Finite Group Databasebeta

← C2×#20022 #6359346

Subgroups — C2×#20022 #6359346

Order 512.

2272 conjugacy classes of subgroups.

The subgroup lattice has 822 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3330C211yesmaximal, characteristic, complemented
2C2×#3294C211yesmaximal, characteristic, complemented
3C2×D4×D8C211yesmaximal, characteristic, complemented
4C2×#3272C211yesmaximal, characteristic, complemented
5#20022C2116yesmaximal, direct product factor
6C2×#1717C211yesmaximal, characteristic, complemented
7C2×#1701C211yesmaximal, characteristic, complemented
8C2×#1687C211yesmaximal, characteristic, complemented
9C2×#1679C211yesmaximal, characteristic, complemented
10C2×#1665C211yesmaximal, characteristic, complemented
11C2×#1625C211yesmaximal, characteristic, complemented
12C2×#1625C211yesmaximal, characteristic, complemented
13C2×#1639C211yesmaximal, characteristic, complemented
14C2×#1639C211yesmaximal, characteristic, complemented
15C2×#1586C211yesmaximal, characteristic, complemented
16C2×#1586C211yesmaximal, characteristic, complemented
17C22×AGL(1,ℤ/8)—21no—
18C23×D8—21no—
19C2×#547C2211yescharacteristic, complemented
20C2×#547C2211yescharacteristic, complemented
21C2×D42C2211yescharacteristic
22C2×D42C2211yescharacteristic
23#3330—24no—
24#3330C2218yescomplemented
25#3294—24no—
26#3294C2218yescomplemented
27D4×D8—24no—
28D4×D8C2218yescomplemented
29#3272—24no—
30#3272C2218yescomplemented
31C2×#493C2211yescharacteristic
32C2×#492C2211yescharacteristic, complemented
33C2×#487C2211yescharacteristic, complemented
34C2×#486C2211yescharacteristic, complemented
35C2×#486C2211yescharacteristic, complemented
36C2×#486C2211yescharacteristic, complemented
37C2×#484—21no—
38C2×#480—21no—
39C2×#474C2211yescharacteristic
40C2×#474C2211yescharacteristic, complemented
41C2×#468—21no—
42C2×#468—21no—
43C2×#466—21no—
44C2×#466—21no—
45C2×#461C2211yescharacteristic
46C2×#461C2211yescharacteristic, complemented
47C2×#459C2211yescharacteristic
48C2×#459C2211yescharacteristic
49C2×#459C2211yescharacteristic, complemented
50C2×#459C2211yescharacteristic, complemented
51C2×#449—21no—
52C2×#449—21no—
53C2×#450—21no—
54C2×#447—21no—
55C2×#447—21no—
56C2×#447—21no—
57C2×C4×D8C2211yescharacteristic
58C2×C4×D8C2211yescharacteristic
59C2×#436C2211yescharacteristic, complemented
60C2×#436C2211yescharacteristic, complemented
61C2×C8×D4C2211yescharacteristic
62C2×C8×D4C2211yescharacteristic, complemented
63C2×#417—21no—
64C22×#102—21no—
65#1717C2218yescomplemented
66#1701C2218yescomplemented
67#1687C2218yescomplemented
