Finite Group Databasebeta

← #27315507

Subgroups — #27315507

Order 13568.

2494 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×#13133193C211yesmaximal, characteristic
2C22×C4⋊C4×D53C211yesmaximal, characteristic
3C2×#16810542C211yesmaximal, characteristic, complemented
4C2×#16810494C212yesmaximal
5#20272979C212yesmaximal, complemented
6#20272978C212yesmaximal, complemented
7#20272969C211yesmaximal, characteristic, complemented
8#20272968C211yesmaximal, characteristic, complemented
9#20272936C212yesmaximal
10#20272936C211yesmaximal, characteristic
11C2×C53×#395C211yesmaximal, characteristic, complemented
12C23×C4×D53C2211yescharacteristic
13C23×C4×D53C2211yescharacteristic
14C23×C4×D53C2211yescharacteristic
15C2×#13133193—24no—
16C2×#13133193—28no—
17C22×C4⋊Dic53C2211yescharacteristic
18C22×C4⋊Dic53C2211yescharacteristic
19C22×#11719919C2211yescharacteristic
20C22×#11719919C2212yes—
21C22×#11719919C2212yes—
22C22×#11719919C2211yescharacteristic
23C2×C4⋊C4×D53—24no—
24C2×C4⋊C4×D53—24no—
25C2×C4⋊C4×D53—24no—
26C22×#11719921C2212yes—
27C22×#11719921C2212yes—
28#16810542—24no—
29#16810494—28no—
30C2×#13133124C2212yes—
31C2×#13133124C2211yescharacteristic
32C2×#13133124C2212yes—
33C2×#13133124C2212yes—
34C2×#13133124C2212yes—
35C2×#13133124C2212yes—
36C2×#13133124C2212yes—
37C23×Q8×C53C2211yescharacteristic
38C22×C4⋊C4×C53C2212yes—
39C22×C4⋊C4×C53C2211yescharacteristic
40C53×#395—24no—
41C2×#95×C53C2211yescharacteristic
42C2×#95×C53C2212yes—
43C24×D53C2311yescharacteristic
44C23×Dic53C2312yes—
45C23×Dic53C2311yescharacteristic
46C23×Dic53C2311yescharacteristic
47C23×Dic53C2312yes—
48C23×Dic53C2311yescharacteristic
49C22×C4×D53—22no—
50C22×C4×D53—22no—
51C22×C4×D53—22no—
52C22×C4×D53—22no—
53C22×C4×D53—22no—
54C22×C4×D53—22no—
55C22×C4×D53—22no—
56C22×C4×D53—24no—
57C22×C4×D53—22no—
58C22×C4×D53—22no—
59C22×C4×D53—22no—
60C22×C4×D53—22no—
61C22×C4×D53—24no—
62C22×C4×D53—42no—
63C22×C4×D53—42no—
64C22×C4×D53D414yes—
65C22×C4×D53Q814yescomplemented
66#13133193—232no—
67C2×C4⋊Dic53—22no—
68C2×C4⋊Dic53—22no—
69C2×C4⋊Dic53—22no—
70C2×C4⋊Dic53—22no—
71C2×C4⋊Dic53—24no—
72C2×#11719919—22no—
73C2×#11719919—22no—
74C2×#11719919—22no—
75C2×#11719919—24no—
76C2×#11719919—24no—
77C2×#11719919—22no—
78C2×#11719919—22no—
79C2×#11719919—24no—
80C2×#11719919—24no—
81C2×#11719919—24no—
82C2×#11719919—42no—
83C2×#11719919D414yes—
84C4⋊C4×D53—232no—
85C2×#11719921—24no—
86C2×#11719921—24no—
87C2×#11719921—24no—
88C2×#11719921—24no—
89C2×#11719921D418yes—
90C2×#11719921Q818yescomplemented
91#13133124—22no—
92#13133124—24no—
93#13133124—24no—
94#13133124—24no—
95#13133124—24no—
96#13133124—24no—
97#13133124—42no—
98C22×Q8×C53—24no—
99C22×Q8×C53—22no—
100C22×Q8×C53—22no—
