Finite Group Databasebeta

← C2×#24724 #6449937

Subgroups — C2×#24724 #6449937

Order 512.

2000 conjugacy classes of subgroups.

The subgroup lattice has 801 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3080C211yesmaximal, characteristic, complemented
2C22×#478C211yesmaximal, characteristic, complemented
3C2×C4×AGL(1,ℤ/8)C211yesmaximal, characteristic
4C2×#2925C211yesmaximal, characteristic, complemented
5#24724C2116yesmaximal, direct product factor
6C2×#2079C211yesmaximal, characteristic, complemented
7C2×#2078C211yesmaximal, characteristic, complemented
8C2×#2051C211yesmaximal, characteristic
9C2×#2051C211yesmaximal, characteristic
10C2×#1998C211yesmaximal, characteristic, complemented
11C2×#1952C211yesmaximal, characteristic, complemented
12C2×#1951C211yesmaximal, characteristic, complemented
13C2×#1950C211yesmaximal, characteristic, complemented
14C2×#1931C211yesmaximal, characteristic, complemented
15C2×#1931C211yesmaximal, characteristic, complemented
16C2×#1800C211yesmaximal, characteristic, complemented
17C22×AGL(1,ℤ/8)C2211yescharacteristic
18C22×#125C2211yescharacteristic
19C2×C4×#41C2211yescharacteristic
20C22×C4×D4C2211yescharacteristic
21#3080—24no—
22#3080C2218yescomplemented
23C2×#479—21no—
24C2×#479—21no—
25C2×#478—21no—
26C2×#478—21no—
27C2×#478—21no—
28C2×#478—21no—
29C2×#478—24no—
30C2×#478—21no—
31C2×#478—21no—
32C2×#478C2218yescomplemented
33C4×AGL(1,ℤ/8)—24no—
34C4×AGL(1,ℤ/8)C2218yes—
35C2×#442—21no—
36C2×#440—21no—
37C2×C4×SD16—21no—
38C2×C4×D8—21no—
39#2925—24no—
40#2925C2218yescomplemented
41C2×#433—21no—
42C2×#433—21no—
43C2×#432—21no—
44C2×#431—21no—
45C22×#108C2211yescharacteristic
46C22×#108C2211yescharacteristic
47C2×#428C2211yescharacteristic
48C2×#428C2211yescharacteristic
49C2×#428C2211yescharacteristic
50C22×#107C2211yescharacteristic
51C22×#106C2211yescharacteristic
52C2×#423C2211yescharacteristic
53C2×#423C2211yescharacteristic
54C22×C4⋊C8C2211yescharacteristic
55C2×#417C2211yescharacteristic
56C2×#417C2211yescharacteristic
57C2×#417C2211yescharacteristic
58C2×#418C2211yescharacteristic
59C22×#102C2211yescharacteristic
60C22×#102C2211yescharacteristic
61C22×#100C2211yescharacteristic
62C22×#100C2211yescharacteristic
63C2×#408C2211yescharacteristic
64C2×#408C2211yescharacteristic
65C2×#405C2211yescharacteristic
66C2×#405C2211yescharacteristic
67C2×C4×M16C2211yescharacteristic
68#2079C2218yescomplemented
69#2078C2218yescomplemented
70#2051C2218yes—
71#2051C2218yes—
72#1998C2218yescomplemented
73#1952C2218yescomplemented
74#1951C2218yescomplemented
75#1950C2218yescomplemented
76#1931C2218yescomplemented
77#1931C2218yescomplemented
78#1800C2218yescomplemented
79C2×#343C2211yescharacteristic
