Finite Group Databasebeta

← #27404410

Subgroups — #27404410

Order 13568.

1386 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16810756C211yesmaximal, characteristic
2C2×#16810733C211yesmaximal, characteristic, complemented
3C22×#13133137C211yesmaximal, characteristic, complemented
4C22⋊C4×D212C211yesmaximal, characteristic, complemented
5#20275590C211yesmaximal, characteristic, complemented
6#20275411C211yesmaximal, characteristic, complemented
7#20275342C211yesmaximal, characteristic, complemented
8#20275144C211yesmaximal, characteristic, complemented
9#20275066C211yesmaximal, characteristic, complemented
10#20275063C211yesmaximal, characteristic, complemented
11#20274975C211yesmaximal, characteristic, complemented
12#20274908C211yesmaximal, characteristic, complemented
13#20274543C211yesmaximal, characteristic, complemented
14#20274493C211yesmaximal, characteristic, complemented
15C53×#2361C211yesmaximal, characteristic, complemented
16C23×D212C2211yescharacteristic
17C22×#11719922C2211yescharacteristic
18C22×#11719922C2211yescharacteristic
19C23×#88322C2211yescharacteristic
20C2×C4×D212C2211yescharacteristic
21C2×C4×D212C2211yescharacteristic
22C2×C22⋊C4×D53—21no—
23#16810756C418yescomplemented
24#16810733—24no—
25C2×#13133148C2211yescharacteristic, complemented
26C2×#13133148C2211yescharacteristic, complemented
27C2×#13133138C2211yescharacteristic, complemented
28C2×#13133138C2211yescharacteristic, complemented
29C2×#13133137—24no—
30C2×#13133137C2211yescharacteristic
31C2×#13133137C2211yescharacteristic
32C2×#13133137C2211yescharacteristic
33C2×#13133137C2211yescharacteristic
34C2×#13133137C2211yescharacteristic
35C2×#13133137C2211yescharacteristic
36C2×C22⋊#88322C2211yescharacteristic
37C2×#13133128C2211yescharacteristic, complemented
38C2×#13133128C2211yescharacteristic, complemented
39#16810525C2211yescharacteristic
40#16810525C2211yescharacteristic
41#16810501—21no—
42#16810501—21no—
43#16810483C2211yescharacteristic
44#16810478—21no—
45#16810385C2211yescharacteristic, complemented
46#16810385C2211yescharacteristic, complemented
47#16810385C2211yescharacteristic, complemented
48#16810385C2211yescharacteristic, complemented
49#16810378C2211yescharacteristic, complemented
50#16810378C2211yescharacteristic, complemented
51C2×#121×C53C2211yescharacteristic
52C2×C4×D4×C53—21no—
53C2×C4×D4×C53C2211yescharacteristic, complemented
54C22×C4⋊C4×C53C2211yescharacteristic
55C53×#390C2211yescharacteristic, complemented
56C53×#389C2211yescharacteristic, complemented
57C53×#388—21no—
58C53×#386—21no—
59C53×#385—21no—
60C4×C4⋊C4×C53C2211yescharacteristic, complemented
61C4×C22⋊C4×C53C2211yescharacteristic
62C24×D53—21no—
63C22×D212—22no—
64C22×D212—22no—
65C22×D212—21no—
66C22×D212—22no—
67C22×D212—41no—
68C22×D212—41no—
69C22×D212C2×C414yescomplemented