101C22×Q8×C53—22no—
102C22×Q8×C53—42no—
103C23×C4×C53C2311yescharacteristic
104C23×C4×C53C2312yes—
105C23×C4×C53C2312yes—
106C23×C4×C53C2311yescharacteristic
107C23×C4×C53C2311yescharacteristic
108C2×C4⋊C4×C53—22no—
109C2×C4⋊C4×C53—22no—
110C2×C4⋊C4×C53—24no—
111C2×C4⋊C4×C53—24no—
112C2×C4⋊C4×C53—42no—
113C2×C4⋊C4×C53D414yes—
114#95×C53—22no—
115#95×C53—24no—
116C24×C53C2411yescharacteristic
117C23×D53—21no—
118C23×D53—21no—
119C23×D53—21no—
120C23×D53—21no—
121C23×D53—22no—
122C23×D53—22no—
123C23×D53C2×D414yes—
124C23×D53C2×D412yes—
125C23×D53C2×Q814yes—
126C23×D53C2×Q812yes—
127C23×D53#4112yes—
128C2×Q8×C53—28no—
129C2×Q8×C53—48no—
130C2×Q8×C53—48no—
131C2×Q8×C53—44no—
132C2×Q8×C53—44no—
133C22×C4×C53—21no—
134C22×C4×C53—21no—
135C22×C4×C53—22no—
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—21no—
144C22×C4×C53—21no—
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×C53—22no—
152C22×C4×C53—22no—
153C22×C4×C53—22no—
154C22×C4×C53—22no—
155C22×C4×C53C2×D414yes—
156C22×C4×C53C2×D412yes—
157C22×C4×C53C2×D412yes—
158C22×C4×C53C2×D412yes—
159C22×C4×C53C2×D412yes—
160C22×C4×C53C2×D412yes—
161C22×C4×C53C2×Q814yes—
162C22×C4×C53C2×Q812yes—
163C22×C4×C53#4112yes—
164C22×Dic53—21no—
165C22×Dic53—21no—
166C22×Dic53—21no—
167C22×Dic53—21no—
168C22×Dic53—22no—
169C22×Dic53—22no—
170C22×Dic53—22no—
171C22×Dic53—22no—
172C22×Dic53—22no—
173C22×Dic53—22no—
174C22×Dic53—21no—
175C22×Dic53—21no—
176C22×Dic53—21no—
177C22×Dic53—21no—
178C22×Dic53—22no—
179C22×Dic53—22no—
180C22×Dic53—22no—
181C22×Dic53—22no—
182C22×Dic53—22no—
183C22×Dic53—22no—
184C22×Dic53—22no—
185C22×Dic53—22no—
186C22×Dic53—22no—
187C22×Dic53—22no—
188C22×Dic53C2×D414yes—
189C22×Dic53C2×D412yes—
190C22×Dic53C2×D412yes—
191C22×Dic53C2×D412yes—
192C22×Dic53C2×Q814yes—
193C22×Dic53C2×Q812yes—
194C22×Dic53#4112yes—
195C2×C4×D53—28no—
196C2×C4×D53—28no—
197C2×C4×D53—28no—
198C2×C4×D53—28no—
199C2×C4×D53—28no—
200C2×C4×D53—28no—
201C2×C4×D53—28no—
202C2×C4×D53—28no—
203C2×C4×D53—28no—
204C2×C4×D53—28no—
205C2×C4×D53—44no—
206C2×C4×D53—48no—
207C2×C4×D53—48no—
208C2×C4×D53—48no—
209C2×C4×D53—48no—
210C2×C4×D53—44no—
211C2×C4×D53—44no—
212C4⋊C4×C53—28no—
213C4⋊C4×C53—48no—
214#11719921—216no—
215#11719921—216no—
216C4⋊Dic53—28no—
217C4⋊Dic53—28no—
218#11719919—28no—
219#11719919—216no—
220#11719919—28no—
221#11719919—48no—
222C23×C53C22×D411yescharacteristic
223C23×C53C22×D411yescharacteristic
224C23×C53C22×D412yes—
225C23×C53C22×D411yescharacteristic
226C23×C53C22×Q811yescharacteristic
227C23×C53C22×Q812yes—
228C23×C53C2×#4111yescharacteristic
229C23×C53C2×#4111yescharacteristic
230C23×C53C2×#4111yescharacteristic
231C23×C53H(5,𝔽2)12yes—
232C23×C532−1+412yes—
233C22×D53—22no—
234C22×D53—22no—
