Finite Group Databasebeta

← #27307456

Subgroups — #27307456

Order 13568.

2950 conjugacy classes of subgroups.

The subgroup lattice has 850 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C22⋊D53C211yesmaximal, characteristic
2C23×#11719919C211yesmaximal, characteristic, complemented
3C2×#16810500C211yesmaximal, characteristic
4C2×#16810500C211yesmaximal, characteristic
5C2×#16810498C211yesmaximal, characteristic, complemented
6C2×#16810497C212yesmaximal, complemented
7#20272979C212yesmaximal, complemented
8#20272959C212yesmaximal, complemented
9#20272950C212yesmaximal, complemented
10#20272937C211yesmaximal, characteristic, complemented
11C53×C22⋊#95C211yesmaximal, characteristic, complemented
12C23×C22⋊D53C2211yescharacteristic
13C24×Dic53C2211yescharacteristic
14C24×Dic53C2211yescharacteristic
15C23×C4×D53C2211yescharacteristic
16C2×C4×C22⋊D53—24no—
17C2×C4×C22⋊D53—24no—
18C2×C4×C22⋊D53—24no—
19C22×C4⋊Dic53C2212yes—
20C22×#11719919—28no—
21C22×#11719919—24no—
22C22×#11719919C2212yes—
23C22×#11719919C2211yescharacteristic
24C22×#11719919C2212yes—
25C22×C22⋊Dic53C2211yescharacteristic
26C22×#11719921C2211yescharacteristic
27C22×#11719921C2212yes—
28C22×#11719921C2212yes—
29C22×C4×Dic53C2211yescharacteristic
30#16810500—24no—
31#16810500C418yescomplemented
32#16810498—24no—
33#16810497—28no—
34C2×#13133124C2212yes—
35C2×#13133124C2212yes—
36C2×#13133124C2212yes—
37C2×#13133124C2212yes—
38C2×#13133124C2212yes—
39C24×C4×C53C2211yescharacteristic
40C22×C22⋊C4×C53C2211yescharacteristic
41C22×C22⋊C4×C53C2211yescharacteristic
42C2×#95×C53C2212yes—
43C2×#95×C53C2212yes—
44C24×D53C2311yescharacteristic
45C22×C22⋊D53—22no—
46C22×C22⋊D53—22no—
47C22×C22⋊D53—22no—
48C22×C22⋊D53—22no—
49C22×C22⋊D53C2×C414yes—
50C22×C22⋊D53D414yes—
51C22×C22⋊D53Q814yes—
52C23×Dic53—22no—
53C23×Dic53—22no—
54C23×Dic53—24no—
55C23×Dic53—24no—
56C23×Dic53—22no—
57C23×Dic53—24no—
58C23×Dic53—22no—
59C23×Dic53—22no—
60C23×Dic53—42no—
61C23×Dic53C2×C414yescomplemented
62C23×Dic53C2311yescharacteristic
63C23×Dic53C2312yes—
64C23×Dic53C2311yescharacteristic
65C23×Dic53C2311yescharacteristic
66C23×Dic53C2312yes—
67C22×C4×D53—22no—
68C22×C4×D53—22no—
69C22×C4×D53—22no—
70C22×C4×D53—24no—
71C22×C4×D53—42no—
72C4×C22⋊D53—232no—
73C2×C4⋊Dic53—24no—
74C2×C4⋊Dic53—24no—
75C2×C4⋊Dic53—42no—
76C2×#11719919—232no—
77C2×#11719919—24no—
78C2×#11719919—24no—
79C2×#11719919—24no—
80C2×#11719919—22no—
81C2×#11719919—24no—
82C2×#11719919—24no—
83C2×#11719919—22no—
84C2×#11719919—22no—
85C2×#11719919D418yescomplemented
86C2×C22⋊Dic53—22no—
87C2×C22⋊Dic53—22no—
88C2×C22⋊Dic53D414yes—
89C2×#11719921—22no—
90C2×#11719921—24no—
91C2×#11719921—22no—
