Finite Group Databasebeta

← #27305884

Subgroups — #27305884

Order 13568.

2550 conjugacy classes of subgroups.

The subgroup lattice has 1202 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13133177C211yesmaximal, characteristic
2C2×#16810539C211yesmaximal, characteristic
3C2×C4⋊C4×Dic53C211yesmaximal, characteristic, complemented
4C2×C22⋊C4×Dic53C211yesmaximal, characteristic, complemented
5C2×C22⋊C4×Dic53C211yesmaximal, characteristic, complemented
6C2×#16810470C211yesmaximal, characteristic, complemented
7C2×#16810470C211yesmaximal, characteristic, complemented
8#20272973C211yesmaximal, characteristic, complemented
9#20272967C211yesmaximal, characteristic, complemented
10#20272963C211yesmaximal, characteristic, complemented
11#20272962C211yesmaximal, characteristic, complemented
12#20272957C211yesmaximal, characteristic, complemented
13#20272954C211yesmaximal, characteristic
14#95×Dic53C211yesmaximal, characteristic, complemented
15C53×#1439C211yesmaximal, characteristic, complemented
16C23×C22⋊D53C2211yescharacteristic
17C24×Dic53C2211yescharacteristic
18C23×C4×D53C2211yescharacteristic
19C2×#13133177—24no—
20C2×#13133177—24no—
21C2×#13133177—24no—
22C22×C4⋊Dic53C2211yescharacteristic
23C22×#11719919C2211yescharacteristic
24C22×C22⋊Dic53C2211yescharacteristic
25C22×C22⋊Dic53C2211yescharacteristic
26C22×#11719921C2211yescharacteristic
27C22×#11719921C2211yescharacteristic
28C22×#11719921C2211yescharacteristic
29C22×#11719921C2211yescharacteristic
30C22×#11719921C2211yescharacteristic
31C22×C4×Dic53C2211yescharacteristic
32C22×C4×Dic53C2211yescharacteristic
33C22×C4×Dic53C2211yescharacteristic
34C22×C4×Dic53C2211yescharacteristic
35C22×C4×Dic53C2211yescharacteristic
36#16810539C418yescomplemented
37C4⋊C4×Dic53—24no—
38C22⋊C4×Dic53—24no—
39C22⋊C4×Dic53—24no—
40#16810470—24no—
41#16810470—24no—
42C2×#13133124C2211yescharacteristic
43C2×#13133124C2211yescharacteristic
44C2×#13133124C2211yescharacteristic
45C2×#13133124C2211yescharacteristic
46C2×#13133124C2211yescharacteristic
47C2×#13133124C2211yescharacteristic
48C2×#13133124C2211yescharacteristic
49C2×#13133124C2211yescharacteristic
50C2×#13133124C2211yescharacteristic
51C2×#13133124C2211yescharacteristic
52C2×#13133124C2211yescharacteristic
53C22×C4⋊C4×C53C2211yescharacteristic
54C22×C22⋊C4×C53C2211yescharacteristic
55C22×C22⋊C4×C53C2211yescharacteristic
56C22×C22⋊C4×C53C2211yescharacteristic
57C2×#95×C53C2211yescharacteristic
58C2×#95×C53C2211yescharacteristic
59C2×#95×C53C2211yescharacteristic
60C24×D53C2311yescharacteristic
61C22×C22⋊D53—22no—
62C22×C22⋊D53—22no—
63C22×C22⋊D53—22no—
64C22×C22⋊D53—22no—
65C22×C22⋊D53—22no—
66C22×C22⋊D53—22no—
67C22×C22⋊D53C2×C414yes—
68C23×Dic53—22no—
69C23×Dic53—22no—
70C23×Dic53—22no—
71C23×Dic53—22no—
72C23×Dic53—22no—
73C23×Dic53—22no—
74C23×Dic53D414yes—
75C23×Dic53C2311yescharacteristic
76C23×Dic53C2311yescharacteristic
77C23×Dic53C2311yescharacteristic
78C23×Dic53C2311yescharacteristic
79C23×Dic53C2311yescharacteristic
80C23×Dic53C2311yescharacteristic
81C23×Dic53C2311yescharacteristic
82C22×C4×D53—22no—
83C22×C4×D53—22no—
84C22×C4×D53—22no—
85C22×C4×D53—22no—
86C22×C4×D53—22no—
87C22×C4×D53—22no—
88C22×C4×D53D414yes—
89#13133177—232no—
90C2×C4⋊Dic53—22no—
91C2×C4⋊Dic53—22no—
92C2×C4⋊Dic53C2×C414yescomplemented
93C2×#11719919—22no—
94C2×#11719919—22no—
95C2×#11719919—22no—