235C22×D53—22no—
236C22×D53—22no—
237C22×D53—22no—
238C22×D53—22no—
239C22×D53—22no—
240C22×D53—22no—
241C22×D53—24no—
242C22×D53—24no—
243C22×D53—24no—
244C22×D53—24no—
245C22×D53—24no—
246C22×D53—24no—
247C22×D53—24no—
248C22×D53—24no—
249C22×D53—24no—
250C22×D53—24no—
251C22×D53#12014yes—
252C22×D53C22⋊Q814yes—
253C22×D53C22⋊Q818yes—
254C22×D53C4⋊Q814yes—
255C22×D53C4⋊Q818yes—
256Q8×C53—416no—
257C2×C4×C53—22no—
258C2×C4×C53—22no—
259C2×C4×C53—22no—
260C2×C4×C53—22no—
261C2×C4×C53—22no—
262C2×C4×C53—22no—
263C2×C4×C53—22no—
264C2×C4×C53—22no—
265C2×C4×C53—24no—
266C2×C4×C53—24no—
267C2×C4×C53—22no—
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—24no—
275C2×C4×C53—41no—
276C2×C4×C53—42no—
277C2×C4×C53—42no—
278C2×C4×C53—41no—
279C2×C4×C53—42no—
280C2×C4×C53—42no—
281C2×C4×C53—42no—
282C2×C4×C53—42no—
283C2×C4×C53—42no—
284C2×C4×C53—42no—
285C2×C4×C53—42no—
286C2×C4×C53#12014yes—
287C2×C4×C53C22⋊Q814yescomplemented
288C2×Dic53—22no—
289C2×Dic53—22no—
290C2×Dic53—22no—
291C2×Dic53—22no—
292C2×Dic53—22no—
293C2×Dic53—22no—
294C2×Dic53—22no—
295C2×Dic53—22no—
296C2×Dic53—22no—
297C2×Dic53—24no—
298C2×Dic53—24no—
299C2×Dic53—22no—
300C2×Dic53—24no—
301C2×Dic53—24no—
302C2×Dic53—24no—
303C2×Dic53—24no—
304C2×Dic53—24no—
305C2×Dic53—41no—
306C2×Dic53—42no—
307C2×Dic53—42no—
308C2×Dic53—41no—
309C2×Dic53—42no—
310C2×Dic53—42no—
311C2×Dic53—42no—
312C2×Dic53—42no—
313C2×Dic53—42no—
314C2×Dic53—42no—
315C2×Dic53—42no—
316C2×Dic53—42no—
317C2×Dic53—42no—
318C2×Dic53C22⋊Q814yescomplemented
319C4×D53—232no—
320C4×D53—416no—
321C4×D53—416no—
322#14720—531nomaximal, Sylow
323C22×C53C2×#12011yescharacteristic
324C22×C53C2×#12011yescharacteristic
325C22×C53C2×C22⋊Q811yescharacteristic
326C22×C53C2×C22⋊Q811yescharacteristic
327C22×C53C2×C22⋊Q812yes—
328C22×C53C2×C22⋊Q811yescharacteristic
329C22×C53#52511yescharacteristic
330C22×C53#52511yescharacteristic
331C22×C53#52511yescharacteristic
332C22×C53C2×C4⋊Q811yescharacteristic
333C22×C53C2×C4⋊Q812yes—
334C22×C53#53411yescharacteristic
335C22×C53#53611yescharacteristic
336C22×C53#53912yes—
337C22×C53#54412yes—
338C22×C53D4212yes—
339C22×C53D4212yes—
340C22×C53#54712yes—
341C22×C53#54712yes—
342C22×C53D4×Q812yes—
343C22×C53D4×Q812yes—
344C22×C53#55412yes—
345C22×C53#55412yes—
346C2×D53—24no—
347C2×D53—24no—
348C2×D53—24no—
349C2×D53—24no—
350C2×D53—24no—
351C2×D53—24no—
352C2×D53—28no—
353C2×D53—28no—
354C2×D53—28no—
355C2×D53—28no—
356C2×D53#39518yescomplemented
357C4×C53—24no—
358C4×C53—24no—
359C4×C53—42no—
360C4×C53—44no—
361C4×C53—44no—
362Dic53—24no—
363Dic53—42no—
364Dic53—42no—
365Dic53—44no—
366Dic53—44no—
367C22×C22⋊Q8—531no—
368C23×C4⋊C4—531no—
369C2×#395—531no—
370C2×#395D5311yescharacteristic, complemented
