Finite Group Databasebeta

← #27320702

Subgroups — #27320702

Order 13568.

1814 conjugacy classes of subgroups.

The subgroup lattice has 830 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16810546C212yesmaximal
2C2×#16810522C211yesmaximal, characteristic, complemented
3C2×#16810519C211yesmaximal, characteristic, complemented
4C2×#16810492C211yesmaximal, characteristic, complemented
5C2×#16810483C211yesmaximal, characteristic
6C2×C4×C22⋊Dic53C211yesmaximal, characteristic
7#20272967C212yesmaximal, complemented
8#20272966C212yesmaximal, complemented
9#20272958C212yesmaximal
10#20272944C211yesmaximal, characteristic, complemented
11C2×C53×#380C211yesmaximal, characteristic
12C22×C4⋊Dic53C2211yescharacteristic
13C22×C4⋊Dic53C2212yes—
14C22×C4⋊Dic53C2211yescharacteristic
15C22×#11719919C2212yes—
16C22×#11719919C2212yes—
17C22×#11719919C2212yes—
18C22×C22⋊Dic53C2212yes—
19C22×C22⋊Dic53C2211yescharacteristic
20C22×C22⋊Dic53C2211yescharacteristic
21C22×C4×Dic53C2211yescharacteristic
22C22×C4×Dic53C2211yescharacteristic
23#16810546—28no—
24#16810522—24no—
25#16810519—24no—
26#16810492—24no—
27#16810483—24no—
28C4×C22⋊Dic53—24no—
29C2×#13133124C2212yes—
30C2×#13133124C2211yescharacteristic
31C2×#13133124C2211yescharacteristic
32C2×#13133124C2212yes—
33C2×#13133124C2212yes—
34C2×#13133124C2212yes—
35C2×#13133124C2212yes—
36C24×C4×C53C2211yescharacteristic
37C22×C4⋊C4×C53C2211yescharacteristic
38C22×C4⋊C4×C53C2211yescharacteristic
39C22×C22⋊C4×C53C2212yes—
40C53×#380—24no—
41C2×#95×C53C2212yes—
42C23×Dic53C2312yes—
43C23×Dic53C2311yescharacteristic
44C23×Dic53C2312yes—
45C23×Dic53C2311yescharacteristic
46C23×Dic53C2311yescharacteristic
47C23×Dic53C2311yescharacteristic
48C2×C4⋊Dic53—22no—
49C2×C4⋊Dic53—22no—
50C2×C4⋊Dic53—22no—
51C2×C4⋊Dic53—22no—
52C2×C4⋊Dic53—22no—
53C2×C4⋊Dic53—24no—
54C2×C4⋊Dic53—24no—
55C2×C4⋊Dic53—24no—
56C2×C4⋊Dic53D414yes—
57C2×#11719919—24no—
58C2×#11719919—24no—
59C2×#11719919—24no—
60C2×#11719919—24no—
61C2×#11719919—24no—
62C2×#11719919—24no—
63C2×#11719919—42no—
64C2×#11719919—42no—
65C2×#11719919—42no—
66C2×C22⋊Dic53—24no—
67C2×C22⋊Dic53—22no—
68C2×C22⋊Dic53—22no—
69C2×C22⋊Dic53—24no—
70C2×C22⋊Dic53—22no—
71C2×C22⋊Dic53—22no—
72C2×C22⋊Dic53—42no—
73C2×C22⋊Dic53D414yes—
74C2×C22⋊Dic53Q814yes—
75C2×C4×Dic53—22no—
76C2×C4×Dic53—22no—
77C2×C4×Dic53—22no—
78C2×C4×Dic53—22no—
79C2×C4×Dic53—22no—
80C2×C4×Dic53D414yes—
81#13133124—24no—
82#13133124—24no—
83#13133124—24no—
84#13133124—22no—
85#13133124—22no—
86#13133124—24no—
87#13133124—42no—
88C25×C53C2311yescharacteristic
89C23×C4×C53—22no—
90C23×C4×C53—22no—
91C23×C4×C53—22no—
92C23×C4×C53—22no—
93C23×C4×C53—22no—
