Finite Group Databasebeta

← #27389781

Subgroups — #27389781

Order 13568.

1552 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×#16810768C211yesmaximal, characteristic
2C2×#16810733C211yesmaximal, characteristic, complemented
3C2×#16810721C211yesmaximal, characteristic, complemented
4C4×#13133191C211yesmaximal, characteristic, complemented
5#20275070C211yesmaximal, characteristic, complemented
6#20275063C211yesmaximal, characteristic, complemented
7#20275037C211yesmaximal, characteristic, complemented
8#20274983C211yesmaximal, characteristic, complemented
9#20274962C211yesmaximal, characteristic, complemented
10#20274914C211yesmaximal, characteristic, complemented
11#20274655C211yesmaximal, characteristic, complemented
12#20274545C211yesmaximal, characteristic, complemented
13#20274540C211yesmaximal, characteristic, complemented
14#20274477C211yesmaximal, characteristic, complemented
15C2×C4×#41×C53C211yesmaximal, characteristic, complemented
16C22×#11719924C2211yescharacteristic
17C22×#11719922C2211yescharacteristic
18C2×#13133191C2211yescharacteristic
19C2×C4×D212C2211yescharacteristic
20C2×C4×C22⋊D53—21no—
21#16810768C418yescomplemented
22#16810733—24no—
23#16810721—24no—
24C2×#13133150C2211yescharacteristic
25C2×#13133148C2211yescharacteristic
26C2×#13133141C2211yescharacteristic
27C2×#13133141C2211yescharacteristic
28C2×#13133141C2211yescharacteristic
29C2×#13133138C2211yescharacteristic
30C2×#13133138C2211yescharacteristic
31C2×#13133138C2211yescharacteristic
32C2×#13133137C2211yescharacteristic
33C2×#13133137C2211yescharacteristic
34C2×C22⋊#88322C2211yescharacteristic
35C2×C22⋊#88322C2211yescharacteristic
36C2×#13133128C2211yescharacteristic
37C2×#13133128C2211yescharacteristic
38#16810525C2211yescharacteristic
39#16810521C2211yescharacteristic
40#16810514—21no—
41#16810502—21no—
42#16810483C2211yescharacteristic
43C4×C4⋊Dic53C2211yescharacteristic
44C4×#11719921—21no—
45#16810385C2211yescharacteristic
46#16810385C2211yescharacteristic
47#16810385C2211yescharacteristic
48#16810385C2211yescharacteristic
49#16810378C2211yescharacteristic
50#16810378C2211yescharacteristic
51C22×#41×C53C2211yescharacteristic
52C4×#41×C53—24no—
53C4×#41×C53—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×C42×C53—21no—
63C22×C42×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—
81C4×C22⋊D53—44no—
82C2×C4⋊Dic53C2311yescharacteristic
83C2×C4⋊Dic53C2311yescharacteristic
84C2×C4⋊Dic53C2311yescharacteristic
85C2×#11719919—21no—
86C2×C22⋊Dic53—21no—
87C2×#11719921—21no—
88C2×#11719921—21no—
89C2×#11719921—21no—
90C2×#11719921—21no—
91C2×C4×Dic53—21no—
92#13133150—22no—
93#13133148—22no—
