Finite Group Databasebeta

← #27306744

Subgroups — #27306744

Order 13568.

2006 conjugacy classes of subgroups.

The subgroup lattice has 826 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13133175C211yesmaximal, characteristic
2C2×#16810522C211yesmaximal, characteristic, complemented
3C2×#16810480C211yesmaximal, characteristic
4C2×C4×#11719921C211yesmaximal, characteristic
5#20272961C212yesmaximal
6#20272957C212yesmaximal
7#20272945C211yesmaximal, characteristic, complemented
8#20272944C211yesmaximal, characteristic, complemented
9#20272944C212yesmaximal, complemented
10#20272939C212yesmaximal, complemented
11C2×C53×#389C211yesmaximal, characteristic, complemented
12C23×C4×D53C2211yescharacteristic
13C2×#13133175—24no—
14C2×#13133175—24no—
15C2×#13133175C418yescomplemented
16C22×C4⋊Dic53C2211yescharacteristic
17C22×C4⋊Dic53C2212yes—
18C22×C4⋊Dic53C2211yescharacteristic
19C22×#11719921C2211yescharacteristic
20C22×#11719921C2211yescharacteristic
21C22×#11719921C2212yes—
22C22×#11719921C2212yes—
23C22×C4×Dic53C2211yescharacteristic
24C22×C4×Dic53C2212yes—
25#16810522—24no—
26#16810480—24no—
27C4×#11719921—24no—
28C2×#13133124C2211yescharacteristic
29C2×#13133124C2212yes—
30C2×#13133124C2212yes—
31C2×#13133124C2212yes—
32C2×#13133124C2212yes—
33C2×#13133124C2211yescharacteristic
34C2×#13133124C2212yes—
35C2×#13133124C2212yes—
36C22×C4⋊C4×C53C2211yescharacteristic
37C22×C4⋊C4×C53C2212yes—
38C22×C4⋊C4×C53C2211yescharacteristic
39C22×C42×C53C2211yescharacteristic
40C53×#389—24no—
41C2×#95×C53C2212yes—
42C24×D53C2311yescharacteristic
43C23×Dic53C2312yes—
44C23×Dic53C2312yes—
45C23×Dic53C2311yescharacteristic
46C23×Dic53C2311yescharacteristic
47C23×Dic53C2311yescharacteristic
48C22×C4×D53—22no—
49C22×C4×D53—22no—
50C22×C4×D53—22no—
51C22×C4×D53—22no—
52C22×C4×D53C2×C414yes—
53C22×C4×D53D414yes—
54C22×C4×D53Q814yes—
55#13133175—232no—
56C2×C4⋊Dic53—22no—
57C2×C4⋊Dic53—22no—
58C2×C4⋊Dic53—24no—
59C2×C4⋊Dic53—22no—
60C2×C4⋊Dic53—22no—
61C2×C4⋊Dic53—22no—
62C2×C4⋊Dic53—24no—
63C2×C4⋊Dic53—42no—
64C2×C4⋊Dic53C2×C414yes—
65C2×#11719921—22no—
66C2×#11719921—22no—
67C2×#11719921—24no—
68C2×#11719921—24no—
69C2×#11719921—24no—
70C2×#11719921—22no—
71C2×#11719921—22no—
72C2×#11719921—22no—
73C2×#11719921—22no—
74C2×#11719921—42no—
75C2×#11719921—42no—
76C2×#11719921C2×C418yes—
77C2×C4×Dic53—24no—
78C2×C4×Dic53—24no—
79C2×C4×Dic53—22no—
80C2×C4×Dic53—22no—
81C2×C4×Dic53—22no—
82C2×C4×Dic53C2×C418yes—
83#13133124—24no—
84#13133124—24no—
85#13133124—22no—
86#13133124—22no—
87#13133124—24no—
88#13133124—24no—
89#13133124—42no—
90#13133124—42no—
