Finite Group Databasebeta

← #27432729

Subgroups — #27432729

Order 13568.

988 conjugacy classes of subgroups.

The subgroup lattice has 728 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16810936C211yesmaximal, characteristic, complemented
2C2×D4×#88322C211yesmaximal, characteristic, complemented
3#20278155C211yesmaximal, characteristic
4#20276206C211yesmaximal, characteristic, complemented
5#20276141C211yesmaximal, characteristic, complemented
6#20276100C211yesmaximal, characteristic, complemented
7#20275897C211yesmaximal, characteristic, complemented
8#20275445C211yesmaximal, characteristic, complemented
9#20275397C211yesmaximal, characteristic, complemented
10#20275141C211yesmaximal, characteristic, complemented
11#20275141C211yesmaximal, characteristic, complemented
12#20274902C211yesmaximal, characteristic, complemented
13#20274742C211yesmaximal, characteristic, complemented
14C2×#16810385C211yesmaximal, characteristic, complemented
15C53×#2486C211yesmaximal, characteristic, complemented
16C23×#88322C2211yescharacteristic
17C23×#88322C2211yescharacteristic
18C2×#13133191C2211yescharacteristic
19C2×#13133191C2211yescharacteristic
20C2×#13133189—21no—
21C22×C4⋊Dic53C2211yescharacteristic
22#16810936—24no—
23D4×#88322—24no—
24C2×#13133150C2211yescharacteristic
25C2×#13133150C2211yescharacteristic
26C2×#13133150C2211yescharacteristic
27C2×#13133150C2211yescharacteristic
28C2×C4⋊#88322C2211yescharacteristic
29C2×#13133137C2211yescharacteristic
30C2×#13133137C2211yescharacteristic
31C2×#13133137C2211yescharacteristic
32C2×#13133137C2211yescharacteristic
33C2×C22⋊#88322C2211yescharacteristic
34C2×C22⋊#88322C2211yescharacteristic
35C2×C4×#88322C2211yescharacteristic
36#16810545—21no—
37#16810539—21no—
38#16810525C2211yescharacteristic
39#16810521C2211yescharacteristic
40#16810500—21no—
41#16810483C2211yescharacteristic
42#16810385C2211yescharacteristic
43#16810385C2211yescharacteristic
44#16810385C2211yescharacteristic
45#16810385C2211yescharacteristic
46#16810385C2211yescharacteristic
47#16810385C2211yescharacteristic
48#16810385C2211yescharacteristic
49#16810385C2211yescharacteristic
50C2×#123×C53—21no—
51C2×C4×D4×C53C2211yescharacteristic
52C22×C4⋊C4×C53C2211yescharacteristic
53C53×#398—21no—
54C53×#397—21no—
55C53×#389C2211yescharacteristic
56C53×#389C2211yescharacteristic
57C53×#381—21no—
58C53×#380C2211yescharacteristic
59C53×#380C2211yescharacteristic
60C53×#380C2211yescharacteristic
61C22×D212C2311yescharacteristic
62C22×C22⋊D53—21no—
63C22×C22⋊D53—21no—
64C23×Dic53—21no—
65C22×#88322—22no—
66C22×#88322—22no—
67C22×#88322—22no—
68C22×#88322—22no—
69C22×#88322—41no—
70C22×#88322—41no—
71C22×#88322C2311yescharacteristic
72C22×#88322C2311yescharacteristic
