
26C2×#13133141C2211yescharacteristic
27C2×#13133141C2211yescharacteristic
28C2×#13133138C2211yescharacteristic
29C2×#13133138C2211yescharacteristic
30C2×#13133138C2211yescharacteristic
31C2×#13133137C2211yescharacteristic
32C2×#13133137C2211yescharacteristic
33C2×C22⋊#88322C2211yescharacteristic
34C2×C22⋊#88322C2211yescharacteristic
35C2×#13133128C2211yescharacteristic
36C2×C4×#88322C2211yescharacteristic
37#16810525C2211yescharacteristic
38#16810523—21no—
39#16810521C2211yescharacteristic
40#16810513—21no—
41#16810499—21no—
42#16810494—21no—
43#16810483C2211yescharacteristic
44C4×C4⋊Dic53C2211yescharacteristic
45#16810385C2211yescharacteristic
46#16810385C2211yescharacteristic
47#16810385C2211yescharacteristic
48#16810385C2211yescharacteristic
49#16810378C2211yescharacteristic
50#16810378C2211yescharacteristic
51C22×#41×C53C2211yescharacteristic
52C53×#520—24no—
53C53×#520—24no—
54C2×C4×Q8×C53C2211yescharacteristic
55C2×C4×Q8×C53C2211yescharacteristic
56C2×C4×D4×C53—21no—
57C2×C4×D4×C53—21no—
58C2×C4×D4×C53C2211yescharacteristic
59C2×C4×D4×C53C2211yescharacteristic
60C2×#117×C53—21no—
61C2×#117×C53C2211yescharacteristic
62C22×C4⋊C4×C53—21no—
63C22×C4⋊C4×C53C2211yescharacteristic
64C22×D212C2311yescharacteristic
65C22×C22⋊D53—21no—
66C22×C4×D53—21no—
67C2×#11719924—22no—
68C2×#11719924—22no—
69C2×#11719924C2×C414yescomplemented
70C2×#11719922—22no—
71C2×#11719922—22no—
72C2×#11719922C2×C414yescomplemented
73C22×#88322C2311yescharacteristic
74C22×#88322C2311yescharacteristic
75C22×#88322C2311yescharacteristic
76C22×#88322C2311yescharacteristic
77#13133191—22no—
78#13133191C2×C414yescomplemented
79C4×D212—22no—
80C4×D212—22no—
81C2×C4⋊Dic53C2311yescharacteristic
82C2×C4⋊Dic53C2311yescharacteristic
83C2×C4⋊Dic53C2311yescharacteristic
84C2×#11719919—21no—
85C2×C22⋊Dic53—21no—
86C2×#11719921—21no—
87C2×#11719921—21no—
88C2×#11719921—21no—
89C2×#11719921—21no—
90C2×C4×Dic53—21no—
91#13133148—22no—
92#13133148—22no—
93#13133141—22no—
94#13133141—22no—
95#13133141C2×C414yescomplemented
96#13133138—22no—
97#13133138—22no—
98#13133138C2×C414yescomplemented
99#13133137—22no—
100#13133137—22no—
101C22⋊#88322—22no—
102C22⋊#88322C2×C414yescomplemented
103#13133128—22no—
104C4×#88322—22no—
105#13133124—21no—
106#13133124—21no—
107#13133124—21no—
108C2×#41×C53—22no—
109C2×#41×C53—22no—
110C2×#41×C53—22no—
111C2×#41×C53—22no—
112C2×#41×C53—22no—
113C2×#41×C53C2×C414yescomplemented
114C22×Q8×C53C2311yescharacteristic
115C22×D4×C53—21no—
116C22×D4×C53C2311yescharacteristic