91C23×C4×C53C2312yes—
92C23×C4×C53C2311yescharacteristic
93C23×C4×C53C2311yescharacteristic
94C23×C4×C53C2312yes—
95C23×C4×C53C2311yescharacteristic
96C2×C4⋊C4×C53—24no—
97C2×C4⋊C4×C53—22no—
98C2×C4⋊C4×C53—22no—
99C2×C4⋊C4×C53—24no—
100C2×C4⋊C4×C53—22no—
101C2×C4⋊C4×C53—42no—
102C2×C4⋊C4×C53C2×C414yes—
103C2×C4⋊C4×C53D414yes—
104C2×C4⋊C4×C53D414yes—
105C2×C42×C53—22no—
106C2×C42×C53—22no—
107C2×C42×C53—22no—
108#95×C53—24no—
109C24×C53C2411yescharacteristic
110C23×D53—21no—
111C23×D53—21no—
112C23×D53—21no—
113C23×D53—21no—
114C23×D53—21no—
115C23×D53—21no—
116C23×D53—21no—
117C23×D53—21no—
118C23×D53—21no—
119C23×D53—21no—
120C23×D53—21no—
121C23×D53—21no—
122C23×D53C22×C412yes—
123C23×D53C2×D412yes—
124C23×D53C2×Q812yes—
125C22×C4×C53—22no—
126C22×C4×C53—22no—
127C22×C4×C53—22no—
128C22×C4×C53—22no—
129C22×C4×C53—21no—
130C22×C4×C53—21no—
131C22×C4×C53—21no—
132C22×C4×C53—21no—
133C22×C4×C53—21no—
134C22×C4×C53—21no—
135C22×C4×C53—21no—
136C22×C4×C53—21no—
137C22×C4×C53—21no—
138C22×C4×C53—21no—
139C22×C4×C53—21no—
140C22×C4×C53—21no—
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×C53C22×C414yes—
149C22×C4×C53C22×C412yes—
150C22×C4×C53C2×D414yes—
151C22×C4×C53C2×D414yes—
152C22×C4×C53C2×D412yes—
153C22×C4×C53C2×D412yes—
154C22×C4×C53C2×D412yes—
155C22×C4×C53C2×Q812yes—
156C22×C4×C53#4112yes—
157C22×C4×C53#4112yes—
158C22×C4×C53#4112yes—
159C22×C4×C53#4112yes—
160C22×Dic53—21no—
161C22×Dic53—21no—
162C22×Dic53—21no—
163C22×Dic53—21no—
164C22×Dic53—21no—
165C22×Dic53—21no—
166C22×Dic53—21no—
167C22×Dic53—22no—
168C22×Dic53—22no—
169C22×Dic53—21no—
170C22×Dic53—22no—
171C22×Dic53—22no—
172C22×Dic53—21no—
173C22×Dic53—21no—
174C22×Dic53—21no—
175C22×Dic53—21no—
176C22×Dic53—22no—
177C22×Dic53—21no—
178C22×Dic53—21no—
179C22×Dic53—22no—
180C22×Dic53—21no—
181C22×Dic53—21no—
182C22×Dic53—22no—
183C22×Dic53—22no—
184C22×Dic53—22no—
185C22×Dic53—22no—
186C22×Dic53—22no—
187C22×Dic53—22no—
188C22×Dic53—22no—
189C22×Dic53C22×C414yes—
190C22×Dic53C22×C412yes—
191C22×Dic53C2×D412yes—
192C22×Dic53C2×Q812yes—
193C22×Dic53#4112yes—
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×D53C4⋊C4116yescomplemented
202C4⋊C4×C53—48no—
203C4⋊C4×C53—44no—
204C4⋊C4×C53C22⋊C4116yescomplemented
205C42×C53—44no—
206#11719921—28no—
207#11719921—28no—
208#11719921—216no—
209#11719921—48no—
210C4⋊Dic53—28no—
211C4⋊Dic53—48no—
212C4⋊Dic53—44no—
213C4×Dic53—216no—
214C4×Dic53—44no—
215C23×C53C23×C411yescharacteristic
216C23×C53C22×D411yescharacteristic
217C23×C53C22×D411yescharacteristic
218C23×C53C22×D411yescharacteristic
219C23×C53C22×Q811yescharacteristic
