Finite Group Databasebeta

← C2×#24769 #6442978

Subgroups — C2×#24769 #6442978

Order 512.

2818 conjugacy classes of subgroups.

The subgroup lattice has 782 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#470C211yesmaximal, characteristic, complemented
2C22×#465C211yesmaximal, characteristic
3C22×#464C211yesmaximal, characteristic, complemented
4C22×#424C211yesmaximal, characteristic, complemented
5C2×#2620C211yesmaximal, characteristic
6C2×#2323C211yesmaximal, characteristic, complemented
7#24769C2116yesmaximal, direct product factor
8C2×#2066C211yesmaximal, characteristic, complemented
9C2×#2065C211yesmaximal, characteristic, complemented
10C2×#2056C211yesmaximal, characteristic, complemented
11C2×#2055C211yesmaximal, characteristic, complemented
12C2×#1983C211yesmaximal, characteristic, complemented
13C2×#1948C211yesmaximal, characteristic, complemented
14C2×#1895C211yesmaximal, characteristic
15C2×#1892C211yesmaximal, characteristic, complemented
16C2×#1803C211yesmaximal, characteristic, complemented
17C23×Q16C2211yescharacteristic
18C23×SD16C2211yescharacteristic
19C23×M16C2211yescharacteristic
20C24×C8C2211yescharacteristic
21C22×#124C2211yescharacteristic
22C22×C22⋊Q8C2211yescharacteristic
23C22×C22⋊Q8C2211yescharacteristic
24C22×#121C2211yescharacteristic
25C22×C4×Q8C2211yescharacteristic
26C22×#117C2211yescharacteristic
27C2×#470—28no—
28C2×#470C2218yescomplemented
29C2×#465—28no—
30C2×#465C2218yes—
31C2×#464—28no—
32C2×#464C2218yescomplemented
33C22×#106C2211yescharacteristic
34C22×#106C2211yescharacteristic
35C2×#424—28no—
36C2×#424C2218yescomplemented
37C22×C4⋊C8C2211yescharacteristic
38C22×C4⋊C8C2211yescharacteristic
39C22×C4⋊C8C2211yescharacteristic
40C22×C4⋊C8C2211yescharacteristic
41C22×#103C2211yescharacteristic
42C22×#103C2211yescharacteristic
43C22×#103C2211yescharacteristic
44C22×#103C2211yescharacteristic
45C22×#103C2211yescharacteristic
46C22×#102C2211yescharacteristic
47C22×#102C2211yescharacteristic
48C22×#102C2211yescharacteristic
49#2620—24no—
50#2620C2218yes—
51C2×#396—21no—
52C2×#396—21no—
53C2×#394—21no—
54C2×#394—21no—
55#2323—24no—
56#2323C2218yescomplemented
57C2×#391C2211yescharacteristic
58C2×#391C2211yescharacteristic
59C2×#390C2211yescharacteristic
60C2×#389—21no—
61C2×#389C2211yescharacteristic
62C2×#388—21no—
63C2×#388—21no—
64C2×#387—21no—
65C2×#384C2211yescharacteristic
66C2×#380C2211yescharacteristic
67C2×C4×C4⋊C4C2211yescharacteristic
68#2066C2218yescomplemented
69#2065C2218yescomplemented
70#2056C2218yescomplemented
71#2055C2218yescomplemented
72#1983C2218yescomplemented
73#1948C2218yescomplemented
74#1895C2218yes—