68#1679C2218yescomplemented
69#1665C2218yescomplemented
70#1639C2218yescomplemented
71#1639C2218yescomplemented
72#1625C2218yescomplemented
73#1625C2218yescomplemented
74#1586C2218yescomplemented
75#1586C2218yescomplemented
76C2×#334C2211yescharacteristic, complemented
77C2×#334C2211yescharacteristic, complemented
78C2×#332C2211yescharacteristic, complemented
79C2×#332C2211yescharacteristic, complemented
80C2×#331C2211yescharacteristic, complemented
81C2×#331C2211yescharacteristic, complemented
82C2×D4⋊C8C2211yescharacteristic
83C2×D4⋊C8C2211yescharacteristic, complemented
84C2×D4⋊C8C2211yescharacteristic, complemented
85C2×D4⋊C8C2211yescharacteristic, complemented
86C2×#322C2211yescharacteristic, complemented
87C22×#41—21no—
88C22×#41—21no—
89C23×D4—21no—
90C23×D4—21no—
91C23×D4—21no—
92C23×D4—21no—
93C2×AGL(1,ℤ/8)—28no—
94C2×AGL(1,ℤ/8)—48no—
95C22×SD16—21no—
96C22×SD16—21no—
97C22×SD16—21no—
98C22×SD16—21no—
99C22×D8—21no—
100C22×D8—21no—
101C22×D8—21no—
102C22×D8—21no—
103C22×D8—28no—
104C22×D8—21no—
105C22×D8—21no—
106C22×D8—48no—
107C22×D8D411yescharacteristic
108C22×D8D411yescharacteristic
109C22×M16—21no—
110C22×M16—21no—
111C23×C8—21no—
112C23×C8—21no—
113#547—22no—
114#547—22no—
115#547—22no—
116#547—22no—
117#547—41no—
118#547—41no—
119#547C2314yescomplemented
120#547C2314yescomplemented
121D42—22no—
122D42—22no—
123D42—22no—
124D42—22no—
125D42—41no—
126D42—41no—
127D42C2314yes—
128D42C2314yes—
129C2×C4⋊Q8C2311yescharacteristic
130C2×C4⋊Q8C2311yescharacteristic
131C2×#127C2311yescharacteristic
132C2×#127C2311yescharacteristic
133C2×#123—41no—
134C2×#123—41no—
135C2×C22⋊Q8—21no—
136C2×C22⋊Q8—21no—
137C2×#121—21no—
138C2×#121—21no—
139C2×#121—21no—
140C2×#121—21no—
141C2×#121—21no—
142C2×#121—21no—
143C2×#120—41no—
144C2×#120—41no—
145C2×C4×D4C2311yescharacteristic
146C2×C4×D4C2311yescharacteristic
147C2×C4×D4C2311yescharacteristic
148C2×C4×D4C2311yescharacteristic
149C22×C4⋊C4—21no—
150C22×C4⋊C4—21no—
151#493—22no—
152#493C2314yes—
153#492—22no—
154#492C2314yescomplemented
155#487—22no—
156#487C2314yescomplemented
157#486—22no—
158#486—41no—
159#486—41no—
160#486C2314yescomplemented
161#486C2314yescomplemented
162#486C2314yescomplemented
163#484—28no—
164#480—28no—
165#474—22no—
166#474—22no—
167#474C2314yes—
168#474C2314yescomplemented
169#468—28no—
170#468—28no—
171#466—28no—
172#466—28no—
173#461—22no—
174#461—22no—
175#461C2314yes—
176#461C2314yescomplemented
177#459—22no—
178#459—22no—
179#459—22no—
180#459—22no—
181#459C2314yes—
182#459C2314yes—
183#459C2314yescomplemented