73C22×#88322C2311yescharacteristic
74C22×#88322C2311yescharacteristic
75#13133191—22no—
76#13133191—22no—
77#13133191—22no—
78#13133191—41no—
79#13133189—44no—
80C2×C4⋊Dic53—21no—
81C2×C4⋊Dic53—22no—
82C2×C4⋊Dic53—41no—
83C2×C4⋊Dic53C2311yescharacteristic
84C2×C4⋊Dic53C2311yescharacteristic
85C2×C4⋊Dic53C2311yescharacteristic
86C2×#11719919—21no—
87C2×C22⋊Dic53—21no—
88C2×#11719921—21no—
89C2×#11719921—21no—
90C2×#11719921—21no—
91C2×#11719921—21no—
92#13133150—22no—
93#13133150—22no—
94#13133150—22no—
95#13133150—41no—
96C4⋊#88322—22no—
97#13133137—22no—
98#13133137—22no—
99#13133137—22no—
100#13133137—41no—
101C22⋊#88322—22no—
102C22⋊#88322D414yescomplemented
103C4×#88322—22no—
104#13133124—21no—
105#13133124—21no—
106C22×D4×C53D411yescharacteristic
107C23×C4×C53—21no—
108C23×C4×C53C2311yescharacteristic
109C23×C4×C53C2311yescharacteristic
110#123×C53—44no—
111C4×D4×C53—22no—
112C4×D4×C53—22no—
113C2×C4⋊C4×C53—21no—
114C2×C4⋊C4×C53—21no—
115C2×C4⋊C4×C53—21no—
116C2×C4⋊C4×C53—22no—
117C2×C4⋊C4×C53—22no—
118C2×C4⋊C4×C53D411yescharacteristic
119C2×C4⋊C4×C53C2311yescharacteristic
120C2×C4⋊C4×C53C2311yescharacteristic
121C2×C4⋊C4×C53C2311yescharacteristic
122C2×C4⋊C4×C53C2311yescharacteristic
123C2×C22⋊C4×C53—21no—
124C2×C22⋊C4×C53—21no—
125C2×C22⋊C4×C53—21no—
126C2×C22⋊C4×C53D411yescharacteristic
127C2×C22⋊C4×C53D411yescharacteristic
128C2×C42×C53C2311yescharacteristic
129#95×C53—21no—
130#95×C53—21no—
131#95×C53—21no—
132#95×C53—21no—
133#95×C53—21no—
134C24×C53C2×D411yescharacteristic
135C24×C53C2×D411yescharacteristic
136C23×D53—21no—
137C2×D4×C53—22no—
138C2×D4×C53—22no—
139C2×D4×C53D814yes—
140C22×C4×C53—21no—
141C22×C4×C53—21no—
142C22×C4×C53—21no—
143C22×C4×C53—21no—
144C22×C4×C53—21no—
145C22×C4×C53—21no—
146C22×C4×C53—21no—
147C22×C4×C53—21no—
148C22×C4×C53—21no—
149C22×C4×C53—21no—
150C22×C4×C53—21no—
151C22×C4×C53—21no—
152C22×C4×C53—21no—
153C22×C4×C53—21no—
154C22×C4×C53—42no—
155C22×C4×C53—42no—
156C22×C4×C53—42no—
157C22×C4×C53C2×D411yescharacteristic
158C22×C4×C53C2×D411yescharacteristic
159C22×C4×C53C2×D411yescharacteristic
160C22×C4×C53C2×D412yes—
161C22×C4×C53C2×D411yescharacteristic
162C22×C4×C53#4112yes—
163C22×C4×C53C2411yescharacteristic
164C2×C22⋊D53—42no—
165C2×C22⋊D53—42no—
166C2×C22⋊D53—42no—
167C2×C22⋊D53—42no—
168C2×C22⋊D53—42no—
169C2×C22⋊D53—81no—
170C22×Dic53—21no—
171C22×Dic53—21no—
172C22×Dic53—21no—
173C22×Dic53—42no—
174C22×Dic53—42no—
175C22×Dic53—81no—
176C2×D212—21no—
177C2×D212—21no—
178C2×D212—21no—
179C2×D212—21no—
180C2×D212—21no—
181C2×D212—21no—
182C4⋊C4×C53—22no—
183C4⋊C4×C53—21no—
184C4⋊C4×C53—21no—
185C4⋊C4×C53—21no—
186C4⋊C4×C53—21no—
187C4⋊C4×C53—21no—
188C4⋊C4×C53—21no—
189C4⋊C4×C53—21no—
190C4⋊C4×C53—21no—
191C4⋊C4×C53—42no—
192C4⋊C4×C53—42no—
