Finite Group Databasebeta

← #27406489

Subgroups — #27406489

Order 13568.

1122 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16810815C211yesmaximal, characteristic
2C2×#16810733C211yesmaximal, characteristic, complemented
3C2×C4×#11719922C211yesmaximal, characteristic, complemented
4#20277626C211yesmaximal, characteristic, complemented
5#20275540C211yesmaximal, characteristic, complemented
6#20275483C211yesmaximal, characteristic, complemented
7#20275415C211yesmaximal, characteristic, complemented
8#20275401C211yesmaximal, characteristic, complemented
9#20275066C211yesmaximal, characteristic, complemented
10#20275066C211yesmaximal, characteristic, complemented
11#20274976C211yesmaximal, characteristic, complemented
12#20274962C211yesmaximal, characteristic, complemented
13#20274590C211yesmaximal, characteristic, complemented
14#20274543C211yesmaximal, characteristic, complemented
15C53×#2366C211yesmaximal, characteristic, complemented
16C22×#11719922C2211yescharacteristic
17C22×#11719922C2211yescharacteristic
18C2×C4×D212C2211yescharacteristic
19C2×C4×D212C2211yescharacteristic
20C2×C4×D212C2211yescharacteristic
21#16810815C418yescomplemented
22#16810733—24no—
23C4×#11719922—24no—
24C2×#13133150C2211yescharacteristic
25C2×#13133148C2211yescharacteristic
26C2×C4⋊#88322C2211yescharacteristic
27C2×#13133138C2211yescharacteristic
28C2×#13133138C2211yescharacteristic
29C2×#13133138C2211yescharacteristic
30C2×#13133138C2211yescharacteristic
31C2×#13133138C2211yescharacteristic
32C2×#13133138C2211yescharacteristic
33C2×#13133137C2211yescharacteristic
34C2×#13133137C2211yescharacteristic
35C2×#13133128C2211yescharacteristic
36C2×#13133128C2211yescharacteristic
37C2×C4×#88322C2211yescharacteristic
38#16810521C2211yescharacteristic
39#16810521C2211yescharacteristic
40#16810494—21no—
41#16810494—21no—
42#16810489C2211yescharacteristic
43#16810482—21no—
44#95×D53—21no—
45#16810385C2211yescharacteristic
46#16810385C2211yescharacteristic
47#16810385C2211yescharacteristic
48#16810385C2211yescharacteristic
49#16810378C2211yescharacteristic
50#16810378C2211yescharacteristic
51C2×#127×C53C2211yescharacteristic
52C2×C4×D4×C53—21no—
53C2×C4×D4×C53C2211yescharacteristic
54C2×C4×D4×C53C2211yescharacteristic
55C53×#390—21no—
56C53×#390C2211yescharacteristic
57C53×#390C2211yescharacteristic
58C53×#386—21no—
59C53×#386—21no—
60C4×C4⋊C4×C53C2211yescharacteristic
61C4×C4⋊C4×C53C2211yescharacteristic
62C22×D212C2311yescharacteristic
63C22×C4×D53—21no—
64C22×C4×D53—21no—
65C22×C4×D53—21no—
66C2×#11719922—22no—
67C2×#11719922—22no—
68C2×#11719922—22no—
69C2×#11719922—22no—
70C2×#11719922C2×C414yescomplemented
71C2×#11719922C2×C414yescomplemented
72C22×#88322C2311yescharacteristic
73C22×#88322C2311yescharacteristic
74C22×#88322C2311yescharacteristic
75C22×#88322C2311yescharacteristic
76C4×D212—22no—
77C4×D212—22no—
78C4×D212—22no—
79C4×D212—41no—
80C4×D212—41no—