94#13133141—22no—
95#13133141—22no—
96#13133141C2×C414yescomplemented
97#13133138—22no—
98#13133138—22no—
99#13133138C2×C414yescomplemented
100#13133137—22no—
101#13133137—22no—
102C22⋊#88322—22no—
103C22⋊#88322C2×C414yescomplemented
104#13133128—22no—
105#13133128—22no—
106#13133124—21no—
107#13133124—21no—
108#13133124—21no—
109C2×#41×C53—22no—
110C2×#41×C53—22no—
111C2×#41×C53—22no—
112C2×#41×C53—22no—
113C2×#41×C53—22no—
114C2×#41×C53C2×C414yescomplemented
115C22×Q8×C53C2311yescharacteristic
116C22×D4×C53—21no—
117C22×D4×C53C2311yescharacteristic
118C23×C4×C53—21no—
119C23×C4×C53—21no—
120C23×C4×C53—21no—
121C23×C4×C53D411yescharacteristic
122C23×C4×C53D411yescharacteristic
123C23×C4×C53C2311yescharacteristic
124C4×Q8×C53—22no—
125C4×Q8×C53—22no—
126C4×Q8×C53—22no—
127C4×Q8×C53D414yescomplemented
128C4×D4×C53—28no—
129C4×D4×C53—28no—
130C4×D4×C53—22no—
131C4×D4×C53—22no—
132C4×D4×C53—22no—
133C4×D4×C53D414yescomplemented
134#117×C53—28no—
135#117×C53—22no—
136#117×C53—22no—
137C2×C4⋊C4×C53—21no—
138C2×C4⋊C4×C53—21no—
139C2×C4⋊C4×C53C2311yescharacteristic
140C2×C4⋊C4×C53C2311yescharacteristic
141C2×C22⋊C4×C53—21no—
142C2×C22⋊C4×C53—21no—
143C2×C22⋊C4×C53—21no—
144C2×C42×C53—28no—
145C2×C42×C53—22no—
146C2×C42×C53—22no—
147C2×C42×C53—21no—
148C2×C42×C53—21no—
149C2×C42×C53—21no—
150C2×C42×C53D411yescharacteristic
151C2×C42×C53D411yescharacteristic
152C2×C42×C53C2311yescharacteristic
153C2×C42×C53C2311yescharacteristic
154C24×C53—21no—
155C24×C53C2×D411yescharacteristic
156C23×D53—21no—
157#41×C53—28no—
158#41×C53—28no—
159#41×C53—28no—
160#41×C53—28no—
161C2×Q8×C53—21no—
162C2×Q8×C53—21no—
163C2×Q8×C53—21no—
164C2×Q8×C53C22×C412yes—
165C2×Q8×C53C2×D412yes—
166C2×Q8×C53#4112yes—
167C2×D4×C53—24no—
168C2×D4×C53—24no—
169C2×D4×C53—24no—
170C2×D4×C53—21no—
171C2×D4×C53—21no—
172C2×D4×C53—21no—
173C2×D4×C53C22×C412yes—
174C2×D4×C53C2×D412yes—
175C2×D4×C53#4112yes—
176C22×C4×C53—24no—
177C22×C4×C53—24no—
178C22×C4×C53—21no—
179C22×C4×C53—24no—
180C22×C4×C53—21no—
181C22×C4×C53—21no—
182C22×C4×C53—21no—
183C22×C4×C53—21no—
184C22×C4×C53—24no—
185C22×C4×C53—21no—
186C22×C4×C53—21no—
187C22×C4×C53—22no—
188C22×C4×C53—22no—
189C22×C4×C53—24no—
190C22×C4×C53—22no—
191C22×C4×C53—41no—
192C22×C4×C53—41no—
193C22×C4×C53—41no—
194C22×C4×C53—42no—
195C22×C4×C53—42no—
196C22×C4×C53—42no—
197C22×C4×C53—42no—
198C22×C4×C53C22×C412yes—
199C22×C4×C53C2×D411yescharacteristic
200C22×C4×C53C2×D411yescharacteristic
201C22×C4×C53C2×D411yescharacteristic
202C22×C4×C53C2×D411yescharacteristic
203C22×C4×C53C2×D411yescharacteristic
204C22×C4×C53#4112yes—
205C22×C4×C53C2411yescharacteristic
206C2×C22⋊D53—24no—
