Finite Group Databasebeta

← #27406685

Subgroups — #27406685

Order 13568.

1066 conjugacy classes of subgroups.

The subgroup lattice has 706 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×SD16×Dic53C211yesmaximal, characteristic, complemented
2C22×#13133149C211yesmaximal, characteristic, complemented
3#20277735C211yesmaximal, characteristic
4#20277724C211yesmaximal, characteristic, complemented
5#20275571C211yesmaximal, characteristic, complemented
6#20275444C211yesmaximal, characteristic, complemented
7#20275351C211yesmaximal, characteristic, complemented
8#20275344C211yesmaximal, characteristic, complemented
9#20275033C211yesmaximal, characteristic
10#20275023C211yesmaximal, characteristic, complemented
11#20274985C211yesmaximal, characteristic, complemented
12#20274978C211yesmaximal, characteristic, complemented
13#106×Dic53C211yesmaximal, characteristic, complemented
14C8×C22⋊Dic53C211yesmaximal, characteristic, complemented
15C2×C53×#465C211yesmaximal, characteristic
16C2×Q8×Dic53C2211yescharacteristic
17C2×D4×Dic53—21no—
18C2×D4×Dic53C2211yescharacteristic
19C22×C4⋊Dic53C2211yescharacteristic
20C22×C4⋊Dic53C2211yescharacteristic
21SD16×Dic53—24no—
22C2×#13133149—24no—
23C2×#13133149C2211yescharacteristic
24C2×#13133149C2211yescharacteristic
25C2×#13133149C2211yescharacteristic
26C2×#13133149C2211yescharacteristic
27C2×#13133141C2211yescharacteristic
28C2×#13133141C2211yescharacteristic
29C2×#13133138C2211yescharacteristic
30C2×#13133138C2211yescharacteristic
31C2×C22⋊#88322C2211yescharacteristic
32C2×C8×Dic53C2211yescharacteristic
33C2×C8×Dic53C2211yescharacteristic
34#16810530C2211yescharacteristic
35#16810526C2211yescharacteristic
36#16810522—21no—
37#16810522C2211yescharacteristic
38#16810522C2211yescharacteristic
39#16810516—21no—
40#16810509—21no—
41#16810503—21no—
42#16810498—21no—
43#16810498—21no—
44C4⋊C4×Dic53C2211yescharacteristic
45C4⋊C4×Dic53C2211yescharacteristic
46C22⋊C4×Dic53—21no—
47C4×C22⋊Dic53C2211yescharacteristic
48#16810385C2211yescharacteristic
49#16810385C2211yescharacteristic
50#16810385C2211yescharacteristic
51#16810385C2211yescharacteristic
52#16810377C2211yescharacteristic
53#16810377C2211yescharacteristic
54C22×SD16×C53C2211yescharacteristic
55C23×C8×C53C2211yescharacteristic
56C2×C22⋊Q8×C53C2211yescharacteristic
57C2×#121×C53C2211yescharacteristic
58C53×#465C418yescomplemented
59C2×#106×C53C2211yescharacteristic
60C2×#103×C53C2211yescharacteristic
61C2×#102×C53C2211yescharacteristic
62C23×Dic53—21no—
63C23×Dic53—21no—
64C23×Dic53—21no—
65C22×#88322C2311yescharacteristic
66C22×#88322C2311yescharacteristic
67Q8×Dic53—22no—
68Q8×Dic53—41no—
69D4×Dic53—22no—
70D4×Dic53—41no—
71D4×Dic53—44no—
72C2×C4⋊Dic53—21no—
73C2×C4⋊Dic53—21no—
74C2×C4⋊Dic53—21no—
75C2×C4⋊Dic53—21no—
76C2×C4⋊Dic53—21no—
77C2×C4⋊Dic53—22no—
78C2×C4⋊Dic53—22no—
79C2×C4⋊Dic53—41no—
80C2×C4⋊Dic53—41no—
81C2×C4⋊Dic53C2311yescharacteristic
82C2×C4⋊Dic53C2311yescharacteristic
83C2×C4⋊Dic53C2311yescharacteristic
84C2×C4⋊Dic53C2311yescharacteristic
85C2×C22⋊Dic53—21no—
86C2×C22⋊Dic53—21no—
87C2×C22⋊Dic53—21no—
88C2×C22⋊Dic53D411yescharacteristic
89C2×C22⋊Dic53D411yescharacteristic
90C2×C4×Dic53—21no—
91C2×C4×Dic53—21no—
92C2×C4×Dic53—21no—
