Finite Group Databasebeta

← #222047

Subgroups — #222047

Order 512.

1167 conjugacy classes of subgroups.

The subgroup lattice has 747 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D4×C4⋊Q8C211yesmaximal, characteristic
2#22750C211yesmaximal, characteristic
3#22750C211yesmaximal, characteristic
4C2×#1556C211yesmaximal, characteristic, complemented
5C22×#332C211yesmaximal, characteristic, complemented
6#9705C211yesmaximal, characteristic, complemented
7#9703C211yesmaximal, characteristic, complemented
8#9140C211yesmaximal, characteristic, complemented
9#9138C211yesmaximal, characteristic, complemented
10#9131C211yesmaximal, characteristic, complemented
11#9129C211yesmaximal, characteristic, complemented
12#8593C211yesmaximal, characteristic, complemented
13#8340C211yesmaximal, characteristic, complemented
14#8340C211yesmaximal, characteristic, complemented
15#8233C211yesmaximal, characteristic, complemented
16C2×D4×Q8—21no—
17C22×C4⋊Q8C2211yescharacteristic
18C22×C4⋊Q8C2211yescharacteristic
19C2×#432C2211yescharacteristic
20C2×#432C2211yescharacteristic
21C22×C4⋊C8C2211yescharacteristic
22C22×C4⋊C8C2211yescharacteristic
23#2868C2211yescharacteristic
24#2857C2211yescharacteristic
25#2857C2211yescharacteristic
26#2551—21no—
27#2551C412yes—
28#2546—21no—
29#2440—21no—
30#2440—21no—
31#2440C412yes—
32#2440C412yes—
33#2434—21no—
34#2434—21no—
35D4×C4⋊C4—21no—
36D4×C4⋊C4C412yes—
37C4×C4⋊Q8C2211yescharacteristic
38C42×D4C2211yescharacteristic
39#1924—21no—
40#1924—21no—
41#1917—21no—
42#1917—21no—
43#1869—21no—
44#1869—21no—
45#1831C2211yescharacteristic
46#1831C2211yescharacteristic
47#1797C2211yescharacteristic
48#1797C2211yescharacteristic
49#1797C2211yescharacteristic
50#1797C2211yescharacteristic
51#1767C2211yescharacteristic
52#1767C2211yescharacteristic
53#1752—21no—
54#1752—21no—
55#1556—24no—
56C2×#332—24no—
57C2×#332C2211yescharacteristic
58C2×#332C2211yescharacteristic
59C2×#332C2211yescharacteristic
60C2×#332C2211yescharacteristic
61C2×#332C2211yescharacteristic
62C2×#332C2211yescharacteristic
63C2×#332C2211yescharacteristic
64C2×#332C2211yescharacteristic
65C2×#332C2211yescharacteristic
66C2×#332C2211yescharacteristic
67C2×#332C2211yescharacteristic
68C2×#332C2211yescharacteristic
69#1296C2211yescharacteristic
70#1296C2211yescharacteristic
71#1296C2211yescharacteristic
72#1296C2211yescharacteristic
73C23×Q8—21no—
74C23×Q8—21no—
75C23×C8—21no—
76C23×C8—21no—
77D4×Q8—44no—
78D4×Q8—44no—
79C2×C4⋊Q8—22no—
80C2×C4⋊Q8—22no—
