Finite Group Databasebeta

← #27306030

Subgroups — #27306030

Order 13568.

1702 conjugacy classes of subgroups.

The subgroup lattice has 808 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16810489C211yesmaximal, characteristic, complemented
2C2×#16810480C211yesmaximal, characteristic
3C2×#16810480C211yesmaximal, characteristic
4C2×C4⋊C4×Dic53C211yesmaximal, characteristic, complemented
5C2×C4×#11719921C211yesmaximal, characteristic
6#20272975C212yesmaximal, complemented
7#20272963C212yesmaximal
8#20272951C212yesmaximal
9#20272944C211yesmaximal, characteristic, complemented
10#20272939C212yesmaximal, complemented
11C53×C4⋊#95C211yesmaximal, characteristic, complemented
12C23×C4×D53C2211yescharacteristic
13C22×C4⋊Dic53C2211yescharacteristic
14C22×C4⋊Dic53C2211yescharacteristic
15C22×#11719921C2212yes—
16C22×#11719921C2212yes—
17C22×#11719921C2211yescharacteristic
18C22×#11719921C2211yescharacteristic
19C22×C4×Dic53C2212yes—
20C22×C4×Dic53C2211yescharacteristic
21#16810489—24no—
22#16810480—24no—
23#16810480—24no—
24C4⋊C4×Dic53—24no—
25C4×#11719921C418yescomplemented
26C2×#13133124C2212yes—
27C2×#13133124C2212yes—
28C2×#13133124C2212yes—
29C2×#13133124C2212yes—
30C2×#13133124C2212yes—
31C2×#13133124C2212yes—
32C2×#13133124C2212yes—
33C2×#13133124C2211yescharacteristic
34C2×#13133124C2211yescharacteristic
35C22×C4⋊C4×C53C2211yescharacteristic
36C22×C4⋊C4×C53C2211yescharacteristic
37C22×C42×C53C2211yescharacteristic
38C2×#95×C53C2212yes—
39C2×#95×C53C2212yes—
40C24×D53C2311yescharacteristic
41C23×Dic53C2312yes—
42C23×Dic53C2311yescharacteristic
43C23×Dic53C2311yescharacteristic
44C23×Dic53C2312yes—
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⋊Dic53D414yes—
59C2×#11719921—22no—
60C2×#11719921—22no—
61C2×#11719921—24no—
62C2×#11719921—24no—
63C2×#11719921—24no—
64C2×#11719921—24no—
65C2×#11719921—22no—
66C2×#11719921—22no—
67C2×#11719921—42no—
68C2×#11719921—42no—
69C2×#11719921C2×C414yes—
70C2×#11719921C2×C414yes—
71C2×C4×Dic53—22no—
72C2×C4×Dic53—24no—
73C2×C4×Dic53—22no—
74C2×C4×Dic53—24no—
75C2×C4×Dic53—42no—
76C2×C4×Dic53C2×C414yes—
77#13133124—24no—
78#13133124—24no—
79#13133124—24no—
80#13133124—24no—
81#13133124—24no—
82#13133124—24no—
83#13133124—42no—
84#13133124C2×C414yes—
85#13133124C2×C414yes—
86C23×C4×C53C2312yes—
87C23×C4×C53C2311yescharacteristic
88C23×C4×C53C2311yescharacteristic
89C23×C4×C53C2312yes—
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×C53—22no—
96C2×C4⋊C4×C53D414yes—
97C2×C42×C53—22no—
98C2×C42×C53—22no—
99C2×C42×C53C2×C414yes—
100#95×C53—42no—
101#95×C53—42no—
102C24×C53C2411yescharacteristic
103C23×D53—21no—
104C23×D53—21no—
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×D53C22×C412yes—
116C23×D53#4112yes—
117C23×D53#4112yes—
118C22×C4×C53—21no—
119C22×C4×C53—21no—
