Finite Group Databasebeta

← C2×#20081 #6359409

Subgroups — C2×#20081 #6359409

Order 512.

1942 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3360C211yesmaximal, characteristic, complemented
2C2×#3335C211yesmaximal, characteristic, complemented
3C2×#3324C211yesmaximal, characteristic, complemented
4C2×#3272C211yesmaximal, characteristic
5#20081C2116yesmaximal, direct product factor
6C2×#1714C211yesmaximal, characteristic, complemented
7C2×#1703C211yesmaximal, characteristic, complemented
8C2×#1691C211yesmaximal, characteristic, complemented
9C2×#1666C211yesmaximal, characteristic, complemented
10C2×#1681C211yesmaximal, characteristic, complemented
11C2×#1650C211yesmaximal, characteristic, complemented
12C2×#1647C211yesmaximal, characteristic, complemented
13C2×#1622C211yesmaximal, characteristic, complemented
14C2×#1629C211yesmaximal, characteristic, complemented
15C2×#1588C211yesmaximal, characteristic, complemented
16C2×#1586C211yesmaximal, characteristic, complemented
17C22×AGL(1,ℤ/8)—21no—
18C2×#556C2211yescharacteristic
19C2×#554C2211yescharacteristic, complemented
20C2×#547C2211yescharacteristic
21C2×D42C2211yescharacteristic
22#3360—24no—
23#3360C2218yescomplemented
24#3335—24no—
25#3335C2218yescomplemented
26#3324—24no—
27#3324C2218yescomplemented
28#3272—24no—
29#3272C2218yes—
30C2×#500C2211yescharacteristic, complemented
31C2×#498C2211yescharacteristic, complemented
32C2×#492C2211yescharacteristic
33C2×#492C2211yescharacteristic
34C2×#488—21no—
35C2×#487C2211yescharacteristic, complemented
36C2×#486C2211yescharacteristic
37C2×#481—21no—
38C2×#482—21no—
39C2×#483—21no—
40C2×#479—21no—
41C2×#475C2211yescharacteristic, complemented
42C2×#476C2211yescharacteristic
43C2×#476C2211yescharacteristic
44C2×#474C2211yescharacteristic
45C2×#468—21no—
46C2×#468—21no—
47C2×#465—21no—
48C2×#460C2211yescharacteristic
49C2×#463—21no—
50C2×#461C2211yescharacteristic
51C2×#461C2211yescharacteristic, complemented
52C2×#459C2211yescharacteristic
53C2×#449—21no—
54C2×#450—21no—
55C2×#450—21no—
56C2×C8×Q8C2211yescharacteristic, complemented
57C2×C4×SD16—21no—
58C2×C4×SD16C2211yescharacteristic
59C2×C4×D8C2211yescharacteristic
60C2×#436C2211yescharacteristic
61C2×#436C2211yescharacteristic
62C2×C8×D4C2211yescharacteristic, complemented
63C22×#106—21no—
64C2×#418—21no—
65#1714C2218yescomplemented
66#1703C2218yescomplemented
67#1691C2218yescomplemented
68#1681C2218yescomplemented
69#1666C2218yescomplemented
70#1650C2218yescomplemented
71#1647C2218yescomplemented
72#1629C2218yescomplemented
73#1622C2218yescomplemented
74#1588C2218yescomplemented
75#1586C2218yescomplemented
76C2×#335C2211yescharacteristic, complemented
77C2×#334C2211yescharacteristic, complemented
