Finite Group Databasebeta

← #27306103

Subgroups — #27306103

Order 13568.

1862 conjugacy classes of subgroups.

The subgroup lattice has 1026 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16810482C211yesmaximal, characteristic
2C2×C4×#11719921C211yesmaximal, characteristic
3C2×#95×D53C211yesmaximal, characteristic
4#20272976C211yesmaximal, characteristic, complemented
5#20272975C211yesmaximal, characteristic, complemented
6#20272973C211yesmaximal, characteristic, complemented
7#20272970C211yesmaximal, characteristic, complemented
8#20272948C211yesmaximal, characteristic, complemented
9#20272946C211yesmaximal, characteristic, complemented
10#20272940C211yesmaximal, characteristic, complemented
11#20272936C211yesmaximal, characteristic
12#20272936C211yesmaximal, characteristic
13#20272936C211yesmaximal, characteristic
14#20272936C211yesmaximal, characteristic
15C53×#1434C211yesmaximal, characteristic, complemented
16C23×C4×D53C2211yescharacteristic
17C23×C4×D53C2211yescharacteristic
18C23×C4×D53C2211yescharacteristic
19C22×#11719919C2211yescharacteristic
20C22×#11719919C2211yescharacteristic
21C22×#11719921C2211yescharacteristic
22C22×#11719921C2211yescharacteristic
23C22×#11719921C2211yescharacteristic
24C22×#11719921C2211yescharacteristic
25C22×C4×Dic53C2211yescharacteristic
26#16810482—24no—
27C4×#11719921—24no—
28C2×#13133124C2211yescharacteristic
29C2×#13133124C2211yescharacteristic
30C2×#13133124C2211yescharacteristic
31C2×#13133124C2211yescharacteristic
32C2×#13133124C2211yescharacteristic
33C2×#13133124C2211yescharacteristic
34C2×#13133124C2211yescharacteristic
35C2×#13133124C2211yescharacteristic
36C2×#13133124C2211yescharacteristic
37C2×#13133124C2211yescharacteristic
38C2×#13133124C2211yescharacteristic
39C2×#13133124C2211yescharacteristic
40C2×#13133124C2211yescharacteristic
41C2×#13133124C2211yescharacteristic
42C2×#13133124C2211yescharacteristic
43C2×#13133124C2211yescharacteristic
44C2×#13133124C2211yescharacteristic
45C2×#13133124C2211yescharacteristic
46#95×D53C418yescomplemented
47C22×C42×C53C2211yescharacteristic
48C2×#95×C53C2211yescharacteristic
49C2×#95×C53C2211yescharacteristic
50C2×#95×C53C2211yescharacteristic
51C2×#95×C53C2211yescharacteristic
52C2×#95×C53C2211yescharacteristic
53C2×#95×C53C2211yescharacteristic
54C24×D53C2311yescharacteristic
55C23×Dic53C2311yescharacteristic
56C23×Dic53C2311yescharacteristic
57C23×Dic53C2311yescharacteristic
58C23×Dic53C2311yescharacteristic
59C23×Dic53C2311yescharacteristic
60C23×Dic53C2311yescharacteristic
61C23×Dic53C2311yescharacteristic
62C22×C4×D53—22no—
63C22×C4×D53—22no—
64C22×C4×D53—22no—
65C22×C4×D53—22no—
66C22×C4×D53—22no—
67C22×C4×D53—22no—
68C22×C4×D53—22no—
69C22×C4×D53—22no—