117C23×C4×C53—21no—
118C23×C4×C53—21no—
119C23×C4×C53—21no—
120C23×C4×C53—21no—
121C23×C4×C53C2311yescharacteristic
122C4×Q8×C53—22no—
123C4×Q8×C53—22no—
124C4×Q8×C53—22no—
125C4×Q8×C53D414yescomplemented
126C4×D4×C53—28no—
127C4×D4×C53—28no—
128C4×D4×C53—22no—
129C4×D4×C53—22no—
130C4×D4×C53—22no—
131C4×D4×C53D414yescomplemented
132#117×C53—28no—
133#117×C53—22no—
134#117×C53—22no—
135C2×C4⋊C4×C53—28no—
136C2×C4⋊C4×C53—22no—
137C2×C4⋊C4×C53—22no—
138C2×C4⋊C4×C53—21no—
139C2×C4⋊C4×C53—21no—
140C2×C4⋊C4×C53—21no—
141C2×C4⋊C4×C53D411yescharacteristic
142C2×C4⋊C4×C53D411yescharacteristic
143C2×C4⋊C4×C53C2311yescharacteristic
144C2×C4⋊C4×C53C2311yescharacteristic
145C2×C22⋊C4×C53—21no—
146C2×C22⋊C4×C53—21no—
147C2×C22⋊C4×C53D411yescharacteristic
148C2×C22⋊C4×C53D411yescharacteristic
149C2×C42×C53—21no—
150C2×C42×C53—21no—
151C2×C42×C53C2311yescharacteristic
152C2×C42×C53C2311yescharacteristic
153C24×C53—21no—
154C24×C53C2×D411yescharacteristic
155C23×D53—21no—
156#41×C53—28no—
157#41×C53—28no—
158#41×C53—28no—
159#41×C53—28no—
160C2×Q8×C53—21no—
161C2×Q8×C53—21no—
162C2×Q8×C53—21no—
163C2×Q8×C53C22×C412yes—
164C2×Q8×C53C2×D412yes—
165C2×Q8×C53#4112yes—
166C2×D4×C53—24no—
167C2×D4×C53—24no—
168C2×D4×C53—24no—
169C2×D4×C53—21no—
170C2×D4×C53—21no—
171C2×D4×C53—21no—
172C2×D4×C53C22×C412yes—
173C2×D4×C53C2×D412yes—
174C2×D4×C53#4112yes—
175C22×C4×C53—24no—
176C22×C4×C53—24no—
177C22×C4×C53—21no—
178C22×C4×C53—24no—
179C22×C4×C53—21no—
180C22×C4×C53—21no—
181C22×C4×C53—21no—
182C22×C4×C53—21no—
183C22×C4×C53—21no—
184C22×C4×C53—21no—
185C22×C4×C53—24no—
186C22×C4×C53—24no—
187C22×C4×C53—24no—
188C22×C4×C53—81no—
189C22×C4×C53—81no—
190C22×C4×C53—81no—
191C22×C4×C53—81no—
192C22×C4×C53—81no—
193C22×C4×C53—81no—
194C22×C4×C53C22×C412yes—
195C22×C4×C53C2×D411yescharacteristic
196C22×C4×C53C2×D411yescharacteristic
197C22×C4×C53C2×D411yescharacteristic
198C22×C4×C53C2×D411yescharacteristic
199C22×C4×C53C2×D411yescharacteristic
200C22×C4×C53#4112yes—
201C22×C4×C53C2411yescharacteristic
202C2×C22⋊D53—24no—
203C2×C22⋊D53—81no—
204C2×C22⋊D53—81no—
205C22×Dic53—21no—
206C22×Dic53—21no—
207C22×Dic53—21no—
208C2×D212—21no—
209C2×D212—21no—
210C2×D212—21no—
211C2×D212—21no—
212C2×D212—21no—
213C2×D212C22×C412yes—
214C2×C4×D53—42no—
215C2×C4×D53—81no—
216C2×C4×D53—81no—
217C4⋊C4×C53—24no—
218C4⋊C4×C53—24no—
219C4⋊C4×C53—22no—
220C4⋊C4×C53—24no—
221C4⋊C4×C53—22no—
222C4⋊C4×C53—21no—
223C4⋊C4×C53—21no—
224C4⋊C4×C53C2×D412yes—
225C4⋊C4×C53C2×D412yes—
