Finite Group Databasebeta

← #27305767

Subgroups — #27305767

Order 13568.

2702 conjugacy classes of subgroups.

The subgroup lattice has 758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D4×Dic53C211yesmaximal, characteristic
2C22×#13133173C211yesmaximal, characteristic, complemented
3C2×C22⋊C4×Dic53C212yesmaximal, complemented
4C2×C22⋊C4×Dic53C211yesmaximal, characteristic, complemented
5#20272967C212yesmaximal, complemented
6#20272962C211yesmaximal, characteristic, complemented
7#20272962C211yesmaximal, characteristic, complemented
8#20272958C212yesmaximal, complemented
9#20272956C211yesmaximal, characteristic
10#95×Dic53C212yesmaximal, complemented
11C53×#1438C211yesmaximal, characteristic
12C24×Dic53C2211yescharacteristic
13C24×Dic53C2211yescharacteristic
14C2×D4×Dic53—24no—
15C2×D4×Dic53—24no—
16C2×D4×Dic53C418yescomplemented
17C2×#13133173—24no—
18C2×#13133173—28no—
19C22×C4⋊Dic53C2211yescharacteristic
20C22×#11719919C2212yes—
21C22×C22⋊Dic53C2212yes—
22C22×C22⋊Dic53C2211yescharacteristic
23C22×C22⋊Dic53C2211yescharacteristic
24C22×C22⋊Dic53C2211yescharacteristic
25C22×C22⋊Dic53C2211yescharacteristic
26C22×C4×Dic53C2212yes—
27C22×C4×Dic53C2211yescharacteristic
28C22×C4×Dic53C2212yes—
29C22⋊C4×Dic53—24no—
30C22⋊C4×Dic53—28no—
31C2×#13133124C2212yes—
32C2×#13133124C2212yes—
33C2×#13133124C2212yes—
34C2×#13133124C2212yes—
35C2×#13133124C2212yes—
36C2×#13133124C2212yes—
37C23×D4×C53C2211yescharacteristic
38C22×C22⋊C4×C53C2212yes—
39C22×C22⋊C4×C53C2211yescharacteristic
40C22×C22⋊C4×C53C2211yescharacteristic
41C2×#95×C53C2212yes—
42C23×Dic53—24no—
43C23×Dic53—24no—
44C23×Dic53—22no—
45C23×Dic53—22no—
46C23×Dic53—24no—
47C23×Dic53—24no—
48C23×Dic53C2×C414yes—
49C23×Dic53C2×C414yes—
50C23×Dic53D414yes—
51C23×Dic53D414yes—
52C23×Dic53C2311yescharacteristic
53C23×Dic53C2311yescharacteristic
54C23×Dic53C2312yes—
55C23×Dic53C2312yes—
56C23×Dic53C2311yescharacteristic
57C23×Dic53C2311yescharacteristic
58D4×Dic53—232no—
59#13133173—232no—
60C2×C4⋊Dic53—22no—
61C2×C4⋊Dic53—22no—
62C2×C4⋊Dic53C2×C414yes—
63C2×#11719919—24no—
64C2×#11719919—24no—
65C2×#11719919—24no—
66C2×C22⋊Dic53—22no—
67C2×C22⋊Dic53—22no—
68C2×C22⋊Dic53—22no—
69C2×C22⋊Dic53—22no—
70C2×C22⋊Dic53—24no—
71C2×C22⋊Dic53—24no—
72C2×C22⋊Dic53—22no—
73C2×C22⋊Dic53—22no—
74C2×C22⋊Dic53—24no—
75C2×C22⋊Dic53—24no—
76C2×C22⋊Dic53—24no—
77C2×C22⋊Dic53C2×C414yes—
78C2×C22⋊Dic53C2×C414yes—
79C2×C4×Dic53—24no—
80C2×C4×Dic53—24no—
81C2×C4×Dic53—22no—
82C2×C4×Dic53—22no—
83C2×C4×Dic53—24no—
84C2×C4×Dic53—24no—
85C2×C4×Dic53—24no—
86C2×C4×Dic53C2×C414yes—
87C2×C4×Dic53D418yescomplemented
88#13133124—24no—
89#13133124—24no—
90#13133124—24no—
91#13133124—24no—