92C2×#11719921—24no—
93C2×#11719921—22no—
94C2×#11719921—24no—
95C2×#11719921—24no—
96C2×#11719921—42no—
97C2×#11719921C2×C418yescomplemented
98C2×C4×Dic53—22no—
99C2×C4×Dic53—22no—
100C2×C4×Dic53—22no—
101#13133124—24no—
102#13133124—24no—
103#13133124—24no—
104#13133124—24no—
105#13133124C2×C418yescomplemented
106C25×C53C2311yescharacteristic
107C23×C4×C53—22no—
108C23×C4×C53—22no—
109C23×C4×C53—24no—
110C23×C4×C53—42no—
111C23×C4×C53D414yes—
112C23×C4×C53C2312yes—
113C23×C4×C53C2312yes—
114C23×C4×C53C2311yescharacteristic
115C23×C4×C53C2311yescharacteristic
116C2×C22⋊C4×C53—22no—
117C2×C22⋊C4×C53—22no—
118C2×C22⋊C4×C53—22no—
119C2×C22⋊C4×C53—22no—
120C2×C22⋊C4×C53—22no—
121C2×C22⋊C4×C53C2×C414yescomplemented
122#95×C53—24no—
123#95×C53—42no—
124C24×C53—22no—
125C24×C53—22no—
126C24×C53—22no—
127C24×C53—22no—
128C24×C53C22×C412yes—
129C24×C53C2×D412yes—
130C24×C53C2×D412yes—
131C24×C53C2×D412yes—
132C24×C53C2×Q812yes—
133C24×C53#4112yes—
134C24×C53#4112yes—
135C24×C53C2411yescharacteristic
136C23×D53—22no—
137C23×D53—21no—
138C23×D53—21no—
139C23×D53—22no—
140C23×D53—21no—
141C23×D53—21no—
142C23×D53—22no—
143C23×D53—22no—
144C23×D53C22×C412yes—
145C23×D53C2×D412yes—
146C23×D53C2×Q812yes—
147C22×C4×C53—21no—
148C22×C4×C53—21no—
149C22×C4×C53—22no—
150C22×C4×C53—28no—
151C22×C4×C53—22no—
152C22×C4×C53—22no—
153C22×C4×C53—21no—
154C22×C4×C53—21no—
155C22×C4×C53—22no—
156C22×C4×C53—22no—
157C22×C4×C53—22no—
158C22×C4×C53—22no—
159C22×C4×C53—22no—
160C22×C4×C53—22no—
161C22×C4×C53—28no—
162C22×C4×C53—22no—
163C22×C4×C53—22no—
164C22×C4×C53—22no—
165C22×C4×C53—22no—
166C22×C4×C53—22no—
167C22×C4×C53—22no—
168C22×C4×C53—22no—
169C22×C4×C53—44no—
170C22×C4×C53—48no—
171C22×C4×C53—48no—
172C22×C4×C53C22×C414yes—
173C22×C4×C53C2×D412yes—
174C22×C4×C53C2×D412yes—
175C22×C4×C53C2×D414yes—
176C2×C22⋊D53—28no—
177C2×C22⋊D53—28no—
178C2×C22⋊D53—28no—
179C2×C22⋊D53—28no—
180C2×C22⋊D53—28no—
181C2×C22⋊D53—28no—
182C2×C22⋊D53C4⋊C4116yescomplemented
183C22×Dic53—28no—
184C22×Dic53—216no—
185C22×Dic53—28no—
186C22×Dic53—28no—
187C22×Dic53—21no—
188C22×Dic53—21no—
189C22×Dic53—22no—
190C22×Dic53—22no—
191C22×Dic53—22no—
192C22×Dic53—22no—
193C22×Dic53—21no—
194C22×Dic53—21no—
195C22×Dic53—216no—
196C22×Dic53—28no—
197C22×Dic53—22no—
198C22×Dic53—22no—
199C22×Dic53—22no—
200C22×Dic53—21no—
201C22×Dic53—21no—
202C22×Dic53—21no—
203C22×Dic53—21no—
204C22×Dic53—22no—
205C22×Dic53—22no—
206C22×Dic53—22no—
207C22×Dic53—22no—
208C22×Dic53—22no—
209C22×Dic53—22no—
210C22×Dic53—22no—
211C22×Dic53—48no—
212C22×Dic53—48no—
213C22×Dic53—44no—
214C22×Dic53—44no—
215C22×Dic53C22×C412yes—
216C22×Dic53C22×C414yes—
