Finite Group Databasebeta

← #777346

Subgroups — #777346

Order 512.

4164 conjugacy classes of subgroups.

The subgroup lattice has 811 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#554C211yesmaximal, characteristic, complemented
2C2×#2536C212yesmaximal, complemented
3C2×#2421C211yesmaximal, characteristic, complemented
4#16605C212yesmaximal, complemented
5#15672C214yesmaximal, complemented
6#15613C214yesmaximal, complemented
7#15230C211yesmaximal, characteristic, complemented
8#15129C211yesmaximal, characteristic, complemented
9#15125C211yesmaximal, characteristic, complemented
10#14933C212yesmaximal, complemented
11#14806C212yesmaximal
12#14190C212yesmaximal, complemented
13#13969C212yesmaximal, complemented
14#13881C212yesmaximal, complemented
15#13872C212yesmaximal, complemented
16C4×#392C211yesmaximal, characteristic
17Q8×#95C211yesmaximal, characteristic, complemented
18C2×#554—216no—
19C2×#554—28no—
20C22×C4⋊Q8C2211yescharacteristic
21C22×#125C2212yes—
22C22×C22⋊Q8C2214yes—
23C22×C22⋊Q8C2211yescharacteristic
24C22×C22⋊Q8C2212yes—
25C22×C4×Q8C2212yes—
26C22×C4×Q8C2211yescharacteristic
27C22×C4×D4C2211yescharacteristic
28C22×C4×D4C2212yes—
29C22×C4×D4C2212yes—
30C23×C4⋊C4C2212yes—
31#2536—216no—
32#2421—28no—
33C2×#400C2212yes—
34C2×#398C2214yes—
35C2×#397C2212yes—
36C2×#394C2212yes—
37C2×#394C2214yes—
38C2×#393C2212yes—
39C2×#392C2211yescharacteristic
40C2×#391C2211yescharacteristic
41C2×#389C2211yescharacteristic
42C2×#388C2214yes—
43C2×#388C2214yes—
44C2×#388C2212yes—
45C2×#387C2212yes—
46C2×#386C2214yes—
47C2×#382C2211yescharacteristic
48C2×#382C2212yes—
49C2×#380C2212yes—
50C2×#380C2212yes—
51C2×#380C2211yescharacteristic
52C2×#380C2212yes—
53C2×C4×C22⋊C4C2211yescharacteristic
54C2×C4×C22⋊C4C2212yes—
55#1446C2212yes—
56#1446C2214yes—
57#1444C2211yescharacteristic
58#1442C2212yes—
59#1442C2214yes—
60#1442C2214yes—
61#1441C2212yes—
62#1441C2214yes—
63#1441C2212yes—
64#1441C2212yes—
65#1441C2214yes—
66#1440C2214yes—
67#1439C2212yes—
68#1439C2212yes—
69#1439C2211yescharacteristic
70#1439C2214yes—
71#1439C2214yes—
72#1438C2211yescharacteristic
73#1438C2212yes—
74#1437C2214yes—
75#1436C2214yes—
76C4⋊#95C2211yescharacteristic
77C4⋊#95C2212yes—
78C4⋊#95C2212yes—
79C4⋊#95C2212yes—
80C4⋊#95C2214yes—
81C4⋊#95C2212yes—
82C22⋊#95C2214yes—
83C22⋊#95C2214yes—
84C22⋊#95C2214yes—
85C4×#95C2211yescharacteristic
86C4×#95C2212yes—
87C23×Q8C2311yescharacteristic
88C23×Q8C2312yes—
89C23×D4C2311yescharacteristic
90C23×D4C2312yes—
91C24×C4C2311yescharacteristic
92C24×C4C2312yes—
93C24×C4C2314yes—
94#554—2128no—
95C2×C4⋊Q8—28no—