120C22×C4×C53—21no—
121C22×C4×C53—21no—
122C22×C4×C53—22no—
123C22×C4×C53—22no—
124C22×C4×C53—22no—
125C22×C4×C53—21no—
126C22×C4×C53—21no—
127C22×C4×C53—21no—
128C22×C4×C53—21no—
129C22×C4×C53—22no—
130C22×C4×C53—21no—
131C22×C4×C53—21no—
132C22×C4×C53—22no—
133C22×C4×C53—22no—
134C22×C4×C53—21no—
135C22×C4×C53—21no—
136C22×C4×C53—22no—
137C22×C4×C53—22no—
138C22×C4×C53—22no—
139C22×C4×C53—22no—
140C22×C4×C53—22no—
141C22×C4×C53—22no—
142C22×C4×C53—22no—
143C22×C4×C53C22×C412yes—
144C22×C4×C53C22×C412yes—
145C22×C4×C53C22×C412yes—
146C22×C4×C53C2×D414yes—
147C22×C4×C53C2×D412yes—
148C22×C4×C53C2×D412yes—
149C22×C4×C53#4112yes—
150C22×C4×C53#4112yes—
151C22×C4×C53#4112yes—
152C22×C4×C53#4112yes—
153C22×Dic53—21no—
154C22×Dic53—21no—
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—22no—
166C22×Dic53—22no—
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—22no—
176C22×Dic53—22no—
177C22×Dic53—22no—
178C22×Dic53—22no—
179C22×Dic53—22no—
180C22×Dic53—22no—
181C22×Dic53—22no—
182C22×Dic53C22×C412yes—
183C22×Dic53C22×C412yes—
184C22×Dic53C22×C412yes—
185C22×Dic53C2×D414yes—
186C22×Dic53#4112yes—
187C22×Dic53#4112yes—
188C2×C4×D53—28no—
189C2×C4×D53—28no—
190C2×C4×D53—28no—
191C2×C4×D53—44no—
192C2×C4×D53—44no—
193C2×C4×D53—44no—
194C2×C4×D53—44no—
195C4⋊C4×C53—28no—
196C4⋊C4×C53—44no—
197C42×C53—28no—
198#11719921—28no—
199#11719921—28no—
200#11719921—48no—
201#11719921—48no—
202C4⋊Dic53—28no—
203C4⋊Dic53—44no—
204C4×Dic53—28no—
205C4×Dic53—48no—
206C23×C53C23×C411yescharacteristic
207C23×C53C22×D411yescharacteristic
208C23×C53C22×D411yescharacteristic
209C23×C53C2×#4111yescharacteristic
210C23×C53C2×#4111yescharacteristic
211C23×C53C2×#4111yescharacteristic
212C23×C53C2×#4111yescharacteristic
213C23×C53C2×#4111yescharacteristic
214C23×C53C2×#4111yescharacteristic
215C23×C53C2×#4111yescharacteristic
216C23×C53C2×#4111yescharacteristic
217C23×C53H(5,𝔽2)11yescharacteristic
218C23×C53H(5,𝔽2)11yescharacteristic
219C23×C532−1+411yescharacteristic
220C23×C532−1+411yescharacteristic
221C22×D53—22no—
222C22×D53—22no—
223C22×D53—22no—
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—41no—
240C22×D53—41no—
241C22×D53—41no—
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#11714yes—
256C2×C4×C53—22no—
257C2×C4×C53—22no—
258C2×C4×C53—22no—
259C2×C4×C53—22no—
260C2×C4×C53—22no—
261C2×C4×C53—22no—
262C2×C4×C53—24no—
263C2×C4×C53—24no—
264C2×C4×C53—24no—
265C2×C4×C53—42no—
266C2×C4×C53—42no—
267C2×C4×C53—41no—
268C2×C4×C53—41no—
269C2×C4×C53—41no—
270C2×C4×C53—41no—
271C2×C4×C53—41no—
272C2×C4×C53—41no—
273C2×C4×C53—42no—
274C2×C4×C53—41no—
275C2×C4×C53—42no—
276C2×C4×C53—41no—
277C2×C4×C53—42no—
278C2×C4×C53—42no—
279C2×C4×C53—42no—
280C2×C4×C53—42no—
281C2×C4×C53—42no—
282C2×C4×C53—42no—
283C2×C4×C53—42no—
284C2×C4×C53#11714yes—