70C22×C4×D53—22no—
71C22×C4×D53—22no—
72C22×C4×D53—41no—
73C22×C4×D53—41no—
74C22×C4×D53—41no—
75C22×C4×D53—41no—
76C22×C4×D53—41no—
77C22×C4×D53—41no—
78C22×C4×D53—41no—
79C22×C4×D53—41no—
80C22×C4×D53C2×C414yes—
81C22×C4×D53C2×C414yes—
82C22×C4×D53C2×C414yes—
83C2×#11719919—22no—
84C2×#11719919—22no—
85C2×#11719919—22no—
86C2×#11719919—22no—
87C2×#11719919—41no—
88C2×#11719919—41no—
89C2×#11719921—22no—
90C2×#11719921—22no—
91C2×#11719921—22no—
92C2×#11719921—22no—
93C2×#11719921—22no—
94C2×#11719921—22no—
95C2×#11719921—22no—
96C2×#11719921—22no—
97C2×#11719921—22no—
98C2×#11719921—22no—
99C2×#11719921D414yes—
100C2×#11719921Q814yes—
101C2×C4×Dic53—22no—
102C2×C4×Dic53—22no—
103C2×C4×Dic53—41no—
104#13133124—22no—
105#13133124—22no—
106#13133124—22no—
107#13133124—22no—
108#13133124—22no—
109#13133124—22no—
110#13133124—41no—
111#13133124—41no—
112#13133124—41no—
113#13133124—41no—
114#13133124—41no—
115#13133124—41no—
116#13133124—41no—
117#13133124—41no—
118#13133124—41no—
119#13133124C2×C414yes—
120#13133124C2×C414yes—
121#13133124C2×C414yes—
122C23×C4×C53C2311yescharacteristic
123C23×C4×C53C2311yescharacteristic
124C23×C4×C53C2311yescharacteristic
125C23×C4×C53C2311yescharacteristic
126C23×C4×C53C2311yescharacteristic
127C23×C4×C53C2311yescharacteristic
128C23×C4×C53C2311yescharacteristic
129C2×C42×C53—22no—
130C2×C42×C53—22no—
131C2×C42×C53—41no—
132#95×C53—22no—
133#95×C53—22no—
134#95×C53—41no—
135#95×C53—41no—
136#95×C53—41no—
137#95×C53C2×C414yes—
138C24×C53C2411yescharacteristic
139C23×D53—21no—
140C23×D53—21no—
141C23×D53—21no—
142C23×D53—21no—
143C23×D53—21no—
144C23×D53—21no—
145C23×D53—21no—
146C23×D53—21no—
147C23×D53C22×C412yes—
148C23×D53C2×D412yes—
149C23×D53C2×Q812yes—
150C23×D53#4112yes—
151C23×D53#4112yes—
152C23×D53#4112yes—
153C23×D53#4112yes—
154C22×C4×C53—21no—
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×C53—21no—
163C22×C4×C53—21no—
164C22×C4×C53—21no—
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—21no—
173C22×C4×C53—21no—
174C22×C4×C53—21no—
175C22×C4×C53—21no—
176C22×C4×C53—21no—
177C22×C4×C53—21no—
178C22×C4×C53—21no—
179C22×C4×C53—21no—
180C22×C4×C53—21no—
181C22×C4×C53—21no—
182C22×C4×C53—21no—
183C22×C4×C53—21no—
184C22×C4×C53—21no—
185C22×C4×C53—21no—
186C22×C4×C53—21no—
187C22×C4×C53—21no—
188C22×C4×C53—21no—
189C22×C4×C53—21no—
190C22×C4×C53—21no—
191C22×C4×C53—21no—
192C22×C4×C53—21no—
193C22×C4×C53—21no—
194C22×C4×C53—21no—
195C22×C4×C53—21no—
196C22×C4×C53C22×C412yes—
197C22×C4×C53C22×C412yes—
198C22×C4×C53C22×C412yes—
199C22×C4×C53C2×D412yes—
200C22×C4×C53C2×Q812yes—
201C22×C4×C53#4112yes—
202C22×C4×C53#4112yes—
203C22×Dic53—21no—
204C22×Dic53—21no—
205C22×Dic53—21no—
206C22×Dic53—21no—
207C22×Dic53—21no—
