Finite Group Databasebeta

← #27307176

Subgroups — #27307176

Order 13568.

1746 conjugacy classes of subgroups.

The subgroup lattice has 814 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16810519C211yesmaximal, characteristic, complemented
2C2×#16810480C211yesmaximal, characteristic
3C2×#16810480C211yesmaximal, characteristic
4C2×C4×#11719921C211yesmaximal, characteristic
5#20272975C212yesmaximal, complemented
6#20272959C212yesmaximal
7#20272953C212yesmaximal
8#20272948C212yesmaximal, complemented
9#20272945C211yesmaximal, characteristic, complemented
10#20272944C211yesmaximal, characteristic, complemented
11C2×C4×C4⋊C4×C53C211yesmaximal, characteristic, complemented
12C23×C4×D53C2211yescharacteristic
13C22×C4⋊Dic53C2211yescharacteristic
14C22×C4⋊Dic53C2211yescharacteristic
15C22×#11719919C2212yes—
16C22×#11719921C2211yescharacteristic
17C22×#11719921C2212yes—
18C22×#11719921C2211yescharacteristic
19C22×#11719921C2212yes—
20C22×C4×Dic53C2211yescharacteristic
21#16810519—24no—
22#16810480—24no—
23#16810480C418yescomplemented
24C4×#11719921—24no—
25C2×#13133124C2212yes—
26C2×#13133124C2211yescharacteristic
27C2×#13133124C2212yes—
28C2×#13133124C2211yescharacteristic
29C2×#13133124C2212yes—
30C2×#13133124C2212yes—
31C2×#13133124C2212yes—
32C2×#13133124C2212yes—
33C2×#13133124C2212yes—
34C22×C4⋊C4×C53C2211yescharacteristic
35C22×C4⋊C4×C53C2211yescharacteristic
36C22×C42×C53C2211yescharacteristic
37C22×C42×C53C2212yes—
38C4×C4⋊C4×C53—24no—
39C2×#95×C53C2212yes—
40C24×D53C2311yescharacteristic
41C23×Dic53C2312yes—
42C23×Dic53C2312yes—
43C23×Dic53C2311yescharacteristic
44C23×Dic53C2311yescharacteristic
45C23×Dic53C2311yescharacteristic
46C22×C4×D53—22no—
47C22×C4×D53—22no—
48C22×C4×D53—22no—
49C22×C4×D53—22no—
50C22×C4×D53—22no—
51C22×C4×D53—22no—
52C22×C4×D53C2×C414yes—
53C2×C4⋊Dic53—22no—
54C2×C4⋊Dic53—22no—
55C2×C4⋊Dic53—22no—
56C2×C4⋊Dic53—22no—
57C2×C4⋊Dic53—22no—
58C2×C4⋊Dic53C2×C414yes—
59C2×#11719919—24no—
60C2×#11719919—24no—
61C2×#11719919—42no—
62C2×#11719921—22no—
63C2×#11719921—24no—
64C2×#11719921—22no—
65C2×#11719921—22no—
66C2×#11719921—24no—
67C2×#11719921—22no—
68C2×#11719921—22no—
69C2×#11719921—42no—
70C2×#11719921—42no—
71C2×#11719921—42no—
72C2×#11719921C2×C418yes—
73C2×#11719921Q814yes—
74C2×C4×Dic53—22no—
75C2×C4×Dic53—22no—
76C2×C4×Dic53—22no—
77#13133124—24no—
78#13133124—22no—
79#13133124—22no—
80#13133124—24no—
81#13133124—24no—
82#13133124—42no—
83#13133124—42no—
84#13133124—42no—
85#13133124C2×C418yes—
86C23×C4×C53C2312yes—
87C23×C4×C53C2312yes—
88C23×C4×C53C2311yescharacteristic
89C23×C4×C53C2311yescharacteristic
