Finite Group Databasebeta

← #6380516

Subgroups — #6380516

Order 512.

2378 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×AGL(1,ℤ/8)C211yesmaximal, characteristic
2#34188C211yesmaximal, characteristic, complemented
3#34181C211yesmaximal, characteristic, complemented
4#22780C214yesmaximal, complemented
5#22776C214yesmaximal, complemented
6#22770C212yesmaximal, complemented
7#22766C212yesmaximal, complemented
8#22762C212yesmaximal, complemented
9#22758C212yesmaximal, complemented
10#21092C212yesmaximal, complemented
11#21036C212yesmaximal, complemented
12#20929C212yesmaximal
13#20764C211yesmaximal, characteristic, complemented
14#20645C211yesmaximal, characteristic, complemented
15C2×#1802C211yesmaximal, characteristic, complemented
16#20441C211yesmaximal, characteristic, complemented
17#20416C212yesmaximal, complemented
18C22×AGL(1,ℤ/8)C2211yescharacteristic
19C2×#518C2212yes—
20C2×C4×#41C2211yescharacteristic
21C22×C4×D4C2211yescharacteristic
22C4×AGL(1,ℤ/8)C4116yescomplemented
23C2×#442C2212yes—
24C2×#440C2212yes—
25C2×C4×SD16C2212yes—
26C2×C4×D8C2212yes—
27C2×#428C2211yescharacteristic
28C22×C4⋊C8C2211yescharacteristic
29C2×#417C2211yescharacteristic
30C2×#418C2211yescharacteristic
31C2×#416C2212yes—
32C22×#102C2212yes—
33C2×#405C2212yes—
34C2×C4×M16C2211yescharacteristic
35#2355C2212yescomplemented
36#2355C2212yescomplemented
37#2354C2212yescomplemented
38#2354C2212yescomplemented
39#2352—22no—
40#2352—22no—
41#2349—22no—
42#2349C2214yes—
43D4×C4⋊C4—21no—
44D4×C4⋊C4—21no—
45D4×C4⋊C4C2212yes—
46D4×C4⋊C4C2212yes—
47#2316C2212yes—
48#2315—22no—
49#2314—22no—
50#2311C2212yes—
51#2285—21no—
52#2285—21no—
53#2285C2211yescharacteristic
54#2285C2211yescharacteristic
55C2×#384C2211yescharacteristic
56C2×#380—22no—
57#2274C2212yes—
58#1936C2214yescomplemented
59#1935C2214yescomplemented
60#1934C2214yescomplemented
61#1933C2214yescomplemented
62#1921C2214yescomplemented
63#1920C2214yescomplemented
64#1919C2214yescomplemented
65#1918C2214yescomplemented
66#1879C2214yes—
67#1879C2214yes—
68#1877C2214yes—
69#1877C2214yes—
70#1836C2214yescomplemented
71#1834C2212yescomplemented
72#1834C2212yescomplemented
73#1805C2212yescomplemented
74#1804C2212yescomplemented
75#1803C2211yescharacteristic, complemented
76#1803C2211yescharacteristic, complemented
77#1802C2212yes—
78#1802C2212yes—
79#1802C2214yes—
80#1802C2211yescharacteristic, complemented
81#1802C2211yescharacteristic, complemented
82#1771C2214yescomplemented
83#1770C2212yescomplemented
84C8×C4⋊C4C2212yescomplemented
85#1762C2214yes—
86#1762C2214yes—
87C4×#102C2214yes—
88C4×#102C2214yes—
89#1736C2212yes—
90#1736C2212yes—
91#1735C2212yes—
92C2×#340C2212yes—