93C2×C4×Dic53C2311yescharacteristic
94C2×C4×Dic53C2311yescharacteristic
95#13133149—22no—
96#13133149—22no—
97#13133149—22no—
98#13133149D414yescomplemented
99#13133141—22no—
100#13133141—41no—
101#13133138—22no—
102#13133138—41no—
103C22⋊#88322—22no—
104C8×Dic53—22no—
105C8×Dic53—22no—
106#13133124—21no—
107#13133124—21no—
108#13133124—21no—
109#13133124—21no—
110#13133124—21no—
111#13133124—21no—
112#13133124D411yescharacteristic
113#13133124D411yescharacteristic
114C22×Q8×C53C2311yescharacteristic
115C22×D4×C53—21no—
116C22×D4×C53C2311yescharacteristic
117C23×C4×C53C2311yescharacteristic
118C2×SD16×C53—22no—
119C2×SD16×C53—22no—
120C2×SD16×C53C2×C414yescomplemented
121C22×C8×C53—22no—
122C22×C8×C53—22no—
123C22×C8×C53C2×C414yescomplemented
124C22×C8×C53C2311yescharacteristic
125C22×C8×C53C2311yescharacteristic
126C22⋊Q8×C53—22no—
127C22⋊Q8×C53C2×C414yescomplemented
128#121×C53—22no—
129#121×C53C2×C414yes—
130C2×C4⋊C4×C53—21no—
131C2×C4⋊C4×C53C2311yescharacteristic
132C2×C4⋊C4×C53C2311yescharacteristic
133C2×C22⋊C4×C53—21no—
134C2×C22⋊C4×C53—21no—
135#106×C53C2×C414yescomplemented
136#103×C53C2×C414yescomplemented
137#102×C53C2×C414yescomplemented
138C24×C53—21no—
139C24×C53C2×D411yescharacteristic
140C2×Q8×C53—21no—
141C2×Q8×C53—21no—
142C2×Q8×C53—21no—
143C2×Q8×C53—21no—
144C2×Q8×C53—21no—
145C2×Q8×C53C22×C412yes—
146C2×D4×C53—24no—
147C2×D4×C53—21no—
148C2×D4×C53—21no—
149C2×D4×C53—21no—
150C2×D4×C53—21no—
151C2×D4×C53—21no—
152C2×D4×C53—42no—
153C2×D4×C53—42no—
154C2×D4×C53C22×C412yes—
155C22×C4×C53—21no—
156C22×C4×C53—21no—
157C22×C4×C53—21no—
158C22×C4×C53—21no—
159C22×C4×C53—21no—
160C22×C4×C53—21no—
161C22×C4×C53—21no—
162C22×C4×C53C22×C412yes—
163C22×C4×C53C2×D411yescharacteristic
164C22×C4×C53#4112yes—
165C22×C4×C53C2411yescharacteristic
166C22×Dic53—21no—
167C22×Dic53—21no—
168C22×Dic53—21no—
169C22×Dic53—21no—
170C22×Dic53—42no—
171C22×Dic53—42no—
172C22×Dic53—42no—
173C22×Dic53—42no—
174C22×Dic53—42no—
175C22×Dic53—42no—
176C22×Dic53—81no—
177C22×Dic53—81no—
178C22×Dic53—81no—
179C22×Dic53C2×D411yescharacteristic
180C22×Dic53C2×D411yescharacteristic
181C22×Dic53C2×D411yescharacteristic
182C22×Dic53C2×D411yescharacteristic
183SD16×C53—28no—
184C2×C8×C53—21no—
185C2×C8×C53—21no—
186C2×C8×C53—28no—
187C2×C8×C53C22×C412yes—
188C2×C8×C53C22×C412yes—
189C2×C8×C53C2×D412yes—
190C2×C8×C53#4112yes—
191C4⋊C4×C53—24no—
192C4⋊C4×C53—21no—
193C4⋊C4×C53—21no—
194C4⋊C4×C53C22×C412yes—
195C4⋊C4×C53C22×C412yes—
196C22⋊C4×C53—24no—
197C22⋊C4×C53—24no—
198C22⋊Dic53—22no—
199C22⋊Dic53—42no—
200C22⋊Dic53—42no—
201C22⋊Dic53—81no—
202C22⋊Dic53SD1614yescomplemented
203C4⋊Dic53—21no—
204C4⋊Dic53—21no—
205C4⋊Dic53—21no—
206C4⋊Dic53—21no—
207C4⋊Dic53—21no—
208C4⋊Dic53—21no—
209C4⋊Dic53—42no—
210C4⋊Dic53—42no—
211C4⋊Dic53—42no—
212C4⋊Dic53—42no—
213C4⋊Dic53—81no—
214C4⋊Dic53C2×D412yes—
215C4⋊Dic53C2×D412yes—
216C4×Dic53—21no—
217C4×Dic53—21no—
218C4×Dic53—21no—
219C4×Dic53—21no—
220C4×Dic53—42no—
221C4×Dic53—42no—
222C4×Dic53—81no—
223C2×#88322—21no—
224C2×#88322—21no—
225C2×#88322—21no—
226C2×#88322—21no—
227C2×#88322—21no—
228C2×#88322—21no—
229C23×C53—21no—
230C23×C53—21no—
231C23×C53—21no—
232C23×C53—21no—
233C23×C53—22no—
234C23×C53—41no—
235C23×C53—41no—
