Finite Group Databasebeta

← #27306639

Subgroups — #27306639

Order 13568.

2374 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13133177C211yesmaximal, characteristic
2C2×#16810523C212yesmaximal
3C2×#16810487C211yesmaximal, characteristic, complemented
4C2×C4⋊C4×Dic53C211yesmaximal, characteristic, complemented
5#20272961C211yesmaximal, characteristic, complemented
6#20272960C211yesmaximal, characteristic, complemented
7#20272957C211yesmaximal, characteristic, complemented
8#20272943C212yesmaximal, complemented
9#20272937C212yesmaximal, complemented
10#20272936C212yesmaximal, complemented
11C53×#1439C211yesmaximal, characteristic, complemented
12C23×C22⋊D53C2211yescharacteristic
13C24×Dic53C2211yescharacteristic
14C23×C4×D53C2211yescharacteristic
15C2×#13133177—24no—
16C2×#13133177—24no—
17C2×#13133177C418yescomplemented
18C22×C4⋊Dic53C2211yescharacteristic
19C22×#11719919C2212yes—
20C22×#11719919C2211yescharacteristic
21C22×C22⋊Dic53C2212yes—
22C22×#11719921C2212yes—
23C22×#11719921C2212yes—
24C22×#11719921C2211yescharacteristic
25C22×C4×Dic53C2212yes—
26C22×C4×Dic53C2211yescharacteristic
27#16810523—28no—
28#16810487—24no—
29C4⋊C4×Dic53—24no—
30C2×#13133124C2212yes—
31C2×#13133124C2212yes—
32C2×#13133124C2211yescharacteristic
33C2×#13133124C2212yes—
34C2×#13133124C2212yes—
35C2×#13133124C2212yes—
36C22×C4⋊C4×C53C2211yescharacteristic
37C22×C22⋊C4×C53C2212yes—
38C22×C22⋊C4×C53C2211yescharacteristic
39C2×#95×C53C2211yescharacteristic
40C2×#95×C53C2212yes—
41C24×D53C2311yescharacteristic
42C22×C22⋊D53—22no—
43C22×C22⋊D53—22no—
44C22×C22⋊D53—22no—
45C22×C22⋊D53—22no—
46C22×C22⋊D53C2×C414yes—
47C22×C22⋊D53D414yes—
48C22×C22⋊D53Q814yes—
49C23×Dic53—22no—
50C23×Dic53—22no—
51C23×Dic53—42no—
52C23×Dic53—42no—
53C23×Dic53C2×C414yes—
54C23×Dic53C2312yes—
55C23×Dic53C2311yescharacteristic
56C23×Dic53C2312yes—
57C23×Dic53C2311yescharacteristic
58C23×Dic53C2311yescharacteristic
59C22×C4×D53—22no—
60C22×C4×D53—22no—
61C22×C4×D53—42no—
62C22×C4×D53—42no—
63C22×C4×D53C2×C414yes—
64#13133177—232no—
65C2×C4⋊Dic53—22no—
66C2×C4⋊Dic53—24no—
67C2×#11719919—22no—
68C2×#11719919—22no—
69C2×#11719919—24no—
70C2×#11719919—24no—
71C2×#11719919—24no—
72C2×#11719919C2×C414yes—
73C2×C22⋊Dic53—24no—
74C2×C22⋊Dic53—24no—
75C2×C22⋊Dic53—42no—
76C2×#11719921—24no—
77C2×#11719921—24no—
78C2×#11719921—22no—
79C2×#11719921—22no—
80C2×#11719921—24no—
81C2×#11719921—24no—
82C2×#11719921—42no—
83C2×#11719921—42no—
84C2×#11719921C2×C414yes—
85C2×C4×Dic53—24no—
86C2×C4×Dic53—24no—
87C2×C4×Dic53—24no—
88C2×C4×Dic53C2×C414yes—
89C2×C4×Dic53D414yes—
90C2×C4×Dic53D414yes—
91#13133124—22no—
92#13133124—24no—
93#13133124—24no—
94#13133124—42no—
95#13133124—42no—
96#13133124—42no—
97C25×C53C2311yescharacteristic
98C23×C4×C53C2312yes—
99C23×C4×C53C2311yescharacteristic
100C23×C4×C53C2312yes—