94C23×C4×C53—22no—
95C23×C4×C53Q814yes—
96C23×C4×C53C2312yes—
97C23×C4×C53C2312yes—
98C23×C4×C53C2311yescharacteristic
99C23×C4×C53C2311yescharacteristic
100C2×C4⋊C4×C53—22no—
101C2×C4⋊C4×C53—22no—
102C2×C4⋊C4×C53—22no—
103C2×C4⋊C4×C53—22no—
104C2×C4⋊C4×C53—22no—
105C2×C4⋊C4×C53D414yes—
106C2×C22⋊C4×C53—24no—
107C2×C22⋊C4×C53—24no—
108C2×C22⋊C4×C53—42no—
109#95×C53—24no—
110C24×C53—21no—
111C24×C53—21no—
112C24×C53—21no—
113C24×C53—21no—
114C24×C53—21no—
115C24×C53—21no—
116C24×C53—21no—
117C24×C53—21no—
118C24×C53—21no—
119C24×C53—21no—
120C24×C53—21no—
121C24×C53—21no—
122C24×C53C2×D412yes—
123C24×C53C2×Q812yes—
124C24×C53C2×Q812yes—
125C24×C53C2411yescharacteristic
126C22×C4×C53—21no—
127C22×C4×C53—22no—
128C22×C4×C53—22no—
129C22×C4×C53—21no—
130C22×C4×C53—21no—
131C22×C4×C53—22no—
132C22×C4×C53—21no—
133C22×C4×C53—21no—
134C22×C4×C53—21no—
135C22×C4×C53—22no—
136C22×C4×C53—22no—
137C22×C4×C53—22no—
138C22×C4×C53—28no—
139C22×C4×C53—28no—
140C22×C4×C53—28no—
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—44no—
149C22×C4×C53—44no—
150C22×C4×C53—44no—
151C22×C4×C53—44no—
152C22×C4×C53C2×D414yes—
153C22×C4×C53C2×D412yes—
154C22×C4×C53C2×D412yes—
155C22×C4×C53C2×D412yes—
156C22×C4×C53C2×Q812yes—
157C22×C4×C53C2×Q812yes—
158C22×C4×C53#4112yes—
159C22×C4×C53#4112yes—
160C22×C4×C53#4112yes—
161C22×Dic53—21no—
162C22×Dic53—21no—
163C22×Dic53—21no—
164C22×Dic53—21no—
165C22×Dic53—21no—
166C22×Dic53—21no—
167C22×Dic53—21no—
168C22×Dic53—21no—
169C22×Dic53—21no—
170C22×Dic53—21no—
171C22×Dic53—21no—
172C22×Dic53—22no—
173C22×Dic53—21no—
174C22×Dic53—22no—
175C22×Dic53—21no—
176C22×Dic53—21no—
177C22×Dic53—21no—
178C22×Dic53—21no—
179C22×Dic53—22no—
180C22×Dic53—22no—
181C22×Dic53—21no—
182C22×Dic53—22no—
183C22×Dic53—21no—
184C22×Dic53—22no—
185C22×Dic53—21no—
186C22×Dic53—21no—
187C22×Dic53—22no—
188C22×Dic53—22no—
189C22×Dic53—22no—
190C22×Dic53—22no—
191C22×Dic53—22no—
192C22×Dic53—22no—
193C22×Dic53—22no—
194C22×Dic53C2×D412yes—
195C22×Dic53C2×D414yes—
196C22×Dic53C2×D412yes—
197C22×Dic53C2×D412yes—
198C22×Dic53C2×D412yes—
199C22×Dic53C2×Q812yes—
200C22×Dic53C2×Q812yes—
201C22×Dic53#4112yes—
202C22×Dic53#4112yes—
203C4⋊C4×C53—28no—
204C4⋊C4×C53—44no—
205C22⋊C4×C53—48no—
206C22⋊Dic53—28no—
207C22⋊Dic53—28no—
208C22⋊Dic53—48no—
209C4⋊Dic53—28no—
210C4⋊Dic53—44no—
211C4⋊Dic53—48no—
212#11719919—48no—
213#11719919—48no—
214#11719919—48no—
215C4×Dic53—28no—
216C4×Dic53—44no—
217C23×C53—22no—
218C23×C53—22no—
219C23×C53—22no—
220C23×C53—22no—
221C23×C53—22no—
222C23×C53—22no—
223C23×C53—22no—
224C23×C53—22no—
225C23×C53—22no—
226C23×C53—22no—
227C23×C53—22no—
228C23×C53—22no—
229C23×C53—22no—