96C2×C22⋊Dic53—22no—
97C2×C22⋊Dic53—22no—
98C2×C22⋊Dic53—22no—
99C2×C22⋊Dic53—22no—
100C2×C22⋊Dic53—22no—
101C2×C22⋊Dic53C2×C414yescomplemented
102C2×#11719921—22no—
103C2×#11719921—22no—
104C2×#11719921—22no—
105C2×#11719921—22no—
106C2×#11719921—22no—
107C2×#11719921—22no—
108C2×#11719921—22no—
109C2×#11719921—22no—
110C2×#11719921—22no—
111C2×#11719921—22no—
112C2×#11719921—22no—
113C2×#11719921—22no—
114C2×#11719921—22no—
115C2×#11719921C2×C414yescomplemented
116C2×#11719921C2×C414yescomplemented
117C2×C4×Dic53—22no—
118C2×C4×Dic53—22no—
119C2×C4×Dic53—22no—
120C2×C4×Dic53—22no—
121C2×C4×Dic53—22no—
122C2×C4×Dic53—22no—
123C2×C4×Dic53—22no—
124C2×C4×Dic53—22no—
125C2×C4×Dic53—22no—
126C2×C4×Dic53—22no—
127C2×C4×Dic53—22no—
128C2×C4×Dic53—22no—
129C2×C4×Dic53—22no—
130C2×C4×Dic53D414yes—
131C2×C4×Dic53D414yescomplemented
132#13133124—22no—
133#13133124—22no—
134#13133124—22no—
135#13133124—22no—
136#13133124—22no—
137#13133124—22no—
138#13133124—22no—
139#13133124—22no—
140#13133124—22no—
141#13133124—22no—
142#13133124C2×C414yescomplemented
143C25×C53C2311yescharacteristic
144C23×C4×C53C2311yescharacteristic
145C23×C4×C53C2311yescharacteristic
146C23×C4×C53C2311yescharacteristic
147C23×C4×C53C2311yescharacteristic
148C23×C4×C53C2311yescharacteristic
149C23×C4×C53C2311yescharacteristic
150C2×C4⋊C4×C53—22no—
151C2×C4⋊C4×C53—22no—
152C2×C4⋊C4×C53—22no—
153C2×C22⋊C4×C53—22no—
154C2×C22⋊C4×C53—22no—
155C2×C22⋊C4×C53—22no—
156C2×C22⋊C4×C53—22no—
157C2×C22⋊C4×C53—22no—
158C2×C22⋊C4×C53—22no—
159C2×C22⋊C4×C53—22no—
160C2×C22⋊C4×C53—22no—
161C2×C22⋊C4×C53C2×C414yescomplemented
162#95×C53—22no—
163#95×C53—22no—
164#95×C53—22no—
165C24×C53—21no—
166C24×C53—21no—
167C24×C53—21no—
168C24×C53—21no—
169C24×C53—21no—
170C24×C53—21no—
171C24×C53—21no—
172C24×C53—21no—
173C24×C53—21no—
174C24×C53—21no—
175C24×C53—21no—
176C24×C53—21no—
177C24×C53C22×C412yes—
178C24×C53C2×D412yes—
179C24×C53#4112yes—
180C24×C53C2411yescharacteristic
181C23×D53—21no—
182C23×D53—21no—
183C23×D53—21no—
184C23×D53—21no—
185C23×D53—21no—
186C23×D53—21no—
187C23×D53—21no—
188C23×D53—21no—
189C23×D53—21no—
190C23×D53—21no—
191C23×D53—21no—
192C23×D53—21no—
193C23×D53C22×C412yes—
194C23×D53C2×D412yes—
195C23×D53#4112yes—
196C22×C4×C53—21no—
197C22×C4×C53—21no—
198C22×C4×C53—21no—
199C22×C4×C53—21no—
200C22×C4×C53—21no—
201C22×C4×C53—21no—
202C22×C4×C53—21no—
203C22×C4×C53—21no—
204C22×C4×C53—21no—
205C22×C4×C53—21no—
206C22×C4×C53—21no—
207C22×C4×C53—21no—
208C22×C4×C53—21no—
209C22×C4×C53—21no—
210C22×C4×C53—21no—
211C22×C4×C53—21no—
212C22×C4×C53—21no—
213C22×C4×C53—21no—
214C22×C4×C53—21no—
215C22×C4×C53—21no—
216C22×C4×C53—21no—
217C22×C4×C53—21no—
218C22×C4×C53—21no—
219C22×C4×C53—21no—
220C22×C4×C53—21no—
221C22×C4×C53—21no—
222C22×C4×C53—21no—
223C22×C4×C53—21no—
224C22×C4×C53—21no—
225C22×C4×C53—21no—
226C22×C4×C53—21no—
227C22×C4×C53—21no—
228C22×C4×C53—21no—
229C22×C4×C53—21no—
230C22×C4×C53C22×C412yes—
231C22×C4×C53C22×C412yes—
232C22×C4×C53C2×D412yes—
233C22×C4×C53C2×D412yes—
234C22×C4×C53C2×D412yes—
235C22×C4×C53#4112yes—
236C22×C4×C53#4112yes—
237C22×C4×C53#4112yes—
238C2×C22⋊D53—28no—
239C2×C22⋊D53—28no—
240C2×C22⋊D53—28no—
241C2×C22⋊D53—28no—
242C2×C22⋊D53—28no—
243C2×C22⋊D53—28no—
244C2×C22⋊D53—28no—
245C22×Dic53—21no—
246C22×Dic53—21no—
247C22×Dic53—21no—
248C22×Dic53—21no—
249C22×Dic53—21no—
250C22×Dic53—21no—