75#1892C2218yescomplemented
76#1803C2218yescomplemented
77C2×#340C2211yescharacteristic
78C2×#340C2211yescharacteristic
79C2×#340C2211yescharacteristic
80C2×#340C2211yescharacteristic
81C23×Q8C2311yescharacteristic
82C23×Q8C2311yescharacteristic
83C23×D4—21no—
84C23×D4C2311yescharacteristic
85C24×C4C2311yescharacteristic
86C22×Q16—24no—
87C22×Q16—24no—
88C22×Q16—42no—
89C22×Q16C2314yes—
90C22×SD16—24no—
91C22×SD16—24no—
92C22×SD16—42no—
93C22×SD16C2314yes—
94C22×M16—24no—
95C22×M16—24no—
96C22×M16—42no—
97C22×M16C2314yes—
98C23×C8—24no—
99C23×C8—24no—
100C23×C8—42no—
101C23×C8C2311yescharacteristic
102C23×C8C2311yescharacteristic
103C23×C8C2314yes—
104C23×C8C2311yescharacteristic
105C23×C8C2311yescharacteristic
106C2×#124—22no—
107C2×#124—24no—
108C2×#124—24no—
109C2×#124C2314yes—
110C2×C22⋊Q8—22no—
111C2×C22⋊Q8—24no—
112C2×C22⋊Q8—22no—
113C2×C22⋊Q8—24no—
114C2×C22⋊Q8—24no—
115C2×C22⋊Q8D418yes—
116C2×C22⋊Q8C2314yes—
117C2×C22⋊Q8C2314yes—
118C2×#121—22no—
119C2×#121—24no—
120C2×#121—24no—
121C2×#121C2314yes—
122C2×C4×Q8—22no—
123C2×C4×Q8—24no—
124C2×C4×Q8—24no—
125C2×C4×Q8C2314yes—
126C2×#117—24no—
127C2×#117—24no—
128C2×#117D414yes—
129C2×#117C2314yes—
130C22×C4⋊C4—21no—
131C22×C4⋊C4—21no—
132C22×C4⋊C4—21no—
133C22×C4⋊C4—21no—
134C22×C4⋊C4—21no—
135C22×C4⋊C4—21no—
136C22×C4⋊C4D411yescharacteristic
137C22×C4⋊C4D411yescharacteristic
138C22×C4⋊C4C2311yescharacteristic
139C22×C4⋊C4C2311yescharacteristic
140C22×C4⋊C4C2311yescharacteristic
141C22×C4⋊C4C2311yescharacteristic
142C22×C4⋊C4C2311yescharacteristic
143C22×C22⋊C4—21no—
144C22×C22⋊C4—21no—
145C22×C22⋊C4—21no—
146C22×C22⋊C4—21no—
147C22×C22⋊C4—21no—
148C22×C22⋊C4—21no—
149C22×C22⋊C4—21no—
150C22×C22⋊C4—21no—
151C22×C22⋊C4D411yescharacteristic
152C22×C22⋊C4D411yescharacteristic
153C22×C42—21no—
154C22×C42—21no—
155C22×C42C2311yescharacteristic
156C22×C42C2311yescharacteristic
157#470—232no—
158#465—232no—
159#464—232no—
160C2×#106—24no—
161C2×#106—24no—
162C2×#106C2314yes—
163C2×#106C2314yes—
164#424—232no—
165C2×C4⋊C8—24no—
166C2×C4⋊C8—24no—
167C2×C4⋊C8—24no—
168C2×C4⋊C8D418yescomplemented
169C2×C4⋊C8C2314yes—
170C2×C4⋊C8C2314yes—
171C2×C4⋊C8C2314yes—
172C2×C4⋊C8C2314yes—
173C2×#103—24no—
174C2×#103—24no—
175C2×#103—24no—
176C2×#103—24no—
177C2×#103—42no—
178C2×#103C2314yes—
179C2×#103C2314yes—
180C2×#103C2314yes—
181C2×#103C2314yes—
182C2×#103C2314yes—
183C2×#102—24no—
184C2×#102—24no—
185C2×#102—42no—
186C2×#102C2314yes—
187C2×#102C2314yes—
188C2×#102C2314yes—
189#396—28no—
190#396—28no—
191#394—28no—
192#394—28no—
193#391—22no—
194#391—22no—
195#391C2314yes—
196#391C2314yes—
197#390—22no—
198#390C2314yes—
199#389—28no—