92#13133124—24no—
93#13133124—24no—
94C25×C53C2311yescharacteristic
95C25×C53C2311yescharacteristic
96C22×D4×C53—22no—
97C22×D4×C53—22no—
98C22×D4×C53—24no—
99C22×D4×C53—24no—
100C22×D4×C53C2×C414yes—
101C23×C4×C53C2312yes—
102C23×C4×C53C2312yes—
103C23×C4×C53C2311yescharacteristic
104C2×C22⋊C4×C53—22no—
105C2×C22⋊C4×C53—22no—
106C2×C22⋊C4×C53—24no—
107C2×C22⋊C4×C53—24no—
108C2×C22⋊C4×C53—24no—
109C2×C22⋊C4×C53—24no—
110C2×C22⋊C4×C53—24no—
111#95×C53—24no—
112C24×C53—22no—
113C24×C53—22no—
114C24×C53—21no—
115C24×C53—21no—
116C24×C53—22no—
117C24×C53—22no—
118C24×C53—22no—
119C24×C53—22no—
120C24×C53—22no—
121C24×C53—22no—
122C24×C53—22no—
123C24×C53—22no—
124C24×C53—22no—
125C24×C53C22×C412yes—
126C24×C53C22×C412yes—
127C24×C53C2×D412yes—
128C24×C53C2×D412yes—
129C24×C53#4114yes—
130C24×C53C2411yescharacteristic
131C2×D4×C53—216no—
132C2×D4×C53—216no—
133C2×D4×C53—28no—
134C2×D4×C53—28no—
135C2×D4×C53—28no—
136C22×C4×C53—21no—
137C22×C4×C53—21no—
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×C53—22no—
148C22×C4×C53—22no—
149C22×C4×C53—22no—
150C22×C4×C53—22no—
151C22×C4×C53C22×C412yes—
152C22×C4×C53C2×D414yes—
153C22×C4×C53#4114yes—
154C22×C4×C53#4114yes—
155C22×Dic53—22no—
156C22×Dic53—22no—
157C22×Dic53—216no—
158C22×Dic53—28no—
159C22×Dic53—216no—
160C22×Dic53—28no—
161C22×Dic53—22no—
162C22×Dic53—22no—
163C22×Dic53—22no—
164C22×Dic53—21no—
165C22×Dic53—21no—
166C22×Dic53—22no—
167C22×Dic53—22no—
168C22×Dic53—21no—
169C22×Dic53—21no—
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—22no—
180C22×Dic53—22no—
181C22×Dic53—28no—
182C22×Dic53—216no—
183C22×Dic53—44no—
184C22×Dic53—48no—
185C22×Dic53—44no—
186C22×Dic53C22⋊C4116yescomplemented
187C22×Dic53C22×C412yes—
188C22×Dic53C22×C412yes—
189C22×Dic53C22×C412yes—
190C22×Dic53C22×C412yes—
191C22×Dic53C2×D414yes—
192C22×Dic53C2×D412yes—
193C22×Dic53C2×D412yes—
194C22×Dic53C2×D412yes—
195C22×Dic53C2×D412yes—
196C22×Dic53C2×D414yes—
197C22×Dic53#4114yes—
198C22×Dic53#4114yes—
199C22⋊C4×C53—216no—
200C22⋊C4×C53—28no—
201C22⋊C4×C53—28no—
202C22⋊Dic53—216no—
203C22⋊Dic53—28no—
204C22⋊Dic53—28no—
205C22⋊Dic53—28no—
206C22⋊Dic53—28no—
207C4⋊Dic53—28no—
208#11719919—216no—
209C4×Dic53—28no—
210C4×Dic53—216no—
211C4×Dic53—48no—
212C23×C53—22no—
213C23×C53—22no—
214C23×C53—22no—
215C23×C53—22no—
216C23×C53—24no—
217C23×C53—24no—
218C23×C53—24no—
219C23×C53—24no—
220C23×C53—22no—
221C23×C53—24no—
222C23×C53—22no—
223C23×C53—24no—
224C23×C53—24no—
225C23×C53—24no—
226C23×C53—24no—
227C23×C53—22no—
228C23×C53—22no—
229C23×C53—24no—
230C23×C53—24no—
231C23×C53—24no—
232C23×C53—24no—
233C23×C53—24no—
234C23×C53—41no—
235C23×C53—42no—
236C23×C53—41no—