371C2×#385—532no—
372#1444—532no—
373#1444—532no—
374#1441—531no—
375#1441—531no—
376C22⋊#95—532no—
377C22⋊#95—531no—
378C2×C53C2×#39511yescharacteristic
379C2×C53#240311yescharacteristic
380C2×C53#240611yescharacteristic
381C2×C53#243411yescharacteristic
382C2×C53#244012yes—
383C2×C53#244012yes—
384C2×C53#244912yes—
385C2×C53#244912yes—
386C2×C53#258311yescharacteristic
387C2×C53#262711yescharacteristic
388C2×C53#284811yescharacteristic
389D53—28no—
390C23×Q8C2×D5311yescharacteristic
391C24×C4—531no—
392C24×C4—531no—
393C24×C4—531no—
394C2×C22⋊Q8—1068no—
395C2×C22⋊Q8—1064no—
396C22×C4⋊C4—531no—
397C22×C4⋊C4—531no—
398C22×C4⋊C4—532no—
399C22×C4⋊C4—531no—
400C22×C4⋊C4—531no—
401C22×C4⋊C4—532no—
402C22×C4⋊C4—1064no—
403C22×C4⋊C4—1064no—
404C22×C4⋊C4—1064no—
405C22×C4⋊C4C2×D5312yes—
406C22×C4⋊C4C2×D5311yescharacteristic
407C22×C22⋊C4—532no—
408C22×C22⋊C4—532no—
409#395—24no—
410#395—1064no—
411#385—1068no—
412C2×#95—531no—
413C2×#95—532no—
414C2×#95—532no—
415C2×#95—532no—
416C2×#95—532no—
417C2×#95—532no—
418C2×#95—532no—
419C2×#95C2×D5311yescharacteristic
420C2×#95C2×D5312yes—
421C53#1472011yescharacteristic, complemented, Sylow
422C25—531no—
423C22×Q8—24no—
424C22×Q8—22no—
425C22×Q8—22no—
426C22×Q8—22no—
427C22×Q8—42no—
428C23×C4—531no—
429C23×C4—532no—
430C23×C4—532no—
431C23×C4—531no—
432C23×C4—531no—
433C23×C4—534no—
434C23×C4—534no—
435C23×C4—1062no—
436C23×C4—1062no—
437C23×C4—1062no—
438C23×C4—1062no—
439C23×C4—1062no—
440C23×C4—1062no—
441C23×C4—1064no—
442C23×C4—1064no—
443C23×C4—1062no—
444C23×C4—1062no—
445C23×C4—1062no—
446C23×C4—1062no—
447C23×C4—1062no—
448C23×C4—2122no—
449C23×C4—2122no—
450C23×C4C22×D5312yes—
451C23×C4C22×D5312yes—
452C23×C4C22×D5311yescharacteristic
453C23×C4C22×D5311yescharacteristic
454C23×C4C22×D5311yescharacteristic
455C22⋊Q8—10632no—
456C2×C4⋊C4—22no—
457C2×C4⋊C4—22no—
458C2×C4⋊C4—24no—
459C2×C4⋊C4—24no—
460C2×C4⋊C4—42no—
461C2×C4⋊C4—534no—
462C2×C4⋊C4—10632no—
463C2×C4⋊C4—1062no—
464C2×C4⋊C4—1062no—
465C2×C4⋊C4—1062no—
466C2×C4⋊C4—1062no—
467C2×C4⋊C4—1064no—
468C2×C4⋊C4—1064no—
469C2×C4⋊C4—1064no—
470C2×C4⋊C4—1062no—
471C2×C4⋊C4—1064no—
472C2×C4⋊C4—1062no—
473C2×C4⋊C4—1062no—
474C2×C4⋊C4—1062no—
475C2×C4⋊C4—1062no—
476C2×C4⋊C4—1064no—
477C2×C4⋊C4—1064no—
478C2×C4⋊C4—2122no—
479C2×C4⋊C4C22⋊D5314yes—
480C2×C22⋊C4—538no—
481C2×C22⋊C4—538no—
482C2×C22⋊C4—1064no—
483C2×C22⋊C4—1064no—
484C2×C22⋊C4—1064no—
485C2×C22⋊C4—1064no—
486#95—22no—
487#95—24no—
488#95—1064no—
489#95—1064no—
490#95—1064no—
491#95—1064no—
492#95—1062no—
493#95—1064no—
494#95—2122no—
495C24—534no—
496C24—532no—
497C24—534no—
498C24—532no—
499C24—532no—
500C24—1061no—
501C24—1061no—
502C24—1061no—
503C24—1061no—
504C24—1062no—
505C24—1062no—
