Finite Group Databasebeta

← #27307461

Subgroups — #27307461

Order 13568.

2590 conjugacy classes of subgroups.

The subgroup lattice has 832 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16810503C211yesmaximal, characteristic
2C2×#16810503C211yesmaximal, characteristic
3C2×#16810495C211yesmaximal, characteristic, complemented
4C22×#13133124C211yesmaximal, characteristic, complemented
5#20272974C212yesmaximal, complemented
6#20272958C212yesmaximal, complemented
7#20272948C212yesmaximal, complemented
8#20272938C211yesmaximal, characteristic, complemented
9#20272938C212yesmaximal, complemented
10#20272937C211yesmaximal, characteristic, complemented
11C22×C4×D4×C53C211yesmaximal, characteristic
12C24×Dic53C2211yescharacteristic
13C24×Dic53C2211yescharacteristic
14C22×#11719919C2212yes—
15C22×C22⋊Dic53C2211yescharacteristic
16C22×C22⋊Dic53C2212yes—
17C22×C22⋊Dic53C2211yescharacteristic
18C22×C22⋊Dic53C2212yes—
19#16810503—24no—
20#16810503C418yescomplemented
21#16810495—24no—
22C2×#13133124—24no—
23C2×#13133124C2212yes—
24C2×#13133124C2212yes—
25C2×#13133124C2212yes—
26C2×#13133124C2212yes—
27C2×#13133124C2212yes—
28C2×#13133124C2212yes—
29C2×#13133124C2212yes—
30C2×#13133124C2212yes—
31C2×#13133124C2212yes—
32C23×D4×C53C2211yescharacteristic
33C24×C4×C53C2211yescharacteristic
34C24×C4×C53C2211yescharacteristic
35C2×C4×D4×C53—24no—
36C2×C4×D4×C53—24no—
37C2×C4×D4×C53—24no—
38C22×C4⋊C4×C53C2211yescharacteristic
39C22×C22⋊C4×C53C2211yescharacteristic
40C22×C22⋊C4×C53C2211yescharacteristic
41C22×C42×C53C2211yescharacteristic
42C23×Dic53—22no—
43C23×Dic53—22no—
44C23×Dic53—22no—
45C23×Dic53—24no—
46C23×Dic53—22no—
47C23×Dic53—22no—
48C23×Dic53—42no—
49C23×Dic53—42no—
50C23×Dic53—42no—
51C23×Dic53C2×C414yescomplemented
52C23×Dic53C2312yes—
53C23×Dic53C2312yes—
54C23×Dic53C2312yes—
55C23×Dic53C2312yes—
56C2×#11719919—24no—
57C2×#11719919—24no—
58C2×#11719919—42no—
59C2×C22⋊Dic53—22no—
60C2×C22⋊Dic53—24no—
61C2×C22⋊Dic53—22no—
62C2×C22⋊Dic53—22no—
63C2×C22⋊Dic53—22no—
64C2×C22⋊Dic53—22no—
65C2×C22⋊Dic53—24no—
66C2×C22⋊Dic53—42no—
67C2×C22⋊Dic53—42no—
68C2×C22⋊Dic53—42no—
69C2×C22⋊Dic53C2×C414yescomplemented
70C2×C22⋊Dic53C2×C418yescomplemented
71#13133124—24no—
72#13133124—24no—
73#13133124—24no—
74#13133124—24no—
75#13133124—24no—
76#13133124—42no—
77#13133124—42no—
78#13133124—42no—
79#13133124C2×C418yescomplemented
80C25×C53C2311yescharacteristic
81C25×C53C2311yescharacteristic
82C22×D4×C53—22no—
83C22×D4×C53—22no—
84C22×D4×C53—22no—
85C22×D4×C53—22no—
86C22×D4×C53C2×C414yes—