237C23×C53—42no—
238C23×C53—41no—
239C23×C53—41no—
240C23×C53—42no—
241C23×C53—42no—
242C23×C53—42no—
243C23×C53—42no—
244C23×C53—42no—
245C23×C53—42no—
246C23×C53—42no—
247C23×C53—42no—
248C23×C53—42no—
249C23×C53—42no—
250C23×C53—42no—
251C23×C53—42no—
252C23×C53C2×C22⋊C414yes—
253C23×C53#11714yescomplemented
254C23×C53C23×C411yescharacteristic
255C23×C53C22×D411yescharacteristic
256C23×C53C22×D411yescharacteristic
257C23×C53C22×D412yes—
258C23×C53C2×#4112yes—
259C23×C53C2×#4112yes—
260C23×C53C2×#4112yes—
261C23×C53C2×#4112yes—
262C23×C53C2×#4112yes—
263D4×C53—232no—
264C2×C4×C53—22no—
265C2×C4×C53—22no—
266C2×C4×C53—24no—
267C2×C4×C53—24no—
268C2×C4×C53—24no—
269C2×C4×C53—24no—
270C2×C4×C53—24no—
271C2×C4×C53—24no—
272C2×C4×C53—24no—
273C2×C4×C53—24no—
274C2×C4×C53—42no—
275C2×C4×C53—42no—
276C2×C4×C53—42no—
277C2×C4×C53—42no—
278C2×C4×C53—42no—
279C2×C4×C53—42no—
280C2×C4×C53—42no—
281C2×C4×C53—42no—
282C2×C4×C53#11714yescomplemented
283C2×Dic53—24no—
284C2×Dic53—22no—
285C2×Dic53—24no—
286C2×Dic53—22no—
287C2×Dic53—232no—
288C2×Dic53—22no—
289C2×Dic53—22no—
290C2×Dic53—24no—
291C2×Dic53—24no—
292C2×Dic53—24no—
293C2×Dic53—24no—
294C2×Dic53—24no—
295C2×Dic53—24no—
296C2×Dic53—24no—
297C2×Dic53—24no—
298C2×Dic53—41no—
299C2×Dic53—42no—
300C2×Dic53—42no—
301C2×Dic53—41no—
302C2×Dic53—42no—
303C2×Dic53—42no—
304C2×Dic53—42no—
305C2×Dic53—41no—
306C2×Dic53—41no—
307C2×Dic53—42no—
308C2×Dic53—42no—
309C2×Dic53—42no—
310C2×Dic53—42no—
311C2×Dic53—42no—
312C2×Dic53—416no—
313C2×Dic53C2×C22⋊C414yes—
314C2×Dic53C2×C22⋊C414yes—
315C2×Dic53C4×D418yes—
316C2×Dic53#12014yes—
317C2×Dic53#12118yes—
318C2×Dic53#12314yes—
319#13839—531nomaximal, Sylow
320C22×C53—24no—
321C22×C53—24no—
322C22×C53—24no—
323C22×C53—28no—
324C22×C53—24no—
325C22×C53—44no—
326C22×C53—44no—
327C22×C53—44no—
328C22×C53—44no—
329C22×C53—44no—
330C22×C53—44no—
331C22×C53—44no—
332C22×C53—44no—
333C22×C53—42no—
334C22×C53—44no—
335C22×C53—44no—
336C22×C53—44no—
337C22×C53—42no—
338C22×C53C22×C22⋊C411yescharacteristic
339C22×C53C2×#11711yescharacteristic
340C22×C53C2×#11711yescharacteristic
341C22×C53C2×C4×D412yes—
342C22×C53C4×#4112yes—
343C22×C53C2×#12011yescharacteristic
344C22×C53C2×#12112yes—
345C22×C53C2×#12311yescharacteristic
346C22×C53#52512yes—
347C22×C53#52512yes—
348C22×C53#52512yes—
349C22×C53#52511yescharacteristic
350C22×C53#52511yescharacteristic
351C22×C53#52512yes—
352C22×C53#52912yes—
353C22×C53#52912yes—
354C22×C53#52912yes—
355C22×C53#52912yes—
356C22×C53#53212yes—
357C22×C53#53212yes—
358C22×C53#53212yes—
359C4×C53—24no—
360C4×C53—44no—
361C4×C53—44no—
362Dic53—24no—
363Dic53—44no—
364Dic53—44no—
365Dic53—42no—
366Dic53—42no—