506C24C23×D5311yescharacteristic
507C2×Q8—28no—
508C2×Q8—48no—
509C2×Q8—48no—
510C2×Q8—44no—
511C2×Q8—44no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—22no—
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—21no—
524C22×C4—21no—
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—22no—
534C22×C4—532no—
535C22×C4—532no—
536C22×C4—532no—
537C22×C4—534no—
538C22×C4—532no—
539C22×C4—532no—
540C22×C4—534no—
541C22×C4—1068no—
542C22×C4—1068no—
543C22×C4—1068no—
544C22×C4—1068no—
545C22×C4—1068no—
546C22×C4—1068no—
547C22×C4—1068no—
548C22×C4—1068no—
549C22×C4—1061no—
550C22×C4—1061no—
551C22×C4—1061no—
552C22×C4—1061no—
553C22×C4—1068no—
554C22×C4—1062no—
555C22×C4—1062no—
556C22×C4—1062no—
557C22×C4—1062no—
558C22×C4—1062no—
559C22×C4—1062no—
560C22×C4—1061no—
561C22×C4—1061no—
562C22×C4—1061no—
563C22×C4—1061no—
564C22×C4—1062no—
565C22×C4—1062no—
566C22×C4—1062no—
567C22×C4—1062no—
568C22×C4—1062no—
569C22×C4—1062no—
570C22×C4—1062no—
571C22×C4—1062no—
572C22×C4—1062no—
573C22×C4—1062no—
574C22×C4—1068no—
575C22×C4—2124no—
576C22×C4—2128no—
577C22×C4—2128no—
578C22×C4—2128no—
579C22×C4—2128no—
580C22×C4—2124no—
581C22×C4—2124no—
582C22×C4D4×D5314yes—
583C22×C4D4×D5312yes—
584C22×C4D4×D5312yes—
585C22×C4Q8×D5314yes—
586C22×C4Q8×D5312yes—
587C22×C4#1171994912yes—
588C22×C4C2×C22⋊D5312yes—
589C22×C4C2×C22⋊D5312yes—
590C22×C4C2×C22⋊D5312yes—
591C4⋊C4—28no—
592C4⋊C4—48no—
593C4⋊C4—1068no—
594C4⋊C4—1068no—
595C4⋊C4—10616no—
596C4⋊C4—1068no—
597C4⋊C4—1068no—
598C4⋊C4—2128no—
599C22⋊C4—10616no—
600C22⋊C4—10616no—
601C23—534no—
602C23—538no—
603C23—534no—
604C23—534no—
605C23—538no—
606C23—1064no—
607C23—1064no—
608C23—1064no—
609C23—1064no—
610C23—1064no—
611C23—1064no—
612C23—1062no—
613C23—1062no—
614C23—1062no—
615C23—1062no—
616C23—1062no—
617C23—1062no—
618C23—1062no—
619C23—1062no—
620C23—1064no—
621C23—1064no—
622C23—1064no—
623C23—1064no—
624C23C2×D4×D5312yes—
625C23C2×D4×D5311yescharacteristic
626C23C2×D4×D5311yescharacteristic
627C23C22×C22⋊D5311yescharacteristic
628C23C2×Q8×D5312yes—
629C23C2×Q8×D5311yescharacteristic
630C23#41×D5311yescharacteristic
631C23#41×D5311yescharacteristic
632C23C2×#1171994911yescharacteristic
633C23#1313326212yes—
634C23#1313326512yes—
635Q8—416no—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—24no—
645C2×C4—24no—
646C2×C4—24no—
647C2×C4—24no—
648C2×C4—24no—
649C2×C4—22no—
650C2×C4—24no—
651C2×C4—24no—
652C2×C4—24no—
653C2×C4—24no—
654C2×C4—42no—
655C2×C4—41no—
656C2×C4—42no—
657C2×C4—42no—
658C2×C4—41no—
659C2×C4—42no—
660C2×C4—42no—
661C2×C4—42no—
662C2×C4—42no—
663C2×C4—42no—
664C2×C4—42no—
665C2×C4—534no—
666C2×C4—10632no—
667C2×C4—1062no—
668C2×C4—1062no—
669C2×C4—1062no—
670C2×C4—1062no—
671C2×C4—1062no—