207C2×C22⋊D53—42no—
208C2×C22⋊D53—42no—
209C22×Dic53—21no—
210C22×Dic53—21no—
211C22×Dic53—21no—
212C2×D212—21no—
213C2×D212—21no—
214C2×D212—21no—
215C2×D212—21no—
216C2×D212—21no—
217C2×D212C22×C412yes—
218C2×C4×D53—42no—
219C2×C4×D53—42no—
220C2×C4×D53—42no—
221C4⋊C4×C53—24no—
222C4⋊C4×C53—24no—
223C4⋊C4×C53—21no—
224C4⋊C4×C53—21no—
225C4⋊C4×C53C2×D412yes—
226C4⋊C4×C53C2×D412yes—
227C22⋊C4×C53—24no—
228C22⋊C4×C53—24no—
229C22⋊C4×C53—24no—
230C42×C53—24no—
231C42×C53—24no—
232C42×C53—22no—
233C42×C53—24no—
234C42×C53—22no—
235C42×C53—21no—
236C42×C53—21no—
237C42×C53C2×D412yes—
238C42×C53C2×D412yes—
239C22⋊Dic53—42no—
240#11719924—28no—
241#11719922—28no—
242#11719921—24no—
243#11719921—42no—
244#11719921—42no—
245#11719921—42no—
246C4⋊Dic53—21no—
247C4⋊Dic53—21no—
248C4⋊Dic53—21no—
249C4⋊Dic53—21no—
250C4⋊Dic53—21no—
251C4⋊Dic53C22×C412yes—
252#11719919—42no—
253C4×Dic53—42no—
254C2×#88322—21no—
255C2×#88322—21no—
256C2×#88322—21no—
257C2×#88322—21no—
258C2×#88322—21no—
259C2×#88322—21no—
260C2×#88322—21no—
261C2×#88322—21no—
262C2×#88322—21no—
263C2×#88322—21no—
264C2×#88322C22×C412yes—
265C2×#88322C22×C412yes—
266C23×C53—22no—
267C23×C53—21no—
268C23×C53—22no—
269C23×C53—21no—
270C23×C53—22no—
271C23×C53—21no—
272C23×C53—21no—
273C23×C53—21no—
274C23×C53—21no—
275C23×C53—41no—
276C23×C53—41no—
277C23×C53—41no—
278C23×C53—41no—
279C23×C53C4×D412yes—
280C23×C53C22×D411yescharacteristic
281C22×D53—22no—
282C22×D53—41no—
283C22×D53—41no—
284C22×D53—41no—
285C22×D53—41no—
286C22×D53—41no—
287C22×D53—41no—
288Q8×C53—22no—
289Q8×C53—22no—
290Q8×C53—22no—
291Q8×C53C4×D414yescomplemented
292D4×C53—216no—
293D4×C53—22no—
294D4×C53—22no—
295D4×C53—22no—
296D4×C53C4×D414yescomplemented
297C2×C4×C53—216no—
298C2×C4×C53—22no—
299C2×C4×C53—21no—
300C2×C4×C53—21no—
301C2×C4×C53—22no—
302C2×C4×C53—21no—
303C2×C4×C53—22no—
304C2×C4×C53—21no—
305C2×C4×C53—21no—
306C2×C4×C53—21no—
307C2×C4×C53—21no—
308C2×C4×C53—21no—
309C2×C4×C53—22no—
310C2×C4×C53—22no—
311C2×C4×C53—22no—
312C2×C4×C53—22no—
313C2×C4×C53—22no—
314C2×C4×C53—22no—
315C2×C4×C53—21no—
316C2×C4×C53—21no—
317C2×C4×C53—21no—
318C2×C4×C53—44no—
319C2×C4×C53—44no—
320C2×C4×C53—48no—
321C2×C4×C53—48no—
322C2×C4×C53—41no—
323C2×C4×C53—41no—
324C2×C4×C53—41no—
325C2×C4×C53—41no—
326C2×C4×C53C4×D412yes—
327C2×C4×C53#12012yes—
328C2×C4×C53#12012yes—
329C2×C4×C53AGL(1,ℤ/8)12yes—
330C2×C4×C53C23×C411yescharacteristic
331C2×C4×C53C22×D411yescharacteristic
332C2×C4×C53C22×D411yescharacteristic
333C2×C4×C53C2×#4111yescharacteristic
334C2×C4×C53C2×#4111yescharacteristic
335C2×C4×C53C2×#4111yescharacteristic
336C22⋊D53—48no—
337C2×Dic53—22no—