217C22×Dic53C2×D412yes—
218C22×Dic53C2×D414yes—
219C22×Dic53C2×D412yes—
220C22×Dic53C2×D412yes—
221C22×Dic53C2×D414yes—
222C22×Dic53C2×Q812yes—
223C22×Dic53#4114yes—
224C2×C4×D53—28no—
225C2×C4×D53—48no—
226C2×C4×D53—48no—
227C2×C4×D53—44no—
228C2×C4×D53—44no—
229C22⋊C4×C53—28no—
230C22⋊C4×C53—44no—
231C22⋊Dic53—28no—
232#11719921—28no—
233#11719921—216no—
234#11719921—48no—
235C4⋊Dic53—48no—
236#11719919—216no—
237#11719919—28no—
238#11719919—216no—
239C4×Dic53—28no—
240C23×C53—24no—
241C23×C53—24no—
242C23×C53—22no—
243C23×C53—22no—
244C23×C53—24no—
245C23×C53—22no—
246C23×C53—22no—
247C23×C53—24no—
248C23×C53—24no—
249C23×C53—24no—
250C23×C53—24no—
251C23×C53—24no—
252C23×C53—24no—
253C23×C53—24no—
254C23×C53—24no—
255C23×C53—24no—
256C23×C53C2×C4⋊C414yes—
257C23×C53C4×D414yes—
258C23×C53C4×D414yes—
259C23×C53#12014yes—
260C23×C53C22⋊Q814yes—
261C23×C53C22⋊Q814yes—
262C23×C53#12314yes—
263C23×C53C23×C411yescharacteristic
264C23×C53C22×D411yescharacteristic
265C23×C53C22×D411yescharacteristic
266C23×C53C22×D412yes—
267C23×C53C22×D411yescharacteristic
268C23×C53C22×Q811yescharacteristic
269C23×C53C2×#4112yes—
270C23×C53C2×#4111yescharacteristic
271C23×C53C2×#4111yescharacteristic
272C23×C53H(5,𝔽2)12yes—
273C23×C532−1+412yes—
274C22×D53—22no—
275C22×D53—22no—
276C22×D53—24no—
277C22×D53—24no—
278C22×D53—22no—
279C22×D53—22no—
280C22×D53—22no—
281C22×D53—22no—
282C22×D53—24no—
283C22×D53—24no—
284C22×D53—24no—
285C22×D53—24no—
286C22×D53—41no—
287C22×D53—42no—
288C22×D53—41no—
289C22×D53—41no—
290C22×D53—41no—
291C22×D53—42no—
292C22×D53—42no—
293C22×D53—42no—
294C22×D53—42no—
295C22×D53—42no—
296C22×D53C2×C4⋊C414yescomplemented
297C2×C4×C53—22no—
298C2×C4×C53—22no—
299C2×C4×C53—24no—
300C2×C4×C53—24no—
301C2×C4×C53—24no—
302C2×C4×C53—24no—
303C2×C4×C53—24no—
304C2×C4×C53—22no—
305C2×C4×C53—22no—
306C2×C4×C53—22no—
307C2×C4×C53—416no—
308C2×C4×C53—42no—
309C2×C4×C53—42no—
310C2×C4×C53—42no—
311C2×C4×C53—42no—
312C2×C4×C53—42no—
313C2×C4×C53—42no—
314C2×C4×C53—42no—
315C2×C4×C53—42no—
316C2×C4×C53—42no—
317C2×C4×C53—42no—
318C2×C4×C53—42no—
319C2×C4×C53—42no—
320C2×C4×C53—42no—
321C2×C4×C53#12014yes—
322C22⋊D53—232no—
323C2×Dic53—232no—
324C2×Dic53—24no—
325C2×Dic53—24no—
326C2×Dic53—22no—
327C2×Dic53—22no—
328C2×Dic53—24no—
329C2×Dic53—22no—
330C2×Dic53—22no—
331C2×Dic53—22no—
332C2×Dic53—22no—
333C2×Dic53—24no—
334C2×Dic53—24no—
335C2×Dic53—24no—
336C2×Dic53—22no—
337C2×Dic53—24no—
338C2×Dic53—22no—
339C2×Dic53—24no—
340C2×Dic53—24no—
341C2×Dic53—24no—
342C2×Dic53—24no—
343C2×Dic53—416no—
344C2×Dic53—41no—
345C2×Dic53—42no—
346C2×Dic53—41no—
347C2×Dic53—41no—
348C2×Dic53—42no—
349C2×Dic53—41no—