96C2×C4⋊Q8—24no—
97C2×#125—216no—
98C2×#125—28no—
99C2×C22⋊Q8—28no—
100C2×C22⋊Q8—28no—
101C2×C22⋊Q8—24no—
102C2×C22⋊Q8—28no—
103C2×C22⋊Q8—216no—
104C2×C22⋊Q8—216no—
105C2×C22⋊Q8—216no—
106C2×C22⋊Q8D4116yescomplemented
107C2×C4×Q8—28no—
108C2×C4×Q8—28no—
109C2×C4×Q8—28no—
110C2×C4×Q8—44no—
111C2×C4×Q8D418yescomplemented
112C2×C4×D4—28no—
113C2×C4×D4—28no—
114C2×C4×D4—216no—
115C2×C4×D4—28no—
116C2×C4×D4—24no—
117C2×C4×D4—28no—
118C2×C4×D4—44no—
119C22×C4⋊C4—28no—
120C22×C4⋊C4—28no—
121C22×C4⋊C4—28no—
122C22×C4⋊C4C2312yes—
123C22×C4⋊C4C2312yes—
124C22×C4⋊C4C2314yes—
125C22×C4⋊C4C2311yescharacteristic
126C22×C4⋊C4C2312yes—
127C22×C4⋊C4C2312yes—
128C22×C4⋊C4C2311yescharacteristic
129C22×C4⋊C4C2311yescharacteristic
130C22×C4⋊C4C2314yes—
131C22×C4⋊C4C2312yes—
132C22×C4⋊C4C2312yes—
133C22×C4⋊C4C2314yes—
134C22×C4⋊C4C2311yescharacteristic
135C22×C4⋊C4C2312yes—
136C22×C22⋊C4C2311yescharacteristic
137C22×C22⋊C4C2312yes—
138C22×C22⋊C4C2314yes—
139C22×C22⋊C4C2312yes—
140C22×C22⋊C4C2312yes—
141C22×C22⋊C4C2311yescharacteristic
142C22×C22⋊C4C2314yes—
143C22×C22⋊C4C2312yes—
144C22×C22⋊C4C2312yes—
145C22×C22⋊C4C2312yes—
146C22×C22⋊C4C2312yes—
147C22×C22⋊C4C2314yes—
148C22×C22⋊C4C2314yes—
149C22×C42C2311yescharacteristic
150C22×C42C2314yes—
151C22×C42C2312yes—
152C22×C42C2311yescharacteristic
153C22×C42C2312yes—
154#400—28no—
155#398—216no—
156#397—28no—
157#394—28no—
158#394—216no—
159#393—44no—
160#392—24no—
161#391—24no—
162#389—24no—
163#388—216no—
164#388—216no—
165#388—28no—
166#387—28no—
167#386—48no—
168#382—24no—
169#382—28no—
170#380—28no—
171#380—24no—
172#380—28no—
173#380—44no—
174C4×C22⋊C4—24no—
175C4×C22⋊C4—28no—
176C2×#95C2311yescharacteristic
177C2×#95C2314yes—
178C2×#95C2312yes—
179C2×#95C2312yes—
180C2×#95C2312yes—
181C2×#95C2312yes—
182C2×#95C2314yes—
183C2×#95C2314yes—
184C2×#95C2311yescharacteristic
185C2×#95C2312yes—
186C2×#95C2312yes—
187C2×#95C2312yes—
188C2×#95C2311yescharacteristic
189C2×#95C2314yes—
190C2×#95C2312yes—
191C2×#95C2312yes—
192C2×#95C2311yescharacteristic
193C2×#95C2314yes—
194C2×#95C2312yes—
195C2×#95C2314yes—
196C2×#95C2312yes—
197C2×#95C2314yes—
198C2×#95C2314yes—
199C2×#95C2314yes—
200C2×#95C2314yes—
201C2×#95C2314yes—
202C25C2411yescharacteristic
203C25C2412yes—
204C22×Q8—28no—
205C22×Q8—24no—
206C22×Q8—24no—
207C22×Q8—22no—
208C22×Q8—22no—
209C22×Q8—42no—
210C22×Q8—44no—
211C22×Q8—42no—
212C22×Q8C2×D418yes—
213C22×Q8C2×D414yes—
214C22×D4—24no—
215C22×D4—24no—
216C22×D4—24no—
217C22×D4—24no—
218C22×D4—24no—
219C22×D4—24no—
220C22×D4—22no—
221C22×D4—24no—
222C22×D4—22no—
223C22×D4—42no—
224C22×D4—42no—