236C23×C53—41no—
237C23×C53—41no—
238C23×C53—41no—
239C23×C53—41no—
240C23×C53C4×D412yes—
241C23×C53C2×SD1612yes—
242C23×C53#13512yes—
243C23×C53C22×D411yescharacteristic
244Q8×C53—22no—
245Q8×C53—22no—
246Q8×C53—41no—
247Q8×C53—41no—
248D4×C53—22no—
249D4×C53—22no—
250D4×C53—48no—
251D4×C53—41no—
252D4×C53—41no—
253C2×C4×C53—21no—
254C2×C4×C53—21no—
255C2×C4×C53—22no—
256C2×C4×C53—22no—
257C2×C4×C53—22no—
258C2×C4×C53—22no—
259C2×C4×C53—22no—
260C2×C4×C53—22no—
261C2×C4×C53—22no—
262C2×C4×C53—41no—
263C2×C4×C53—41no—
264C2×C4×C53—41no—
265C2×C4×C53—41no—
266C2×C4×C53—41no—
267C2×C4×C53—41no—
268C2×C4×C53C4×D412yes—
269C2×C4×C53C23×C411yescharacteristic
270C2×C4×C53C22×D411yescharacteristic
271C2×C4×C53C2×#4111yescharacteristic
272C2×C4×C53C2×#4111yescharacteristic
273C2×C4×C53H(5,𝔽2)11yescharacteristic
274C2×C4×C532−1+411yescharacteristic
275C2×Dic53—21no—
276C2×Dic53—21no—
277C2×Dic53—21no—
278C2×Dic53—21no—
279C2×Dic53—22no—
280C2×Dic53—22no—
281C2×Dic53—21no—
282C2×Dic53—21no—
283C2×Dic53—21no—
284C2×Dic53—21no—
285C2×Dic53—21no—
286C2×Dic53—21no—
287C2×Dic53—41no—
288C2×Dic53—41no—
289C2×Dic53—41no—
290C2×Dic53—41no—
291C2×Dic53—41no—
292C2×Dic53—41no—
293C2×Dic53—41no—
294C2×Dic53—41no—
295C2×Dic53—41no—
296C2×Dic53—41no—
297C2×Dic53—84no—
298C2×Dic53—84no—
299C2×Dic53—84no—
300C2×Dic53C2×SD1612yes—
301C2×Dic53C2×SD1612yes—
302C8×C53—22no—
303C8×C53C4×D414yescomplemented
304#88322—41no—
305#88322—41no—
306#23022—531nomaximal, Sylow
307C22×C53—22no—
308C22×C53—22no—
309C22×C53—22no—
310C22×C53—22no—
311C22×C53—22no—
312C22×C53—22no—
313C22×C53—42no—
314C22×C53—42no—
315C22×C53—42no—
316C22×C53—81no—
317C22×C53—81no—
318C22×C53—81no—
319C22×C53—81no—
320C22×C53C4×SD1614yescomplemented
321C22×C53C2×C4×D411yescharacteristic
322C22×C53D4211yescharacteristic
323C22×C53#54711yescharacteristic
324C22×C53C22×SD1611yescharacteristic
325C22×C53C2×#13511yescharacteristic
326C22×C53#57711yescharacteristic
327C22×C53#57711yescharacteristic
328C4×C53—22no—
329C4×C53—42no—
330C4×C53—42no—
331C4×C53—42no—
332C4×C53C2×C4×D411yescharacteristic
333C4×C53#52011yescharacteristic
334C4×C53#54811yescharacteristic
335C4×C53#55311yescharacteristic
336Dic53—22no—
337Dic53—22no—
338Dic53—41no—
339Dic53—42no—
340Dic53—41no—
341Dic53—42no—
342Dic53—81no—
343Dic53—81no—
344C2×#465D5311yescharacteristic
345C2×C4×SD16—531no—
346C22×#106—531no—
347#2361—531no—
348#2360—531no—
349#1968—531no—
350#1941—531no—
351#1927—531no—
352#1926—531no—
353#1874—531no—
354#1872—531no—
355#1865—531no—
356#1864—531no—
357C4×#106—531no—
358C8×C22⋊C4—531no—
359C2×C53—24no—
360C2×C53—82no—
361C2×C53#236111yescharacteristic
362C2×C53C2×C4×SD1611yescharacteristic
363C2×C53#295211yescharacteristic
364C2×C53D4×SD1611yescharacteristic
365C2×C53#328211yescharacteristic
366C2×C53#333511yescharacteristic
367C2×C53#333711yescharacteristic
368C22×SD16C2×D5311yescharacteristic
369C23×C8C2×D5311yescharacteristic
370C2×C22⋊Q8C2×D5311yescharacteristic
371C2×#121C2×D5311yescharacteristic
372C2×C4×Q8—531no—
373C2×C4×D4—531no—
374C2×C4×D4—1061no—
375C22×C4⋊C4—531no—
376C22×C4⋊C4—531no—
377#465Dic5318yescomplemented
378C4×SD16—1064no—
379C2×#106—531no—
380C2×#106—531no—
381C2×#106—531no—
382C2×#106—531no—