78C2×#333C2211yescharacteristic, complemented
79C2×#332C2211yescharacteristic, complemented
80C2×#332C2211yescharacteristic, complemented
81C2×#331C2211yescharacteristic
82C2×Q8⋊C8C2211yescharacteristic, complemented
83C2×D4⋊C8C2211yescharacteristic
84C2×D4⋊C8C2211yescharacteristic
85C2×D4⋊C8C2211yescharacteristic, complemented
86C2×#322C2211yescharacteristic, complemented
87C22×#41—21no—
88C23×D4—21no—
89C23×D4—21no—
90C2×AGL(1,ℤ/8)—28no—
91C2×AGL(1,ℤ/8)—48no—
92C22×SD16—21no—
93C22×SD16—21no—
94C22×SD16—21no—
95C22×SD16—21no—
96C22×SD16—21no—
97C22×SD16—41no—
98C22×SD16D411yescharacteristic
99C22×D8—21no—
100C22×D8D411yescharacteristic
101C22×M16—21no—
102C22×M16—21no—
103C23×C8—21no—
104#556—22no—
105#556—22no—
106#556—41no—
107#556C2314yes—
108#554—22no—
109#554—22no—
110#554—41no—
111#554C2314yescomplemented
112#547—22no—
113#547—22no—
114#547—41no—
115#547C2314yes—
116D42—22no—
117D42—22no—
118D42—41no—
119D42C2314yes—
120C2×C4⋊Q8C2311yescharacteristic
121C2×C4⋊Q8C2311yescharacteristic
122C2×C4⋊Q8C2311yescharacteristic
123C2×#127C2311yescharacteristic
124C2×#126—41no—
125C2×#125—21no—
126C2×#124—21no—
127C2×#123—41no—
128C2×C22⋊Q8—21no—
129C2×C22⋊Q8—21no—
130C2×C22⋊Q8—21no—
131C2×C22⋊Q8—41no—
132C2×#121—21no—
133C2×#121—21no—
134C2×#121—21no—
135C2×#120—41no—
136C2×C4×Q8—21no—
137C2×C4×Q8C2311yescharacteristic
138C2×C4×D4—21no—
139C2×C4×D4C2311yescharacteristic
140C2×C4×D4C2311yescharacteristic
141C2×C4×D4C2311yescharacteristic
142C2×#117—21no—
143C22×C4⋊C4—21no—
144C22×C4⋊C4—21no—
145#500—41no—
146#500C2314yescomplemented
147#498—22no—
148#498C2314yescomplemented
149#492—22no—
150#492—41no—
151#492C2314yes—
152#492C2314yes—
153#488—28no—
154#487—22no—
155#487C2314yescomplemented
156#486—22no—
157#486C2314yes—
158#483—28no—
159#482—28no—
160#481—28no—
161#479—28no—
162#476—22no—
163#476—22no—
164#476C2314yes—
165#476C2314yes—
166#475—22no—
167#475C2314yescomplemented
168#474—22no—
169#474C2314yes—
170#468—28no—
171#468—28no—
172#465—28no—
173#463—28no—
174#461—22no—
175#461—22no—
176#461C2314yes—
177#461C2314yescomplemented
178#460—22no—
179#460C2314yes—
180#459—22no—
181#459C2314yes—
182#450—28no—
183#450—28no—
184#449—28no—
185C8×Q8—22no—
186C8×Q8C2314yescomplemented
187C4×SD16—28no—
188C4×SD16D414yes—
189C4×SD16C2314yes—
190C4×D8D414yes—
191C4×D8C2314yes—
192#436—22no—
193#436—22no—
194#436C2314yes—
195#436C2314yes—
196C8×D4—22no—
197C8×D4C2314yescomplemented
198C2×#107—21no—
199C2×#107—41no—
200C2×#107D411yescharacteristic
201C2×#106—21no—
202C2×#106—21no—
203C2×#106—21no—
204C2×#106—21no—
205C2×#106—21no—
206C2×#106—28no—
207C2×#106D411yescharacteristic
208C2×C4⋊C8—21no—
209C2×C4⋊C8C2311yescharacteristic