93#1729C2212yes—
94C22×#41C2311yescharacteristic
95C23×D4C2311yescharacteristic
96C24×C4—21no—
97C2×AGL(1,ℤ/8)—24no—
98C2×AGL(1,ℤ/8)—24no—
99C2×AGL(1,ℤ/8)C2×C418yes—
100C22×SD16C2312yes—
101C22×D8C2312yes—
102C22×M16C2311yescharacteristic
103C22×M16C2311yescharacteristic
104C23×C8C2312yes—
105#518—28no—
106#518—44no—
107C4×#41—24no—
108C4×#41C2×C418yescomplemented
109C2×C4×Q8C2311yescharacteristic
110C2×C4×Q8C2311yescharacteristic
111C2×C4×D4—21no—
112C2×C4×D4—21no—
113C2×C4×D4—22no—
114C2×C4×D4—22no—
115C2×C4×D4—21no—
116C2×C4×D4—21no—
117C2×C4×D4—24no—
118C2×C4×D4C2×C418yes—
119C2×C4×D4C2314yes—
120C2×C4×D4C2314yes—
121C2×C4×D4C2312yes—
122C2×C4×D4C2312yes—
123C2×C4×D4C2311yescharacteristic
124C2×C4×D4C2311yescharacteristic
125C2×#117—22no—
126C2×#117—22no—
127C2×#117—21no—
128C2×#117C2312yes—
129C2×#117C2311yescharacteristic
130C2×#117C2312yes—
131C22×C4⋊C4—21no—
132C22×C4⋊C4—21no—
133C22×C4⋊C4—22no—
134C22×C4⋊C4—22no—
135C22×C4⋊C4C2312yes—
136C22×C4⋊C4C2311yescharacteristic
137C22×C22⋊C4—21no—
138C22×C22⋊C4—24no—
139C22×C42—21no—
140C22×C42C2311yescharacteristic
141#442C2×C4116yescomplemented
142#440C2×C4116yescomplemented
143C4×SD16C2×C4116yescomplemented
144C4×D8C2×C4116yescomplemented
145#428C2×C418yescomplemented
146C2×#107C2312yes—
147C2×#106C2312yes—
148C2×C4⋊C8—24no—
149C2×C4⋊C8C2311yescharacteristic
150C2×C4⋊C8C2311yescharacteristic
151C2×C4⋊C8C2312yes—
152#418C2×C418yes—
153#417C2×C418yescomplemented
154#416—44no—
155C2×#103C2312yes—
156C2×#103C2312yes—
157C2×#103C2312yes—
158C2×#102—28no—
159C2×#102C2314yes—
160C2×#102C2314yes—
161C2×#102C2312yes—
162C2×#102C2312yes—
163C2×#102C2312yes—
164C2×#102C2312yes—
165C2×#102C2312yes—
166#405—44no—
167C4×M16C2×C418yescomplemented
168C2×#97C2314yes—
169C2×#97C2312yes—
170C2×C4×C8C2314yes—
171C2×C4×C8C2312yes—
172#391C2314yes—
173#390C2314yes—
174#389—22no—
175#389—22no—
176#389C2314yes—
177#389C2314yes—
178#388—24no—
179#388—24no—
180#387—24no—
181#387—24no—
182#386—24no—
183#385—24no—
184#385—24no—
185#385—24no—
186#385—24no—
187#384—21no—
188#384—21no—
189#384D411yescharacteristic
190#384D411yescharacteristic
191#384C2312yes—
192#384C2312yes—
193#384C2311yescharacteristic
194#384C2311yescharacteristic
195#382—22no—
196#382—22no—
197#382D412yes—
198#382C2312yes—
199#380—21no—
200#380—21no—
201#380—22no—
202#380—22no—
203#380—22no—
204#380—22no—
205#380—22no—
206#380—22no—
207#380—24no—
208#380—24no—
209#380D412yes—
210#380D412yes—
211C4×C4⋊C4—22no—
212C4×C4⋊C4—22no—
213C4×C4⋊C4—22no—
214C4×C4⋊C4—22no—
215C4×C4⋊C4—21no—
216C4×C4⋊C4—21no—
217C4×C4⋊C4C2314yes—
218C4×C4⋊C4C2314yes—
219C4×C4⋊C4C2312yes—
220C4×C4⋊C4C2312yes—
221C4×C22⋊C4—24no—
222C2×#95—24no—