383C2×#106—1064no—
384C2×#106C2×D5311yescharacteristic
385C2×#103—531no—
386C2×#103—531no—
387C2×#103C2×D5311yescharacteristic
388C2×#102—531no—
389C2×#102—531no—
390C2×#102C2×D5311yescharacteristic
391C2×C22⋊C8—531no—
392C2×C4×C8—531no—
393C2×C4×C8—531no—
394#391—531no—
395#390—531no—
396#389—531no—
397#389—531no—
398#389—1061no—
399#388—1061no—
400#387—1061no—
401#386—1061no—
402#385—1061no—
403#385—1061no—
404C4×C4⋊C4—531no—
405C4×C4⋊C4—531no—
406C4×C22⋊C4—531no—
407C4×C22⋊C4—1061no—
408#340—531no—
409#340—531no—
410#340—531no—
411#340—531no—
412#336—531no—
413#336—531no—
414C53#2302211yescharacteristic, complemented, Sylow
415C22×Q8C22×D5311yescharacteristic
416C22×D4—21no—
417C22×D4C22×D5311yescharacteristic
418C23×C4—1061no—
419C23×C4—1061no—
420C23×C4—1061no—
421C23×C4C22×D5311yescharacteristic
422C2×SD16—22no—
423C2×SD16—22no—
424C2×SD16C2×Dic5314yescomplemented
425C22×C8—22no—
426C22×C8—22no—
427C22×C8—531no—
428C22×C8—531no—
429C22×C8C2×Dic5314yescomplemented
430C22×C8C22×D5311yescharacteristic
431C22×C8C22×D5311yescharacteristic
432C22⋊Q8—22no—
433C22⋊Q8C2×Dic5314yescomplemented
434#121—22no—
435#121C2×Dic5314yes—
436C4×Q8—1062no—
437C4×Q8—2121no—
438C4×D4—1062no—
439C4×D4—2121no—
440C4×D4—2124no—
441C2×C4⋊C4—21no—
442C2×C4⋊C4—531no—
443C2×C4⋊C4—531no—
444C2×C4⋊C4—531no—
445C2×C4⋊C4—531no—
446C2×C4⋊C4—1062no—
447C2×C4⋊C4—1062no—
448C2×C4⋊C4—1061no—
449C2×C4⋊C4—1061no—
450C2×C4⋊C4—1061no—
451C2×C4⋊C4—1061no—
452C2×C4⋊C4—1061no—
453C2×C4⋊C4—2121no—
454C2×C4⋊C4—2121no—
455C2×C4⋊C4C22×D5311yescharacteristic
456C2×C4⋊C4C22×D5311yescharacteristic
457C2×C22⋊C4—21no—
458C2×C22⋊C4—21no—
459C2×C22⋊C4—531no—
460C2×C22⋊C4—531no—
461C2×C22⋊C4—1061no—
462C2×C22⋊C4—1061no—
463C2×C22⋊C4—1061no—
464C2×C42—531no—
465C2×C42—531no—
466C2×C42—1061no—
467C2×C42—1061no—
468C2×C42—1061no—
469#106—534no—
470#106—1062no—
471#106—1062no—
472#106—1062no—
473#106C2×Dic5314yescomplemented
474#103—1062no—
475#103—2121no—
476#103C2×Dic5314yescomplemented
477#102—1062no—
478#102—2121no—
479#102C2×Dic5314yescomplemented
480C22⋊C8—1062no—
481C4×C8—1062no—
482C4×C8—1062no—
483#95—531no—
484#95—531no—
485#95—1061no—
486#95—1061no—
487#95—1061no—
488#95—1061no—
489#95—1061no—
490#95—1061no—
491C24—21no—
492C24D4×D5311yescharacteristic
493C2×Q8—21no—
494C2×Q8—21no—
495C2×Q8—21no—
496C2×Q8—21no—
497C2×Q8—21no—
498C2×Q8C22×Dic5312yes—
499C2×D4—24no—
500C2×D4—21no—
501C2×D4—21no—
502C2×D4—21no—
503C2×D4—21no—
504C2×D4—21no—
505C2×D4—42no—
506C2×D4—42no—
507C2×D4C22×Dic5312yes—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—531no—
516C22×C4—531no—
517C22×C4—531no—
518C22×C4—531no—
519C22×C4—1061no—
520C22×C4—1061no—
521C22×C4—1061no—
522C22×C4—1061no—
523C22×C4—4241no—
524C22×C4—4241no—
525C22×C4—4241no—
526C22×C4—2122no—
527C22×C4—2122no—
528C22×C4—2122no—
529C22×C4—2122no—
530C22×C4—2122no—
531C22×C4—2122no—
532C22×C4D4×D5311yescharacteristic
533C22×C4#1171994712yes—
534C22×C4C22×Dic5312yes—
535C22×C4C23×D5311yescharacteristic
536SD16—28no—
537C2×C8—21no—
538C2×C8—21no—
539C2×C8—28no—
540C2×C8—1061no—
541C2×C8—1061no—
542C2×C8—1061no—
543C2×C8—1061no—
544C2×C8—1061no—
545C2×C8—1061no—
546C2×C8D4×D5312yes—
547C2×C8#1171994712yes—
548C2×C8C22×Dic5312yes—
549C2×C8C22×Dic5312yes—
