Finite Group Databasebeta

← #27432719

Subgroups — #27432719

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×#16810937C211yesmaximal, characteristic, complemented
2#20279023C211yesmaximal, characteristic, complemented
3#20278155C211yesmaximal, characteristic
4#20276203C211yesmaximal, characteristic, complemented
5#20276138C211yesmaximal, characteristic, complemented
6#20276102C211yesmaximal, characteristic, complemented
7#20275898C211yesmaximal, characteristic, complemented
8#20275448C211yesmaximal, characteristic, complemented
9#20275398C211yesmaximal, characteristic, complemented
10#20275143C211yesmaximal, characteristic, complemented
11#20275143C211yesmaximal, characteristic, complemented
12#20274905C211yesmaximal, characteristic, complemented
13#20274744C211yesmaximal, characteristic, complemented
14C2×#16810386C211yesmaximal, characteristic, complemented
15C2×C8×D4×C53C211yesmaximal, characteristic, complemented
16C2×#13133198—21no—
17C2×#13133191C2211yescharacteristic
18C2×#13133191C2211yescharacteristic
19C2×#13133189—21no—
20C22×C4⋊Dic53C2211yescharacteristic
21C22×C4⋊Dic53C2211yescharacteristic
22#16810937—24no—
23C2×#13133151C2211yescharacteristic
24C2×#13133151C2211yescharacteristic
25C2×#13133151C2211yescharacteristic
26C2×#13133151C2211yescharacteristic
27C2×#13133139C2211yescharacteristic
28C2×#13133139C2211yescharacteristic
29C2×#13133139C2211yescharacteristic
30C2×#13133139C2211yescharacteristic
31#16810553—21no—
32#16810548—21no—
33#16810545—21no—
34#16810539—21no—
35#16810525C2211yescharacteristic
36#16810521C2211yescharacteristic
37#16810521C2211yescharacteristic
38#16810521C2211yescharacteristic
39#16810500—21no—
40#16810484—21no—
41#16810483C2211yescharacteristic
42#16810483C2211yescharacteristic
43#16810483C2211yescharacteristic
44#16810483C2211yescharacteristic
45#16810386C2211yescharacteristic
46#16810386C2211yescharacteristic
47#16810386C2211yescharacteristic
48#16810386C2211yescharacteristic
49#16810386C2211yescharacteristic
50#16810386C2211yescharacteristic
51#16810386C2211yescharacteristic
52#16810386C2211yescharacteristic
53C23×C8×C53C2211yescharacteristic
54C23×C8×C53C2211yescharacteristic
55C2×C4×D4×C53C2211yescharacteristic
56C8×D4×C53—24no—
57C2×C4⋊C8×C53C2211yescharacteristic
58C2×C22⋊C8×C53C2211yescharacteristic
59C2×C22⋊C8×C53C2211yescharacteristic
60C2×C4×C8×C53C2211yescharacteristic
61C22×D212C2311yescharacteristic
62C22×C22⋊D53—21no—
63C22×C22⋊D53—21no—
64C23×Dic53—21no—
65C23×Dic53—21no—
66#13133198—44no—
67#13133191—22no—
68#13133191—22no—
69#13133191—22no—
70#13133191—41no—
71#13133189—44no—
72C2×C4⋊Dic53—21no—
73C2×C4⋊Dic53—21no—
74C2×C4⋊Dic53—22no—
75C2×C4⋊Dic53—22no—