210C2×C4⋊C8C2311yescharacteristic
211C2×C4⋊C8C2311yescharacteristic
212C2×C4⋊C8C2311yescharacteristic
213#418—28no—
214C2×#103—21no—
215C2×#103—21no—
216C2×#103—21no—
217C2×#103—21no—
218C2×#103—21no—
219C2×#103D411yescharacteristic
220C2×#102—21no—
221C2×#102—21no—
222C2×#102—21no—
223C2×#102—21no—
224C2×#102—21no—
225C2×#102—21no—
226C2×#102—21no—
227C2×#102D411yescharacteristic
228C2×#102D411yescharacteristic
229C2×#102D411yescharacteristic
230C2×C22⋊C8—21no—
231C2×C22⋊C8—21no—
232C2×C22⋊C8—21no—
233C2×C4×C8—21no—
234C2×C4×C8C2311yescharacteristic
235C2×C4×C8C2311yescharacteristic
236C2×C4×C8C2311yescharacteristic
237#335C2314yescomplemented
238#334C2314yescomplemented
239#333C2314yescomplemented
240#332C2314yescomplemented
241#332C2314yescomplemented
242#331C2314yes—
243Q8⋊C8C2314yescomplemented
244D4⋊C8C2314yes—
245D4⋊C8C2314yes—
246D4⋊C8C2314yescomplemented
247#322C2314yescomplemented
248C25—41no—
249C2×#41—24no—
250C2×#41—42no—
251C2×#41—44no—
252C2×#41—82no—
253C22×Q8—21no—
254C22×Q8—21no—
255C22×Q8—21no—
256C22×Q8C2×D411yescharacteristic
257C22×D4—24no—
258C22×D4—24no—
259C22×D4—21no—
260C22×D4—21no—
261C22×D4—21no—
262C22×D4—42no—
263C22×D4—42no—
264C22×D4—41no—
265C22×D4—41no—
266C22×D4—44no—
267C22×D4—44no—
268C22×D4—41no—
269C22×D4—82no—
270C22×D4—82no—
271C22×D4C2×D411yescharacteristic
272C22×D4C2×D411yescharacteristic
273C22×D4C2×D411yescharacteristic
274C23×C4—21no—
275C23×C4—21no—
276C23×C4—21no—
277C23×C4—41no—
278C23×C4—41no—
279AGL(1,ℤ/8)—432no—
280C2×SD16—24no—
281C2×SD16—24no—
282C2×SD16—24no—
283C2×SD16—24no—
284C2×SD16—24no—
285C2×SD16—42no—
286C2×SD16—44no—
287C2×SD16—44no—
288C2×SD16—44no—
289C2×SD16—44no—
290C2×SD16—82no—
291C2×SD16—84no—
292C2×SD16—82no—
293C2×SD16C2×D414yes—
294C2×D8—24no—
295C2×D8—24no—
296C2×D8—44no—
297C2×D8C2×D414yes—
298C2×M16—24no—
299C2×M16—24no—
300C2×M16—44no—
301C2×M16—82no—
302C22×C8—21no—
303C22×C8—21no—
304C22×C8—21no—
305C22×C8—21no—
306C22×C8—21no—
307C22×C8—24no—
308C22×C8—44no—
309C22×C8C2×D411yescharacteristic
310C22×C8C2×D411yescharacteristic
311C22×C8C2×D411yescharacteristic
312C22×C8C2×D411yescharacteristic
313C4⋊Q8—21no—
314C4⋊Q8—21no—
315C4⋊Q8—21no—
316C4⋊Q8—21no—
317C4⋊Q8—21no—
318C4⋊Q8—21no—
319C4⋊Q8—21no—
320C4⋊Q8—21no—
321C4⋊Q8—21no—
322C4⋊Q8C2412yes—
323C4⋊Q8C2412yes—
324C4⋊Q8C2412yes—
325#127—21no—
326#127—21no—
327#127—21no—
328#127C2412yes—
329#126—44no—
330#126—44no—
331#125—24no—
332#125—42no—
333#124—24no—
334#124—42no—
335#123—44no—
336#123—44no—
337C22⋊Q8—24no—
338C22⋊Q8—24no—
339C22⋊Q8—24no—
340C22⋊Q8—44no—
341C22⋊Q8—44no—
342C22⋊Q8—42no—
343C22⋊Q8—42no—
344C22⋊Q8—42no—
345#121—24no—
346#121—24no—
347#121—24no—
348#121—42no—
349#121—42no—
350#121—42no—
351#120—44no—
352#120—44no—