223#340C2314yes—
224#340C2314yes—
225#340C2312yes—
226#340C2312yes—
227#340C2312yes—
228#340C2312yes—
229#340C2314yes—
230#340C2314yes—
231#340C2314yes—
232#340C2314yes—
233#336C2314yes—
234#336C2314yes—
235C25—21no—
236C2×#41—22no—
237C2×#41—22no—
238C2×#41—22no—
239C2×#41—22no—
240C2×#41—22no—
241C2×#41C22×C414yes—
242C22×Q8C2411yescharacteristic
243C22×D4—21no—
244C22×D4—21no—
245C22×D4—22no—
246C22×D4—22no—
247C22×D4—22no—
248C22×D4C22×C414yes—
249C22×D4#4114yes—
250C22×D4#4114yes—
251C22×D4C2411yescharacteristic
252C22×D4C2412yes—
253C23×C4—21no—
254C23×C4—22no—
255C23×C4—21no—
256C23×C4—21no—
257C23×C4—21no—
258C23×C4—28no—
259C23×C4—22no—
260C23×C4—22no—
261C23×C4—24no—
262C23×C4—24no—
263C23×C4—82no—
264C23×C4—82no—
265C23×C4C2×D411yescharacteristic
266C23×C4C2×D411yescharacteristic
267C23×C4C2411yescharacteristic
268AGL(1,ℤ/8)—232no—
269C2×SD16—24no—
270C2×SD16—24no—
271C2×SD16C22×C418yes—
272C2×D8—24no—
273C2×D8—24no—
274C2×D8C22×C418yes—
275C2×M16—22no—
276C2×M16—22no—
277C2×M16—22no—
278C2×M16—22no—
279C2×M16C22×C414yes—
280C2×M16C22×C414yes—
281C22×C8—24no—
282C22×C8—24no—
283C22×C8—24no—
284C22×C8C2412yes—
285C22×C8C2412yes—
286C22×C8C2412yes—
287C22×C8C2412yes—
288C4×Q8—22no—
289C4×Q8—22no—
290C4×Q8C22×C414yes—
291C4×Q8C22×C414yes—
292C4×D4—28no—
293C4×D4—28no—
294C4×D4—28no—
295C4×D4—28no—
296C4×D4—28no—
297C4×D4—28no—
298C4×D4—24no—
299C4×D4—24no—
300C4×D4—22no—
301C4×D4—22no—
302C4×D4—44no—
303C4×D4—44no—
304C4×D4—48no—
305C4×D4—48no—
306C4×D4C22×C418yes—
307C4×D4C22×C418yes—
308C4×D4C22×C414yes—
309C4×D4C22×C414yes—
310#117—22no—
311#117—24no—
312#117—24no—
313#117—28no—
314#117—24no—
315#117—24no—
316#117—84no—
317#117—84no—
318#117C22×C414yes—
319C2×C4⋊C4—21no—
320C2×C4⋊C4—21no—
321C2×C4⋊C4—21no—
322C2×C4⋊C4—22no—
323C2×C4⋊C4—24no—
324C2×C4⋊C4—24no—
325C2×C4⋊C4—21no—
326C2×C4⋊C4—21no—
327C2×C4⋊C4—22no—
328C2×C4⋊C4—22no—
329C2×C4⋊C4—22no—
330C2×C4⋊C4—24no—
331C2×C4⋊C4—24no—
332C2×C4⋊C4—22no—
333C2×C4⋊C4—22no—
334C2×C4⋊C4—21no—
335C2×C4⋊C4—21no—
336C2×C4⋊C4—84no—
337C2×C4⋊C4—84no—
338C2×C4⋊C4—82no—
339C2×C4⋊C4—82no—
340C2×C4⋊C4C22×C414yes—
341C2×C4⋊C4C2×D412yes—
342C2×C4⋊C4C2×D412yes—
343C2×C4⋊C4C2×D412yes—
344C2×C4⋊C4C2×D412yes—
345C2×C4⋊C4C2×D412yes—
346C2×C4⋊C4C2×D412yes—
347C2×C4⋊C4C2414yes—
348C2×C4⋊C4C2412yes—
349C2×C4⋊C4C2412yes—
350C2×C4⋊C4C2412yes—
351C2×C4⋊C4C2411yescharacteristic
352C2×C4⋊C4C2411yescharacteristic
353C2×C22⋊C4—21no—
354C2×C22⋊C4—28no—
355C2×C22⋊C4—22no—
356C2×C22⋊C4—22no—
357C2×C22⋊C4—21no—
358C2×C22⋊C4—21no—
359C2×C22⋊C4—22no—
360C2×C22⋊C4—24no—
361C2×C22⋊C4—24no—
362C2×C22⋊C4—24no—
363C2×C22⋊C4—24no—
364C2×C22⋊C4—416no—
365C2×C22⋊C4C2×D414yes—
366C2×C42—21no—
367C2×C42—21no—