225C22×D4#4114yes—
226C23×C4—28no—
227C23×C4—24no—
228C23×C4—24no—
229C23×C4—24no—
230C23×C4—24no—
231C23×C4—24no—
232C23×C4—24no—
233C23×C4—28no—
234C23×C4—28no—
235C23×C4—24no—
236C23×C4—22no—
237C23×C4—24no—
238C23×C4—22no—
239C23×C4—22no—
240C23×C4—44no—
241C23×C4—44no—
242C23×C4—44no—
243C23×C4—44no—
244C23×C4C2×D418yes—
245C23×C4C2412yes—
246C23×C4C2412yes—
247C23×C4C2414yes—
248C23×C4C2411yescharacteristic
249C23×C4C2411yescharacteristic
250C23×C4C2411yescharacteristic
251C23×C4C2411yescharacteristic
252C23×C4C2412yes—
253C23×C4C2414yes—
254C23×C4C2412yes—
255C23×C4C2412yes—
256C23×C4C2412yes—
257C23×C4C2412yes—
258C23×C4C2411yescharacteristic
259C23×C4C2411yescharacteristic
260C4⋊Q8—232no—
261#125—264no—
262C22⋊Q8—2128no—
263C22⋊Q8—264no—
264C22⋊Q8—416no—
265C4×Q8—232no—
266C4×Q8—432no—
267C4×D4—264no—
268C4×D4—232no—
269C4×D4—432no—
270C2×C4⋊C4—264no—
271C2×C4⋊C4—24no—
272C2×C4⋊C4—28no—
273C2×C4⋊C4—28no—
274C2×C4⋊C4—28no—
275C2×C4⋊C4—24no—
276C2×C4⋊C4—24no—
277C2×C4⋊C4—24no—
278C2×C4⋊C4—22no—
279C2×C4⋊C4—28no—
280C2×C4⋊C4—24no—
281C2×C4⋊C4—28no—
282C2×C4⋊C4—28no—
283C2×C4⋊C4—28no—
284C2×C4⋊C4—24no—
285C2×C4⋊C4—24no—
286C2×C4⋊C4—28no—
287C2×C4⋊C4—24no—
288C2×C4⋊C4—22no—
289C2×C4⋊C4—24no—
290C2×C4⋊C4—28no—
291C2×C4⋊C4—22no—
292C2×C4⋊C4—24no—
293C2×C4⋊C4—24no—
294C2×C4⋊C4—28no—
295C2×C4⋊C4—24no—
296C2×C4⋊C4—24no—
297C2×C4⋊C4—24no—
298C2×C4⋊C4—22no—
299C2×C4⋊C4—22no—
300C2×C4⋊C4—24no—
301C2×C4⋊C4—42no—
302C2×C4⋊C4—44no—
303C2×C4⋊C4C2×D414yes—
304C2×C4⋊C4C2×D418yes—
305C2×C4⋊C4C2×D418yes—
306C2×C4⋊C4C2×D4116yes—
307C2×C22⋊C4—24no—
308C2×C22⋊C4—24no—
309C2×C22⋊C4—24no—
310C2×C22⋊C4—28no—
311C2×C22⋊C4—28no—
312C2×C22⋊C4—24no—
313C2×C22⋊C4—28no—
314C2×C22⋊C4—24no—
315C2×C22⋊C4—28no—
316C2×C22⋊C4—24no—
317C2×C22⋊C4—28no—
318C2×C22⋊C4—22no—
319C2×C22⋊C4—24no—
320C2×C22⋊C4—28no—
321C2×C22⋊C4—24no—
322C2×C22⋊C4—28no—
323C2×C22⋊C4—24no—
324C2×C22⋊C4—22no—
325C2×C22⋊C4—22no—
326C2×C22⋊C4—28no—
327C2×C22⋊C4—24no—
328C2×C22⋊C4—24no—
329C2×C22⋊C4—24no—
330C2×C22⋊C4—24no—
331C2×C22⋊C4—24no—
332C2×C22⋊C4—22no—
333C2×C22⋊C4—22no—
334C2×C22⋊C4—28no—
335C2×C22⋊C4—42no—
336C2×C22⋊C4—42no—
337C2×C22⋊C4—42no—
338C2×C22⋊C4—44no—
339C2×C22⋊C4—41no—
340C2×C22⋊C4—42no—
341C2×C22⋊C4—42no—
342C2×C22⋊C4—44no—
343C2×C22⋊C4—44no—
344C2×C22⋊C4C2×D4116yes—
345C2×C42—28no—
346C2×C42—24no—
347C2×C42—24no—
348C2×C42—24no—
349C2×C42—28no—
350C2×C42—22no—
351C2×C42—28no—
352C2×C42—24no—
353C2×C42—44no—
354C2×C42C2×D418yes—
355C2×C42C2×D414yes—
356C2×C42#4118yes—
357#95—22no—
358#95—22no—
359#95—24no—
360#95—28no—
361#95—28no—
362#95—24no—
363#95—28no—
