Finite Group Databasebeta

← #27390361

Subgroups — #27390361

Order 13568.

1140 conjugacy classes of subgroups.

The subgroup lattice has 718 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16810821C211yesmaximal, characteristic
2C2×#16810726C211yesmaximal, characteristic, complemented
3C2×#16810724C211yesmaximal, characteristic, complemented
4#20277279C211yesmaximal, characteristic
5C4×Q8×Dic53C211yesmaximal, characteristic, complemented
6#20275640C211yesmaximal, characteristic
7#20275472C211yesmaximal, characteristic, complemented
8#20275336C211yesmaximal, characteristic, complemented
9#20275332C211yesmaximal, characteristic, complemented
10#20275070C211yesmaximal, characteristic, complemented
11#20274718C211yesmaximal, characteristic, complemented
12#20274567C211yesmaximal, characteristic, complemented
13#20274542C211yesmaximal, characteristic, complemented
14#20274539C211yesmaximal, characteristic, complemented
15C53×#1880C211yesmaximal, characteristic, complemented
16C22×#11719924C2211yescharacteristic
17C2×#13133213C2211yescharacteristic
18C2×Q8×Dic53C2211yescharacteristic
19C2×Q8×Dic53C2211yescharacteristic
20C2×D4×Dic53C2211yescharacteristic
21C2×#13133179C2211yescharacteristic
22C2×#13133177—21no—
23C2×#13133177—21no—
24#16810821C418yescomplemented
25#16810726—24no—
26#16810724—24no—
27C2×#13133151C2211yescharacteristic
28C2×#13133150C2211yescharacteristic
29C2×#13133146C2211yescharacteristic
30C2×#13133146C2211yescharacteristic
31C2×#13133141C2211yescharacteristic
32C2×#13133139C2211yescharacteristic
33C2×#13133139C2211yescharacteristic
34C2×#13133138C2211yescharacteristic
35C2×#13133138C2211yescharacteristic
36C2×#13133137C2211yescharacteristic
37C2×#13133127C2211yescharacteristic
38C2×#13133127C2211yescharacteristic
39#16810525C2211yescharacteristic
40#16810523—21no—
41#16810523—21no—
42#16810492C2211yescharacteristic
43C4⋊C4×Dic53—21no—
44C4⋊C4×Dic53—21no—
45C4⋊C4×Dic53C2211yescharacteristic
46C4⋊C4×Dic53C2211yescharacteristic
47C4×C4⋊Dic53—21no—
48C4×C4⋊Dic53C2211yescharacteristic
49C42×Dic53—21no—
50C42×Dic53C2211yescharacteristic
51#16810386C2211yescharacteristic
52#16810385C2211yescharacteristic
53#16810385C2211yescharacteristic
54#16810378C2211yescharacteristic
55C22×SD16×C53C2211yescharacteristic
56C2×C4×Q8×C53C2211yescharacteristic
57C2×#103×C53C2211yescharacteristic
58C2×#102×C53C2211yescharacteristic
59C53×#390C2211yescharacteristic
60C53×#340C2211yescharacteristic
61C53×#336C2211yescharacteristic
62C22×D212C2311yescharacteristic
63C22×C22⋊D53—21no—
64C22×C22⋊D53—21no—
65C23×Dic53—21no—
66C22×C4×D53—21no—
67C2×#11719924—22no—
68C2×#11719924—22no—
69C2×#11719924C2×C414yescomplemented
70C22×#88322C2311yescharacteristic
71C22×#88322C2311yescharacteristic
72#13133213—22no—
73#13133213C2×C414yes—
74Q8×Dic53—22no—
75Q8×Dic53—22no—
76Q8×Dic53C2×C414yescomplemented
77Q8×Dic53D414yescomplemented
78D4×Dic53—22no—
79D4×Dic53—22no—
80#13133179—22no—
81#13133179—22no—
82#13133177—44no—
83#13133177—44no—
84C2×C4⋊Dic53—21no—
85C2×C4⋊Dic53—21no—
86C2×C4⋊Dic53C2311yescharacteristic
87C2×C4⋊Dic53C2311yescharacteristic
88C2×C4⋊Dic53C2311yescharacteristic
89C2×#11719919—21no—
90C2×#11719919—21no—
91C2×C22⋊Dic53—21no—
92C2×#11719921—21no—