87C22×D4×C53D414yes—
88C22×D4×C53Q814yes—
89C23×C4×C53—22no—
90C23×C4×C53—22no—
91C23×C4×C53—22no—
92C23×C4×C53—22no—
93C23×C4×C53—22no—
94C23×C4×C53—24no—
95C23×C4×C53—24no—
96C23×C4×C53—42no—
97C23×C4×C53—42no—
98C23×C4×C53D414yes—
99C23×C4×C53C2311yescharacteristic
100C23×C4×C53C2311yescharacteristic
101C23×C4×C53C2311yescharacteristic
102C23×C4×C53C2311yescharacteristic
103C23×C4×C53C2311yescharacteristic
104C4×D4×C53—232no—
105C2×C4⋊C4×C53—22no—
106C2×C4⋊C4×C53—22no—
107C2×C4⋊C4×C53—22no—
108C2×C22⋊C4×C53—22no—
109C2×C22⋊C4×C53—22no—
110C2×C22⋊C4×C53—22no—
111C2×C22⋊C4×C53—22no—
112C2×C22⋊C4×C53—22no—
113C2×C22⋊C4×C53D414yes—
114C2×C42×C53—22no—
115C2×C42×C53—22no—
116C2×C42×C53—22no—
117C24×C53—22no—
118C24×C53—22no—
119C24×C53—22no—
120C24×C53—22no—
121C24×C53—21no—
122C24×C53—21no—
123C24×C53—22no—
124C24×C53—21no—
125C24×C53—21no—
126C24×C53—22no—
127C24×C53—22no—
128C24×C53—22no—
129C24×C53C22×C412yes—
130C24×C53C22×C412yes—
131C24×C53C2×D412yes—
132C24×C53C2×D412yes—
133C24×C53C2×D412yes—
134C24×C53C2×D412yes—
135C24×C53C2×Q812yes—
136C24×C53C2×Q812yes—
137C24×C53#4112yes—
138C24×C53#4112yes—
139C24×C53C2411yescharacteristic
140C2×D4×C53—28no—
141C2×D4×C53—28no—
142C2×D4×C53—28no—
143C2×D4×C53—28no—
144C2×D4×C53—28no—
145C2×D4×C53—28no—
146C2×D4×C53C4⋊C4116yescomplemented
147C22×C4×C53—21no—
148C22×C4×C53—21no—
149C22×C4×C53—21no—
150C22×C4×C53—21no—
151C22×C4×C53—21no—
152C22×C4×C53—21no—
153C22×C4×C53—22no—
154C22×C4×C53—28no—
155C22×C4×C53—28no—
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—22no—
163C22×C4×C53—22no—
164C22×C4×C53—22no—
165C22×C4×C53—22no—
166C22×C4×C53—22no—
167C22×C4×C53—22no—
168C22×C4×C53—28no—
169C22×C4×C53—44no—
170C22×C4×C53—48no—
171C22×C4×C53—48no—
172C22×C4×C53—48no—
173C22×C4×C53—48no—
174C22×C4×C53—44no—
175C22×C4×C53—44no—
176C22×C4×C53C22×C412yes—
177C22×C4×C53C2×D412yes—
178C22×C4×C53C2×D412yes—
179C22×C4×C53C2×D412yes—
180C22×C4×C53C2×D412yes—
181C22×C4×C53C2×D412yes—
182C22×C4×C53C2×Q812yes—
183C22×C4×C53#4114yes—
184C22×Dic53—28no—
185C22×Dic53—28no—
186C22×Dic53—22no—
187C22×Dic53—22no—
188C22×Dic53—22no—
189C22×Dic53—22no—
190C22×Dic53—22no—
191C22×Dic53—22no—
192C22×Dic53—22no—
193C22×Dic53—22no—
194C22×Dic53—22no—
195C22×Dic53—22no—
196C22×Dic53—22no—
197C22×Dic53—22no—
198C22×Dic53—22no—
199C22×Dic53—22no—
200C22×Dic53—22no—
201C22×Dic53—22no—
202C22×Dic53—22no—
203C22×Dic53—22no—
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—48no—
214C22×Dic53—44no—
215C22×Dic53—44no—
216C22×Dic53—44no—
217C22×Dic53—48no—