350C2×Dic53—42no—
351C2×Dic53—42no—
352C2×Dic53—42no—
353C2×Dic53—42no—
354C2×Dic53C2×C4⋊C414yescomplemented
355C2×Dic53C4×D418yescomplemented
356C4×D53—416no—
357#14015—531nomaximal, Sylow
358C22×C53—24no—
359C22×C53—24no—
360C22×C53—28no—
361C22×C53—28no—
362C22×C53—24no—
363C22×C53—24no—
364C22×C53—24no—
365C22×C53—28no—
366C22×C53—28no—
367C22×C53—24no—
368C22×C53#38518yescomplemented
369C22×C53C22×C4⋊C411yescharacteristic
370C22×C53C2×C4×D412yes—
371C22×C53C2×C4×D411yescharacteristic
372C22×C53C2×C4×D411yescharacteristic
373C22×C53#52012yes—
374C22×C53C2×#12011yescharacteristic
375C22×C53C2×#12011yescharacteristic
376C22×C53C2×C22⋊Q811yescharacteristic
377C22×C53C2×C22⋊Q811yescharacteristic
378C22×C53C2×#12311yescharacteristic
379C22×C53#52512yes—
380C22×C53#52511yescharacteristic
381C22×C53#53411yescharacteristic
382C22×C53#53611yescharacteristic
383C22×C53#53912yes—
384C22×C53D4212yes—
385C22×C53D4212yes—
386C22×C53#54712yes—
387C22×C53#54712yes—
388C22×C53#54812yes—
389C22×C53D4×Q812yes—
390C22×C53#55312yes—
391C22×C53#55412yes—
392C2×D53—28no—
393C2×D53—24no—
394C2×D53—42no—
395C2×D53—42no—
396C2×D53—44no—
397C2×D53—42no—
398C2×D53—42no—
399C2×D53—42no—
400C2×D53—44no—
401C2×D53—44no—
402C2×D53—42no—
403C4×C53—24no—
404C4×C53—44no—
405C4×C53—42no—
406C4×C53—82no—
407Dic53—24no—
408Dic53—28no—
409Dic53—42no—
410Dic53—44no—
411Dic53—42no—
412C22×C4×D4—531no—
413C23×C4⋊C4—531no—
414C2×#386—531no—
415C2×#386—531no—
416C2×#385—532no—
417C2×#385—531no—
418#1444—532no—
419#1439—532no—
420#1436—532no—
421C22⋊#95—531no—
422C22⋊#95D5311yescharacteristic, complemented
423C2×C53—28no—
424C2×C53C2×#38511yescharacteristic
425C2×C53C4×#12011yescharacteristic
426C2×C53#232211yescharacteristic
427C2×C53D4×C4⋊C412yes—
428C2×C53#236112yes—
429C2×C53#240311yescharacteristic
430C2×C53#240611yescharacteristic
431C2×C53#240911yescharacteristic
432C2×C53#244312yes—
433C2×C53#244912yes—
434C2×C53#257911yescharacteristic
435D53—44no—
436C23×D4—531no—
437C24×C4—531no—
438C24×C4—531no—
439C24×C4—531no—
440C24×C4C2×D5311yescharacteristic
441C2×C4×D4—1064no—
442C2×C4×D4—1064no—
443C2×C4×D4—1064no—
444C22×C4⋊C4—532no—
445C22×C4⋊C4—532no—
446C22×C4⋊C4—531no—
447C22×C4⋊C4—532no—
448C22×C4⋊C4—1068no—
449C22×C4⋊C4—1064no—
450C22×C22⋊C4—531no—
451C22×C22⋊C4—532no—
452C22×C22⋊C4—531no—
453C22×C22⋊C4—532no—
454C22×C22⋊C4C2×D5311yescharacteristic
455C22×C22⋊C4C2×D5311yescharacteristic
456C22×C42—531no—
457#386—538no—
458#386—1064no—
459#385—1068no—
460#385—1064no—
461C2×#95—532no—
462C2×#95—532no—
463C2×#95—532no—
464C2×#95—532no—
465C2×#95—532no—
466C2×#95C2×D5312yes—
467C2×#95C2×D5312yes—
468C53#1401511yescharacteristic, complemented, Sylow