93C2×#11719921—21no—
94C2×#11719921—21no—
95C2×C4×Dic53—21no—
96C2×C4×Dic53—21no—
97C2×C4×Dic53—21no—
98C2×C4×Dic53—21no—
99C2×C4×Dic53—21no—
100C2×C4×Dic53D411yescharacteristic
101C2×C4×Dic53D411yescharacteristic
102C2×C4×Dic53D411yescharacteristic
103C2×C4×Dic53D411yescharacteristic
104C2×C4×Dic53C2311yescharacteristic
105C2×C4×Dic53C2311yescharacteristic
106#13133151—22no—
107#13133150—22no—
108#13133146—22no—
109#13133146C2×C414yescomplemented
110#13133141—22no—
111#13133139—22no—
112#13133139C2×C414yescomplemented
113#13133138—22no—
114#13133138C2×C414yescomplemented
115#13133137—22no—
116#13133127—22no—
117#13133127—22no—
118#13133124—21no—
119#13133124—21no—
120#13133124—21no—
121C22×Q8×C53C2311yescharacteristic
122C22×D4×C53C2311yescharacteristic
123C2×SD16×C53—22no—
124C2×SD16×C53—22no—
125C2×SD16×C53C2×C414yescomplemented
126C22×C8×C53C2311yescharacteristic
127C22×C8×C53C2311yescharacteristic
128C4×Q8×C53—22no—
129C4×Q8×C53—22no—
130C2×C4⋊C4×C53—21no—
131C2×C4⋊C4×C53C2311yescharacteristic
132C2×C4⋊C4×C53C2311yescharacteristic
133C2×C22⋊C4×C53—21no—
134C2×C22⋊C4×C53—21no—
135C2×C42×C53—21no—
136C2×C42×C53C2311yescharacteristic
137#103×C53—22no—
138#102×C53—22no—
139C24×C53—21no—
140C23×D53—21no—
141C2×Q8×C53—21no—
142C2×Q8×C53—21no—
143C2×Q8×C53—21no—
144C2×Q8×C53C22×C412yes—
145C2×Q8×C53C2×D412yes—
146C2×Q8×C53#4112yes—
147C2×D4×C53—21no—
148C2×D4×C53—21no—
149C2×D4×C53—21no—
150C2×D4×C53—21no—
151C2×D4×C53—21no—
152C2×D4×C53C22×C412yes—
153C22×C4×C53—21no—
154C22×C4×C53—21no—
155C22×C4×C53—21no—
156C22×C4×C53C2×D411yescharacteristic
157C22×C4×C53C2×D411yescharacteristic
158C22×C4×C53C2411yescharacteristic
159C2×C22⋊D53—24no—
160C2×C22⋊D53—24no—
161C2×C22⋊D53—42no—
162C2×C22⋊D53—42no—
163C2×C22⋊D53—42no—
164C2×C22⋊D53—42no—
165C22×Dic53—21no—
166C22×Dic53—21no—
167C22×Dic53—21no—
168C22×Dic53—42no—
169C22×Dic53—42no—
170C22×Dic53—42no—
171C22×Dic53C2×D411yescharacteristic
172C22×Dic53C2×D411yescharacteristic
173C22×Dic53C2×D411yescharacteristic
174C22×Dic53C2×D411yescharacteristic
175C2×D212—21no—
176C2×D212—21no—
177C2×D212—21no—
178C2×D212—21no—
179C2×D212—21no—
180C2×D212C22×C412yes—
181C2×C4×D53—42no—
182C2×C4×D53—42no—
183C2×C4×D53—42no—
184SD16×C53—28no—
185C2×C8×C53—21no—
186C2×C8×C53—21no—
187C2×C8×C53—21no—
188C2×C8×C53—21no—
189C2×C8×C53—21no—
190C2×C8×C53C22×C412yes—
191C4⋊C4×C53—24no—
192C4⋊C4×C53—21no—
193C4⋊C4×C53—21no—
194C4⋊C4×C53—21no—
195C4⋊C4×C53#4112yes—
196C22⋊C4×C53—42no—
197C22⋊C4×C53—42no—
198C42×C53—24no—
199C42×C53—21no—
200C42×C53—21no—
201C22⋊Dic53—42no—
202#11719924—28no—
203#11719921—42no—
204#11719921—42no—
205#11719921—42no—
206C4⋊Dic53—21no—
207C4⋊Dic53—21no—
208C4⋊Dic53—24no—
209C4⋊Dic53—24no—
210C4⋊Dic53—21no—
211C4⋊Dic53—21no—
212C4⋊Dic53C22×C412yes—
213C4⋊Dic53C2×D412yes—
214#11719919—42no—
215#11719919—42no—
216C4×Dic53—22no—
217C4×Dic53—24no—
218C4×Dic53—24no—
219C4×Dic53—22no—
220C4×Dic53—22no—
221C4×Dic53—41no—
222C4×Dic53—42no—
223C4×Dic53—42no—
224C4×Dic53—42no—
225C4×Dic53C22×C412yes—
226C4×Dic53C2×D412yes—
227C4×Dic53#4112yes—
228C4×Dic53#4112yes—
229C2×#88322—21no—
230C2×#88322—21no—
231C2×#88322—21no—
232C2×#88322—21no—
233C2×#88322—21no—
234C2×#88322C22×C412yes—
235C23×C53—22no—