338C2×Dic53—41no—
339C2×Dic53—41no—
340C2×Dic53—41no—
341C2×Dic53—41no—
342C2×Dic53—41no—
343C2×Dic53—41no—
344C2×Dic53—41no—
345C2×Dic53—41no—
346D212—22no—
347D212—22no—
348D212—41no—
349D212—41no—
350C4×D53—84no—
351#88322—22no—
352#88322—22no—
353#88322—41no—
354#88322—41no—
355#21456—531nomaximal, Sylow
356C22×C53—22no—
357C22×C53—22no—
358C22×C53—22no—
359C22×C53—24no—
360C22×C53—41no—
361C22×C53—42no—
362C22×C53—41no—
363C22×C53—42no—
364C22×C53—42no—
365C22×C53—42no—
366C22×C53—41no—
367C22×C53—42no—
368C22×C53—41no—
369C22×C53—42no—
370C22×C53C2×C4×D411yescharacteristic
371C22×C53C2×#12011yescharacteristic
372C22×C53#52511yescharacteristic
373C22×C53C2×AGL(1,ℤ/8)11yescharacteristic
374C22×C53#57511yescharacteristic
375C22×C53#57511yescharacteristic
376C22×C53#57511yescharacteristic
377C2×D53—42no—
378C2×D53—42no—
379C2×D53—42no—
380C2×D53—81no—
381C2×D53—81no—
382C2×D53—81no—
383C2×D53—81no—
384C4×C53—22no—
385C4×C53—22no—
386C4×C53—22no—
387C4×C53—22no—
388C4×C53—24no—
389C4×C53—41no—
390C4×C53—42no—
391C4×C53—42no—
392C4×C53C2×C4×D411yescharacteristic
393C4×C53C2×C4×D411yescharacteristic
394C4×C53#52511yescharacteristic
395C4×C53#52511yescharacteristic
396Dic53—42no—
397Dic53—81no—
398Dic53—81no—
399C2×C4×#41D5311yescharacteristic, complemented
400C2×#449—531no—
401C2×#442—531no—
402C2×#440—531no—
403C4×#121—531no—
404#1880—531no—
405#1879—531no—
406#1875—531no—
407#1865—531no—
408#1862—531no—
409#1854—531no—
410#1788—531no—
411#1763—531no—
412#1762—531no—
413#1749—531no—
414C2×C53—42no—
415C2×C53—44no—
416C2×C53C4×#12011yescharacteristic
417C2×C53#294311yescharacteristic
418C2×C53C4×AGL(1,ℤ/8)11yescharacteristic
419C2×C53#300511yescharacteristic
420C2×C53#300611yescharacteristic
421C2×C53#311111yescharacteristic
422C2×C53#311511yescharacteristic
423D53—82no—
424C22×#41C2×D5311yescharacteristic
425C22×SD16—531no—
426C22×D8—531no—
427C2×#121—531no—
428C4×#41—24no—
429C4×#41—24no—
430C2×C4×Q8C2×D5311yescharacteristic
431C2×C4×Q8C2×D5311yescharacteristic
432C2×C4×D4—21no—
433C2×C4×D4—21no—
434C2×C4×D4—531no—
435C2×C4×D4—1061no—
436C2×C4×D4C2×D5311yescharacteristic
437C2×C4×D4C2×D5311yescharacteristic
438C2×#117—21no—
439C2×#117C2×D5311yescharacteristic
440C22×C42—21no—
441C22×C42C2×D5311yescharacteristic
442#449—538no—
443#442—1064no—
444#440—1064no—
445C2×#107—531no—
446C2×#106—531no—
447C2×#103—531no—
448C2×#103—531no—
449C2×#103—531no—
450C2×#102—531no—
451C2×#102—531no—
452C2×#102—531no—
453C2×#102—531no—
454C2×#102—531no—
455C2×C22⋊C8—531no—
456C2×C22⋊C8—531no—
457C2×#97—531no—
458C2×#97—531no—
459#390—531no—
460#389—531no—
461#388—1061no—
462#386—1061no—
463#380—531no—