76C2×C4⋊Dic53—22no—
77C2×C4⋊Dic53—41no—
78C2×C4⋊Dic53C2311yescharacteristic
79C2×C4⋊Dic53C2311yescharacteristic
80C2×C4⋊Dic53C2311yescharacteristic
81C2×C4⋊Dic53C2311yescharacteristic
82C2×C4⋊Dic53C2311yescharacteristic
83C2×C4⋊Dic53C2311yescharacteristic
84C2×C4⋊Dic53C2311yescharacteristic
85C2×#11719919—21no—
86C2×#11719919—21no—
87C2×#11719919—21no—
88C2×C22⋊Dic53—21no—
89C2×C22⋊Dic53—21no—
90C2×C22⋊Dic53—21no—
91C2×C22⋊Dic53—21no—
92C2×#11719921—21no—
93C2×#11719921—21no—
94C2×#11719921—21no—
95C2×#11719921—21no—
96#13133151—22no—
97#13133151—22no—
98#13133151—22no—
99#13133151—41no—
100#13133139—22no—
101#13133139—22no—
102#13133139—22no—
103#13133139—41no—
104#13133124—21no—
105#13133124—21no—
106#13133124—21no—
107#13133124—21no—
108#13133124—21no—
109#13133124—21no—
110#13133124—21no—
111C22×D4×C53D411yescharacteristic
112C23×C4×C53C2311yescharacteristic
113C23×C4×C53C2311yescharacteristic
114C22×C8×C53—22no—
115C22×C8×C53—22no—
116C22×C8×C53—22no—
117C22×C8×C53—22no—
118C22×C8×C53—41no—
119C22×C8×C53—41no—
120C22×C8×C53C2311yescharacteristic
121C22×C8×C53C2311yescharacteristic
122C22×C8×C53C2311yescharacteristic
123C22×C8×C53C2311yescharacteristic
124C4×D4×C53—22no—
125C4×D4×C53—22no—
126C2×C4⋊C4×C53D411yescharacteristic
127C2×C22⋊C4×C53D411yescharacteristic
128C2×C22⋊C4×C53D411yescharacteristic
129C2×C42×C53C2311yescharacteristic
130C4⋊C8×C53—22no—
131C22⋊C8×C53—22no—
132C22⋊C8×C53D414yescomplemented
133C4×C8×C53—22no—
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×C53C2×D411yescharacteristic
151C22×C4×C53C2×D411yescharacteristic
152C22×C4×C53C2×D411yescharacteristic
153C22×C4×C53C2×D412yes—
154C22×C4×C53C2×D411yescharacteristic
155C22×C4×C53#4112yes—
156C22×C4×C53C2411yescharacteristic
157C2×C22⋊D53—42no—
158C2×C22⋊D53—42no—
159C2×C22⋊D53—42no—
160C2×C22⋊D53—42no—
161C2×C22⋊D53—42no—
162C2×C22⋊D53—81no—
163C22×Dic53—21no—
164C22×Dic53—21no—
165C22×Dic53—21no—
166C22×Dic53—21no—
167C22×Dic53—21no—
168C22×Dic53—21no—
169C22×Dic53—21no—
170C22×Dic53—42no—
171C22×Dic53—42no—
172C22×Dic53—42no—
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—
182C2×C8×C53—21no—
183C2×C8×C53—21no—
184C2×C8×C53—21no—
185C2×C8×C53—21no—
186C2×C8×C53—21no—
187C2×C8×C53—21no—
188C2×C8×C53—21no—
189C2×C8×C53—21no—
190C2×C8×C53—21no—
191C2×C8×C53—44no—
192C2×C8×C53—44no—
193C2×C8×C53C2×D412yes—
194C2×C8×C53C2×D412yes—
195C2×C8×C53#4112yes—
196C4⋊C4×C53—22no—
197C22⋊C4×C53—22no—
198C22⋊C4×C53—22no—
199C42×C53—21no—
200C42×C53—21no—
201C22⋊Dic53—42no—
202C22⋊Dic53—42no—
203C22⋊Dic53—42no—
204C22⋊Dic53—42no—
205#11719921—42no—
206#11719921—42no—
207#11719921—42no—
208#11719921—81no—
209C4⋊Dic53—21no—
210C4⋊Dic53—21no—