81C4×D212C2×C414yescomplemented
82C2×C4⋊Dic53C2311yescharacteristic
83C2×C4⋊Dic53C2311yescharacteristic
84C2×C4⋊Dic53C2311yescharacteristic
85C2×#11719919—21no—
86C2×#11719919—21no—
87C2×#11719921—21no—
88C2×#11719921—21no—
89C2×#11719921—21no—
90#13133150—22no—
91#13133148—22no—
92C4⋊#88322C2×C414yescomplemented
93#13133138—22no—
94#13133138—22no—
95#13133138—41no—
96#13133138—41no—
97#13133138C2×C414yescomplemented
98#13133138C2×C414yescomplemented
99#13133137—22no—
100#13133137D414yescomplemented
101#13133128—22no—
102#13133128—22no—
103C4×#88322—22no—
104#13133124—21no—
105#13133124—21no—
106#13133124—21no—
107#13133124—21no—
108C22×D4×C53—21no—
109C22×D4×C53—21no—
110C22×D4×C53C2311yescharacteristic
111C22×D4×C53C2311yescharacteristic
112C23×C4×C53—21no—
113C23×C4×C53—21no—
114#127×C53—22no—
115#127×C53C2×C414yescomplemented
116C4×D4×C53—22no—
117C4×D4×C53—22no—
118C4×D4×C53—41no—
119C4×D4×C53—41no—
120C4×D4×C53—44no—
121C2×C4⋊C4×C53D411yescharacteristic
122C2×C4⋊C4×C53D411yescharacteristic
123C2×C4⋊C4×C53C2311yescharacteristic
124C2×C4⋊C4×C53C2311yescharacteristic
125C2×C22⋊C4×C53—21no—
126C2×C22⋊C4×C53—21no—
127C2×C22⋊C4×C53—21no—
128C2×C22⋊C4×C53—21no—
129C2×C22⋊C4×C53—21no—
130C2×C22⋊C4×C53—21no—
131C2×C42×C53—21no—
132C2×C42×C53C2311yescharacteristic
133C2×C42×C53C2311yescharacteristic
134C2×C42×C53C2311yescharacteristic
135#95×C53—21no—
136#95×C53D411yescharacteristic
137#95×C53D411yescharacteristic
138C24×C53—21no—
139C24×C53—21no—
140C23×D53—21no—
141C2×D4×C53—24no—
142C2×D4×C53—24no—
143C2×D4×C53—21no—
144C2×D4×C53—21no—
145C2×D4×C53—21no—
146C2×D4×C53—21no—
147C2×D4×C53—21no—
148C2×D4×C53—21no—
149C2×D4×C53—21no—
150C2×D4×C53—21no—
151C2×D4×C53—21no—
152C2×D4×C53—21no—
153C2×D4×C53—42no—
154C2×D4×C53—42no—
155C2×D4×C53—81no—
156C2×D4×C53—81no—
157C2×D4×C53C22×C412yes—
158C2×D4×C53C22×C412yes—
159C22×C4×C53—21no—
160C22×C4×C53—21no—
161C22×C4×C53—42no—
162C22×C4×C53—42no—
163C22×C4×C53—42no—
164C22×C4×C53—42no—
165C22×C4×C53—81no—
166C22×C4×C53—81no—
167C22×C4×C53C2×D411yescharacteristic
168C22×C4×C53C2×D411yescharacteristic
169C22×C4×C53C2×D411yescharacteristic
170C22×C4×C53C2×D411yescharacteristic
171C22×C4×C53C2×D411yescharacteristic
172C22×C4×C53C2×D411yescharacteristic
173C22×C4×C53C2411yescharacteristic
174C22×Dic53—21no—
175C22×Dic53—21no—
176C22×Dic53—21no—
177C2×D212—21no—
178C2×D212—21no—
179C2×D212—21no—
180C2×D212C22×C412yes—
181C2×D212C2×D412yes—
182C2×D212#4112yes—
183C2×C4×D53—24no—
184C2×C4×D53—42no—
185C2×C4×D53—42no—
186C2×C4×D53—42no—
187C2×C4×D53—42no—
188C2×C4×D53—81no—
189C2×C4×D53—81no—
190C2×C4×D53—81no—
191C2×C4×D53—81no—
192C4⋊C4×C53—22no—
193C4⋊C4×C53—21no—
194C4⋊C4×C53—21no—
195C4⋊C4×C53—21no—
196C4⋊C4×C53—41no—
197C4⋊C4×C53C2×D412yes—
198C22⋊C4×C53—42no—
199C22⋊C4×C53—42no—
200C22⋊C4×C53—42no—
201C22⋊C4×C53—42no—
202C22⋊C4×C53—81no—
203C22⋊C4×C53—81no—
204C42×C53—21no—
205C42×C53—21no—
206C42×C53—21no—