469C25—531no—
470C25C22×D5311yescharacteristic
471C22×D4—534no—
472C22×D4—534no—
473C22×D4—534no—
474C22×D4—1062no—
475C22×D4—1062no—
476C22×D4—1062no—
477C22×D4—1062no—
478C23×C4—22no—
479C23×C4—22no—
480C23×C4—24no—
481C23×C4—42no—
482C23×C4—532no—
483C23×C4—531no—
484C23×C4—534no—
485C23×C4—531no—
486C23×C4—531no—
487C23×C4—532no—
488C23×C4—1062no—
489C23×C4—1062no—
490C23×C4—1064no—
491C23×C4—1064no—
492C23×C4—1064no—
493C23×C4—1062no—
494C23×C4—1062no—
495C23×C4—1062no—
496C23×C4—1062no—
497C23×C4—1062no—
498C23×C4—1062no—
499C23×C4—1064no—
500C23×C4—2122no—
501C23×C4—2122no—
502C23×C4D21214yes—
503C23×C4C22×D5312yes—
504C23×C4C22×D5312yes—
505C23×C4C22×D5311yescharacteristic
506C23×C4C22×D5311yescharacteristic
507C4×D4—10632no—
508C2×C4⋊C4—538no—
509C2×C4⋊C4—1064no—
510C2×C4⋊C4—1064no—
511C2×C4⋊C4—1062no—
512C2×C4⋊C4—1062no—
513C2×C4⋊C4—10632no—
514C2×C4⋊C4—1064no—
515C2×C4⋊C4—1064no—
516C2×C4⋊C4—1062no—
517C2×C4⋊C4—1064no—
518C2×C4⋊C4—1064no—
519C2×C4⋊C4—1064no—
520C2×C4⋊C4—2122no—
521C2×C22⋊C4—22no—
522C2×C22⋊C4—22no—
523C2×C22⋊C4—22no—
524C2×C22⋊C4—22no—
525C2×C22⋊C4—22no—
526C2×C22⋊C4—534no—
527C2×C22⋊C4—538no—
528C2×C22⋊C4—1062no—
529C2×C22⋊C4—1064no—
530C2×C22⋊C4—1064no—
531C2×C22⋊C4—1062no—
532C2×C22⋊C4—1062no—
533C2×C22⋊C4—1062no—
534C2×C22⋊C4—1062no—
535C2×C22⋊C4—1064no—
536C2×C22⋊C4—1064no—
537C2×C22⋊C4—2122no—
538C2×C22⋊C4C4×D5314yescomplemented
539C2×C42—1062no—
540C2×C42—1062no—
541C2×C42—1062no—
542#95—24no—
543#95—42no—
544#95—538no—
545#95—1064no—
546#95—1064no—
547#95—1064no—
548#95—1064no—
549C24—22no—
550C24—22no—
551C24—22no—
552C24—22no—
553C24—532no—
554C24—532no—
555C24—532no—
556C24—1062no—
557C24—1061no—
558C24—1061no—
559C24—1062no—
560C24—1061no—
561C24—1061no—
562C24—1062no—
563C24—1062no—
564C24C2×C4×D5312yes—
565C24C2×D21212yes—
566C24#1171994512yes—
567C24D4×D5312yes—
568C24D4×D5312yes—
569C24#1171994712yes—
570C24Q8×D5312yes—
571C24C23×D5311yescharacteristic
572C2×D4—5316no—
573C2×D4—1068no—
574C2×D4—1068no—
575C2×D4—1068no—
576C2×D4—1068no—
577C2×D4—1068no—
578C2×D4—1068no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—22no—
582C22×C4—28no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—28no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—44no—
602C22×C4—48no—
603C22×C4—48no—
604C22×C4—532no—
605C22×C4—534no—
606C22×C4—532no—
607C22×C4—534no—
608C22×C4—532no—
609C22×C4—534no—
610C22×C4—532no—
611C22×C4—532no—
612C22×C4—534no—
613C22×C4—1068no—
614C22×C4—10616no—
615C22×C4—1068no—
616C22×C4—10616no—
617C22×C4—1068no—
618C22×C4—1068no—
619C22×C4—1061no—
620C22×C4—1062no—
621C22×C4—1061no—
622C22×C4—1062no—
623C22×C4—1062no—