285C2×C4×C53C4×D414yes—
286C2×C4×C53C4×D414yes—
287C2×C4×C53#12114yes—
288C2×C4×C53#12314yes—
289C2×C4×C53#12414yes—
290C2×C4×C53#12614yes—
291C2×Dic53—22no—
292C2×Dic53—22no—
293C2×Dic53—22no—
294C2×Dic53—22no—
295C2×Dic53—22no—
296C2×Dic53—22no—
297C2×Dic53—22no—
298C2×Dic53—22no—
299C2×Dic53—22no—
300C2×Dic53—22no—
301C2×Dic53—22no—
302C2×Dic53—22no—
303C2×Dic53—24no—
304C2×Dic53—24no—
305C2×Dic53—24no—
306C2×Dic53—41no—
307C2×Dic53—41no—
308C2×Dic53—41no—
309C2×Dic53—41no—
310C2×Dic53—42no—
311C2×Dic53—42no—
312C2×Dic53—41no—
313C2×Dic53—42no—
314C2×Dic53—41no—
315C2×Dic53—42no—
316C2×Dic53—41no—
317C2×Dic53—41no—
318C2×Dic53—42no—
319C2×Dic53—42no—
320C2×Dic53—42no—
321C2×Dic53—42no—
322C2×Dic53—42no—
323C2×Dic53—42no—
324C2×Dic53—42no—
325C2×Dic53#11714yes—
326C4×D53—416no—
327#13875—531nomaximal, Sylow
328C22×C53C2×#11711yescharacteristic
329C22×C53C2×#11711yescharacteristic
330C22×C53C2×#11711yescharacteristic
331C22×C53C2×C4×D411yescharacteristic
332C22×C53C2×C4×D411yescharacteristic
333C22×C53#52011yescharacteristic
334C22×C53#52011yescharacteristic
335C22×C53C2×#12111yescharacteristic
336C22×C53C2×#12311yescharacteristic
337C22×C53C2×#12411yescharacteristic
338C22×C53C2×#12611yescharacteristic
339C22×C53#52911yescharacteristic
340C22×C53#52911yescharacteristic
341C22×C53#52911yescharacteristic
342C22×C53#52911yescharacteristic
343C22×C53#54011yescharacteristic
344C22×C53#54111yescharacteristic
345C22×C53#54211yescharacteristic
346C22×C53#54211yescharacteristic
347C22×C53#54611yescharacteristic
348C22×C53#54611yescharacteristic
349C22×C53#54611yescharacteristic
350C22×C53#54711yescharacteristic
351C22×C53#54811yescharacteristic
352C22×C53#54811yescharacteristic
353C22×C53#54811yescharacteristic
354C22×C53#55011yescharacteristic
355C22×C53#55211yescharacteristic
356C22×C53#55211yescharacteristic
357C22×C53#55211yescharacteristic
358C22×C53#55311yescharacteristic
359C22×C53#55311yescharacteristic
360C22×C53#55311yescharacteristic
361C22×C53#55511yescharacteristic
362C22×C53#55611yescharacteristic
363C2×D53—24no—
364C2×D53—24no—
365C2×D53—24no—
366C2×D53—42no—
367C2×D53—42no—
368C2×D53—42no—
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—
378C4×C53—42no—
379C4×C53—42no—
380C4×C53—44no—
381C4×C53—82no—
382C4×C53#38818yes—
383Dic53—24no—
384Dic53—42no—
385Dic53—44no—
386Dic53—42no—
387Dic53—82no—
388C2×#382—531no—
389C2×#380—531no—
390C2×#380—531no—
391C2×C4×C4⋊C4—531no—
392C2×C4×C22⋊C4—531no—
393#1443—532no—
394#1440—532no—
395#1437—532no—
396C4⋊#95—531no—
397C4⋊#95D5311yescharacteristic, complemented
398#1434—532no—
399C2×C53#228311yescharacteristic
400C2×C53C2×#38811yescharacteristic
401C2×C53#231411yescharacteristic
402C2×C53#235211yescharacteristic
403C2×C53#235211yescharacteristic