236C23×C53—41no—
237C23×C53—41no—
238C23×C53—41no—
239C23×C53—41no—
240C23×C53—41no—
241C23×C53—41no—
242C23×C53C22×D411yescharacteristic
243C22×D53—22no—
244C22×D53—41no—
245C22×D53—41no—
246C22×D53—41no—
247C22×D53—41no—
248C22×D53—41no—
249C22×D53—41no—
250Q8×C53—22no—
251Q8×C53—22no—
252Q8×C53—22no—
253Q8×C53C4×D414yescomplemented
254D4×C53—22no—
255D4×C53—22no—
256D4×C53—41no—
257D4×C53—41no—
258C2×C4×C53—22no—
259C2×C4×C53—22no—
260C2×C4×C53—22no—
261C2×C4×C53—21no—
262C2×C4×C53—21no—
263C2×C4×C53—22no—
264C2×C4×C53—21no—
265C2×C4×C53—21no—
266C2×C4×C53—21no—
267C2×C4×C53—41no—
268C2×C4×C53—41no—
269C2×C4×C53—41no—
270C2×C4×C53—41no—
271C2×C4×C53—41no—
272C2×C4×C53AGL(1,ℤ/8)12yes—
273C2×C4×C53C23×C411yescharacteristic
274C2×C4×C53C22×D411yescharacteristic
275C2×C4×C53C2×#4111yescharacteristic
276C2×C4×C53C2×#4111yescharacteristic
277C2×C4×C53C2×#4111yescharacteristic
278C2×C4×C53C2×#4111yescharacteristic
279C22⋊D53—48no—
280C22⋊D53—48no—
281C2×Dic53—21no—
282C2×Dic53—21no—
283C2×Dic53—21no—
284C2×Dic53—21no—
285C2×Dic53—21no—
286C2×Dic53—21no—
287C2×Dic53—22no—
288C2×Dic53—22no—
289C2×Dic53—41no—
290C2×Dic53—41no—
291C2×Dic53—41no—
292C2×Dic53—41no—
293C2×Dic53—41no—
294C2×Dic53—41no—
295C2×Dic53—41no—
296C2×Dic53—84no—
297C2×Dic53C4×D412yes—
298C2×Dic53C4×D412yes—
299C2×Dic53#12112yes—
300C2×Dic53#12112yes—
301C2×Dic53AGL(1,ℤ/8)12yes—
302C2×Dic53#13712yes—
303D212—22no—
304D212—22no—
305D212—41no—
306D212—41no—
307C4×D53—84no—
308C8×C53—22no—
309C8×C53—41no—
310#88322—22no—
311#88322—41no—
312#21505—531nomaximal, Sylow
313C22×C53—42no—
314C22×C53—42no—
315C22×C53—42no—
316C22×C53—81no—
317C22×C53—81no—
318C22×C53—81no—
319C22×C53—81no—
320C22×C53C2×C4×D411yescharacteristic
321C22×C53C2×#12111yescharacteristic
322C22×C53#52511yescharacteristic
323C22×C53C2×AGL(1,ℤ/8)11yescharacteristic
324C22×C53C2×AGL(1,ℤ/8)11yescharacteristic
325C22×C53C2×#13711yescharacteristic
326C22×C53#57511yescharacteristic
327C2×D53—42no—
328C2×D53—42no—
329C2×D53—42no—
330C2×D53—81no—
331C2×D53—81no—
332C2×D53—81no—
333C2×D53—81no—
334C4×C53—22no—
335C4×C53—24no—
336C4×C53—41no—
337C4×C53—42no—
338C4×C53—81no—
339C4×C53C2×C4×D411yescharacteristic
340C4×C53C4×#4111yescharacteristic
341C4×C53#52911yescharacteristic
342C4×C53#53211yescharacteristic
343Dic53—22no—
344Dic53—22no—
345Dic53—22no—
346Dic53—42no—
347Dic53—42no—
348Dic53—81no—
349Dic53#44014yescomplemented
350C2×#460—531no—
351C2×#440—531no—
352C2×#440—531no—
353C4×#127—531no—
354C42×Q8—531no—
355#1982—531no—
356#1947—531no—
357#1925—531no—
358#1925—531no—
359#1880—531no—
360#1880D5311yescharacteristic, complemented
361#1803—531no—
362#1767—531no—
363#1762—531no—
364#1762—531no—
365C2×C53—82no—
366C2×C53C4×#12111yescharacteristic
367C2×C53C2×#44011yescharacteristic
368C2×C53C4×AGL(1,ℤ/8)11yescharacteristic
369C2×C53#303711yescharacteristic
370C2×C53#303811yescharacteristic
371C2×C53#311211yescharacteristic
372C2×C53#311511yescharacteristic
373D53—82no—
374C22×SD16—531no—
375C22×SD16C2×D5311yescharacteristic
376C2×#127—531no—
377C2×C4×Q8—531no—
378C2×C4×Q8—531no—
379C2×C4×Q8C2×D5311yescharacteristic
380C2×C4×D4—531no—
381C2×C4×D4—531no—
382C2×C4×D4—1061no—
383C2×C4×D4—1061no—
384#460—538no—
385#440—1064no—