368C2×C42—21no—
369C2×C42—28no—
370C2×C42—22no—
371C2×C42—24no—
372C2×C42—24no—
373C2×C42C22×C414yes—
374C2×C42C2×D411yescharacteristic
375C2×C42C2×D411yescharacteristic
376C2×C42#4114yes—
377C2×C42C2414yes—
378C2×C42C2411yescharacteristic
379C2×C42C2411yescharacteristic
380#107C22×C418yes—
381#106C22×C418yes—
382C4⋊C8—22no—
383C4⋊C8—22no—
384C4⋊C8—24no—
385#103—42no—
386#103—42no—
387#103C22×C418yes—
388#102—28no—
389#102—28no—
390#102—42no—
391#102—42no—
392#102C22×C418yes—
393#102C22×C418yes—
394#102C22×C418yes—
395#97—44no—
396#97C22×C418yes—
397C4×C8—44no—
398C4×C8C22×C418yes—
399#95—22no—
400#95—24no—
401#95—24no—
402#95—24no—
403#95—24no—
404#95—24no—
405#95—24no—
406#95—22no—
407#95C2×D414yes—
408#95C2×D414yes—
409C24—22no—
410C24—24no—
411C24—24no—
412C24—24no—
413C24—21no—
414C24—81no—
415C24—81no—
416C24—81no—
417C24—81no—
418C24C22×D411yescharacteristic
419#41—28no—
420#41—28no—
421#41—44no—
422#41—44no—
423C2×Q8—21no—
424C2×Q8—21no—
425C2×Q8—21no—
426C2×Q8—21no—
427C2×Q8—21no—
428C2×Q8C23×C412yes—
429C2×D4—24no—
430C2×D4—24no—
431C2×D4—28no—
432C2×D4—24no—
433C2×D4—24no—
434C2×D4—28no—
435C2×D4—28no—
436C2×D4—22no—
437C2×D4—21no—
438C2×D4—21no—
439C2×D4—21no—
440C2×D4—22no—
441C2×D4—21no—
442C2×D4—22no—
443C2×D4—21no—
444C2×D4—42no—
445C2×D4—42no—
446C2×D4#117116yescomplemented
447C2×D4C23×C412yes—
448C2×D4C23×C414yes—
449C2×D4C2×#4114yes—
450C2×D4C2×#4114yes—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—22no—
457C22×C4—24no—
458C22×C4—24no—
459C22×C4—24no—
460C22×C4—24no—
461C22×C4—28no—
462C22×C4—28no—
463C22×C4—24no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—41no—
467C22×C4—41no—
468C22×C4—42no—
469C22×C4—42no—
470C22×C4—48no—
471C22×C4—48no—
472C22×C4—42no—
473C22×C4—42no—
474C22×C4—44no—
475C22×C4—42no—
476C22×C4—44no—
477C22×C4—42no—
478C22×C4—44no—
479C22×C4—816no—
480C22×C4—82no—
481C22×C4—82no—
482C22×C4—84no—
483C22×C4—84no—
484C22×C4—84no—
485C22×C4—84no—
486C22×C4—81no—
487C22×C4—81no—
488C22×C4—82no—
489C22×C4—82no—
490C22×C4C4×D414yes—
491C22×C4C4×D414yes—
492C22×C4C23×C412yes—
493C22×C4C22×D414yes—
494C22×C4C22×D414yes—
495C22×C4C22×D411yescharacteristic
496C22×C4C22×D411yescharacteristic
497C22×C4C22×D411yescharacteristic
498C22×C4C22×D411yescharacteristic
499C22×C4C22×D411yescharacteristic
500C22×C4C2×#4112yes—
501C22×C4C2×#4112yes—
502C22×C4C2×#4112yes—
503C22×C4H(5,𝔽2)12yes—
504C22×C42−1+412yes—
505C22×C4C2511yescharacteristic
506SD16—216no—
507D8—216no—
508M16—28no—
509M16—28no—
510C2×C8—22no—
511C2×C8—22no—
512C2×C8—22no—
513C2×C8—22no—
514C2×C8—22no—
515C2×C8—22no—
516C2×C8—22no—
517C2×C8—22no—
518C2×C8—22no—
519C2×C8—22no—
520C2×C8—48no—
521C2×C8C23×C414yes—
