Finite Group Databasebeta

← #27315419

Subgroups — #27315419

Order 13568.

2842 conjugacy classes of subgroups.

The subgroup lattice has 758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13133199C211yesmaximal, characteristic
2C22×C42×D53C211yesmaximal, characteristic, complemented
3C2×#16810499C212yesmaximal
4C2×#16810485C211yesmaximal, characteristic, complemented
5#20272952C212yesmaximal, complemented
6#20272952C211yesmaximal, characteristic, complemented
7#20272950C211yesmaximal, characteristic, complemented
8#20272949C212yesmaximal, complemented
9#20272948C211yesmaximal, characteristic, complemented
10#20272936C212yesmaximal, complemented
11C53×#1437C211yesmaximal, characteristic, complemented
12C23×C22⋊D53C2211yescharacteristic
13C23×C4×D53C2212yes—
14C23×C4×D53C2211yescharacteristic
15C2×#13133199—24no—
16C2×#13133199—24no—
17C2×#13133199C418yescomplemented
18C22×C4⋊Dic53C2211yescharacteristic
19C22×#11719919C2211yescharacteristic
20C22×C22⋊Dic53C2212yes—
21C22×C22⋊Dic53C2211yescharacteristic
22C22×#11719921C2212yes—
23C22×#11719921C2211yescharacteristic
24C22×C4×Dic53C2212yes—
25C22×C4×Dic53C2211yescharacteristic
26C2×C42×D53—28no—
27C2×C42×D53—24no—
28#16810499—28no—
29#16810485—24no—
30C2×#13133124C2212yes—
31C2×#13133124C2212yes—
32C2×#13133124C2212yes—
33C2×#13133124C2212yes—
34C2×#13133124C2211yescharacteristic
35C2×#13133124C2212yes—
36C2×#13133124C2212yes—
37C22×C22⋊C4×C53C2212yes—
38C22×C22⋊C4×C53C2211yescharacteristic
39C22×C42×C53C2211yescharacteristic
40C2×#95×C53C2212yes—
41C2×#95×C53C2211yescharacteristic
42C24×D53C2311yescharacteristic
43C22×C22⋊D53—24no—
44C22×C22⋊D53—22no—
45C22×C22⋊D53—22no—
46C22×C22⋊D53—24no—
47C22×C22⋊D53C2×C414yes—
48C23×Dic53C2312yes—
49C23×Dic53C2311yescharacteristic
50C23×Dic53C2311yescharacteristic
51C23×Dic53C2311yescharacteristic
52C23×Dic53C2312yes—
53C22×C4×D53—24no—
54C22×C4×D53—24no—
55C22×C4×D53—24no—
56C22×C4×D53—24no—
57C22×C4×D53—24no—
58C22×C4×D53—24no—
59C22×C4×D53—24no—
60C22×C4×D53—24no—
61C22×C4×D53C2×C414yes—
62C22×C4×D53D418yes—
63C22×C4×D53D414yes—
64C22×C4×D53D414yes—
65#13133199—232no—
66C2×C4⋊Dic53—22no—
67C2×C4⋊Dic53—22no—
68C2×C4⋊Dic53C2×C414yescomplemented
69C2×#11719919—22no—
70C2×#11719919—22no—
71C2×#11719919C2×C414yescomplemented
72C2×C22⋊Dic53—22no—
73C2×C22⋊Dic53—22no—
74C2×C22⋊Dic53—24no—
75C2×C22⋊Dic53—24no—
76C2×C22⋊Dic53—24no—
77C2×C22⋊Dic53C2×C414yescomplemented
78C2×#11719921—22no—
79C2×#11719921—22no—
80C2×#11719921—24no—
81C2×#11719921—24no—
82C2×#11719921—24no—
83C2×#11719921C2×C414yes—
84C2×C4×Dic53—22no—
85C2×C4×Dic53—24no—
86C2×C4×Dic53—24no—
87C2×C4×Dic53—24no—
88C2×C4×Dic53—24no—
89C42×D53—232no—
90#13133124—24no—
91#13133124—22no—
92#13133124—24no—