81C2×C4⋊Q8—22no—
82C2×C4⋊Q8—22no—
83C2×C4⋊Q8—22no—
84C2×C4⋊Q8—21no—
85C2×C4⋊Q8—21no—
86C2×C4⋊Q8—21no—
87C2×C4⋊Q8—21no—
88C2×C4⋊Q8—21no—
89C2×C4⋊Q8—21no—
90C2×C4⋊Q8—41no—
91C2×C4⋊Q8—41no—
92C2×C4⋊Q8—41no—
93C2×C4⋊Q8—41no—
94C2×C4⋊Q8C2×C412yes—
95C2×C4⋊Q8C2×C412yes—
96C2×C4⋊Q8C2311yescharacteristic
97C2×C4⋊Q8C2311yescharacteristic
98C2×C4⋊Q8C2311yescharacteristic
99C2×C22⋊Q8—21no—
100C2×C22⋊Q8—21no—
101C2×C22⋊Q8—22no—
102C2×C22⋊Q8—22no—
103C2×C4×Q8—21no—
104C2×C4×D4—22no—
105C2×C4×D4C2×C411yescharacteristic
106C2×C4×D4D411yescharacteristic
107C2×C4×D4D411yescharacteristic
108C22×C4⋊C4—21no—
109C22×C4⋊C4—21no—
110C22×C4⋊C4C2×C412yes—
111C22×C4⋊C4C2×C412yes—
112C22×C42C2311yescharacteristic
113C22×C42C2311yescharacteristic
114#432—22no—
115#432—22no—
116#432—41no—
117#432—41no—
118C2×C4⋊C8—22no—
119C2×C4⋊C8—22no—
120C2×C4⋊C8—21no—
121C2×C4⋊C8—21no—
122C2×C4⋊C8—41no—
123C2×C4⋊C8—41no—
124C2×C4⋊C8C2311yescharacteristic
125C2×C4⋊C8C2311yescharacteristic
126C2×C4⋊C8C2311yescharacteristic
127C2×C4⋊C8C2311yescharacteristic
128C2×C4⋊C8C2311yescharacteristic
129C2×C4⋊C8C2311yescharacteristic
130C2×C4⋊C8C2311yescharacteristic
131C2×C4⋊C8C2311yescharacteristic
132C2×C22⋊C8—21no—
133C2×C22⋊C8—21no—
134C2×C22⋊C8—21no—
135C2×C22⋊C8—21no—
136C2×C22⋊C8—21no—
137C2×C22⋊C8—21no—
138C2×#97—21no—
139C2×#97—21no—
140C2×#97—21no—
141C2×#97—21no—
142#398—22no—
143#398—22no—
144#395—22no—
145#395—22no—
146#395—22no—
147#395—22no—
148#391—21no—
149#391—21no—
150#391—21no—
151#389—22no—
152#389—22no—
153#389—21no—
154#389—21no—
155#389—21no—
156#389C2×C412yes—
157#389C2×C412yes—
158#389C2×C412yes—
159#385—22no—
160#385—22no—
161#385—22no—
162#385—22no—
163#384—21no—
164#384—21no—
165#384C2×C412yes—
166#384C2×C412yes—
167#384C2311yescharacteristic
168#380—21no—
169#380—21no—
170#380C2×C412yes—
171#380C2×C412yes—
172C4×C4⋊C4—21no—
173C4×C4⋊C4C2×C412yes—
174C4×C4⋊C4C2×C411yescharacteristic
175C4×C4⋊C4D411yescharacteristic
176C4×C4⋊C4D411yescharacteristic
177C4×C22⋊C4C2×C411yescharacteristic
178C4×C22⋊C4C2×C411yescharacteristic
179C4×C22⋊C4D411yescharacteristic
180C4×C22⋊C4D411yescharacteristic
181C4×C22⋊C4D411yescharacteristic
182C4×C22⋊C4D411yescharacteristic
183C43C2311yescharacteristic
184#336—21no—
185#336—21no—
186#336—21no—
187#336—21no—
188#336—21no—
189#336—21no—
190#336—21no—
191#336—21no—
192#336—21no—
193#336—21no—
194#332—22no—
195#332—22no—
196#332—22no—
197#332—22no—
198#332—22no—
199#332—22no—
200#332—22no—
201#332—41no—
202#332—41no—
203#332—41no—