90C23×C4×C53C2311yescharacteristic
91C2×C4⋊C4×C53—22no—
92C2×C4⋊C4×C53—22no—
93C2×C4⋊C4×C53—22no—
94C2×C4⋊C4×C53—22no—
95C2×C4⋊C4×C53C2×C414yes—
96C2×C4⋊C4×C53D414yes—
97C2×C42×C53—24no—
98C2×C42×C53—22no—
99C2×C42×C53—22no—
100C2×C42×C53—42no—
101C2×C42×C53—42no—
102C2×C42×C53D414yes—
103#95×C53—24no—
104C24×C53C2411yescharacteristic
105C23×D53—21no—
106C23×D53—21no—
107C23×D53—21no—
108C23×D53—21no—
109C23×D53—21no—
110C23×D53—21no—
111C23×D53—21no—
112C23×D53—21no—
113C23×D53—21no—
114C23×D53—21no—
115C23×D53—21no—
116C23×D53—21no—
117C23×D53C22×C412yes—
118C23×D53C2×Q812yes—
119C23×D53#4112yes—
120C22×C4×C53—21no—
121C22×C4×C53—21no—
122C22×C4×C53—21no—
123C22×C4×C53—21no—
124C22×C4×C53—22no—
125C22×C4×C53—22no—
126C22×C4×C53—21no—
127C22×C4×C53—21no—
128C22×C4×C53—22no—
129C22×C4×C53—22no—
130C22×C4×C53—21no—
131C22×C4×C53—21no—
132C22×C4×C53—22no—
133C22×C4×C53—22no—
134C22×C4×C53—22no—
135C22×C4×C53—22no—
136C22×C4×C53—22no—
137C22×C4×C53—22no—
138C22×C4×C53—21no—
139C22×C4×C53—22no—
140C22×C4×C53—22no—
141C22×C4×C53—21no—
142C22×C4×C53C22×C414yes—
143C22×C4×C53C22×C412yes—
144C22×C4×C53C2×D414yes—
145C22×C4×C53C2×D412yes—
146C22×C4×C53C2×D412yes—
147C22×C4×C53C2×D412yes—
148C22×C4×C53C2×D412yes—
149C22×C4×C53C2×Q812yes—
150C22×C4×C53#4112yes—
151C22×C4×C53#4112yes—
152C22×C4×C53#4112yes—
153C22×C4×C53#4112yes—
154C22×C4×C53#4112yes—
155C22×Dic53—21no—
156C22×Dic53—21no—
157C22×Dic53—21no—
158C22×Dic53—21no—
159C22×Dic53—21no—
160C22×Dic53—22no—
161C22×Dic53—21no—
162C22×Dic53—22no—
163C22×Dic53—21no—
164C22×Dic53—21no—
165C22×Dic53—21no—
166C22×Dic53—21no—
167C22×Dic53—22no—
168C22×Dic53—22no—
169C22×Dic53—21no—
170C22×Dic53—21no—
171C22×Dic53—21no—
172C22×Dic53—21no—
173C22×Dic53—21no—
174C22×Dic53—21no—
175C22×Dic53—22no—
176C22×Dic53—22no—
177C22×Dic53—21no—
178C22×Dic53—21no—
179C22×Dic53—22no—
180C22×Dic53—22no—
181C22×Dic53—22no—
182C22×Dic53—22no—
183C22×Dic53—22no—
184C22×Dic53—22no—
185C22×Dic53—22no—
186C22×Dic53C22×C412yes—
187C22×Dic53C22×C414yes—
188C22×Dic53C2×Q812yes—
189C22×Dic53#4112yes—
190C2×C4×D53—28no—
191C2×C4×D53—28no—
192C2×C4×D53—28no—
193C2×C4×D53—44no—
194C2×C4×D53—44no—
195C2×C4×D53—44no—
196C2×C4×D53—44no—
197C4⋊C4×C53—28no—
198C4⋊C4×C53—28no—
199C42×C53—28no—
200C42×C53—48no—
201#11719921—28no—
202#11719921—28no—
203#11719921—48no—
204#11719921—48no—
205C4⋊Dic53—28no—
206C4⋊Dic53—44no—
207#11719919—48no—
208C4×Dic53—44no—
209C23×C53C23×C411yescharacteristic
210C23×C53C22×D411yescharacteristic
211C23×C53C22×D411yescharacteristic
212C23×C53C22×Q811yescharacteristic
213C23×C53C2×#4111yescharacteristic