251C22×Dic53—21no—
252C22×Dic53—21no—
253C22×Dic53—21no—
254C22×Dic53—21no—
255C22×Dic53—21no—
256C22×Dic53—21no—
257C22×Dic53—21no—
258C22×Dic53—21no—
259C22×Dic53—21no—
260C22×Dic53—21no—
261C22×Dic53—21no—
262C22×Dic53—21no—
263C22×Dic53—21no—
264C22×Dic53—21no—
265C22×Dic53—21no—
266C22×Dic53—21no—
267C22×Dic53—21no—
268C22×Dic53—21no—
269C22×Dic53—21no—
270C22×Dic53—21no—
271C22×Dic53—21no—
272C22×Dic53—21no—
273C22×Dic53—21no—
274C22×Dic53—21no—
275C22×Dic53—21no—
276C22×Dic53—21no—
277C22×Dic53—21no—
278C22×Dic53—21no—
279C22×Dic53—28no—
280C22×Dic53—28no—
281C22×Dic53—28no—
282C22×Dic53—44no—
283C22×Dic53—44no—
284C22×Dic53—44no—
285C22×Dic53—44no—
286C22×Dic53C22×C412yes—
287C22×Dic53C22×C412yes—
288C22×Dic53C22×C412yes—
289C22×Dic53C2×D412yes—
290C22×Dic53C2×D412yes—
291C22×Dic53C2×D412yes—
292C22×Dic53C2×D412yes—
293C22×Dic53C2×D412yes—
294C22×Dic53C2×D412yes—
295C22×Dic53C2×D412yes—
296C22×Dic53#4112yes—
297C22×Dic53#4112yes—
298C22×Dic53#4112yes—
299C22×Dic53#4112yes—
300C22×Dic53#4112yes—
301C2×C4×D53—28no—
302C2×C4×D53—28no—
303C2×C4×D53—28no—
304C2×C4×D53—44no—
305C2×C4×D53—44no—
306C2×C4×D53—44no—
307C2×C4×D53—44no—
308C4⋊C4×C53—28no—
309C22⋊C4×C53—28no—
310C22⋊C4×C53—28no—
311C22⋊C4×C53—28no—
312C22⋊Dic53—28no—
313C22⋊Dic53—28no—
314#11719921—28no—
315#11719921—28no—
316#11719921—28no—
317#11719921—28no—
318#11719921—28no—
319C4⋊Dic53—28no—
320#11719919—28no—
321C4×Dic53—28no—
322C4×Dic53—28no—
323C4×Dic53—44no—
324C4×Dic53—44no—
325C4×Dic53—44no—
326C23×C53—22no—
327C23×C53—22no—
328C23×C53—22no—
329C23×C53—22no—
330C23×C53—22no—
331C23×C53—22no—
332C23×C53—22no—
333C23×C53—22no—
334C23×C53—22no—
335C23×C53—22no—
336C23×C53—22no—
337C23×C53—22no—
338C23×C53—22no—
339C23×C53—22no—
340C23×C53—22no—
341C23×C53—22no—
342C23×C53—22no—
343C23×C53—22no—
344C23×C53—41no—
345C23×C53—41no—
346C23×C53—41no—
347C23×C53—41no—
348C23×C53—41no—
349C23×C53—41no—
350C23×C53—41no—
351C23×C53—41no—
352C23×C53—41no—
353C23×C53—41no—
354C23×C53—41no—
355C23×C53—41no—
356C23×C53—41no—
357C23×C53—41no—
358C23×C53—41no—
359C23×C53—41no—
360C23×C53C4×D414yes—
361C23×C53C23×C411yescharacteristic
362C23×C53C22×D411yescharacteristic
363C23×C53C22×D411yescharacteristic
364C23×C53C22×D411yescharacteristic
365C23×C53C22×D411yescharacteristic
366C23×C53C2×#4111yescharacteristic
367C23×C53C2×#4111yescharacteristic
368C23×C53C2×#4111yescharacteristic
369C23×C53C2×#4111yescharacteristic
370C23×C53C2×#4111yescharacteristic
371C23×C53C2×#4111yescharacteristic
372C23×C53C2×#4111yescharacteristic
373C23×C53C2×#4111yescharacteristic
374C23×C53C2×#4111yescharacteristic
375C23×C53C2×#4111yescharacteristic
376C22×D53—22no—
377C22×D53—22no—
378C22×D53—22no—
379C22×D53—22no—
380C22×D53—22no—
381C22×D53—22no—
382C22×D53—22no—
383C22×D53—22no—
384C22×D53—22no—
385C22×D53—22no—
386C22×D53—22no—
387C22×D53—22no—
388C22×D53—22no—
389C22×D53—22no—
390C22×D53—22no—
391C22×D53—22no—
392C22×D53—22no—
393C22×D53—22no—
394C22×D53—41no—
395C22×D53—41no—
396C22×D53—41no—
397C22×D53—41no—
398C22×D53—41no—
399C22×D53—41no—
400C22×D53—41no—
401C22×D53—41no—
402C22×D53—41no—
403C22×D53—41no—
404C22×D53—41no—
405C22×D53—41no—
406C22×D53—41no—
407C22×D53—41no—
408C22×D53—41no—
409C22×D53—41no—
410C22×D53C4×D414yes—
411C2×C4×C53—22no—
412C2×C4×C53—22no—
413C2×C4×C53—22no—
414C2×C4×C53—22no—
415C2×C4×C53—22no—