93#13133124—24no—
94#13133124—24no—
95#13133124—24no—
96#13133124—24no—
97C25×C53C2311yescharacteristic
98C23×C4×C53C2312yes—
99C23×C4×C53C2311yescharacteristic
100C23×C4×C53C2311yescharacteristic
101C23×C4×C53C2312yes—
102C2×C22⋊C4×C53—22no—
103C2×C22⋊C4×C53—22no—
104C2×C22⋊C4×C53—24no—
105C2×C22⋊C4×C53—24no—
106C2×C22⋊C4×C53—24no—
107C2×C22⋊C4×C53C2×C414yescomplemented
108C2×C42×C53—22no—
109C2×C42×C53—24no—
110#95×C53—22no—
111#95×C53—24no—
112C24×C53—21no—
113C24×C53—21no—
114C24×C53—22no—
115C24×C53—22no—
116C24×C53—22no—
117C24×C53—22no—
118C24×C53—22no—
119C24×C53—22no—
120C24×C53C22×C412yes—
121C24×C53C2411yescharacteristic
122C23×D53—22no—
123C23×D53—22no—
124C23×D53—22no—
125C23×D53—22no—
126C23×D53C22×C412yes—
127C23×D53C2×D412yes—
128C23×D53C2×D412yes—
129C23×D53C2×D414yes—
130C23×D53#4114yes—
131C22×C4×C53—22no—
132C22×C4×C53—22no—
133C22×C4×C53—22no—
134C22×C4×C53—22no—
135C22×C4×C53—22no—
136C22×C4×C53—22no—
137C22×C4×C53—21no—
138C22×C4×C53—21no—
139C22×C4×C53—22no—
140C22×C4×C53—22no—
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×C412yes—
149C22×C4×C53C22×C412yes—
150C22×C4×C53C2×D412yes—
151C22×C4×C53C2×D412yes—
152C22×C4×C53C2×D414yes—
153C22×C4×C53#4114yes—
154C22×C4×C53#4114yes—
155C2×C22⋊D53—28no—
156C2×C22⋊D53—216no—
157C2×C22⋊D53—44no—
158C2×C22⋊D53—48no—
159C2×C22⋊D53—44no—
160C22×Dic53—22no—
161C22×Dic53—22no—
162C22×Dic53—22no—
163C22×Dic53—22no—
164C22×Dic53—22no—
165C22×Dic53—22no—
166C22×Dic53—22no—
167C22×Dic53—21no—
168C22×Dic53—21no—
169C22×Dic53—21no—
170C22×Dic53—21no—
171C22×Dic53—22no—
172C22×Dic53—22no—
173C22×Dic53—22no—
174C22×Dic53—22no—
175C22×Dic53—22no—
176C22×Dic53—22no—
177C22×Dic53—22no—
178C22×Dic53—22no—
179C22×Dic53—22no—
180C22×Dic53—22no—
181C22×Dic53C22×C412yes—
182C22×Dic53C22×C412yes—
183C22×Dic53C22×C412yes—
184C22×Dic53C2×D412yes—
185C22×Dic53C2×D412yes—
186C22×Dic53C2×D414yes—
187C22×Dic53#4114yes—
188C22×Dic53#4114yes—
189C2×C4×D53—216no—
190C2×C4×D53—216no—
191C2×C4×D53—216no—
192C2×C4×D53—216no—
193C2×C4×D53—216no—
194C2×C4×D53—216no—
195C2×C4×D53—28no—
196C2×C4×D53—216no—
197C2×C4×D53—28no—
198C2×C4×D53—216no—
199C2×C4×D53—216no—
200C2×C4×D53C22⋊C4116yescomplemented
201C22⋊C4×C53—28no—
202C22⋊C4×C53—48no—
203C42×C53—28no—
204C22⋊Dic53—28no—
205C22⋊Dic53—48no—
206#11719921—28no—
207#11719921—48no—
208C4⋊Dic53—28no—
209#11719919—28no—
210C4×Dic53—28no—
211C4×Dic53—216no—
212C23×C53—22no—
213C23×C53—24no—
214C23×C53—24no—
215C23×C53—22no—
216C23×C53—22no—
217C23×C53—41no—
218C23×C53—42no—
219C23×C53—41no—
220C23×C53—42no—
221C23×C53—42no—
222C23×C53—42no—
223C23×C53—42no—
224C23×C53—42no—
225C23×C53—42no—
226C23×C53—42no—
227C23×C53—42no—
228C23×C53—42no—
229C23×C53—42no—