353C4×Q8—21no—
354C4×Q8—21no—
355C4×Q8—24no—
356C4×Q8—42no—
357C4×Q8C2×D412yes—
358C4×Q8C2412yes—
359C4×D4—24no—
360C4×D4—21no—
361C4×D4—21no—
362C4×D4—21no—
363C4×D4—21no—
364C4×D4—21no—
365C4×D4—21no—
366C4×D4—42no—
367C4×D4C2×D412yes—
368C4×D4C2×D412yes—
369C4×D4C2×D412yes—
370C4×D4C2412yes—
371C4×D4C2412yes—
372C4×D4C2412yes—
373#117—24no—
374#117—42no—
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—24no—
383C2×C4⋊C4—24no—
384C2×C4⋊C4—42no—
385C2×C4⋊C4—42no—
386C2×C4⋊C4—41no—
387C2×C4⋊C4—41no—
388C2×C4⋊C4—41no—
389C2×C4⋊C4—41no—
390C2×C4⋊C4C2×D411yescharacteristic
391C2×C4⋊C4C2×D411yescharacteristic
392C2×C4⋊C4C2×D411yescharacteristic
393C2×C4⋊C4C2×D411yescharacteristic
394C2×C22⋊C4—21no—
395C2×C22⋊C4—21no—
396C2×C22⋊C4—21no—
397C2×C22⋊C4—41no—
398C2×C22⋊C4—41no—
399C2×C22⋊C4—41no—
400C2×C22⋊C4—41no—
401C2×C22⋊C4—41no—
402C2×C42—21no—
403C2×C42—41no—
404C2×C42C2411yescharacteristic
405#107—24no—
406#107—44no—
407#107C2×D414yes—
408#106—24no—
409#106—24no—
410#106—24no—
411#106—24no—
412#106—24no—
413#106C2×D414yes—
414C4⋊C8—24no—
415C4⋊C8—21no—
416C4⋊C8—21no—
417C4⋊C8—21no—
418C4⋊C8—21no—
419C4⋊C8C2412yes—
420C4⋊C8C2412yes—
421C4⋊C8C2412yes—
422C4⋊C8C2412yes—
423#103—24no—
424#103—24no—
425#103—24no—
426#103—24no—
427#103—24no—
428#103C2×D414yes—
429#102—24no—
430#102—24no—
431#102—24no—
432#102—24no—
433#102—24no—
434#102—24no—
435#102—24no—
436#102C2×D414yes—
437#102C2×D414yes—
438#102C2×D414yes—
439C22⋊C8—24no—
440C22⋊C8—24no—
441C22⋊C8—24no—
442C4×C8—24no—
443C4×C8—21no—
444C4×C8C2×D412yes—
445C4×C8C2×D412yes—
446C4×C8C2412yes—
447C4×C8C2412yes—
448C4×C8C2412yes—
449C24—21no—
450C24—21no—
451C24—21no—
452C24—44no—
453C24—41no—
454C24—84no—
455C24—84no—
456C24—162no—
457#41—48no—
458#41—84no—
459#41—88no—
460C2×Q8—21no—
461C2×Q8—22no—
462C2×Q8—22no—
463C2×Q8—22no—
464C2×Q8—22no—
465C2×Q8—22no—
466C2×Q8—41no—
467C2×Q8—41no—
468C2×Q8—41no—
469C2×Q8—42no—
470C2×Q8—42no—
471C2×Q8—42no—
472C2×Q8—42no—
473C2×Q8—82no—
474C2×Q8C22×D412yes—
475C2×D4—21no—
476C2×D4—21no—
477C2×D4—21no—
478C2×D4—22no—
479C2×D4—22no—
480C2×D4—22no—
481C2×D4—22no—
482C2×D4—22no—
483C2×D4—22no—
484C2×D4—22no—
485C2×D4—22no—
486C2×D4—44no—
487C2×D4—44no—
488C2×D4—48no—
489C2×D4—48no—
490C2×D4—44no—
491C2×D4—41no—
492C2×D4—41no—
493C2×D4—41no—
494C2×D4—42no—
495C2×D4—42no—
496C2×D4—42no—
497C2×D4—42no—
498C2×D4—82no—
499C2×D4—84no—
500C2×D4—84no—
501C2×D4—88no—
502C2×D4—88no—
503C2×D4—84no—
504C2×D4—84no—
505C2×D4—84no—
506C2×D4AGL(1,ℤ/8)14yes—
507C2×D4C22×D412yes—
508C2×D4C22×D412yes—
509C2×D4C22×D412yes—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—44no—
522C22×C4—44no—
523C22×C4—42no—
524C22×C4—42no—
525C22×C4—42no—
526C22×C4—42no—
527C22×C4—42no—