80C2×#343C2211yescharacteristic
81C2×#343C2211yescharacteristic
82C2×#343C2211yescharacteristic
83C2×#343C2211yescharacteristic
84C2×#343C2211yescharacteristic
85C2×#341C2211yescharacteristic
86C2×#341C2211yescharacteristic
87C22×#41C2311yescharacteristic
88C23×D4C2311yescharacteristic
89C24×C4—21no—
90C2×AGL(1,ℤ/8)—22no—
91C2×AGL(1,ℤ/8)—24no—
92C2×AGL(1,ℤ/8)—24no—
93C2×AGL(1,ℤ/8)C2314yes—
94C22×SD16—21no—
95C22×D8—21no—
96C22×M16C2311yescharacteristic
97C22×M16C2311yescharacteristic
98C22×M16C2311yescharacteristic
99C22×M16C2311yescharacteristic
100C22×M16C2311yescharacteristic
101C22×M16C2311yescharacteristic
102C23×C8C2311yescharacteristic
103C23×C8C2311yescharacteristic
104C2×#125—21no—
105C2×#125—22no—
106C2×#125—21no—
107C2×#125—21no—
108C2×#125—21no—
109C2×#125—22no—
110C2×#125—22no—
111C2×#125C2314yes—
112C4×#41—22no—
113C4×#41—22no—
114C4×#41D414yes—
115C4×#41C2314yes—
116C2×C4×Q8D411yescharacteristic
117C2×C4×Q8D411yescharacteristic
118C2×C4×D4—21no—
119C2×C4×D4—21no—
120C2×C4×D4—21no—
121C2×C4×D4—22no—
122C2×C4×D4—21no—
123C2×C4×D4—21no—
124C2×C4×D4—21no—
125C2×C4×D4—22no—
126C2×C4×D4—22no—
127C2×C4×D4D411yescharacteristic
128C2×C4×D4D411yescharacteristic
129C2×C4×D4C2314yes—
130C2×#117—21no—
131C2×#117C2311yescharacteristic
132C22×C4⋊C4—21no—
133C22×C4⋊C4—21no—
134C22×C4⋊C4C2311yescharacteristic
135C22×C4⋊C4C2311yescharacteristic
136C22×C4⋊C4C2311yescharacteristic
137C22×C22⋊C4—21no—
138C22×C42—21no—
139C22×C42C2311yescharacteristic
140#479—28no—
141#479—28no—
142#478—28no—
143#478—28no—
144#478—28no—
145#478—28no—
146#478—28no—
147#478—28no—
148#442—28no—
149#440—28no—
150C4×SD16—28no—
151C4×D8—28no—
152#433—28no—
153#433—28no—
154#432—28no—
155#431—28no—
156C2×#108—24no—
157C2×#108—24no—
158C2×#108C2314yes—
159C2×#108C2314yes—
160#428—22no—
161#428—22no—
162#428—22no—
163#428C2314yes—
164#428C2314yes—
165#428C2314yes—
166C2×#107—21no—
167C2×#107—21no—
168C2×#107—22no—
169C2×#107—21no—
170C2×#107—21no—
171C2×#107—21no—
172C2×#107C2314yes—
173C2×#106—21no—
174C2×#106—21no—
175C2×#106—22no—
176C2×#106—21no—
177C2×#106—21no—
178C2×#106—21no—
179C2×#106C2314yes—
180#423—22no—
181#423—22no—
182#423C2314yes—
183#423C2314yes—
184C2×C4⋊C8—21no—
185C2×C4⋊C8—21no—
186C2×C4⋊C8—21no—
187C2×C4⋊C8—21no—
188C2×C4⋊C8D411yescharacteristic
189C2×C4⋊C8D411yescharacteristic
190C2×C4⋊C8D411yescharacteristic
191C2×C4⋊C8D411yescharacteristic
192C2×C4⋊C8D414yes—
193C2×C4⋊C8C2314yes—
194#418—22no—
195#418C2314yes—
196#417—22no—
197#417—22no—
198#417—22no—
199#417C2314yes—
200#417C2314yes—
201#417C2314yes—
202C2×#103—21no—
203C2×#103—21no—
204C2×#103—21no—
205C2×#102—21no—
206C2×#102—21no—
207C2×#102—21no—
208C2×#102—21no—
209C2×#102—21no—
210C2×#102—22no—