226C22⋊C4×C53—24no—
227C22⋊C4×C53—24no—
228C22⋊C4×C53—22no—
229C22⋊C4×C53—22no—
230C42×C53—24no—
231C42×C53—24no—
232C42×C53—21no—
233C42×C53—21no—
234C42×C53C2×D412yes—
235C42×C53C2×D412yes—
236C22⋊Dic53—81no—
237#11719924—28no—
238#11719922—28no—
239#11719921—24no—
240#11719921—42no—
241#11719921—81no—
242#11719921—81no—
243C4⋊Dic53—21no—
244C4⋊Dic53—21no—
245C4⋊Dic53—21no—
246C4⋊Dic53—21no—
247C4⋊Dic53—21no—
248C4⋊Dic53C22×C412yes—
249#11719919—81no—
250C4×Dic53—81no—
251C2×#88322—21no—
252C2×#88322—21no—
253C2×#88322—21no—
254C2×#88322—21no—
255C2×#88322—21no—
256C2×#88322—21no—
257C2×#88322—21no—
258C2×#88322—21no—
259C2×#88322—21no—
260C2×#88322—21no—
261C2×#88322C22×C412yes—
262C2×#88322C22×C412yes—
263C23×C53—22no—
264C23×C53—21no—
265C23×C53—22no—
266C23×C53—21no—
267C23×C53—22no—
268C23×C53—21no—
269C23×C53—21no—
270C23×C53—21no—
271C23×C53—21no—
272C23×C53—41no—
273C23×C53—41no—
274C23×C53—41no—
275C23×C53—41no—
276C23×C53C4×D412yes—
277C23×C53C22×D411yescharacteristic
278C22×D53—22no—
279C22×D53—41no—
280C22×D53—41no—
281C22×D53—41no—
282C22×D53—41no—
283C22×D53—41no—
284C22×D53—41no—
285Q8×C53—22no—
286Q8×C53—22no—
287Q8×C53—22no—
288Q8×C53C4×D414yes—
289D4×C53—216no—
290D4×C53—22no—
291D4×C53—22no—
292D4×C53—22no—
293D4×C53C4×D414yes—
294C2×C4×C53—216no—
295C2×C4×C53—22no—
296C2×C4×C53—21no—
297C2×C4×C53—22no—
298C2×C4×C53—21no—
299C2×C4×C53—22no—
300C2×C4×C53—21no—
301C2×C4×C53—21no—
302C2×C4×C53—21no—
303C2×C4×C53—21no—
304C2×C4×C53—22no—
305C2×C4×C53—22no—
306C2×C4×C53—22no—
307C2×C4×C53—22no—
308C2×C4×C53—22no—
309C2×C4×C53—22no—
310C2×C4×C53—21no—
311C2×C4×C53—21no—
312C2×C4×C53—21no—
313C2×C4×C53—21no—
314C2×C4×C53—21no—
315C2×C4×C53—21no—
316C2×C4×C53—41no—
317C2×C4×C53—41no—
318C2×C4×C53—41no—
319C2×C4×C53—41no—
320C2×C4×C53—84no—
321C2×C4×C53—84no—
322C2×C4×C53—84no—
323C2×C4×C53C4×D412yes—
324C2×C4×C53#12012yes—
325C2×C4×C53#12012yes—
326C2×C4×C53C23×C411yescharacteristic
327C2×C4×C53C22×D411yescharacteristic
328C2×C4×C53C22×D411yescharacteristic
329C2×C4×C53C2×#4111yescharacteristic
330C2×C4×C53C2×#4111yescharacteristic
331C2×C4×C53C2×#4111yescharacteristic
332C22⋊D53—84no—
333C2×Dic53—22no—
334C2×Dic53—41no—
335C2×Dic53—41no—
336C2×Dic53—41no—
337C2×Dic53—41no—
338C2×Dic53—41no—
339C2×Dic53—41no—
340C2×Dic53—41no—
341C2×Dic53—41no—
342D212—22no—
343D212—22no—
344D212—41no—
345D212—41no—
346C4×D53—84no—
347#88322—22no—
348#88322—22no—
349#88322—41no—
350#88322—41no—
351#21464—531nomaximal, Sylow
352C22×C53—22no—
353C22×C53—22no—