184#459C2314yescomplemented
185#450—28no—
186#449—28no—
187#449—28no—
188#447—28no—
189#447—28no—
190#447—28no—
191C4×D8D414yes—
192C4×D8D414yes—
193C4×D8C2314yes—
194C4×D8C2314yes—
195#436—22no—
196#436—22no—
197#436C2314yescomplemented
198#436C2314yescomplemented
199C8×D4—22no—
200C8×D4—22no—
201C8×D4C2314yes—
202C8×D4C2314yescomplemented
203C2×#107—21no—
204C2×#107—21no—
205C2×#107D411yescharacteristic
206C2×#107D411yescharacteristic
207C2×C4⋊C8C2311yescharacteristic
208C2×C4⋊C8C2311yescharacteristic
209C2×C4⋊C8C2311yescharacteristic
210C2×C4⋊C8C2311yescharacteristic
211#417—28no—
212C2×#103—21no—
213C2×#103—21no—
214C2×#103—21no—
215C2×#103—21no—
216C2×#102—21no—
217C2×#102—21no—
218C2×#102—21no—
219C2×#102—21no—
220C2×#102—21no—
221C2×#102—21no—
222C2×#102—21no—
223C2×#102—21no—
224C2×#102—28no—
225C2×#102—41no—
226C2×#102—41no—
227C2×#102D411yescharacteristic
228C2×#102D411yescharacteristic
229C2×#102D411yescharacteristic
230C2×#102D411yescharacteristic
231C2×C22⋊C8—21no—
232C2×C22⋊C8—21no—
233C2×C22⋊C8—21no—
234C2×C22⋊C8—21no—
235C2×C4×C8C2311yescharacteristic
236C2×C4×C8C2311yescharacteristic
237C2×C4×C8C2311yescharacteristic
238#334C2314yescomplemented
239#334C2314yescomplemented
240#332C2314yescomplemented
241#332C2314yescomplemented
242#331C2314yescomplemented
243#331C2314yescomplemented
244D4⋊C8C2314yes—
245D4⋊C8C2314yescomplemented
246D4⋊C8C2314yescomplemented
247D4⋊C8C2314yescomplemented
248#322C2314yescomplemented
249C25—41no—
250C25—41no—
251C2×#41—24no—
252C2×#41—24no—
253C2×#41—42no—
254C2×#41—42no—
255C2×#41—44no—
256C2×#41—44no—
257C2×#41—82no—
258C2×#41—82no—
259C22×Q8—21no—
260C22×Q8—21no—
261C22×D4—24no—
262C22×D4—24no—
263C22×D4—24no—
264C22×D4—24no—
265C22×D4—21no—
266C22×D4—21no—
267C22×D4—21no—
268C22×D4—21no—
269C22×D4—21no—
270C22×D4—21no—
271C22×D4—42no—
272C22×D4—42no—
273C22×D4—42no—
274C22×D4—42no—
275C22×D4—41no—
276C22×D4—41no—
277C22×D4—41no—
278C22×D4—41no—
279C22×D4—44no—
280C22×D4—44no—
281C22×D4—44no—
282C22×D4—44no—
283C22×D4—41no—
284C22×D4—41no—
285C22×D4—82no—
286C22×D4—82no—
287C22×D4—82no—
288C22×D4—82no—
289C22×D4C2×D411yescharacteristic
290C22×D4C2×D411yescharacteristic
291C22×D4C2×D411yescharacteristic
292C22×D4C2×D411yescharacteristic
293C23×C4—21no—
294C23×C4—21no—
295C23×C4—21no—
296C23×C4—21no—
297C23×C4—41no—
298C23×C4—41no—
299AGL(1,ℤ/8)—432no—
300C2×SD16—24no—
301C2×SD16—24no—
302C2×SD16—24no—
303C2×SD16—24no—
304C2×SD16—44no—
305C2×SD16—44no—
306C2×SD16—82no—
307C2×SD16—82no—
308C2×D8—24no—
309C2×D8—24no—
310C2×D8—24no—
311C2×D8—24no—
312C2×D8—24no—
313C2×D8—24no—