211C4⋊Dic53—21no—
212C4⋊Dic53—21no—
213C4⋊Dic53—21no—
214C4⋊Dic53—21no—
215C4⋊Dic53—21no—
216C4⋊Dic53—21no—
217C4⋊Dic53—21no—
218C4⋊Dic53—21no—
219C4⋊Dic53—21no—
220C4⋊Dic53—21no—
221C4⋊Dic53—21no—
222C4⋊Dic53—42no—
223C4⋊Dic53—42no—
224C4⋊Dic53#4112yes—
225#11719919—42no—
226#11719919—42no—
227#11719919—42no—
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#12112yes—
270C2×C4×C53C2×D812yes—
271C2×C4×C53C22×D411yescharacteristic
272C2×C4×C53C2×#4111yescharacteristic
273C2×C4×C53C2×#4111yescharacteristic
274C2×C4×C53C2×#4111yescharacteristic
275C2×C4×C53H(5,𝔽2)11yescharacteristic
276C2×C4×C532−1+411yescharacteristic
277C22⋊D53—84no—
278C22⋊D53—84no—
279C2×Dic53—22no—
280C2×Dic53—41no—
281C2×Dic53—41no—
282C2×Dic53—41no—
283C2×Dic53—41no—
284C2×Dic53—41no—
285C2×Dic53—41no—
286C2×Dic53—41no—
287C2×Dic53—41no—
288C2×Dic53—41no—
289C2×Dic53—41no—
290C2×Dic53—41no—
291C2×Dic53—41no—
292C2×Dic53—41no—
293C2×Dic53—41no—
294C2×Dic53—41no—
295C2×Dic53—41no—
296C2×Dic53—41no—
297C2×Dic53—41no—
298C2×Dic53—41no—
299C2×Dic53—41no—
300C2×Dic53—84no—
301C2×Dic53—84no—
302D212—41no—
303D212—41no—
304D212—41no—
305D212—41no—
306C8×C53—22no—
307C8×C53—22no—
308C8×C53—22no—
309C8×C53—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#52911yescharacteristic
344C4×C53#53911yescharacteristic
345C4×C53#54611yescharacteristic
346C4×C53#54711yescharacteristic
347Dic53—42no—
348Dic53—81no—
349Dic53—81no—
350Dic53—81no—
351Dic53—81no—
352Dic53—81no—
353Dic53—81no—
354C2×#480—531no—
355C2×C8×D4D5311yescharacteristic, complemented
356#2486—531no—
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×C8C2×D5311yescharacteristic
380C23×C8C2×D5311yescharacteristic
381C2×#123—1061no—
382C2×#121—531no—
383C2×#121—531no—
384C2×#121—1061no—
385C2×C4×D4C2×D5311yescharacteristic
386C22×C4⋊C4—531no—
387C22×C4⋊C4—531no—
388#480—1064no—
389C8×D4—24no—
390C2×#107—531no—
391C2×#107—531no—
392C2×#107—531no—
393C2×#107—531no—
394C2×C4⋊C8C2×D5311yescharacteristic
395C2×#102—531no—
396C2×#102—531no—
397C2×#102—531no—
398C2×#102—531no—
399C2×C22⋊C8C2×D5311yescharacteristic
400C2×C22⋊C8C2×D5311yescharacteristic
401C2×C4×C8C2×D5311yescharacteristic
402#398—1061no—
403#397—1061no—
404#396—1061no—
405#394—1061no—
406#390—531no—
407#389—531no—
408#389—531no—
409#389—531no—
410#386—1061no—
411#381—1061no—
412#380—531no—
413#380—531no—
414#380—531no—
415#380—531no—
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×D4D21211yescharacteristic
429C23×C4—1061no—
430C23×C4—1061no—
431C23×C4C22×D5311yescharacteristic
432C23×C4C22×D5311yescharacteristic
433C22×C8—22no—
434C22×C8—22no—
435C22×C8—22no—
436C22×C8—22no—
437C22×C8—41no—
438C22×C8—41no—