70C22×D212C2311yescharacteristic
71C22×D212C2311yescharacteristic
72C22×C4×D53—21no—
73C22×C4×D53—21no—
74C2×#11719922—22no—
75C2×#11719922—22no—
76C2×#11719922—41no—
77C2×#11719922—41no—
78C2×#11719922C2×C414yescomplemented
79C2×#11719922C2×C414yescomplemented
80C22×#88322—22no—
81C22×#88322—22no—
82C22×#88322—41no—
83C22×#88322C2311yescharacteristic
84C22×#88322C2311yescharacteristic
85C22×#88322C2311yescharacteristic
86C22×#88322C2311yescharacteristic
87C4×D212—22no—
88C4×D212—22no—
89C4×D212—41no—
90C4×D212—41no—
91C2×C4⋊Dic53C2311yescharacteristic
92C2×C4⋊Dic53C2311yescharacteristic
93C2×C22⋊Dic53—21no—
94C2×#11719921—21no—
95C2×#11719921—21no—
96C2×#11719921—21no—
97C2×#11719921—21no—
98C2×#11719921—21no—
99C2×#11719921—21no—
100C22⋊C4×D53—44no—
101#13133148—22no—
102#13133148—41no—
103#13133138—22no—
104#13133138—41no—
105#13133137—22no—
106#13133137—22no—
107#13133137—22no—
108#13133137C2×C414yescomplemented
109#13133137C2×C414yescomplemented
110#13133137D414yescomplemented
111C22⋊#88322C2×C414yescomplemented
112#13133128—22no—
113#13133128—41no—
114#13133124—21no—
115C22×D4×C53—21no—
116C22×D4×C53C2311yescharacteristic
117C23×C4×C53—21no—
118C23×C4×C53—21no—
119C23×C4×C53C2311yescharacteristic
120#121×C53—22no—
121#121×C53C2×C414yescomplemented
122C4×D4×C53—22no—
123C4×D4×C53—41no—
124C4×D4×C53—44no—
125C2×C4⋊C4×C53—21no—
126C2×C4⋊C4×C53—21no—
127C2×C4⋊C4×C53—22no—
128C2×C4⋊C4×C53—41no—
129C2×C4⋊C4×C53C2311yescharacteristic
130C2×C4⋊C4×C53C2311yescharacteristic
131C2×C4⋊C4×C53C2311yescharacteristic
132C2×C22⋊C4×C53—21no—
133C2×C22⋊C4×C53—21no—
134C2×C22⋊C4×C53—21no—
135C2×C22⋊C4×C53—21no—
136C2×C22⋊C4×C53D411yescharacteristic
137C2×C22⋊C4×C53D411yescharacteristic
138C2×C42×C53—21no—
139C2×C42×C53C2311yescharacteristic
140C2×C42×C53C2311yescharacteristic
141#95×C53—21no—
142#95×C53—21no—
143#95×C53D411yescharacteristic
144#95×C53D411yescharacteristic
145C24×C53—21no—
146C24×C53C2×D411yescharacteristic
147C23×D53—21no—
148C23×D53—21no—
149C23×D53—24no—
150C23×D53—42no—
151C23×D53—42no—
152C23×D53—42no—
153C23×D53—42no—
154C23×D53—81no—
155C23×D53—81no—
156C2×D4×C53—24no—
157C2×D4×C53—21no—
158C2×D4×C53—21no—
159C2×D4×C53—21no—
160C2×D4×C53—21no—
161C2×D4×C53—21no—
162C2×D4×C53—42no—
163C2×D4×C53—42no—
164C2×D4×C53C22×C412yes—
165C22×C4×C53—21no—
166C22×C4×C53—21no—
167C22×C4×C53—21no—
168C22×C4×C53—21no—
169C22×C4×C53—21no—
170C22×C4×C53—21no—
171C22×C4×C53—21no—
172C22×C4×C53—42no—
173C22×C4×C53—42no—
174C22×C4×C53—42no—
175C22×C4×C53—42no—
176C22×C4×C53—81no—
177C22×C4×C53—81no—
178C22×C4×C53C22×C412yes—
179C22×C4×C53C2×D411yescharacteristic
180C22×C4×C53C2×D411yescharacteristic
181C22×C4×C53C2×D411yescharacteristic
182C22×C4×C53C2×D411yescharacteristic
183C22×C4×C53C2×D411yescharacteristic
184C22×C4×C53#4112yes—
185C22×C4×C53C2411yescharacteristic