214C23×C53C2×#4111yescharacteristic
215C23×C53C2×#4111yescharacteristic
216C23×C53C2×#4111yescharacteristic
217C23×C53C2×#4111yescharacteristic
218C23×C53C2×#4111yescharacteristic
219C23×C53C2×#4111yescharacteristic
220C23×C53H(5,𝔽2)11yescharacteristic
221C23×C53H(5,𝔽2)11yescharacteristic
222C23×C53H(5,𝔽2)11yescharacteristic
223C23×C532−1+411yescharacteristic
224C22×D53—22no—
225C22×D53—22no—
226C22×D53—22no—
227C22×D53—22no—
228C22×D53—22no—
229C22×D53—22no—
230C22×D53—22no—
231C22×D53—22no—
232C22×D53—22no—
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—22no—
242C22×D53—41no—
243C22×D53—41no—
244C22×D53—41no—
245C22×D53—41no—
246C22×D53—41no—
247C22×D53—41no—
248C22×D53—41no—
249C22×D53—41no—
250C22×D53—41no—
251C22×D53—41no—
252C22×D53—41no—
253C22×D53—41no—
254C22×D53—41no—
255C22×D53—41no—
256C22×D53—41no—
257C22×D53—41no—
258C22×D53C4×Q814yes—
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—24no—
268C2×C4×C53—24no—
269C2×C4×C53—22no—
270C2×C4×C53—22no—
271C2×C4×C53—22no—
272C2×C4×C53—24no—
273C2×C4×C53—24no—
274C2×C4×C53—42no—
275C2×C4×C53—42no—
276C2×C4×C53—42no—
277C2×C4×C53—42no—
278C2×C4×C53—42no—
279C2×C4×C53—42no—
280C2×C4×C53—41no—
281C2×C4×C53—41no—
282C2×C4×C53—42no—
283C2×C4×C53—42no—
284C2×C4×C53—41no—
285C2×C4×C53—41no—
286C2×C4×C53#11714yes—
287C2×C4×C53C4×D414yes—
288C2×C4×C53C4×D414yes—
289C2×C4×C53#12114yes—
290C2×C4×C53C22⋊Q814yes—
291C2×C4×C53#12314yes—
292C2×C4×C53#12414yes—
293C2×C4×C53#12614yes—
294C2×Dic53—22no—
295C2×Dic53—22no—
296C2×Dic53—22no—
297C2×Dic53—24no—
298C2×Dic53—24no—
299C2×Dic53—24no—
300C2×Dic53—22no—
301C2×Dic53—22no—
302C2×Dic53—22no—
303C2×Dic53—22no—
304C2×Dic53—22no—
305C2×Dic53—22no—
306C2×Dic53—41no—
307C2×Dic53—41no—
308C2×Dic53—41no—
309C2×Dic53—41no—
310C2×Dic53—41no—
311C2×Dic53—41no—
312C2×Dic53—41no—
313C2×Dic53—41no—
314C2×Dic53—41no—
315C2×Dic53—42no—
316C2×Dic53—42no—
317C2×Dic53—41no—
318C2×Dic53—42no—
319C2×Dic53—41no—
320C2×Dic53—42no—
321C2×Dic53—41no—
322C2×Dic53—42no—
323C2×Dic53—42no—
324C2×Dic53—42no—
325C2×Dic53—42no—
326C2×Dic53—42no—
327C2×Dic53—42no—
328C2×Dic53—42no—
329C4×D53—416no—
330#13993—531nomaximal, Sylow
331C22×C53C2×#11711yescharacteristic
332C22×C53C2×C4×D411yescharacteristic
333C22×C53C2×C4×D411yescharacteristic
334C22×C53C2×C4×Q811yescharacteristic
335C22×C53C4×#4111yescharacteristic
336C22×C53#51811yescharacteristic
337C22×C53#52011yescharacteristic
338C22×C53C2×#12111yescharacteristic
339C22×C53C2×C22⋊Q811yescharacteristic
340C22×C53C2×#12311yescharacteristic
341C22×C53#52511yescharacteristic
342C22×C53C2×#12411yescharacteristic
343C22×C53C2×#12611yescharacteristic