204#332—41no—
205#332D414yescomplemented
206C22×Q8—22no—
207C22×Q8—22no—
208C22×Q8—21no—
209C22×Q8—21no—
210C22×Q8—21no—
211C22×Q8—42no—
212C22×Q8—42no—
213C22×Q8—42no—
214C22×Q8—42no—
215C22×Q8—42no—
216C22×Q8—42no—
217C22×Q8—42no—
218C22×Q8—42no—
219C22×Q8—81no—
220C22×Q8—81no—
221C22×Q8—81no—
222C22×Q8—81no—
223C22×D4C22⋊C411yescharacteristic
224C23×C4—22no—
225C23×C4—22no—
226C23×C4C22×C411yescharacteristic
227C23×C4C22×C411yescharacteristic
228C23×C4C2×D411yescharacteristic
229C23×C4C2×D411yescharacteristic
230C23×C4C2×D411yescharacteristic
231C23×C4C2×D411yescharacteristic
232C22×C8—21no—
233C22×C8—21no—
234C22×C8—21no—
235C22×C8—21no—
236C22×C8—21no—
237C22×C8—21no—
238C22×C8—21no—
239C22×C8—21no—
240C22×C8—42no—
241C22×C8—42no—
242C22×C8—42no—
243C22×C8—42no—
244C22×C8—81no—
245C22×C8—81no—
246C4⋊Q8—24no—
247C4⋊Q8—24no—
248C4⋊Q8—21no—
249C4⋊Q8—21no—
250C4⋊Q8—21no—
251C4⋊Q8—21no—
252C4⋊Q8—21no—
253C4⋊Q8—21no—
254C4⋊Q8—21no—
255C4⋊Q8—21no—
256C4⋊Q8—21no—
257C4⋊Q8—21no—
258C4⋊Q8—42no—
259C4⋊Q8—42no—
260C4⋊Q8—42no—
261C4⋊Q8—42no—
262C4⋊Q8—42no—
263C4⋊Q8—42no—
264C4⋊Q8—42no—
265C4⋊Q8—42no—
266C4⋊Q8—42no—
267C4⋊Q8—42no—
268C4⋊Q8—42no—
269C4⋊Q8—42no—
270C4⋊Q8—48no—
271C4⋊Q8—81no—
272C4⋊Q8—81no—
273C4⋊Q8C2×D412yes—
274C4⋊Q8#4112yes—
275C22⋊Q8—48no—
276C22⋊Q8—48no—
277C22⋊Q8—42no—
278C22⋊Q8—42no—
279C22⋊Q8—42no—
280C22⋊Q8—42no—
281C4×Q8—42no—
282C4×Q8—42no—
283C4×D4—24no—
284C4×D4—22no—
285C4×D4—22no—
286C4×D4—22no—
287C4×D4—22no—
288C4×D4—48no—
289C2×C4⋊C4—21no—
290C2×C4⋊C4—24no—
291C2×C4⋊C4—24no—
292C2×C4⋊C4—22no—
293C2×C4⋊C4—22no—
294C2×C4⋊C4—22no—
295C2×C4⋊C4—22no—
296C2×C4⋊C4—22no—
297C2×C4⋊C4—22no—
298C2×C4⋊C4—22no—
299C2×C4⋊C4—22no—
300C2×C4⋊C4—22no—
301C2×C4⋊C4—21no—
302C2×C4⋊C4—21no—
303C2×C4⋊C4—21no—
304C2×C4⋊C4—21no—
305C2×C4⋊C4—22no—
306C2×C4⋊C4—22no—
307C2×C4⋊C4—42no—
308C2×C4⋊C4—42no—
309C2×C4⋊C4—42no—
310C2×C4⋊C4—42no—
311C2×C4⋊C4—42no—
312C2×C4⋊C4—42no—
313C2×C4⋊C4C22⋊C411yescharacteristic
314C2×C4⋊C4C22⋊C411yescharacteristic
315C2×C4⋊C4C22⋊C411yescharacteristic
316C2×C4⋊C4C22×C412yes—
317C2×C4⋊C4C22×C412yes—
318C2×C4⋊C4C22×C412yes—
319C2×C4⋊C4C22×C412yes—
320C2×C22⋊C4—22no—
321C2×C22⋊C4—22no—
322C2×C22⋊C4C22⋊C411yescharacteristic
323C2×C22⋊C4C22⋊C411yescharacteristic
324C2×C22⋊C4C22⋊C411yescharacteristic
325C2×C22⋊C4C22⋊C411yescharacteristic
326C2×C22⋊C4C22⋊C411yescharacteristic
327C2×C22⋊C4C22⋊C411yescharacteristic
328C2×C42—21no—
329C2×C42—21no—
330C2×C42—21no—
331C2×C42—21no—
332C2×C42—21no—
333C2×C42—21no—