186C22×Dic53—21no—
187C22×Dic53—21no—
188C2×D212—21no—
189C2×D212—21no—
190C2×D212—21no—
191C2×D212—21no—
192C2×D212—21no—
193C2×D212—21no—
194C2×D212—21no—
195C2×D212—28no—
196C2×D212—24no—
197C2×D212—21no—
198C2×D212—44no—
199C2×D212—44no—
200C2×D212—44no—
201C2×D212—42no—
202C2×D212—42no—
203C2×D212C22×C412yes—
204C2×D212C22×C412yes—
205C2×D212C2×D412yes—
206C2×D212#4112yes—
207C2×C4×D53—42no—
208C2×C4×D53—42no—
209C2×C4×D53—42no—
210C2×C4×D53—42no—
211C2×C4×D53—81no—
212C2×C4×D53—81no—
213C4⋊C4×C53—21no—
214C4⋊C4×C53—21no—
215C4⋊C4×C53—21no—
216C4⋊C4×C53—21no—
217C4⋊C4×C53—42no—
218C4⋊C4×C53—42no—
219C4⋊C4×C53C22×C412yes—
220C4⋊C4×C53C2×D412yes—
221C22⋊C4×C53—22no—
222C22⋊C4×C53—22no—
223C22⋊C4×C53—24no—
224C22⋊C4×C53—42no—
225C22⋊C4×C53—42no—
226C22⋊C4×C53—81no—
227C42×C53—21no—
228C42×C53—21no—
229C42×C53—21no—
230C42×C53—21no—
231C42×C53—42no—
232C22⋊Dic53—42no—
233#11719922—28no—
234#11719922—44no—
235#11719921—42no—
236#11719921—42no—
237#11719921—42no—
238#11719921—42no—
239#11719921—81no—
240#11719921—81no—
241C4⋊Dic53—21no—
242C4⋊Dic53—21no—
243C4⋊Dic53—21no—
244C4⋊Dic53—21no—
245C2×#88322—21no—
246C2×#88322—21no—
247C2×#88322—21no—
248C2×#88322—21no—
249C2×#88322—21no—
250C2×#88322—21no—
251C2×#88322—21no—
252C2×#88322—21no—
253C2×#88322—21no—
254C2×#88322—44no—
255C2×#88322C22×C412yes—
256C2×#88322C22×C412yes—
257C2×#88322C2×D412yes—
258C23×C53—21no—
259C23×C53—21no—
260C23×C53—21no—
261C23×C53—21no—
262C23×C53—22no—
263C23×C53—41no—
264C23×C53—41no—
265C23×C53—41no—
266C23×C53—41no—
267C23×C53—41no—
268C23×C53—41no—
269C23×C53C4×D412yes—
270C23×C53AGL(1,ℤ/8)12yes—
271C23×C53AGL(1,ℤ/8)12yes—
272C23×C53C22×D411yescharacteristic
273C22×D53—22no—
274C22×D53—22no—
275C22×D53—22no—
276C22×D53—22no—
277C22×D53—48no—
278C22×D53—41no—
279C22×D53—41no—
280C22×D53—41no—
281C22×D53—41no—
282C22×D53—41no—
283C22×D53—41no—
284C22×D53—41no—
285C22×D53—41no—
286C22×D53—41no—
287C22×D53—41no—
288C22×D53—48no—
289C22×D53—84no—
290C22×D53—84no—
291C22×D53—84no—
292C22×D53—84no—
293C22×D53—84no—
294D4×C53—22no—
295D4×C53—22no—
296D4×C53—48no—
297D4×C53—41no—
298D4×C53—41no—
299C2×C4×C53—21no—
300C2×C4×C53—21no—
301C2×C4×C53—22no—
302C2×C4×C53—22no—
303C2×C4×C53—22no—
304C2×C4×C53—22no—
305C2×C4×C53—22no—
306C2×C4×C53—21no—
307C2×C4×C53—22no—
308C2×C4×C53—21no—
309C2×C4×C53—21no—
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—21no—
317C2×C4×C53—21no—
318C2×C4×C53—21no—
319C2×C4×C53—41no—
320C2×C4×C53—41no—
321C2×C4×C53—41no—
322C2×C4×C53—41no—
323C2×C4×C53—41no—
324C2×C4×C53—41no—
325C2×C4×C53—41no—
326C2×C4×C53—84no—
327C2×C4×C53—84no—
328C2×C4×C53C4×D412yes—
329C2×C4×C53C23×C411yescharacteristic
330C2×C4×C53C22×D411yescharacteristic
331C2×C4×C53C2×#4111yescharacteristic
332C2×C4×C53C2×#4111yescharacteristic
333C2×C4×C53H(5,𝔽2)11yescharacteristic