314C2×D8—24no—
315C2×D8—24no—
316C2×D8—44no—
317C2×D8—432no—
318C2×D8—44no—
319C2×D8—44no—
320C2×D8—44no—
321C2×D8—82no—
322C2×D8—82no—
323C2×D8C2×D414yes—
324C2×D8C2×D414yes—
325C2×M16—24no—
326C2×M16—24no—
327C2×M16—44no—
328C2×M16—82no—
329C22×C8—21no—
330C22×C8—21no—
331C22×C8—21no—
332C22×C8—21no—
333C22×C8—21no—
334C22×C8—24no—
335C22×C8—24no—
336C22×C8—44no—
337C22×C8—82no—
338C22×C8C2×D411yescharacteristic
339C22×C8C2×D411yescharacteristic
340C22×C8C2×D411yescharacteristic
341C22×C8C2×D411yescharacteristic
342C4⋊Q8—21no—
343C4⋊Q8—21no—
344C4⋊Q8—21no—
345C4⋊Q8—21no—
346C4⋊Q8—21no—
347C4⋊Q8—21no—
348C4⋊Q8C2412yes—
349C4⋊Q8C2412yes—
350#127—21no—
351#127—21no—
352#127—21no—
353#127—21no—
354#127—21no—
355#127—21no—
356#127C2412yes—
357#127C2412yes—
358#123—44no—
359#123—44no—
360#123—44no—
361#123—44no—
362C22⋊Q8—24no—
363C22⋊Q8—24no—
364C22⋊Q8—42no—
365C22⋊Q8—42no—
366#121—24no—
367#121—24no—
368#121—24no—
369#121—24no—
370#121—24no—
371#121—24no—
372#121—42no—
373#121—42no—
374#121—42no—
375#121—42no—
376#121—42no—
377#121—42no—
378#120—44no—
379#120—44no—
380#120—44no—
381#120—44no—
382C4×D4—21no—
383C4×D4—21no—
384C4×D4—21no—
385C4×D4—21no—
386C4×D4—21no—
387C4×D4—21no—
388C4×D4—21no—
389C4×D4—21no—
390C4×D4C2×D412yes—
391C4×D4C2×D412yes—
392C4×D4C2×D412yes—
393C4×D4C2×D412yes—
394C4×D4C2412yes—
395C4×D4C2412yes—
396C4×D4C2412yes—
397C4×D4C2412yes—
398C2×C4⋊C4—21no—
399C2×C4⋊C4—21no—
400C2×C4⋊C4—21no—
401C2×C4⋊C4—21no—
402C2×C4⋊C4—24no—
403C2×C4⋊C4—24no—
404C2×C4⋊C4—42no—
405C2×C4⋊C4—42no—
406C2×C4⋊C4—41no—
407C2×C4⋊C4—41no—
408C2×C4⋊C4C2×D411yescharacteristic
409C2×C4⋊C4C2×D411yescharacteristic
410C2×C4⋊C4C2×D411yescharacteristic
411C2×C4⋊C4C2×D411yescharacteristic
412C2×C22⋊C4—21no—
413C2×C22⋊C4—21no—
414C2×C22⋊C4—21no—
415C2×C22⋊C4—21no—
416C2×C22⋊C4—41no—
417C2×C22⋊C4—41no—
418C2×C22⋊C4—41no—
419C2×C22⋊C4—41no—
420C2×C42C2411yescharacteristic
421#107—24no—
422#107—24no—
423#107C2×D414yes—
424#107C2×D414yes—
425C4⋊C8—21no—
426C4⋊C8—21no—
427C4⋊C8—21no—
428C4⋊C8—21no—
429C4⋊C8C2412yes—
430C4⋊C8C2412yes—
431C4⋊C8C2412yes—
432C4⋊C8C2412yes—
433#103—24no—
434#103—24no—
435#103—24no—
436#103—24no—
437#102—24no—
438#102—24no—
439#102—24no—
440#102—24no—
441#102—24no—
442#102—24no—
443#102—24no—
444#102—24no—
445#102—44no—
446#102—44no—
447#102C2×D414yes—
448#102C2×D414yes—
449#102C2×D414yes—
450#102C2×D414yes—
451C22⋊C8—24no—
452C22⋊C8—24no—
453C22⋊C8—24no—
454C22⋊C8—24no—
455C4×C8—21no—
456C4×C8C2×D412yes—
457C4×C8C2×D412yes—
458C4×C8C2412yes—
459C4×C8C2412yes—
460C4×C8C2412yes—
461C24—21no—