528C22×C4—42no—
529C22×C4—41no—
530C22×C4—41no—
531C22×C4—41no—
532C22×C4—84no—
533C22×C4—162no—
534C22×C4C22×D411yescharacteristic
535C22×C4C22×D411yescharacteristic
536C22×C4H(5,𝔽2)11yescharacteristic
537SD16—44no—
538SD16—48no—
539SD16—48no—
540SD16—48no—
541SD16—84no—
542SD16—88no—
543SD16—84no—
544D8—28no—
545D8—48no—
546M16—48no—
547M16—84no—
548C2×C8—24no—
549C2×C8—22no—
550C2×C8—22no—
551C2×C8—22no—
552C2×C8—22no—
553C2×C8—22no—
554C2×C8—22no—
555C2×C8—22no—
556C2×C8—22no—
557C2×C8—22no—
558C2×C8—48no—
559C2×C8—42no—
560C2×C8—42no—
561C2×C8—42no—
562C2×C8—42no—
563C2×C8C22×D412yes—
564C2×C8C22×D412yes—
565C2×C8C22×D412yes—
566C2×C8C22×D412yes—
567C4⋊C4—22no—
568C4⋊C4—21no—
569C4⋊C4—21no—
570C4⋊C4—21no—
571C4⋊C4—21no—
572C4⋊C4—22no—
573C4⋊C4—22no—
574C4⋊C4—22no—
575C4⋊C4—22no—
576C4⋊C4—22no—
577C4⋊C4—22no—
578C4⋊C4—22no—
579C4⋊C4—44no—
580C4⋊C4—44no—
581C4⋊C4—44no—
582C4⋊C4—44no—
583C4⋊C4—41no—
584C4⋊C4—41no—
585C4⋊C4—41no—
586C4⋊C4—41no—
587C4⋊C4—41no—
588C4⋊C4—41no—
589C4⋊C4C22×D412yes—
590C4⋊C4C22×D412yes—
591C4⋊C4C22×D412yes—
592C4⋊C4C22×D412yes—
593C22⋊C4—22no—
594C22⋊C4—22no—
595C22⋊C4—22no—
596C22⋊C4—22no—
597C22⋊C4—22no—
598C22⋊C4—22no—
599C22⋊C4—44no—
600C22⋊C4—44no—
601C22⋊C4—44no—
602C22⋊C4—44no—
603C22⋊C4—44no—
604C42—22no—
605C42—22no—
606C42—44no—
607C42C22×D411yescharacteristic
608C42C22×D411yescharacteristic
609C42H(5,𝔽2)11yescharacteristic
610C42C2511yescharacteristic
611C23—22no—
612C23—24no—
613C23—22no—
614C23—22no—
615C23—42no—
616C23—42no—
617C23—42no—
618C23—42no—
619C23—42no—
620C23—42no—
621C23—42no—
622C23—42no—
623C23—42no—
624C23—88no—
625C23—88no—
626C23—82no—
627C23—82no—
628C23—82no—
629C23—164no—
630C23—1616no—
631C23D4211yescharacteristic
632Q8—22no—
633Q8—22no—
634Q8—42no—
635Q8—42no—
636Q8—42no—
637Q8—42no—
638Q8—42no—
639Q8—82no—
640Q8—82no—
641Q8—82no—
642Q8—161no—
643D4—24no—
644D4—22no—
645D4—22no—
646D4—22no—
647D4—22no—
648D4—22no—
649D4—42no—
650D4—42no—
651D4—42no—
652D4—42no—
653D4—42no—
654D4—42no—
655D4—82no—
656D4—88no—
657D4—88no—
658D4—88no—
659D4—82no—
660D4—82no—
661D4—161no—
662D4C2×AGL(1,ℤ/8)14yes—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—42no—
670C2×C4—42no—
671C2×C4—42no—
672C2×C4—42no—
673C2×C4—42no—
674C2×C4—44no—
675C2×C4—44no—
676C2×C4—44no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—88no—
687C2×C4—82no—
688C2×C4—82no—
689C2×C4—82no—
690C2×C4—164no—
691C2×C4D4211yescharacteristic
692C2×C4D4211yescharacteristic
693C2×C4D4211yescharacteristic
694C2×C4C2×AGL(1,ℤ/8)12yes—
695C2×C4#57512yes—
696C2×C4#57712yes—
697C2×C4#57712yes—
698C2×C4C23×D411yescharacteristic
699C2×C4C23×D411yescharacteristic
700C2×C4C2×H(5,𝔽2)11yescharacteristic
701C8—24no—
702C8—22no—
703C8—22no—
