Finite Group Databasebeta

← #27305390

Subgroups — #27305390

Order 13568.

2686 conjugacy classes of subgroups.

The subgroup lattice has 762 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13133177C211yesmaximal, characteristic
2C2×#16810499C212yesmaximal
3C2×C4×#11719921C211yesmaximal, characteristic, complemented
4C2×#95×D53C211yesmaximal, characteristic, complemented
5#20272952C211yesmaximal, characteristic, complemented
6#20272950C211yesmaximal, characteristic, complemented
7#20272948C211yesmaximal, characteristic, complemented
8#20272941C212yesmaximal, complemented
9#20272937C212yesmaximal, complemented
10#20272936C212yesmaximal, complemented
11C53×#1437C211yesmaximal, characteristic, complemented
12C23×C22⋊D53C2211yescharacteristic
13C24×Dic53C2211yescharacteristic
14C23×C4×D53C2212yes—
15C23×C4×D53C2211yescharacteristic
16C2×#13133177—24no—
17C2×#13133177—24no—
18C2×#13133177C418yescomplemented
19C22×#11719919C2211yescharacteristic
20C22×C22⋊Dic53C2212yes—
21C22×#11719921C2211yescharacteristic
22C22×#11719921C2212yes—
23C22×C4×Dic53C2211yescharacteristic
24C22×C4×Dic53C2211yescharacteristic
25#16810499C4116yescomplemented
26C4×#11719921—24no—
27C2×#13133124C2212yes—
28C2×#13133124C2212yes—
29C2×#13133124C2211yescharacteristic
30C2×#13133124C2212yes—
31C2×#13133124C2212yes—
32C2×#13133124C2212yes—
33C2×#13133124C2212yes—
34C2×#13133124C2212yes—
35#95×D53—24no—
36C22×C22⋊C4×C53C2211yescharacteristic
37C22×C22⋊C4×C53C2212yes—
38C22×C42×C53C2211yescharacteristic
39C2×#95×C53C2211yescharacteristic
40C2×#95×C53C2212yes—
41C24×D53C2311yescharacteristic
42C22×C22⋊D53—22no—
43C22×C22⋊D53—22no—
44C22×C22⋊D53—24no—
45C22×C22⋊D53C2×C418yes—
46C22×C22⋊D53C2×C414yes—
47C23×Dic53—22no—
48C23×Dic53—22no—
49C23×Dic53—42no—
50C23×Dic53—42no—
51C23×Dic53C2×C414yescomplemented
52C23×Dic53C2312yes—
53C23×Dic53C2311yescharacteristic
54C23×Dic53C2312yes—
55C23×Dic53C2311yescharacteristic
56C23×Dic53C2311yescharacteristic
57C22×C4×D53—24no—
58C22×C4×D53—24no—
59C22×C4×D53—42no—
60C22×C4×D53—42no—
61C22×C4×D53—42no—
62C22×C4×D53—42no—
63C22×C4×D53—42no—
64C22×C4×D53—42no—
65C22×C4×D53C2×C414yes—
66C22×C4×D53C2×C418yescomplemented
67C22×C4×D53D414yes—
68C22×C4×D53D414yes—
69#13133177—232no—
70C2×#11719919—22no—
71C2×#11719919—22no—
72C2×#11719919C2×C414yescomplemented
73C2×C22⋊Dic53—42no—
74C2×C22⋊Dic53—42no—
75C2×C22⋊Dic53C2×C418yescomplemented
76C2×#11719921—22no—
77C2×#11719921—22no—
78C2×#11719921—24no—
79C2×#11719921—24no—
80C2×#11719921C2×C414yes—
81C2×#11719921C2×C418yescomplemented
82C2×C4×Dic53—22no—
83C2×C4×Dic53—22no—
84C2×C4×Dic53—22no—
85C2×C4×Dic53—42no—
86C2×C4×Dic53C2×C414yescomplemented
87#13133124—22no—
88#13133124—24no—
89#13133124—24no—
90#13133124—42no—
91#13133124—42no—
92#13133124—42no—
93#13133124C2×C418yescomplemented
94#13133124C2×C418yescomplemented
95C25×C53C2311yescharacteristic
96C23×C4×C53C2312yes—
97C23×C4×C53C2311yescharacteristic
98C23×C4×C53C2312yes—
99C23×C4×C53C2311yescharacteristic
100C2×C22⋊C4×C53—22no—
101C2×C22⋊C4×C53—22no—
102C2×C22⋊C4×C53—42no—
103C2×C22⋊C4×C53—42no—
104C2×C22⋊C4×C53C2×C414yescomplemented
105C2×C22⋊C4×C53C2×C418yescomplemented