354C22×C53—22no—
355C22×C53—24no—
356C22×C53—41no—
357C22×C53—42no—
358C22×C53—41no—
359C22×C53—42no—
360C22×C53—42no—
361C22×C53—42no—
362C22×C53—41no—
363C22×C53—42no—
364C22×C53—41no—
365C22×C53—42no—
366C22×C53C2×C4×D411yescharacteristic
367C22×C53C2×#12011yescharacteristic
368C22×C53#52511yescharacteristic
369C22×C53#57611yescharacteristic
370C22×C53#57711yescharacteristic
371C22×C53#57711yescharacteristic
372C22×C53#57711yescharacteristic
373C2×D53—42no—
374C2×D53—42no—
375C2×D53—42no—
376C2×D53—81no—
377C2×D53—81no—
378C2×D53—81no—
379C2×D53—81no—
380C4×C53—22no—
381C4×C53—22no—
382C4×C53—22no—
383C4×C53—24no—
384C4×C53—41no—
385C4×C53—41no—
386C4×C53—42no—
387C4×C53—42no—
388C4×C53C2×C4×D411yescharacteristic
389C4×C53C2×C4×D411yescharacteristic
390C4×C53#52511yescharacteristic
391C4×C53#52511yescharacteristic
392Dic53—42no—
393Dic53—81no—
394Dic53—81no—
395C2×#520D5311yescharacteristic, complemented
396C2×#449—531no—
397C2×#442—531no—
398C2×C4×SD16—531no—
399#2324—531no—
400#1880—531no—
401#1879—531no—
402#1874—531no—
403#1865—531no—
404#1864—531no—
405#1853—531no—
406#1788—531no—
407#1763—531no—
408C4×#102—531no—
409#1750—531no—
410C2×C53—42no—
411C2×C53—44no—
412C2×C53C4×#12011yescharacteristic
413C2×C53#294611yescharacteristic
414C2×C53#295211yescharacteristic
415C2×C53#301011yescharacteristic
416C2×C53#301211yescharacteristic
417C2×C53#311911yescharacteristic
418C2×C53#312511yescharacteristic
419D53—82no—
420C22×#41C2×D5311yescharacteristic
421C22×SD16—531no—
422C22×D8—531no—
423C2×#121—531no—
424#520—24no—
425#520—24no—
426C2×C4×Q8C2×D5311yescharacteristic
427C2×C4×Q8C2×D5311yescharacteristic
428C2×C4×D4—21no—
429C2×C4×D4—21no—
430C2×C4×D4—531no—
431C2×C4×D4C2×D5311yescharacteristic
432C2×C4×D4C2×D5311yescharacteristic
433C2×#117—21no—
434C2×#117C2×D5311yescharacteristic
435C22×C4⋊C4—21no—
436C22×C4⋊C4C2×D5311yescharacteristic
437#449—538no—
438#442—1064no—
439C4×SD16—1064no—
440C2×#106—531no—
441C2×#106—531no—
442C2×#103—531no—
443C2×#103—531no—
444C2×#103—531no—
445C2×#102—531no—
446C2×#102—531no—
447C2×#102—531no—
448C2×#102—531no—
449C2×#102—531no—
450C2×C22⋊C8—531no—
451C2×C22⋊C8—531no—
452C2×#97—531no—
453C2×C4×C8—531no—
454#390—531no—
455#390—1061no—
456#389—531no—
457#388—1061no—
458#386—1061no—
459#385—1061no—
460#380—531no—
461C4×C4⋊C4—531no—
462#340—531no—
463#340—531no—
464#340—531no—
465#340—531no—
466#336—531no—
467#336—531no—
468C53#2146411yescharacteristic, complemented, Sylow
469C2×#41—22no—
470C2×#41—22no—