462C24—21no—
463C24—21no—
464C24—21no—
465C24—44no—
466C24—44no—
467C24—41no—
468C24—41no—
469C24—84no—
470C24—84no—
471C24—84no—
472C24—84no—
473C24—162no—
474C24—162no—
475#41—48no—
476#41—48no—
477#41—84no—
478#41—84no—
479#41—88no—
480#41—88no—
481C2×Q8—22no—
482C2×Q8—22no—
483C2×Q8—41no—
484C2×Q8—41no—
485C2×Q8—42no—
486C2×Q8—42no—
487C2×Q8—42no—
488C2×Q8—42no—
489C2×D4—21no—
490C2×D4—21no—
491C2×D4—21no—
492C2×D4—21no—
493C2×D4—22no—
494C2×D4—22no—
495C2×D4—22no—
496C2×D4—22no—
497C2×D4—22no—
498C2×D4—22no—
499C2×D4—22no—
500C2×D4—22no—
501C2×D4—22no—
502C2×D4—22no—
503C2×D4—22no—
504C2×D4—22no—
505C2×D4—44no—
506C2×D4—44no—
507C2×D4—44no—
508C2×D4—44no—
509C2×D4—48no—
510C2×D4—48no—
511C2×D4—48no—
512C2×D4—48no—
513C2×D4—44no—
514C2×D4—44no—
515C2×D4—41no—
516C2×D4—41no—
517C2×D4—41no—
518C2×D4—41no—
519C2×D4—41no—
520C2×D4—41no—
521C2×D4—42no—
522C2×D4—42no—
523C2×D4—42no—
524C2×D4—42no—
525C2×D4—42no—
526C2×D4—42no—
527C2×D4—42no—
528C2×D4—42no—
529C2×D4—82no—
530C2×D4—82no—
531C2×D4—84no—
532C2×D4—84no—
533C2×D4—84no—
534C2×D4—84no—
535C2×D4—88no—
536C2×D4—88no—
537C2×D4—88no—
538C2×D4—88no—
539C2×D4—84no—
540C2×D4—84no—
541C2×D4—84no—
542C2×D4—84no—
543C2×D4—84no—
544C2×D4—84no—
545C2×D4AGL(1,ℤ/8)14yes—
546C2×D4AGL(1,ℤ/8)14yescomplemented
547C2×D4C22×D412yes—
548C2×D4C22×D412yes—
549C2×D4C22×D412yes—
550C2×D4C22×D412yes—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—44no—
564C22×C4—44no—
565C22×C4—42no—
566C22×C4—42no—
567C22×C4—42no—
568C22×C4—42no—
569C22×C4—42no—
570C22×C4—42no—
571C22×C4—42no—
572C22×C4—42no—
573C22×C4—41no—
574C22×C4—41no—
575C22×C4—84no—
576C22×C4—84no—
577C22×C4C22×D411yescharacteristic
578C22×C4C22×D411yescharacteristic
579C22×C4H(5,𝔽2)11yescharacteristic
580SD16—48no—
581SD16—48no—
582SD16—84no—
583SD16—84no—
584D8—28no—
585D8—28no—
586D8—48no—
587D8—48no—
588D8—48no—
589D8—48no—
590D8—84no—
591D8—84no—
592M16—48no—
593M16—84no—
594C2×C8—22no—
595C2×C8—22no—
596C2×C8—22no—
597C2×C8—22no—
598C2×C8—22no—
599C2×C8—22no—
600C2×C8—22no—
601C2×C8—22no—
602C2×C8—22no—
603C2×C8—48no—
604C2×C8—42no—
605C2×C8—42no—
606C2×C8—42no—
607C2×C8—42no—
608C2×C8—42no—
609C2×C8—84no—
610C2×C8C22×D412yes—
611C2×C8C22×D412yes—
612C2×C8C22×D412yes—
613C2×C8C22×D412yes—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—21no—
617C4⋊C4—21no—
618C4⋊C4—22no—
619C4⋊C4—22no—
620C4⋊C4—22no—
621C4⋊C4—22no—
622C4⋊C4—44no—
623C4⋊C4—44no—
624C4⋊C4—41no—
625C4⋊C4—41no—
626C4⋊C4—41no—
627C4⋊C4—41no—
628C4⋊C4C22×D412yes—
629C4⋊C4C22×D412yes—
630C4⋊C4C22×D412yes—
631C4⋊C4C22×D412yes—
632C22⋊C4—22no—