364#95—24no—
365#95—28no—
366#95—24no—
367#95—24no—
368#95—24no—
369#95—24no—
370#95—24no—
371#95—22no—
372#95—24no—
373#95—22no—
374#95—42no—
375#95—44no—
376#95—44no—
377#95—44no—
378#95—44no—
379#95—44no—
380#95—44no—
381#95—44no—
382#95—42no—
383C24—22no—
384C24—22no—
385C24—22no—
386C24—22no—
387C24—22no—
388C24—22no—
389C24—22no—
390C24—22no—
391C24—22no—
392C24—22no—
393C24—22no—
394C24—22no—
395C24—21no—
396C24—22no—
397C24—22no—
398C24—21no—
399C24—21no—
400C24—21no—
401C24—21no—
402C24—22no—
403C24—21no—
404C24—22no—
405C24C22×D414yes—
406C24C2×#4114yes—
407C24H(5,𝔽2)12yes—
408C242−1+414yes—
409C24C2511yescharacteristic
410C2×Q8—216no—
411C2×Q8—28no—
412C2×Q8—28no—
413C2×Q8—216no—
414C2×Q8—216no—
415C2×Q8—88no—
416C2×Q8—84no—
417C2×Q8—88no—
418C2×Q8—84no—
419C2×Q8#120116yes—
420C2×D4—28no—
421C2×D4—28no—
422C2×D4—216no—
423C2×D4—216no—
424C2×D4—216no—
425C2×D4—28no—
426C2×D4—48no—
427C2×D4—48no—
428C2×D4—48no—
429C2×D4—48no—
430C2×D4—48no—
431C2×D4—48no—
432C22×C4—22no—
433C22×C4—24no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—24no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—24no—
444C22×C4—24no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—24no—
451C22×C4—21no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—24no—
463C22×C4—24no—
464C22×C4—24no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—24no—
468C22×C4—21no—
469C22×C4—232no—
470C22×C4—216no—
471C22×C4—216no—
472C22×C4—216no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—22no—
476C22×C4—21no—
477C22×C4—24no—
478C22×C4—22no—
479C22×C4—24no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—24no—
484C22×C4—24no—
485C22×C4—21no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—21no—
490C22×C4—24no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—24no—
494C22×C4—21no—
495C22×C4—24no—
496C22×C4—24no—
497C22×C4—21no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—21no—
503C22×C4—22no—
504C22×C4—24no—
505C22×C4—22no—
506C22×C4—21no—
507C22×C4—48no—
508C22×C4—48no—
509C22×C4—48no—
510C22×C4—48no—
511C22×C4—44no—
512C22×C4—44no—
513C22×C4—44no—
514C22×C4—48no—
515C22×C4—48no—
516C22×C4—88no—
517C22×C4—88no—
518C22×C4—88no—
519C22×C4—88no—
520C22×C4—88no—
521C22×C4—88no—
522C22×C4C22×D412yes—
523C22×C4C22×D414yes—
524C22×C4C22×D418yes—
525C22×C4C22×D414yes—
526C22×C4C22×D414yes—
527C22×C4C22×D418yes—
528C22×C4C22×D412yes—
529C22×C4C22×D412yes—
530C22×C4C22×D414yes—
531C22×C4C2×#4114yes—
532C22×C4C2×#4114yes—
533C22×C4C2×#4112yes—
534C22×C4C2×#4114yes—
535C22×C4H(5,𝔽2)12yes—
536C22×C42−1+412yes—
537C22×C42−1+412yes—