208C22×Dic53—21no—
209C22×Dic53—21no—
210C22×Dic53—21no—
211C22×Dic53—21no—
212C22×Dic53—21no—
213C22×Dic53—21no—
214C22×Dic53—21no—
215C22×Dic53—21no—
216C22×Dic53—21no—
217C22×Dic53—21no—
218C22×Dic53—21no—
219C22×Dic53—21no—
220C22×Dic53—21no—
221C22×Dic53—21no—
222C22×Dic53—21no—
223C22×Dic53—21no—
224C22×Dic53—21no—
225C22×Dic53—21no—
226C22×Dic53—21no—
227C22×Dic53—21no—
228C22×Dic53—21no—
229C22×Dic53—21no—
230C22×Dic53—21no—
231C22×Dic53—21no—
232C22×Dic53—21no—
233C22×Dic53—21no—
234C22×Dic53—21no—
235C22×Dic53—21no—
236C22×Dic53—21no—
237C22×Dic53—21no—
238C22×Dic53—21no—
239C22×Dic53—21no—
240C22×Dic53—21no—
241C22×Dic53—21no—
242C22×Dic53—21no—
243C22×Dic53—21no—
244C22×Dic53—21no—
245C22×Dic53C22×C412yes—
246C22×Dic53C22×C412yes—
247C22×Dic53C22×C412yes—
248C22×Dic53C2×D412yes—
249C22×Dic53C2×Q812yes—
250C22×Dic53#4112yes—
251C22×Dic53#4112yes—
252C2×C4×D53—28no—
253C2×C4×D53—28no—
254C2×C4×D53—28no—
255C2×C4×D53—28no—
256C2×C4×D53—28no—
257C2×C4×D53—44no—
258C2×C4×D53—44no—
259C2×C4×D53—44no—
260C2×C4×D53—44no—
261C2×C4×D53—44no—
262C2×C4×D53—44no—
263C2×C4×D53—44no—
264C2×C4×D53—44no—
265C2×C4×D53—44no—
266C2×C4×D53—44no—
267C2×C4×D53—44no—
268C2×C4×D53—44no—
269C2×C4×D53—44no—
270C2×C4×D53—44no—
271C2×C4×D53—44no—
272C2×C4×D53—44no—
273C42×C53—44no—
274#11719921—28no—
275#11719921—28no—
276#11719921—44no—
277#11719921—44no—
278#11719919—44no—
279#11719919—44no—
280C4×Dic53—44no—
281C23×C53C23×C411yescharacteristic
282C23×C53C22×D411yescharacteristic
283C23×C53C22×Q811yescharacteristic
284C23×C53C2×#4111yescharacteristic
285C23×C53C2×#4111yescharacteristic
286C23×C53C2×#4111yescharacteristic
287C23×C53C2×#4111yescharacteristic
288C23×C53C2×#4111yescharacteristic
289C23×C53C2×#4111yescharacteristic
290C23×C53C2×#4111yescharacteristic
291C23×C53C2×#4111yescharacteristic
292C23×C53H(5,𝔽2)11yescharacteristic
293C23×C53H(5,𝔽2)11yescharacteristic
294C23×C53H(5,𝔽2)11yescharacteristic
295C23×C53H(5,𝔽2)11yescharacteristic
296C22×D53—22no—
297C22×D53—22no—
298C22×D53—22no—
299C22×D53—22no—
300C22×D53—22no—
301C22×D53—22no—
302C22×D53—22no—
303C22×D53—22no—
304C22×D53—22no—
305C22×D53—22no—
306C22×D53—22no—
307C22×D53—22no—
308C22×D53—22no—
309C22×D53—22no—
310C22×D53—22no—
311C22×D53—22no—
312C22×D53—22no—
313C22×D53—22no—
314C22×D53—22no—
315C22×D53—22no—
316C22×D53—22no—
317C22×D53—22no—
318C22×D53—22no—
319C22×D53—22no—
320C22×D53—22no—
321C22×D53—22no—
322C22×D53—22no—
323C22×D53—22no—
324C22×D53#11714yes—
325C22×D53C4×D414yes—
326C22×D53C4×Q814yes—
327C22×D53C22⋊Q814yes—
328C22×D53#12314yes—
329C22×D53#12514yes—
330C22×D53#12614yes—
331C2×C4×C53—22no—
332C2×C4×C53—22no—
333C2×C4×C53—22no—
334C2×C4×C53—22no—
335C2×C4×C53—22no—
336C2×C4×C53—22no—