416C2×C4×C53—22no—
417C2×C4×C53—22no—
418C2×C4×C53—22no—
419C2×C4×C53—22no—
420C2×C4×C53—22no—
421C2×C4×C53—22no—
422C2×C4×C53—22no—
423C2×C4×C53—22no—
424C2×C4×C53—22no—
425C2×C4×C53—22no—
426C2×C4×C53—22no—
427C2×C4×C53—22no—
428C2×C4×C53—22no—
429C2×C4×C53—22no—
430C2×C4×C53—22no—
431C2×C4×C53—22no—
432C2×C4×C53—41no—
433C2×C4×C53—41no—
434C2×C4×C53—41no—
435C2×C4×C53—41no—
436C2×C4×C53—41no—
437C2×C4×C53—41no—
438C2×C4×C53—41no—
439C2×C4×C53—41no—
440C2×C4×C53—41no—
441C2×C4×C53—41no—
442C2×C4×C53—41no—
443C2×C4×C53—41no—
444C2×C4×C53—41no—
445C2×C4×C53—41no—
446C2×C4×C53—41no—
447C2×C4×C53—41no—
448C2×C4×C53—41no—
449C2×C4×C53—41no—
450C2×C4×C53—41no—
451C2×C4×C53—41no—
452C2×C4×C53C4×D414yescomplemented
453C22⋊D53—232no—
454C2×Dic53—22no—
455C2×Dic53—22no—
456C2×Dic53—22no—
457C2×Dic53—22no—
458C2×Dic53—22no—
459C2×Dic53—22no—
460C2×Dic53—22no—
461C2×Dic53—22no—
462C2×Dic53—22no—
463C2×Dic53—22no—
464C2×Dic53—22no—
465C2×Dic53—22no—
466C2×Dic53—22no—
467C2×Dic53—22no—
468C2×Dic53—22no—
469C2×Dic53—22no—
470C2×Dic53—22no—
471C2×Dic53—22no—
472C2×Dic53—22no—
473C2×Dic53—22no—
474C2×Dic53—22no—
475C2×Dic53—41no—
476C2×Dic53—41no—
477C2×Dic53—41no—
478C2×Dic53—41no—
479C2×Dic53—41no—
480C2×Dic53—41no—
481C2×Dic53—41no—
482C2×Dic53—41no—
483C2×Dic53—41no—
484C2×Dic53—41no—
485C2×Dic53—41no—
486C2×Dic53—41no—
487C2×Dic53—41no—
488C2×Dic53—41no—
489C2×Dic53—41no—
490C2×Dic53—41no—
491C2×Dic53—41no—
492C2×Dic53—41no—
493C2×Dic53—41no—
494C2×Dic53—41no—
495C2×Dic53—416no—
496C2×Dic53C4×D414yes—
497C2×Dic53#12014yes—
498C2×Dic53#12114yes—
499C2×Dic53#12114yes—
500C2×Dic53#12114yes—
501C2×Dic53#12314yes—
502C2×Dic53#12314yes—
503C2×Dic53#12414yes—
504C4×D53—416no—
505C4×#394—531nomaximal, Sylow
506C22×C53—24no—
507C22×C53—24no—
508C22×C53—24no—
509C22×C53—42no—
510C22×C53—42no—
511C22×C53—42no—
512C22×C53—42no—
513C22×C53—42no—
514C22×C53—42no—
515C22×C53—42no—
516C22×C53—42no—
517C22×C53—42no—
518C22×C53—42no—
519C22×C53—42no—
520C22×C53—42no—
521C22×C53C2×C4×D411yescharacteristic
522C22×C53C2×C4×D411yescharacteristic
523C22×C53C2×C4×D411yescharacteristic
524C22×C53C2×C4×D411yescharacteristic
525C22×C53C4×#4111yescharacteristic
526C22×C53C4×#4111yescharacteristic
527C22×C53C4×#4111yescharacteristic
528C22×C53C2×#12011yescharacteristic
529C22×C53C2×#12111yescharacteristic
530C22×C53C2×#12111yescharacteristic
531C22×C53C2×#12111yescharacteristic
532C22×C53C2×#12311yescharacteristic
533C22×C53C2×#12311yescharacteristic
534C22×C53#52511yescharacteristic
535C22×C53#52511yescharacteristic
536C22×C53#52511yescharacteristic
537C22×C53#52511yescharacteristic
538C22×C53#52511yescharacteristic
539C22×C53#52511yescharacteristic
540C22×C53#52511yescharacteristic
541C22×C53#52511yescharacteristic
542C22×C53C2×#12411yescharacteristic
543C22×C53#52911yescharacteristic
544C22×C53#52911yescharacteristic
545C22×C53#52911yescharacteristic
546C22×C53#52911yescharacteristic
547C22×C53#52911yescharacteristic
548C22×C53#52911yescharacteristic
549C22×C53#52911yescharacteristic
550C22×C53#52911yescharacteristic
551C22×C53#52911yescharacteristic
552C22×C53#53211yescharacteristic
553C22×C53#53211yescharacteristic
554C22×C53#53211yescharacteristic
555C22×C53#53211yescharacteristic
556C2×D53—24no—
557C2×D53—24no—
558C2×D53—24no—
559C2×D53—42no—
560C2×D53—42no—
561C2×D53—42no—
562C2×D53—42no—
563C2×D53—42no—
564C2×D53—42no—