538C4⋊C4—232no—
539C4⋊C4—28no—
540C4⋊C4—216no—
541C4⋊C4—28no—
542C4⋊C4—216no—
543C4⋊C4—216no—
544C4⋊C4—232no—
545C4⋊C4—48no—
546C4⋊C4—416no—
547C4⋊C4—44no—
548C4⋊C4—48no—
549C4⋊C4—44no—
550C4⋊C4—48no—
551C4⋊C4—48no—
552C22⋊C4—216no—
553C22⋊C4—232no—
554C22⋊C4—48no—
555C22⋊C4—48no—
556C22⋊C4—48no—
557C22⋊C4—416no—
558C22⋊C4—44no—
559C22⋊C4—48no—
560C22⋊C4—48no—
561C22⋊C4—416no—
562C22⋊C4—48no—
563C22⋊C4—44no—
564C22⋊C4—88no—
565C42—216no—
566C42—28no—
567C42—216no—
568C42—416no—
569C42—44no—
570C23—24no—
571C23—24no—
572C23—24no—
573C23—24no—
574C23—24no—
575C23—24no—
576C23—24no—
577C23—24no—
578C23—24no—
579C23—24no—
580C23—24no—
581C23—24no—
582C23—24no—
583C23—24no—
584C23—24no—
585C23—24no—
586C23—24no—
587C23—24no—
588C23—22no—
589C23—24no—
590C23—24no—
591C23—22no—
592C23—22no—
593C23—42no—
594C23—42no—
595C23—42no—
596C23—42no—
597C23—42no—
598C23—42no—
599C23—42no—
600C23—42no—
601C23—42no—
602C23—42no—
603C23—42no—
604C23—42no—
605C23—42no—
606C23—42no—
607C23—42no—
608C23—42no—
609C23—41no—
610C23—41no—
611C23—41no—
612C23—42no—
613C23—42no—
614C23—41no—
615C23—42no—
616C23—42no—
617C23—41no—
618C23—42no—
619C23—42no—
620C23—41no—
621C23—42no—
622C23—42no—
623C23—41no—
624C23—42no—
625C23—41no—
626C23—42no—
627C23#54818yes—
628C23C23×D411yescharacteristic
629C23C23×D412yes—
630C23C22×#4112yes—
631C23C22×#4111yescharacteristic
632C23C2×H(5,𝔽2)11yescharacteristic
633C23C2×H(5,𝔽2)11yescharacteristic
634C23C2×2−1+411yescharacteristic
635C23C2×2−1+412yes—
636C23C2×2−1+411yescharacteristic
637C23#58512yes—
638C23#58511yescharacteristic
639Q8—232no—
640Q8—816no—
641D4—232no—
642D4—432no—
643C2×C4—22no—
644C2×C4—24no—
645C2×C4—24no—
646C2×C4—28no—
647C2×C4—28no—
648C2×C4—24no—
649C2×C4—22no—
650C2×C4—24no—
651C2×C4—22no—
652C2×C4—24no—
653C2×C4—24no—
654C2×C4—28no—
655C2×C4—24no—
656C2×C4—24no—
657C2×C4—24no—
658C2×C4—24no—
659C2×C4—24no—
660C2×C4—24no—
661C2×C4—28no—
662C2×C4—22no—
663C2×C4—24no—
664C2×C4—24no—
665C2×C4—24no—
666C2×C4—28no—
667C2×C4—22no—
668C2×C4—24no—
669C2×C4—42no—
670C2×C4—42no—
671C2×C4—42no—
672C2×C4—42no—
673C2×C4—42no—
674C2×C4—42no—
675C2×C4—44no—
676C2×C4—44no—
677C2×C4—44no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—44no—
682C2×C4—44no—
683C2×C4—44no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—432no—
690C2×C4—42no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—42no—
696C2×C4—41no—
697C2×C4—44no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—44no—
701C2×C4—41no—
702C2×C4—44no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—44no—
707C2×C4—41no—
708C2×C4—42no—