471C2×#41—22no—
472C2×#41—22no—
473C2×#41—22no—
474C2×#41C4×D5314yescomplemented
475C22×Q8C22×D5311yescharacteristic
476C22×D4—21no—
477C22×D4—531no—
478C22×D4—1061no—
479C22×D4C22×D5311yescharacteristic
480C23×C4—21no—
481C23×C4—21no—
482C23×C4—21no—
483C23×C4—21no—
484C23×C4—1061no—
485C23×C4C22×D5311yescharacteristic
486C2×SD16—534no—
487C2×SD16—1062no—
488C2×SD16—1062no—
489C2×D8—534no—
490C2×D8—1062no—
491C2×D8—1062no—
492C22×C8—531no—
493C22×C8—531no—
494C22×C8—531no—
495C22×C8—531no—
496#121—534no—
497#121—1062no—
498C4×Q8—22no—
499C4×Q8—22no—
500C4×Q8—22no—
501C4×Q8C22⋊D5314yescomplemented
502C4×D4—28no—
503C4×D4—28no—
504C4×D4—22no—
505C4×D4—22no—
506C4×D4—22no—
507C4×D4—1062no—
508C4×D4—1062no—
509C4×D4C22⋊D5314yescomplemented
510#117—28no—
511#117—22no—
512#117—22no—
513C2×C4⋊C4—28no—
514C2×C4⋊C4—21no—
515C2×C4⋊C4—21no—
516C2×C4⋊C4—21no—
517C2×C4⋊C4—22no—
518C2×C4⋊C4—22no—
519C2×C4⋊C4—531no—
520C2×C4⋊C4—531no—
521C2×C4⋊C4—531no—
522C2×C4⋊C4—1061no—
523C2×C4⋊C4C22⋊D5311yescharacteristic
524C2×C4⋊C4C22⋊D5311yescharacteristic
525C2×C4⋊C4C22×D5311yescharacteristic
526C2×C4⋊C4C22×D5311yescharacteristic
527C2×C22⋊C4—21no—
528C2×C22⋊C4—21no—
529C2×C22⋊C4—1061no—
530C2×C22⋊C4—1061no—
531C2×C22⋊C4—1061no—
532C2×C22⋊C4—1061no—
533C2×C22⋊C4—1061no—
534C2×C22⋊C4C22⋊D5311yescharacteristic
535C2×C22⋊C4C22⋊D5311yescharacteristic
536C2×C42—21no—
537C2×C42—21no—
538C2×C42—1061no—
539C2×C42C22×D5311yescharacteristic
540C2×C42C22×D5311yescharacteristic
541#106—1062no—
542#106—1062no—
543#103—534no—
544#103—1062no—
545#103—1062no—
546#102—534no—
547#102—1062no—
548#102—1062no—
549#102—1062no—
550#102—1062no—
551C22⋊C8—534no—
552C22⋊C8—1062no—
553#97—1062no—
554C4×C8—1062no—
555#95—1061no—
556#95—1061no—
557#95—1061no—
558C24—21no—
559C24—1061no—
560C24C2×C22⋊D5311yescharacteristic
561#41—28no—
562#41—28no—
563#41—28no—
564#41—28no—
565C2×Q8—21no—
566C2×Q8—21no—
567C2×Q8—21no—
568C2×Q8C2×C4×D5312yes—
569C2×Q8#1171994512yes—
570C2×Q8C2×C22⋊D5312yes—
571C2×D4—24no—
572C2×D4—24no—
573C2×D4—24no—
574C2×D4—21no—
575C2×D4—21no—
576C2×D4—21no—
577C2×D4—532no—
578C2×D4—1064no—
579C2×D4—1061no—
580C2×D4—1061no—
581C2×D4—1061no—
582C2×D4—1061no—
583C2×D4—1061no—
584C2×D4—4241no—
585C2×D4—4241no—
586C2×D4C2×C4×D5312yes—
587C2×D4#1171994512yes—
588C2×D4C2×C22⋊D5312yes—
589C22×C4—24no—
590C22×C4—24no—
591C22×C4—21no—
592C22×C4—24no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—24no—
600C22×C4—24no—
601C22×C4—24no—
602C22×C4—81no—
603C22×C4—81no—
604C22×C4—81no—