404C2×C53#235211yescharacteristic
405C2×C53#235411yescharacteristic
406C2×C53#242011yescharacteristic
407C2×C53#242111yescharacteristic
408C2×C53#242611yescharacteristic
409C2×C53#242711yescharacteristic
410C2×C53#248911yescharacteristic
411C2×C53#249011yescharacteristic
412C2×C53#249411yescharacteristic
413C2×C53#249511yescharacteristic
414D53—44no—
415C24×C4—531no—
416C22×C4⋊C4—531no—
417C22×C4⋊C4—531no—
418C22×C4⋊C4C2×D5311yescharacteristic
419C22×C4⋊C4C2×D5311yescharacteristic
420C22×C22⋊C4—531no—
421C22×C22⋊C4—531no—
422C22×C22⋊C4—532no—
423C22×C22⋊C4—532no—
424C22×C42—531no—
425C22×C42—532no—
426C22×C42C2×D5311yescharacteristic
427#382—1064no—
428#380—1064no—
429#380—1064no—
430C4×C4⋊C4—1064no—
431C4×C22⋊C4—538no—
432C2×#95—531no—
433C2×#95—531no—
434C2×#95—532no—
435C2×#95—532no—
436C2×#95—532no—
437C2×#95—532no—
438C2×#95—532no—
439C2×#95—532no—
440C2×#95—532no—
441C2×#95C2×D5312yes—
442C2×#95C2×D5312yes—
443C53#1387511yescharacteristic, complemented, Sylow
444C25—531no—
445C23×C4—531no—
446C23×C4—532no—
447C23×C4—531no—
448C23×C4—531no—
449C23×C4—534no—
450C23×C4—532no—
451C23×C4—1062no—
452C23×C4—1062no—
453C23×C4—1062no—
454C23×C4—1062no—
455C23×C4—1062no—
456C23×C4—1062no—
457C23×C4C22×D5312yes—
458C23×C4C22×D5311yescharacteristic
459C23×C4C22×D5311yescharacteristic
460C23×C4C22×D5312yes—
461C23×C4C22×D5311yescharacteristic
462C2×C4⋊C4—22no—
463C2×C4⋊C4—22no—
464C2×C4⋊C4—22no—
465C2×C4⋊C4—22no—
466C2×C4⋊C4—22no—
467C2×C4⋊C4—534no—
468C2×C4⋊C4—1062no—
469C2×C4⋊C4—1062no—
470C2×C4⋊C4—1062no—
471C2×C4⋊C4—1062no—
472C2×C4⋊C4—1062no—
473C2×C4⋊C4D21214yes—
474C2×C22⋊C4—534no—
475C2×C22⋊C4—534no—
476C2×C22⋊C4—1062no—
477C2×C22⋊C4—1062no—
478C2×C22⋊C4—1062no—
479C2×C22⋊C4—1062no—
480C2×C22⋊C4—1064no—
481C2×C22⋊C4—1064no—
482C2×C22⋊C4—1064no—
483C2×C22⋊C4—1064no—
484C2×C22⋊C4—2122no—
485C2×C22⋊C4—2122no—
486C2×C42—22no—
487C2×C42—22no—
488C2×C42—534no—
489C2×C42—1062no—
490C2×C42—1062no—
491C2×C42—1064no—
492C2×C42—1064no—
493C2×C42—2122no—
494C2×C42C4×D5314yes—
495#95—42no—
496#95—42no—
497#95—534no—
498#95—534no—
499#95—1064no—
500#95—1064no—
501#95—1064no—
502#95—1064no—
503#95—1064no—
504#95—1064no—
505#95—2122no—
506C24—532no—
507C24—532no—
508C24—532no—
509C24—1061no—
510C24—1061no—
511C24—1061no—
512C24—1061no—
513C24—1061no—
514C24—1061no—
515C24—1061no—
516C24—1061no—
517C24—1061no—
518C24—1061no—
519C24—1061no—
520C24—1061no—
521C24C23×D5311yescharacteristic
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—532no—
548C22×C4—532no—
549C22×C4—532no—
550C22×C4—532no—
551C22×C4—532no—
552C22×C4—534no—
553C22×C4—1061no—
554C22×C4—1061no—
555C22×C4—1061no—
556C22×C4—1061no—
557C22×C4—1061no—
558C22×C4—1061no—
559C22×C4—1061no—
560C22×C4—1062no—
561C22×C4—1062no—
562C22×C4—1062no—
563C22×C4—1061no—
564C22×C4—1061no—