522C2×C8C23×C414yes—
523C4⋊C4—24no—
524C4⋊C4—24no—
525C4⋊C4—24no—
526C4⋊C4—24no—
527C4⋊C4—24no—
528C4⋊C4—24no—
529C4⋊C4—24no—
530C4⋊C4—22no—
531C4⋊C4—21no—
532C4⋊C4—21no—
533C4⋊C4—24no—
534C4⋊C4—22no—
535C4⋊C4—22no—
536C4⋊C4—22no—
537C4⋊C4—22no—
538C4⋊C4—24no—
539C4⋊C4—42no—
540C4⋊C4—42no—
541C4⋊C4—44no—
542C4⋊C4—44no—
543C4⋊C4—42no—
544C4⋊C4—44no—
545C4⋊C4—42no—
546C4⋊C4—81no—
547C4⋊C4—81no—
548C4⋊C4—82no—
549C4⋊C4—82no—
550C4⋊C4—84no—
551C4⋊C4—84no—
552C4⋊C4C23×C412yes—
553C4⋊C4C23×C412yes—
554C4⋊C4C23×C414yes—
555C22⋊C4—24no—
556C22⋊C4—28no—
557C22⋊C4—28no—
558C22⋊C4—28no—
559C22⋊C4—24no—
560C22⋊C4—24no—
561C22⋊C4—48no—
562C22⋊C4—48no—
563C22⋊C4—44no—
564C22⋊C4—84no—
565C22⋊C4—84no—
566C42—24no—
567C42—24no—
568C42—24no—
569C42—24no—
570C42—24no—
571C42—44no—
572C42—84no—
573C42—84no—
574C42C4×D414yes—
575C42C4×D414yes—
576C42C23×C412yes—
577C42C23×C412yes—
578C42C2×#4112yes—
579C42C2×#4112yes—
580C23—21no—
581C23—21no—
582C23—21no—
583C23—21no—
584C23—24no—
585C23—24no—
586C23—24no—
587C23—216no—
588C23—22no—
589C23—42no—
590C23—42no—
591C23—42no—
592C23—42no—
593C23—41no—
594C23—41no—
595C23—41no—
596C23—41no—
597C23—41no—
598C23—41no—
599C23—84no—
600C23—84no—
601C23—84no—
602C23—84no—
603C23—84no—
604C23—84no—
605C23C2×C4×D412yes—
606C23#54612yes—
607C23#54812yes—
608C23C23×D411yescharacteristic
609Q8—22no—
610Q8—22no—
611Q8—41no—
612Q8—41no—
613D4—216no—
614D4—22no—
615D4—24no—
616D4—22no—
617D4—24no—
618D4—24no—
619D4—48no—
620D4—41no—
621D4—41no—
622D4C2×#11718yes—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—28no—
630C2×C4—24no—
631C2×C4—24no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—24no—
636C2×C4—24no—
637C2×C4—24no—
638C2×C4—24no—
639C2×C4—24no—
640C2×C4—44no—
641C2×C4—48no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—42no—
648C2×C4—42no—
649C2×C4—41no—
650C2×C4—48no—
651C2×C4—48no—
652C2×C4—416no—
653C2×C4—44no—
654C2×C4—42no—
655C2×C4—42no—
656C2×C4—42no—
657C2×C4—42no—
658C2×C4—44no—
659C2×C4—44no—
660C2×C4—42no—
661C2×C4—42no—
662C2×C4—88no—
663C2×C4—84no—
664C2×C4—168no—
665C2×C4—168no—
666C2×C4—164no—
667C2×C4C2×#11714yes—
668C2×C4C2×C4×D412yes—
669C2×C4C2×C4×D412yes—
670C2×C4C2×C4×D412yes—
671C2×C4C2×C4×D412yes—
672C2×C4C2×C4×D412yes—
673C2×C4#52014yes—
674C2×C4#54612yes—
675C2×C4#54812yes—
676C2×C4#55214yes—
677C2×C4#55314yes—
678C2×C4#57612yes—
679C2×C4#57712yes—
680C2×C4C24×C411yescharacteristic
681C2×C4C22×#4111yescharacteristic
682C2×C4C22×#4111yescharacteristic
683C2×C4C22×#4111yescharacteristic
684C2×C4C2×H(5,𝔽2)11yescharacteristic
685C2×C4C2×2−1+411yescharacteristic
686C8—24no—
687C8—24no—
688C8—42no—
689C8—42no—
690C22—22no—
691C22—22no—
692C22—22no—