211C2×#102—21no—
212C2×#102—21no—
213C2×#102—22no—
214C2×#102—21no—
215C2×#102—21no—
216C2×#102C2314yes—
217C2×#102C2314yes—
218C2×#100—24no—
219C2×#100—24no—
220C2×#100C2314yes—
221C2×#100C2314yes—
222#408—22no—
223#408—22no—
224#408C2314yes—
225#408C2314yes—
226C2×C22⋊C8—21no—
227C2×C22⋊C8—21no—
228C2×C22⋊C8—21no—
229C2×C22⋊C8—21no—
230#405—22no—
231#405—22no—
232#405C2314yes—
233#405C2314yes—
234C4×M16—22no—
235C4×M16C2314yes—
236C2×#97—21no—
237C2×#97—21no—
238C2×#97—21no—
239C2×C4×C8—21no—
240C2×C4×C8—21no—
241C2×C4×C8—21no—
242#343C2314yes—
243#343C2314yes—
244#343C2314yes—
245#343C2314yes—
246#343C2314yes—
247#343C2314yes—
248#341C2314yes—
249#341C2314yes—
250C25—21no—
251C2×#41—21no—
252C2×#41—21no—
253C2×#41—22no—
254C2×#41—22no—
255C2×#41—22no—
256C2×#41—22no—
257C2×#41C2×D412yes—
258C2×#41C2412yes—
259C22×Q8C2×D411yescharacteristic
260C22×D4—21no—
261C22×D4—21no—
262C22×D4—21no—
263C22×D4—21no—
264C22×D4—21no—
265C22×D4—22no—
266C22×D4—21no—
267C22×D4—22no—
268C22×D4—22no—
269C22×D4C2×D411yescharacteristic
270C22×D4#4114yes—
271C22×D4C2412yes—
272C23×C4—21no—
273C23×C4—21no—
274C23×C4—21no—
275C23×C4—21no—
276C23×C4—21no—
277C23×C4—21no—
278C23×C4—24no—
279C23×C4—42no—
280C23×C4—41no—
281C23×C4—41no—
282C23×C4—84no—
283C23×C4#4111yescharacteristic
284C23×C4#4111yescharacteristic
285C23×C4C2411yescharacteristic
286AGL(1,ℤ/8)—216no—
287AGL(1,ℤ/8)—28no—
288AGL(1,ℤ/8)—28no—
289C2×SD16—28no—
290C2×SD16—24no—
291C2×D8—28no—
292C2×D8—24no—
293C2×M16—21no—
294C2×M16—22no—
295C2×M16—21no—
296C2×M16—21no—
297C2×M16—21no—
298C2×M16—21no—
299C2×M16—21no—
300C2×M16—22no—
301C2×M16—22no—
302C2×M16—22no—
303C2×M16—22no—
304C2×M16—22no—
305C2×M16—22no—
306C2×M16—22no—
307C2×M16—22no—
308C2×M16—22no—
309C2×M16—22no—
310C2×M16#4114yes—
311C2×M16C2412yes—
312C2×M16C2412yes—
313C2×M16C2412yes—
314C2×M16C2412yes—
315C2×M16C2412yes—
316C2×M16C2412yes—
317C22×C8—21no—
318C22×C8—22no—
319C22×C8—22no—
320C22×C8—22no—
321C22×C8—22no—
322C22×C8—21no—
323C22×C8—21no—
324C22×C8—21no—
325C22×C8—21no—
326C22×C8—21no—
327C22×C8C2×D411yescharacteristic
328C22×C8C2×D411yescharacteristic
329C22×C8C2×D411yescharacteristic
330C22×C8C2×D411yescharacteristic
331C22×C8C2×D412yes—
332C22×C8C2×D412yes—
333C22×C8C2412yes—
334C22×C8C2412yes—
335#125—24no—
336#125—24no—
337#125—24no—
338#125—24no—
339#125—42no—
340#125—42no—
341#125—42no—
342#125—42no—
343C4×Q8—22no—
344C4×Q8—22no—
345C4×Q8C2×D414yes—
346C4×Q8C2×D414yes—
347C4×D4—24no—
348C4×D4—24no—
349C4×D4—24no—
350C4×D4—24no—
351C4×D4—22no—
352C4×D4—22no—
353C4×D4—24no—
354C4×D4—24no—
355C4×D4—24no—
356C4×D4—24no—
357C4×D4—42no—
358C4×D4—42no—
359C4×D4—42no—
360C4×D4—42no—
361C4×D4C2×D414yes—
362C4×D4C2×D414yes—