367Dic53#38618yes—
368C22×C4×D4—531no—
369C22×#117—531no—
370C2×C4×C22⋊C4—532no—
371C2×C4×C22⋊C4—531no—
372#1441—532no—
373#1440—531no—
374#1440—531no—
375#1439—532no—
376#1438—531no—
377#1438D5311yescharacteristic
378C4×#95—532no—
379C2×C53—44no—
380C2×C53—44no—
381C2×C53#228011yescharacteristic
382C2×C53C2×#38611yescharacteristic
383C2×C53#229012yes—
384C2×C53#229312yes—
385C2×C53#229711yescharacteristic
386C2×C53#238812yes—
387C2×C53#239212yes—
388C2×C53#239212yes—
389C2×C53#239512yes—
390C23×D4C2×D5311yescharacteristic
391C24×C4—531no—
392C24×C4—531no—
393C2×C4×D4—538no—
394C2×C4×D4—1064no—
395C2×C4×D4—1064no—
396C2×#117—1068no—
397C2×#117—1064no—
398C22×C4⋊C4—531no—
399C22×C4⋊C4—532no—
400C22×C22⋊C4—531no—
401C22×C22⋊C4—531no—
402C22×C22⋊C4—531no—
403C22×C22⋊C4—532no—
404C22×C22⋊C4—531no—
405C22×C22⋊C4C2×D5311yescharacteristic
406C22×C22⋊C4C2×D5312yes—
407C22×C22⋊C4C2×D5311yescharacteristic
408C22×C42—532no—
409C22×C42—531no—
410C22×C42—532no—
411C4×C22⋊C4—1068no—
412C4×C22⋊C4—1064no—
413C2×#95—532no—
414C2×#95—532no—
415C2×#95—532no—
416C2×#95—532no—
417C2×#95—532no—
418C2×#95—532no—
419C2×#95C2×D5312yes—
420C53#1383911yescharacteristic, complemented, Sylow
421C25C22×D5311yescharacteristic
422C25C22×D5311yescharacteristic
423C22×D4—22no—
424C22×D4—22no—
425C22×D4—24no—
426C22×D4—24no—
427C22×D4C4×D5314yes—
428C23×C4—531no—
429C23×C4—534no—
430C23×C4—534no—
431C23×C4—534no—
432C23×C4—531no—
433C23×C4—534no—
434C23×C4—532no—
435C23×C4—531no—
436C23×C4—532no—
437C23×C4—531no—
438C23×C4—1064no—
439C23×C4—1064no—
440C23×C4—1062no—
441C23×C4—1062no—
442C23×C4—1064no—
443C23×C4—1064no—
444C23×C4C22×D5312yes—
445C23×C4C22×D5312yes—
446C23×C4C22×D5311yescharacteristic
447C4×D4—10632no—
448#117—10632no—
449C2×C4⋊C4—534no—
450C2×C4⋊C4—1064no—
451C2×C4⋊C4—1064no—
452C2×C4⋊C4—1062no—
453C2×C4⋊C4—1062no—
454C2×C4⋊C4—1064no—
455C2×C22⋊C4—22no—
456C2×C22⋊C4—22no—
457C2×C22⋊C4—24no—
458C2×C22⋊C4—24no—
459C2×C22⋊C4—24no—
460C2×C22⋊C4—24no—
461C2×C22⋊C4—24no—
462C2×C22⋊C4—534no—
463C2×C22⋊C4—534no—
464C2×C22⋊C4—1064no—
465C2×C22⋊C4—1062no—
466C2×C22⋊C4—1062no—
467C2×C22⋊C4—1064no—
468C2×C22⋊C4—1064no—
469C2×C22⋊C4—1064no—
470C2×C22⋊C4—1062no—
471C2×C22⋊C4—1062no—
472C2×C22⋊C4—1062no—
473C2×C22⋊C4—1062no—
474C2×C22⋊C4—1064no—
475C2×C42—534no—
476C2×C42—538no—
477C2×C42—1064no—
478C2×C42—1064no—
479C2×C42—1062no—
480C2×C42—1062no—
481C2×C42—1064no—
482C2×C42—1064no—
483C2×C42—1064no—
484#95—24no—
485#95—1064no—
486#95—1064no—
487#95—1064no—
488#95—1064no—
489#95—1064no—
490#95—1064no—
491C24—22no—
492C24—22no—
493C24—21no—
494C24—21no—
495C24—22no—
496C24—22no—
497C24—22no—
498C24—22no—
499C24—22no—
500C24—22no—
501C24—22no—