220C23×C53C2×#4111yescharacteristic
221C23×C53C2×#4111yescharacteristic
222C23×C53C2×#4111yescharacteristic
223C23×C53C2×#4111yescharacteristic
224C23×C53C2×#4111yescharacteristic
225C23×C53C2×#4111yescharacteristic
226C23×C53H(5,𝔽2)11yescharacteristic
227C23×C53H(5,𝔽2)11yescharacteristic
228C23×C532−1+411yescharacteristic
229C23×C532−1+411yescharacteristic
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—22no—
243C22×D53—22no—
244C22×D53—22no—
245C22×D53—22no—
246C22×D53—22no—
247C22×D53—22no—
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×D53—41no—
259C22×D53—41no—
260C22×D53—41no—
261C22×D53—41no—
262C22×D53—41no—
263C22×D53—41no—
264C22×D53C2×C4⋊C414yes—
265C2×C4×C53—24no—
266C2×C4×C53—24no—
267C2×C4×C53—24no—
268C2×C4×C53—24no—
269C2×C4×C53—24no—
270C2×C4×C53—24no—
271C2×C4×C53—22no—
272C2×C4×C53—22no—
273C2×C4×C53—22no—
274C2×C4×C53—22no—
275C2×C4×C53—22no—
276C2×C4×C53—22no—
277C2×C4×C53—41no—
278C2×C4×C53—41no—
279C2×C4×C53—41no—
280C2×C4×C53—41no—
281C2×C4×C53—41no—
282C2×C4×C53—41no—
283C2×C4×C53—41no—
284C2×C4×C53—41no—
285C2×C4×C53—42no—
286C2×C4×C53—42no—
287C2×C4×C53—42no—
288C2×C4×C53—42no—
289C2×C4×C53—42no—
290C2×C4×C53—42no—
291C2×C4×C53—42no—
292C2×C4×C53C2×C22⋊C418yes—
293C2×C4×C53C2×C22⋊C414yes—
294C2×C4×C53C2×C4⋊C414yes—
295C2×C4×C53#11714yes—
296C2×C4×C53#12114yes—
297C2×C4×C53#12114yes—
298C2×C4×C53C22⋊Q814yes—
299C2×C4×C53C22⋊Q814yes—
300C2×Dic53—22no—
301C2×Dic53—22no—
302C2×Dic53—22no—
303C2×Dic53—22no—
304C2×Dic53—22no—
305C2×Dic53—22no—
306C2×Dic53—24no—
307C2×Dic53—24no—
308C2×Dic53—24no—
309C2×Dic53—22no—
310C2×Dic53—22no—
311C2×Dic53—22no—
312C2×Dic53—22no—
313C2×Dic53—22no—
314C2×Dic53—22no—
315C2×Dic53—41no—
316C2×Dic53—41no—
317C2×Dic53—41no—
318C2×Dic53—41no—
319C2×Dic53—41no—
320C2×Dic53—42no—
321C2×Dic53—42no—
322C2×Dic53—42no—
323C2×Dic53—42no—
324C2×Dic53—41no—
325C2×Dic53—41no—
326C2×Dic53—41no—
327C2×Dic53—42no—
328C2×Dic53—42no—
329C2×Dic53—42no—
330C2×Dic53—42no—
331C2×Dic53—42no—
332C2×Dic53—42no—
333C2×Dic53—42no—
334C2×Dic53C2×C4⋊C414yes—
335C4×D53—232no—
336#13951—531nomaximal, Sylow
337C22×C53C22×C22⋊C411yescharacteristic
338C22×C53C22×C4⋊C411yescharacteristic
339C22×C53C2×#11711yescharacteristic
340C22×C53C4×#4111yescharacteristic
341C22×C53C4×#4111yescharacteristic
342C22×C53#52011yescharacteristic
343C22×C53#52011yescharacteristic
344C22×C53C2×#12111yescharacteristic
345C22×C53C2×#12111yescharacteristic
346C22×C53C2×C22⋊Q811yescharacteristic
347C22×C53C2×C22⋊Q811yescharacteristic
348C22×C53#52511yescharacteristic
349C22×C53#52511yescharacteristic