464C4×C4⋊C4—531no—
465C4×C22⋊C4—1061no—
466#340—531no—
467#340—531no—
468#340—531no—
469#340—531no—
470#336—531no—
471#336—531no—
472C53#2145611yescharacteristic, complemented, Sylow
473C2×#41—22no—
474C2×#41—22no—
475C2×#41—22no—
476C2×#41—22no—
477C2×#41—22no—
478C2×#41C4×D5314yescomplemented
479C22×Q8C22×D5311yescharacteristic
480C22×D4—21no—
481C22×D4—531no—
482C22×D4—1061no—
483C22×D4C22×D5311yescharacteristic
484C23×C4—21no—
485C23×C4—21no—
486C23×C4—21no—
487C23×C4—1061no—
488C23×C4C22⋊D5311yescharacteristic
489C23×C4C22⋊D5311yescharacteristic
490C23×C4C22×D5311yescharacteristic
491C2×SD16—534no—
492C2×SD16—1062no—
493C2×SD16—1062no—
494C2×D8—534no—
495C2×D8—1062no—
496C2×D8—1062no—
497C22×C8—531no—
498C22×C8—531no—
499C22×C8—531no—
500C22×C8—531no—
501#121—534no—
502#121—1062no—
503C4×Q8—22no—
504C4×Q8—22no—
505C4×Q8—22no—
506C4×Q8C22⋊D5314yescomplemented
507C4×D4—28no—
508C4×D4—28no—
509C4×D4—22no—
510C4×D4—22no—
511C4×D4—22no—
512C4×D4—1062no—
513C4×D4—1062no—
514C4×D4—2124no—
515C4×D4C22⋊D5314yescomplemented
516#117—28no—
517#117—22no—
518#117—22no—
519C2×C4⋊C4—21no—
520C2×C4⋊C4—21no—
521C2×C4⋊C4—531no—
522C2×C4⋊C4—531no—
523C2×C4⋊C4—531no—
524C2×C4⋊C4—1061no—
525C2×C4⋊C4C22×D5311yescharacteristic
526C2×C4⋊C4C22×D5311yescharacteristic
527C2×C22⋊C4—21no—
528C2×C22⋊C4—21no—
529C2×C22⋊C4—21no—
530C2×C22⋊C4—1061no—
531C2×C22⋊C4—1061no—
532C2×C22⋊C4—1061no—
533C2×C22⋊C4—1061no—
534C2×C22⋊C4—1061no—
535C2×C42—28no—
536C2×C42—21no—
537C2×C42—21no—
538C2×C42—21no—
539C2×C42—22no—
540C2×C42—22no—
541C2×C42—1061no—
542C2×C42C22⋊D5311yescharacteristic
543C2×C42C22⋊D5311yescharacteristic
544C2×C42C22×D5311yescharacteristic
545C2×C42C22×D5311yescharacteristic
546#107—1062no—
547#106—1062no—
548#103—534no—
549#103—1062no—
550#103—1062no—
551#102—534no—
552#102—1062no—
553#102—1062no—
554#102—1062no—
555#102—1062no—
556C22⋊C8—534no—
557C22⋊C8—1062no—
558#97—1062no—
559#97—1062no—
560#95—1061no—
561#95—1061no—
562#95—1061no—
563C24—21no—
564C24—1061no—
565C24C2×C22⋊D5311yescharacteristic
566#41—28no—
567#41—28no—
568#41—28no—
569#41—28no—
570C2×Q8—21no—
571C2×Q8—21no—
572C2×Q8—21no—
573C2×Q8C2×C4×D5312yes—
574C2×Q8#1171994512yes—
575C2×Q8C2×C22⋊D5312yes—
576C2×D4—24no—
577C2×D4—24no—
578C2×D4—24no—
579C2×D4—21no—
580C2×D4—21no—
581C2×D4—21no—
582C2×D4—532no—
583C2×D4—1064no—
584C2×D4—1061no—
585C2×D4—1061no—
586C2×D4—1061no—
587C2×D4—1061no—
588C2×D4—1061no—
589C2×D4—2122no—
590C2×D4—2122no—
591C2×D4C2×C4×D5312yes—
592C2×D4#1171994512yes—
593C2×D4C2×C22⋊D5312yes—
594C22×C4—24no—
595C22×C4—24no—
596C22×C4—21no—
597C22×C4—24no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—24no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—24no—