337C2×C4×C53—22no—
338C2×C4×C53—22no—
339C2×C4×C53—22no—
340C2×C4×C53—22no—
341C2×C4×C53—22no—
342C2×C4×C53—22no—
343C2×C4×C53—22no—
344C2×C4×C53—22no—
345C2×C4×C53—22no—
346C2×C4×C53—22no—
347C2×C4×C53—22no—
348C2×C4×C53—22no—
349C2×C4×C53—41no—
350C2×C4×C53—41no—
351C2×C4×C53—41no—
352C2×C4×C53—41no—
353C2×C4×C53—41no—
354C2×C4×C53—41no—
355C2×C4×C53—41no—
356C2×C4×C53—41no—
357C2×C4×C53—41no—
358C2×C4×C53—41no—
359C2×C4×C53—41no—
360C2×C4×C53—41no—
361C2×C4×C53—41no—
362C2×C4×C53—41no—
363C2×C4×C53—41no—
364C2×C4×C53—41no—
365C2×C4×C53—41no—
366C2×C4×C53—41no—
367C2×C4×C53—41no—
368C2×C4×C53—41no—
369C2×C4×C53—41no—
370C2×C4×C53—41no—
371C2×C4×C53—41no—
372C2×C4×C53—41no—
373C2×C4×C53—41no—
374C2×C4×C53—41no—
375C2×C4×C53—41no—
376C2×C4×C53—41no—
377C2×C4×C53—41no—
378C2×C4×C53—41no—
379C2×C4×C53#11714yes—
380C2×Dic53—22no—
381C2×Dic53—22no—
382C2×Dic53—22no—
383C2×Dic53—22no—
384C2×Dic53—22no—
385C2×Dic53—22no—
386C2×Dic53—22no—
387C2×Dic53—22no—
388C2×Dic53—22no—
389C2×Dic53—22no—
390C2×Dic53—22no—
391C2×Dic53—22no—
392C2×Dic53—22no—
393C2×Dic53—22no—
394C2×Dic53—22no—
395C2×Dic53—22no—
396C2×Dic53—22no—
397C2×Dic53—22no—
398C2×Dic53—41no—
399C2×Dic53—41no—
400C2×Dic53—41no—
401C2×Dic53—41no—
402C2×Dic53—41no—
403C2×Dic53—41no—
404C2×Dic53—41no—
405C2×Dic53—41no—
406C2×Dic53—41no—
407C2×Dic53—41no—
408C2×Dic53—41no—
409C2×Dic53—41no—
410C2×Dic53—41no—
411C2×Dic53—41no—
412C2×Dic53—41no—
413C2×Dic53—41no—
414C2×Dic53—41no—
415C2×Dic53—41no—
416C2×Dic53—41no—
417C2×Dic53—41no—
418C2×Dic53—41no—
419C2×Dic53—41no—
420C2×Dic53—41no—
421C2×Dic53—41no—
422C2×Dic53—41no—
423C2×Dic53—41no—
424C2×Dic53—41no—
425C2×Dic53—41no—
426C2×Dic53—41no—
427C2×Dic53—41no—
428C2×Dic53#11714yes—
429C4×D53—416no—
430C4×D53—416no—
431C4×D53—416no—
432#13883—531nomaximal, Sylow
433C22×C53C2×#11711yescharacteristic
434C22×C53C2×#11711yescharacteristic
435C22×C53C2×#11711yescharacteristic
436C22×C53C2×C4×D411yescharacteristic
437C22×C53C2×C4×Q811yescharacteristic
438C22×C53#51811yescharacteristic
439C22×C53#51811yescharacteristic
440C22×C53C2×C22⋊Q811yescharacteristic
441C22×C53C2×#12311yescharacteristic
442C22×C53C2×#12511yescharacteristic
443C22×C53C2×#12611yescharacteristic
444C22×C53#52911yescharacteristic
445C22×C53#52911yescharacteristic
446C22×C53#52911yescharacteristic
447C22×C53#52911yescharacteristic
448C22×C53#53811yescharacteristic
449C22×C53#53811yescharacteristic
450C22×C53#53811yescharacteristic
451C22×C53#53811yescharacteristic
452C22×C53#54611yescharacteristic
453C22×C53#54611yescharacteristic
454C22×C53#54611yescharacteristic
455C22×C53#54611yescharacteristic
456C22×C53#55111yescharacteristic
457C22×C53#55111yescharacteristic
458C22×C53#55111yescharacteristic