200#389—22no—
201#389C2314yes—
202#388—28no—
203#388—28no—
204#387—28no—
205#384—22no—
206#384C2314yes—
207#380—22no—
208#380C2314yes—
209C4×C4⋊C4—22no—
210C4×C4⋊C4C2314yes—
211C2×#95—21no—
212C2×#95—21no—
213C2×#95—21no—
214C2×#95—21no—
215C2×#95—21no—
216C2×#95—21no—
217C2×#95—21no—
218#340C2314yes—
219#340C2314yes—
220#340C2314yes—
221#340C2314yes—
222C25—21no—
223C25C2×D411yescharacteristic
224C22×Q8—21no—
225C22×Q8—21no—
226C22×Q8—22no—
227C22×Q8—22no—
228C22×Q8—22no—
229C22×Q8—22no—
230C22×Q8—22no—
231C22×Q8—22no—
232C22×Q8—22no—
233C22×Q8—22no—
234C22×Q8—22no—
235C22×Q8—22no—
236C22×Q8—22no—
237C22×Q8C2×D414yes—
238C22×Q8C2412yes—
239C22×Q8C2412yes—
240C22×D4—24no—
241C22×D4—22no—
242C22×D4—22no—
243C22×D4—21no—
244C22×D4—22no—
245C22×D4—22no—
246C22×D4—22no—
247C22×D4—22no—
248C22×D4—44no—
249C22×D4—82no—
250C22×D4—82no—
251C22×D4C2412yes—
252C23×C4—22no—
253C23×C4—22no—
254C23×C4—22no—
255C23×C4—22no—
256C23×C4—21no—
257C23×C4—21no—
258C23×C4—21no—
259C23×C4—21no—
260C23×C4—21no—
261C23×C4—21no—
262C23×C4—21no—
263C23×C4C2×D411yescharacteristic
264C23×C4C2×D411yescharacteristic
265C23×C4C2×D412yes—
266C23×C4C2×D411yescharacteristic
267C23×C4C2×D411yescharacteristic
268C23×C4C2×D411yescharacteristic
269C23×C4C2×D414yes—
270C23×C4#4114yes—
271C23×C4C2412yes—
272C23×C4C2411yescharacteristic
273C2×Q16—28no—
274C2×Q16—28no—
275C2×Q16—44no—
276C2×Q16—416no—
277C2×SD16—28no—
278C2×SD16—28no—
279C2×SD16—44no—
280C2×SD16—416no—
281C2×M16—28no—
282C2×M16—28no—
283C2×M16—44no—
284C2×M16—416no—
285C22×C8—22no—
286C22×C8—22no—
287C22×C8—22no—
288C22×C8—22no—
289C22×C8—22no—
290C22×C8—22no—
291C22×C8—28no—
292C22×C8—22no—
293C22×C8—22no—
294C22×C8—22no—
295C22×C8—22no—
296C22×C8—28no—
297C22×C8—44no—
298C22×C8—416no—
299C22×C8C2×D414yes—
300C22×C8C2×D414yes—
301C22×C8C2412yes—
302C22×C8C2412yes—
303C22×C8C2412yes—
304C22×C8C2412yes—
305#124—28no—
306#124—28no—
307#124—48no—
308C22⋊Q8—216no—
309C22⋊Q8—28no—
310C22⋊Q8—28no—
311C22⋊Q8—28no—
312C22⋊Q8—48no—
313C22⋊Q8C2×D4116yes—
314#121—28no—
315#121—28no—
316#121—48no—
317C4×Q8—28no—
318C4×Q8—28no—
319C4×Q8—48no—
320#117—216no—
321#117—28no—
322#117—28no—
323C2×C4⋊C4—28no—
324C2×C4⋊C4—24no—
325C2×C4⋊C4—24no—
326C2×C4⋊C4—24no—
327C2×C4⋊C4—21no—
328C2×C4⋊C4—22no—
329C2×C4⋊C4—22no—
330C2×C4⋊C4—22no—
331C2×C4⋊C4—22no—
332C2×C4⋊C4—22no—
333C2×C4⋊C4—22no—
334C2×C4⋊C4—22no—
335C2×C4⋊C4—22no—
336C2×C4⋊C4—22no—
337C2×C4⋊C4—24no—
338C2×C4⋊C4—24no—
339C2×C4⋊C4—21no—
340C2×C4⋊C4—21no—
341C2×C4⋊C4—21no—
342C2×C4⋊C4—21no—
343C2×C4⋊C4—24no—
344C2×C4⋊C4—24no—
345C2×C4⋊C4—24no—
346C2×C4⋊C4—44no—
347C2×C4⋊C4—44no—
348C2×C4⋊C4—82no—