502C24—22no—
503C24—22no—
504C24C2×C4×D5312yes—
505C24C2×C4×D5312yes—
506C24D4×D5312yes—
507C24D4×D5312yes—
508C24#1171994714yes—
509C24C23×D5311yescharacteristic
510C2×D4—216no—
511C2×D4—216no—
512C2×D4—28no—
513C2×D4—28no—
514C2×D4—28no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
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—532no—
531C22×C4—534no—
532C22×C4—532no—
533C22×C4—532no—
534C22×C4—534no—
535C22×C4—5316no—
536C22×C4—532no—
537C22×C4—532no—
538C22×C4—532no—
539C22×C4—532no—
540C22×C4—532no—
541C22×C4—534no—
542C22×C4—534no—
543C22×C4—1068no—
544C22×C4—10616no—
545C22×C4—10616no—
546C22×C4—1068no—
547C22×C4—1068no—
548C22×C4—10616no—
549C22×C4—1062no—
550C22×C4—1062no—
551C22×C4—1062no—
552C22×C4—1062no—
553C22×C4—1062no—
554C22×C4—1061no—
555C22×C4—1061no—
556C22×C4—1062no—
557C22×C4—1062no—
558C22×C4—1061no—
559C22×C4—1061no—
560C22×C4—1062no—
561C22×C4—1062no—
562C22×C4—1062no—
563C22×C4—1062no—
564C22×C4—1062no—
565C22×C4—1062no—
566C22×C4—1062no—
567C22×C4—1062no—
568C22×C4—1062no—
569C22×C4—1062no—
570C22×C4—1062no—
571C22×C4—2124no—
572C22×C4—2128no—
573C22×C4—2124no—
574C22×C4C2×C4×D5312yes—
575C22×C4D4×D5314yes—
576C22×C4#1171994714yes—
577C22×C4#1171994714yes—
578C4⋊C4—1068no—
579C4⋊C4—10616no—
580C22⋊C4—28no—
581C22⋊C4—216no—
582C22⋊C4—28no—
583C22⋊C4—1068no—
584C22⋊C4—1068no—
585C22⋊C4—1068no—
586C22⋊C4—10616no—
587C22⋊C4—1068no—
588C42—10616no—
589C42—1068no—
590C42—2128no—
591C23—22no—
592C23—22no—
593C23—22no—
594C23—22no—
595C23—24no—
596C23—24no—
597C23—24no—
598C23—24no—
599C23—22no—
600C23—24no—
601C23—22no—
602C23—22no—
603C23—24no—
604C23—24no—
605C23—24no—
606C23—24no—
607C23—24no—
608C23—22no—
609C23—24no—
610C23—24no—
611C23—24no—
612C23—24no—
613C23—41no—
614C23—42no—
615C23—41no—
616C23—42no—
617C23—41no—
618C23—41no—
619C23—42no—
620C23—42no—
621C23—42no—
622C23—42no—
623C23—42no—
624C23—42no—
625C23—42no—
626C23—42no—
627C23—42no—
628C23—42no—
629C23—42no—
630C23—42no—
631C23C22⋊C4×D5314yes—
632C23#1313317314yescomplemented
633C23C22×C4×D5311yescharacteristic
634C23C2×D4×D5311yescharacteristic
635C23C2×D4×D5311yescharacteristic
636C23C2×D4×D5312yes—
637C23#41×D5312yes—
638C23#41×D5312yes—
639C23C2×#1171994712yes—
640C23C2×#1171994712yes—
641C23C2×#1171994712yes—
642D4—232no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—24no—
646C2×C4—24no—
647C2×C4—24no—
648C2×C4—24no—
649C2×C4—24no—
650C2×C4—24no—
651C2×C4—24no—
652C2×C4—24no—
653C2×C4—42no—
654C2×C4—42no—
655C2×C4—42no—
656C2×C4—42no—
657C2×C4—42no—
658C2×C4—42no—
659C2×C4—42no—
660C2×C4—42no—
661C2×C4—534no—
662C2×C4—538no—
663C2×C4—534no—
664C2×C4—538no—
665C2×C4—534no—
666C2×C4—534no—