565C2×D53—42no—
566C2×D53—42no—
567C2×D53—42no—
568C2×D53—42no—
569C2×D53—42no—
570C2×D53—42no—
571C4×C53—24no—
572C4×C53—42no—
573C4×C53—42no—
574C4×C53—42no—
575C4×C53—42no—
576C4×C53—42no—
577Dic53—24no—
578Dic53—42no—
579Dic53—42no—
580Dic53—42no—
581Dic53—42no—
582Dic53—42no—
583Dic53#39418yescomplemented
584C22×C4×D4—531no—
585C2×#394—531no—
586C2×C4×C4⋊C4—531no—
587C2×C4×C22⋊C4—531no—
588C2×C4×C22⋊C4—531no—
589C2×C4×C22⋊C4—531no—
590C2×C4×C22⋊C4—531no—
591#1442—531no—
592#1441—531no—
593#1440—531no—
594#1440—531no—
595#1439—531no—
596#1439D5311yescharacteristic, complemented
597#1438—531no—
598C4×#95—531no—
599C2×C53—44no—
600C2×C53C4×#12011yescharacteristic
601C2×C53C4×#12111yescharacteristic
602C2×C53C4×#12111yescharacteristic
603C2×C53C4×#12111yescharacteristic
604C2×C53C4×#12311yescharacteristic
605C2×C53C4×#12311yescharacteristic
606C2×C53C4×#12411yescharacteristic
607C2×C53C2×#39411yescharacteristic
608C2×C53#238811yescharacteristic
609C2×C53#239211yescharacteristic
610C2×C53#239211yescharacteristic
611C2×C53#239211yescharacteristic
612C2×C53#239511yescharacteristic
613C2×C53#239511yescharacteristic
614C2×C53#239811yescharacteristic
615D53—44no—
616C23×D4—531no—
617C24×C4—531no—
618C24×C4—531no—
619C2×C4×D4—1064no—
620C2×C4×D4—1064no—
621C2×C4×D4—1064no—
622C22×C4⋊C4—531no—
623C22×C4⋊C4—531no—
624C22×C4⋊C4C2×D5311yescharacteristic
625C22×C22⋊C4—531no—
626C22×C22⋊C4—531no—
627C22×C22⋊C4—531no—
628C22×C22⋊C4—531no—
629C22×C22⋊C4—531no—
630C22×C22⋊C4—531no—
631C22×C22⋊C4—531no—
632C22×C22⋊C4C2×D5311yescharacteristic
633C22×C22⋊C4C2×D5311yescharacteristic
634C22×C22⋊C4C2×D5311yescharacteristic
635C22×C42—531no—
636C22×C42—531no—
637C22×C42—531no—
638C22×C42—531no—
639C22×C42—531no—
640#394—538no—
641C4×C4⋊C4—1064no—
642C4×C22⋊C4—1064no—
643C4×C22⋊C4—1064no—
644C4×C22⋊C4—1064no—
645C4×C22⋊C4—1064no—
646C2×#95—531no—
647C2×#95—531no—
648C2×#95—531no—
649C2×#95—531no—
650C2×#95—531no—
651C2×#95—531no—
652C2×#95—531no—
653C2×#95—531no—
654C2×#95—531no—
655C2×#95—531no—
656C2×#95—531no—
657C2×#95C2×D5311yescharacteristic
658C2×#95C2×D5311yescharacteristic
659C2×#95C2×D5311yescharacteristic
660C53C4×#39411yescharacteristic, complemented, Sylow
661C25—531no—
662C25C22×D5311yescharacteristic
663C22×D4—534no—
664C22×D4—1062no—
665C22×D4—1062no—
666C22×D4—1062no—
667C22×D4—1062no—
668C22×D4—1062no—
669C22×D4—1062no—
670C23×C4—531no—
671C23×C4—531no—
672C23×C4—534no—
673C23×C4—531no—
674C23×C4—531no—
675C23×C4—531no—
676C23×C4—531no—
677C23×C4—531no—
678C23×C4—534no—
679C23×C4—1062no—
680C23×C4—1062no—
681C23×C4—1062no—
682C23×C4—1062no—
683C23×C4—1062no—
684C23×C4—1062no—
685C23×C4—1062no—
686C23×C4—1062no—
687C23×C4—1062no—
688C23×C4—1062no—
689C23×C4—1062no—
690C23×C4—1062no—
691C23×C4C22×D5311yescharacteristic
692C23×C4C22×D5311yescharacteristic
693C23×C4C22×D5311yescharacteristic
694C23×C4C22×D5311yescharacteristic
695C23×C4C22×D5311yescharacteristic
696C23×C4C22×D5311yescharacteristic
697C4×D4—10632no—
698C2×C4⋊C4—22no—
699C2×C4⋊C4—22no—
700C2×C4⋊C4—22no—
701C2×C4⋊C4—534no—
702C2×C4⋊C4—1062no—
703C2×C4⋊C4—1062no—
704C2×C4⋊C4—1062no—
705C2×C4⋊C4—1062no—
706C2×C4⋊C4—1062no—
707C2×C22⋊C4—22no—
708C2×C22⋊C4—22no—
709C2×C22⋊C4—22no—
710C2×C22⋊C4—22no—
711C2×C22⋊C4—22no—
712C2×C22⋊C4—22no—
713C2×C22⋊C4—22no—
714C2×C22⋊C4—22no—
715C2×C22⋊C4—534no—
716C2×C22⋊C4—534no—