608C22×C4—22no—
609C22×C4—41no—
610C22×C4—41no—
611C22×C4—41no—
612C22×C4—42no—
613C22×C4—42no—
614C22×C4—42no—
615C22×C4—42no—
616C22×C4—1061no—
617C22×C4—1061no—
618C22×C4—1061no—
619C22×C4—2122no—
620C22×C4—2122no—
621C22×C4—2122no—
622C22×C4C2×C4×D5312yes—
623C22×C4#1171994512yes—
624C22×C4C2×C22⋊D5311yescharacteristic
625C22×C4C2×C22⋊D5311yescharacteristic
626C22×C4C2×C22⋊D5311yescharacteristic
627C22×C4C2×C22⋊D5311yescharacteristic
628C22×C4C2×C22⋊D5311yescharacteristic
629C22×C4C23×D5311yescharacteristic
630SD16—1068no—
631D8—1068no—
632C2×C8—532no—
633C2×C8—532no—
634C2×C8—1061no—
635C2×C8—1061no—
636C2×C8—1061no—
637C2×C8—1061no—
638C2×C8—1061no—
639C2×C8—1061no—
640C2×C8—1061no—
641C2×C8—1061no—
642C2×C8—1061no—
643C2×C8—1061no—
644C4⋊C4—24no—
645C4⋊C4—24no—
646C4⋊C4—21no—
647C4⋊C4—21no—
648C4⋊C4—532no—
649C4⋊C4—1061no—
650C4⋊C4—1061no—
651C4⋊C4—1061no—
652C4⋊C4—1061no—
653C4⋊C4—1061no—
654C4⋊C4—2122no—
655C4⋊C4C2×C22⋊D5312yes—
656C4⋊C4C2×C22⋊D5312yes—
657C22⋊C4—24no—
658C22⋊C4—24no—
659C22⋊C4—24no—
660C22⋊C4—1064no—
661C22⋊C4—2122no—
662C22⋊C4—2122no—
663C22⋊C4—2122no—
664C22⋊C4—2122no—
665C42—24no—
666C42—24no—
667C42—22no—
668C42—24no—
669C42—22no—
670C42—21no—
671C42—21no—
672C42—2122no—
673C42C2×C22⋊D5312yes—
674C42C2×C22⋊D5312yes—
675C23—22no—
676C23—21no—
677C23—22no—
678C23—21no—
679C23—22no—
680C23—21no—
681C23—21no—
682C23—21no—
683C23—21no—
684C23—41no—
685C23—41no—
686C23—41no—
687C23—41no—
688C23—1062no—
689C23—2121no—
690C23—2121no—
691C23—2121no—
692C23—2121no—
693C23—2121no—
694C23—2121no—
695C23C4×C22⋊D5312yes—
696C23C22×C22⋊D5311yescharacteristic
697Q8—22no—
698Q8—22no—
699Q8—22no—
700Q8C4×C22⋊D5314yescomplemented
701D4—216no—
702D4—22no—
703D4—22no—
704D4—22no—
705D4—1062no—
706D4—1062no—
707D4—2128no—
708D4—2121no—
709D4—2121no—
710D4C4×C22⋊D5314yescomplemented
711C2×C4—216no—
712C2×C4—22no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—22no—
716C2×C4—21no—
717C2×C4—22no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—21no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—44no—
733C2×C4—44no—
734C2×C4—48no—
735C2×C4—48no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—1062no—
741C2×C4—4244no—
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×C4C4×C22⋊D5312yes—
751C2×C4#1313318612yes—
752C2×C4#1313318612yes—
753C2×C4#1313324212yes—
754C2×C4C22×C4×D5311yescharacteristic
755C2×C4C22×C22⋊D5311yescharacteristic
756C2×C4C22×C22⋊D5311yescharacteristic
757C2×C4C2×#1171994511yescharacteristic
758C2×C4C2×#1171994511yescharacteristic
759C2×C4C2×#1171994511yescharacteristic