334C2×C42—21no—
335C2×C42—21no—
336C2×C42—22no—
337C2×C42C22×C411yescharacteristic
338C2×C42C22×C411yescharacteristic
339C2×C42C22×C411yescharacteristic
340C2×C42C22×C411yescharacteristic
341C2×C42C2×D411yescharacteristic
342C2×C42C2×D411yescharacteristic
343C2×C42C2×D411yescharacteristic
344C2×C42C2×D411yescharacteristic
345C2×C42C2×D411yescharacteristic
346C2×C42C2×D411yescharacteristic
347C2×C42C2×D411yescharacteristic
348C2×C42C2×D411yescharacteristic
349C2×C42C2411yescharacteristic
350C4⋊C8—21no—
351C4⋊C8—21no—
352C4⋊C8—21no—
353C4⋊C8—21no—
354C4⋊C8—21no—
355C4⋊C8—21no—
356C4⋊C8—21no—
357C4⋊C8—21no—
358C4⋊C8—21no—
359C4⋊C8—21no—
360C4⋊C8—21no—
361C4⋊C8—21no—
362C4⋊C8—21no—
363C4⋊C8—21no—
364C4⋊C8—42no—
365C4⋊C8—42no—
366C4⋊C8C2×D412yes—
367C4⋊C8C2×D412yes—
368C22⋊C8—42no—
369C22⋊C8—42no—
370C22⋊C8—42no—
371C22⋊C8—42no—
372C22⋊C8—81no—
373C22⋊C8—81no—
374#97—42no—
375#97—42no—
376#97—81no—
377#97—81no—
378#95—22no—
379#95—22no—
380#95—22no—
381#95—22no—
382#95—22no—
383#95—22no—
384#95C22⋊C411yescharacteristic
385#95C22⋊C411yescharacteristic
386#95C22⋊C411yescharacteristic
387#95C22⋊C411yescharacteristic
388#95C22⋊C411yescharacteristic
389#95C22⋊C411yescharacteristic
390C24C2×C22⋊C411yescharacteristic
391C24C2×C22⋊C411yescharacteristic
392C2×Q8—22no—
393C2×Q8—22no—
394C2×Q8—44no—
395C2×Q8—44no—
396C2×Q8—44no—
397C2×Q8—41no—
398C2×Q8—41no—
399C2×Q8—41no—
400C2×Q8—41no—
401C2×Q8—41no—
402C2×Q8—41no—
403C2×Q8—41no—
404C2×Q8—41no—
405C2×Q8—41no—
406C2×Q8—41no—
407C2×Q8—41no—
408C2×Q8—41no—
409C2×Q8—41no—
410C2×Q8—41no—
411C2×Q8—41no—
412C2×Q8—41no—
413C2×Q8—44no—
414C2×Q8—82no—
415C2×Q8—82no—
416C2×Q8—84no—
417C2×Q8—84no—
418C2×Q8—84no—
419C2×Q8—84no—
420C2×Q8—84no—
421C2×Q8—84no—
422C2×Q8—84no—
423C2×Q8—84no—
424C2×D4—22no—
425C2×D4—22no—
426C2×D4#10114yes—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—41no—
458C22×C4—41no—
459C22×C4—44no—
460C22×C4—44no—
461C22×C4—44no—
462C22×C4—44no—
463C22×C4—82no—
464C22×C4—82no—
465C22×C4C2×C22⋊C411yescharacteristic
466C22×C4C2×C22⋊C411yescharacteristic
467C22×C4C2×C22⋊C411yescharacteristic
468C22×C4C2×C22⋊C411yescharacteristic
469C22×C4C2×C22⋊C411yescharacteristic
470C22×C4C2×C22⋊C411yescharacteristic
471C22×C4C2×C22⋊C411yescharacteristic
472C22×C4C2×C22⋊C411yescharacteristic
473C22×C4C2×C22⋊C411yescharacteristic
474C22×C4C2×C22⋊C411yescharacteristic
475C22×C4AGL(1,ℤ/8)12yes—
476C22×C4AGL(1,ℤ/8)12yes—
477C22×C4#13712yes—
478C22×C4#13712yes—
479C22×C4C23×C411yescharacteristic