605C22×C4—81no—
606C22×C4—81no—
607C22×C4—81no—
608C22×C4—1061no—
609C22×C4—1061no—
610C22×C4—1061no—
611C22×C4—4241no—
612C22×C4—4241no—
613C22×C4—2122no—
614C22×C4C2×C4×D5312yes—
615C22×C4#1171994512yes—
616C22×C4C2×C22⋊D5311yescharacteristic
617C22×C4C2×C22⋊D5311yescharacteristic
618C22×C4C2×C22⋊D5311yescharacteristic
619C22×C4C2×C22⋊D5311yescharacteristic
620C22×C4C2×C22⋊D5311yescharacteristic
621C22×C4C23×D5311yescharacteristic
622SD16—1068no—
623D8—1068no—
624C2×C8—532no—
625C2×C8—532no—
626C2×C8—1061no—
627C2×C8—1061no—
628C2×C8—1061no—
629C2×C8—1061no—
630C2×C8—1061no—
631C2×C8—1061no—
632C2×C8—1061no—
633C2×C8—1061no—
634C2×C8—1061no—
635C2×C8—1061no—
636C4⋊C4—24no—
637C4⋊C4—24no—
638C4⋊C4—22no—
639C4⋊C4—24no—
640C4⋊C4—22no—
641C4⋊C4—21no—
642C4⋊C4—21no—
643C4⋊C4—532no—
644C4⋊C4—1061no—
645C4⋊C4—1061no—
646C4⋊C4—1061no—
647C4⋊C4—1061no—
648C4⋊C4—1061no—
649C4⋊C4—4241no—
650C4⋊C4C2×C22⋊D5312yes—
651C4⋊C4C2×C22⋊D5312yes—
652C22⋊C4—24no—
653C22⋊C4—24no—
654C22⋊C4—22no—
655C22⋊C4—22no—
656C22⋊C4—1064no—
657C22⋊C4—4241no—
658C22⋊C4—4241no—
659C22⋊C4—4241no—
660C22⋊C4—2122no—
661C42—24no—
662C42—24no—
663C42—21no—
664C42—21no—
665C42—4241no—
666C42C2×C22⋊D5312yes—
667C42C2×C22⋊D5312yes—
668C23—22no—
669C23—21no—
670C23—22no—
671C23—21no—
672C23—22no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—21no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—1062no—
682C23—2121no—
683C23—2121no—
684C23—2121no—
685C23—2121no—
686C23—2121no—
687C23—2121no—
688C23C4×C22⋊D5312yes—
689C23C22×C22⋊D5311yescharacteristic
690Q8—22no—
691Q8—22no—
692Q8—22no—
693Q8C4×C22⋊D5314yes—
694D4—216no—
695D4—22no—
696D4—22no—
697D4—22no—
698D4—1062no—
699D4—1062no—
700D4—4244no—
701D4—2121no—
702D4—2121no—
703D4C4×C22⋊D5314yes—
704C2×C4—216no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—22no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—84no—
731C2×C4—84no—
732C2×C4—84no—
733C2×C4—1062no—
734C2×C4—4244no—
735C2×C4—2121no—
736C2×C4—2121no—
737C2×C4—2121no—
738C2×C4—2121no—
739C2×C4—2121no—
740C2×C4—2121no—
741C2×C4—2121no—
742C2×C4—2121no—
743C2×C4C4×C22⋊D5312yes—
744C2×C4#1313318612yes—
745C2×C4#1313318612yes—
746C2×C4C22×C4×D5311yescharacteristic
747C2×C4C22×C22⋊D5311yescharacteristic
748C2×C4C22×C22⋊D5311yescharacteristic
749C2×C4C2×#1171994511yescharacteristic
750C2×C4C2×#1171994511yescharacteristic
751C2×C4C2×#1171994511yescharacteristic
752C8—1062no—
753C8—1062no—
754C8—2121no—
755C8—2121no—
756C22—22no—
757C22—22no—
758C22—22no—
759C22—24no—