363#117—21no—
364#117—21no—
365#117—24no—
366#117—24no—
367#117C2×D412yes—
368#117C2412yes—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—24no—
384C2×C4⋊C4—24no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—42no—
389C2×C4⋊C4—42no—
390C2×C4⋊C4—41no—
391C2×C4⋊C4—41no—
392C2×C4⋊C4—41no—
393C2×C4⋊C4—41no—
394C2×C4⋊C4C2×D411yescharacteristic
395C2×C4⋊C4C2×D411yescharacteristic
396C2×C4⋊C4C2412yes—
397C2×C4⋊C4C2412yes—
398C2×C4⋊C4C2412yes—
399C2×C22⋊C4—21no—
400C2×C22⋊C4—21no—
401C2×C22⋊C4—21no—
402C2×C22⋊C4—24no—
403C2×C22⋊C4—42no—
404C2×C22⋊C4—41no—
405C2×C22⋊C4—41no—
406C2×C42—21no—
407C2×C42—21no—
408C2×C42—21no—
409C2×C42—24no—
410C2×C42—24no—
411C2×C42C2×D411yescharacteristic
412C2×C42C2×D411yescharacteristic
413C2×C42C2×D411yescharacteristic
414C2×C42C2×D412yes—
415C2×C42C2×D412yes—
416C2×C42C2×D411yescharacteristic
417C2×C42#4112yes—
418C2×C42C2412yes—
419#108—28no—
420#108—28no—
421#107—24no—
422#107—24no—
423#107—24no—
424#107—24no—
425#107—24no—
426#106—24no—
427#106—24no—
428#106—24no—
429#106—24no—
430#106—24no—
431C4⋊C8—24no—
432C4⋊C8—24no—
433C4⋊C8—24no—
434C4⋊C8—24no—
435C4⋊C8C2×D414yes—
436C4⋊C8C2×D414yes—
437C4⋊C8C2×D414yes—
438C4⋊C8C2×D414yes—
439#103—24no—
440#103—24no—
441#103—24no—
442#102—24no—
443#102—24no—
444#102—24no—
445#102—24no—
446#102—24no—
447#102—24no—
448#102—24no—
449#102—24no—
450#102—24no—
451#100—28no—
452#100—28no—
453C22⋊C8—24no—
454C22⋊C8—24no—
455C22⋊C8—24no—
456C22⋊C8—24no—
457#97—24no—
458#97—24no—
459#97—24no—
460C4×C8—24no—
461C4×C8—24no—
462C4×C8—24no—
463C24—21no—
464C24—24no—
465C24—22no—
466C24—41no—
467C24—41no—
468C24—42no—
469C24—82no—
470C24—82no—
471C24C2×#4111yescharacteristic
472#41—24no—
473#41—24no—
474#41—22no—
475#41—22no—
476#41—22no—
477#41—22no—
478#41—42no—
479#41—42no—
480#41—42no—
481#41—42no—
482C2×Q8—21no—
483C2×Q8—22no—
484C2×Q8—22no—
485C2×Q8C22×D412yes—
486C2×D4—22no—
487C2×D4—22no—
488C2×D4—21no—
489C2×D4—22no—
490C2×D4—24no—
491C2×D4—24no—
492C2×D4—22no—
493C2×D4—24no—
494C2×D4—24no—
495C2×D4—24no—
496C2×D4—22no—
497C2×D4—22no—
498C2×D4—22no—
499C2×D4—22no—
500C2×D4—22no—
501C2×D4—42no—
502C2×D4—42no—
503C2×D4—41no—
504C2×D4—41no—
505C2×D4—42no—
506C2×D4—42no—
507C2×D4—42no—
508C2×D4—42no—
509C2×D4—42no—
510C2×D4C22×D412yes—
511C2×D4C2×#4114yes—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—22no—
516C22×C4—24no—
517C22×C4—22no—
518C22×C4—24no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—42no—
523C22×C4—42no—
524C22×C4—44no—
525C22×C4—42no—
526C22×C4—42no—
527C22×C4—41no—
528C22×C4—41no—
529C22×C4—41no—
530C22×C4—41no—
531C22×C4—41no—
532C22×C4—41no—
533C22×C4—44no—
534C22×C4—44no—
535C22×C4—82no—
536C22×C4—84no—
537C22×C4—84no—
538C22×C4—88no—