334C2×C4×C53H(5,𝔽2)11yescharacteristic
335C2×Dic53—41no—
336C2×Dic53—41no—
337C2×Dic53—41no—
338C2×Dic53—41no—
339C2×Dic53—41no—
340C2×Dic53—41no—
341D212—22no—
342D212—22no—
343D212—22no—
344D212—22no—
345D212—22no—
346D212—48no—
347D212—41no—
348D212—41no—
349D212C4×D414yescomplemented
350C4×D53—84no—
351C4×D53—84no—
352#88322—22no—
353#88322—22no—
354#88322—22no—
355#88322—41no—
356#22858—531nomaximal, Sylow
357C22×C53—22no—
358C22×C53—22no—
359C22×C53—22no—
360C22×C53—22no—
361C22×C53—22no—
362C22×C53—22no—
363C22×C53—42no—
364C22×C53—42no—
365C22×C53—42no—
366C22×C53—81no—
367C22×C53—81no—
368C22×C53—81no—
369C22×C53—81no—
370C22×C53#44214yescomplemented
371C22×C53C2×C4×D411yescharacteristic
372C22×C53D4211yescharacteristic
373C22×C53#54611yescharacteristic
374C22×C53C2×AGL(1,ℤ/8)11yescharacteristic
375C22×C53C2×AGL(1,ℤ/8)11yescharacteristic
376C22×C53#57611yescharacteristic
377C22×C53#57711yescharacteristic
378C2×D53—24no—
379C2×D53—42no—
380C2×D53—42no—
381C2×D53—42no—
382C2×D53—42no—
383C2×D53—42no—
384C2×D53—42no—
385C2×D53—42no—
386C2×D53—42no—
387C2×D53—42no—
388C2×D53—816no—
389C2×D53—81no—
390C2×D53—81no—
391C2×D53—81no—
392C2×D53—81no—
393C4×C53—22no—
394C4×C53—42no—
395C4×C53—41no—
396C4×C53—42no—
397C4×C53—41no—
398C4×C53—41no—
399C4×C53—41no—
400C4×C53—81no—
401C4×C53C2×C4×D411yescharacteristic
402C4×C53#51811yescharacteristic
403C4×C53#54611yescharacteristic
404C4×C53#55111yescharacteristic
405Dic53—81no—
406Dic53—81no—
407C2×#447—531no—
408C2×#442—531no—
409C22×#102—531no—
410#2361D5311yescharacteristic, complemented
411D4×C22⋊C4—531no—
412#1972—531no—
413#1936—531no—
414#1926—531no—
415#1893—531no—
416#1879—531no—
417#1879—531no—
418#1864—531no—
419#1853—531no—
420#1762—531no—
421#1752—531no—
422C2×C53—24no—
423C2×C53—82no—
424C2×C53#235811yescharacteristic
425C2×C53C2×#44211yescharacteristic
426C2×C53#294611yescharacteristic
427C2×C53#326411yescharacteristic
428C2×C53#326511yescharacteristic
429C2×C53#330611yescharacteristic
430C2×C53#331811yescharacteristic
431D53—44no—
432D53—82no—
433C23×D4—531no—
434C22×D8—531no—
435C22×D8—531no—
436C23×C8—531no—
437C2×#121C2×D5311yescharacteristic
438C2×C4×D4—21no—
439C2×C4×D4—531no—
440C2×C4×D4—531no—
441C2×C4×D4C2×D5311yescharacteristic, complemented
442C22×C4⋊C4C2×D5311yescharacteristic
443C22×C22⋊C4—1061no—
444#447—538no—
445#442—1064no—
446C2×#106—531no—
447C2×#106—531no—
448C2×#102—531no—
449C2×#102—531no—
450C2×#102—531no—
451C2×#102—531no—
452C2×#102—531no—
453C2×#102—531no—
454C2×#102—531no—
455C2×#102—531no—
456C2×#102—1064no—
457C2×C22⋊C8—531no—
458C2×#97—531no—
459C2×#97—531no—
460#390—531no—
461#390—531no—
462#390C2×D5311yescharacteristic, complemented
463#389C2×D5311yescharacteristic, complemented
464#388—21no—
465#386—21no—
466#386—1061no—
467#386—1061no—
468#385—21no—