230C23×C53—22no—
231C23×C53—22no—
232C23×C53—22no—
233C23×C53—22no—
234C23×C53—22no—
235C23×C53—41no—
236C23×C53—41no—
237C23×C53—41no—
238C23×C53—41no—
239C23×C53—41no—
240C23×C53—41no—
241C23×C53—41no—
242C23×C53—41no—
243C23×C53—41no—
244C23×C53—41no—
245C23×C53—41no—
246C23×C53—41no—
247C23×C53—41no—
248C23×C53—41no—
249C23×C53—41no—
250C23×C53—41no—
251C23×C53C4⋊Q814yes—
252C23×C53C22×D411yescharacteristic
253C23×C53C22×D411yescharacteristic
254C23×C53C22×D411yescharacteristic
255C23×C53C22×D411yescharacteristic
256C23×C53C22×Q811yescharacteristic
257C23×C53C22×Q811yescharacteristic
258C23×C53C2×#4111yescharacteristic
259C23×C53C2×#4111yescharacteristic
260C23×C53C2×#4111yescharacteristic
261C23×C53C2×#4111yescharacteristic
262C23×C53C2×#4111yescharacteristic
263C23×C53H(5,𝔽2)11yescharacteristic
264C23×C53H(5,𝔽2)11yescharacteristic
265C23×C532−1+411yescharacteristic
266C23×C532−1+411yescharacteristic
267C2×C4×C53—24no—
268C2×C4×C53—22no—
269C2×C4×C53—22no—
270C2×C4×C53—22no—
271C2×C4×C53—24no—
272C2×C4×C53—24no—
273C2×C4×C53—41no—
274C2×C4×C53—41no—
275C2×C4×C53—41no—
276C2×C4×C53—42no—
277C2×C4×C53—41no—
278C2×C4×C53—42no—
279C2×C4×C53—42no—
280C2×C4×C53—42no—
281C2×C4×C53—416no—
282C2×C4×C53—42no—
283C2×C4×C53—42no—
284C2×C4×C53—42no—
285C2×C4×C53—42no—
286C2×C4×C53—42no—
287C2×C4×C53—42no—
288C2×C4×C53—42no—
289C2×C4×C53#12114yes—
290C2×C4×C53#12114yes—
291C2×C4×C53#12114yes—
292C2×C4×C53C22⋊Q814yes—
293C2×C4×C53C22⋊Q814yes—
294C2×C4×C53C22⋊Q814yes—
295C2×C4×C53#12614yes—
296C2×Dic53—22no—
297C2×Dic53—22no—
298C2×Dic53—22no—
299C2×Dic53—22no—
300C2×Dic53—22no—
301C2×Dic53—22no—
302C2×Dic53—22no—
303C2×Dic53—22no—
304C2×Dic53—22no—
305C2×Dic53—22no—
306C2×Dic53—22no—
307C2×Dic53—22no—
308C2×Dic53—24no—
309C2×Dic53—22no—
310C2×Dic53—22no—
311C2×Dic53—22no—
312C2×Dic53—24no—
313C2×Dic53—24no—
314C2×Dic53—22no—
315C2×Dic53—22no—
316C2×Dic53—22no—
317C2×Dic53—41no—
318C2×Dic53—41no—
319C2×Dic53—42no—
320C2×Dic53—41no—
321C2×Dic53—41no—
322C2×Dic53—42no—
323C2×Dic53—42no—
324C2×Dic53—41no—
325C2×Dic53—42no—
326C2×Dic53—41no—
327C2×Dic53—41no—
328C2×Dic53—41no—
329C2×Dic53—42no—
330C2×Dic53—42no—
331C2×Dic53—42no—
332C2×Dic53—42no—
333C2×Dic53—42no—
334C2×Dic53—42no—
335C2×Dic53—42no—
336C2×Dic53#12114yes—
337C2×Dic53C22⋊Q814yes—
338#15131—531nomaximal, Sylow
339C22×C53—24no—
340C22×C53—24no—
341C22×C53—24no—
342C22×C53—42no—
343C22×C53—42no—
344C22×C53—42no—
345C22×C53—42no—
346C22×C53—42no—
347C22×C53—42no—
348C22×C53—42no—
349C22×C53—42no—
350C22×C53—42no—
351C22×C53—42no—
352C22×C53—42no—
353C22×C53—42no—
354C22×C53C2×#12111yescharacteristic
355C22×C53C2×#12111yescharacteristic