459C22×C53#55111yescharacteristic
460C22×C53#55311yescharacteristic
461C22×C53#55311yescharacteristic
462C22×C53#55311yescharacteristic
463C22×C53#55311yescharacteristic
464C22×C53#55411yescharacteristic
465C22×C53#55411yescharacteristic
466C22×C53#55411yescharacteristic
467C22×C53#55411yescharacteristic
468C2×D53—24no—
469C2×D53—24no—
470C2×D53—24no—
471C2×D53—24no—
472C2×D53—24no—
473C2×D53—24no—
474C2×D53—24no—
475C2×D53—24no—
476C2×D53—24no—
477C2×D53—24no—
478C2×D53—24no—
479C2×D53—24no—
480C2×D53—24no—
481C2×D53—24no—
482C2×D53#38718yes—
483C4×C53—24no—
484C4×C53—42no—
485C4×C53—42no—
486C4×C53—42no—
487C4×C53—42no—
488C4×C53—81no—
489C4×C53—81no—
490Dic53—24no—
491Dic53—42no—
492Dic53—42no—
493Dic53—42no—
494Dic53—42no—
495Dic53—81no—
496Dic53—81no—
497C2×#380—531no—
498C2×C4×C22⋊C4—531no—
499C22×#95—531no—
500#1443—531no—
501#1443—531no—
502#1442—531no—
503#1442—531no—
504#1436—531no—
505#1436—531no—
506#1434—531no—
507#1434D5311yescharacteristic, complemented
508C22⋊#95—531no—
509C22⋊#95—531no—
510C22⋊#95—531no—
511C22⋊#95—531no—
512C2×C53#228311yescharacteristic
513C2×C53C2×#38711yescharacteristic
514C2×C53#231211yescharacteristic
515C2×C53#234211yescharacteristic
516C2×C53#234211yescharacteristic
517C2×C53#234511yescharacteristic
518C2×C53#234511yescharacteristic
519C2×C53#244411yescharacteristic
520C2×C53#244411yescharacteristic
521C2×C53#245011yescharacteristic
522C2×C53#245011yescharacteristic
523C2×C53#250511yescharacteristic
524C2×C53#250511yescharacteristic
525C2×C53#251011yescharacteristic
526C2×C53#251011yescharacteristic
527D53—28no—
528C24×C4—531no—
529C24×C4—531no—
530C24×C4—531no—
531C22×C4⋊C4—531no—
532C22×C4⋊C4—531no—
533C22×C22⋊C4—531no—
534C22×C22⋊C4—531no—
535C22×C22⋊C4—531no—
536C22×C22⋊C4—531no—
537C22×C42—531no—
538C22×C42C2×D5311yescharacteristic
539#380—1064no—
540C4×C22⋊C4—1064no—
541C2×#95—531no—
542C2×#95—531no—
543C2×#95—531no—
544C2×#95—538no—
545C2×#95—531no—
546C2×#95—531no—
547C2×#95—531no—
548C2×#95—531no—
549C2×#95—531no—
550C2×#95—531no—
551C2×#95—531no—
552C2×#95—531no—
553C2×#95—531no—
554C2×#95—531no—
555C2×#95—531no—
556C2×#95—531no—
557C2×#95—531no—
558C2×#95—531no—
559C2×#95—531no—
560C2×#95C2×D5311yescharacteristic
561C2×#95C2×D5311yescharacteristic
562C2×#95C2×D5311yescharacteristic
563C2×#95C2×D5311yescharacteristic
564C2×#95C2×D5311yescharacteristic
565C2×#95C2×D5311yescharacteristic
566C53#1388311yescharacteristic, complemented, Sylow
567C25—531no—
568C23×C4—531no—
569C23×C4—531no—
570C23×C4—531no—
571C23×C4—531no—
572C23×C4—531no—
573C23×C4—534no—
574C23×C4—534no—
575C23×C4—534no—
576C23×C4—531no—
577C23×C4—531no—
578C23×C4—1062no—
579C23×C4—1062no—
580C23×C4—1062no—
581C23×C4—1062no—
582C23×C4—1062no—
583C23×C4—1062no—