344C22×C53#52911yescharacteristic
345C22×C53#53311yescharacteristic
346C22×C53#53511yescharacteristic
347C22×C53#53711yescharacteristic
348C22×C53#54011yescharacteristic
349C22×C53#54211yescharacteristic
350C22×C53#54611yescharacteristic
351C22×C53#54611yescharacteristic
352C22×C53D4×Q811yescharacteristic
353C22×C53#55011yescharacteristic
354C22×C53#55211yescharacteristic
355C22×C53#55311yescharacteristic
356C22×C53#55311yescharacteristic
357C22×C53#55311yescharacteristic
358C22×C53#55311yescharacteristic
359C22×C53#55311yescharacteristic
360C22×C53#55411yescharacteristic
361C22×C53#55411yescharacteristic
362C22×C53#55411yescharacteristic
363C22×C53#55511yescharacteristic
364C22×C53#55611yescharacteristic
365C22×C53#55611yescharacteristic
366C2×D53—24no—
367C2×D53—24no—
368C2×D53—24no—
369C2×D53—42no—
370C2×D53—42no—
371C2×D53—42no—
372C2×D53—42no—
373C2×D53—42no—
374C2×D53—42no—
375C2×D53—42no—
376C2×D53—42no—
377C2×D53—42no—
378C2×D53—42no—
379C2×D53—42no—
380C2×D53—42no—
381C4×C53—24no—
382C4×C53—44no—
383C4×C53—42no—
384C4×C53—44no—
385C4×C53#38818yes—
386Dic53—44no—
387Dic53—42no—
388Dic53—42no—
389Dic53—42no—
390Dic53—82no—
391C2×#389—531no—
392C2×#380—531no—
393C2×#380—531no—
394C2×C4×C4⋊C4D5311yescharacteristic, complemented
395C2×C4×C22⋊C4—531no—
396#1443—532no—
397#1439—532no—
398#1437—532no—
399#1436—532no—
400C4⋊#95—531no—
401C4⋊#95—531no—
402C2×C53C2×#38811yescharacteristic
403C2×C53C4×C22⋊Q811yescharacteristic
404C2×C53#232411yescharacteristic
405C2×C53#234511yescharacteristic
406C2×C53#234711yescharacteristic
407C2×C53#236011yescharacteristic
408C2×C53#236311yescharacteristic
409C2×C53#248511yescharacteristic
410C2×C53#248711yescharacteristic
411C2×C53#249011yescharacteristic
412C2×C53#249211yescharacteristic
413C2×C53#249411yescharacteristic
414C2×C53#249711yescharacteristic
415C2×C53#253511yescharacteristic
416C2×C53#253811yescharacteristic
417D53—44no—
418C24×C4—531no—
419C22×C4⋊C4—531no—
420C22×C4⋊C4—531no—
421C22×C4⋊C4—532no—
422C22×C4⋊C4C2×D5311yescharacteristic
423C22×C4⋊C4C2×D5311yescharacteristic
424C22×C22⋊C4—531no—
425C22×C22⋊C4—532no—
426C22×C22⋊C4—531no—
427C22×C22⋊C4—532no—
428C22×C42—531no—
429C22×C42C2×D5311yescharacteristic
430C22×C42C2×D5312yes—
431#389—1064no—
432#380—538no—
433#380—1064no—
434C4×C4⋊C4—24no—
435C4×C22⋊C4—1064no—
436C2×#95—532no—
437C2×#95—532no—
438C2×#95—531no—
439C2×#95—532no—
440C2×#95—532no—
441C2×#95—531no—
442C2×#95—532no—
443C2×#95—532no—
444C2×#95—532no—
445C2×#95C2×D5312yes—
446C53#1399311yescharacteristic, complemented, Sylow
447C25—531no—
448C23×C4—532no—
449C23×C4—531no—
450C23×C4—531no—