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—1062no—
574C22×C4—1061no—
575C22×C4—1068no—
576C22×C4—1068no—
577C22×C4—1068no—
578C22×C4—1062no—
579C22×C4—1062no—
580C22×C4—1062no—
581C22×C4—1062no—
582C22×C4—1062no—
583C22×C4—1062no—
584C22×C4—1062no—
585C22×C4—2124no—
586C22×C4—2124no—
587C22×C4—2124no—
588C22×C4—2124no—
589C22×C4C2×C4×D5312yes—
590C22×C4C2×C4×D5312yes—
591C22×C4C2×C4×D5312yes—
592C22×C4C2×D21214yes—
593C22×C4C2×D21212yes—
594C22×C4#1171994512yes—
595C22×C4D4×D5312yes—
596C22×C4#1171994712yes—
597C22×C4#1171994712yes—
598C22×C4#1171994912yes—
599C4⋊C4—28no—
600C4⋊C4—44no—
601C4⋊C4—1068no—
602C4⋊C4—2124no—
603C22⋊C4—1068no—
604C22⋊C4—1068no—
605C22⋊C4—2128no—
606C22⋊C4—2128no—
607C42—28no—
608C42—1068no—
609C42—2128no—
610C23—534no—
611C23—1062no—
612C23—1062no—
613C23—1062no—
614C23—1062no—
615C23—1062no—
616C23—1062no—
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—2121no—
630C23—2121no—
631C23—2121no—
632C23—2121no—
633C23—2121no—
634C23—2121no—
635C23—2121no—
636C23—2121no—
637C23—2121no—
638C23—2121no—
639C23—2121no—
640C23—2121no—
641C23—2121no—
642C23—2121no—
643C23—2121no—
644C23—2121no—
645C23C22×C4×D5311yescharacteristic
646C23C2×D4×D5311yescharacteristic
647C23C22×D21211yescharacteristic
648C23#41×D5311yescharacteristic
649C23#41×D5311yescharacteristic
650C23#41×D5311yescharacteristic
651C23#41×D5311yescharacteristic
652C23C2×#1171994711yescharacteristic
653C23C2×#1171994711yescharacteristic
654C23C2×#1171994511yescharacteristic
655C23C2×#1171994911yescharacteristic
656C23#1313326211yescharacteristic
657C23#1313326211yescharacteristic
658C23#1313326511yescharacteristic
659C23#1313326511yescharacteristic
660C2×C4—24no—
661C2×C4—24no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—24no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—42no—
676C2×C4—41no—
677C2×C4—42no—
678C2×C4—41no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—534no—
689C2×C4—1062no—
690C2×C4—1062no—
691C2×C4—1062no—
692C2×C4—1062no—
693C2×C4—1062no—
694C2×C4—1062no—
695C2×C4—1064no—
696C2×C4—1064no—
697C2×C4—1062no—
698C2×C4—1062no—
699C2×C4—1062no—
700C2×C4—1062no—
701C2×C4—1062no—
702C2×C4—1062no—
703C2×C4—1064no—
704C2×C4—2122no—
705C2×C4—2122no—
706C2×C4—2122no—
707C2×C4—2122no—
708C2×C4—2122no—
709C2×C4—2122no—
710C2×C4—2122no—
711C2×C4—2122no—
712C2×C4—2121no—
713C2×C4—2122no—
714C2×C4—2121no—
715C2×C4—2121no—
716C2×C4—2121no—
717C2×C4—2121no—
718C2×C4—2121no—
719C2×C4—2121no—
720C2×C4—2121no—
721C2×C4—2122no—
722C2×C4—2122no—
723C2×C4—21216no—
724C2×C4#1313317514yes—
725C2×C4#1313317714yes—
726C2×C4C4×D21214yes—
727C2×C4#1313319214yes—
728C2×C4#1313320114yes—
729C2×C4#1313320314yes—
730C2×C4#1313321214yes—
731C22—1064no—
732C22—1064no—
733C22—1064no—
734C22—2122no—
735C22—2122no—
736C22—2122no—