439C22×C8C22×D5311yescharacteristic
440C22×C8C22×D5311yescharacteristic
441C22×C8C22×D5311yescharacteristic
442C22×C8C22×D5311yescharacteristic
443#123—2124no—
444#121—1062no—
445#121—1062no—
446#121—1062no—
447#121—2121no—
448#121—2124no—
449C4×D4—22no—
450C4×D4—22no—
451C2×C4⋊C4—531no—
452C2×C4⋊C4—531no—
453C2×C4⋊C4—531no—
454C2×C4⋊C4—531no—
455C2×C4⋊C4—531no—
456C2×C4⋊C4—531no—
457C2×C4⋊C4—531no—
458C2×C4⋊C4—1062no—
459C2×C4⋊C4—1062no—
460C2×C4⋊C4—1062no—
461C2×C4⋊C4—1061no—
462C2×C4⋊C4—1061no—
463C2×C4⋊C4—1061no—
464C2×C4⋊C4—1061no—
465C2×C4⋊C4—1061no—
466C2×C4⋊C4—2121no—
467C2×C4⋊C4D21211yescharacteristic
468C2×C22⋊C4—1061no—
469C2×C22⋊C4—1061no—
470C2×C22⋊C4—1061no—
471C2×C22⋊C4—1061no—
472C2×C22⋊C4—1061no—
473C2×C22⋊C4—1061no—
474C2×C22⋊C4—1061no—
475C2×C22⋊C4—1061no—
476C2×C22⋊C4D21211yescharacteristic
477C2×C22⋊C4D21211yescharacteristic
478C2×C42C22×D5311yescharacteristic
479#107—1062no—
480#107—1062no—
481#107—1062no—
482#107—2121no—
483C4⋊C8—22no—
484#102—1062no—
485#102—1062no—
486#102—1062no—
487#102—2121no—
488C22⋊C8—22no—
489C22⋊C8C22⋊D5314yescomplemented
490C4×C8—22no—
491#95—1061no—
492#95—1061no—
493#95—1061no—
494#95—1061no—
495#95—1061no—
496#95—1061no—
497#95—1061no—
498C24—1061no—
499C24C2×D21211yescharacteristic
500C24C2×D21211yescharacteristic
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×D4D42414yes—
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—1061no—
527C22×C4—1061no—
528C22×C4—1061no—
529C22×C4—1061no—
530C22×C4—1061no—
531C22×C4—1061no—
532C22×C4—1061no—
533C22×C4—4241no—
534C22×C4—2122no—
535C22×C4—2122no—
536C22×C4—2122no—
537C22×C4—2122no—
538C22×C4—2122no—
539C22×C4C2×D21211yescharacteristic
540C22×C4C2×D21211yescharacteristic
541C22×C4C2×D21211yescharacteristic
542C22×C4C2×D21211yescharacteristic
543C22×C4#1171994512yes—
544C22×C4C2×C22⋊D5312yes—
545C22×C4C23×D5311yescharacteristic
546C2×C8—21no—
547C2×C8—21no—
548C2×C8—21no—
549C2×C8—21no—
550C2×C8—21no—
551C2×C8—21no—
552C2×C8—21no—
553C2×C8—21no—
554C2×C8—21no—
555C2×C8—44no—
556C2×C8—44no—
557C2×C8#1171994712yes—
558C2×C8C2×C22⋊D5312yes—
559C2×C8C2×C22⋊D5312yes—
560C4⋊C4—22no—
561C4⋊C4—532no—
562C4⋊C4—1061no—
563C4⋊C4—1061no—
564C4⋊C4—1061no—
565C4⋊C4—1061no—
566C4⋊C4—1061no—
567C4⋊C4—1061no—
568C4⋊C4—1061no—
569C4⋊C4—1061no—
570C4⋊C4—1061no—
571C4⋊C4—1061no—
572C4⋊C4—1061no—
573C4⋊C4—1061no—
574C4⋊C4—1061no—
575C4⋊C4—2122no—
576C4⋊C4—2122no—
577C4⋊C4—2122no—
578C4⋊C4—2122no—
579C4⋊C4—2122no—
580C22⋊C4—22no—
581C22⋊C4—22no—
582C22⋊C4—4241no—
583C22⋊C4—2122no—
584C22⋊C4—2122no—
585C22⋊C4—2122no—
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#1313319112yes—
610C23C2×D42412yes—
611C23C2×D42412yes—
612C23#1313323912yes—