207C42×C53—21no—
208C42×C53—42no—
209C42×C53C22×C412yes—
210C42×C53#4112yes—
211#11719922—28no—
212#11719922—28no—
213#11719921—24no—
214#11719921—42no—
215#11719921—42no—
216C4⋊Dic53—21no—
217C4⋊Dic53—21no—
218C4⋊Dic53—21no—
219C4⋊Dic53—21no—
220C4⋊Dic53—21no—
221C4⋊Dic53C22×C412yes—
222#11719919—81no—
223#11719919—81no—
224C2×#88322—21no—
225C2×#88322—21no—
226C2×#88322—21no—
227C2×#88322—21no—
228C2×#88322—21no—
229C2×#88322—21no—
230C2×#88322—21no—
231C2×#88322—21no—
232C2×#88322—21no—
233C2×#88322C22×C412yes—
234C2×#88322C22×C412yes—
235C2×#88322C2×D412yes—
236C23×C53—22no—
237C23×C53—22no—
238C23×C53—41no—
239C23×C53—41no—
240C23×C53—41no—
241C23×C53—41no—
242C23×C53—41no—
243C23×C53—41no—
244C23×C53—41no—
245C23×C53—41no—
246C23×C53—41no—
247C23×C53—41no—
248C23×C53—41no—
249C23×C53—41no—
250C23×C53C22×D411yescharacteristic
251C22×D53—22no—
252C22×D53—22no—
253C22×D53—22no—
254C22×D53—41no—
255C22×D53—41no—
256C22×D53—41no—
257C22×D53—41no—
258D4×C53—22no—
259D4×C53—22no—
260D4×C53—22no—
261D4×C53—22no—
262D4×C53—48no—
263D4×C53—41no—
264D4×C53—41no—
265D4×C53—41no—
266D4×C53—41no—
267D4×C53—84no—
268C2×C4×C53—21no—
269C2×C4×C53—21no—
270C2×C4×C53—21no—
271C2×C4×C53—21no—
272C2×C4×C53—21no—
273C2×C4×C53—21no—
274C2×C4×C53—21no—
275C2×C4×C53—22no—
276C2×C4×C53—21no—
277C2×C4×C53—21no—
278C2×C4×C53—21no—
279C2×C4×C53—21no—
280C2×C4×C53—21no—
281C2×C4×C53—21no—
282C2×C4×C53—21no—
283C2×C4×C53—21no—
284C2×C4×C53—41no—
285C2×C4×C53—41no—
286C2×C4×C53—41no—
287C2×C4×C53—41no—
288C2×C4×C53—41no—
289C2×C4×C53—84no—
290C2×C4×C53—84no—
291C2×C4×C53C4×D412yes—
292C2×C4×C53C4×D412yes—
293C2×C4×C53AGL(1,ℤ/8)12yes—
294C2×C4×C53C23×C411yescharacteristic
295C2×C4×C53C22×D411yescharacteristic
296C2×C4×C53C2×#4111yescharacteristic
297C2×C4×C53C2×#4111yescharacteristic
298C2×C4×C53H(5,𝔽2)11yescharacteristic
299C2×C4×C532−1+411yescharacteristic
300C2×Dic53—22no—
301C2×Dic53—41no—
302C2×Dic53—41no—
303C2×Dic53—41no—
304C2×Dic53—41no—
305C2×Dic53—41no—
306C2×Dic53—41no—
307C2×Dic53—41no—
308C2×Dic53—41no—
309D212—22no—
310D212—22no—
311D212—22no—
312D212C4×D414yescomplemented
313C4×D53—84no—
314C4×D53—84no—
315C4×D53—84no—
316#88322—22no—
317#88322—22no—
318#88322—22no—
319#88322—41no—
320#23008—531nomaximal, Sylow
321C22×C53—42no—
322C22×C53—42no—
323C22×C53—42no—
324C22×C53—42no—
325C22×C53—42no—
326C22×C53—42no—
327C22×C53—81no—
328C22×C53—81no—
329C22×C53—81no—
330C22×C53—81no—
331C22×C53—81no—
332C22×C53—81no—
333C22×C53—81no—
334C22×C53—81no—
335C22×C53C2×C4×D411yescharacteristic
336C22×C53D4211yescharacteristic
337C22×C53#54811yescharacteristic
338C22×C53C2×AGL(1,ℤ/8)11yescharacteristic
339C22×C53#57511yescharacteristic
340C22×C53#57611yescharacteristic
341C22×C53#57611yescharacteristic
342C2×D53—24no—
343C2×D53—42no—
344C2×D53—42no—
345C2×D53—42no—
346C2×D53—42no—
347C2×D53—42no—
348C2×D53—42no—
349C4×C53—22no—
350C4×C53—22no—
351C4×C53—22no—