106C2×C42×C53—22no—
107C2×C42×C53—42no—
108#95×C53—22no—
109#95×C53—42no—
110C24×C53—21no—
111C24×C53—21no—
112C24×C53—22no—
113C24×C53—22no—
114C24×C53—22no—
115C24×C53—22no—
116C24×C53—22no—
117C24×C53C22×C414yes—
118C24×C53C22×C412yes—
119C24×C53C2411yescharacteristic
120C23×D53—22no—
121C23×D53—22no—
122C23×D53—22no—
123C23×D53—22no—
124C23×D53C22×C412yes—
125C23×D53C22×C414yes—
126C23×D53C2×D412yes—
127C23×D53C2×D412yes—
128C23×D53#4114yes—
129C22×C4×C53—22no—
130C22×C4×C53—22no—
131C22×C4×C53—22no—
132C22×C4×C53—22no—
133C22×C4×C53—21no—
134C22×C4×C53—21no—
135C22×C4×C53—22no—
136C22×C4×C53—22no—
137C22×C4×C53—22no—
138C22×C4×C53—22no—
139C22×C4×C53—22no—
140C22×C4×C53—22no—
141C22×C4×C53—22no—
142C22×C4×C53—22no—
143C22×C4×C53—22no—
144C22×C4×C53—22no—
145C22×C4×C53—22no—
146C22×C4×C53—22no—
147C22×C4×C53C22×C414yes—
148C22×C4×C53C22×C414yes—
149C22×C4×C53C22×C412yes—
150C22×C4×C53C22×C412yes—
151C22×C4×C53C2×D412yes—
152C22×C4×C53C2×D412yes—
153C2×C22⋊D53—28no—
154C2×C22⋊D53—28no—
155C2×C22⋊D53—216no—
156C2×C22⋊D53—216no—
157C2×C22⋊D53C42116yescomplemented
158C22×Dic53—21no—
159C22×Dic53—21no—
160C22×Dic53—22no—
161C22×Dic53—22no—
162C22×Dic53—22no—
163C22×Dic53—22no—
164C22×Dic53—22no—
165C22×Dic53—21no—
166C22×Dic53—21no—
167C22×Dic53—22no—
168C22×Dic53—22no—
169C22×Dic53—22no—
170C22×Dic53—22no—
171C22×Dic53—22no—
172C22×Dic53—22no—
173C22×Dic53—22no—
174C22×Dic53—22no—
175C22×Dic53—22no—
176C22×Dic53—22no—
177C22×Dic53—22no—
178C22×Dic53—22no—
179C22×Dic53—28no—
180C22×Dic53—48no—
181C22×Dic53—48no—
182C22×Dic53—44no—
183C22×Dic53—44no—
184C22×Dic53C22×C414yes—
185C22×Dic53C22×C414yes—
186C22×Dic53C22×C412yes—
187C22×Dic53C22×C414yes—
188C22×Dic53C22×C412yes—
189C22×Dic53C22×C412yes—
190C22×Dic53C2×D412yes—
191C22×Dic53C2×D412yes—
192C2×C4×D53—216no—
193C2×C4×D53—48no—
194C2×C4×D53—48no—
195C2×C4×D53—48no—
196C2×C4×D53—48no—
197C2×C4×D53—44no—
198C2×C4×D53—44no—
199C2×C4×D53—48no—
200C2×C4×D53—48no—
201C2×C4×D53—48no—
202C2×C4×D53—48no—
203C2×C4×D53C22⋊C4116yescomplemented
204C22⋊C4×C53—28no—
205C22⋊C4×C53—48no—
206C42×C53—44no—
207C22⋊Dic53—48no—
208#11719921—28no—
209#11719921—216no—
210#11719919—28no—
211C4×Dic53—28no—
212C4×Dic53—44no—
213C23×C53—22no—
214C23×C53—22no—
215C23×C53—24no—
216C23×C53—24no—
217C23×C53—24no—
218C23×C53—24no—
219C23×C53—24no—
220C23×C53—24no—
221C23×C53—24no—
222C23×C53—24no—
223C23×C53—42no—
224C23×C53—41no—
225C23×C53—41no—
226C23×C53—41no—
227C23×C53—41no—
228C23×C53—42no—
229C23×C53—42no—
230C23×C53—42no—
231C23×C53—42no—
232C23×C53—42no—
233C23×C53C2×C4214yes—
234C23×C53C23×C411yescharacteristic
235C23×C53C23×C412yes—
236C23×C53C22×D411yescharacteristic
237C23×C53C22×D411yescharacteristic
238C23×C53C2×#4112yes—
239C23×C53H(5,𝔽2)12yes—
240C23×C53H(5,𝔽2)12yes—
241C23×C53H(5,𝔽2)12yes—
242C23×C532−1+412yes—
243C22×D53—24no—
244C22×D53—24no—
245C22×D53—24no—
246C22×D53—24no—
247C22×D53—24no—
248C22×D53—24no—
249C22×D53—24no—
250C22×D53—22no—
251C22×D53—22no—
252C22×D53—22no—
253C22×D53—22no—
254C22×D53—24no—
255C22×D53—24no—
256C22×D53—24no—
257C22×D53—24no—
258C22×D53—24no—
259C22×D53C2×C4214yes—