386#440—1064no—
387C2×#107—531no—
388C2×#107—531no—
389C2×C4⋊C8—531no—
390C2×C4⋊C8—531no—
391C2×#103—531no—
392C2×#103C2×D5311yescharacteristic
393C2×#102—531no—
394C2×#102—531no—
395C2×#102—531no—
396C2×#102—531no—
397C2×#102—531no—
398C2×#102C2×D5311yescharacteristic
399C2×#97—531no—
400C2×#97—531no—
401#390—531no—
402#390—1061no—
403#390—1061no—
404#390C2×D5311yescharacteristic
405#384—531no—
406C4×C4⋊C4—531no—
407C4×C4⋊C4—531no—
408C4×C4⋊C4—531no—
409C4×C4⋊C4—1061no—
410C4×C4⋊C4—1061no—
411C4×C4⋊C4—1061no—
412C43—531no—
413C43—1061no—
414#340—531no—
415#340—531no—
416#340—531no—
417#340C2×D5311yescharacteristic
418#336—531no—
419#336C2×D5311yescharacteristic
420C53#2150511yescharacteristic, complemented, Sylow
421C22×Q8C22×D5311yescharacteristic
422C22×D4—531no—
423C22×D4—1061no—
424C22×D4—1061no—
425C22×D4C22×D5311yescharacteristic
426C23×C4—1061no—
427C23×C4—1061no—
428C2×SD16—22no—
429C2×SD16—22no—
430C2×SD16—534no—
431C2×SD16—1062no—
432C2×SD16—1062no—
433C2×SD16C4×D5314yescomplemented
434C22×C8—531no—
435C22×C8—531no—
436C22×C8C22×D5311yescharacteristic
437C22×C8C22×D5311yescharacteristic
438#127—534no—
439#127—1062no—
440C4×Q8—22no—
441C4×Q8—22no—
442C4×Q8—534no—
443C4×Q8—534no—
444C4×Q8—1062no—
445C4×Q8—1062no—
446C4×D4—1062no—
447C4×D4—1062no—
448C4×D4—1062no—
449C4×D4—1062no—
450C4×D4—2124no—
451C4×D4—2124no—
452C2×C4⋊C4—21no—
453C2×C4⋊C4—531no—
454C2×C4⋊C4—531no—
455C2×C4⋊C4—531no—
456C2×C4⋊C4—1061no—
457C2×C4⋊C4—1061no—
458C2×C4⋊C4—1061no—
459C2×C4⋊C4—1061no—
460C2×C4⋊C4C22×D5311yescharacteristic
461C2×C4⋊C4C22×D5311yescharacteristic
462C2×C22⋊C4—21no—
463C2×C22⋊C4—21no—
464C2×C22⋊C4—1061no—
465C2×C22⋊C4—1061no—
466C2×C22⋊C4—1061no—
467C2×C22⋊C4—1061no—
468C2×C42—21no—
469C2×C42—531no—
470C2×C42—531no—
471C2×C42—531no—
472C2×C42—531no—
473C2×C42—531no—
474C2×C42—531no—
475C2×C42—1061no—
476C2×C42—1061no—
477C2×C42—1061no—
478C2×C42—1061no—
479C2×C42—1061no—
480C2×C42C22×D5311yescharacteristic
481#107—1062no—
482#107—1062no—
483C4⋊C8—534no—
484C4⋊C8—1062no—
485#103—22no—
486#103—1062no—
487#102—22no—
488#102—534no—
489#102—534no—
490#102—1062no—
491#102—1062no—
492#102—1062no—
493#97—1062no—
494#97—1062no—
495#95—1061no—
496#95—1061no—
497#95—1061no—
498C24—21no—
499C24—1061no—
500C2×Q8—21no—
501C2×Q8—21no—
502C2×Q8—21no—
503C2×Q8C2×C4×D5312yes—
504C2×Q8D4×D5312yes—
505C2×Q8#1171994712yes—
506C2×D4—21no—
507C2×D4—21no—
508C2×D4—21no—
509C2×D4—21no—
510C2×D4—21no—
511C2×D4—532no—
512C2×D4—1064no—
513C2×D4—1064no—
514C2×D4—1061no—
515C2×D4—1061no—
516C2×D4—1061no—
517C2×D4—1061no—
518C2×D4—1061no—
519C2×D4—2122no—
520C2×D4—2122no—
521C2×D4—2122no—
522C2×D4—2122no—
523C2×D4C2×C4×D5312yes—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—531no—
528C22×C4—531no—
529C22×C4—531no—
530C22×C4—531no—
531C22×C4—1061no—
532C22×C4—1061no—
533C22×C4—1061no—
534C22×C4—2122no—
535C22×C4—2122no—
536C22×C4—2122no—
537C22×C4—2122no—
538C22×C4—2122no—
539C22×C4—2122no—
540C22×C4D4×D5311yescharacteristic
541C22×C4D4×D5311yescharacteristic
542C22×C4C23×D5311yescharacteristic
543SD16—28no—
544SD16—1068no—
545C2×C8—21no—
546C2×C8—21no—
547C2×C8—21no—
548C2×C8—21no—
549C2×C8—21no—
550C2×C8—532no—
551C2×C8—1061no—
552C2×C8—1061no—
553C2×C8—1061no—
554C2×C8—1061no—