352C4×C53—41no—
353C4×C53—42no—
354C4×C53—41no—
355C4×C53—41no—
356C4×C53—81no—
357C4×C53C2×C4×D411yescharacteristic
358C4×C53#52011yescharacteristic
359C4×C53#54711yescharacteristic
360C4×C53#55311yescharacteristic
361Dic53—42no—
362Dic53—81no—
363Dic53—81no—
364C2×#459—531no—
365C2×#442—531no—
366C2×C4×D8—531no—
367#2366D5311yescharacteristic, complemented
368#2349—531no—
369#1961—531no—
370#1949—531no—
371#1936—531no—
372#1934—531no—
373#1879—531no—
374#1879—531no—
375#1864—531no—
376#1862—531no—
377#1771—531no—
378#1762—531no—
379C2×C53—82no—
380C2×C53—82no—
381C2×C53#236111yescharacteristic
382C2×C53C4×AGL(1,ℤ/8)11yescharacteristic
383C2×C53#294811yescharacteristic
384C2×C53#326411yescharacteristic
385C2×C53#326811yescharacteristic
386C2×C53#336611yescharacteristic
387C2×C53#337011yescharacteristic
388D53—44no—
389C22×D8—531no—
390C22×D8—531no—
391C2×#127C2×D5311yescharacteristic
392C2×C4×D4—21no—
393C2×C4×D4—531no—
394C2×C4×D4—531no—
395C2×C4×D4—531no—
396C2×C4×D4C2×D5311yescharacteristic
397C2×C4×D4C2×D5311yescharacteristic
398#459—538no—
399#442—1064no—
400C4×D8—1064no—
401C2×#107—531no—
402C2×#106—531no—
403C2×C4⋊C8—531no—
404C2×#102—531no—
405C2×#102—531no—
406C2×#102—531no—
407C2×#102—531no—
408C2×#102—531no—
409C2×#102—531no—
410C2×#102—531no—
411C2×#102—531no—
412C2×#97—531no—
413C2×#97—531no—
414C2×C4×C8—531no—
415#390—21no—
416#390C2×D5311yescharacteristic
417#390C2×D5311yescharacteristic
418#389—531no—
419#389—531no—
420#386—21no—
421#386—21no—
422#385—1061no—
423#385—1061no—
424#382—531no—
425#380—1061no—
426C4×C4⋊C4C2×D5311yescharacteristic
427C4×C4⋊C4C2×D5311yescharacteristic
428C2×#95—1061no—
429#340—531no—
430#340—531no—
431#340—531no—
432#340—531no—
433#336—531no—
434#336—531no—
435C53#2300811yescharacteristic, complemented, Sylow
436C22×D4—21no—
437C22×D4—21no—
438C22×D4—531no—
439C22×D4C22×D5311yescharacteristic
440C22×D4C22×D5311yescharacteristic
441C23×C4—21no—
442C23×C4—21no—
443C23×C4—1061no—
444C23×C4—1061no—
445C23×C4—1061no—
446C2×D8—534no—
447C2×D8—534no—
448C2×D8—1062no—
449C2×D8—1062no—
450C2×D8—1062no—
451C2×D8—1062no—
452C22×C8—531no—
453C22×C8—531no—
454C22×C8—531no—
455C22×C8—531no—
456#127—22no—
457#127C4×D5314yescomplemented
458C4×D4—22no—
459C4×D4—22no—
460C4×D4—41no—
461C4×D4—41no—
462C4×D4—44no—
463C4×D4—534no—
464C4×D4—1062no—
465C4×D4—1062no—
466C4×D4—1062no—
467C4×D4—2121no—
468C4×D4—2121no—
469C2×C4⋊C4—531no—
470C2×C4⋊C4—531no—
471C2×C4⋊C4—531no—
472C2×C4⋊C4—1061no—
473C2×C4⋊C4—1061no—
474C2×C4⋊C4C22⋊D5311yescharacteristic
475C2×C4⋊C4C22⋊D5311yescharacteristic
476C2×C4⋊C4C22×D5311yescharacteristic
477C2×C4⋊C4C22×D5311yescharacteristic
478C2×C22⋊C4—21no—
479C2×C22⋊C4—21no—
480C2×C22⋊C4—21no—
481C2×C22⋊C4—21no—
482C2×C22⋊C4—21no—
483C2×C22⋊C4—21no—
484C2×C22⋊C4—1061no—
485C2×C22⋊C4—1061no—
486C2×C22⋊C4—1061no—
487C2×C42—21no—
488C2×C42C22×D5311yescharacteristic
489C2×C42C22×D5311yescharacteristic