260C22×D53C2×C22⋊C414yes—
261C22×D53#11714yes—
262C22×D53C4×D418yes—
263C22×D53C4×D418yes—
264C2×C4×C53—24no—
265C2×C4×C53—24no—
266C2×C4×C53—22no—
267C2×C4×C53—22no—
268C2×C4×C53—22no—
269C2×C4×C53—24no—
270C2×C4×C53—24no—
271C2×C4×C53—24no—
272C2×C4×C53—24no—
273C2×C4×C53—24no—
274C2×C4×C53—24no—
275C2×C4×C53—24no—
276C2×C4×C53—42no—
277C2×C4×C53—42no—
278C2×C4×C53—42no—
279C2×C4×C53—41no—
280C2×C4×C53—41no—
281C2×C4×C53—42no—
282C2×C4×C53—42no—
283C2×C4×C53—42no—
284C2×C4×C53—42no—
285C2×C4×C53—42no—
286C2×C4×C53—42no—
287C2×C4×C53C2×C22⋊C414yes—
288C22⋊D53—232no—
289C2×Dic53—22no—
290C2×Dic53—22no—
291C2×Dic53—24no—
292C2×Dic53—24no—
293C2×Dic53—24no—
294C2×Dic53—24no—
295C2×Dic53—22no—
296C2×Dic53—22no—
297C2×Dic53—22no—
298C2×Dic53—24no—
299C2×Dic53—24no—
300C2×Dic53—24no—
301C2×Dic53—24no—
302C2×Dic53—24no—
303C2×Dic53—24no—
304C2×Dic53—24no—
305C2×Dic53—416no—
306C2×Dic53—42no—
307C2×Dic53—42no—
308C2×Dic53—41no—
309C2×Dic53—41no—
310C2×Dic53—42no—
311C2×Dic53—42no—
312C2×Dic53—42no—
313C2×Dic53—42no—
314C2×Dic53—42no—
315C2×Dic53—42no—
316C2×Dic53—42no—
317C2×Dic53C2×C4214yes—
318C2×Dic53C2×C22⋊C414yes—
319C4×D53—416no—
320C4×D53—432no—
321#13784—531nomaximal, Sylow
322C22×C53—24no—
323C22×C53—28no—
324C22×C53—42no—
325C22×C53—42no—
326C22×C53—44no—
327C22×C53—44no—
328C22×C53—44no—
329C22×C53—44no—
330C22×C53—44no—
331C22×C53C22×C4211yescharacteristic
332C22×C53C22×C22⋊C411yescharacteristic
333C22×C53C2×#11711yescharacteristic
334C22×C53C2×C4×D412yes—
335C22×C53C2×C4×D412yes—
336C22×C53#51812yes—
337C22×C53#51812yes—
338C22×C53#51812yes—
339C22×C53#52012yes—
340C22×C53#52012yes—
341C22×C53#52012yes—
342C22×C53#53412yes—
343C22×C53#53411yescharacteristic
344C22×C53#53411yescharacteristic
345C22×C53#53511yescharacteristic
346C22×C53#53611yescharacteristic
347C22×C53#53712yes—
348C22×C53#53812yes—
349C22×C53#53812yes—
350C22×C53#53912yes—
351C22×C53#53912yes—
352C2×D53—24no—
353C2×D53—24no—
354C2×D53—28no—
355C2×D53—28no—
356C2×D53—28no—
357C2×D53—28no—
358C2×D53—28no—
359C2×D53—28no—
360C2×D53C4×C22⋊C418yes—
361C4×C53—24no—
362C4×C53—42no—
363C4×C53—44no—
364C4×C53—44no—
365Dic53—24no—
366Dic53—24no—
367Dic53—42no—
368Dic53—44no—
369Dic53—44no—
370C22×C4×D4—531no—
371C2×#386—532no—
372C2×C4×C22⋊C4—531no—
373C22×#95—531no—
374#1437—531no—
375#1437D5311yescharacteristic, complemented
376#1436—531no—
377#1436—531no—
378#1434—532no—
379C22⋊#95—532no—
380C22⋊#95—532no—
381C2×C53—44no—
382C2×C53C2×C4×C22⋊C411yescharacteristic
383C2×C53#227512yes—
384C2×C53#230811yescharacteristic
385C2×C53#231111yescharacteristic
386C2×C53#231812yes—
387C2×C53#232112yes—
388C2×C53#232212yes—
389C2×C53#232512yes—
390C2×C53#232512yes—
391D53—28no—
392C23×D4—531no—
393C24×C4—531no—
394C24×C4—531no—
395C24×C4—532no—
396C2×C4×D4—538no—
397C2×C4×D4—1064no—
398C2×C4×D4—1064no—
399C22×C4⋊C4—531no—
400C22×C22⋊C4—531no—
401C22×C22⋊C4—532no—
402C22×C22⋊C4—532no—
403C22×C22⋊C4C2×D5311yescharacteristic
404C22×C22⋊C4C2×D5312yes—
405C22×C42—531no—
406C22×C42—531no—
407C22×C42C2×D5311yescharacteristic
408#386—5316no—
409C4×C22⋊C4—1064no—
410C2×#95—532no—
411C2×#95—532no—
412C2×#95—532no—
413C2×#95—532no—