717C2×C22⋊C4—534no—
718C2×C22⋊C4—1062no—
719C2×C22⋊C4—1062no—
720C2×C22⋊C4—1062no—
721C2×C22⋊C4—1062no—
722C2×C22⋊C4—1062no—
723C2×C22⋊C4—1062no—
724C2×C22⋊C4—1062no—
725C2×C22⋊C4—1062no—
726C2×C22⋊C4—1062no—
727C2×C22⋊C4—1062no—
728C2×C22⋊C4—1062no—
729C2×C22⋊C4—1062no—
730C2×C22⋊C4—1062no—
731C2×C22⋊C4—1062no—
732C2×C22⋊C4—1062no—
733C2×C22⋊C4—1062no—
734C2×C22⋊C4—1062no—
735C2×C22⋊C4—1062no—
736C2×C22⋊C4C4×D5314yescomplemented
737C2×C42—534no—
738C2×C42—534no—
739C2×C42—1062no—
740C2×C42—1062no—
741C2×C42—1062no—
742C2×C42—1062no—
743C2×C42—1062no—
744C2×C42—1062no—
745C2×C42—1062no—
746C2×C42—1062no—
747C2×C42—1062no—
748C2×C42—1062no—
749C2×C42—1062no—
750C2×C42—1062no—
751C2×C42—1062no—
752#95—22no—
753#95—22no—
754#95—22no—
755#95—534no—
756#95—1062no—
757#95—1062no—
758#95—1062no—
759#95—1062no—
760#95—1062no—
761#95—1062no—
762#95—1062no—
763#95—1062no—
764#95—1062no—
765#95—1062no—
766C24—21no—
767C24—21no—
768C24—21no—
769C24—21no—
770C24—21no—
771C24—21no—
772C24—21no—
773C24—21no—
774C24—21no—
775C24—21no—
776C24—21no—
777C24—21no—
778C24—532no—
779C24—532no—
780C24—532no—
781C24—1061no—
782C24—1061no—
783C24—1061no—
784C24—1061no—
785C24—1061no—
786C24—1061no—
787C24—1061no—
788C24—1061no—
789C24—1061no—
790C24—1061no—
791C24—1061no—
792C24—1061no—
793C24C2×C4×D5312yes—
794C24D4×D5312yes—
795C24#1171994912yes—
796C24C23×D5311yescharacteristic
797C2×D4—1068no—
798C2×D4—1068no—
799C2×D4—1068no—
800C2×D4—1068no—
801C2×D4—1068no—
802C2×D4—1068no—
803C2×D4—1068no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—532no—
839C22×C4—532no—
840C22×C4—532no—
841C22×C4—532no—
842C22×C4—532no—
843C22×C4—532no—
844C22×C4—532no—
845C22×C4—532no—
846C22×C4—532no—
847C22×C4—532no—
848C22×C4—532no—
849C22×C4—532no—
850C22×C4—532no—
851C22×C4—532no—
852C22×C4—532no—
853C22×C4—1068no—
854C22×C4—1068no—
855C22×C4—1068no—
856C22×C4—1068no—
857C22×C4—1068no—
858C22×C4—1068no—
859C22×C4—1061no—
860C22×C4—1061no—
861C22×C4—1061no—
862C22×C4—1061no—
863C22×C4—1061no—
864C22×C4—1061no—
865C22×C4—1061no—
866C22×C4—1061no—
867C22×C4—1061no—
868C22×C4—1061no—
869C22×C4—1061no—
870C22×C4—1061no—
871C22×C4—1061no—
872C22×C4—1061no—
873C22×C4—1061no—
874C22×C4—1061no—
875C22×C4—1061no—
876C22×C4—1061no—
877C22×C4—1061no—
878C22×C4—1061no—
879C22×C4—1061no—
880C22×C4—1061no—
881C22×C4—1061no—
882C22×C4—1061no—
883C22×C4—1061no—
884C22×C4—1061no—
885C22×C4—1061no—
886C22×C4—1061no—
887C22×C4—1061no—
888C22×C4—1061no—
889C22×C4—1061no—
890C22×C4—1061no—
891C22×C4—1061no—
892C22×C4—1061no—
893C22×C4—2124no—
894C22×C4—2124no—
895C22×C4—2124no—
896C22×C4—2124no—
897C22×C4—2124no—
898C22×C4—2124no—
899C22×C4—2124no—
900C22×C4—2124no—
901C22×C4C2×C4×D5312yes—
902C22×C4C2×C4×D5312yes—
903C22×C4D4×D5312yes—
904C22×C4D4×D5312yes—
905C22×C4D4×D5312yes—
906C22×C4#1171994712yes—
907C22×C4#1171994712yes—
908C22×C4#1171994712yes—
909C4⋊C4—28no—
910C4⋊C4—1068no—
911C4⋊C4—1068no—
912C22⋊C4—28no—
913C22⋊C4—28no—
914C22⋊C4—28no—
915C22⋊C4—1068no—
916C22⋊C4—1068no—
917C22⋊C4—1068no—
918C22⋊C4—1068no—
919C22⋊C4—1068no—
920C22⋊C4—1068no—
921C22⋊C4—1068no—
922C42—1068no—
923C42—1068no—
924C42—2124no—
925C42—2124no—
926C42—2124no—
927C23—22no—
928C23—22no—
929C23—22no—
930C23—22no—
931C23—22no—
932C23—22no—
933C23—22no—
934C23—22no—
935C23—22no—
936C23—22no—
937C23—22no—
938C23—22no—
939C23—22no—
940C23—22no—
941C23—22no—