101C23×C4×C53C2311yescharacteristic
102C2×C4⋊C4×C53—22no—
103C2×C4⋊C4×C53—24no—
104C2×C22⋊C4×C53—24no—
105C2×C22⋊C4×C53—22no—
106C2×C22⋊C4×C53—22no—
107C2×C22⋊C4×C53—24no—
108C2×C22⋊C4×C53—42no—
109C2×C22⋊C4×C53C2×C414yes—
110#95×C53—22no—
111#95×C53—42no—
112C24×C53—21no—
113C24×C53—21no—
114C24×C53—22no—
115C24×C53—22no—
116C24×C53—21no—
117C24×C53—21no—
118C24×C53—22no—
119C24×C53—22no—
120C24×C53C22×C412yes—
121C24×C53C2×D412yes—
122C24×C53C2×Q812yes—
123C24×C53C2411yescharacteristic
124C23×D53—21no—
125C23×D53—21no—
126C23×D53—22no—
127C23×D53—22no—
128C23×D53—21no—
129C23×D53—21no—
130C23×D53—22no—
131C23×D53—22no—
132C23×D53C22×C412yes—
133C23×D53C2×D412yes—
134C23×D53C2×Q812yes—
135C22×C4×C53—22no—
136C22×C4×C53—22no—
137C22×C4×C53—22no—
138C22×C4×C53—21no—
139C22×C4×C53—21no—
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×C53—22no—
152C22×C4×C53—22no—
153C22×C4×C53—22no—
154C22×C4×C53C22×C412yes—
155C22×C4×C53C22×C412yes—
156C22×C4×C53C2×D412yes—
157C22×C4×C53C2×D412yes—
158C22×C4×C53#4114yes—
159C2×C22⋊D53—28no—
160C2×C22⋊D53—28no—
161C2×C22⋊D53—28no—
162C2×C22⋊D53—28no—
163C2×C22⋊D53—28no—
164C2×C22⋊D53—28no—
165C2×C22⋊D53C4⋊C4116yescomplemented
166C22×Dic53—22no—
167C22×Dic53—22no—
168C22×Dic53—22no—
169C22×Dic53—22no—
170C22×Dic53—21no—
171C22×Dic53—21no—
172C22×Dic53—22no—
173C22×Dic53—22no—
174C22×Dic53—22no—
175C22×Dic53—22no—
176C22×Dic53—22no—
177C22×Dic53—22no—
178C22×Dic53—28no—
179C22×Dic53—22no—
180C22×Dic53—22no—
181C22×Dic53—22no—
182C22×Dic53—22no—
183C22×Dic53—22no—
184C22×Dic53—22no—
185C22×Dic53—22no—
186C22×Dic53—48no—
187C22×Dic53—44no—
188C22×Dic53—48no—
189C22×Dic53—44no—
190C22×Dic53C22×C412yes—
191C22×Dic53C22×C412yes—
192C22×Dic53C22×C412yes—
193C22×Dic53C2×D412yes—
194C22×Dic53C2×D412yes—
195C22×Dic53C2×D412yes—
196C22×Dic53C2×D412yes—
197C22×Dic53C2×D412yes—
198C22×Dic53C2×Q812yes—
199C22×Dic53#4114yes—
200C22×Dic53#4112yes—
201C22×Dic53#4112yes—
202C2×C4×D53—28no—
203C2×C4×D53—48no—
204C2×C4×D53—44no—
205C2×C4×D53—48no—
206C2×C4×D53—44no—
207C4⋊C4×C53—28no—
208C22⋊C4×C53—28no—
209C22⋊C4×C53—48no—
210C22⋊Dic53—48no—
211#11719921—28no—
212#11719921—48no—
213#11719921—48no—
214C4⋊Dic53—28no—
215#11719919—28no—
216#11719919—48no—
217C4×Dic53—48no—
218C4×Dic53C22⋊C4116yescomplemented
219C23×C53—22no—
220C23×C53—22no—
221C23×C53—24no—
222C23×C53—24no—
223C23×C53—22no—
224C23×C53—22no—
225C23×C53—22no—
226C23×C53—22no—
227C23×C53—24no—
228C23×C53—24no—
229C23×C53—24no—
230C23×C53—24no—
231C23×C53—41no—
232C23×C53—41no—
233C23×C53—42no—
234C23×C53—41no—
235C23×C53—42no—
236C23×C53—41no—
237C23×C53—42no—
238C23×C53—42no—
239C23×C53—42no—
240C23×C53—42no—
241C23×C53C2×C4⋊C414yes—
242C23×C53C23×C411yescharacteristic
243C23×C53C22×D411yescharacteristic
244C23×C53C22×D411yescharacteristic
245C23×C53C22×D411yescharacteristic
246C23×C53C22×Q811yescharacteristic