230C23×C53—42no—
231C23×C53—41no—
232C23×C53—41no—
233C23×C53C23×C411yescharacteristic
234C23×C53C22×D411yescharacteristic
235C23×C53C22×D411yescharacteristic
236C23×C53C22×D412yes—
237C23×C53C2×#4112yes—
238C23×C53C2×#4112yes—
239C23×C53C2×#4112yes—
240C23×C53C2×#4112yes—
241C23×C53C2×#4112yes—
242C22×D53—24no—
243C22×D53—22no—
244C22×D53—22no—
245C22×D53—24no—
246C22×D53—24no—
247C22×D53—24no—
248C22×D53—24no—
249C22×D53—24no—
250C22×D53—24no—
251C22×D53—24no—
252C22×D53—24no—
253C22×D53—24no—
254C22×D53—24no—
255C22×D53—24no—
256C22×D53—22no—
257C22×D53—22no—
258C22×D53C2×C22⋊C414yes—
259C22×D53C4×D418yes—
260C22×D53#12014yes—
261C22×D53#12118yes—
262C22×D53#12314yes—
263C2×C4×C53—24no—
264C2×C4×C53—24no—
265C2×C4×C53—22no—
266C2×C4×C53—24no—
267C2×C4×C53—24no—
268C2×C4×C53—22no—
269C2×C4×C53—24no—
270C2×C4×C53—24no—
271C2×C4×C53—24no—
272C2×C4×C53—24no—
273C2×C4×C53—22no—
274C2×C4×C53—24no—
275C2×C4×C53—42no—
276C2×C4×C53—41no—
277C2×C4×C53—41no—
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—42no—
285C2×C4×C53C2×C22⋊C414yes—
286C2×C4×C53#12318yescomplemented
287C22⋊D53—416no—
288C2×Dic53—24no—
289C2×Dic53—24no—
290C2×Dic53—22no—
291C2×Dic53—24no—
292C2×Dic53—22no—
293C2×Dic53—24no—
294C2×Dic53—24no—
295C2×Dic53—24no—
296C2×Dic53—24no—
297C2×Dic53—24no—
298C2×Dic53—22no—
299C2×Dic53—22no—
300C2×Dic53—24no—
301C2×Dic53—22no—
302C2×Dic53—22no—
303C2×Dic53—41no—
304C2×Dic53—42no—
305C2×Dic53—41no—
306C2×Dic53—42no—
307C2×Dic53—42no—
308C2×Dic53—42no—
309C2×Dic53—42no—
310C2×Dic53—42no—
311C2×Dic53—42no—
312C2×Dic53—42no—
313C2×Dic53—42no—
314C2×Dic53—42no—
315C2×Dic53C2×C22⋊C414yes—
316C2×Dic53#12318yescomplemented
317C4×D53—264no—
318C4×D53—232no—
319#14706—531nomaximal, Sylow
320C22×C53—42no—
321C22×C53—42no—
322C22×C53—42no—
323C22×C53—44no—
324C22×C53—44no—
325C22×C53—82no—
326C22×C53—82no—
327C22×C53—82no—
328C22×C53—82no—
329C22×C53C22×C22⋊C411yescharacteristic
330C22×C53C2×C4×D412yes—
331C22×C53C4×#4112yes—
332C22×C53C4×#4111yescharacteristic
333C22×C53C4×#4111yescharacteristic
334C22×C53C2×#12011yescharacteristic
335C22×C53C2×#12112yes—
336C22×C53C2×#12312yes—
337C22×C53C2×#12311yescharacteristic
338C22×C53C2×#12312yes—
339C22×C53#52512yes—
340C22×C53#52512yes—
341C22×C53#52512yes—
342C22×C53#52512yes—
343C22×C53#52912yes—
344C22×C53#52912yes—
345C22×C53#52912yes—
346C22×C53#52912yes—
347C22×C53#53212yes—
348C22×C53#53211yescharacteristic
349C22×C53#53211yescharacteristic
350C2×D53—28no—
351C2×D53—28no—
352C2×D53—28no—
353C2×D53—28no—
354C2×D53—24no—
355C2×D53—24no—
356C2×D53—28no—
357C2×D53—28no—
358C2×D53#38618yes—
359C4×C53—28no—
360C4×C53—24no—
361C4×C53—42no—
362C4×C53—82no—
363Dic53—28no—
364Dic53—24no—
365Dic53—42no—