349C2×C4⋊C4—82no—
350C2×C4⋊C4—82no—
351C2×C4⋊C4C2×D414yes—
352C2×C4⋊C4C2×D414yes—
353C2×C4⋊C4C2×D414yes—
354C2×C4⋊C4C2412yes—
355C2×C4⋊C4C2412yes—
356C2×C4⋊C4C2412yes—
357C2×C4⋊C4C2412yes—
358C2×C4⋊C4C2412yes—
359C2×C22⋊C4—28no—
360C2×C22⋊C4—24no—
361C2×C22⋊C4—24no—
362C2×C22⋊C4—24no—
363C2×C22⋊C4—24no—
364C2×C22⋊C4—24no—
365C2×C22⋊C4—24no—
366C2×C22⋊C4—24no—
367C2×C22⋊C4—24no—
368C2×C22⋊C4—24no—
369C2×C22⋊C4—24no—
370C2×C22⋊C4—44no—
371C2×C22⋊C4—44no—
372C2×C22⋊C4—44no—
373C2×C22⋊C4—44no—
374C2×C22⋊C4—82no—
375C2×C22⋊C4—82no—
376C2×C22⋊C4—82no—
377C2×C22⋊C4C2×D414yes—
378C2×C22⋊C4C2×D414yes—
379C2×C42—22no—
380C2×C42—22no—
381C2×C42—24no—
382C2×C42—24no—
383C2×C42—44no—
384C2×C42—82no—
385C2×C42C2×D412yes—
386C2×C42C2×D412yes—
387C2×C42C2×D414yes—
388C2×C42#4114yes—
389C2×C42C2412yes—
390C2×C42C2412yes—
391#106—28no—
392#106—28no—
393C4⋊C8—28no—
394C4⋊C8—28no—
395C4⋊C8—28no—
396C4⋊C8C2×D4116yescomplemented
397#103—28no—
398#103—28no—
399#103—28no—
400#103—28no—
401#103—44no—
402#102—28no—
403#102—28no—
404#102—44no—
405#95—24no—
406#95—24no—
407#95—24no—
408#95—24no—
409#95—24no—
410#95—24no—
411#95—24no—
412C24—22no—
413C24—22no—
414C24—22no—
415C24—22no—
416C24—22no—
417C24—22no—
418C24—22no—
419C24—42no—
420C24—42no—
421C24—42no—
422C24—42no—
423C24—42no—
424C24—42no—
425C24—42no—
426C24#12114yes—
427C24C22×D412yes—
428C24C22×D411yescharacteristic
429C2×Q8—24no—
430C2×Q8—22no—
431C2×Q8—28no—
432C2×Q8—28no—
433C2×Q8—22no—
434C2×Q8—22no—
435C2×Q8—22no—
436C2×Q8—22no—
437C2×Q8—22no—
438C2×Q8—22no—
439C2×Q8—22no—
440C2×Q8—22no—
441C2×Q8—22no—
442C2×Q8—22no—
443C2×Q8—42no—
444C2×Q8—42no—
445C2×Q8—42no—
446C2×Q8—42no—
447C2×Q8—42no—
448C2×Q8—44no—
449C2×Q8—44no—
450C2×Q8—44no—
451C2×Q8—44no—
452C2×Q8—44no—
453C2×Q8—44no—
454C2×Q8C22×D414yes—
455C2×D4—22no—
456C2×D4—22no—
457C2×D4—22no—
458C2×D4—22no—
459C2×D4—22no—
460C2×D4—22no—
461C2×D4—48no—
462C2×D4—42no—
463C2×D4—42no—
464C2×D4—42no—
465C2×D4—44no—
466C2×D4—44no—
467C2×D4—44no—
468C2×D4—44no—
469C2×D4—84no—
470C2×D4—84no—
471C2×D4—816no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—24no—
479C22×C4—24no—
480C22×C4—28no—
481C22×C4—28no—
482C22×C4—28no—
483C22×C4—28no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—24no—
491C22×C4—24no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—42no—
504C22×C4—42no—
505C22×C4—42no—
506C22×C4—42no—
507C22×C4—42no—
508C22×C4—42no—
509C22×C4—42no—
510C22×C4—42no—
511C22×C4—42no—
512C22×C4—42no—
513C22×C4—42no—
514C22×C4—42no—
515C22×C4—42no—
516C22×C4—42no—
517C22×C4—42no—
518C22×C4—42no—
519C22×C4—42no—
520C22×C4—42no—
521C22×C4—42no—
522C22×C4#12114yes—
523C22×C4#12114yes—