247C23×C53C2×#4111yescharacteristic
248C23×C53C2×#4111yescharacteristic
249C23×C53C2×#4112yes—
250C23×C53C2×#4112yes—
251C23×C53H(5,𝔽2)12yes—
252C23×C53H(5,𝔽2)12yes—
253C22×D53—22no—
254C22×D53—22no—
255C22×D53—24no—
256C22×D53—24no—
257C22×D53—22no—
258C22×D53—22no—
259C22×D53—22no—
260C22×D53—22no—
261C22×D53—24no—
262C22×D53—24no—
263C22×D53—24no—
264C22×D53—24no—
265C22×D53—41no—
266C22×D53—41no—
267C22×D53—42no—
268C22×D53—41no—
269C22×D53—42no—
270C22×D53—41no—
271C22×D53—42no—
272C22×D53—42no—
273C22×D53—42no—
274C22×D53—42no—
275C22×D53C2×C4⋊C414yes—
276C2×C4×C53—24no—
277C2×C4×C53—22no—
278C2×C4×C53—22no—
279C2×C4×C53—24no—
280C2×C4×C53—22no—
281C2×C4×C53—24no—
282C2×C4×C53—24no—
283C2×C4×C53—24no—
284C2×C4×C53—24no—
285C2×C4×C53—42no—
286C2×C4×C53—41no—
287C2×C4×C53—42no—
288C2×C4×C53—41no—
289C2×C4×C53—42no—
290C2×C4×C53—42no—
291C2×C4×C53—42no—
292C2×C4×C53—42no—
293C2×C4×C53—42no—
294C2×C4×C53—42no—
295C2×C4×C53—42no—
296C2×C4×C53—42no—
297C2×C4×C53—42no—
298C2×C4×C53—42no—
299C2×C4×C53C2×C22⋊C414yes—
300C22⋊D53—232no—
301C2×Dic53—24no—
302C2×Dic53—22no—
303C2×Dic53—24no—
304C2×Dic53—22no—
305C2×Dic53—22no—
306C2×Dic53—24no—
307C2×Dic53—24no—
308C2×Dic53—24no—
309C2×Dic53—24no—
310C2×Dic53—416no—
311C2×Dic53—42no—
312C2×Dic53—42no—
313C2×Dic53—41no—
314C2×Dic53—42no—
315C2×Dic53—41no—
316C2×Dic53—42no—
317C2×Dic53—42no—
318C2×Dic53—42no—
319C2×Dic53—42no—
320C2×Dic53—42no—
321C2×Dic53—42no—
322C2×Dic53—42no—
323C2×Dic53—42no—
324C2×Dic53—42no—
325C2×Dic53C2×C22⋊C414yes—
326C2×Dic53C2×C22⋊C414yes—
327C2×Dic53C2×C4⋊C414yes—
328C2×Dic53#11714yes—
329C2×Dic53#12114yes—
330C2×Dic53#12114yes—
331C2×Dic53C22⋊Q814yes—
332C2×Dic53C22⋊Q814yes—
333C4×D53—416no—
334#13941—531nomaximal, Sylow
335C22×C53—28no—
336C22×C53—24no—
337C22×C53—42no—
338C22×C53—44no—
339C22×C53—42no—
340C22×C53—42no—
341C22×C53—44no—
342C22×C53—42no—
343C22×C53—42no—
344C22×C53—44no—
345C22×C53—42no—
346C22×C53C22×C22⋊C411yescharacteristic
347C22×C53C22×C4⋊C411yescharacteristic
348C22×C53C2×#11711yescharacteristic
349C22×C53C4×#4112yes—
350C22×C53#51812yes—
351C22×C53C2×#12111yescharacteristic
352C22×C53C2×#12111yescharacteristic
353C22×C53C2×C22⋊Q811yescharacteristic
354C22×C53C2×C22⋊Q811yescharacteristic
355C22×C53#52511yescharacteristic
356C22×C53#52511yescharacteristic
357C22×C53#53212yes—
358C22×C53#53511yescharacteristic
359C22×C53#53512yes—
360C22×C53#53511yescharacteristic
361C22×C53#54612yes—
362C22×C53#54612yes—
363C22×C53#55312yes—
364C22×C53#55312yes—
365C22×C53#55412yes—
366C22×C53#55412yes—
367C22×C53#55912yes—
368C22×C53#55912yes—
369C2×D53—28no—
370C2×D53—24no—
371C2×D53—42no—
372C2×D53—44no—
373C2×D53—42no—
374C2×D53—42no—
375C2×D53—44no—
376C2×D53—42no—
377C2×D53—42no—
378C2×D53—44no—
379C2×D53—42no—
380C4×C53—24no—
381C4×C53—42no—
382C4×C53—44no—