366Dic53—42no—
367Dic53—82no—
368C22×#123—531no—
369C23×C42—531no—
370C2×#386—532no—
371C2×#381—531no—
372#1437—532no—
373#1437—531no—
374#1437D5311yescharacteristic, complemented
375#1436—531no—
376#1436—532no—
377#1436—531no—
378C22⋊#95—532no—
379C2×C53—82no—
380C2×C53C2×#38611yescharacteristic
381C2×C53#229711yescharacteristic
382C2×C53#229711yescharacteristic
383C2×C53C4×#12312yes—
384C2×C53C4×#12312yes—
385C2×C53#284912yes—
386C2×C53#285312yes—
387C2×C53#285412yes—
388C2×C53#285412yes—
389D53—28no—
390C23×D4—531no—
391C24×C4—531no—
392C24×C4—532no—
393C2×#123—538no—
394C2×#123—1064no—
395C2×#123—1064no—
396C22×C4⋊C4—531no—
397C22×C4⋊C4—531no—
398C22×C22⋊C4—531no—
399C22×C22⋊C4—531no—
400C22×C22⋊C4—532no—
401C22×C22⋊C4—532no—
402C22×C22⋊C4C2×D5312yes—
403C22×C22⋊C4C2×D5311yescharacteristic
404C22×C42—532no—
405C22×C42—531no—
406C22×C42—1064no—
407C22×C42—1068no—
408C22×C42C2×D5311yescharacteristic
409#386—1068no—
410#381—1064no—
411C2×#95—532no—
412C2×#95—532no—
413C2×#95—532no—
414C2×#95—532no—
415C2×#95—532no—
416C2×#95—532no—
417C2×#95—531no—
418C2×#95C2×D5312yes—
419C2×#95C2×D5311yescharacteristic
420C53#1470611yescharacteristic, complemented, Sylow
421C25—531no—
422C25C22×D5311yescharacteristic
423C22×D4—534no—
424C22×D4—1062no—
425C22×D4—1062no—
426C22×D4—1064no—
427C22×D4—1064no—
428C23×C4—531no—
429C23×C4—532no—
430C23×C4—534no—
431C23×C4—534no—
432C23×C4—534no—
433C23×C4—531no—
434C23×C4—531no—
435C23×C4—538no—
436C23×C4—532no—
437C23×C4—1064no—
438C23×C4—1064no—
439C23×C4—1064no—
440C23×C4—1064no—
441C23×C4—1064no—
442C23×C4—1064no—
443C23×C4—1064no—
444C23×C4—1064no—
445C23×C4C22×D5312yes—
446C23×C4C22×D5311yescharacteristic
447C23×C4C22×D5311yescharacteristic
448C23×C4C22×D5312yes—
449#123—10632no—
450C2×C4⋊C4—534no—
451C2×C4⋊C4—534no—
452C2×C4⋊C4—1062no—
453C2×C4⋊C4—1062no—
454C2×C4⋊C4—1062no—
455C2×C4⋊C4—1062no—
456C2×C22⋊C4—22no—
457C2×C22⋊C4—22no—
458C2×C22⋊C4—24no—
459C2×C22⋊C4—24no—
460C2×C22⋊C4—24no—
461C2×C22⋊C4—534no—
462C2×C22⋊C4—534no—
463C2×C22⋊C4—1062no—
464C2×C22⋊C4—1062no—
465C2×C22⋊C4—1062no—
466C2×C22⋊C4—1062no—
467C2×C22⋊C4—1064no—
468C2×C22⋊C4—1064no—
469C2×C22⋊C4—1064no—
470C2×C22⋊C4—1064no—
471C2×C22⋊C4—1064no—
472C2×C22⋊C4—1064no—
473C2×C22⋊C4C4×D5314yescomplemented
474C2×C42—22no—
475C2×C42—24no—
476C2×C42—10632no—
477C2×C42—1064no—
478C2×C42—1064no—
479C2×C42—1064no—
480C2×C42—1062no—
481C2×C42—1064no—
482#95—22no—
483#95—24no—
484#95—1064no—
485#95—1064no—
486#95—1064no—
487#95—1064no—
488#95—1064no—
489#95—1062no—
490#95—1064no—
491C24—21no—
492C24—21no—
493C24—22no—
494C24—22no—
495C24—22no—
496C24—22no—
497C24—22no—
498C24—22no—
499C24—532no—
500C24—532no—
501C24—532no—
502C24—534no—
503C24—534no—