490C2×C42C22×D5311yescharacteristic
491#107—1062no—
492#106—1062no—
493C4⋊C8—534no—
494#102—534no—
495#102—534no—
496#102—534no—
497#102—1062no—
498#102—1062no—
499#102—1062no—
500#102—2121no—
501#102—2121no—
502#97—1062no—
503#97—1062no—
504C4×C8—1062no—
505#95—21no—
506#95—1061no—
507#95—1061no—
508#95—1061no—
509#95—1061no—
510#95C22⋊D5311yescharacteristic
511#95C22⋊D5311yescharacteristic
512C24—21no—
513C24—21no—
514C24—1061no—
515C2×D4—24no—
516C2×D4—24no—
517C2×D4—21no—
518C2×D4—21no—
519C2×D4—21no—
520C2×D4—21no—
521C2×D4—21no—
522C2×D4—21no—
523C2×D4—21no—
524C2×D4—21no—
525C2×D4—21no—
526C2×D4—21no—
527C2×D4—42no—
528C2×D4—42no—
529C2×D4—81no—
530C2×D4—81no—
531C2×D4—532no—
532C2×D4—532no—
533C2×D4—532no—
534C2×D4—1061no—
535C2×D4—1061no—
536C2×D4—1061no—
537C2×D4C2×C4×D5312yes—
538C2×D4C2×C4×D5312yes—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—42no—
542C22×C4—42no—
543C22×C4—42no—
544C22×C4—42no—
545C22×C4—81no—
546C22×C4—81no—
547C22×C4—1061no—
548C22×C4—1064no—
549C22×C4—1061no—
550C22×C4—1061no—
551C22×C4—4241no—
552C22×C4—4241no—
553C22×C4—4241no—
554C22×C4—4241no—
555C22×C4—2122no—
556C22×C4—2122no—
557C22×C4—2122no—
558C22×C4—2122no—
559C22×C4C2×C22⋊D5311yescharacteristic
560C22×C4C2×C22⋊D5311yescharacteristic
561C22×C4C2×C22⋊D5311yescharacteristic
562C22×C4C2×C22⋊D5311yescharacteristic
563C22×C4C2×C22⋊D5311yescharacteristic
564C22×C4C2×C22⋊D5311yescharacteristic
565C22×C4C23×D5311yescharacteristic
566D8—1068no—
567D8—1068no—
568C2×C8—532no—
569C2×C8—532no—
570C2×C8—532no—
571C2×C8—1061no—
572C2×C8—1061no—
573C2×C8—1061no—
574C2×C8—1061no—
575C2×C8—1061no—
576C2×C8—1061no—
577C2×C8—1061no—
578C2×C8—1061no—
579C2×C8—1061no—
580C4⋊C4—22no—
581C4⋊C4—21no—
582C4⋊C4—21no—
583C4⋊C4—21no—
584C4⋊C4—41no—
585C4⋊C4—532no—
586C4⋊C4—1061no—
587C4⋊C4—1061no—
588C4⋊C4—1061no—
589C4⋊C4—1061no—
590C4⋊C4—1061no—
591C4⋊C4—4241no—
592C4⋊C4—4241no—
593C4⋊C4D4×D5312yes—
594C22⋊C4—42no—
595C22⋊C4—42no—
596C22⋊C4—42no—
597C22⋊C4—42no—
598C22⋊C4—81no—
599C22⋊C4—81no—
600C22⋊C4—1064no—
601C22⋊C4—2122no—
602C22⋊C4—2122no—
603C42—21no—
604C42—21no—
605C42—21no—
606C42—21no—
607C42—42no—
608C42C2×C4×D5312yes—
609C42#1171994512yes—
610C23—22no—
611C23—22no—
612C23—41no—
613C23—41no—
614C23—41no—
615C23—41no—
616C23—41no—
617C23—41no—
618C23—41no—
619C23—41no—
620C23—41no—
621C23—41no—
622C23—41no—
623C23—41no—
624C23—1062no—
625C23—1062no—
626C23—1062no—
627C23—2121no—
628C23—2121no—
629C23—2121no—
630C23—2121no—
631C23C22×C22⋊D5311yescharacteristic
632D4—22no—
633D4—22no—
634D4—22no—
635D4—22no—
636D4—48no—
637D4—41no—
638D4—41no—
639D4—41no—
640D4—41no—
641D4—84no—
642D4—534no—
643D4—1062no—
644D4—1062no—
645D4—1062no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—22no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—84no—
668C2×C4—84no—
669C2×C4—1062no—
670C2×C4—4244no—
671C2×C4—4244no—
672C2×C4—4244no—
673C2×C4—2121no—
674C2×C4—2121no—