383C4×C53—82no—
384Dic53—24no—
385Dic53—42no—
386Dic53—44no—
387Dic53—82no—
388Dic53#38018yes—
389C22×C4×D4—531no—
390C2×#390—532no—
391C2×#382—531no—
392C2×C4×C4⋊C4—531no—
393#1439—531no—
394#1439—531no—
395#1439—531no—
396#1439D5311yescharacteristic, complemented
397C4⋊#95—532no—
398C22⋊#95—532no—
399C22⋊#95—532no—
400C2×C53—44no—
401C2×C53C2×#38011yescharacteristic
402C2×C53#229711yescharacteristic
403C2×C53#230911yescharacteristic
404C2×C53#234912yes—
405C2×C53#235712yes—
406C2×C53#253511yescharacteristic
407C2×C53#253511yescharacteristic
408C2×C53#254412yes—
409C2×C53#256612yes—
410C2×C53#258011yescharacteristic
411C2×C53#258011yescharacteristic
412D53—44no—
413C23×D4—531no—
414C24×C4—531no—
415C24×C4—531no—
416C2×C4×D4—538no—
417C2×C4×D4—1064no—
418C2×C4×D4—1064no—
419C22×C4⋊C4—531no—
420C22×C4⋊C4—532no—
421C22×C4⋊C4—531no—
422C22×C4⋊C4C2×D5311yescharacteristic
423C22×C22⋊C4—531no—
424C22×C22⋊C4—532no—
425C22×C22⋊C4—532no—
426C22×C22⋊C4—532no—
427C22×C22⋊C4C2×D5312yes—
428C22×C22⋊C4C2×D5311yescharacteristic
429C22×C42—531no—
430C22×C42—532no—
431#390—1068no—
432#382—1064no—
433C4×C4⋊C4—1064no—
434C2×#95—532no—
435C2×#95—532no—
436C2×#95—531no—
437C2×#95—532no—
438C2×#95—532no—
439C2×#95—532no—
440C2×#95C2×D5311yescharacteristic
441C2×#95C2×D5312yes—
442C53#1394111yescharacteristic, complemented, Sylow
443C25—531no—
444C25C22×D5311yescharacteristic
445C22×D4—534no—
446C22×D4—534no—
447C22×D4—534no—
448C22×D4—1062no—
449C22×D4—1062no—
450C22×D4—1062no—
451C22×D4—1062no—
452C23×C4—531no—
453C23×C4—531no—
454C23×C4—532no—
455C23×C4—531no—
456C23×C4—534no—
457C23×C4—534no—
458C23×C4—532no—
459C23×C4—1062no—
460C23×C4—1062no—
461C23×C4—1062no—
462C23×C4—1062no—
463C23×C4—2122no—
464C23×C4—2122no—
465C23×C4—2122no—
466C23×C4—2122no—
467C23×C4C22×D5312yes—
468C23×C4C22×D5311yescharacteristic
469C23×C4C22×D5312yes—
470C23×C4C22×D5311yescharacteristic
471C4×D4—10632no—
472C2×C4⋊C4—22no—
473C2×C4⋊C4—24no—
474C2×C4⋊C4—534no—
475C2×C4⋊C4—1062no—
476C2×C4⋊C4—1062no—
477C2×C4⋊C4—1064no—
478C2×C4⋊C4—1062no—
479C2×C4⋊C4—1064no—
480C2×C4⋊C4—1064no—
481C2×C4⋊C4—1064no—
482C2×C22⋊C4—22no—
483C2×C22⋊C4—22no—
484C2×C22⋊C4—24no—
485C2×C22⋊C4—24no—
486C2×C22⋊C4—42no—
487C2×C22⋊C4—534no—
488C2×C22⋊C4—1062no—
489C2×C22⋊C4—1062no—
490C2×C22⋊C4—1064no—
491C2×C22⋊C4—1064no—
492C2×C22⋊C4—1064no—
493C2×C22⋊C4—1064no—
494C2×C22⋊C4—1064no—
495C2×C22⋊C4—1064no—
496C2×C22⋊C4—2122no—
497C2×C22⋊C4—2122no—
498C2×C22⋊C4—2122no—
499C2×C22⋊C4C4×D5314yes—
500C2×C42—534no—
501C2×C42—534no—
502C2×C42—534no—
503C2×C42—1064no—
504C2×C42—1064no—
505C2×C42—1064no—
506#95—22no—
507#95—42no—
508#95—1064no—
509#95—1064no—
510#95—1062no—
511#95—2122no—
512#95—2122no—
513#95—2122no—
514C24—21no—
515C24—21no—
516C24—22no—
517C24—21no—
518C24—21no—
519C24—22no—
520C24—22no—
521C24—22no—
522C24—532no—
523C24—532no—