218C22×Dic53—44no—
219C22×Dic53C22×C414yes—
220C22×Dic53C22×C414yes—
221C22×Dic53#4114yes—
222C4⋊C4×C53—28no—
223C22⋊C4×C53—28no—
224C22⋊C4×C53—28no—
225C42×C53—28no—
226C22⋊Dic53—28no—
227C22⋊Dic53—48no—
228C22⋊Dic53—48no—
229C22⋊Dic53—44no—
230#11719919—48no—
231C23×C53—24no—
232C23×C53—24no—
233C23×C53—22no—
234C23×C53—22no—
235C23×C53—24no—
236C23×C53—22no—
237C23×C53—22no—
238C23×C53—24no—
239C23×C53—24no—
240C23×C53—24no—
241C23×C53—24no—
242C23×C53—24no—
243C23×C53—24no—
244C23×C53—24no—
245C23×C53—24no—
246C23×C53—24no—
247C23×C53—22no—
248C23×C53—22no—
249C23×C53—24no—
250C23×C53—24no—
251C23×C53—22no—
252C23×C53—22no—
253C23×C53—22no—
254C23×C53—22no—
255C23×C53—24no—
256C23×C53—24no—
257C23×C53—24no—
258C23×C53—24no—
259C23×C53—41no—
260C23×C53—41no—
261C23×C53—42no—
262C23×C53—41no—
263C23×C53—41no—
264C23×C53—42no—
265C23×C53—42no—
266C23×C53—42no—
267C23×C53—42no—
268C23×C53—42no—
269C23×C53C2×C4⋊C414yes—
270C23×C53C2×C4⋊C414yes—
271C23×C53C4×D414yes—
272C23×C53C4×D414yes—
273C23×C53#12014yes—
274C23×C53C22⋊Q814yes—
275C23×C53C22⋊Q814yes—
276C23×C53#12314yes—
277C23×C53C23×C411yescharacteristic
278C23×C53C22×D411yescharacteristic
279C23×C53C22×D411yescharacteristic
280C23×C53C22×D411yescharacteristic
281C23×C53C22×Q811yescharacteristic
282C23×C53C2×#4112yes—
283C23×C53C2×#4112yes—
284C23×C53C2×#4111yescharacteristic
285C23×C53C2×#4111yescharacteristic
286C23×C53H(5,𝔽2)12yes—
287C23×C53H(5,𝔽2)12yes—
288D4×C53—232no—
289C2×C4×C53—22no—
290C2×C4×C53—22no—
291C2×C4×C53—22no—
292C2×C4×C53—22no—
293C2×C4×C53—22no—
294C2×C4×C53—22no—
295C2×C4×C53—22no—
296C2×C4×C53—22no—
297C2×C4×C53—24no—
298C2×C4×C53—24no—
299C2×C4×C53—22no—
300C2×C4×C53—22no—
301C2×C4×C53—22no—
302C2×C4×C53—22no—
303C2×C4×C53—22no—
304C2×C4×C53—24no—
305C2×C4×C53—24no—
306C2×C4×C53—416no—
307C2×C4×C53—416no—
308C2×C4×C53—41no—
309C2×C4×C53—41no—
310C2×C4×C53—41no—
311C2×C4×C53—41no—
312C2×C4×C53—42no—
313C2×C4×C53—42no—
314C2×C4×C53—42no—
315C2×C4×C53—42no—
316C2×C4×C53C2×C4⋊C414yes—
317C2×C4×C53#12314yes—
318C2×Dic53—24no—
319C2×Dic53—24no—
320C2×Dic53—24no—
321C2×Dic53—24no—
322C2×Dic53—24no—
323C2×Dic53—24no—
324C2×Dic53—24no—
325C2×Dic53—24no—
326C2×Dic53—24no—
327C2×Dic53—416no—
328C2×Dic53—416no—
329C2×Dic53—42no—
330C2×Dic53—42no—
331C2×Dic53—42no—
332C2×Dic53—42no—
333C2×Dic53—42no—
334C2×Dic53—42no—
335C2×Dic53—42no—
336C2×Dic53—42no—
337C2×Dic53—42no—
338C2×Dic53—42no—
339C2×Dic53—42no—
340C2×Dic53—42no—
341C2×Dic53—42no—
342C2×Dic53—42no—
343C2×Dic53—42no—
344C2×Dic53—42no—
345C2×Dic53—42no—