193C4⋊C4×C53—42no—
194C22⋊C4×C53—22no—
195C22⋊C4×C53—22no—
196C22⋊C4×C53—42no—
197C22⋊C4×C53—42no—
198C22⋊C4×C53—42no—
199C42×C53—21no—
200C42×C53—21no—
201C22⋊Dic53—42no—
202#11719921—42no—
203#11719921—42no—
204#11719921—42no—
205#11719921—81no—
206C4⋊Dic53—21no—
207C4⋊Dic53—21no—
208C4⋊Dic53—21no—
209C4⋊Dic53—21no—
210C4⋊Dic53—21no—
211C4⋊Dic53—42no—
212C4⋊Dic53#4112yes—
213#11719919—42no—
214C2×#88322—21no—
215C2×#88322—21no—
216C2×#88322—21no—
217C2×#88322—21no—
218C2×#88322—21no—
219C2×#88322—21no—
220C2×#88322—21no—
221C2×#88322—21no—
222C2×#88322—21no—
223C2×#88322—44no—
224C2×#88322—44no—
225C2×#88322C2×D412yes—
226C2×#88322C2×D412yes—
227C2×#88322#4112yes—
228C23×C53—21no—
229C23×C53—21no—
230C23×C53—21no—
231C23×C53—21no—
232C23×C53—21no—
233C23×C53—21no—
234C23×C53—21no—
235C23×C53—21no—
236C23×C53—21no—
237C23×C53—21no—
238C23×C53#12112yes—
239C23×C53C2×D812yes—
240C23×C53C2×D812yes—
241C23×C53#13512yes—
242C23×C53C22×D411yescharacteristic
243C22×D53—41no—
244C22×D53—41no—
245C22×D53—41no—
246C22×D53—41no—
247C22×D53—41no—
248C22×D53—41no—
249C22×D53—41no—
250D4×C53—28no—
251C2×C4×C53—21no—
252C2×C4×C53—21no—
253C2×C4×C53—21no—
254C2×C4×C53—21no—
255C2×C4×C53—22no—
256C2×C4×C53—22no—
257C2×C4×C53—22no—
258C2×C4×C53—22no—
259C2×C4×C53—21no—
260C2×C4×C53—21no—
261C2×C4×C53—21no—
262C2×C4×C53—21no—
263C2×C4×C53—21no—
264C2×C4×C53—21no—
265C2×C4×C53—41no—
266C2×C4×C53—41no—
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—41no—
274C2×C4×C53—41no—
275C2×C4×C53—41no—
276C2×C4×C53—41no—
277C2×C4×C53—41no—
278C2×C4×C53—41no—
279C2×C4×C53—41no—
280C2×C4×C53—41no—
281C2×C4×C53—84no—
282C2×C4×C53#12112yes—
283C2×C4×C53C2×D812yes—
284C2×C4×C53C22×D411yescharacteristic
285C2×C4×C53C2×#4111yescharacteristic
286C2×C4×C53C2×#4111yescharacteristic
287C2×C4×C53C2×#4111yescharacteristic
288C2×C4×C53H(5,𝔽2)11yescharacteristic
289C2×C4×C532−1+411yescharacteristic
290C22⋊D53—84no—
291C22⋊D53—84no—
292C2×Dic53—22no—
293C2×Dic53—41no—
294C2×Dic53—41no—
295C2×Dic53—41no—
296C2×Dic53—41no—
297C2×Dic53—41no—
298C2×Dic53—41no—
299C2×Dic53—41no—
300C2×Dic53—41no—
301C2×Dic53—84no—
302D212—41no—
303D212—41no—
304D212—41no—
305D212—41no—
306#88322—22no—
307#88322—22no—
308#88322—22no—
309#88322—41no—
310#25232—531nomaximal, Sylow
311C22×C53—22no—
312C22×C53—22no—
313C22×C53—22no—
314C22×C53—22no—
315C22×C53—22no—
316C22×C53—22no—
317C22×C53—22no—
318C22×C53—22no—
319C22×C53—22no—
320C22×C53—41no—
321C22×C53—41no—
322C22×C53—41no—
323C22×C53—41no—
324C22×C53#46614yes—
325C22×C53C2×#12111yescharacteristic
326C22×C53#54611yescharacteristic
327C22×C53#54711yescharacteristic
328C22×C53C22×D811yescharacteristic
329C22×C53C2×#13511yescharacteristic
330C22×C53#57711yescharacteristic