350C22×C53#53311yescharacteristic
351C22×C53#53311yescharacteristic
352C22×C53#53511yescharacteristic
353C22×C53#53611yescharacteristic
354C22×C53#54411yescharacteristic
355C22×C53#54411yescharacteristic
356C22×C53#54611yescharacteristic
357C22×C53#54611yescharacteristic
358C22×C53#54711yescharacteristic
359C22×C53#54711yescharacteristic
360C22×C53#54811yescharacteristic
361C22×C53#54811yescharacteristic
362C22×C53#55011yescharacteristic
363C22×C53#55011yescharacteristic
364C22×C53#55211yescharacteristic
365C22×C53#55211yescharacteristic
366C22×C53#55311yescharacteristic
367C22×C53#55311yescharacteristic
368C22×C53#55511yescharacteristic
369C22×C53#55511yescharacteristic
370C22×C53#55611yescharacteristic
371C22×C53#55611yescharacteristic
372C2×D53—24no—
373C2×D53—24no—
374C2×D53—24no—
375C2×D53—42no—
376C2×D53—42no—
377C2×D53—42no—
378C2×D53—42no—
379C2×D53—42no—
380C2×D53—42no—
381C2×D53—42no—
382C2×D53—42no—
383C2×D53—42no—
384C2×D53—42no—
385C2×D53—42no—
386C2×D53—42no—
387C4×C53—28no—
388C4×C53—42no—
389C4×C53—42no—
390C4×C53—82no—
391C4×C53#38018yes—
392Dic53—24no—
393Dic53—44no—
394Dic53—42no—
395Dic53—42no—
396Dic53—82no—
397C22×#117—531no—
398C2×#389—531no—
399C2×#389D5311yescharacteristic, complemented
400C2×#380—531no—
401C2×C4×C22⋊C4—531no—
402#1439—532no—
403#1439—532no—
404C4⋊#95—531no—
405C4⋊#95—531no—
406C4⋊#95—532no—
407#1434—532no—
408C2×C53C2×#38011yescharacteristic
409C2×C53#229611yescharacteristic
410C2×C53#231711yescharacteristic
411C2×C53#233911yescharacteristic
412C2×C53#234111yescharacteristic
413C2×C53#234611yescharacteristic
414C2×C53#234711yescharacteristic
415C2×C53#241411yescharacteristic
416C2×C53#241411yescharacteristic
417C2×C53#241511yescharacteristic
418C2×C53#241511yescharacteristic
419C2×C53#243911yescharacteristic
420C2×C53#243911yescharacteristic
421C2×C53#244111yescharacteristic
422C2×C53#244111yescharacteristic
423D53—44no—
424C24×C4—531no—
425C2×#117—538no—
426C2×#117—1064no—
427C2×#117—1064no—
428C22×C4⋊C4—531no—
429C22×C4⋊C4—531no—
430C22×C4⋊C4—532no—
431C22×C4⋊C4C2×D5311yescharacteristic
432C22×C4⋊C4C2×D5312yes—
433C22×C4⋊C4C2×D5311yescharacteristic
434C22×C22⋊C4—532no—
435C22×C22⋊C4—531no—
436C22×C22⋊C4—531no—
437C22×C22⋊C4—532no—
438C22×C42—532no—
439C22×C42—531no—
440C22×C42C2×D5311yescharacteristic
441#389—24no—
442#389—1064no—
443#380—1064no—
444C4×C22⋊C4—1064no—
445C2×#95—531no—
446C2×#95—532no—
447C2×#95—532no—
448C2×#95—532no—
449C2×#95—532no—
450C2×#95—531no—
451C2×#95—532no—
452C2×#95—532no—
453C2×#95C2×D5312yes—
454C53#1395111yescharacteristic, complemented, Sylow
455C25—531no—