346C2×Dic53—42no—
347C2×Dic53—42no—
348#14016—531nomaximal, Sylow
349C22×C53—24no—
350C22×C53—24no—
351C22×C53—28no—
352C22×C53—28no—
353C22×C53—24no—
354C22×C53—24no—
355C22×C53—28no—
356C22×C53—28no—
357C22×C53—24no—
358C22×C53—24no—
359C22×C53—28no—
360C22×C53—24no—
361C22×C53—42no—
362C22×C53—42no—
363C22×C53—44no—
364C22×C53—42no—
365C22×C53—42no—
366C22×C53—44no—
367C22×C53—44no—
368C22×C53—42no—
369C22×C53—42no—
370C22×C53#38518yes—
371C22×C53C22×C4⋊C411yescharacteristic
372C22×C53C2×C4×D411yescharacteristic
373C22×C53C2×C4×D411yescharacteristic
374C22×C53C4×#4112yes—
375C22×C53#51812yes—
376C22×C53C2×#12011yescharacteristic
377C22×C53C2×C22⋊Q811yescharacteristic
378C22×C53C2×C22⋊Q811yescharacteristic
379C22×C53C2×#12311yescharacteristic
380C22×C53C2×#12311yescharacteristic
381C22×C53#52511yescharacteristic
382C22×C53#52912yes—
383C22×C53#53411yescharacteristic
384C22×C53#53511yescharacteristic
385C22×C53#53812yes—
386C22×C53#54612yes—
387C22×C53#54612yes—
388C22×C53#54612yes—
389C22×C53#54612yes—
390C22×C53#55312yes—
391C22×C53#55312yes—
392C22×C53#55412yes—
393C22×C53#55412yes—
394C4×C53—24no—
395C4×C53—24no—
396C4×C53—42no—
397C4×C53—42no—
398C4×C53—42no—
399Dic53—44no—
400Dic53—44no—
401Dic53—44no—
402Dic53—82no—
403C22×C4×D4D5311yescharacteristic
404C2×#386—531no—
405C2×#386—531no—
406C2×#385—531no—
407C22×#95—531no—
408#1442—532no—
409#1439—532no—
410#1436—532no—
411C22⋊#95—531no—
412C22⋊#95—532no—
413C22⋊#95—531no—
414C2×C53—28no—
415C2×C53—44no—
416C2×C53C2×#38511yescharacteristic
417C2×C53C4×#12311yescharacteristic
418C2×C53#232111yescharacteristic
419C2×C53#234912yes—
420C2×C53#236412yes—
421C2×C53#240411yescharacteristic
422C2×C53#240511yescharacteristic
423C2×C53#244412yes—
424C2×C53#245012yes—
425C2×C53#248711yescharacteristic
426C2×C53#257911yescharacteristic
427C23×D4C2×D5311yescharacteristic
428C24×C4—531no—
429C24×C4—531no—
430C24×C4C2×D5311yescharacteristic
431C24×C4C2×D5311yescharacteristic
432C2×C4×D4—24no—
433C2×C4×D4—24no—
434C2×C4×D4—24no—
435C22×C4⋊C4—532no—
436C22×C4⋊C4C2×D5311yescharacteristic
437C22×C22⋊C4—531no—
438C22×C22⋊C4—532no—
439C22×C22⋊C4—531no—
440C22×C22⋊C4—532no—
441C22×C22⋊C4C2×D5311yescharacteristic
442C22×C22⋊C4C2×D5311yescharacteristic
443C22×C42C2×D5311yescharacteristic
444#386—538no—
445#386—1064no—
446#385—1064no—
447C2×#95—532no—
448C2×#95—532no—
449C2×#95—532no—
450C2×#95—532no—
451C2×#95—532no—
452C2×#95—532no—
453C2×#95—532no—
454C2×#95—532no—
455C2×#95—532no—
456C2×#95—1064no—
457C53#1401611yescharacteristic, complemented, Sylow