504C24—1062no—
505C24—1062no—
506C24—1062no—
507C24—1062no—
508C24C2×C4×D5312yes—
509C24C23×D5311yescharacteristic
510C2×D4—1068no—
511C2×D4—10616no—
512C2×D4—2124no—
513C2×D4—2128no—
514C2×D4—2124no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—532no—
533C22×C4—532no—
534C22×C4—534no—
535C22×C4—532no—
536C22×C4—534no—
537C22×C4—534no—
538C22×C4—5316no—
539C22×C4—532no—
540C22×C4—532no—
541C22×C4—10616no—
542C22×C4—1068no—
543C22×C4—10616no—
544C22×C4—10616no—
545C22×C4—10616no—
546C22×C4—1068no—
547C22×C4—10616no—
548C22×C4—10616no—
549C22×C4—10616no—
550C22×C4—10616no—
551C22×C4—1062no—
552C22×C4—1062no—
553C22×C4—1062no—
554C22×C4—1062no—
555C22×C4—1062no—
556C22×C4—1062no—
557C22×C4—10616no—
558C22×C4—1062no—
559C22×C4—1061no—
560C22×C4—1061no—
561C22×C4—1061no—
562C22×C4—1061no—
563C22×C4—1062no—
564C22×C4—1062no—
565C22×C4—1062no—
566C22×C4—1062no—
567C22×C4—1062no—
568C22×C4—1062no—
569C22×C4—1062no—
570C22×C4—1062no—
571C22×C4—1062no—
572C22×C4—1062no—
573C22×C4C2×C4×D5312yes—
574C22×C4C2×C4×D5312yes—
575C22×C4#1171994514yes—
576C22×C4D4×D5312yes—
577C22×C4D4×D5312yes—
578C22×C4D4×D5314yes—
579C22×C4#1171994714yes—
580C4⋊C4—1068no—
581C4⋊C4—1068no—
582C22⋊C4—28no—
583C22⋊C4—48no—
584C22⋊C4—1068no—
585C22⋊C4—1068no—
586C22⋊C4—2128no—
587C22⋊C4—2128no—
588C42—28no—
589C42—10616no—
590C42—1068no—
591C23—22no—
592C23—24no—
593C23—24no—
594C23—22no—
595C23—22no—
596C23—41no—
597C23—42no—
598C23—42no—
599C23—41no—
600C23—42no—
601C23—42no—
602C23—42no—
603C23—42no—
604C23—42no—
605C23—42no—
606C23—42no—
607C23—42no—
608C23—42no—
609C23—42no—
610C23—41no—
611C23—41no—
612C23—534no—
613C23—538no—
614C23—534no—
615C23—538no—
616C23—534no—
617C23—1064no—
618C23—1062no—
619C23—1062no—
620C23—1064no—
621C23—1064no—
622C23—1064no—
623C23—1064no—
624C23—1064no—
625C23—1064no—
626C23—1064no—
627C23—1064no—
628C23—1064no—
629C23—1064no—
630C23—1064no—
631C23—1062no—
632C23—1062no—
633C23C22×C4×D5311yescharacteristic
634C23C2×D4×D5311yescharacteristic
635C23C2×D4×D5311yescharacteristic
636C23C2×D4×D5312yes—
637C23#41×D5312yes—
638C23#41×D5312yes—
639C23#41×D5312yes—
640C23C2×#1171994712yes—
641C23C2×#1171994512yes—
642D4—21216no—
643C2×C4—24no—
644C2×C4—24no—
645C2×C4—22no—
646C2×C4—24no—
647C2×C4—24no—
648C2×C4—22no—
649C2×C4—24no—
650C2×C4—24no—
651C2×C4—24no—
652C2×C4—24no—
653C2×C4—22no—
654C2×C4—24no—
655C2×C4—42no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—42no—
659C2×C4—42no—
660C2×C4—42no—
661C2×C4—42no—
662C2×C4—42no—
663C2×C4—42no—
664C2×C4—42no—
665C2×C4—534no—
666C2×C4—538no—
667C2×C4—10632no—
668C2×C4—10664no—
669C2×C4—1064no—
670C2×C4—1064no—
671C2×C4—1062no—
672C2×C4—1064no—
673C2×C4—1062no—
674C2×C4—1064no—
675C2×C4—1064no—