414C2×#95—531no—
415C2×#95—532no—
416C2×#95—532no—
417C2×#95—532no—
418C2×#95—1064no—
419C2×#95C2×D5311yescharacteristic
420C2×#95C2×D5312yes—
421C53#1378411yescharacteristic, complemented, Sylow
422C25—531no—
423C25C22×D5311yescharacteristic
424C22×D4—534no—
425C22×D4—538no—
426C22×D4—1062no—
427C22×D4—1062no—
428C22×D4—1064no—
429C23×C4—531no—
430C23×C4—531no—
431C23×C4—534no—
432C23×C4—534no—
433C23×C4—534no—
434C23×C4—532no—
435C23×C4—531no—
436C23×C4—532no—
437C23×C4—534no—
438C23×C4—538no—
439C23×C4—1064no—
440C23×C4—1064no—
441C23×C4—1062no—
442C23×C4—1062no—
443C23×C4—2122no—
444C23×C4—2122no—
445C23×C4—2122no—
446C23×C4—2122no—
447C23×C4—2122no—
448C23×C4—2122no—
449C23×C4—2122no—
450C23×C4—2122no—
451C23×C4C22×D5312yes—
452C23×C4C22×D5311yescharacteristic
453C23×C4C22×D5312yes—
454C23×C4C22×D5311yescharacteristic
455C4×D4—10632no—
456C2×C4⋊C4—534no—
457C2×C4⋊C4—1062no—
458C2×C4⋊C4—1062no—
459C2×C22⋊C4—22no—
460C2×C22⋊C4—22no—
461C2×C22⋊C4—42no—
462C2×C22⋊C4—42no—
463C2×C22⋊C4—534no—
464C2×C22⋊C4—538no—
465C2×C22⋊C4—538no—
466C2×C22⋊C4—1062no—
467C2×C22⋊C4—1062no—
468C2×C22⋊C4—1064no—
469C2×C22⋊C4—1064no—
470C2×C22⋊C4—2122no—
471C2×C22⋊C4—2122no—
472C2×C22⋊C4C4×D5314yescomplemented
473C2×C22⋊C4C4×D5318yescomplemented
474C2×C42—22no—
475C2×C42—42no—
476C2×C42—534no—
477C2×C42—1062no—
478C2×C42—1062no—
479C2×C42—1062no—
480C2×C42—2122no—
481#95—22no—
482#95—42no—
483#95—538no—
484#95—538no—
485#95—1064no—
486#95—1064no—
487#95—1062no—
488#95—2122no—
489#95—2122no—
490#95—2122no—
491C24—21no—
492C24—21no—
493C24—22no—
494C24—22no—
495C24—22no—
496C24—22no—
497C24—22no—
498C24—532no—
499C24—534no—
500C24—532no—
501C24—532no—
502C24—534no—
503C24—1062no—
504C24—1062no—
505C24—1062no—
506C24—1062no—
507C24C2×C4×D5314yes—
508C24C2×C4×D5312yes—
509C24C23×D5311yescharacteristic
510C2×D4—5316no—
511C2×D4—1068no—
512C2×D4—1068no—
513C2×D4—10616no—
514C2×D4—10616no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—534no—
534C22×C4—532no—
535C22×C4—532no—
536C22×C4—532no—
537C22×C4—532no—
538C22×C4—5316no—
539C22×C4—534no—
540C22×C4—534no—
541C22×C4—532no—
542C22×C4—10616no—
543C22×C4—1068no—
544C22×C4—1061no—
545C22×C4—1061no—
546C22×C4—1062no—
547C22×C4—1062no—
548C22×C4—1062no—
549C22×C4—1062no—
550C22×C4—1062no—
551C22×C4—1061no—
552C22×C4—1061no—
553C22×C4—1062no—
554C22×C4—1062no—
555C22×C4—1062no—
556C22×C4—1062no—
557C22×C4—1062no—
558C22×C4—1062no—
559C22×C4—1062no—
560C22×C4—1062no—
561C22×C4—1062no—
562C22×C4—1062no—
563C22×C4—1062no—
564C22×C4—1062no—
565C22×C4—2128no—
566C22×C4—2128no—
567C22×C4—2124no—
568C22×C4—2124no—
569C22×C4—2128no—
570C22×C4—2128no—
571C22×C4—2128no—
572C22×C4—2128no—
573C22×C4—2128no—
574C22×C4—2128no—
575C22×C4—2128no—
576C22×C4—2128no—
577C22×C4—2124no—
578C22×C4—2124no—
579C22×C4C2×C4×D5314yes—
580C22×C4C2×C4×D5314yes—
581C22×C4C2×C4×D5312yes—
582C22×C4C2×C4×D5312yes—
583C22×C4D4×D5312yes—
584C22×C4D4×D5312yes—
585C4⋊C4—1068no—
586C22⋊C4—28no—
587C22⋊C4—48no—
588C22⋊C4—1068no—
589C22⋊C4—10616no—
590C22⋊C4—2128no—
591C42—44no—
592C42—1068no—
593C42—2124no—
594C23—22no—
595C23—22no—
596C23—24no—
597C23—24no—
598C23—24no—