539C22×C4—88no—
540C22×C4—82no—
541C22×C4—82no—
542C22×C4—82no—
543C22×C4#12111yescharacteristic
544C22×C4#12111yescharacteristic
545C22×C4#12111yescharacteristic
546C22×C4#12111yescharacteristic
547C22×C4#12112yes—
548C22×C4#12112yes—
549C22×C4C22×D411yescharacteristic
550C22×C4C22×D411yescharacteristic
551C22×C4C22×D411yescharacteristic
552C22×C4C22×D411yescharacteristic
553C22×C4C2×#4112yes—
554C22×C4C2×#4112yes—
555C22×C4C2×#4111yescharacteristic
556C22×C4C2×#4112yes—
557C22×C4C2×#4112yes—
558C22×C42−1+412yes—
559C22×C42−1+412yes—
560C22×C4C2511yescharacteristic
561SD16—216no—
562D8—216no—
563M16—24no—
564M16—22no—
565M16—22no—
566M16—22no—
567M16—22no—
568M16—22no—
569M16—22no—
570M16—22no—
571M16—22no—
572M16—22no—
573M16—22no—
574M16—22no—
575M16—42no—
576M16—42no—
577M16—42no—
578M16—42no—
579M16—42no—
580M16C2×#4114yes—
581C2×C8—24no—
582C2×C8—22no—
583C2×C8—22no—
584C2×C8—22no—
585C2×C8—22no—
586C2×C8—24no—
587C2×C8—24no—
588C2×C8—22no—
589C2×C8—22no—
590C2×C8—22no—
591C2×C8—22no—
592C2×C8—22no—
593C2×C8—22no—
594C2×C8—22no—
595C2×C8—22no—
596C2×C8—22no—
597C2×C8—22no—
598C2×C8—42no—
599C2×C8—42no—
600C2×C8—42no—
601C2×C8—42no—
602C2×C8—42no—
603C2×C8C22×D412yes—
604C2×C8C22×D412yes—
605C2×C8C22×D412yes—
606C2×C8C22×D412yes—
607C4⋊C4—24no—
608C4⋊C4—24no—
609C4⋊C4—21no—
610C4⋊C4—21no—
611C4⋊C4—22no—
612C4⋊C4—22no—
613C4⋊C4—22no—
614C4⋊C4—22no—
615C4⋊C4—22no—
616C4⋊C4—22no—
617C4⋊C4—41no—
618C4⋊C4—41no—
619C4⋊C4—41no—
620C4⋊C4—41no—
621C4⋊C4—41no—
622C4⋊C4—41no—
623C4⋊C4—44no—
624C4⋊C4—44no—
625C4⋊C4—44no—
626C4⋊C4—44no—
627C4⋊C4C22×D412yes—
628C4⋊C4C22×D412yes—
629C22⋊C4—22no—
630C22⋊C4—22no—
631C22⋊C4—24no—
632C22⋊C4—24no—
633C22⋊C4—44no—
634C22⋊C4—44no—
635C42—22no—
636C42—24no—
637C42—24no—
638C42—22no—
639C42#12112yes—
640C42#12112yes—
641C42#12112yes—
642C42#12112yes—
643C42C22×D412yes—
644C42C22×D412yes—
645C42C22×D412yes—
646C42C22×D412yes—
647C23—22no—
648C23—22no—
649C23—22no—
650C23—24no—
651C23—42no—
652C23—42no—
653C23—44no—
654C23—44no—
655C23—42no—
656C23—42no—
657C23—42no—
658C23—82no—
659C23—82no—
660C23—88no—
661C23—82no—
662C23—82no—
663C23—88no—
664C23—82no—
665C23—82no—
666C23C2×#12111yescharacteristic
667C23C2×#12111yescharacteristic
668C23#55212yes—
669C23#55612yes—
670C23C22×#4111yescharacteristic
671Q8—22no—
672Q8—22no—
673Q8—42no—
674D4—22no—
675D4—24no—
676D4—22no—
677D4—24no—
678D4—44no—
679D4—42no—
680D4—42no—
681D4—44no—
682D4—44no—
683D4—42no—
684D4—42no—
685D4—42no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—48no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—44no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—84no—
708C2×C4—88no—
709C2×C4—88no—
710C2×C4—82no—
711C2×C4—82no—