480C22×C4C22×D411yescharacteristic
481C22×C4C22×D411yescharacteristic
482C2×C8—22no—
483C2×C8—22no—
484C2×C8—41no—
485C2×C8—41no—
486C2×C8—41no—
487C2×C8—41no—
488C2×C8—41no—
489C2×C8—41no—
490C2×C8—41no—
491C2×C8—41no—
492C2×C8—41no—
493C2×C8—41no—
494C2×C8—41no—
495C2×C8—41no—
496C2×C8—41no—
497C2×C8—41no—
498C2×C8—41no—
499C2×C8—41no—
500C2×C8—41no—
501C2×C8—41no—
502C2×C8—41no—
503C2×C8—41no—
504C2×C8—41no—
505C2×C8—41no—
506C2×C8—84no—
507C2×C8—84no—
508C4⋊C4—22no—
509C4⋊C4—22no—
510C4⋊C4—22no—
511C4⋊C4—22no—
512C4⋊C4—22no—
513C4⋊C4—22no—
514C4⋊C4—22no—
515C4⋊C4—22no—
516C4⋊C4—22no—
517C4⋊C4—22no—
518C4⋊C4—44no—
519C4⋊C4—44no—
520C4⋊C4—44no—
521C4⋊C4—44no—
522C4⋊C4—42no—
523C4⋊C4—44no—
524C4⋊C4—44no—
525C4⋊C4—44no—
526C4⋊C4—44no—
527C4⋊C4—41no—
528C4⋊C4—41no—
529C4⋊C4—41no—
530C4⋊C4—41no—
531C4⋊C4—41no—
532C4⋊C4—41no—
533C4⋊C4—41no—
534C4⋊C4—41no—
535C4⋊C4—44no—
536C4⋊C4—82no—
537C4⋊C4—82no—
538C4⋊C4C4×D414yes—
539C22⋊C4—22no—
540C22⋊C4—22no—
541C22⋊C4—22no—
542C22⋊C4—22no—
543C22⋊C4—22no—
544C22⋊C4—22no—
545C22⋊C4—44no—
546C22⋊C4—44no—
547C42—21no—
548C42—21no—
549C42—21no—
550C42—21no—
551C42—21no—
552C42—21no—
553C42—21no—
554C42—21no—
555C42—21no—
556C42—21no—
557C42—21no—
558C42—21no—
559C42—21no—
560C42—21no—
561C42—21no—
562C42—21no—
563C42—21no—
564C42—21no—
565C42—21no—
566C42—21no—
567C42—22no—
568C42—41no—
569C42—44no—
570C42C22×D411yescharacteristic
571C42C2×#4111yescharacteristic
572C42H(5,𝔽2)11yescharacteristic
573C42H(5,𝔽2)11yescharacteristic
574C23—21no—
575C23—21no—
576C23—21no—
577C23—21no—
578C23—21no—
579C23—21no—
580C23—21no—
581C23—21no—
582C23—21no—
583C23—21no—
584C23C2×#10112yes—
585C23C2×#10112yes—
586C23#41812yes—
587C23#41912yes—
588C23C22×C22⋊C411yescharacteristic
589Q8—42no—
590Q8—42no—
591Q8—42no—
592Q8—42no—
593Q8—88no—
594Q8—88no—
595Q8—81no—
596Q8—81no—
597Q8—81no—
598Q8—81no—
599Q8—81no—
600Q8—81no—
601Q8—81no—
602Q8—81no—
603D4—28no—
604C2×C4—21no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—22no—
613C2×C4—22no—
614C2×C4—22no—
615C2×C4—22no—
616C2×C4—22no—
617C2×C4—22no—
618C2×C4—22no—
619C2×C4—22no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—24no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—42no—
643C2×C4—42no—
644C2×C4—42no—
645C2×C4—42no—
646C2×C4—42no—
647C2×C4—42no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—42no—
657C2×C4—42no—
658C2×C4—42no—
659C2×C4—42no—
660C2×C4—42no—
661C2×C4—42no—
662C2×C4—42no—
663C2×C4—42no—
664C2×C4—42no—
665C2×C4—88no—
666C2×C4—88no—