524C22×C4#12114yes—
525C22×C4#12118yes—
526C22×C4C22×D412yes—
527C22×C4C22×D412yes—
528C22×C4C22×D412yes—
529C22×C4C22×D412yes—
530C22×C4C22×D412yes—
531C22×C4C22×D414yes—
532C22×C4C22×D411yescharacteristic
533C22×C4C22×D412yes—
534C22×C4C22×D412yes—
535C22×C4C2×#4114yes—
536C22×C4C2×#4112yes—
537C22×C4C2×#4112yes—
538C22×C4H(5,𝔽2)12yes—
539C22×C42−1+412yes—
540C22×C4C2511yescharacteristic
541Q16—416no—
542SD16—416no—
543M16—416no—
544C2×C8—28no—
545C2×C8—28no—
546C2×C8—22no—
547C2×C8—22no—
548C2×C8—22no—
549C2×C8—22no—
550C2×C8—22no—
551C2×C8—22no—
552C2×C8—22no—
553C2×C8—22no—
554C2×C8—22no—
555C2×C8—22no—
556C2×C8—416no—
557C2×C8—44no—
558C2×C8—44no—
559C2×C8C22×D414yes—
560C2×C8C22×D414yes—
561C4⋊C4—216no—
562C4⋊C4—28no—
563C4⋊C4—28no—
564C4⋊C4—24no—
565C4⋊C4—22no—
566C4⋊C4—22no—
567C4⋊C4—22no—
568C4⋊C4—22no—
569C4⋊C4—22no—
570C4⋊C4—22no—
571C4⋊C4—22no—
572C4⋊C4—22no—
573C4⋊C4—22no—
574C4⋊C4—42no—
575C4⋊C4—42no—
576C4⋊C4—42no—
577C4⋊C4—48no—
578C4⋊C4—48no—
579C4⋊C4—42no—
580C4⋊C4—84no—
581C4⋊C4—84no—
582C4⋊C4—84no—
583C4⋊C4C22×D414yes—
584C22⋊C4—216no—
585C22⋊C4—28no—
586C22⋊C4—28no—
587C22⋊C4—48no—
588C22⋊C4—48no—
589C22⋊C4—48no—
590C22⋊C4—48no—
591C22⋊C4—84no—
592C22⋊C4—84no—
593C22⋊C4—84no—
594C42—24no—
595C42—22no—
596C42—22no—
597C42—48no—
598C42—84no—
599C42#12118yes—
600C42C22×D414yes—
601C42C2×#4114yes—
602C23—22no—
603C23—28no—
604C23—22no—
605C23—28no—
606C23—28no—
607C23—22no—
608C23—22no—
609C23—22no—
610C23—22no—
611C23—44no—
612C23—44no—
613C23—44no—
614C23—44no—
615C23—42no—
616C23—42no—
617C23—42no—
618C23—42no—
619C23—42no—
620C23—42no—
621C23—42no—
622C23—84no—
623C23—84no—
624C23—84no—
625C23—84no—
626C23—84no—
627C23—84no—
628C23—84no—
629C23C2×#12114yes—
630C23C2×#12112yes—
631C23C2×#12112yes—
632C23#53712yes—
633C23#57712yes—
634C23#57712yes—
635C23#57712yes—
636C23#57812yes—
637C23C23×D411yescharacteristic
638Q8—24no—
639Q8—24no—
640Q8—48no—
641Q8—42no—
642Q8—42no—
643Q8—42no—
644Q8—42no—
645Q8—42no—
646Q8—42no—
647Q8—84no—
648D4—42no—
649D4—42no—
650D4—42no—
651D4—42no—
652D4—816no—
653D4—84no—
654C2×C4—22no—
655C2×C4—28no—
656C2×C4—22no—
657C2×C4—28no—
658C2×C4—28no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—216no—
664C2×C4—24no—
665C2×C4—24no—
666C2×C4—24no—
667C2×C4—24no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—24no—
671C2×C4—24no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—42no—
677C2×C4—48no—
678C2×C4—42no—
679C2×C4—48no—
680C2×C4—44no—
681C2×C4—44no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—84no—
700C2×C4—84no—
701C2×C4—84no—
702C2×C4—84no—
703C2×C4—84no—
704C2×C4C2×#12114yes—
705C2×C4C2×#12114yes—