584C23×C4—1062no—
585C23×C4—1062no—
586C23×C4—1062no—
587C23×C4—1062no—
588C23×C4—2121no—
589C23×C4—2121no—
590C23×C4—2121no—
591C23×C4—2121no—
592C23×C4—2121no—
593C23×C4—2121no—
594C23×C4—2121no—
595C23×C4—2121no—
596C23×C4C22×D5311yescharacteristic
597C23×C4C22×D5311yescharacteristic
598C23×C4C22×D5311yescharacteristic
599C23×C4C22×D5311yescharacteristic
600C23×C4C22×D5311yescharacteristic
601C23×C4C22×D5311yescharacteristic
602C23×C4C22×D5311yescharacteristic
603C2×C4⋊C4—1062no—
604C2×C4⋊C4—1062no—
605C2×C4⋊C4—1062no—
606C2×C4⋊C4—1062no—
607C2×C4⋊C4—2121no—
608C2×C4⋊C4—2121no—
609C2×C22⋊C4—534no—
610C2×C22⋊C4—534no—
611C2×C22⋊C4—1062no—
612C2×C22⋊C4—1062no—
613C2×C22⋊C4—1062no—
614C2×C22⋊C4—1062no—
615C2×C22⋊C4—1062no—
616C2×C22⋊C4—1062no—
617C2×C22⋊C4—1062no—
618C2×C22⋊C4—1062no—
619C2×C22⋊C4—1062no—
620C2×C22⋊C4—1062no—
621C2×C42—22no—
622C2×C42—22no—
623C2×C42—41no—
624C2×C42—1062no—
625C2×C42—1062no—
626C2×C42—2121no—
627#95—22no—
628#95—22no—
629#95—41no—
630#95—41no—
631#95—41no—
632#95—534no—
633#95—534no—
634#95—534no—
635#95—1062no—
636#95—1062no—
637#95—1062no—
638#95—1062no—
639#95—1062no—
640#95—1062no—
641#95—2121no—
642#95—2121no—
643#95—2121no—
644#95—2121no—
645#95—2121no—
646#95—2121no—
647#95—2121no—
648#95—2121no—
649#95—2121no—
650#95C4×D5314yes—
651C24—532no—
652C24—532no—
653C24—532no—
654C24—532no—
655C24—532no—
656C24—532no—
657C24—532no—
658C24—1061no—
659C24—1061no—
660C24—1061no—
661C24—1061no—
662C24—1061no—
663C24—1061no—
664C24—1061no—
665C24—1061no—
666C24C23×D5311yescharacteristic
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—532no—
710C22×C4—532no—
711C22×C4—532no—
712C22×C4—532no—
713C22×C4—532no—
714C22×C4—532no—
715C22×C4—532no—
716C22×C4—1068no—
717C22×C4—1068no—
718C22×C4—1068no—
719C22×C4—1068no—
720C22×C4—1061no—
721C22×C4—1061no—
722C22×C4—1061no—
723C22×C4—1061no—
724C22×C4—1061no—
725C22×C4—1061no—
726C22×C4—1061no—
727C22×C4—1061no—
728C22×C4—1061no—
729C22×C4—1061no—
730C22×C4—1061no—
731C22×C4—1061no—
732C22×C4—1061no—
733C22×C4—1061no—
734C22×C4—1061no—
735C22×C4—1061no—
736C22×C4—1061no—
737C22×C4—1061no—
738C22×C4—1061no—
739C22×C4—1061no—
740C22×C4—1061no—
741C22×C4—1061no—
742C22×C4—1061no—
743C22×C4—1061no—
744C22×C4—1061no—
745C22×C4—1061no—
746C22×C4—1061no—
747C22×C4—1061no—
748C22×C4—1068no—
749C22×C4—1061no—
750C22×C4—1061no—
751C22×C4—1061no—
752C22×C4—1061no—
753C22×C4—1061no—
754C22×C4—1061no—
755C22×C4—1061no—
756C22×C4—1061no—
757C22×C4—1061no—
758C22×C4—1061no—
759C22×C4—1061no—
760C22×C4—1061no—
761C22×C4—1061no—
762C22×C4—1061no—
763C22×C4—2124no—
764C22×C4—2124no—
765C22×C4—2124no—
766C22×C4—2124no—
767C22×C4—2124no—
768C22×C4—2124no—
769C22×C4—2124no—
770C22×C4—2124no—
771C22×C4—2124no—