555C2×C8—1061no—
556C2×C8C2×C4×D5312yes—
557C4⋊C4—24no—
558C4⋊C4—21no—
559C4⋊C4—21no—
560C4⋊C4—21no—
561C4⋊C4—532no—
562C4⋊C4—532no—
563C4⋊C4—1064no—
564C4⋊C4—1064no—
565C4⋊C4—1061no—
566C4⋊C4—1061no—
567C4⋊C4—1061no—
568C4⋊C4—1061no—
569C4⋊C4—2122no—
570C4⋊C4—2122no—
571C4⋊C4#1171994712yes—
572C22⋊C4—42no—
573C22⋊C4—42no—
574C22⋊C4—2122no—
575C22⋊C4—2122no—
576C22⋊C4—2122no—
577C22⋊C4—2122no—
578C42—24no—
579C42—21no—
580C42—21no—
581C42—532no—
582C42—532no—
583C42—532no—
584C42—532no—
585C42—1062no—
586C42—1062no—
587C42—1064no—
588C42—1064no—
589C42—1062no—
590C42—2121no—
591C42—2122no—
592C42—2122no—
593C42—2122no—
594C23—22no—
595C23—41no—
596C23—41no—
597C23—41no—
598C23—41no—
599C23—41no—
600C23—41no—
601C23—1062no—
602C23—2121no—
603C23—2121no—
604C23—2121no—
605C23—2121no—
606C23—2121no—
607C23—2121no—
608C23C2×D4×D5311yescharacteristic
609Q8—22no—
610Q8—22no—
611Q8—22no—
612Q8#1313317714yescomplemented
613D4—22no—
614D4—22no—
615D4—41no—
616D4—41no—
617D4—1062no—
618D4—1062no—
619D4—2128no—
620D4—2128no—
621D4—2121no—
622D4—2121no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—21no—
626C2×C4—22no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—22no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—532no—
638C2×C4—532no—
639C2×C4—532no—
640C2×C4—532no—
641C2×C4—532no—
642C2×C4—532no—
643C2×C4—1061no—
644C2×C4—1061no—
645C2×C4—1061no—
646C2×C4—1061no—
647C2×C4—1061no—
648C2×C4—1061no—
649C2×C4—1062no—
650C2×C4—1062no—
651C2×C4—4244no—
652C2×C4—4244no—
653C2×C4—2121no—
654C2×C4—2121no—
655C2×C4—2121no—
656C2×C4—2121no—
657C2×C4—2121no—
658C2×C4—2121no—
659C2×C4—2121no—
660C2×C4#1313324412yes—
661C2×C4C22×C4×D5311yescharacteristic
662C2×C4C2×D4×D5311yescharacteristic
663C2×C4#41×D5311yescharacteristic
664C2×C4#41×D5311yescharacteristic
665C2×C4C2×#1171994711yescharacteristic
666C2×C4C2×#1171994711yescharacteristic
667C8—22no—
668C8—41no—
669C8—1062no—
670C8—2121no—
671C22—42no—
672C22—42no—
673C22—42no—
674C22—81no—
675C22—81no—
676C22—81no—
677C22—81no—
678C22—4241no—
679C22—4241no—
680C22—4241no—
681C22—4241no—
682C22—2122no—
683C22—2122no—
684C22—2122no—
685C22C4×D4×D5311yescharacteristic
686C22#121×D5311yescharacteristic
687C22#1681112911yescharacteristic
688C22AGL(1,ℤ/8)×D5311yescharacteristic
689C22C2×#1313324411yescharacteristic
690C22#137×D5311yescharacteristic
691C22#1681142011yescharacteristic
692C4—22no—
693C4—24no—
694C4—41no—
695C4—42no—
696C4—81no—
697C4—534no—
698C4—1062no—
699C4—1062no—
700C4—1062no—
701C4—4241no—
702C4—2122no—
703C4—2122no—
704C4C2×#1313317711yescharacteristic
705C4C4×#1171994711yescharacteristic
706C4#1681115011yescharacteristic
707C4#1681116811yescharacteristic
708C2—82no—
709C2—4242no—
710C2#2027722511yescharacteristic
711C2#440×D5311yescharacteristic
712C2C4×#1313324411yescharacteristic
713C2#2028418511yescharacteristic
714C2#2028419211yescharacteristic
715C2#2028483211yescharacteristic
716C2#2028485911yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutatorC2×C4×C53C23×C4
FrattiniC22×C4C23×D53
FittingC53×#1880C2
socleC23×C53C22×D4
prime radicalC2×#13133213C22
cosocleC22×C4×C53C24
hypercenter#1880D53
hypocenterC53#21505
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1880