469#380—531no—
470#379—1061no—
471C4×C4⋊C4C2×D5311yescharacteristic, complemented
472C4×C22⋊C4C2×D5311yescharacteristic
473#340—531no—
474#340—531no—
475#340—531no—
476#340—531no—
477#336—531no—
478#336—531no—
479C53#2285811yescharacteristic, complemented, Sylow
480C25—1061no—
481C22×D4—21no—
482C22×D4—534no—
483C22×D4—531no—
484C22×D4—531no—
485C22×D4—1062no—
486C22×D4—1062no—
487C22×D4—1062no—
488C22×D4—1061no—
489C22×D4—2121no—
490C22×D4—2121no—
491C22×D4C22×D5311yescharacteristic
492C23×C4—21no—
493C23×C4—21no—
494C23×C4—1061no—
495C23×C4—1061no—
496C23×C4C22×D5311yescharacteristic
497C2×D8—534no—
498C2×D8—534no—
499C2×D8—1062no—
500C2×D8—1062no—
501C2×D8—2121no—
502C2×D8—2121no—
503C22×C8—531no—
504C22×C8—531no—
505C22×C8—531no—
506C22×C8—531no—
507C22×C8—1062no—
508C22×C8—1062no—
509C22×C8—2121no—
510#121—22no—
511#121C4×D5314yescomplemented
512C4×D4—22no—
513C4×D4—41no—
514C4×D4—44no—
515C4×D4—1062no—
516C4×D4—1062no—
517C4×D4—2121no—
518C4×D4—2121no—
519C2×C4⋊C4—22no—
520C2×C4⋊C4—21no—
521C2×C4⋊C4—21no—
522C2×C4⋊C4—41no—
523C2×C4⋊C4—531no—
524C2×C4⋊C4—531no—
525C2×C4⋊C4C22×D5311yescharacteristic
526C2×C4⋊C4C22×D5311yescharacteristic
527C2×C4⋊C4C22×D5311yescharacteristic
528C2×C22⋊C4—21no—
529C2×C22⋊C4—21no—
530C2×C22⋊C4—21no—
531C2×C22⋊C4—21no—
532C2×C22⋊C4—1061no—
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×C22⋊C4C22⋊D5311yescharacteristic
541C2×C22⋊C4C22⋊D5311yescharacteristic
542C2×C42—21no—
543C2×C42C22×D5311yescharacteristic
544C2×C42C22×D5311yescharacteristic
545#106—1062no—
546#106—2121no—
547#102—534no—
548#102—534no—
549#102—534no—
550#102—1062no—
551#102—1062no—
552#102—1062no—
553#102—1062no—
554#102—2121no—
555C22⋊C8—534no—
556#97—1062no—
557#97—2121no—
558#95—21no—
559#95—21no—
560#95—1061no—
561#95C22⋊D5311yescharacteristic
562#95C22⋊D5311yescharacteristic
563C24—21no—
564C24—1061no—
565C24—1064no—
566C24—1061no—
567C24—4241no—
568C24—4241no—
569C24—2122no—
570C24—2122no—
571C24—2122no—
572C24—2122no—
573C24C2×C22⋊D5311yescharacteristic
574C2×D4—24no—
575C2×D4—21no—
576C2×D4—21no—
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—21no—
580C2×D4—42no—
581C2×D4—42no—
582C2×D4—532no—
583C2×D4—532no—
584C2×D4—532no—
585C2×D4—532no—
586C2×D4—1068no—
587C2×D4—1064no—
588C2×D4—1061no—
589C2×D4—1061no—
590C2×D4—1061no—
591C2×D4—1061no—
592C2×D4—1061no—
593C2×D4—1061no—
594C2×D4—1061no—
595C2×D4—1061no—
596C2×D4—2124no—
597C2×D4—2124no—
598C2×D4—2124no—
599C2×D4—2122no—
600C2×D4—2122no—
601C2×D4C2×C4×D5312yes—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—42no—
610C22×C4—42no—
611C22×C4—42no—
612C22×C4—42no—
613C22×C4—81no—
614C22×C4—81no—
615C22×C4—1061no—
616C22×C4—1061no—
617C22×C4—4241no—
618C22×C4—4241no—
619C22×C4—2122no—
620C22×C4—2122no—
621C22×C4—2122no—
622C22×C4—2122no—
623C22×C4C2×C4×D5312yes—
624C22×C4#1171994512yes—