672C2×C4—1062no—
673C2×C4—1064no—
674C2×C4—1064no—
675C2×C4—1064no—
676C2×C4—1064no—
677C2×C4—1064no—
678C2×C4—1062no—
679C2×C4—1062no—
680C2×C4—1062no—
681C2×C4—1064no—
682C2×C4—1062no—
683C2×C4—1064no—
684C2×C4—21216no—
685C2×C4—21216no—
686C2×C4—2122no—
687C2×C4—2122no—
688C2×C4—2122no—
689C2×C4—2121no—
690C2×C4—2122no—
691C2×C4—2122no—
692C2×C4—2121no—
693C2×C4—2122no—
694C2×C4—2122no—
695C2×C4—2122no—
696C2×C4—2122no—
697C2×C4—2122no—
698C2×C4—2122no—
699C2×C4#1313318514yes—
700C2×C4#1313319314yescomplemented
701C22—538no—
702C22—1064no—
703C22—1064no—
704C22—1064no—
705C22—1064no—
706C22—1064no—
707C22—1068no—
708C22—1068no—
709C22—1064no—
710C22—1068no—
711C22—1068no—
712C22#120×D5311yescharacteristic
713C22C2×#1313318511yescharacteristic
714C22C22⋊Q8×D5311yescharacteristic
715C22C22⋊Q8×D5311yescharacteristic
716C22C22⋊Q8×D5312yes—
717C22C2×#1313319311yescharacteristic
718C22#1681113011yescharacteristic
719C22#1681113611yescharacteristic
720C22#1681113611yescharacteristic
721C22C4⋊Q8×D5311yescharacteristic
722C22C4⋊Q8×D5312yes—
723C22#1681118311yescharacteristic
724C22#1681119811yescharacteristic
725C22#1681121912yes—
726C22#1681125012yes—
727C22#1681125512yes—
728C22D4×C22⋊D5312yes—
729C22#1681127512yes—
730C22#1681127612yes—
731C22Q8×C22⋊D5312yes—
732C22#1681128812yes—
733C22#1681132712yes—
734C22#1681133412yes—
735C4—24no—
736C4—24no—
737C4—42no—
738C4—44no—
739C4—44no—
740C4—1064no—
741C4—2122no—
742C4—2122no—
743C4—2124no—
744C4—2124no—
745C2—1068no—
746C2#395×D5311yescharacteristic
747C2#2027802611yescharacteristic
748C2#2027805111yescharacteristic
749C2#2027835611yescharacteristic
750C2#2027841012yes—
751C2#2027841312yes—
752C2#2027851712yes—
753C2#2027852112yes—
754C2#2028009111yescharacteristic
755C2#2028052711yescharacteristic
756C2#2028299911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D53
commutator, socle, cosocleC24×C53C24
FittingC2×C53×#395C2
prime radicalC24×D53C23
hypercenterC2×#395D53
hypocenterC53#14720
LCSG ▷ C24×C53 ▷ C53
UCSC1 ◁ C24 ◁ C2×#395

Complements

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

NH ≅ G/Ntype
3. C2×#16810542C2semidirect
5. #20272979C2semidirect
6. #20272978C2semidirect
7. #20272969C2semidirect
8. #20272968C2semidirect
11. C2×C53×#395C2semidirect
65. C22×C4×D53Q8semidirect
90. C2×#11719921Q8semidirect
287. C2×C4×C53C22⋊Q8semidirect
318. C2×Dic53C22⋊Q8semidirect
356. C2×D53#395semidirect
370. C2×#395D53semidirect
421. C53#14720semidirect
700. C2×C4#13133193semidirect

Maximal subgroups

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

subgroupindex
C22×#131331932
C22×C4⋊C4×D532
C2×#168105422
C2×#168104942
#202729792
#202729782
#202729692
#202729682
#202729362
C2×C53×#3952
#1472053