599C23—24no—
600C23—24no—
601C23—24no—
602C23—24no—
603C23—24no—
604C23—42no—
605C23—41no—
606C23—41no—
607C23—41no—
608C23—41no—
609C23—42no—
610C23—42no—
611C23—42no—
612C23—42no—
613C23—42no—
614C23—534no—
615C23—534no—
616C23—534no—
617C23—538no—
618C23—538no—
619C23—1064no—
620C23—1064no—
621C23—1064no—
622C23—1064no—
623C23—1064no—
624C23—1064no—
625C23—1064no—
626C23—1062no—
627C23—1062no—
628C23—1062no—
629C23—1062no—
630C23—1064no—
631C23—1064no—
632C23—1064no—
633C23—1064no—
634C23—1064no—
635C23C42×D5314yes—
636C23C22×C4×D5311yescharacteristic
637C23C22×C4×D5312yes—
638C23C2×D4×D5311yescharacteristic
639C23C2×D4×D5311yescharacteristic
640C23#41×D5312yes—
641C23#1313326212yes—
642C23#1313326212yes—
643C23#1313326312yes—
644C23#1313326412yes—
645D4—10632no—
646C2×C4—24no—
647C2×C4—24no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—24no—
652C2×C4—24no—
653C2×C4—24no—
654C2×C4—24no—
655C2×C4—24no—
656C2×C4—24no—
657C2×C4—24no—
658C2×C4—42no—
659C2×C4—42no—
660C2×C4—41no—
661C2×C4—42no—
662C2×C4—41no—
663C2×C4—42no—
664C2×C4—42no—
665C2×C4—42no—
666C2×C4—42no—
667C2×C4—42no—
668C2×C4—42no—
669C2×C4—534no—
670C2×C4—534no—
671C2×C4—1062no—
672C2×C4—1062no—
673C2×C4—1064no—
674C2×C4—1064no—
675C2×C4—1064no—
676C2×C4—1064no—
677C2×C4—1062no—
678C2×C4—1062no—
679C2×C4—1062no—
680C2×C4—1064no—
681C2×C4—1064no—
682C2×C4—1064no—
683C2×C4—1064no—
684C2×C4—1064no—
685C2×C4—1064no—
686C2×C4—1064no—
687C2×C4—21216no—
688C2×C4—21232no—
689C2×C4—21216no—
690C2×C4—2122no—
691C2×C4—2122no—
692C2×C4—2121no—
693C2×C4—2122no—
694C2×C4—2121no—
695C2×C4—2122no—
696C2×C4—2122no—
697C2×C4—2122no—
698C2×C4—2122no—
699C2×C4—2122no—
700C2×C4—2122no—
701C2×C4C22⋊C4×D5314yes—
702C22—24no—
703C22—28no—
704C22—42no—
705C22—42no—
706C22—44no—
707C22—44no—
708C22—44no—
709C22—44no—
710C22—44no—
711C22—538no—
712C22—1064no—
713C22—1064no—
714C22—1068no—
715C22—1068no—
716C22—1068no—
717C22—1068no—
718C22—1068no—
719C22—1068no—
720C22C2×C42×D5311yescharacteristic
721C22C2×C22⋊C4×D5311yescharacteristic
722C22#117×D5311yescharacteristic
723C22C4×D4×D5312yes—
724C22C4×D4×D5312yes—
725C22#1681109512yes—
726C22#1681109512yes—
727C22#1681109612yes—
728C22#1681110212yes—
729C22#1681110212yes—
730C22#1681110312yes—
731C22#1681118112yes—
732C22#1681118311yescharacteristic
733C22#1681118411yescharacteristic
734C22#1681118611yescharacteristic
735C22#1681119311yescharacteristic
736C22#1681120212yes—
737C22#1681120512yes—
738C22#1681120712yes—
739C22#1681121412yes—
740C22#1681121612yes—
741C4—24no—
742C4—42no—
743C4—44no—
744C4—44no—
745C4—1064no—
746C4—1064no—
747C4—2122no—
748C4—2124no—
749C4—2124no—
750C2—44no—
751C2—1068no—
752C2C4×C22⋊C4×D5311yescharacteristic
753C2#2027707412yes—
754C2#2027728911yescharacteristic
755C2#2027730511yescharacteristic
756C2#2027734512yes—
757C2#2027737412yes—
758C2#2027738512yes—
759C2#2027741712yes—
760C2#2027741912yes—
subgroupG/H
center, FrattiniC24C23×D53
commutatorC22×C53C22×C42
FittingC53×#1437C2
socle, cosocleC24×C53C24
prime radicalC23×C22⋊D53C22
hypercenter#1437D53
hypocenterC53#13784
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C24 ◁ #1437