942C23—22no—
943C23—22no—
944C23—22no—
945C23—41no—
946C23—41no—
947C23—41no—
948C23—41no—
949C23—41no—
950C23—41no—
951C23—41no—
952C23—41no—
953C23—41no—
954C23—41no—
955C23—41no—
956C23—41no—
957C23—41no—
958C23—41no—
959C23—41no—
960C23—41no—
961C23—534no—
962C23—1062no—
963C23—1062no—
964C23—1062no—
965C23—1062no—
966C23—1062no—
967C23—1062no—
968C23—1062no—
969C23—1062no—
970C23—1062no—
971C23—1062no—
972C23—1062no—
973C23—1062no—
974C23—1062no—
975C23—1062no—
976C23—1062no—
977C23—1062no—
978C23—1062no—
979C23—1062no—
980C23—2121no—
981C23—2121no—
982C23—2121no—
983C23—2121no—
984C23—2121no—
985C23—2121no—
986C23—2121no—
987C23—2121no—
988C23—2121no—
989C23—2121no—
990C23—2121no—
991C23—2121no—
992C23—2121no—
993C23—2121no—
994C23—2121no—
995C23—2121no—
996C23#1313317914yes—
997C23C22×C4×D5311yescharacteristic
998C23C2×D4×D5311yescharacteristic
999C23C2×D4×D5311yescharacteristic
1000C23C2×D4×D5311yescharacteristic
1001C23C2×D4×D5311yescharacteristic
1002C23#41×D5311yescharacteristic
1003C23#41×D5311yescharacteristic
1004C23#41×D5311yescharacteristic
1005C23#41×D5311yescharacteristic
1006C23#41×D5311yescharacteristic
1007C23#41×D5311yescharacteristic
1008C23C2×#1171994711yescharacteristic
1009C23C2×#1171994711yescharacteristic
1010C23C2×#1171994711yescharacteristic
1011C23C2×#1171994911yescharacteristic
1012D4—10632no—
1013C2×C4—22no—
1014C2×C4—22no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—22no—
1020C2×C4—22no—
1021C2×C4—22no—
1022C2×C4—22no—
1023C2×C4—22no—
1024C2×C4—22no—
1025C2×C4—22no—
1026C2×C4—22no—
1027C2×C4—22no—
1028C2×C4—22no—
1029C2×C4—22no—
1030C2×C4—22no—
1031C2×C4—22no—
1032C2×C4—22no—
1033C2×C4—22no—
1034C2×C4—41no—
1035C2×C4—41no—
1036C2×C4—41no—
1037C2×C4—41no—
1038C2×C4—41no—
1039C2×C4—41no—
1040C2×C4—41no—
1041C2×C4—41no—
1042C2×C4—41no—
1043C2×C4—41no—
1044C2×C4—41no—
1045C2×C4—41no—
1046C2×C4—41no—
1047C2×C4—41no—
1048C2×C4—41no—
1049C2×C4—41no—
1050C2×C4—41no—
1051C2×C4—41no—
1052C2×C4—41no—
1053C2×C4—41no—
1054C2×C4—534no—
1055C2×C4—534no—
1056C2×C4—534no—
1057C2×C4—534no—
1058C2×C4—534no—
1059C2×C4—534no—
1060C2×C4—534no—
1061C2×C4—534no—
1062C2×C4—1062no—
1063C2×C4—1062no—
1064C2×C4—1062no—
1065C2×C4—1062no—
1066C2×C4—1062no—
1067C2×C4—1062no—
1068C2×C4—1062no—
1069C2×C4—1062no—
1070C2×C4—1062no—
1071C2×C4—1062no—
1072C2×C4—1062no—
1073C2×C4—1062no—
1074C2×C4—1062no—
1075C2×C4—1062no—
1076C2×C4—1062no—
1077C2×C4—1062no—
1078C2×C4—1062no—
1079C2×C4—1062no—
1080C2×C4—1062no—
1081C2×C4—1062no—
1082C2×C4—1062no—
1083C2×C4—21216no—
1084C2×C4—21216no—
1085C2×C4—2121no—
1086C2×C4—2121no—
1087C2×C4—2121no—
1088C2×C4—2121no—
1089C2×C4—2121no—
1090C2×C4—2121no—
1091C2×C4—2121no—
1092C2×C4—2121no—
1093C2×C4—2121no—
1094C2×C4—2121no—
1095C2×C4—2121no—
1096C2×C4—2121no—
1097C2×C4—2121no—
1098C2×C4—2121no—
1099C2×C4—2121no—
1100C2×C4—2121no—
1101C2×C4—2121no—
1102C2×C4—2121no—
1103C2×C4—2121no—
1104C2×C4—2121no—
1105C2×C4#1313317714yescomplemented
1106C22—24no—
1107C22—24no—
1108C22—24no—
1109C22—42no—
1110C22—42no—
1111C22—42no—
1112C22—42no—
1113C22—42no—
1114C22—42no—
1115C22—42no—
1116C22—42no—
1117C22—42no—
1118C22—42no—
1119C22—42no—
1120C22—42no—
1121C22—1064no—
1122C22—1064no—
1123C22—1064no—
1124C22—2122no—
1125C22—2122no—
1126C22—2122no—
1127C22—2122no—
1128C22—2122no—
1129C22—2122no—
1130C22—2122no—
1131C22—2122no—
1132C22—2122no—
1133C22—2122no—