550C4⋊C4—24no—
551C4⋊C4—21no—
552C4⋊C4—21no—
553C4⋊C4—532no—
554C4⋊C4—532no—
555C4⋊C4—1061no—
556C4⋊C4—1061no—
557C4⋊C4—1061no—
558C4⋊C4—1061no—
559C4⋊C4—1061no—
560C4⋊C4—1061no—
561C4⋊C4—4241no—
562C4⋊C4—2122no—
563C4⋊C4—2122no—
564C4⋊C4—2122no—
565C4⋊C4—2122no—
566C4⋊C4C22×Dic5312yes—
567C4⋊C4C22×Dic5312yes—
568C22⋊C4—24no—
569C22⋊C4—24no—
570C22⋊C4—534no—
571C22⋊C4—1062no—
572C22⋊C4—4241no—
573C22⋊C4—2122no—
574C22⋊C4—2122no—
575C42—1061no—
576C42—1061no—
577C42—1061no—
578C42—1061no—
579C42—4241no—
580C42—2122no—
581C42—2122no—
582C23—21no—
583C23—21no—
584C23—21no—
585C23—21no—
586C23—22no—
587C23—41no—
588C23—41no—
589C23—41no—
590C23—41no—
591C23—41no—
592C23—41no—
593C23D4×Dic5312yes—
594C23SD16×D5312yes—
595C23#1313323812yes—
596C23C2×D4×D5311yescharacteristic
597Q8—22no—
598Q8—22no—
599Q8—41no—
600Q8—41no—
601D4—22no—
602D4—22no—
603D4—48no—
604D4—41no—
605D4—41no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—22no—
609C2×C4—22no—
610C2×C4—22no—
611C2×C4—22no—
612C2×C4—22no—
613C2×C4—22no—
614C2×C4—22no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—41no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—532no—
622C2×C4—532no—
623C2×C4—1061no—
624C2×C4—1061no—
625C2×C4—1061no—
626C2×C4—1061no—
627C2×C4—1061no—
628C2×C4—1061no—
629C2×C4—1061no—
630C2×C4—1061no—
631C2×C4—1061no—
632C2×C4—1061no—
633C2×C4—1062no—
634C2×C4—1062no—
635C2×C4—4244no—
636C2×C4—4244no—
637C2×C4—4244no—
638C2×C4—2121no—
639C2×C4—2121no—
640C2×C4—2121no—
641C2×C4—2121no—
642C2×C4—2121no—
643C2×C4—2121no—
644C2×C4—2121no—
645C2×C4—2121no—
646C2×C4—2121no—
647C2×C4—2121no—
648C2×C4D4×Dic5312yes—
649C2×C4C23×Dic5311yescharacteristic
650C2×C4C2×D4×D5311yescharacteristic
651C2×C4C2×#1171994711yescharacteristic
652C2×C4C2×#1171994711yescharacteristic
653C2×C4#1313326311yescharacteristic
654C2×C4#1313326411yescharacteristic
655C8—22no—
656C8—2121no—
657C8—2121no—
658C8D4×Dic5314yescomplemented
659C22—22no—
660C22—22no—
661C22—22no—
662C22—22no—
663C22—22no—
664C22—22no—
665C22—42no—
666C22—42no—
667C22—42no—
668C22—81no—
669C22—81no—
670C22—81no—
671C22—81no—
672C22SD16×Dic5314yescomplemented
673C22C2×D4×Dic5311yescharacteristic
674C22#1681125711yescharacteristic
675C22#1681127311yescharacteristic
676C22C2×SD16×D5311yescharacteristic
677C22C2×#1313323811yescharacteristic
678C22#1681143011yescharacteristic
679C22#1681143011yescharacteristic
680C4—22no—
681C4—42no—
682C4—42no—
683C4—42no—
684C4—1062no—
685C4—1062no—
686C4—4241no—
687C4—4241no—
688C4—2121no—
689C4—2122no—
690C4—2121no—
691C4—2122no—
692C4C2×D4×Dic5311yescharacteristic
693C4#1681110611yescharacteristic
694C4#1681127911yescharacteristic
695C4#1681132511yescharacteristic
696C2—24no—
697C2—82no—
698C2#2027773511yescharacteristic
699C2C2×SD16×Dic5311yescharacteristic
700C2#2028359911yescharacteristic
701C2#2028640811yescharacteristic
702C2#2028641911yescharacteristic
703C2#2028706711yescharacteristic
704C2#2028710011yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutatorC2×C4×C53C23×C4
FrattiniC22×C4C23×D53
FittingC2×C53×#465C2
socleC23×C53C22×D4
prime radicalC2×#121×C53C22
cosocleC22×C4×C53C24
hypercenterC2×#465D53
hypocenterC53#23022
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#465