Complements

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

NH ≅ G/Ntype
3. C2×C4×#11719921C2semidirect
4. C2×#95×D53C2semidirect
5. #20272952C2semidirect
6. #20272950C2semidirect
7. #20272948C2semidirect
8. #20272941C2semidirect
9. #20272937C2semidirect
10. #20272936C2semidirect
11. C53×#1437C2semidirect
18. C2×#13133177C4semidirect
25. #16810499C4semidirect
51. C23×Dic53C2×C4semidirect
66. C22×C4×D53C2×C4semidirect
72. C2×#11719919C2×C4semidirect
75. C2×C22⋊Dic53C2×C4semidirect
81. C2×#11719921C2×C4semidirect
86. C2×C4×Dic53C2×C4semidirect
93. #13133124C2×C4semidirect
94. #13133124C2×C4semidirect
104. C2×C22⋊C4×C53C2×C4semidirect
105. C2×C22⋊C4×C53C2×C4semidirect
157. C2×C22⋊D53C42semidirect
203. C2×C4×D53C22⋊C4semidirect
375. #1437D53semidirect
421. C53#13784semidirect
472. C2×C22⋊C4C4×D53semidirect
473. C2×C22⋊C4C4×D53semidirect

Maximal subgroups

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

subgroupindex
C22×#131331772
C2×#168104992
C2×C4×#117199212
C2×#95×D532
#202729522
#202729502
#202729482
#202729412
#202729372
#202729362
C53×#14372
#1378453