704C8—22no—
705C8—22no—
706C8—42no—
707C8—42no—
708C8—42no—
709C8—42no—
710C22—24no—
711C22—42no—
712C22—48no—
713C22—42no—
714C22—42no—
715C22—42no—
716C22—42no—
717C22—42no—
718C22—42no—
719C22—42no—
720C22—84no—
721C22—84no—
722C22—82no—
723C22—82no—
724C22—82no—
725C22—1616no—
726C22—164no—
727C22#326512yes—
728C22#326712yes—
729C22#329112yes—
730C22C2×D4211yescharacteristic
731C4—21no—
732C4—21no—
733C4—42no—
734C4—42no—
735C4—42no—
736C4—42no—
737C4—42no—
738C4—82no—
739C4—82no—
740C4—82no—
741C4#326512yes—
742C4#326712yes—
743C4C22×AGL(1,ℤ/8)11yescharacteristic
744C4C2×#57511yescharacteristic
745C4C2×#57711yescharacteristic
746C4C2×#57711yescharacteristic
747C2—44no—
748C2—82no—
749C2—82no—
750C2—162no—
751C2#2008114yesdirect product factor
752C2C2×#326511yescharacteristic
753C2C2×#326711yescharacteristic
754C2C2×#329111yescharacteristic
subgroupG/H
center, socleC23D42
commutator, Frattini, cosocleC42C25
prime radicalC2×#3272C2
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×#3360C2semidirect
2. C2×#3335C2semidirect
3. C2×#3324C2semidirect
5. #20081C2direct (N × H)
6. C2×#1714C2semidirect
7. C2×#1703C2semidirect
8. C2×#1691C2semidirect
9. C2×#1666C2semidirect
10. C2×#1681C2semidirect
11. C2×#1650C2semidirect
12. C2×#1647C2semidirect
13. C2×#1622C2semidirect
14. C2×#1629C2semidirect
15. C2×#1588C2semidirect
16. C2×#1586C2semidirect
19. C2×#554C22semidirect
23. #3360C22semidirect
25. #3335C22semidirect
27. #3324C22semidirect
30. C2×#500C22semidirect
31. C2×#498C22semidirect
35. C2×#487C22semidirect
41. C2×#475C22semidirect
51. C2×#461C22semidirect
56. C2×C8×Q8C22semidirect
62. C2×C8×D4C22semidirect
65. #1714C22semidirect
66. #1703C22semidirect
67. #1691C22semidirect
68. #1681C22semidirect
69. #1666C22semidirect
70. #1650C22semidirect
71. #1647C22semidirect
72. #1629C22semidirect
73. #1622C22semidirect
74. #1588C22semidirect
75. #1586C22semidirect
76. C2×#335C22semidirect
77. C2×#334C22semidirect
78. C2×#333C22semidirect
79. C2×#332C22semidirect
80. C2×#332C22semidirect
82. C2×Q8⋊C8C22semidirect
85. C2×D4⋊C8C22semidirect
86. C2×#322C22semidirect
111. #554C23semidirect
146. #500C23semidirect
148. #498C23semidirect
155. #487C23semidirect
167. #475C23semidirect
177. #461C23semidirect
186. C8×Q8C23semidirect
197. C8×D4C23semidirect
237. #335C23semidirect
238. #334C23semidirect
239. #333C23semidirect
240. #332C23semidirect
241. #332C23semidirect
243. Q8⋊C8C23semidirect
246. D4⋊C8C23semidirect
247. #322C23semidirect
751. C2#20081direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#33602
C2×#33352
C2×#33242
C2×#32722
#200812
C2×#17142
C2×#17032
C2×#16912
C2×#16662
C2×#16812
C2×#16502
C2×#16472
C2×#16222
C2×#16292
C2×#15882
C2×#15862