456C23×C4—531no—
457C23×C4—534no—
458C23×C4—534no—
459C23×C4—534no—
460C23×C4—531no—
461C23×C4—532no—
462C23×C4—531no—
463C23×C4—532no—
464C23×C4—1062no—
465C23×C4—1062no—
466C23×C4—1062no—
467C23×C4—1062no—
468C23×C4C22×D5312yes—
469C23×C4C22×D5311yescharacteristic
470C23×C4C22×D5311yescharacteristic
471C23×C4C22×D5312yes—
472C23×C4C22×D5311yescharacteristic
473#117—10632no—
474C2×C4⋊C4—22no—
475C2×C4⋊C4—24no—
476C2×C4⋊C4—22no—
477C2×C4⋊C4—24no—
478C2×C4⋊C4—22no—
479C2×C4⋊C4—42no—
480C2×C4⋊C4—534no—
481C2×C4⋊C4—1062no—
482C2×C4⋊C4—1062no—
483C2×C4⋊C4—1064no—
484C2×C4⋊C4—1064no—
485C2×C4⋊C4—1062no—
486C2×C4⋊C4—1062no—
487C2×C4⋊C4—1062no—
488C2×C4⋊C4—2122no—
489C2×C4⋊C4C4×D5314yes—
490C2×C4⋊C4D21214yes—
491C2×C4⋊C4C22⋊D5314yes—
492C2×C22⋊C4—538no—
493C2×C22⋊C4—1062no—
494C2×C22⋊C4—1062no—
495C2×C22⋊C4—1062no—
496C2×C22⋊C4—1062no—
497C2×C22⋊C4—1064no—
498C2×C22⋊C4—1062no—
499C2×C22⋊C4—1062no—
500C2×C22⋊C4—1064no—
501C2×C22⋊C4—1064no—
502C2×C22⋊C4—2122no—
503C2×C22⋊C4—2122no—
504C2×C42—22no—
505C2×C42—22no—
506C2×C42—22no—
507C2×C42—538no—
508C2×C42—1064no—
509C2×C42—1064no—
510C2×C42—1062no—
511C2×C42—1062no—
512C2×C42—1062no—
513#95—24no—
514#95—1064no—
515#95—1062no—
516#95—1062no—
517#95—1064no—
518#95—1064no—
519#95—1064no—
520#95—2122no—
521#95—2122no—
522C24—532no—
523C24—532no—
524C24—532no—
525C24—1061no—
526C24—1061no—
527C24—1061no—
528C24—1061no—
529C24—1061no—
530C24—1061no—
531C24—1061no—
532C24—1061no—
533C24—1061no—
534C24—1061no—
535C24—1061no—
536C24—1061no—
537C24C23×D5311yescharacteristic
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—532no—
562C22×C4—532no—
563C22×C4—532no—
564C22×C4—5316no—
565C22×C4—534no—
566C22×C4—532no—
567C22×C4—532no—
568C22×C4—1061no—
569C22×C4—1061no—
570C22×C4—1061no—
571C22×C4—1061no—
572C22×C4—1068no—
573C22×C4—1068no—
574C22×C4—1068no—
575C22×C4—1068no—
576C22×C4—1068no—
577C22×C4—1068no—
578C22×C4—1061no—
579C22×C4—1061no—
580C22×C4—1062no—
581C22×C4—1061no—
582C22×C4—1062no—
583C22×C4—1061no—
584C22×C4—1062no—
585C22×C4—1061no—
586C22×C4—1062no—
587C22×C4—1061no—
588C22×C4—1061no—
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—1062no—
598C22×C4—1062no—
599C22×C4—1062no—
600C22×C4—1062no—
601C22×C4—1062no—
602C22×C4—1062no—
603C22×C4C2×C4×D5314yes—
604C22×C4C2×C4×D5312yes—
605C22×C4C2×D21214yes—
606C22×C4C2×D21212yes—
607C22×C4D4×D5312yes—
608C22×C4#1171994712yes—
609C22×C4#1171994712yes—
610C22×C4Q8×D5312yes—
611C22×C4#1171994912yes—
612C22×C4#1171994912yes—
613C22×C4C2×C22⋊D5314yes—
614C22×C4C2×C22⋊D5312yes—
615C4⋊C4—48no—
616C4⋊C4—44no—
617C4⋊C4—1068no—