625C22×C4C2×C22⋊D5311yescharacteristic
626C22×C4C2×C22⋊D5311yescharacteristic
627C22×C4C2×C22⋊D5311yescharacteristic
628C22×C4C2×C22⋊D5311yescharacteristic
629C22×C4C2×C22⋊D5311yescharacteristic
630C22×C4C23×D5311yescharacteristic
631D8—1068no—
632D8—2124no—
633C2×C8—532no—
634C2×C8—532no—
635C2×C8—532no—
636C2×C8—1061no—
637C2×C8—1061no—
638C2×C8—1061no—
639C2×C8—1061no—
640C2×C8—1061no—
641C2×C8—1061no—
642C2×C8—1061no—
643C2×C8—1061no—
644C2×C8—1061no—
645C2×C8—2124no—
646C4⋊C4—21no—
647C4⋊C4—21no—
648C4⋊C4—21no—
649C4⋊C4—21no—
650C4⋊C4—42no—
651C4⋊C4—42no—
652C4⋊C4—1061no—
653C4⋊C4—1061no—
654C4⋊C4—1061no—
655C4⋊C4—1061no—
656C4⋊C4C2×C4×D5312yes—
657C4⋊C4D4×D5312yes—
658C22⋊C4—22no—
659C22⋊C4—22no—
660C22⋊C4—24no—
661C22⋊C4—42no—
662C22⋊C4—42no—
663C22⋊C4—81no—
664C22⋊C4—4241no—
665C22⋊C4—4241no—
666C22⋊C4—2122no—
667C22⋊C4—2122no—
668C22⋊C4—2122no—
669C22⋊C4—2122no—
670C22⋊C4—2122no—
671C42—21no—
672C42—21no—
673C42—21no—
674C42—21no—
675C42—42no—
676C23—21no—
677C23—21no—
678C23—21no—
679C23—21no—
680C23—22no—
681C23—41no—
682C23—41no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23—41no—
687C23—1062no—
688C23—1062no—
689C23—1062no—
690C23—1062no—
691C23—4244no—
692C23—4244no—
693C23—4244no—
694C23—4244no—
695C23—4244no—
696C23—2128no—
697C23—2121no—
698C23—2121no—
699C23—2121no—
700C23—2121no—
701C23—2128no—
702C23—2121no—
703C23—2121no—
704C23—2121no—
705C23—2121no—
706C23—2121no—
707C23—2121no—
708C23C4×C22⋊D5312yes—
709C23#1313324212yes—
710C23#1313324312yes—
711C23C22×C22⋊D5311yescharacteristic
712D4—22no—
713D4—22no—
714D4—48no—
715D4—41no—
716D4—41no—
717D4—534no—
718D4—1062no—
719D4—1062no—
720D4—1062no—
721D4—1062no—
722D4—1062no—
723D4—2128no—
724D4—2121no—
725D4—2121no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—21no—
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—22no—
744C2×C4—21no—
745C2×C4—21no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—84no—
754C2×C4—84no—
755C2×C4—4244no—
756C2×C4—4244no—
757C2×C4—2121no—
758C2×C4—2121no—
759C2×C4—2121no—
760C2×C4—2121no—
761C2×C4—2121no—
762C2×C4—2121no—
763C2×C4C4×C22⋊D5312yes—
764C2×C4C22×C4×D5311yescharacteristic
765C2×C4C2×D4×D5311yescharacteristic
766C2×C4#41×D5311yescharacteristic
767C2×C4C2×#1171994511yescharacteristic
768C2×C4#1313326211yescharacteristic
769C2×C4#1313326311yescharacteristic
770C8—1062no—
771C8—1062no—
772C8—1062no—
773C8—2121no—
774C22—22no—
775C22—22no—
776C22—22no—
777C22—22no—
778C22—22no—
779C22—22no—
780C22—42no—
781C22—42no—
782C22—42no—
783C22—81no—
784C22—81no—
785C22—81no—
786C22—81no—
787C22—1064no—
788C22—42416no—
789C22—4241no—
790C22—4241no—
791C22—4241no—
792C22—4241no—
793C22—2122no—
794C22—2122no—
795C22—2122no—
796C22—2122no—
797C22—2122no—
798C22—2122no—
799C22—2122no—
800C22—2122no—
801C22—2122no—
802C22#1681073314yescomplemented