676C2×C4—1064no—
677C2×C4—1064no—
678C2×C4—1064no—
679C2×C4—1062no—
680C2×C4—1062no—
681C2×C4—1064no—
682C2×C4—1062no—
683C2×C4—1062no—
684C2×C4—2122no—
685C2×C4—2122no—
686C2×C4—2122no—
687C2×C4—2122no—
688C2×C4—2122no—
689C2×C4—2122no—
690C2×C4—2122no—
691C2×C4—2121no—
692C2×C4—2122no—
693C2×C4—2121no—
694C2×C4—2122no—
695C2×C4—2122no—
696C2×C4C22⋊C4×D5314yes—
697C2×C4#1313319918yescomplemented
698C22—42no—
699C22—42no—
700C22—42no—
701C22—44no—
702C22—44no—
703C22—82no—
704C22—82no—
705C22—82no—
706C22—82no—
707C22—538no—
708C22—1068no—
709C22—1068no—
710C22—1068no—
711C22—1068no—
712C22—1064no—
713C22—1064no—
714C22—1068no—
715C22—1068no—
716C22C2×C22⋊C4×D5311yescharacteristic
717C22C4×D4×D5312yes—
718C22C4×#1171994712yes—
719C22#1681109111yescharacteristic
720C22C4×#1171994511yescharacteristic
721C22#120×D5311yescharacteristic
722C22#121×D5312yes—
723C22#123×D5312yes—
724C22#123×D5311yescharacteristic
725C22C2×#1313319912yes—
726C22#1681113212yes—
727C22#1681113212yes—
728C22#1681113312yes—
729C22#1681113312yes—
730C22#1681115112yes—
731C22#1681115212yes—
732C22#1681115512yes—
733C22#1681115612yes—
734C22#1681117012yes—
735C22#1681117111yescharacteristic
736C22#1681117211yescharacteristic
737C4—28no—
738C4—24no—
739C4—42no—
740C4—82no—
741C4—1068no—
742C4—1064no—
743C4—4242no—
744C4—2122no—
745C4—2122no—
746C2—82no—
747C2—1068no—
748C2#386×D5311yescharacteristic
749C2#2027720111yescharacteristic
750C2#2027720211yescharacteristic
751C2C4×#1313319912yes—
752C2#2027724212yes—
753C2#2028300612yes—
754C2#2028303512yes—
755C2#2028304212yes—
756C2#2028304512yes—
subgroupG/H
center, FrattiniC24C23×D53
commutatorC23×C53C23×C4
FittingC53×#1437C2
socle, cosocleC24×C53C24
prime radicalC23×C22⋊D53C22
hypercenter#1437D53
hypocenterC53#14706
LCSG ▷ C23×C53 ▷ C53
UCSC1 ◁ C24 ◁ #1437

Complements

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

NH ≅ G/Ntype
2. C22×C42×D53C2semidirect
4. C2×#16810485C2semidirect
5. #20272952C2semidirect
6. #20272952C2semidirect
7. #20272950C2semidirect
8. #20272949C2semidirect
9. #20272948C2semidirect
10. #20272936C2semidirect
11. C53×#1437C2semidirect
17. C2×#13133199C4semidirect
68. C2×C4⋊Dic53C2×C4semidirect
71. C2×#11719919C2×C4semidirect
77. C2×C22⋊Dic53C2×C4semidirect
107. C2×C22⋊C4×C53C2×C4semidirect
200. C2×C4×D53C22⋊C4semidirect
286. C2×C4×C53#123semidirect
316. C2×Dic53#123semidirect
374. #1437D53semidirect
420. C53#14706semidirect
473. C2×C22⋊C4C4×D53semidirect
697. C2×C4#13133199semidirect

Maximal subgroups

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

subgroupindex
C22×#131331992
C22×C42×D532
C2×#168104992
C2×#168104852
#202729522
#202729502
#202729492
#202729482
#202729362
C53×#14372
#1470653