Complements

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

NH ≅ G/Ntype
1. C2×SD16×Dic53C2semidirect
2. C22×#13133149C2semidirect
4. #20277724C2semidirect
5. #20275571C2semidirect
6. #20275444C2semidirect
7. #20275351C2semidirect
8. #20275344C2semidirect
10. #20275023C2semidirect
11. #20274985C2semidirect
12. #20274978C2semidirect
13. #106×Dic53C2semidirect
14. C8×C22⋊Dic53C2semidirect
58. C53×#465C4semidirect
98. #13133149D4semidirect
120. C2×SD16×C53C2×C4semidirect
123. C22×C8×C53C2×C4semidirect
127. C22⋊Q8×C53C2×C4semidirect
135. #106×C53C2×C4semidirect
136. #103×C53C2×C4semidirect
137. #102×C53C2×C4semidirect
202. C22⋊Dic53SD16semidirect
303. C8×C53C4×D4semidirect
320. C22×C53C4×SD16semidirect
377. #465Dic53semidirect
414. C53#23022semidirect
424. C2×SD16C2×Dic53semidirect
429. C22×C8C2×Dic53semidirect
433. C22⋊Q8C2×Dic53semidirect
473. #106C2×Dic53semidirect
476. #103C2×Dic53semidirect
479. #102C2×Dic53semidirect
658. C8D4×Dic53semidirect
672. C22SD16×Dic53semidirect

Maximal subgroups

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

subgroupindex
C2×SD16×Dic532
C22×#131331492
#202777352
#202777242
#202755712
#202754442
#202753512
#202753442
#202750332
#202750232
#202749852
#202749782
#106×Dic532
C8×C22⋊Dic532
C2×C53×#4652
#2302253