772C22×C4—2124no—
773C22×C4—2124no—
774C22×C4—2124no—
775C22×C4—2124no—
776C22×C4—2124no—
777C22×C4—2124no—
778C22×C4—2124no—
779C22×C4C2×C4×D5312yes—
780C22×C4C2×C4×D5312yes—
781C22×C4C2×C4×D5312yes—
782C22×C4#1171994512yes—
783C22×C4#1171994512yes—
784C22×C4D4×D5312yes—
785C22×C4Q8×D5312yes—
786C4⋊C4—2124no—
787C4⋊C4—2124no—
788C22⋊C4—1068no—
789C22⋊C4—1068no—
790C22⋊C4—2124no—
791C22⋊C4—2124no—
792C42—44no—
793C42—2124no—
794C23—534no—
795C23—534no—
796C23—534no—
797C23—534no—
798C23—534no—
799C23—534no—
800C23—534no—
801C23—1062no—
802C23—1062no—
803C23—1062no—
804C23—1062no—
805C23—1062no—
806C23—1062no—
807C23—1062no—
808C23—1062no—
809C23—1062no—
810C23—1062no—
811C23—1062no—
812C23—1062no—
813C23—1062no—
814C23—1062no—
815C23—1062no—
816C23—1062no—
817C23—1062no—
818C23—1062no—
819C23—1062no—
820C23—1062no—
821C23—1062no—
822C23—1062no—
823C23—1062no—
824C23—1062no—
825C23—1062no—
826C23—1062no—
827C23—1062no—
828C23—1062no—
829C23C22×C4×D5311yescharacteristic
830C23C2×D4×D5311yescharacteristic
831C23C2×Q8×D5311yescharacteristic
832C23#41×D5311yescharacteristic
833C23#41×D5311yescharacteristic
834C23#41×D5311yescharacteristic
835C23#41×D5311yescharacteristic
836C23#41×D5311yescharacteristic
837C23#41×D5311yescharacteristic
838C23C2×#1171994511yescharacteristic
839C23C2×#1171994511yescharacteristic
840C23#1313326211yescharacteristic
841C23#1313326211yescharacteristic
842C23#1313326311yescharacteristic
843C23#1313326311yescharacteristic
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—41no—
892C2×C4—534no—
893C2×C4—1062no—
894C2×C4—1062no—
895C2×C4—1062no—
896C2×C4—1062no—
897C2×C4—1062no—
898C2×C4—1062no—
899C2×C4—1062no—
900C2×C4—1062no—
901C2×C4—1062no—
902C2×C4—1062no—
903C2×C4—1062no—
904C2×C4—1062no—
905C2×C4—1062no—
906C2×C4—1062no—
907C2×C4—1062no—
908C2×C4—1062no—
909C2×C4—1062no—
910C2×C4—1062no—
911C2×C4—21216no—
912C2×C4—21216no—
913C2×C4—21216no—
914C2×C4—2121no—
915C2×C4—2121no—
916C2×C4—2121no—
917C2×C4—2121no—
918C2×C4—2121no—
919C2×C4—2121no—
920C2×C4—2121no—
921C2×C4—2121no—
922C2×C4—2121no—
923C2×C4—2121no—
924C2×C4—2121no—
925C2×C4—2121no—
926C2×C4—2121no—
927C2×C4—2121no—
928C2×C4—2121no—
929C2×C4—2121no—
930C2×C4—2121no—
931C2×C4—2121no—
932C2×C4—2121no—
933C2×C4—2121no—
934C2×C4—2121no—
935C2×C4—2121no—
936C2×C4—2121no—
937C2×C4—2121no—
938C2×C4—2121no—
939C2×C4—2121no—
940C2×C4—2121no—
941C2×C4—2121no—
942C2×C4—2121no—
943C2×C4—2121no—
944C2×C4#1313317414yes—
945C22—538no—
946C22—1064no—
947C22—1064no—
948C22—1064no—
949C22—1064no—
950C22—1064no—
951C22—1064no—
952C22—1064no—
953C22—1064no—
954C22—1064no—
955C22—1064no—
956C22—1064no—
957C22—1064no—
958C22—1064no—
959C22—1064no—
960C22#117×D5311yescharacteristic
961C22#117×D5311yescharacteristic