331C22×C53#57811yescharacteristic
332C2×D53—81no—
333C2×D53—81no—
334C2×D53—81no—
335C2×D53—81no—
336C2×D53—81no—
337C2×D53—81no—
338C2×D53—81no—
339C4×C53—22no—
340C4×C53—22no—
341C4×C53—41no—
342C4×C53—41no—
343C4×C53—81no—
344C4×C53—81no—
345C4×C53—81no—
346C4×C53—81no—
347C4×C53#52911yescharacteristic
348C4×C53#53911yescharacteristic
349C4×C53#54611yescharacteristic
350C4×C53#54711yescharacteristic
351Dic53—42no—
352Dic53—81no—
353Dic53—81no—
354C2×#480—531no—
355C2×C8×D4—531no—
356#2486D5311yescharacteristic, complemented
357#2416—531no—
358#2086—531no—
359#2075—531no—
360#2067—531no—
361#2033—531no—
362#1942—531no—
363#1934—531no—
364#1893—531no—
365#1893—531no—
366#1852—531no—
367#1808—531no—
368C2×#340—531no—
369C2×C53—24no—
370C2×C53—42no—
371C2×C53#242511yescharacteristic
372C2×C53C2×#46611yescharacteristic
373C2×C53#306311yescharacteristic
374C2×C53#329411yescharacteristic
375C2×C53#330011yescharacteristic
376C2×C53#333411yescharacteristic
377C2×C53#333711yescharacteristic
378D53—161no—
379C23×C8—531no—
380C23×C8—531no—
381C2×#123—21no—
382C2×#121—531no—
383C2×#121—531no—
384C2×#121—1061no—
385C2×C4×D4C2×D5311yescharacteristic
386C22×C4⋊C4—531no—
387C22×C4⋊C4C2×D5311yescharacteristic
388#480—1064no—
389C8×D4—1064no—
390C2×#107—531no—
391C2×#107—531no—
392C2×#107—531no—
393C2×#107—531no—
394C2×C4⋊C8—531no—
395C2×#102—531no—
396C2×#102—531no—
397C2×#102—531no—
398C2×#102—531no—
399C2×C22⋊C8—531no—
400C2×C22⋊C8—531no—
401C2×C4×C8—531no—
402#398—21no—
403#397—21no—
404#396—1061no—
405#394—1061no—
406#390—531no—
407#389—531no—
408#389C2×D5311yescharacteristic
409#389C2×D5311yescharacteristic
410#386—1061no—
411#381—21no—
412#380—531no—
413#380C2×D5311yescharacteristic
414#380C2×D5311yescharacteristic
415#380C2×D5311yescharacteristic
416#340—531no—
417#340—531no—
418#340—531no—
419#340—531no—
420#340—531no—
421#340—531no—
422#340—531no—
423#340—531no—
424C53#2523211yescharacteristic, complemented, Sylow
425C22×D4—531no—
426C22×D4—1061no—
427C22×D4—1061no—
428C22×D4C22⋊D5311yescharacteristic
429C23×C4—21no—
430C23×C4—1061no—
431C23×C4C22×D5311yescharacteristic
432C23×C4C22×D5311yescharacteristic
433C22×C8—531no—
434C22×C8—531no—
435C22×C8—531no—
436C22×C8—531no—
437C22×C8—1062no—
438C22×C8—1062no—
439C22×C8—1062no—
440C22×C8—1062no—
441C22×C8—2121no—
442C22×C8—2121no—
443#123—44no—
444#121—1062no—
445#121—1062no—
446#121—1062no—
447#121—2121no—
448#121—2124no—
449C4×D4—22no—
450C4×D4—22no—
451C2×C4⋊C4—22no—
452C2×C4⋊C4—22no—
453C2×C4⋊C4—21no—
454C2×C4⋊C4—21no—
455C2×C4⋊C4—21no—
456C2×C4⋊C4—531no—
457C2×C4⋊C4—531no—
458C2×C4⋊C4—531no—
459C2×C4⋊C4—1062no—
460C2×C4⋊C4—1061no—
461C2×C4⋊C4—1061no—
462C2×C4⋊C4—2121no—
463C2×C4⋊C4C22⋊D5311yescharacteristic
464C2×C4⋊C4C22×D5311yescharacteristic