709C2×C4—44no—
710C2×C4—41no—
711C2×C4—44no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—44no—
715C2×C4—42no—
716C2×C4—41no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—44no—
721C2×C4—44no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—832no—
725C2×C4—88no—
726C2×C4C2×#12018yes—
727C2×C4C2×#12014yes—
728C2×C4#53214yes—
729C2×C4#53714yes—
730C2×C4#54618yes—
731C2×C4#54718yes—
732C2×C4#54814yes—
733C22—28no—
734C22—28no—
735C22—28no—
736C22—44no—
737C22—44no—
738C22—44no—
739C22—44no—
740C22—44no—
741C22—44no—
742C22—44no—
743C22—44no—
744C22—44no—
745C22—44no—
746C22—44no—
747C22—44no—
748C22—42no—
749C22—44no—
750C22—44no—
751C22—42no—
752C22—42no—
753C22—81no—
754C22—82no—
755C22—81no—
756C22—82no—
757C22—81no—
758C22—81no—
759C22C22×#12011yescharacteristic
760C22C2×#53211yescharacteristic
761C22C2×#53711yescharacteristic
762C22C2×#54612yes—
763C22C2×#54712yes—
764C22C2×#54812yes—
765C22C2×#54811yescharacteristic
766C22#347512yes—
767C22#348611yescharacteristic
768C22#348612yes—
769C22#348811yescharacteristic
770C22#348812yes—
771C22#349212yes—
772C22#349512yes—
773C22#350011yescharacteristic
774C22#350012yes—
775C22#350712yes—
776C22#351511yescharacteristic
777C22#351911yescharacteristic
778C22#354112yes—
779C22#354411yescharacteristic
780C22#354711yescharacteristic
781C22#356312yes—
782C4—28no—
783C4—24no—
784C4—44no—
785C4—44no—
786C4—44no—
787C4—44no—
788C4—48no—
789C4—42no—
790C4—81no—
791C4—84no—
792C4—81no—
793C4—81no—
794C4—82no—
795C4—82no—
796C4#243018yes—
797C2—48no—
798C2—82no—
799C2C2×#243011yescharacteristic
800C2#3592611yescharacteristic
801C2#3608211yescharacteristic
802C2#3653411yescharacteristic
803C2#3657511yescharacteristic
804C2#3912611yescharacteristic
805C2#4279011yescharacteristic
806C2#4492112yes—
807C2#4511412yes—
808C2#5902412yes—
809C2#5931712yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC2×#392C22
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C22×#554C2semidirect
2. C2×#2536C2semidirect
3. C2×#2421C2semidirect
4. #16605C2semidirect
5. #15672C2semidirect
6. #15613C2semidirect
7. #15230C2semidirect
8. #15129C2semidirect
9. #15125C2semidirect
10. #14933C2semidirect
12. #14190C2semidirect
13. #13969C2semidirect
14. #13881C2semidirect
15. #13872C2semidirect
17. Q8×#95C2semidirect
106. C2×C22⋊Q8D4semidirect
111. C2×C4×Q8D4semidirect

Maximal subgroups

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

subgroupindex
C22×#5542
C2×#25362
C2×#24212
#166052
#156722
#156132
#152302
#151292
#151252
#149332
#148062
#141902
#139692
#138812
#138722
C4×#3922
Q8×#952