451C23×C4—531no—
452C23×C4—534no—
453C23×C4—532no—
454C23×C4—1062no—
455C23×C4—1062no—
456C23×C4—1062no—
457C23×C4—1062no—
458C23×C4—1062no—
459C23×C4—1062no—
460C23×C4C22×D5312yes—
461C23×C4C22×D5312yes—
462C23×C4C22×D5311yescharacteristic
463C23×C4C22×D5311yescharacteristic
464C23×C4C22×D5311yescharacteristic
465C2×C4⋊C4—22no—
466C2×C4⋊C4—22no—
467C2×C4⋊C4—22no—
468C2×C4⋊C4—22no—
469C2×C4⋊C4—534no—
470C2×C4⋊C4—1062no—
471C2×C4⋊C4—1062no—
472C2×C4⋊C4—1064no—
473C2×C4⋊C4—1064no—
474C2×C4⋊C4—1062no—
475C2×C4⋊C4—1062no—
476C2×C4⋊C4—1062no—
477C2×C4⋊C4—2122no—
478C2×C4⋊C4C4×D5314yes—
479C2×C4⋊C4D21214yes—
480C2×C22⋊C4—534no—
481C2×C22⋊C4—538no—
482C2×C22⋊C4—1062no—
483C2×C22⋊C4—1062no—
484C2×C22⋊C4—1062no—
485C2×C22⋊C4—1062no—
486C2×C22⋊C4—1062no—
487C2×C22⋊C4—1064no—
488C2×C22⋊C4—1064no—
489C2×C22⋊C4—2122no—
490C2×C22⋊C4—2122no—
491C2×C22⋊C4—2122no—
492C2×C42—22no—
493C2×C42—22no—
494C2×C42—24no—
495C2×C42—42no—
496C2×C42—42no—
497C2×C42—1062no—
498C2×C42—1062no—
499C2×C42—1062no—
500C2×C42C22⋊D5314yes—
501#95—24no—
502#95—538no—
503#95—1064no—
504#95—1064no—
505#95—1064no—
506#95—1062no—
507#95—1062no—
508#95—2122no—
509#95—2122no—
510#95—2122no—
511C24—532no—
512C24—532no—
513C24—532no—
514C24—1061no—
515C24—1061no—
516C24—1061no—
517C24—1061no—
518C24—1061no—
519C24—1061no—
520C24—1061no—
521C24—1061no—
522C24—1061no—
523C24—1061no—
524C24—1061no—
525C24—1061no—
526C24C23×D5311yescharacteristic
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—22no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—21no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—21no—
549C22×C4—532no—
550C22×C4—534no—
551C22×C4—532no—
552C22×C4—532no—
553C22×C4—1061no—
554C22×C4—1061no—
555C22×C4—1061no—
556C22×C4—1061no—
557C22×C4—1061no—
558C22×C4—1062no—
559C22×C4—1061no—
560C22×C4—1061no—
561C22×C4—1062no—
562C22×C4—1061no—
563C22×C4—1061no—
564C22×C4—1062no—
565C22×C4—1061no—
566C22×C4—1061no—
567C22×C4—1061no—
568C22×C4—1061no—
569C22×C4—1062no—
570C22×C4—1061no—
571C22×C4—1061no—
572C22×C4—1062no—
573C22×C4—1061no—
574C22×C4—1061no—
575C22×C4—1062no—
576C22×C4—1061no—
577C22×C4—1068no—
578C22×C4—1068no—
579C22×C4—1068no—
580C22×C4—1062no—
581C22×C4—1062no—
582C22×C4—1062no—
583C22×C4—1062no—
584C22×C4—1062no—
585C22×C4—1062no—
586C22×C4—1062no—
587C22×C4—2124no—
588C22×C4—2124no—
589C22×C4—2124no—
590C22×C4—2124no—
591C22×C4C2×C4×D5314yes—
592C22×C4C2×C4×D5312yes—
593C22×C4C2×D21214yes—
594C22×C4C2×D21212yes—
595C22×C4#1171994512yes—
596C22×C4#1171994512yes—
597C22×C4#1171994512yes—
598C22×C4#1171994512yes—
599C22×C4Q8×D5312yes—
600C22×C4#1171994912yes—