458C25C22×D5311yescharacteristic
459C25C22×D5311yescharacteristic
460C22×D4—22no—
461C22×D4—22no—
462C22×D4—22no—
463C22×D4—22no—
464C22×D4Dic10614yes—
465C22×D4C4×D5314yes—
466C22×D4C22⋊D5314yes—
467C23×C4—22no—
468C23×C4—22no—
469C23×C4—22no—
470C23×C4—24no—
471C23×C4—22no—
472C23×C4—22no—
473C23×C4—24no—
474C23×C4—42no—
475C23×C4—42no—
476C23×C4—532no—
477C23×C4—532no—
478C23×C4—532no—
479C23×C4—534no—
480C23×C4—532no—
481C23×C4—1064no—
482C23×C4—1062no—
483C23×C4—1062no—
484C23×C4—1062no—
485C23×C4—1062no—
486C23×C4—1062no—
487C23×C4—2122no—
488C23×C4—2122no—
489C23×C4—2122no—
490C23×C4C22⋊D5314yes—
491C23×C4C22×D5311yescharacteristic
492C23×C4C22×D5311yescharacteristic
493C23×C4C22×D5311yescharacteristic
494C23×C4C22×D5311yescharacteristic
495C23×C4C22×D5311yescharacteristic
496C4×D4—232no—
497C2×C4⋊C4—22no—
498C2×C4⋊C4—22no—
499C2×C4⋊C4—22no—
500C2×C4⋊C4—1064no—
501C2×C4⋊C4—1064no—
502C2×C4⋊C4—2122no—
503C2×C22⋊C4—22no—
504C2×C22⋊C4—22no—
505C2×C22⋊C4—22no—
506C2×C22⋊C4—22no—
507C2×C22⋊C4—22no—
508C2×C22⋊C4—534no—
509C2×C22⋊C4—538no—
510C2×C22⋊C4—1062no—
511C2×C22⋊C4—1062no—
512C2×C22⋊C4—1064no—
513C2×C22⋊C4—1062no—
514C2×C22⋊C4—1062no—
515C2×C22⋊C4—1064no—
516C2×C22⋊C4—1062no—
517C2×C22⋊C4—2122no—
518C2×C22⋊C4—2122no—
519C2×C22⋊C4—2122no—
520C2×C22⋊C4C22⋊D5314yes—
521C2×C42—22no—
522C2×C42—22no—
523C2×C42—22no—
524#95—538no—
525#95—1064no—
526#95—1064no—
527#95—1064no—
528#95—1064no—
529#95—1064no—
530#95—2122no—
531#95—2122no—
532#95—2122no—
533C24—22no—
534C24—22no—
535C24—22no—
536C24—22no—
537C24—21no—
538C24—21no—
539C24—22no—
540C24—22no—
541C24—21no—
542C24—21no—
543C24—22no—
544C24—22no—
545C24C2×Dic10612yes—
546C24C2×Dic10612yes—
547C24C2×C4×D5312yes—
548C24C2×C4×D5312yes—
549C24#1171994512yes—
550C24#1171994512yes—
551C24C2×C22⋊D5312yes—
552C24C2×C22⋊D5312yes—
553C24C2×C22⋊D5312yes—
554C24C2×C22⋊D5312yes—
555C24C23×D5311yescharacteristic
556C2×D4—28no—
557C2×D4—28no—
558C2×D4—28no—
559C2×D4—28no—
560C2×D4—28no—
561C2×D4—28no—
562C2×D4#11719919116yescomplemented
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—22no—
570C22×C4—28no—
571C22×C4—28no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—28no—
585C22×C4—44no—
586C22×C4—48no—
587C22×C4—48no—
588C22×C4—48no—
589C22×C4—48no—
590C22×C4—44no—
591C22×C4—44no—
592C22×C4—534no—
593C22×C4—534no—
594C22×C4—534no—
595C22×C4—1068no—
596C22×C4—1068no—
597C22×C4—1062no—
598C22×C4—1062no—
599C22×C4—1062no—
600C22×C4—1062no—
601C22×C4—1062no—
602C22×C4—1062no—
603C22×C4—1062no—
604C22×C4—1062no—