624C22×C4—1061no—
625C22×C4—1062no—
626C22×C4—1061no—
627C22×C4—1068no—
628C22×C4—1062no—
629C22×C4—1062no—
630C22×C4—1062no—
631C22×C4—1061no—
632C22×C4—1061no—
633C22×C4—1062no—
634C22×C4—1061no—
635C22×C4—1061no—
636C22×C4—1062no—
637C22×C4—1062no—
638C22×C4—1062no—
639C22×C4—1062no—
640C22×C4—1062no—
641C22×C4—1062no—
642C22×C4—2128no—
643C22×C4—2128no—
644C22×C4—2124no—
645C22×C4—2128no—
646C22×C4—2128no—
647C22×C4—2124no—
648C22×C4—2124no—
649C22×C4—2124no—
650C22×C4C2×C4×D5314yes—
651C22×C4C2×D21212yes—
652C22×C4C2×D21212yes—
653C22×C4D4×D5314yes—
654C4⋊C4—10616no—
655C4⋊C4—1068no—
656C4⋊C4—10616no—
657C4⋊C4—2128no—
658C22⋊C4—28no—
659C22⋊C4—44no—
660C22⋊C4—10616no—
661C22⋊C4—1068no—
662C22⋊C4—1068no—
663C22⋊C4—2128no—
664C42—1068no—
665C23—24no—
666C23—24no—
667C23—24no—
668C23—24no—
669C23—24no—
670C23—24no—
671C23—24no—
672C23—24no—
673C23—22no—
674C23—24no—
675C23—22no—
676C23—22no—
677C23—22no—
678C23—24no—
679C23—24no—
680C23—24no—
681C23—534no—
682C23—1064no—
683C23—1064no—
684C23—1064no—
685C23—1064no—
686C23—1062no—
687C23—1062no—
688C23—1064no—
689C23—1062no—
690C23—1062no—
691C23—1062no—
692C23—1062no—
693C23—1064no—
694C23—2122no—
695C23—2122no—
696C23—2122no—
697C23—2121no—
698C23—2122no—
699C23—2121no—
700C23—2121no—
701C23—2121no—
702C23—2122no—
703C23—2122no—
704C23C4⋊C4×D5314yes—
705C23#1313317714yes—
706C23C4×D21214yes—
707C23#1313318714yes—
708C23#1313319514yes—
709C23#1313319714yes—
710C23#1313319914yes—
711C23C22×C4×D5311yescharacteristic
712C23C2×D4×D5311yescharacteristic
713C23C2×D4×D5311yescharacteristic
714C23C2×D4×D5312yes—
715C23C22×D21211yescharacteristic
716C23C2×Q8×D5311yescharacteristic
717C23#41×D5312yes—
718C23C2×#1171994711yescharacteristic
719C23C2×#1171994511yescharacteristic
720C23#1313326212yes—
721C23#1313326412yes—
722D4—10632no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—24no—
726C2×C4—24no—
727C2×C4—24no—
728C2×C4—24no—
729C2×C4—24no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—416no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—534no—
748C2×C4—538no—
749C2×C4—10632no—
750C2×C4—1064no—
751C2×C4—1062no—
752C2×C4—1064no—
753C2×C4—1062no—
754C2×C4—1062no—
755C2×C4—1064no—
756C2×C4—1062no—
757C2×C4—1062no—
758C2×C4—1062no—
759C2×C4—1064no—
760C2×C4—1064no—
761C2×C4—1064no—
762C2×C4—1064no—
763C2×C4—1062no—
764C2×C4—1062no—
765C2×C4—1064no—
766C2×C4—1064no—
767C2×C4—1064no—
768C2×C4—1064no—
769C2×C4—21216no—
770C2×C4—21216no—
771C2×C4—2122no—
772C2×C4—2122no—
773C2×C4—2121no—
774C2×C4—2121no—
775C2×C4—2121no—
776C2×C4—2122no—
777C2×C4—2121no—
778C2×C4—2122no—
779C2×C4—2122no—
780C2×C4—2122no—
781C2×C4#1313318714yes—
782C22—24no—