601C22×C4C2×C22⋊D5312yes—
602C22×C4C2×C22⋊D5312yes—
603C22×C4C2×C22⋊D5312yes—
604C4⋊C4—28no—
605C4⋊C4—28no—
606C4⋊C4—1068no—
607C4⋊C4—2128no—
608C4⋊C4—2124no—
609C22⋊C4—1068no—
610C22⋊C4—1068no—
611C22⋊C4—2128no—
612C22⋊C4—2128no—
613C42—28no—
614C42—48no—
615C42—2124no—
616C23—534no—
617C23—1062no—
618C23—1062no—
619C23—1062no—
620C23—1062no—
621C23—1062no—
622C23—1062no—
623C23—1062no—
624C23—1062no—
625C23—1062no—
626C23—1062no—
627C23—1062no—
628C23—1062no—
629C23—1062no—
630C23—1062no—
631C23—1062no—
632C23—1062no—
633C23—1062no—
634C23—1062no—
635C23—2121no—
636C23—2121no—
637C23—2121no—
638C23—2121no—
639C23—2121no—
640C23—2121no—
641C23—2121no—
642C23—2121no—
643C23—2121no—
644C23—2121no—
645C23—2121no—
646C23—2121no—
647C23—2121no—
648C23—2121no—
649C23—2121no—
650C23—2121no—
651C23C22×C4×D5311yescharacteristic
652C23C22×C22⋊D5311yescharacteristic
653C23C22×D21211yescharacteristic
654C23C2×Q8×D5311yescharacteristic
655C23#41×D5311yescharacteristic
656C23#41×D5311yescharacteristic
657C23C2×#1171994511yescharacteristic
658C23C2×#1171994511yescharacteristic
659C23C2×#1171994511yescharacteristic
660C23C2×#1171994511yescharacteristic
661C23C2×#1171994911yescharacteristic
662C23#1313326211yescharacteristic
663C23#1313326211yescharacteristic
664C23#1313326311yescharacteristic
665C23#1313326411yescharacteristic
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—24no—
673C2×C4—24no—
674C2×C4—24no—
675C2×C4—24no—
676C2×C4—24no—
677C2×C4—24no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—1062no—
694C2×C4—1062no—
695C2×C4—1062no—
696C2×C4—1062no—
697C2×C4—1062no—
698C2×C4—1062no—
699C2×C4—1064no—
700C2×C4—1062no—
701C2×C4—1064no—
702C2×C4—1064no—
703C2×C4—1062no—
704C2×C4—1062no—
705C2×C4—2122no—
706C2×C4—2122no—
707C2×C4—2122no—
708C2×C4—2122no—
709C2×C4—2122no—
710C2×C4—2122no—
711C2×C4—2122no—
712C2×C4—2122no—
713C2×C4—2121no—
714C2×C4—2121no—
715C2×C4—2122no—
716C2×C4—2122no—
717C2×C4—2121no—
718C2×C4—2122no—
719C2×C4—2121no—
720C2×C4—2121no—
721C2×C4—2121no—
722C2×C4—2121no—
723C2×C4—2121no—
724C2×C4—2121no—
725C2×C4—2121no—
726C2×C4—2121no—
727C2×C4—2121no—
728C2×C4—21216no—
729C2×C4#1313317414yes—
730C2×C4C4×C22⋊D5314yes—
731C2×C4C4×D21214yes—
732C2×C4#1313319114yes—
733C2×C4#1313319314yes—
734C2×C4#1313320014yes—
735C2×C4#1313320514yes—
736C2×C4#1313321114yes—
737C22—1064no—
738C22—1064no—
739C22—1064no—
740C22—2122no—
741C22—2122no—
742C22—2122no—
743C22—2122no—
744C22—2122no—
745C22—2122no—
746C22—2122no—
747C22—2122no—
748C22—2122no—
749C22—2122no—
750C22—2122no—
751C22—2122no—
752C22C2×#1313317411yescharacteristic
753C22C2×C4×C22⋊D5311yescharacteristic