760C8—1062no—
761C8—1062no—
762C8—2121no—
763C8—2121no—
764C22—22no—
765C22—22no—
766C22—22no—
767C22—24no—
768C22—41no—
769C22—42no—
770C22—41no—
771C22—42no—
772C22—42no—
773C22—42no—
774C22—41no—
775C22—42no—
776C22—41no—
777C22—42no—
778C22—4241no—
779C22—4241no—
780C22—4241no—
781C22—4241no—
782C22—2122no—
783C22—2122no—
784C22—2122no—
785C22C2×C4×C22⋊D5311yescharacteristic
786C22C2×#1313318611yescharacteristic
787C22#1681113411yescharacteristic
788C22C2×#1313324211yescharacteristic
789C22#1681142111yescharacteristic
790C22#1681142111yescharacteristic
791C22#1681142111yescharacteristic
792C4—22no—
793C4—22no—
794C4—22no—
795C4—22no—
796C4—24no—
797C4—41no—
798C4—42no—
799C4—42no—
800C4—4241no—
801C4—4241no—
802C4—2122no—
803C4C2×C4×C22⋊D5311yescharacteristic
804C4C2×C4×C22⋊D5311yescharacteristic
805C4#1681113411yescharacteristic
806C4#1681113411yescharacteristic
807C2—42no—
808C2—44no—
809C2—4242no—
810C2C4×#1313318611yescharacteristic
811C2#2028351311yescharacteristic
812C2C4×#1313324211yescharacteristic
813C2#2028395711yescharacteristic
814C2#2028396711yescharacteristic
815C2#2028482411yescharacteristic
816C2#2028486611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D53
commutatorC2×C4×C53C23×C4
FrattiniC22×C4C23×D53
FittingC2×C4×#41×C53C2
socleC23×C53C22×D4
prime radicalC2×#16810768C2
cosocleC22×C4×C53C24
hypercenterC2×C4×#41D53
hypocenterC53#21456
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×C4×#41

Complements

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

NH ≅ G/Ntype
2. C2×#16810733C2semidirect
3. C2×#16810721C2semidirect
4. C4×#13133191C2semidirect
5. #20275070C2semidirect
6. #20275063C2semidirect
7. #20275037C2semidirect
8. #20274983C2semidirect
9. #20274962C2semidirect
10. #20274914C2semidirect
11. #20274655C2semidirect
12. #20274545C2semidirect
13. #20274540C2semidirect
14. #20274477C2semidirect
15. C2×C4×#41×C53C2semidirect
21. #16810768C4semidirect
69. C2×#11719924C2×C4semidirect
72. C2×#11719922C2×C4semidirect
78. #13133191C2×C4semidirect
96. #13133141C2×C4semidirect
99. #13133138C2×C4semidirect
103. C22⋊#88322C2×C4semidirect
114. C2×#41×C53C2×C4semidirect
127. C4×Q8×C53D4semidirect
133. C4×D4×C53D4semidirect
291. Q8×C53C4×D4semidirect
296. D4×C53C4×D4semidirect
399. C2×C4×#41D53semidirect
472. C53#21456semidirect
478. C2×#41C4×D53semidirect
506. C4×Q8C22⋊D53semidirect
515. C4×D4C22⋊D53semidirect
700. Q8C4×C22⋊D53semidirect
710. D4C4×C22⋊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×#168107212
C4×#131331912
#202750702
#202750632
#202750372
#202749832
#202749622
#202749142
#202746552
#202745452
#202745402
#202744772
C2×C4×#41×C532
#2145653