783C22—24no—
784C22—24no—
785C22—24no—
786C22—28no—
787C22—24no—
788C22—28no—
789C22—28no—
790C22—24no—
791C22—28no—
792C22—1068no—
793C22—1064no—
794C22—2122no—
795C22—2122no—
796C22—2122no—
797C22—2122no—
798C22—2122no—
799C22—2124no—
800C22—2124no—
801C22—2122no—
802C22—2124no—
803C22#1681049718yescomplemented
804C22C2×C4⋊C4×D5311yescharacteristic
805C22C4×D4×D5312yes—
806C22C2×#1313317711yescharacteristic
807C22C2×C4×D21211yescharacteristic
808C22#1681110212yes—
809C22C2×#1313318711yescharacteristic
810C22C2×#1313318711yescharacteristic
811C22C2×#1313319511yescharacteristic
812C22C2×#1313319711yescharacteristic
813C22C2×#1313319911yescharacteristic
814C22#1681113212yes—
815C22#1681113511yescharacteristic
816C22#1681118511yescharacteristic
817C22#1681119911yescharacteristic
818C22#1681121512yes—
819C22#1681125512yes—
820C22#1681125512yes—
821C22#1681127112yes—
822C22#1681127112yes—
823C22#1681127912yes—
824C22#1681128612yes—
825C22#1681131612yes—
826C22#1681132712yes—
827C4—24no—
828C4—42no—
829C4—44no—
830C4—82no—
831C4—1064no—
832C4—1068no—
833C4—2122no—
834C4—2124no—
835C4—2122no—
836C2—28no—
837C2—2124no—
838C2C2×#1681049711yescharacteristic
839C2C4×#1313318711yescharacteristic
840C2#2027738611yescharacteristic
841C2#2027761312yes—
842C2#2027772612yes—
843C2#2027802811yescharacteristic
844C2#2027805211yescharacteristic
845C2#2027808111yescharacteristic
846C2#2027845212yes—
847C2#2027852612yes—
848C2#2028006411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D53
commutatorC23×C53C23×C4
FittingC53×C22⋊#95C2
socle, cosocleC24×C53C24
prime radicalC23×C22⋊D53C22
hypercenterC22⋊#95D53
hypocenterC53#14015
LCSG ▷ C23×C53 ▷ C53
UCSC1 ◁ C24 ◁ C22⋊#95

Complements

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

NH ≅ G/Ntype
2. C23×#11719919C2semidirect
5. C2×#16810498C2semidirect
6. C2×#16810497C2semidirect
7. #20272979C2semidirect
8. #20272959C2semidirect
9. #20272950C2semidirect
10. #20272937C2semidirect
11. C53×C22⋊#95C2semidirect
31. #16810500C4semidirect
61. C23×Dic53C2×C4semidirect
85. C2×#11719919D4semidirect
97. C2×#11719921C2×C4semidirect
105. #13133124C2×C4semidirect
121. C2×C22⋊C4×C53C2×C4semidirect
182. C2×C22⋊D53C4⋊C4semidirect
296. C22×D53C2×C4⋊C4semidirect
354. C2×Dic53C2×C4⋊C4semidirect
355. C2×Dic53C4×D4semidirect
368. C22×C53#385semidirect
422. C22⋊#95D53semidirect
468. C53#14015semidirect
538. C2×C22⋊C4C4×D53semidirect
803. C22#16810497semidirect

Maximal subgroups

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

subgroupindex
C22×C4×C22⋊D532
C23×#117199192
C2×#168105002
C2×#168104982
C2×#168104972
#202729792
#202729592
#202729502
#202729372
C53×C22⋊#952
#1401553