803C22C2×C4×C22⋊D5311yescharacteristic
804C22D4×C22⋊D5311yescharacteristic
805C22#1681126111yescharacteristic
806C22C2×#1313324211yescharacteristic
807C22C2×#1313324311yescharacteristic
808C22#1681142611yescharacteristic
809C22#1681143111yescharacteristic
810C4—22no—
811C4—41no—
812C4—42no—
813C4—41no—
814C4—41no—
815C4—41no—
816C4—42no—
817C4—81no—
818C4—4241no—
819C4—4241no—
820C4C4×D4×D5311yescharacteristic
821C4#1681109511yescharacteristic
822C4#1681126911yescharacteristic
823C4#1681130211yescharacteristic
824C2—24no—
825C2—82no—
826C2—4242no—
827C2—2124no—
828C2#2027769211yescharacteristic
829C2C2×#1681073311yescharacteristic
830C2#2028354311yescharacteristic
831C2#2028619111yescharacteristic
832C2#2028621111yescharacteristic
833C2#2028667011yescharacteristic
834C2#2028685011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D53
commutatorC2×C4×C53C23×C4
FrattiniC22×C4C23×D53
FittingC53×#2361C2
socleC23×C53C22×D4
prime radicalC2×#16810756C2
cosocleC22×C4×C53C24
hypercenter#2361D53
hypocenterC53#22858
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2361

Complements

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

NH ≅ G/Ntype
2. C2×#16810733C2semidirect
3. C22×#13133137C2semidirect
4. C22⋊C4×D212C2semidirect
5. #20275590C2semidirect
6. #20275411C2semidirect
7. #20275342C2semidirect
8. #20275144C2semidirect
9. #20275066C2semidirect
10. #20275063C2semidirect
11. #20274975C2semidirect
12. #20274908C2semidirect
13. #20274543C2semidirect
14. #20274493C2semidirect
15. C53×#2361C2semidirect
23. #16810756C4semidirect
25. C2×#13133148C22semidirect
26. C2×#13133148C22semidirect
27. C2×#13133138C22semidirect
28. C2×#13133138C22semidirect
37. C2×#13133128C22semidirect
38. C2×#13133128C22semidirect
45. #16810385C22semidirect
46. #16810385C22semidirect
47. #16810385C22semidirect
48. #16810385C22semidirect
49. #16810378C22semidirect
50. #16810378C22semidirect
53. C2×C4×D4×C53C22semidirect
55. C53×#390C22semidirect
56. C53×#389C22semidirect
60. C4×C4⋊C4×C53C22semidirect
69. C22×D212C2×C4semidirect
78. C2×#11719922C2×C4semidirect
79. C2×#11719922C2×C4semidirect
108. #13133137C2×C4semidirect
109. #13133137C2×C4semidirect
110. #13133137D4semidirect
111. C22⋊#88322C2×C4semidirect
121. #121×C53C2×C4semidirect
349. D212C4×D4semidirect
370. C22×C53#442semidirect
410. #2361D53semidirect
441. C2×C4×D4C2×D53semidirect
462. #390C2×D53semidirect
463. #389C2×D53semidirect
471. C4×C4⋊C4C2×D53semidirect
479. C53#22858semidirect
511. #121C4×D53semidirect
802. C22#16810733semidirect

Maximal subgroups

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

subgroupindex
C2×#168107562
C2×#168107332
C22×#131331372
C22⋊C4×D2122
#202755902
#202754112
#202753422
#202751442
#202750662
#202750632
#202749752
#202749082
#202745432
#202744932
C53×#23612
#2285853