633C22⋊C4—22no—
634C22⋊C4—22no—
635C22⋊C4—22no—
636C22⋊C4—22no—
637C22⋊C4—22no—
638C22⋊C4—22no—
639C22⋊C4—22no—
640C22⋊C4—44no—
641C22⋊C4—44no—
642C22⋊C4—44no—
643C22⋊C4—44no—
644C42C22×D411yescharacteristic
645C42C22×D411yescharacteristic
646C42H(5,𝔽2)11yescharacteristic
647C42C2511yescharacteristic
648C23—22no—
649C23—22no—
650C23—24no—
651C23—24no—
652C23—22no—
653C23—22no—
654C23—42no—
655C23—42no—
656C23—42no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23—42no—
665C23—42no—
666C23—88no—
667C23—88no—
668C23—88no—
669C23—88no—
670C23—82no—
671C23—82no—
672C23—82no—
673C23—82no—
674C23—82no—
675C23—82no—
676C23—164no—
677C23—164no—
678C23—1616no—
679C23—1616no—
680C23D4211yescharacteristic
681Q8—42no—
682Q8—42no—
683Q8—42no—
684Q8—42no—
685Q8—82no—
686Q8—82no—
687D4—24no—
688D4—24no—
689D4—22no—
690D4—22no—
691D4—22no—
692D4—22no—
693D4—22no—
694D4—22no—
695D4—42no—
696D4—42no—
697D4—42no—
698D4—42no—
699D4—42no—
700D4—42no—
701D4—42no—
702D4—42no—
703D4—42no—
704D4—42no—
705D4—82no—
706D4—82no—
707D4—88no—
708D4—88no—
709D4—88no—
710D4—88no—
711D4—88no—
712D4—88no—
713D4—82no—
714D4—82no—
715D4—82no—
716D4—82no—
717D4—161no—
718D4—161no—
719D4C2×AGL(1,ℤ/8)14yes—
720D4C2×AGL(1,ℤ/8)14yescomplemented
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—44no—
731C2×C4—44no—
732C2×C4—44no—
733C2×C4—44no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—88no—
745C2×C4—88no—
746C2×C4—82no—
747C2×C4—82no—
748C2×C4D4211yescharacteristic
749C2×C4D4211yescharacteristic
750C2×C4D4211yescharacteristic
751C2×C4C2×AGL(1,ℤ/8)12yes—
752C2×C4C2×AGL(1,ℤ/8)12yes—
753C2×C4#57612yes—
754C2×C4#57612yes—
755C2×C4C23×D411yescharacteristic
756C2×C4C23×D411yescharacteristic
757C2×C4C2×H(5,𝔽2)11yescharacteristic
758C8—22no—
759C8—22no—
760C8—22no—
761C8—22no—
762C8—42no—
763C8—42no—
764C8—42no—
765C8—42no—
766C8—42no—
767C22—24no—
768C22—24no—
769C22—48no—
770C22—48no—
771C22—42no—
772C22—42no—
773C22—42no—
774C22—42no—
775C22—42no—
776C22—42no—
777C22—42no—
778C22—42no—
779C22—42no—
780C22—42no—
781C22—84no—
782C22—84no—
783C22—82no—
784C22—82no—
785C22—82no—
786C22—82no—
787C22—82no—
788C22—82no—
789C22—1616no—
790C22—1616no—
791C22—164no—
792C22—164no—
793C22#326412yes—
794C22#326412yes—
795C22#329012yes—
796C22C2×D4211yescharacteristic
797C4—21no—
798C4—21no—
799C4—42no—
800C4—42no—
801C4—42no—
802C4—42no—
803C4—82no—
804C4—82no—
805C4#326412yes—
806C4#326412yes—
807C4C22×AGL(1,ℤ/8)11yescharacteristic
808C4C22×AGL(1,ℤ/8)11yescharacteristic
809C4C2×#57611yescharacteristic
810C4C2×#57611yescharacteristic
811C2—44no—