1134C22—2122no—
1135C22—2122no—
1136C22C4×D4×D5311yescharacteristic
1137C22C4×D4×D5311yescharacteristic
1138C22C2×#1313317711yescharacteristic
1139C22C2×#1313317911yescharacteristic
1140C22C4×#1171994711yescharacteristic
1141C22C4×#1171994711yescharacteristic
1142C22#1681109111yescharacteristic
1143C22#120×D5311yescharacteristic
1144C22#121×D5311yescharacteristic
1145C22#121×D5311yescharacteristic
1146C22#121×D5311yescharacteristic
1147C22#123×D5311yescharacteristic
1148C22#123×D5311yescharacteristic
1149C22#1681112911yescharacteristic
1150C22#1681112911yescharacteristic
1151C22#1681113111yescharacteristic
1152C22#1681113311yescharacteristic
1153C22#1681113311yescharacteristic
1154C22#1681113611yescharacteristic
1155C22#1681113611yescharacteristic
1156C22#1681113611yescharacteristic
1157C22#124×D5311yescharacteristic
1158C22#1681115011yescharacteristic
1159C22#1681115011yescharacteristic
1160C22#1681115211yescharacteristic
1161C22#1681115211yescharacteristic
1162C22#1681115611yescharacteristic
1163C22#1681115611yescharacteristic
1164C22#1681115911yescharacteristic
1165C22#1681115911yescharacteristic
1166C22#1681115911yescharacteristic
1167C22#1681116811yescharacteristic
1168C22#1681116811yescharacteristic
1169C22#1681116811yescharacteristic
1170C22#1681117111yescharacteristic
1171C4—24no—
1172C4—42no—
1173C4—42no—
1174C4—42no—
1175C4—42no—
1176C4—42no—
1177C4—538no—
1178C4—1064no—
1179C4—2122no—
1180C4—2122no—
1181C4—2122no—
1182C4—2122no—
1183C4—2122no—
1184C2—44no—
1185C2—2124no—
1186C2#2027721611yescharacteristic
1187C2#2027722111yescharacteristic
1188C2#2027722511yescharacteristic
1189C2#2027723111yescharacteristic
1190C2#2027723411yescharacteristic
1191C2#2027724211yescharacteristic
1192C2#2027725611yescharacteristic
1193C2#394×D5311yescharacteristic
1194C2#2027792711yescharacteristic
1195C2#2027795811yescharacteristic
1196C2#2027796011yescharacteristic
1197C2#2027796011yescharacteristic
1198C2#2027797311yescharacteristic
1199C2#2027798011yescharacteristic
1200C2#2027799711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D53
commutatorC23×C53C23×C4
FittingC53×#1439C2
socle, cosocleC24×C53C24
prime radicalC23×C22⋊D53C22
hypercenter#1439D53
hypocenterC53C4×#394
LCSG ▷ C23×C53 ▷ C53
UCSC1 ◁ C24 ◁ #1439

Complements

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

NH ≅ G/Ntype
3. C2×C4⋊C4×Dic53C2semidirect
4. C2×C22⋊C4×Dic53C2semidirect
5. C2×C22⋊C4×Dic53C2semidirect
6. C2×#16810470C2semidirect
7. C2×#16810470C2semidirect
8. #20272973C2semidirect
9. #20272967C2semidirect
10. #20272963C2semidirect
11. #20272962C2semidirect
12. #20272957C2semidirect
14. #95×Dic53C2semidirect
15. C53×#1439C2semidirect
36. #16810539C4semidirect
92. C2×C4⋊Dic53C2×C4semidirect
101. C2×C22⋊Dic53C2×C4semidirect
115. C2×#11719921C2×C4semidirect
116. C2×#11719921C2×C4semidirect
131. C2×C4×Dic53D4semidirect
142. #13133124C2×C4semidirect
161. C2×C22⋊C4×C53C2×C4semidirect
452. C2×C4×C53C4×D4semidirect
583. Dic53#394semidirect
596. #1439D53semidirect
660. C53C4×#394semidirect
736. C2×C22⋊C4C4×D53semidirect
1105. C2×C4#13133177semidirect

Maximal subgroups

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

subgroupindex
C22×#131331772
C2×#168105392
C2×C4⋊C4×Dic532
C2×C22⋊C4×Dic532
C2×#168104702
#202729732
#202729672
#202729632
#202729622
#202729572
#202729542
#95×Dic532
C53×#14392
C4×#39453