712C2×C4—82no—
713C2×C4—82no—
714C2×C4—82no—
715C2×C4—82no—
716C2×C4—82no—
717C2×C4—82no—
718C2×C4—82no—
719C2×C4C2×#12112yes—
720C2×C4C2×#12112yes—
721C2×C4C2×#12112yes—
722C2×C4C2×#12112yes—
723C2×C4C2×#12111yescharacteristic
724C2×C4C2×#12111yescharacteristic
725C2×C4#52512yes—
726C2×C4#52512yes—
727C2×C4#53612yes—
728C2×C4#53612yes—
729C2×C4#54712yes—
730C2×C4#54712yes—
731C2×C4#54812yes—
732C2×C4#54812yes—
733C2×C4#55212yes—
734C2×C4#55612yes—
735C2×C4C23×D411yescharacteristic
736C2×C4C23×D411yescharacteristic
737C2×C4C22×#4111yescharacteristic
738C2×C4C22×#4111yescharacteristic
739C2×C4C2×2−1+411yescharacteristic
740C2×C4C2×2−1+411yescharacteristic
741C8—24no—
742C8—22no—
743C8—22no—
744C8—22no—
745C8—22no—
746C8—42no—
747C8—42no—
748C8—42no—
749C8—42no—
750C8—42no—
751C22—21no—
752C22—21no—
753C22—21no—
754C22—21no—
755C22—24no—
756C22—24no—
757C22—42no—
758C22—42no—
759C22—42no—
760C22—44no—
761C22—84no—
762C22—88no—
763C22—84no—
764C22—82no—
765C22—82no—
766C22—84no—
767C22—88no—
768C22#241512yes—
769C22#241512yes—
770C22#306712yes—
771C22#306812yes—
772C22C22×#12111yescharacteristic
773C22C2×#55211yescharacteristic
774C22C2×#55611yescharacteristic
775C4—22no—
776C4—22no—
777C4—22no—
778C4—22no—
779C4—42no—
780C4—42no—
781C4—42no—
782C4—82no—
783C4—82no—
784C4—82no—
785C4#241512yes—
786C4#241512yes—
787C4C2×#52511yescharacteristic
788C4C2×#53611yescharacteristic
789C4C2×#54711yescharacteristic
790C4C2×#54811yescharacteristic
791C2—22no—
792C2—21no—
793C2—21no—
794C2—82no—
795C2—84no—
796C2#2472414yesdirect product factor
797C2C2×#241511yescharacteristic
798C2C2×#306711yescharacteristic
799C2C2×#306811yescharacteristic
subgroupG/H
center, socleC23C2×#121
commutator, Frattini, cosocleC22×C4C25
prime radicalC22×AGL(1,ℤ/8)C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C22×C42 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3080C2semidirect
2. C22×#478C2semidirect
4. C2×#2925C2semidirect
5. #24724C2direct (N × H)
6. C2×#2079C2semidirect
7. C2×#2078C2semidirect
10. C2×#1998C2semidirect
11. C2×#1952C2semidirect
12. C2×#1951C2semidirect
13. C2×#1950C2semidirect
14. C2×#1931C2semidirect
15. C2×#1931C2semidirect
16. C2×#1800C2semidirect
22. #3080C22semidirect
32. C2×#478C22semidirect
40. #2925C22semidirect
68. #2079C22semidirect
69. #2078C22semidirect
72. #1998C22semidirect
73. #1952C22semidirect
74. #1951C22semidirect
75. #1950C22semidirect
76. #1931C22semidirect
77. #1931C22semidirect
78. #1800C22semidirect
796. C2#24724direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#30802
C22×#4782
C2×C4×AGL(1,ℤ/8)2
C2×#29252
#247242
C2×#20792
C2×#20782
C2×#20512
C2×#19982
C2×#19522
C2×#19512
C2×#19502
C2×#19312
C2×#18002