812C2—44no—
813C2—82no—
814C2—82no—
815C2—162no—
816C2—162no—
817C2#2002214yesdirect product factor
818C2C2×#326411yescharacteristic
819C2C2×#326411yescharacteristic
820C2C2×#329011yescharacteristic
subgroupG/H
center, socleC23D42
commutator, Frattini, cosocleC42C25
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C23 ◁ C2×C42 ◁ G
LECSG ▷ C42 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3330C2semidirect
2. C2×#3294C2semidirect
3. C2×D4×D8C2semidirect
4. C2×#3272C2semidirect
5. #20022C2direct (N × H)
6. C2×#1717C2semidirect
7. C2×#1701C2semidirect
8. C2×#1687C2semidirect
9. C2×#1679C2semidirect
10. C2×#1665C2semidirect
11. C2×#1625C2semidirect
12. C2×#1625C2semidirect
13. C2×#1639C2semidirect
14. C2×#1639C2semidirect
15. C2×#1586C2semidirect
16. C2×#1586C2semidirect
19. C2×#547C22semidirect
20. C2×#547C22semidirect
24. #3330C22semidirect
26. #3294C22semidirect
28. D4×D8C22semidirect
30. #3272C22semidirect
32. C2×#492C22semidirect
33. C2×#487C22semidirect
34. C2×#486C22semidirect
35. C2×#486C22semidirect
36. C2×#486C22semidirect
40. C2×#474C22semidirect
46. C2×#461C22semidirect
49. C2×#459C22semidirect
50. C2×#459C22semidirect
59. C2×#436C22semidirect
60. C2×#436C22semidirect
62. C2×C8×D4C22semidirect
65. #1717C22semidirect
66. #1701C22semidirect
67. #1687C22semidirect
68. #1679C22semidirect
69. #1665C22semidirect
70. #1639C22semidirect
71. #1639C22semidirect
72. #1625C22semidirect
73. #1625C22semidirect
74. #1586C22semidirect
75. #1586C22semidirect
76. C2×#334C22semidirect
77. C2×#334C22semidirect
78. C2×#332C22semidirect
79. C2×#332C22semidirect
80. C2×#331C22semidirect
81. C2×#331C22semidirect
83. C2×D4⋊C8C22semidirect
84. C2×D4⋊C8C22semidirect
85. C2×D4⋊C8C22semidirect
86. C2×#322C22semidirect
119. #547C23semidirect
120. #547C23semidirect
154. #492C23semidirect
156. #487C23semidirect
160. #486C23semidirect
161. #486C23semidirect
162. #486C23semidirect
168. #474C23semidirect
176. #461C23semidirect
183. #459C23semidirect
184. #459C23semidirect
197. #436C23semidirect
198. #436C23semidirect
202. C8×D4C23semidirect
238. #334C23semidirect
239. #334C23semidirect
240. #332C23semidirect
241. #332C23semidirect
242. #331C23semidirect
243. #331C23semidirect
245. D4⋊C8C23semidirect
246. D4⋊C8C23semidirect
247. D4⋊C8C23semidirect
248. #322C23semidirect
546. C2×D4AGL(1,ℤ/8)semidirect
720. D4C2×AGL(1,ℤ/8)semidirect
817. C2#20022direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#33302
C2×#32942
C2×D4×D82
C2×#32722
#200222
C2×#17172
C2×#17012
C2×#16872
C2×#16792
C2×#16652
C2×#16252
C2×#16392
C2×#15862