760C22—41no—
761C22—42no—
762C22—41no—
763C22—42no—
764C22—41no—
765C22—42no—
766C22—42no—
767C22—42no—
768C22—41no—
769C22—42no—
770C22—4241no—
771C22—4241no—
772C22—4241no—
773C22—4241no—
774C22—2122no—
775C22—2122no—
776C22—2122no—
777C22C2×C4×C22⋊D5311yescharacteristic
778C22C2×#1313318611yescharacteristic
779C22#1681113411yescharacteristic
780C22#1681142611yescharacteristic
781C22#1681143111yescharacteristic
782C22#1681143111yescharacteristic
783C22#1681143411yescharacteristic
784C4—22no—
785C4—22no—
786C4—22no—
787C4—24no—
788C4—41no—
789C4—41no—
790C4—42no—
791C4—42no—
792C4—4241no—
793C4—4241no—
794C4—2122no—
795C4C2×C4×C22⋊D5311yescharacteristic
796C4C2×C4×C22⋊D5311yescharacteristic
797C4#1681113411yescharacteristic
798C4#1681113411yescharacteristic
799C2—42no—
800C2—44no—
801C2—4242no—
802C2C4×#1313318611yescharacteristic
803C2#2028354311yescharacteristic
804C2#2028359611yescharacteristic
805C2#2028400111yescharacteristic
806C2#2028401911yescharacteristic
807C2#2028491411yescharacteristic
808C2#2028499211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D53
commutatorC2×C4×C53C23×C4
FrattiniC22×C4C23×D53
FittingC2×C53×#520C2
socleC23×C53C22×D4
prime radicalC2×#16810768C2
cosocleC22×C4×C53C24
hypercenterC2×#520D53
hypocenterC53#21464
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#520

Complements

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

NH ≅ G/Ntype
2. C2×#16810733C2semidirect
3. C2×C4×#11719924C2semidirect
4. #20277408C2semidirect
5. #20275070C2semidirect
6. #20275063C2semidirect
7. #20275032C2semidirect
8. #20274983C2semidirect
9. #20274976C2semidirect
10. #20274908C2semidirect
11. #20274655C2semidirect
12. #20274545C2semidirect
13. C4×#13133138C2semidirect
14. #20274481C2semidirect
15. C2×C53×#520C2semidirect
20. #16810768C4semidirect
69. C2×#11719924C2×C4semidirect
72. C2×#11719922C2×C4semidirect
78. #13133191C2×C4semidirect
95. #13133141C2×C4semidirect
98. #13133138C2×C4semidirect
102. C22⋊#88322C2×C4semidirect
113. C2×#41×C53C2×C4semidirect
125. C4×Q8×C53D4semidirect
131. C4×D4×C53D4semidirect
395. C2×#520D53semidirect
468. C53#21464semidirect
474. C2×#41C4×D53semidirect
501. C4×Q8C22⋊D53semidirect
509. C4×D4C22⋊D53semidirect

Maximal subgroups

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

subgroupindex
C2×#168107682
C2×#168107332
C2×C4×#117199242
#202774082
#202750702
#202750632
#202750322
#202749832
#202749762
#202749082
#202746552
#202745452
C4×#131331382
#202744812
C2×C53×#5202
#2146453