675C2×C4—2121no—
676C2×C4—2121no—
677C2×C4—2121no—
678C2×C4—2121no—
679C2×C4—2121no—
680C2×C4—2121no—
681C2×C4C4×C22⋊D5312yes—
682C2×C4C4×C22⋊D5312yes—
683C2×C4#1313324312yes—
684C2×C4C22×C4×D5311yescharacteristic
685C2×C4C2×D4×D5311yescharacteristic
686C2×C4#41×D5311yescharacteristic
687C2×C4C2×#1171994511yescharacteristic
688C2×C4#1313326211yescharacteristic
689C2×C4#1313326411yescharacteristic
690C8—1062no—
691C8—1062no—
692C8—1062no—
693C8—2121no—
694C22—42no—
695C22—42no—
696C22—42no—
697C22—42no—
698C22—42no—
699C22—42no—
700C22—81no—
701C22—81no—
702C22—81no—
703C22—81no—
704C22—81no—
705C22—81no—
706C22—81no—
707C22—81no—
708C22—1064no—
709C22—2122no—
710C22—2122no—
711C22—2122no—
712C22—2122no—
713C22—2122no—
714C22—2122no—
715C22C2×C4×C22⋊D5311yescharacteristic
716C22D4×C22⋊D5311yescharacteristic
717C22#1681128011yescharacteristic
718C22C2×#1313324311yescharacteristic
719C22#1681142111yescharacteristic
720C22#1681142611yescharacteristic
721C22#1681142611yescharacteristic
722C4—22no—
723C4—22no—
724C4—22no—
725C4—41no—
726C4—41no—
727C4—41no—
728C4—42no—
729C4—81no—
730C4—4241no—
731C4—4241no—
732C4—2122no—
733C4C4×D4×D5311yescharacteristic
734C4#1681110211yescharacteristic
735C4#1681127811yescharacteristic
736C4#1681132311yescharacteristic
737C2—82no—
738C2—82no—
739C2—2124no—
740C2#2027772711yescharacteristic
741C2C4×#1313324311yescharacteristic
742C2#2028356511yescharacteristic
743C2#2028619111yescharacteristic
744C2#2028625611yescharacteristic
745C2#2028741811yescharacteristic
746C2#2028746211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D53
commutatorC2×C4×C53C23×C4
FrattiniC22×C4C23×D53
FittingC53×#2366C2
socleC23×C53C22×D4
prime radicalC2×#16810815C2
cosocleC22×C4×C53C24
hypercenter#2366D53
hypocenterC53#23008
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2366

Complements

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

NH ≅ G/Ntype
2. C2×#16810733C2semidirect
3. C2×C4×#11719922C2semidirect
4. #20277626C2semidirect
5. #20275540C2semidirect
6. #20275483C2semidirect
7. #20275415C2semidirect
8. #20275401C2semidirect
9. #20275066C2semidirect
10. #20275066C2semidirect
11. #20274976C2semidirect
12. #20274962C2semidirect
13. #20274590C2semidirect
14. #20274543C2semidirect
15. C53×#2366C2semidirect
21. #16810815C4semidirect
70. C2×#11719922C2×C4semidirect
71. C2×#11719922C2×C4semidirect
81. C4×D212C2×C4semidirect
92. C4⋊#88322C2×C4semidirect
97. #13133138C2×C4semidirect
98. #13133138C2×C4semidirect
100. #13133137D4semidirect
115. #127×C53C2×C4semidirect
312. D212C4×D4semidirect
367. #2366D53semidirect
435. C53#23008semidirect
457. #127C4×D53semidirect

Maximal subgroups

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

subgroupindex
C2×#168108152
C2×#168107332
C2×C4×#117199222
#202776262
#202755402
#202754832
#202754152
#202754012
#202750662
#202749762
#202749622
#202745902
#202745432
C53×#23662
#2300853