667C2×C4C2×#10112yes—
668C2×C4#41812yes—
669C2×C4#41912yes—
670C2×C4C2×C4×D411yescharacteristic
671C2×C4#51811yescharacteristic
672C2×C4D4211yescharacteristic
673C2×C4D4211yescharacteristic
674C2×C4#54611yescharacteristic
675C2×C4#54611yescharacteristic
676C2×C4C2×AGL(1,ℤ/8)11yescharacteristic
677C2×C4C2×AGL(1,ℤ/8)11yescharacteristic
678C2×C4C2×#13711yescharacteristic
679C2×C4C2×#13711yescharacteristic
680C2×C4#57611yescharacteristic
681C2×C4#57711yescharacteristic
682C2×C4#57711yescharacteristic
683C2×C4#57811yescharacteristic
684C8—42no—
685C8—42no—
686C8—81no—
687C8—81no—
688C8—81no—
689C8—81no—
690C8—81no—
691C8—81no—
692C22—22no—
693C22—22no—
694C22—22no—
695C22—22no—
696C22—22no—
697C22—22no—
698C22—22no—
699C22—22no—
700C22—22no—
701C22—41no—
702C22—41no—
703C22—41no—
704C22—41no—
705C22#155614yescomplemented
706C22D4×C22⋊C411yescharacteristic
707C22C22×#10111yescharacteristic
708C22#288911yescharacteristic
709C22C2×#41811yescharacteristic
710C22C2×#41911yescharacteristic
711C22#289711yescharacteristic
712C22#289811yescharacteristic
713C4—22no—
714C4—21no—
715C4—21no—
716C4—22no—
717C4—22no—
718C4—41no—
719C4—41no—
720C4—41no—
721C4—41no—
722C4—41no—
723C4—41no—
724C4—44no—
725C4—41no—
726C4—82no—
727C4—82no—
728C4—82no—
729C4#326411yescharacteristic
730C4#326511yescharacteristic
731C4#326611yescharacteristic
732C4#327011yescharacteristic
733C4#331011yescharacteristic
734C4#331211yescharacteristic
735C4#331811yescharacteristic
736C4#332011yescharacteristic
737C2—24no—
738C2—42no—
739C2C2×#155611yescharacteristic
740C2#1775911yescharacteristic
741C2#1776111yescharacteristic
742C2#1777411yescharacteristic
743C2D4×#10111yescharacteristic
744C2#2242311yescharacteristic
745C2#2242511yescharacteristic
subgroupG/H
center, socleC23C22×C22⋊C4
commutatorC22×C4C23×C4
Frattini, cosocleC2×C42C24
prime radicalC22×D4C22⋊C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23 ◁ C42×D4 ◁ G
LECSG ▷ C2×C42 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
4. C2×#1556C2semidirect
5. C22×#332C2semidirect
6. #9705C2semidirect
7. #9703C2semidirect
8. #9140C2semidirect
9. #9138C2semidirect
10. #9131C2semidirect
11. #9129C2semidirect
12. #8593C2semidirect
13. #8340C2semidirect
14. #8340C2semidirect
15. #8233C2semidirect
205. #332D4semidirect
705. C22#1556semidirect

Maximal subgroups

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

subgroupindex
D4×C4⋊Q82
#227502
C2×#15562
C22×#3322
#97052
#97032
#91402
#91382
#91312
#91292
#85932
#83402
#82332