618C4⋊C4—2128no—
619C4⋊C4—2124no—
620C4⋊C4#11719921116yescomplemented
621C22⋊C4—1068no—
622C22⋊C4—1068no—
623C22⋊C4—10616no—
624C22⋊C4—2128no—
625C42—44no—
626C42—10616no—
627C42—2124no—
628C23—534no—
629C23—1062no—
630C23—1062no—
631C23—1062no—
632C23—1062no—
633C23—1062no—
634C23—1062no—
635C23—1062no—
636C23—1062no—
637C23—1062no—
638C23—1062no—
639C23—1062no—
640C23—1062no—
641C23—1062no—
642C23—1062no—
643C23—1062no—
644C23—1062no—
645C23—1062no—
646C23—1062no—
647C23—2121no—
648C23—2121no—
649C23—2121no—
650C23—2121no—
651C23—2121no—
652C23—2121no—
653C23—2121no—
654C23—2121no—
655C23—2121no—
656C23—2121no—
657C23—2121no—
658C23—2121no—
659C23—2121no—
660C23—2121no—
661C23—2121no—
662C23—2121no—
663C23C22×C4×D5311yescharacteristic
664C23C2×D4×D5311yescharacteristic
665C23C22×C22⋊D5311yescharacteristic
666C23C22×D21211yescharacteristic
667C23C2×Q8×D5311yescharacteristic
668C23#41×D5311yescharacteristic
669C23#41×D5311yescharacteristic
670C23C2×#1171994711yescharacteristic
671C23C2×#1171994711yescharacteristic
672C23C2×#1171994911yescharacteristic
673C23C2×#1171994911yescharacteristic
674C23#1313326211yescharacteristic
675C23#1313326311yescharacteristic
676C23#1313326411yescharacteristic
677C23#1313326511yescharacteristic
678C2×C4—24no—
679C2×C4—24no—
680C2×C4—24no—
681C2×C4—24no—
682C2×C4—24no—
683C2×C4—24no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—534no—
706C2×C4—1062no—
707C2×C4—1062no—
708C2×C4—1062no—
709C2×C4—1062no—
710C2×C4—1062no—
711C2×C4—1062no—
712C2×C4—10632no—
713C2×C4—1062no—
714C2×C4—1062no—
715C2×C4—1062no—
716C2×C4—1064no—
717C2×C4—1062no—
718C2×C4—1064no—
719C2×C4—1064no—
720C2×C4—1062no—
721C2×C4—1062no—
722C2×C4—2122no—
723C2×C4—2122no—
724C2×C4—2122no—
725C2×C4—2122no—
726C2×C4—2122no—
727C2×C4—2122no—
728C2×C4—2122no—
729C2×C4—2121no—
730C2×C4—2122no—
731C2×C4—2122no—
732C2×C4—2122no—
733C2×C4—2122no—
734C2×C4—2121no—
735C2×C4—2121no—
736C2×C4—2121no—
737C2×C4—2121no—
738C2×C4—2121no—
739C2×C4—2121no—
740C2×C4—2121no—
741C2×C4C2×#1171992118yes—
742C2×C4C2×#1171992114yes—
743C2×C4C4⋊C4×D5314yes—
744C2×C4#1313317514yes—
745C2×C4#1313318814yes—
746C2×C4#1313319214yes—
747C2×C4#1313319314yes—
748C2×C4#1313319714yes—
749C22—1064no—
750C22—1064no—
751C22—1064no—
752C22—2122no—
753C22—2122no—
754C22—2122no—
755C22—2122no—
756C22—2122no—
757C22—2122no—
758C22—2122no—
759C22—2122no—
760C22—2122no—
761C22—2122no—
762C22—2122no—
763C22—2122no—
764C22C22×#1171992111yescharacteristic
765C22C2×C4⋊C4×D5311yescharacteristic
766C22C2×#1313317511yescharacteristic
767C22C4×#1171994711yescharacteristic