605C22×C4—1062no—
606C22×C4—1062no—
607C22×C4—1062no—
608C22×C4—1062no—
609C22×C4—1062no—
610C22×C4—1062no—
611C22×C4—1062no—
612C22×C4—1062no—
613C22×C4—1062no—
614C22×C4—1062no—
615C22×C4—1062no—
616C22×C4—1062no—
617C22×C4—1062no—
618C22×C4—1062no—
619C22×C4—1062no—
620C22×C4—1062no—
621C22×C4—1062no—
622C22×C4—2128no—
623C22×C4—2128no—
624C22×C4—2128no—
625C22×C4—2124no—
626C22×C4—2124no—
627C22×C4—2124no—
628C22×C4—2128no—
629C22×C4—2124no—
630C22×C4C2×Dic10612yes—
631C22×C4C2×C4×D5312yes—
632C22×C4#1171994714yes—
633C22×C4C2×C22⋊D5312yes—
634C22×C4C2×C22⋊D5312yes—
635C22×C4C2×C22⋊D5312yes—
636C22×C4C2×C22⋊D5312yes—
637C22×C4C2×C22⋊D5312yes—
638C4⋊C4—28no—
639C4⋊C4—2128no—
640C22⋊C4—28no—
641C22⋊C4—28no—
642C22⋊C4—1068no—
643C22⋊C4—2128no—
644C22⋊C4—2128no—
645C22⋊C4—2124no—
646C42—28no—
647C23—24no—
648C23—24no—
649C23—24no—
650C23—24no—
651C23—24no—
652C23—24no—
653C23—24no—
654C23—24no—
655C23—22no—
656C23—22no—
657C23—24no—
658C23—22no—
659C23—22no—
660C23—24no—
661C23—24no—
662C23—24no—
663C23—24no—
664C23—24no—
665C23—24no—
666C23—22no—
667C23—22no—
668C23—24no—
669C23—24no—
670C23—22no—
671C23—22no—
672C23—22no—
673C23—22no—
674C23—24no—
675C23—42no—
676C23—42no—
677C23—42no—
678C23—41no—
679C23—41no—
680C23—42no—
681C23—41no—
682C23—41no—
683C23—42no—
684C23—42no—
685C23C2×#1171991914yes—
686C23C2×#1171991914yes—
687C23C4×C22⋊D5314yes—
688C23C4×C22⋊D5314yes—
689C23#1313318614yes—
690C23#1313319614yes—
691C23#1313319614yes—
692C23#1313320014yes—
693C23C22×C4×D5311yescharacteristic
694C23C22×C22⋊D5311yescharacteristic
695C23C22×C22⋊D5311yescharacteristic
696C23C22×C22⋊D5311yescharacteristic
697C23C22×Dic10611yescharacteristic
698C23#41×D5312yes—
699C23C2×#1171994712yes—
700C23C2×#1171994511yescharacteristic
701C23C2×#1171994511yescharacteristic
702C23#1313326212yes—
703C23#1313326312yes—
704D4—232no—
705C2×C4—24no—
706C2×C4—24no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—24no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—24no—
722C2×C4—416no—
723C2×C4—416no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—42no—
732C2×C4—1064no—
733C2×C4—1064no—
734C2×C4—1064no—
735C2×C4—1064no—
736C2×C4—1064no—
737C2×C4—1064no—
738C2×C4—1064no—
739C2×C4—1064no—
740C2×C4—1064no—
741C2×C4—2122no—
742C2×C4—2122no—
743C2×C4—2122no—
744C2×C4—2122no—
745C2×C4—2122no—
746C2×C4—2122no—
747C2×C4—2122no—
748C2×C4—21216no—
749C2×C4—21216no—
750C2×C4—2122no—
751C2×C4—2122no—
752C2×C4—2122no—
753C2×C4—2122no—
754C2×C4—2122no—
755C2×C4—2122no—
756C2×C4—2122no—
757C2×C4—2122no—