356C22×C53C2×#12111yescharacteristic
357C22×C53C2×#12111yescharacteristic
358C22×C53C2×C22⋊Q811yescharacteristic
359C22×C53C2×C22⋊Q811yescharacteristic
360C22×C53C2×C22⋊Q811yescharacteristic
361C22×C53C2×C22⋊Q811yescharacteristic
362C22×C53C2×#12611yescharacteristic
363C22×C53C2×C4⋊Q811yescharacteristic
364C22×C53#53211yescharacteristic
365C22×C53#53311yescharacteristic
366C22×C53#53311yescharacteristic
367C22×C53#53711yescharacteristic
368C22×C53#53711yescharacteristic
369C22×C53#54011yescharacteristic
370C22×C53#54111yescharacteristic
371C22×C53#54411yescharacteristic
372C22×C53#54411yescharacteristic
373C22×C53D4211yescharacteristic
374C22×C53D4211yescharacteristic
375C22×C53#54611yescharacteristic
376C22×C53#54711yescharacteristic
377C22×C53#54711yescharacteristic
378C22×C53#54711yescharacteristic
379C22×C53#54811yescharacteristic
380C22×C53D4×Q811yescharacteristic
381C22×C53D4×Q811yescharacteristic
382C22×C53#55011yescharacteristic
383C22×C53#55211yescharacteristic
384C22×C53#55311yescharacteristic
385C22×C53#55411yescharacteristic
386C22×C53#55411yescharacteristic
387C22×C53#55511yescharacteristic
388C22×C53#55611yescharacteristic
389C4×C53—42no—
390C4×C53—44no—
391C4×C53—82no—
392C4×C53#39618yescomplemented
393Dic53—24no—
394Dic53—24no—
395Dic53—44no—
396Dic53—42no—
397Dic53—42no—
398Dic53—82no—
399C2×#396—532no—
400C2×#389—531no—
401C2×#389—531no—
402C2×#384—531no—
403C2×#380—531no—
404C2×#380D5311yescharacteristic
405C2×C4×C22⋊C4—531no—
406#1441—532no—
407#1441—532no—
408#1439—532no—
409C4⋊#95—531no—
410C2×C53—44no—
411C2×C53C2×#39611yescharacteristic
412C2×C53#241611yescharacteristic
413C2×C53#241711yescharacteristic
414C2×C53#242811yescharacteristic
415C2×C53#242911yescharacteristic
416C2×C53#243911yescharacteristic
417C2×C53#244011yescharacteristic
418C2×C53#244011yescharacteristic
419C2×C53#244111yescharacteristic
420C2×C53#249611yescharacteristic
421C2×C53#249711yescharacteristic
422C2×C53#253711yescharacteristic
423C2×C53#253811yescharacteristic
424C2×C53#262911yescharacteristic
425C2×C53#285711yescharacteristic
426C24×C4C2×D5311yescharacteristic
427C22×C4⋊C4—531no—
428C22×C4⋊C4—532no—
429C22×C4⋊C4—531no—
430C22×C4⋊C4—532no—
431C22×C4⋊C4—532no—
432C22×C4⋊C4—532no—
433C22×C4⋊C4C2×D5311yescharacteristic
434C22×C4⋊C4C2×D5311yescharacteristic
435C22×C22⋊C4—531no—
436C22×C22⋊C4—531no—
437C22×C22⋊C4—532no—
438C22×C22⋊C4C2×D5312yes—
439C22×C42—531no—
440C22×C42—531no—
441#396—1068no—
442#389—1064no—
443#389—1064no—
444#384—1064no—
445#380—24no—
446#380—1064no—
447C4×C22⋊C4—1064no—
448C2×#95—532no—
449C2×#95—532no—
450C2×#95—532no—
451C2×#95—531no—
452C2×#95—531no—
453C2×#95—532no—
454C2×#95—532no—