693C22—22no—
694C22—22no—
695C22—22no—
696C22—28no—
697C22—44no—
698C22—44no—
699C22—44no—
700C22—44no—
701C22—44no—
702C22—44no—
703C22—42no—
704C22—42no—
705C22—42no—
706C22—816no—
707C22—81no—
708C22—81no—
709C22—81no—
710C22—81no—
711C22#235214yes—
712C22C22×C4×D411yescharacteristic
713C22C2×#54611yescharacteristic
714C22C2×#54811yescharacteristic
715C22C2×#57611yescharacteristic
716C22C2×#57711yescharacteristic
717C22#358511yescharacteristic
718C22#358611yescharacteristic
719C4—22no—
720C4—22no—
721C4—22no—
722C4—42no—
723C4—44no—
724C4—44no—
725C4—42no—
726C4—42no—
727C4—44no—
728C4—82no—
729C4—82no—
730C4—84no—
731C4#235214yes—
732C4#294614yes—
733C4C22×#11711yescharacteristic
734C4C2×#52011yescharacteristic
735C4C2×#55211yescharacteristic
736C4C2×#55311yescharacteristic
737C2—24no—
738C2—48no—
739C2—82no—
740C2C2×#235211yescharacteristic
741C2C2×#294611yescharacteristic
742C2#6017011yescharacteristic
743C2#6119911yescharacteristic
744C2#6120011yescharacteristic
745C2#6133911yescharacteristic
746C2#6134011yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutatorC2×C4C24×C4
Frattini, cosocleC22×C4C25
prime radicalC22×AGL(1,ℤ/8)C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2285 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #34188C2semidirect
3. #34181C2semidirect
4. #22780C2semidirect
5. #22776C2semidirect
6. #22770C2semidirect
7. #22766C2semidirect
8. #22762C2semidirect
9. #22758C2semidirect
10. #21092C2semidirect
11. #21036C2semidirect
13. #20764C2semidirect
14. #20645C2semidirect
15. C2×#1802C2semidirect
16. #20441C2semidirect
17. #20416C2semidirect
22. C4×AGL(1,ℤ/8)C4semidirect
35. #2355C22semidirect
36. #2355C22semidirect
37. #2354C22semidirect
38. #2354C22semidirect
58. #1936C22semidirect
59. #1935C22semidirect
60. #1934C22semidirect
61. #1933C22semidirect
62. #1921C22semidirect
63. #1920C22semidirect
64. #1919C22semidirect
65. #1918C22semidirect
70. #1836C22semidirect
71. #1834C22semidirect
72. #1834C22semidirect
73. #1805C22semidirect
74. #1804C22semidirect
75. #1803C22semidirect
76. #1803C22semidirect
80. #1802C22semidirect
81. #1802C22semidirect
82. #1771C22semidirect
83. #1770C22semidirect
84. C8×C4⋊C4C22semidirect
108. C4×#41C2×C4semidirect
141. #442C2×C4semidirect
142. #440C2×C4semidirect
143. C4×SD16C2×C4semidirect
144. C4×D8C2×C4semidirect
145. #428C2×C4semidirect
153. #417C2×C4semidirect
167. C4×M16C2×C4semidirect
446. C2×D4#117semidirect

Maximal subgroups

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

subgroupindex
C2×C4×AGL(1,ℤ/8)2
#341882
#341812
#227802
#227762
#227702
#227662
#227622
#227582
#210922
#210362
#209292
#207642
#206452
C2×#18022
#204412
#204162