524C24—532no—
525C24—1061no—
526C24—1061no—
527C24—1062no—
528C24—1061no—
529C24—1061no—
530C24—1062no—
531C24—1062no—
532C24—1062no—
533C24C2×C4×D5312yes—
534C24D4×D5312yes—
535C24Q8×D5312yes—
536C24C23×D5311yescharacteristic
537C2×D4—5316no—
538C2×D4—1068no—
539C2×D4—1068no—
540C2×D4—1068no—
541C2×D4—1068no—
542C2×D4—1068no—
543C2×D4—1068no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—532no—
564C22×C4—532no—
565C22×C4—532no—
566C22×C4—532no—
567C22×C4—532no—
568C22×C4—532no—
569C22×C4—532no—
570C22×C4—532no—
571C22×C4—532no—
572C22×C4—532no—
573C22×C4—532no—
574C22×C4—534no—
575C22×C4—1068no—
576C22×C4—1068no—
577C22×C4—1062no—
578C22×C4—1062no—
579C22×C4—1062no—
580C22×C4—1062no—
581C22×C4—1061no—
582C22×C4—1061no—
583C22×C4—1062no—
584C22×C4—1062no—
585C22×C4—1062no—
586C22×C4—1062no—
587C22×C4—1062no—
588C22×C4—1062no—
589C22×C4—1062no—
590C22×C4—1062no—
591C22×C4—1062no—
592C22×C4—1062no—
593C22×C4—1062no—
594C22×C4—1062no—
595C22×C4—1062no—
596C22×C4—2128no—
597C22×C4—2124no—
598C22×C4—2128no—
599C22×C4—2124no—
600C22×C4—2128no—
601C22×C4—2124no—
602C22×C4—2128no—
603C22×C4—2124no—
604C22×C4C2×C4×D5312yes—
605C22×C4C2×C4×D5312yes—
606C22×C4D4×D5312yes—
607C22×C4D4×D5312yes—
608C22×C4#1171994714yes—
609C4⋊C4—28no—
610C4⋊C4—1068no—
611C4⋊C4—1068no—
612C4⋊C4—2128no—
613C22⋊C4—28no—
614C22⋊C4—48no—
615C22⋊C4—1068no—
616C22⋊C4—2128no—
617C22⋊C4—2128no—
618C22⋊C4—2128no—
619C42—5316no—
620C42—2128no—
621C23—24no—
622C23—22no—
623C23—24no—
624C23—22no—
625C23—24no—
626C23—24no—
627C23—24no—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—22no—
632C23—24no—
633C23—42no—
634C23—42no—
635C23—42no—
636C23—42no—
637C23—41no—
638C23—41no—
639C23—42no—
640C23—41no—
641C23—42no—
642C23—41no—
643C23—534no—
644C23—1064no—
645C23—1062no—
646C23—1064no—
647C23—1062no—
648C23—1064no—
649C23—1064no—
650C23—1064no—
651C23—1062no—
652C23—1062no—
653C23—1062no—
654C23—1062no—
655C23—1064no—
656C23—2122no—
657C23—2122no—
658C23—2122no—
659C23—2122no—
660C23—2121no—
661C23—2121no—
662C23—2122no—
663C23—2121no—
664C23—2122no—
665C23—2121no—
666C23C4⋊C4×D5314yes—
667C23C22×C4×D5311yescharacteristic
668C23C2×D4×D5311yescharacteristic
669C23C2×D4×D5311yescharacteristic
670C23C2×D4×D5311yescharacteristic
671C23C2×Q8×D5311yescharacteristic
672C23#41×D5312yes—
673C23#41×D5311yescharacteristic
674C23#41×D5311yescharacteristic
675C23C2×#1171994712yes—
676C23#1313326212yes—
677C23#1313326312yes—
678D4—10632no—
679C2×C4—24no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—24no—
683C2×C4—24no—
684C2×C4—22no—
685C2×C4—24no—
686C2×C4—24no—
687C2×C4—24no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—41no—
692C2×C4—42no—
693C2×C4—41no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—534no—
703C2×C4—534no—
704C2×C4—534no—
705C2×C4—534no—
706C2×C4—534no—
707C2×C4—534no—