758C2×C4—2122no—
759C2×C4—2122no—
760C2×C4—2122no—
761C2×C4—2122no—
762C2×C4C2×#1171991914yes—
763C2×C4#1313319814yes—
764C22—28no—
765C22—28no—
766C22—24no—
767C22—24no—
768C22—28no—
769C22—24no—
770C22—28no—
771C22—24no—
772C22—24no—
773C22—24no—
774C22—28no—
775C22—24no—
776C22—44no—
777C22—44no—
778C22—42no—
779C22—42no—
780C22—42no—
781C22—44no—
782C22—42no—
783C22—42no—
784C22—42no—
785C22#1681049618yes—
786C22C22×#1171991911yescharacteristic
787C22C2×C4×C22⋊D5311yescharacteristic
788C22C2×C4×C22⋊D5311yescharacteristic
789C22C4×#1171994712yes—
790C22#1681109512yes—
791C22C2×#1313318611yescharacteristic
792C22C2×#1313319611yescharacteristic
793C22C2×#1313319611yescharacteristic
794C22C2×#1313319811yescharacteristic
795C22C2×#1313320011yescharacteristic
796C22#1681113011yescharacteristic
797C22#1681115312yes—
798C22#1681118211yescharacteristic
799C22#1681118711yescharacteristic
800C22#1681120612yes—
801C22#1681126112yes—
802C22#1681126112yes—
803C22#1681126712yes—
804C22#1681126712yes—
805C22#1681131912yes—
806C22#1681132212yes—
807C22#1681133012yes—
808C22#1681133212yes—
809C4—24no—
810C4—24no—
811C4—42no—
812C4—42no—
813C4—42no—
814C4—4242no—
815C4—2124no—
816C4—2124no—
817C4—2124no—
818C2—28no—
819C2—44no—
820C2C2×#1681049611yescharacteristic
821C2C4×#1313319811yescharacteristic
822C2#2027736911yescharacteristic
823C2#2027762012yes—
824C2#2027776012yes—
825C2#2027803011yescharacteristic
826C2#2027803811yescharacteristic
827C2#2027845912yes—
828C2#2027853312yes—
829C2#2027903211yescharacteristic
830C2#2028005811yescharacteristic
subgroupG/H
center, FrattiniC24C23×D53
commutatorC23×C53C23×C4
FittingC22×C4×D4×C53C2
socle, cosocleC24×C53C24
prime radicalC23×D4×C53C22
hypercenterC22×C4×D4D53
hypocenterC53#14016
LCSG ▷ C23×C53 ▷ C53
UCSC1 ◁ C24 ◁ C22×C4×D4

Complements

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

NH ≅ G/Ntype
3. C2×#16810495C2semidirect
4. C22×#13133124C2semidirect
5. #20272974C2semidirect
6. #20272958C2semidirect
7. #20272948C2semidirect
8. #20272938C2semidirect
9. #20272938C2semidirect
10. #20272937C2semidirect
20. #16810503C4semidirect
51. C23×Dic53C2×C4semidirect
69. C2×C22⋊Dic53C2×C4semidirect
70. C2×C22⋊Dic53C2×C4semidirect
79. #13133124C2×C4semidirect
146. C2×D4×C53C4⋊C4semidirect
457. C53#14016semidirect
562. C2×D4#11719919semidirect

Maximal subgroups

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

subgroupindex
C2×#168105032
C2×#168104952
C22×#131331242
#202729742
#202729582
#202729482
#202729382
#202729372
C22×C4×D4×C532
#1401653