706C2×C4C2×#12114yes—
707C2×C4C2×#12112yes—
708C2×C4C2×#12112yes—
709C2×C4#53712yes—
710C2×C4D4214yes—
711C2×C4#54714yes—
712C2×C4#54814yes—
713C2×C4#55314yes—
714C2×C4C23×D411yescharacteristic
715C2×C4C23×D411yescharacteristic
716C2×C4C22×#4111yescharacteristic
717C2×C4C22×#4111yescharacteristic
718C2×C4C2×H(5,𝔽2)11yescharacteristic
719C2×C4C2×2−1+411yescharacteristic
720C8—24no—
721C8—24no—
722C8—42no—
723C8—42no—
724C22—24no—
725C22—24no—
726C22—24no—
727C22—42no—
728C22—42no—
729C22—416no—
730C22—42no—
731C22—42no—
732C22—82no—
733C22—82no—
734C22—82no—
735C22—82no—
736C22—82no—
737C22—82no—
738C22—82no—
739C22—168no—
740C22#241614yes—
741C22#304314yes—
742C22#304614yes—
743C22#306014yes—
744C22#306314yes—
745C22#325814yes—
746C22#326314yes—
747C22C22×#12111yescharacteristic
748C22C22×#12111yescharacteristic
749C22C2×#53711yescharacteristic
750C22C2×#57711yescharacteristic
751C22C2×#57711yescharacteristic
752C22C2×#57711yescharacteristic
753C22C2×#57811yescharacteristic
754C4—24no—
755C4—24no—
756C4—24no—
757C4—44no—
758C4—42no—
759C4—42no—
760C4—44no—
761C4—82no—
762C4—82no—
763C4—82no—
764C4—82no—
765C4—82no—
766C4#241614yes—
767C4C2×D4211yescharacteristic
768C4C2×#54711yescharacteristic
769C4C2×#54811yescharacteristic
770C4C2×#55311yescharacteristic
771C2—44no—
772C2—162no—
773C2#2476918yesdirect product factor
774C2C2×#241611yescharacteristic
775C2C2×#304311yescharacteristic
776C2C2×#304611yescharacteristic
777C2C2×#306011yescharacteristic
778C2C2×#306311yescharacteristic
779C2C2×#325811yescharacteristic
780C2C2×#326311yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC22×#121C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C22×#117 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C22×#470C2semidirect
3. C22×#464C2semidirect
4. C22×#424C2semidirect
6. C2×#2323C2semidirect
7. #24769C2direct (N × H)
8. C2×#2066C2semidirect
9. C2×#2065C2semidirect
10. C2×#2056C2semidirect
11. C2×#2055C2semidirect
12. C2×#1983C2semidirect
13. C2×#1948C2semidirect
15. C2×#1892C2semidirect
16. C2×#1803C2semidirect
28. C2×#470C22semidirect
32. C2×#464C22semidirect
36. C2×#424C22semidirect
56. #2323C22semidirect
68. #2066C22semidirect
69. #2065C22semidirect
70. #2056C22semidirect
71. #2055C22semidirect
72. #1983C22semidirect
73. #1948C22semidirect
75. #1892C22semidirect
76. #1803C22semidirect
168. C2×C4⋊C8D4semidirect
396. C4⋊C8C2×D4semidirect
773. C2#24769direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#4702
C22×#4652
C22×#4642
C22×#4242
C2×#26202
C2×#23232
#247692
C2×#20662
C2×#20652
C2×#20562
C2×#20552
C2×#19832
C2×#19482
C2×#18952
C2×#18922
C2×#18032