455C2×#95C2×D5312yes—
456C53#1513111yescharacteristic, complemented, Sylow
457C25C22×D5311yescharacteristic
458C23×C4—22no—
459C23×C4—22no—
460C23×C4—22no—
461C23×C4—22no—
462C23×C4—22no—
463C23×C4—22no—
464C23×C4—531no—
465C23×C4—531no—
466C23×C4—532no—
467C23×C4—531no—
468C23×C4—531no—
469C23×C4—532no—
470C23×C4Dic10614yes—
471C23×C4C22×D5312yes—
472C23×C4C22×D5311yescharacteristic
473C23×C4C22×D5312yes—
474C23×C4C22×D5311yescharacteristic
475C2×C4⋊C4—22no—
476C2×C4⋊C4—22no—
477C2×C4⋊C4—22no—
478C2×C4⋊C4—22no—
479C2×C4⋊C4—22no—
480C2×C4⋊C4—534no—
481C2×C4⋊C4—1062no—
482C2×C4⋊C4—1062no—
483C2×C4⋊C4—1064no—
484C2×C4⋊C4—1064no—
485C2×C4⋊C4—1064no—
486C2×C4⋊C4—1064no—
487C2×C4⋊C4—1064no—
488C2×C4⋊C4—1064no—
489C2×C4⋊C4—1064no—
490C2×C4⋊C4—1064no—
491C2×C4⋊C4—1062no—
492C2×C4⋊C4—1062no—
493C2×C4⋊C4—1062no—
494C2×C4⋊C4—1064no—
495C2×C4⋊C4—2122no—
496C2×C4⋊C4—2122no—
497C2×C4⋊C4—2122no—
498C2×C4⋊C4C22⋊D5314yes—
499C2×C22⋊C4—24no—
500C2×C22⋊C4—24no—
501C2×C22⋊C4—42no—
502C2×C22⋊C4—534no—
503C2×C22⋊C4—534no—
504C2×C22⋊C4—1062no—
505C2×C22⋊C4—1062no—
506C2×C22⋊C4—1062no—
507C2×C22⋊C4—1062no—
508C2×C22⋊C4—1064no—
509C2×C22⋊C4—1064no—
510C2×C22⋊C4—2122no—
511C2×C42—534no—
512C2×C42—1062no—
513C2×C42—1062no—
514C2×C42—1062no—
515C2×C42—1062no—
516C2×C42—1062no—
517#95—24no—
518#95—1062no—
519#95—1062no—
520#95—1064no—
521#95—1064no—
522#95—1064no—
523#95—1064no—
524#95—2122no—
525C24—21no—
526C24—21no—
527C24—21no—
528C24—21no—
529C24—21no—
530C24—21no—
531C24—21no—
532C24—21no—
533C24—21no—
534C24—21no—
535C24—21no—
536C24—21no—
537C24C2×Dic10612yes—
538C24D4×D5312yes—
539C24Q8×D5312yes—
540C24C23×D5311yescharacteristic
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—21no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—28no—
554C22×C4—28no—
555C22×C4—28no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—44no—
564C22×C4—44no—
565C22×C4—44no—
566C22×C4—44no—
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—532no—
576C22×C4—1061no—
577C22×C4—1061no—
578C22×C4—1061no—
579C22×C4—1061no—
580C22×C4—1061no—
581C22×C4—1061no—
582C22×C4—1061no—
583C22×C4—1061no—
584C22×C4—1061no—
585C22×C4—1061no—
586C22×C4—1062no—
587C22×C4—1061no—
588C22×C4—1062no—
589C22×C4—1061no—
590C22×C4—1061no—
591C22×C4—1061no—
592C22×C4—1062no—
593C22×C4—1061no—
594C22×C4—1061no—
595C22×C4—1062no—
596C22×C4—1062no—
597C22×C4—1061no—
598C22×C4—1061no—
599C22×C4—1062no—
600C22×C4—1061no—
601C22×C4—1061no—
602C22×C4—1062no—
603C22×C4—1062no—
604C22×C4—1062no—
605C22×C4—1062no—
606C22×C4—1062no—
607C22×C4—1062no—
608C22×C4—1062no—
609C22×C4C2×Dic10612yes—
610C22×C4C2×Dic10612yes—
611C22×C4#1171994512yes—
612C22×C4D4×D5312yes—