708C2×C4—534no—
709C2×C4—534no—
710C2×C4—1064no—
711C2×C4—1062no—
712C2×C4—1064no—
713C2×C4—1062no—
714C2×C4—1064no—
715C2×C4—1064no—
716C2×C4—1062no—
717C2×C4—1064no—
718C2×C4—1064no—
719C2×C4—21216no—
720C2×C4—21216no—
721C2×C4—2122no—
722C2×C4—2122no—
723C2×C4—2122no—
724C2×C4—2122no—
725C2×C4—2122no—
726C2×C4—2122no—
727C2×C4—2122no—
728C2×C4—2122no—
729C2×C4—2122no—
730C2×C4—2122no—
731C2×C4—2121no—
732C2×C4—2122no—
733C2×C4—2122no—
734C2×C4—2121no—
735C2×C4C22⋊C4×D5314yes—
736C22—24no—
737C22—28no—
738C22—42no—
739C22—42no—
740C22—42no—
741C22—42no—
742C22—42no—
743C22—44no—
744C22—44no—
745C22—44no—
746C22—42no—
747C22—1064no—
748C22—1068no—
749C22—2122no—
750C22—2122no—
751C22—2122no—
752C22—2122no—
753C22—2122no—
754C22—2124no—
755C22—2124no—
756C22—2124no—
757C22—2122no—
758C22C2×C22⋊C4×D5311yescharacteristic
759C22C2×C4⋊C4×D5311yescharacteristic
760C22#117×D5311yescharacteristic
761C22C4×#1171994712yes—
762C22#1681109512yes—
763C22#121×D5311yescharacteristic
764C22#121×D5311yescharacteristic
765C22C22⋊Q8×D5311yescharacteristic
766C22C22⋊Q8×D5311yescharacteristic
767C22#1681112911yescharacteristic
768C22#1681113111yescharacteristic
769C22#1681116812yes—
770C22#1681118611yescharacteristic
771C22#1681118912yes—
772C22#1681119111yescharacteristic
773C22#1681126012yes—
774C22#1681126512yes—
775C22#1681131612yes—
776C22#1681132412yes—
777C22#1681132712yes—
778C22#1681133112yes—
779C22#1681135512yes—
780C22#1681135712yes—
781C4—24no—
782C4—42no—
783C4—44no—
784C4—82no—
785C4—538no—
786C4—1064no—
787C4—4242no—
788C4—2122no—
789C4—2124no—
790C2—44no—
791C2—2124no—
792C2#380×D5311yescharacteristic
793C2#2027720011yescharacteristic
794C2#2027729411yescharacteristic
795C2#2027762112yes—
796C2#2027768512yes—
797C2#2027961111yescharacteristic
798C2#2027961311yescharacteristic
799C2#2027968112yes—
800C2#2027991012yes—
801C2#2028006811yescharacteristic
802C2#2028007011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D53
commutatorC23×C53C23×C4
FittingC53×#1439C2
socle, cosocleC24×C53C24
prime radicalC23×C22⋊D53C22
hypercenter#1439D53
hypocenterC53#13941
LCSG ▷ C23×C53 ▷ C53
UCSC1 ◁ C24 ◁ #1439

Complements

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

NH ≅ G/Ntype
3. C2×#16810487C2semidirect
4. C2×C4⋊C4×Dic53C2semidirect
5. #20272961C2semidirect
6. #20272960C2semidirect
7. #20272957C2semidirect
8. #20272943C2semidirect
9. #20272937C2semidirect
10. #20272936C2semidirect
11. C53×#1439C2semidirect
17. C2×#13133177C4semidirect
165. C2×C22⋊D53C4⋊C4semidirect
218. C4×Dic53C22⋊C4semidirect
396. #1439D53semidirect
442. C53#13941semidirect

Maximal subgroups

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

subgroupindex
C22×#131331772
C2×#168105232
C2×#168104872
C2×C4⋊C4×Dic532
#202729612
#202729602
#202729572
#202729432
#202729372
#202729362
C53×#14392
#1394153