768C22C4×#1171994911yescharacteristic
769C22#1681110211yescharacteristic
770C22#1681110511yescharacteristic
771C22C2×#1313318811yescharacteristic
772C22C2×#1313319211yescharacteristic
773C22C2×#1313319311yescharacteristic
774C22C2×#1313319711yescharacteristic
775C22#1681113311yescharacteristic
776C22#1681113611yescharacteristic
777C22#1681117811yescharacteristic
778C22#1681117911yescharacteristic
779C22#1681118911yescharacteristic
780C22#1681119611yescharacteristic
781C22#1681125011yescharacteristic
782C22#1681125311yescharacteristic
783C22#1681126711yescharacteristic
784C22#1681126811yescharacteristic
785C22#1681127211yescharacteristic
786C22#1681127711yescharacteristic
787C22#1681128411yescharacteristic
788C22#1681128511yescharacteristic
789C22#1681129211yescharacteristic
790C22#1681129511yescharacteristic
791C22#1681131111yescharacteristic
792C22#1681131511yescharacteristic
793C22#1681132511yescharacteristic
794C22#1681132611yescharacteristic
795C22#1681133711yescharacteristic
796C22#1681133911yescharacteristic
797C22#1681134411yescharacteristic
798C22#1681134711yescharacteristic
799C4—28no—
800C4—42no—
801C4—42no—
802C4—82no—
803C4—1064no—
804C4—4242no—
805C4—2124no—
806C4—2122no—
807C4—2122no—
808C4#1681048018yes—
809C2—2124no—
810C2C2×#1681048011yescharacteristic
811C2#2027719611yescharacteristic
812C2#2027733711yescharacteristic
813C2#2027754011yescharacteristic
814C2#2027755311yescharacteristic
815C2#2027759911yescharacteristic
816C2#2027760711yescharacteristic
817C2#2027812911yescharacteristic
818C2#2027813111yescharacteristic
819C2#2027814011yescharacteristic
820C2#2027814211yescharacteristic
821C2#2027840211yescharacteristic
822C2#2027840411yescharacteristic
823C2#2027842411yescharacteristic
824C2#2027842611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D53
commutatorC23×C53C23×C4
FittingC2×C53×#389C2
socle, cosocleC24×C53C24
prime radicalC24×D53C23
hypercenterC2×#389D53
hypocenterC53#13951
LCSG ▷ C23×C53 ▷ C53
UCSC1 ◁ C24 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
2. C2×#16810522C2semidirect
7. #20272945C2semidirect
8. #20272944C2semidirect
9. #20272944C2semidirect
10. #20272939C2semidirect
11. C2×C53×#389C2semidirect
15. C2×#13133175C4semidirect
201. C2×C4×D53C4⋊C4semidirect
204. C4⋊C4×C53C22⋊C4semidirect
399. C2×#389D53semidirect
454. C53#13951semidirect
620. C4⋊C4#11719921semidirect

Maximal subgroups

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

subgroupindex
C22×#131331752
C2×#168105222
C2×#168104802
C2×C4×#117199212
#202729612
#202729572
#202729452
#202729442
#202729392
C2×C53×#3892
#1395153