962C22C2×#1313317411yescharacteristic
963C22C4×D4×D5311yescharacteristic
964C22C4×Q8×D5311yescharacteristic
965C22#1681109511yescharacteristic
966C22#1681109511yescharacteristic
967C22C22⋊Q8×D5311yescharacteristic
968C22#123×D5311yescharacteristic
969C22#125×D5311yescharacteristic
970C22#126×D5311yescharacteristic
971C22#1681115111yescharacteristic
972C22#1681115111yescharacteristic
973C22#1681115111yescharacteristic
974C22#1681115111yescharacteristic
975C22#1681120511yescharacteristic
976C22#1681120711yescharacteristic
977C22#1681120911yescharacteristic
978C22#1681121211yescharacteristic
979C22#1681126311yescharacteristic
980C22#1681126511yescharacteristic
981C22#1681126911yescharacteristic
982C22#1681127011yescharacteristic
983C22#1681129711yescharacteristic
984C22#1681129811yescharacteristic
985C22#1681130211yescharacteristic
986C22#1681130311yescharacteristic
987C22#1681131711yescharacteristic
988C22#1681131811yescharacteristic
989C22#1681132311yescharacteristic
990C22#1681132411yescharacteristic
991C22#1681132711yescharacteristic
992C22#1681132811yescharacteristic
993C22#1681132911yescharacteristic
994C22#1681133311yescharacteristic
995C4—24no—
996C4—42no—
997C4—42no—
998C4—42no—
999C4—42no—
1000C4—81no—
1001C4—81no—
1002C4—1064no—
1003C4—4241no—
1004C4—4241no—
1005C4—2122no—
1006C4—2122no—
1007C4—2122no—
1008C4—2122no—
1009C2—1068no—
1010C2#2027710711yescharacteristic
1011C2#387×D5311yescharacteristic
1012C2#2027730911yescharacteristic
1013C2#2027755811yescharacteristic
1014C2#2027755911yescharacteristic
1015C2#2027758811yescharacteristic
1016C2#2027758911yescharacteristic
1017C2#2027846411yescharacteristic
1018C2#2027847211yescharacteristic
1019C2#2027853811yescharacteristic
1020C2#2027854611yescharacteristic
1021C2#2027921511yescharacteristic
1022C2#2027922311yescharacteristic
1023C2#2027927411yescharacteristic
1024C2#2027928211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D53
commutatorC23×C53C23×C4
FittingC53×#1434C2
socle, cosocleC24×C53C24
prime radicalC24×D53C23
hypercenter#1434D53
hypocenterC53#13883
LCSG ▷ C23×C53 ▷ C53
UCSC1 ◁ C24 ◁ #1434

Complements

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

NH ≅ G/Ntype
4. #20272976C2semidirect
5. #20272975C2semidirect
6. #20272973C2semidirect
7. #20272970C2semidirect
8. #20272948C2semidirect
9. #20272946C2semidirect
10. #20272940C2semidirect
15. C53×#1434C2semidirect
46. #95×D53C4semidirect
507. #1434D53semidirect
566. C53#13883semidirect

Maximal subgroups

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

subgroupindex
C2×#168104822
C2×C4×#117199212
C2×#95×D532
#202729762
#202729752
#202729732
#202729702
#202729482
#202729462
#202729402
#202729362
C53×#14342
#1388353