754C22C2×C4×D21211yescharacteristic
755C22C4×Q8×D5311yescharacteristic
756C22C4×#1171994911yescharacteristic
757C22#1681109511yescharacteristic
758C22#1681110211yescharacteristic
759C22C2×#1313319111yescharacteristic
760C22C2×#1313319311yescharacteristic
761C22C2×#1313320011yescharacteristic
762C22#1681113011yescharacteristic
763C22C2×#1313320511yescharacteristic
764C22C2×#1313321111yescharacteristic
765C22#1681116011yescharacteristic
766C22#1681117711yescharacteristic
767C22#1681119011yescharacteristic
768C22#1681120111yescharacteristic
769C22#1681122411yescharacteristic
770C22#1681123811yescharacteristic
771C22#1681126811yescharacteristic
772C22#1681126811yescharacteristic
773C22Q8×D21211yescharacteristic
774C22#1681129511yescharacteristic
775C22#1681131211yescharacteristic
776C22#1681131711yescharacteristic
777C22#1681132111yescharacteristic
778C22#1681132111yescharacteristic
779C22#1681132311yescharacteristic
780C22#1681132311yescharacteristic
781C22#1681132811yescharacteristic
782C22#1681132811yescharacteristic
783C22#1681133311yescharacteristic
784C22#1681133611yescharacteristic
785C22#1681134111yescharacteristic
786C22#1681134611yescharacteristic
787C4—24no—
788C4—44no—
789C4—44no—
790C4—42no—
791C4—4242no—
792C4—2122no—
793C4—2122no—
794C4—2122no—
795C4—2124no—
796C4#1681051418yes—
797C2—2124no—
798C2C2×#1681051411yescharacteristic
799C2C4×#1313319311yescharacteristic
800C2#2027740211yescharacteristic
801C2#2027758811yescharacteristic
802C2#2027760411yescharacteristic
803C2#2027772211yescharacteristic
804C2#2027775511yescharacteristic
805C2#2027900611yescharacteristic
806C2#2027902611yescharacteristic
807C2#2027906111yescharacteristic
808C2#2027908311yescharacteristic
809C2#2027910911yescharacteristic
810C2#2027914211yescharacteristic
811C2#2027961211yescharacteristic
812C2#2027963311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D53
commutatorC23×C53C23×C4
FittingC2×C4×C4⋊C4×C53C2
socle, cosocleC24×C53C24
prime radicalC24×D53C23
hypercenterC2×C4×C4⋊C4D53
hypocenterC53#13993
LCSG ▷ C23×C53 ▷ C53
UCSC1 ◁ C24 ◁ C2×C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#16810519C2semidirect
5. #20272975C2semidirect
8. #20272948C2semidirect
9. #20272945C2semidirect
10. #20272944C2semidirect
11. C2×C4×C4⋊C4×C53C2semidirect
23. #16810480C4semidirect
394. C2×C4×C4⋊C4D53semidirect
446. C53#13993semidirect

Maximal subgroups

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

subgroupindex
C2×#168105192
C2×#168104802
C2×C4×#117199212
#202729752
#202729592
#202729532
#202729482
#202729452
#202729442
C2×C4×C4⋊C4×C532
#1399353