613C22×C4D4×D5312yes—
614C22×C4#1171994712yes—
615C22×C4#1171994712yes—
616C22×C4C2×C22⋊D5314yes—
617C22×C4C2×C22⋊D5312yes—
618C4⋊C4—28no—
619C4⋊C4—44no—
620C4⋊C4—1068no—
621C4⋊C4—2128no—
622C4⋊C4—2128no—
623C4⋊C4—2128no—
624C4⋊C4—2128no—
625C4⋊C4—2124no—
626C22⋊C4—48no—
627C22⋊C4—1068no—
628C22⋊C4—1068no—
629C22⋊C4—2128no—
630C42—1068no—
631C42—2124no—
632C23—22no—
633C23—22no—
634C23—22no—
635C23—22no—
636C23—22no—
637C23—22no—
638C23—22no—
639C23—22no—
640C23—22no—
641C23—22no—
642C23—22no—
643C23—22no—
644C23—22no—
645C23—22no—
646C23—22no—
647C23—22no—
648C23—22no—
649C23—22no—
650C23—41no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23—41no—
655C23—41no—
656C23—41no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23#1313321614yes—
667C23C2×D4×D5311yescharacteristic
668C23C2×D4×D5311yescharacteristic
669C23C2×D4×D5311yescharacteristic
670C23C22×C22⋊D5311yescharacteristic
671C23C2×Q8×D5311yescharacteristic
672C23C22×Dic10611yescharacteristic
673C23#41×D5311yescharacteristic
674C23#41×D5311yescharacteristic
675C23C2×#1171994711yescharacteristic
676C23C2×#1171994711yescharacteristic
677C23C2×#1171994511yescharacteristic
678C23#1313326211yescharacteristic
679C23#1313326311yescharacteristic
680C23#1313326411yescharacteristic
681C23#1313326511yescharacteristic
682C2×C4—24no—
683C2×C4—24no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—24no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—42no—
696C2×C4—416no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—534no—
705C2×C4—534no—
706C2×C4—1062no—
707C2×C4—1062no—
708C2×C4—1062no—
709C2×C4—1062no—
710C2×C4—1062no—
711C2×C4—1062no—
712C2×C4—1062no—
713C2×C4—1062no—
714C2×C4—1062no—
715C2×C4—1062no—
716C2×C4—1062no—
717C2×C4—1062no—
718C2×C4—1064no—
719C2×C4—1062no—
720C2×C4—1062no—
721C2×C4—1062no—
722C2×C4—1062no—
723C2×C4—1064no—
724C2×C4—1062no—
725C2×C4—1062no—
726C2×C4—1064no—
727C2×C4—2122no—
728C2×C4—2122no—
729C2×C4—2122no—
730C2×C4—2122no—
731C2×C4—2122no—
732C2×C4—2122no—
733C2×C4—2122no—
734C2×C4—2121no—
735C2×C4—2122no—
736C2×C4—2121no—
737C2×C4—2121no—
738C2×C4—2121no—
739C2×C4—2121no—
740C2×C4—2121no—
741C2×C4—2122no—
742C2×C4—2121no—
743C2×C4—2121no—
744C2×C4—2122no—
745C2×C4—2122no—
746C2×C4#1313318814yes—
747C2×C4#1313318914yes—
748C2×C4#1313319014yes—
749C2×C4#1313319414yes—
750C2×C4#1313319414yes—
751C2×C4#1313319614yes—
752C2×C4#1313321014yes—
753C22—24no—
754C22—24no—
755C22—24no—
756C22—42no—
757C22—42no—
758C22—42no—
759C22—42no—
760C22—42no—
761C22—42no—
762C22—42no—
763C22—42no—
764C22—42no—
765C22—42no—
766C22—42no—
767C22—42no—
768C22#121×D5311yescharacteristic
769C22C2×#1313318811yescharacteristic