737C22—2122no—
738C22—2122no—
739C22—2122no—
740C22—2122no—
741C22—2122no—
742C22—2122no—
743C22—2122no—
744C22—2122no—
745C22—2122no—
746C22#117×D5311yescharacteristic
747C22#117×D5311yescharacteristic
748C22C2×#1313317511yescharacteristic
749C22C2×#1313317711yescharacteristic
750C22C2×C4×D21211yescharacteristic
751C22#1681110411yescharacteristic
752C22#1681110411yescharacteristic
753C22C2×#1313319211yescharacteristic
754C22C2×#1313320111yescharacteristic
755C22C2×#1313320311yescharacteristic
756C22C2×#1313321211yescharacteristic
757C22#1681115211yescharacteristic
758C22#1681115211yescharacteristic
759C22#1681115811yescharacteristic
760C22#1681115811yescharacteristic
761C22#1681122711yescharacteristic
762C22#1681123411yescharacteristic
763C22#1681124711yescharacteristic
764C22#1681124711yescharacteristic
765C22#1681126811yescharacteristic
766C22#1681126811yescharacteristic
767C22#1681127011yescharacteristic
768C22#1681127511yescharacteristic
769C22#1681128311yescharacteristic
770C22#1681128511yescharacteristic
771C22#1681128511yescharacteristic
772C22#1681129111yescharacteristic
773C22#1681130711yescharacteristic
774C22#1681131411yescharacteristic
775C22#1681131411yescharacteristic
776C22#1681132011yescharacteristic
777C22#1681132311yescharacteristic
778C22#1681132311yescharacteristic
779C22#1681133711yescharacteristic
780C22#1681134411yescharacteristic
781C4—42no—
782C4—42no—
783C4—44no—
784C4—82no—
785C4—1064no—
786C4—4242no—
787C4—2124no—
788C4—2122no—
789C4—2122no—
790C4#1681051518yes—
791C2—2124no—
792C2#2027710811yescharacteristic
793C2C2×#1681051511yescharacteristic
794C2#2027732311yescharacteristic
795C2#2027763711yescharacteristic
796C2#2027764711yescharacteristic
797C2#2027764711yescharacteristic
798C2#2027765911yescharacteristic
799C2#2027820511yescharacteristic
800C2#2027821611yescharacteristic
801C2#2027827911yescharacteristic
802C2#2027829011yescharacteristic
803C2#2027905411yescharacteristic
804C2#2027906511yescharacteristic
805C2#2027911311yescharacteristic
806C2#2027912411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D53
commutatorC23×C53C23×C4
FittingC53×C4⋊#95C2
socle, cosocleC24×C53C24
prime radicalC24×D53C23
hypercenterC4⋊#95D53
hypocenterC53#13875
LCSG ▷ C23×C53 ▷ C53
UCSC1 ◁ C24 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
1. C2×#16810489C2semidirect
4. C2×C4⋊C4×Dic53C2semidirect
6. #20272975C2semidirect
9. #20272944C2semidirect
10. #20272939C2semidirect
11. C53×C4⋊#95C2semidirect
25. C4×#11719921C4semidirect
397. C4⋊#95D53semidirect
443. C53#13875semidirect

Maximal subgroups

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

subgroupindex
C2×#168104892
C2×#168104802
C2×C4⋊C4×Dic532
C2×C4×#117199212
#202729752
#202729632
#202729512
#202729442
#202729392
C53×C4⋊#952
#1387553