Complements

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

NH ≅ G/Ntype
2. C2×#16810726C2semidirect
3. C2×#16810724C2semidirect
5. C4×Q8×Dic53C2semidirect
7. #20275472C2semidirect
8. #20275336C2semidirect
9. #20275332C2semidirect
10. #20275070C2semidirect
11. #20274718C2semidirect
12. #20274567C2semidirect
13. #20274542C2semidirect
14. #20274539C2semidirect
15. C53×#1880C2semidirect
24. #16810821C4semidirect
69. C2×#11719924C2×C4semidirect
76. Q8×Dic53C2×C4semidirect
77. Q8×Dic53D4semidirect
109. #13133146C2×C4semidirect
112. #13133139C2×C4semidirect
114. #13133138C2×C4semidirect
125. C2×SD16×C53C2×C4semidirect
253. Q8×C53C4×D4semidirect
349. Dic53#440semidirect
360. #1880D53semidirect
420. C53#21505semidirect
433. C2×SD16C4×D53semidirect
612. Q8#13133177semidirect

Maximal subgroups

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

subgroupindex
C2×#168108212
C2×#168107262
C2×#168107242
#202772792
C4×Q8×Dic532
#202756402
#202754722
#202753362
#202753322
#202750702
#202747182
#202745672
#202745422
#202745392
C53×#18802
#2150553