770C22C2×#1313318911yescharacteristic
771C22C2×#1313319011yescharacteristic
772C22C22⋊Q8×D5311yescharacteristic
773C22C2×#1313319411yescharacteristic
774C22C2×#1313319411yescharacteristic
775C22C2×#1313319611yescharacteristic
776C22C2×#1313321011yescharacteristic
777C22C2×#1313321611yescharacteristic
778C22#1681116811yescharacteristic
779C22#1681117511yescharacteristic
780C22#1681117611yescharacteristic
781C22#1681120211yescharacteristic
782C22#1681120311yescharacteristic
783C22#1681122611yescharacteristic
784C22#1681123311yescharacteristic
785C22#1681125111yescharacteristic
786C22#1681125411yescharacteristic
787C22D4×C22⋊D5311yescharacteristic
788C22#1681125711yescharacteristic
789C22#1681127011yescharacteristic
790C22#1681127211yescharacteristic
791C22#1681127311yescharacteristic
792C22#1681127411yescharacteristic
793C22#1681128311yescharacteristic
794C22#1681128611yescharacteristic
795C22Q8×C22⋊D5311yescharacteristic
796C22#1681129211yescharacteristic
797C22#1681131211yescharacteristic
798C22#1681131711yescharacteristic
799C22#1681132811yescharacteristic
800C22#1681133111yescharacteristic
801C22#1681133711yescharacteristic
802C22#1681134411yescharacteristic
803C4—44no—
804C4—42no—
805C4—82no—
806C4—1064no—
807C4—1064no—
808C4—4242no—
809C4—2124no—
810C4—2122no—
811C4—2122no—
812C4#1681054618yescomplemented
813C2—44no—
814C2C2×#1681054611yescharacteristic
815C2#2027815711yescharacteristic
816C2#2027816811yescharacteristic
817C2#2027829911yescharacteristic
818C2#2027831011yescharacteristic
819C2#2027840711yescharacteristic
820C2#2027841111yescharacteristic
821C2#2027841811yescharacteristic
822C2#2027842211yescharacteristic
823C2#2027913911yescharacteristic
824C2#2027915011yescharacteristic
825C2#2027962911yescharacteristic
826C2#2027963411yescharacteristic
827C2#2028054911yescharacteristic
828C2#2028306511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D53
commutator, socle, cosocleC24×C53C24
FittingC2×C53×#380C2
prime radicalC25×C53C23
hypercenterC2×#380D53
hypocenterC53#15131
LCSG ▷ C24×C53 ▷ C53
UCSC1 ◁ C24 ◁ C2×#380

Complements

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

NH ≅ G/Ntype
2. C2×#16810522C2semidirect
3. C2×#16810519C2semidirect
4. C2×#16810492C2semidirect
7. #20272967C2semidirect
8. #20272966C2semidirect
10. #20272944C2semidirect
392. C4×C53#396semidirect
456. C53#15131semidirect
812. C4#16810546semidirect

Maximal subgroups

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

subgroupindex
C2×#168105462
C2×#168105222
C2×#168105192
C2×#168104922
C2×#168104832
C2×C4×C22⋊Dic532
#202729672
#202729662
#202729582
#202729442
C2×C53×#3802
#1513153