667C2×C4—10632no—
668C2×C4—1064no—
669C2×C4—1062no—
670C2×C4—1064no—
671C2×C4—1062no—
672C2×C4—1062no—
673C2×C4—1062no—
674C2×C4—1064no—
675C2×C4—1064no—
676C2×C4—1064no—
677C2×C4—1064no—
678C2×C4—1064no—
679C2×C4—1064no—
680C2×C4—1064no—
681C2×C4—1064no—
682C2×C4—21216no—
683C2×C4—2121no—
684C2×C4—2122no—
685C2×C4—2122no—
686C2×C4—2121no—
687C2×C4—2122no—
688C2×C4—2122no—
689C2×C4—2122no—
690C2×C4—2121no—
691C2×C4—2121no—
692C2×C4—2122no—
693C2×C4—2122no—
694C2×C4—2122no—
695C2×C4—2122no—
696C2×C4—2122no—
697C2×C4#1313317314yescomplemented
698C22—24no—
699C22—24no—
700C22—24no—
701C22—28no—
702C22—24no—
703C22—42no—
704C22—44no—
705C22—44no—
706C22—44no—
707C22—44no—
708C22—44no—
709C22—44no—
710C22—44no—
711C22—44no—
712C22—44no—
713C22—42no—
714C22—44no—
715C22—44no—
716C22C2×C22⋊C4×D5311yescharacteristic
717C22C2×#1313317311yescharacteristic
718C22C2×#1313317311yescharacteristic
719C22C4×D4×D5312yes—
720C22C4×#1171994712yes—
721C22#120×D5311yescharacteristic
722C22#121×D5312yes—
723C22#123×D5311yescharacteristic
724C22#1681112912yes—
725C22#1681112912yes—
726C22#1681112912yes—
727C22#1681112911yescharacteristic
728C22#1681113111yescharacteristic
729C22#1681113312yes—
730C22#1681115012yes—
731C22#1681115212yes—
732C22#1681115412yes—
733C22#1681115412yes—
734C22#1681116812yes—
735C22#1681116812yes—
736C22#1681117112yes—
737C4—24no—
738C4—44no—
739C4—44no—
740C4—538no—
741C4—1064no—
742C4—2122no—
743C4—2124no—
744C4—2124no—
745C4—2122no—
746C2—44no—
747C2—44no—
748C2#2027709311yescharacteristic
749C2#386×D5311yescharacteristic
750C2#2027715512yes—
751C2#2027717712yes—
752C2#2027720011yescharacteristic
753C2#2027792712yes—
754C2#2027795012yes—
755C2#2027795812yes—
756C2#2027797112yes—
subgroupG/H
center, FrattiniC24C23×D53
commutatorC23×C53C23×C4
FittingC53×#1438C2
socle, cosocleC24×C53C24
prime radicalC23×D4×C53C22
hypercenter#1438D53
hypocenterC53#13839
LCSG ▷ C23×C53 ▷ C53
UCSC1 ◁ C24 ◁ #1438

Complements

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

NH ≅ G/Ntype
2. C22×#13133173C2semidirect
3. C2×C22⋊C4×Dic53C2semidirect
4. C2×C22⋊C4×Dic53C2semidirect
5. #20272967C2semidirect
6. #20272962C2semidirect
7. #20272962C2semidirect
8. #20272958C2semidirect
10. #95×Dic53C2semidirect
16. C2×D4×Dic53C4semidirect
87. C2×C4×Dic53D4semidirect
186. C22×Dic53C22⋊C4semidirect
253. C23×C53#117semidirect
282. C2×C4×C53#117semidirect
420. C53#13839semidirect
632. C23#13133173semidirect
697. C2×C4#13133173semidirect

Maximal subgroups

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

subgroupindex
C22×D4×Dic532
C22×#131331732
C2×C22⋊C4×Dic532
#202729672
#202729622
#202729582
#202729562
#95×Dic532
C53×#14382
#1383953