613C23C22×D21211yescharacteristic
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—1062no—
640C2×C4—4244no—
641C2×C4—4244no—
642C2×C4—2121no—
643C2×C4—2121no—
644C2×C4—2121no—
645C2×C4—2121no—
646C2×C4—2121no—
647C2×C4—2121no—
648C2×C4—2121no—
649C2×C4—2121no—
650C2×C4—2121no—
651C2×C4—2121no—
652C2×C4—2121no—
653C2×C4—2121no—
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#1313319112yes—
663C2×C4C2×D42412yes—
664C2×C4C22×C22⋊D5311yescharacteristic
665C2×C4#41×D5311yescharacteristic
666C2×C4C2×#1171994711yescharacteristic
667C2×C4C2×#1171994511yescharacteristic
668C2×C4#1313326211yescharacteristic
669C2×C4#1313326411yescharacteristic
670C8—22no—
671C8—22no—
672C8—22no—
673C8—41no—
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#1681085914yes—
695C22C2×#1313319111yescharacteristic
696C22#1681126811yescharacteristic
697C22#1681127711yescharacteristic
698C22C22×D42411yescharacteristic
699C22C2×#1313323911yescharacteristic
700C22#1681143511yescharacteristic
701C22#1681144011yescharacteristic
702C4—22no—
703C4—22no—
704C4—41no—
705C4—41no—
706C4—4241no—
707C4—4241no—
708C4—4241no—
709C4—4241no—
710C4—4241no—
711C4—4241no—
712C4—2122no—
713C4#1681115311yescharacteristic
714C4#1681121511yescharacteristic
715C4#1681126711yescharacteristic
716C4#1681127211yescharacteristic
717C2—24no—
718C2—42no—
719C2—8481no—
720C2#2027826011yescharacteristic
721C2C2×#1681085911yescharacteristic
722C2#2028440611yescharacteristic
723C2#2028652911yescharacteristic
724C2#2028660411yescharacteristic
725C2#2028706311yescharacteristic
726C2#2028709611yescharacteristic
subgroupG/H
centerC23C22×D212
commutator, cosocleC22×C4×C53C24
FrattiniC22×C4C23×D53
FittingC2×C8×D4×C53C2
socleC23×C53C22×D4
prime radical#20278155C2
hypercenterC2×C8×D4D53
hypocenterC53#25232
LCSG ▷ C22×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×C8×D4

Complements

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

NH ≅ G/Ntype
1. C2×#16810937C2semidirect
2. #20279023C2semidirect
4. #20276203C2semidirect
5. #20276138C2semidirect
6. #20276102C2semidirect
7. #20275898C2semidirect
8. #20275448C2semidirect
9. #20275398C2semidirect
10. #20275143C2semidirect
11. #20275143C2semidirect
12. #20274905C2semidirect
13. #20274744C2semidirect
14. C2×#16810386C2semidirect
15. C2×C8×D4×C53C2semidirect
132. C22⋊C8×C53D4semidirect
355. C2×C8×D4D53semidirect
424. C53#25232semidirect
489. C22⋊C8C22⋊D53semidirect

Maximal subgroups

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

subgroupindex
C2×#168109372
#202790232
#202781552
#202762032
#202761382
#202761022
#202758982
#202754482
#202753982
#202751432
#202749052
#202747442
C2×#168103862
C2×C8×D4×C532
#2523253