465C2×C4⋊C4C22×D5311yescharacteristic
466C2×C4⋊C4C22×D5311yescharacteristic
467C2×C4⋊C4C22×D5311yescharacteristic
468C2×C22⋊C4—21no—
469C2×C22⋊C4—21no—
470C2×C22⋊C4—21no—
471C2×C22⋊C4—1061no—
472C2×C22⋊C4—1061no—
473C2×C22⋊C4—1061no—
474C2×C22⋊C4—1061no—
475C2×C22⋊C4—1061no—
476C2×C22⋊C4C22⋊D5311yescharacteristic
477C2×C22⋊C4C22⋊D5311yescharacteristic
478C2×C42C22×D5311yescharacteristic
479#107—1062no—
480#107—1062no—
481#107—1062no—
482#107—2121no—
483C4⋊C8—1062no—
484#102—1062no—
485#102—1062no—
486#102—1062no—
487#102—2121no—
488C22⋊C8—534no—
489C22⋊C8—1062no—
490C4×C8—1062no—
491#95—21no—
492#95—21no—
493#95—21no—
494#95—21no—
495#95—21no—
496#95—1061no—
497#95—1061no—
498C24—1061no—
499C24C2×C22⋊D5311yescharacteristic
500C24C2×C22⋊D5311yescharacteristic
501C2×D4—22no—
502C2×D4—22no—
503C2×D4—1061no—
504C2×D4—1061no—
505C2×D4—1061no—
506C2×D4—1061no—
507C2×D4—1061no—
508C2×D4—1061no—
509C2×D4—4241no—
510C2×D4—2122no—
511C2×D4—2122no—
512C2×D4—2122no—
513C2×D4—2122no—
514C2×D4—2122no—
515C2×D4#1171992214yes—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—42no—
531C22×C4—42no—
532C22×C4—42no—
533C22×C4—1061no—
534C22×C4—1061no—
535C22×C4—1061no—
536C22×C4—4241no—
537C22×C4—2122no—
538C22×C4—2122no—
539C22×C4D4×D5312yes—
540C22×C4#1171994712yes—
541C22×C4C2×C22⋊D5311yescharacteristic
542C22×C4C2×C22⋊D5311yescharacteristic
543C22×C4C2×C22⋊D5311yescharacteristic
544C22×C4C2×C22⋊D5311yescharacteristic
545C22×C4C23×D5311yescharacteristic
546C2×C8—532no—
547C2×C8—532no—
548C2×C8—532no—
549C2×C8—1061no—
550C2×C8—1061no—
551C2×C8—1061no—
552C2×C8—1061no—
553C2×C8—1061no—
554C2×C8—1061no—
555C2×C8—1061no—
556C2×C8—1061no—
557C2×C8—1061no—
558C2×C8—2124no—
559C2×C8—2124no—
560C4⋊C4—22no—
561C4⋊C4—21no—
562C4⋊C4—21no—
563C4⋊C4—21no—
564C4⋊C4—21no—
565C4⋊C4—21no—
566C4⋊C4—21no—
567C4⋊C4—21no—
568C4⋊C4—21no—
569C4⋊C4—42no—
570C4⋊C4—42no—
571C4⋊C4—42no—
572C4⋊C4—532no—
573C4⋊C4—1061no—
574C4⋊C4—1061no—
575C4⋊C4—1061no—
576C4⋊C4—1061no—
577C4⋊C4—1061no—
578C4⋊C4—2122no—
579C4⋊C4—2122no—
580C22⋊C4—22no—
581C22⋊C4—22no—
582C22⋊C4—42no—
583C22⋊C4—42no—
584C22⋊C4—42no—
585C22⋊C4—4241no—
586C22⋊C4—2122no—
587C22⋊C4—2122no—
588C22⋊C4—2122no—
589C22⋊C4—2122no—
590C42—21no—
591C42—21no—
592C23—21no—
593C23—21no—
594C23—21no—
595C23—21no—
596C23—21no—
597C23—21no—
598C23—21no—
599C23—21no—
600C23—21no—
601C23—21no—
602C23—2121no—
603C23—2121no—
604C23—2121no—
605C23—2121no—
606C23—2121no—
607C23—2121no—
608C23—2121no—
609C23#1313318912yes—
610C23C2×#1171992212yes—
611C23C2×#1171992212yes—
612C23#1313323712yes—
613C23C22×C22⋊D5311yescharacteristic
614D4—28no—
615D4—4244no—
616D4—4244no—
617D4—2121no—
618D4—2121no—
619D4—2121no—
620D4—2121no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—41no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—84no—
652C2×C4—1062no—
653C2×C4—4244no—
654C2×C4—2121no—
655C2×C4—2121no—
656C2×C4—2121no—
657C2×C4—2121no—
658C2×C4—2121no—
659C2×C4—2121no—
660C2×C4—2121no—
661C2×C4—2121no—
662C2×C4#1313318912yes—
663C2×C4C2×#1171992212yes—
664C2×C4C2×D4×D5311yescharacteristic
665C2×C4#41×D5311yescharacteristic
666C2×C4#41×D5311yescharacteristic
667C2×C4C2×#1171994711yescharacteristic
668C2×C4#1313326311yescharacteristic
669C2×C4#1313326411yescharacteristic
670C8—1062no—
671C8—1062no—
672C8—1062no—
673C8—2121no—
674C22—22no—
675C22—22no—
676C22—22no—
677C22—22no—
678C22—22no—
679C22—22no—
680C22—22no—
681C22—22no—
682C22—22no—
683C22—41no—
684C22—41no—
685C22—41no—
686C22—41no—
687C22—4241no—
688C22—4241no—
689C22—4241no—
690C22—4241no—
691C22—4241no—
692C22—4241no—
693C22—4241no—
694C22#1681085714yes—
695C22C2×#1313318911yescharacteristic
696C22#1681126111yescharacteristic
697C22#1681127211yescharacteristic
698C22C22×#1171992211yescharacteristic
699C22C2×#1313323711yescharacteristic
700C22#1681143111yescharacteristic
701C22#1681143811yescharacteristic
702C4—22no—
703C4—22no—
704C4—41no—
705C4—41no—
706C4—81no—
707C4—81no—
708C4—81no—
709C4—81no—
710C4—4241no—
711C4—4241no—
712C4—2122no—
713C4#1681115011yescharacteristic
714C4#1681121711yescharacteristic
715C4#1681126511yescharacteristic
716C4#1681127111yescharacteristic
717C2—24no—
718C2—42no—
719C2—8481no—
720C2#2027827011yescharacteristic
721C2C2×#1681085711yescharacteristic
722C2#2028440211yescharacteristic
723C2#2028652211yescharacteristic
724C2#2028659611yescharacteristic
725C2#2028705811yescharacteristic
726C2#2028709411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D53
commutator, cosocleC22×C4×C53C24
FrattiniC22×C4C23×D53
FittingC53×#2486C2
socleC23×C53C22×D4
prime radical#20278155C2
hypercenter#2486D53
hypocenterC53#25232
LCSG ▷ C22×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2486

Complements

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

NH ≅ G/Ntype
1. C2×#16810936C2semidirect
2. C2×D4×#88322C2semidirect
4. #20276206C2semidirect
5. #20276141C2semidirect
6. #20276100C2semidirect
7. #20275897C2semidirect
8. #20275445C2semidirect
9. #20275397C2semidirect
10. #20275141C2semidirect
11. #20275141C2semidirect
12. #20274902C2semidirect
13. #20274742C2semidirect
14. C2×#16810385C2semidirect
15. C53×#2486C2semidirect
102. C22⋊#88322D4semidirect
356. #2486D53semidirect
424. C53#25232semidirect

Maximal subgroups

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

subgroupindex
C2×#168109362
C2×D4×#883222
#202781552
#202762062
#202761412
#202761002
#202758972
#202754452
#202753972
#202751412
#202749022
#202747422
C2×#168103852
C53×#24862
#2523253